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Whisper : a computer implementation using analogues in reasoning Funt, Brian 1976

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liLFEASCNING t y EEIAN V. FUNT E . S c , U n i v e r s i t y of B r i t i s h C o l u m b i a , 1971 M . S c , U n i v e r s i t y of E r i t i s h C o l u m b i a , 1973 A T h e s i s S u b m i t t e d In P a r t i a l F u l f i l m e n t Of The Bequirements For The Degree Cf l e c t o r Cf P h i l o s o p h y In The Department Of Computer S c i e n c e We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o the r e q u i r e d s t a n d a r d THE UNIVEHSITY CF BRITISH COLUMBIA March, 1976 In p r e s e n t i n g t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced degree at the U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by the Head o f my Department o r by h i s r e p r e s e n t a t i v e s . It i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Department o f Computer Science The U n i v e r s i t y o f B r i t i s h C o l u m b i a 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date March 31, 1976 i ABSTRACT T h i s t h e s i s concerns the use of an analogue as an a i d to a problem s o l v i n g program. A -working system, the advantages of the analogue i t uses, the mechanisms r e g u i r e d , and the i n t e r a c t i o n of ether forms of knowledge are d e s c r i b e d . The program, WHISPEB, uses a diagram together with procedures f o r modifying i t , as an analogue of a s i t u a t i o n i n v o l v i n g a stack of a r b i t r a r i l y shaped r i g i d bodies. I t determines a s t a c k ' s s t a b i l i t y and p r e d i c t s the motions cf any unst a b l e o b j e c t by examining the s i t u a t i o n ' s diagram. The analogue i s p a r t i c u l a r l y v a l u a b l e i n d e t e c t i n g d i s c o n t i n u i t i e s i n an o b j e c t ' s motion. For example, c o l l i s i o n s with other o b j e c t s or c l i f f s an o b j e c t might s l i d e over can be 'seen' i n the diagram r a t h e r than having to be i n f e r r e d frcm a d e s c r i p t i o n of the s i t u a t i o n . HHTSPEB uses a simulated p a r a l l e l p r o c e s s i n g ' r e t i n a ' to look at the diagram which i s encoded i n a two-dimensional a r r a y . I t c o n s i s t s of a f i x e d number of p r o c e s s o r s o p e r a t i n g i n p a r a l l e l and communicating only with t h e i r immediate neighbours. HHISPEE's r e t i n a resembles the human r e t i n a i n some r e s p e c t s . I t s r e s o l u t i o n decreases away from i t s c e n t e r . I t can be moved to f i x a t e on d i f f e r e n t s e c t i o n s of a diagram. i i A s e t o f domain i n d e p e n d e n t f e a t u r e s a r a e x t r a c t e d f r o m K H I S P E E ' s d i a g r a m s by p r o c e d u r e s , c a l l e d p e r c e p t u a l p r i m i t i v e s , w n i c h e x e c u t e cn t h e p a r a l l e l p r o c e s s i n g r e t i n a . E x ample f e a t u r e s a r e : s ymmetry o f an o b j e c t , s i m i l a r i t y o f two o b j e c t s , and c o n t a c t s c f an o b j e c t w i t h e t h e r o b j e c t s . I n a d d i t i o n t o t h e s e p r i m i t i v e s , t h e r e t i n a can be used t o ' v i s u a l i z e 1 t h e r o t a t i o n o f an o b j e c t w i t h o u t h a v i n g t c move i t d i r e c t l y i n t h e d i a y r a in. The a d v a n t a g e s o f a n a l o g u e s a r e c l a s s i f i e d i n t e r m s c f two c a t e g o r i e s a c c o r d i n g t o w h e t h e r a c o r r e s p o n d e n c e e x i s t s b e t w e e n t h e b e h a v i o u r o f t h e a n a l o g u e and t h e b e h a v i o u r o f t h e e x t e r n a l s i t u a t i o n , o r w h e t h e r a c o r r e s p o n d e n c e e x i s t s b e t w e e n t h e s t a t i c c o n f i g u r a t i o n s o f t h e a n a l o g u e and t h o s e o f t h e e x t e r n a l s i t u a t i o n . Seme r e a s o n s f o r t h e e f f e c t i v e n e s s o f a n a l o g u e s a r e p r e s e n t e d . i i i T a b l e Of C o n t e n t s C h a p t e r I: I n t r o d u c t i o n 1 1-1 A n a l o g u e s I n A P r o b l e m S o l v i n g S y s t e m 1 I- 2 The I n t e r n a l / E x t e r n a l Q u e s t i o n 11 C h a p t e r I I : H H I S P E E : A S y s t e m E m p l o y i n g A n a l o g u e s 15 I I - 1 The P r o b l e m Domain 16 I I -2 S y s t e m O v e r v i e w 20 1.1-3 WHISPER'S Q u a l i t a t i v e P h y s i c a l K n o w l e d g e 26 I I - 3 . 1 S t a b i l i t y T e s t i n g 26 I I - 3 . 2 O b j e c t A m a l g a m a t i o n . . . . . . . . . . . . . . . . . . . . . . 29 I I - 3 . 3 S i n g l e O b j e c t S t a b i l i t y 31 I I - 3 . 3 . 1 B a l a n c i n g O b j e c t s 33 1 1 - 3 , 3 . 2 F o r c e s On c o s u p p o r t e r s 35 I I - 4 R o t a t i o n Of O b j e c t s 40 I I -4. . 1 F i n d i n g D i s c o n t i n u i t y P o i n t s Of R o t a t i o n s 43 I I - 4 . 1 . 1 The Empty S p a c e P r o b l e m . . . . . . . . . . . . . . . . 44 I I - 4 . 1 . 2 How WHISPEE F i n d s D i s c o n t i n u i t y P o i n t s . 46 I I - 4 . 2 C h a r a c t e r i s t i c s Of V i s u a l i z a t i o n . . . . . . . . . 46 I I - 4 . 2 . 1 S u r p r i s e C o l l i s i o n s 48 I I - 5 U p d a t i n g T h e D iagram To R e f l e c t A R o t a t i o n 50 I I - 5 . 1 G r i p e S i t u a t i o n s . . . . 5 0 I I - 5 . 2 A d v a n t a g e s Of T h e F e e d b a c k Method 54 I I -6 The E y e Movement P r o t o c o l 56 i v II-7 Subseguent Snapshots Of Chain Reaction Problem . 60 II-7. 1 The Frame Problem 60 '11-7.2 The T h i r d find F i n a l Snapshots 64 II - 8 T r a n s l a t i o n a l S t a b i l i t y 70 II-9 S l i d i n g An Object Along An I r r e g u l a r Surface ... 74 II-9.1 Surface Examination 74 I I - 9.2 Advantages Of The Analogue In S l i d e s ..... 80 11-10 Updating The Diagram To R e f l e c t A S l i d e .. 83 I I - 11 Summary Of Q u a l i t a t i v e Knowledge 89 Chapter I I I : The Retina And I t s P r i m i t i v e Percepts ..... 90 III- 1 I n t r o d u c t i o n 90 III-2 The R e t i n a l Simulation 93 I I I - 2.1 R e t i n a l Geometry - The Periphery 93 III-2.2 R e t i n a l Geometry - The Retina's Center .. 97 III-2.3 The Retina As A Data S t r u c t u r e 99 III-2.4 The Retina's Computational S t r u c t u r e .... 100 III-2.5 Comparison B i t h Perceptrons ............. 103 III-2. 6 Comparison With Baker's Machine ......... 10 4 I I I - 3 The P e r c e p t u a l P r i m i t i v e s 105 III-3.1 Center Of Area 105 III-3.2 Contact F i n d i n g 107 III-3.3 F i n d i n g Nearest And F a r t h e s t Bubbles .... 109 III-3.4 V i s u a l i z a t i o n 110 III-3.5 Symmetry 112 III-3.6 S i m i l a r i t y T e s t i n g 115 III-3.7 R e t i n a l S c a l i n g . 117 III-3.8 Curve Features .... 120 I I I - 4 Summary Of Ret i n a And P e r c e p t u a l P r i m i t i v e s ... 124 I I I - 5 Implementation D e t a i l s 125 III-5.1 Languages 125 I I I - 5.2 Timings . , 125 Chapter IV: Human And Machine Use Of Analogues 127 IV- 1 I n t r o d u c t i o n 127 IV-2 Analogy And Analogues 130 IV-3 I n t e r a c t i o n With An Analogue 137 IV-4 Advantages Of Analogues 141 IV- 4. 1 Behavioural Advantages 142 IV-4. 1.1 S t i c k i n e s s 143 IV-4. 1.2 I m p l i c i t D e r i v a t i o n 147 IV-4. 1.3 The Amalgamation Problem 149 IV-4.2 C o n f i g u r a t i o n a l Advantages 153 IV-4.2.1 F i r s t Approximation Diagrams ........... 154 IV-4. 2.2 Changing L e v e l Of D e t a i l 158 IV-4.2.3 Planning 161 IV-4. 2. 4 The P u l l e y 163 IV- 5 Why Analogues Work: Some S p e c u l a t i o n s .......... 180 Chapter V: V i s u a l Imagery And WHISPER *s Retina 184 V- 1 I n t r o d u c t i o n 184 V-2 F i l l i n g The Retina 186 v i V-3 advantages 189 V- 4 R e l a t i o n s h i p To V i s u a l Imagery 191 Chapter VI : C o n c l u s i o n 195 V I - 1 L i m i t a t i o n s And Future D i r e c t i o n s . . . . . . . . . . . . . . 195 V I -1 .1 P h y s i c a l Knowledge 195 V I -1 .2 The R e t i n a And P e r c e p t u a l P r i m i t i v e s . . . . . 197 VI -1*3 L i m i t a t i o n s Cf Analogues 198 V I -1 .4 P s y c h o l o g i c a l C o r r e l a t i o n 199 VI -2 Key Ideas 201 V I -2 . 1 The Analogue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 V I -2 .2 B e n e f i t s Of The Analogue To WHISPER 201 V I - 2 . 3 The R e t i n a 204 VI -3 C l o s i n g Remarks 205 F o o t n o t e s 206 B i b l i o g r a p h y • • • • «» * • • 210 v i i ACK NOHLEDGHENT I w o u l d l i k e t o e x p r e s s my a p p r e c i a t i o n t o a l l t h e p e o p l e who h a v e c o n t r i b u t e d t h e i r e n e r g y and i n s i g h t t o t h i s work. I n p a r t i c u l a r , Raymond B e i t e r , my t h e s i s s u p e r v i s o r , h a s p r o v i d e d e s s e n t i a l e n c o u r a g e m e n t and c r i t i c i s m . I e s p e c i a l l y t h a n k him f o r t h e many e x c i t i n g c o n v e r s a t i o n s we have bad i n w h i c h many i d e a s t o o k s h a p e . A l a n M a c k w o r t h i s a v e r y k n o w l e d g e a b l e and c o n s t r u c t i v e c r i t i c who on s e v e r a l o c c a s i o n s p r e v e n t e d me f r o m r e - i n v e n t i n g t h e w h e e l . I am a l s o g r a t e f u l t o h i m f o r s u g g e s t i n g WHISPER'S ' f a l l i n g o b j e c t s ' d o m a i n . I t h a n k R i c h a r d R o s e n b e r g f o r h i s s u p p o r t , comments, and c r i t i c i s m s t h r o u g h o u t t h e numerous y e a r s s i n c e he f i r s t i n t r o d u c e d me t o A r t i f i c i a l I n t e l l i g e n c e . T h e r e a r e many o t h e r {people, G o r d o n M c C a l l a , P e t e r Rowat, M i k e K u t t n e r , G r e g S h a n n a n , J i m D a v i d s o n , a nd B i l l H a v e n s , who h a v e been b o t h e n c o u r a g i n g and a p p r o p r i a t e l y s k e p t i c a l . I t h a n k K a r e n f o r r e a d i n g , c o m m e n t i n g o n , and t y p i n g t h e t h e s i s d r a f t s , and most i m p o r t a n t l y f o r b e i n g h e r s e l f . The f i n a n c i a l s u p p o r t o f t h e N a t i o n a l R e s e a r c h C o u n c i l o f Ca n a d a g r a n t A7642 i s g r a t e f u l l y a c k n o w l e d g e d . 1 Cha£ter_Ii_IntloductioB Iz3_liB§^S!3S,§§_ZS-A-££SfelgS-§gAliBg-SY§tgB C o n c e p t u a l l y simple problems should be answered with c o n c e p t u a l l y simple s o l u t i o n s . These r a r e l y are obtained by a r t i f i c i a l I n t e l l i g e n c e systems; p a r a d o x i c a l l y , the f i e l d ' s methods are more s u c c e s s f u l l y a p p l i e d to d i f f i c u l t problems than t o ones c h i l d r e n can s o l v e . 1 One major advantage that c h i l d r e n have i n comparison tc problem s o l v i n g systems i s t h e i r sensory access to the e x t e r n a l world. They b e n e f i t from experimenting »ith the environment. I t i s e a s i e r to observe the e f f e c t s of a change, than to i n f e r them from a d e s c r i p t i o n of the environment and a knowledge of i t s p h y s i c a l laws. S i m i l a r l y , when d i r e c t i n t e r a c t i o n with a s i t u a t i o n i s i m p o s s i b l e , i t i s e a s i e r t o p r e d i c t the outcome of a proposed change by observing the outcome of an analogous change made to an analogous s i t u a t i o n . Diagrams, maps, s c a l e models, and computer s i m u l a t i o n s are analogues which people r o u t i n e l y use as an a i d i n re a s o n i n g . T h i s t h e s i s e x p l o r e s analogues: how they are i n c o r p o r a t e d i n t o a problem s o l v i n g system, the way the e n t i r e system i s thereby s i m p l i f i e d , and the s o l u t i o n s they enable the system to d i s c o v e r . Problem s o l v i n g progresses s i m u l t a n e o u s l y on s e v e r a l l e v e l s . P c l y a 2 has i d e n t i f i e d f o u r which he terms: the 2 • h e u r i s t i c l e v e l ' , the 'mathematical l e v e l ' , the ' r e l a t i o n a l l e v e l ' , and the 'image l e v e l ' . R e l a t i n g these to the A r t i f i c i a l I n t e l l i g e n c e c o n t e x t : (i) The ' h e u r i s t i c l e v e l ' corresponds to the g o a l - o r i e n t e d approach. At each stage i n the search f o r a s o l u t i o n the aim i s to accomplish a r e l e v a n t goal pr sub-goal. ( i i ) The 'mathematical l e v e l ' corresponds to the c u r r e n t l y invoked e g u a t i o n , a s s e r t i o n , or procedure. ( i i i ) The ' r e l a t i o n a l l e v e l ' corresponds to the complete t r e e cf the search space, the branches which have a l r e a d y been e x p l o r e d , and the branch c u r r e n t l y being i n v e s t i g a t e d . Thus, three of these l e v e l s have c o u n t e r p a r t s i n problem s o l v i n g systems. I t i s the 'image l e v e l ' which has thus f a r been ignored. "Cn the uppermost l e v e l , the im_age_level, we see the e v o l u t i o n of the i n v e s t i g a t e d geometric f i g u r e i n the problem s o l v e r ' s mind. At each stage, the problem s o l v e r has a mental p i c t u r e cf the geometric f i g u r e he e x p l o r e s , but t h i s p i c t u r e changes i n t r a n s i t i o n to the next s t a g e ; some d e t a i l s may recede i n t o the background, other d e t a i l s come to our a t t e n t i c n , new d e t a i l s are added." 3 I f a diagram i s admitted as well as a 'mental p i c t u r e ' , then analogues correspond to t h i s l e v e l . The major q u e s t i o n s are: why and i n what ways i s the image l e v e l u s e f u l , how i s i t used, what mechanisms are r e q u i r e d to make use cf i t , how does i t i n t e r a c t with the other l e v e l s . WHISPER, a computer program, demonstrates the advantage and f e a s i b i l i t y of using analogues i n r e a s o n i n g . I t makes hypotheses and draws c o n c l u s i o n s based on the s t a t e of the 3 diagram. There i s continual interaction between WHISPER'S knowledge of the problem domain and the diagram as the solution progresses. WHISPEB can 'look* at the diagram, making changes and modifications to i t as the action unfolds. WHISPER'S task i s determining the s t a b i l i t y of a stack of objects, and predicting what happens i f any of them are unstable. Figure 1-1 depicts a t y p i c a l configuration of objects. WHISPER, using a diagram of thi s s i t u a t i o n , determines that object B 'hangs over too f a r ' , and w i l l f a l l . I t then envisions B's toppling motion and foresees i t s c o l l i s i o n with D. The diagram i s then updated r e f l e c t i n g the re s u l t i n g s i t u a t i o n (figure 1-2). This i s the f i r s t in a sequence of 'snapshots*, each portraying a new event in the collapse of the o r i g i n a l structure. WHISPEB sees from the diagram of t h i s new situ a t i o n that B upsets the balance of D on C, envisions the rotation of D u n t i l i t h i t s the table, and creates a new diagram (corresponding to the s i t u a t i o n of figure 1-3). The causal connection between B and D i s found through the diagram, not though l o g i c a l inference about the shapes, positions or objects' l o c i of motion. With nothing to support B, i t continues f a l l i n g u n t i l i t h i t s D again (figure 1-4). The three 'snapshot' diagrams (figures 1-2 through 1-4) constitute WHISPER'S description of the solution. The o v e r a l l structure and organization of the WHISPER system i s shown in figure 1-5; i t s e s s e n t i a l components are: the q u a l i t a t i v e physical knowledge, the r e t i n a , the redrawing f I 1 Instructs Changes Re-drawing Transformations Rotations & Translations High Level Reasoner Qualitative Physical Knowledge Experiment Answer to Question THE DIAGRAMMATIC ANALOGUE Asks Questions About Diagram Retinal Supervisor Send Algorithms P a r a l l e l Processing Retina Looks F I G U R E X-5 7 t r a n s f o r m a t i o n p r o c e d u r e s , and t h e diagram. The q u a l i t a t i v e p h y s i c a l knowledge i s the domain dependent p a r t o f t h e system, c o n s i s t i n g of ' s p e c i a l i s t ' p r o c e d u r e s e x p r e s s i n g elements of the b e h a v i o u r of r i g i d b o d i e s when a c t e d upon by g r a v i t y . The r e t i n a i s a s p e c i a l l y s t r u c t u r e d p a r a l l e l p r o c e s s o r which ' l o o k s ' a t t h e diagrams. I t f o l l o w s i n s t r u c t i o n s from the q u a l i t a t i v e p h y s i c a l knowledge ' s p e c i a l i s t s * . Changes are made t o t h e diagram by the r e d r a w i n g t r a n s f o r m a t i o n s . They a l s o a r e under t h e command of the q u a l i t a t i v e knowledge s p e c i a l i s t s . The diagram f u n c t i o n s as the system's c h i e f r e p r e s e n t a t i o n of t h e problem s i t u a t i o n . Together the diagram and r e d r a w i n g t r a n s f o r m a t i o n s which modify i t are an analogue ( d o t t e d bcx) of WHISPER*s problem s i t u a t i o n s . The i n t e r a c t i o n w i t h the analogue i s by e x p e r i m e n t a t i o n . Knowledge of p h y s i c s i s r e p r e s e n t e d p r o c e d u r a l l y , each s p e c i a l i s t e n c a p s u l a t i n g a q u a l i t a t i v e p i e c e of knowledge such a s ; * i f t h e c e n t e r o f g r a v i t y of an o b j e c t does not have s u p p o r t s t o both i t s l e f t and r i g h t , t h e n i t hangs over too f a r ' , o r ' i f an o b j e c t hangs over t o o f a r , then i t w i l l t o p p l e , r o t a t i n g about t h e n e a r e s t s u p p o r t p o i n t t o t h e c e n t e r c f g r a v i t y * . The q u a l i t a t i v e p h y s i c a l knowledge i s the t o p l e v e l o f t h e WHISPER system. In c o n t r a s t t o Fahlman's 4 BUILD system, WHISPER*s u n d e r s t a n d i n g of P h y s i c s i s c l o s e r t o a c h i l d ' s than an e n g i n e e r ' s . When a »specialist* r e q u i r e s i n f o r m a t i o n about the s t a t e o f the worl d i n d e c i d i n g the a p p l i c a b i l i t y o f i t s knowledge to 8 t h e c u r r e n t s i t u a t i o n , i t sends a r e q u e s t t o the r e t i n a t c examine the diagram f o r the presence of a s p e c i f i c f e a t u r e . The ' s p e c i a l i s t 1 i n t e r p r e t s the f e a t u r e r e l a t i v e t o the c u r r e n t domain. For example, a ' s p e c i a l i s t * which needs t o knew i f o b j e c t X s u p p o r t s o b j e c t i , a s k s t h e r e t i n a t o see i f ¥ i s above X and Y touches X i n the diagram. I f the . q u a l i t a t i v e knowledge d i s c o v e r s t h a t a change of s t a t e , an a c t i o n , w i l l o c c u r i n t h e w o r l d , then i t c a l l s t h e r e d r a w i n g t r a n s f o r m a t i o n t o modify t h e diagram to r e f l e c t the e f f e c t s o f t h i s a c t i o n . The purpose o f the r e t i n a i s t o e x t r a c t i n f o r m a t i o n from t h e diagram i n response t o g u e r i e s from the q u a l i t a t i v e p h y s i c a l knowledge s p e c i a l i s t s . I t s r o l e p a r a l l e l s the human eye and i t s e a r l y p e r c e p t u a l p r o c e s s i n g s t a g e s . The r e t i n a i s b a s i c a l l y a p a r a l l e l p r o c e s s o r , and a l g o r i t h m s , c a l l e d p e r c e p t u a l _ p r i m i f i v e s , have been d e s i g n e d t o e x e c u t e cn i t . Due t o p a r a l l e l i s m , t h e i r e x e c u t i o n t i m e s a re o f the same o r d e r of magnitude as more c o n v e n t i o n a l o p e r a t i o n s . Each p e r c e p t u a l p r i m i t i v e d e t e r m i n e s whether a p a r t i c u l a r f e a t u r e e x i s t s i n the diagram as seen from the c u r r e n t l o c a t i o n of the r e t i n a . The diagram t h e r e t i n a ' l o o k s ' a t i s t h e p a t t e r n formed by v a l u e s i n a t w o - d i m e n s i o n a l a r r a y . The c o m b i n a t i o n of HHISPER's r e t i n a and a r r a y diagrams p a r a l l e l s human use of diagrams r e p r e s e n t e d on paper, not human v i s u a l imagery. Paper i s s i m u l a t e d by t h e a r r a y . The diagram o f the scene o f f i g u r e 1 - 1 which WHISPER uses i s shown i n f i g u r e I I - 1 . A problem i s s t a t e d t o HHISPER as a diagram o f t h i s t y p e . They 9 a r e c o n s t r u c t e d so t h a t o b j e c t s ' shapes and p o s i t i o n s are r e p r e s e n t e d by c o r r e s p o n d i n g shapes and p o s i t i o n s i n the diagram. The diagram a l l o w s WHISPEB t o work w i t h both convex and concave i r r e g u l a r l y shaped o b j e c t s w i t h o u t added d i f f i c u l t y . F o r easy r e c o g n i t i o n , each o b j e c t i s shaded a d i f f e r e n t c o l o u r , and c o n t o u r s of o b j e c t s are shaded a c o l o u r r e l a t e d t o the c o l o u r of t h e i r i n t e r i o r s . The c o m b i n a t i o n o f t h e diagram and t r a n s f o r m a t i o n s a p p l i e d t o i t i s an analogue of a s i t u a t i o n i n v o l v i n g a s t a c k of p h y s i c a l o b j e c t s . An ana l o g y e x i s t s both between t h e s t a t i c s t a t e s of the diagram and the s t a t i c s t a t e s o f the p h y s i c a l s i t u a t i o n , and between t h e dynamic b e h a v i o u r c f o b j e c t s i n the diagram and t h e b e h a v i o u r of o b j e c t s i n the w o r l d . C l e a r l y , t h e b e h a v i o u r i n t h e diagram and b e h a v i o u r i n t h e wo r l d a r e not i d e n t i c a l . O b j e c t s i n the diagram do not a u t o m a t i c a l l y b e g i n t o move as do o b j e c t s i n the r e a l w o r l d . However, many a s p e c t s o f an o b j e c t ' s dynamic b e h a v i o u r a r e p r o p e r l y p o r t r a y e d when i t moves i n the diagram. I f an o b j e c t moving i n t h e diagram c o l l i d e s w i t h a n o t h e r o b j e c t , then a c o l l i s i o n w i l l a l s o o c c u r i n the w o r l d . I f a path i s c l e a r i n the diagram, then i t i s a l s o c l e a r i n t h e w o r l d . Moving an o b j e c t a l s o causes i t s s u p p o r t and c o n t a c t r e l a t i o n s h i p s t o change. The m o d i f i e d diagram a u t o m a t i c a l l y r e f l e c t s t h e s e changed r e l a t i o n s h i p s . N e i t h e r c o l l i s i c n nor the changed s u p p o r t r e l a t i o n s h i p s have t o be e x p l i c i t l y computed to r e f l e c t t he s i d e e f f e c t s of a c t i o n ; they a r e s i m p l y observed i n the diagram. T h i s r e s u l t s from the 10 r e p r e s e n t a t i o n of s p a t i a l r e l a t i o n s h i p s i n the wo r l d by a n a l o g o u s s p a t i a l r e l a t i o n s h i p s i n the diagram, and the r e p r e s e n t a t i o n of a c t i o n i n t h e world by analogous a c t i o n i n the diagram. 11 lz1-2h§_Ifiterna1/Extersal_C;uestion To the machine, there i s no sharp d i s t i n c t i o n between a diagram represented e x t e r n a l l y on a piece of paper and a diagram represented i n t e r n a l l y as a two-dimensional a r r a y . Such a d i s t i n c t i o n i s dependent upon a c e n t r a l q u e s t i o n : Hhere does the computer end and the r e s t of the world begin? What i s e x t e r n a l to the machine and what i s i n t e r n a l ? To understand t h a t t h e r e i s no s t r a i g h t f o r w a r d answer, c o n s i d e r the example of a movable head d i s k d r i v e . I t i s g e n e r a l l y c o n s i d e r e d that the i n f o r m a t i o n s t o r e d on the d i s k i s i n t e r n a l to the machine. I s t h i s i n f o r m a t i o n any more i n t e r n a l than the marks on a p i e c e of paper to the human b r a i n when i t i s scanned by the human eye? P o r t a b i l i t y has been the primary c o n s i d e r a t i o n i n d e c i d i n g what i s and what i s not part of the computational s t r u c t u r e of a machine cr of o u r s e l v e s as human beings. Houghly, an e n t i t y ' s p o r t a b l e computational s t r u c t u r e i s the minimal part of i t which must be t r a n s p o r t e d i n order t h a t i t compute the same r e s u l t s at a new l o c a t i o n . For a human the p o r t a b l e computational s t r u c t u r e c o n s i s t s of h i s / h e r body. Whether t h i s i s the minimal computational s t r u c t u r e i s another q u e s t i o n ; c e r t a i n l y we cannot thi n k without a b r a i n and enough b o d i l y s t r u c t u r e t o support i t , A thought process dependent upon co u n t i n g one's f i n g e r s should not be' r u l e d out as i n v a l i d ; peoples' f i n g e r s are part of t h e i r p o r t a b l e s t r u c t u r e . The 12 computational s t r u c t u r e of a computer c o n s i s t s of a processor, memory, and perhaps an input/output mechanism. In t h i s framework the d i s k d r i v e i s simply c o n s i d e r e d to be a form of memory, and an eye to be an input d e v i c e . C l a s s i f y i n g the computational s t r u c t u r e of a computer i n t h i s say i s p o s s i b l y too narrow and c o n f i n i n g . Space, time and mass may a l s o l e g i t i m a t e l y be c o n s i d e r e d as p a r t of the p o r t a b l e computational s t r u c t u r e of a machine, because they are omnipresent. Sherever the machine i s moved they w i l l be p r e s e n t , so i n a sense they are an i n t e g r a l part of any machine. To what extent can space, time and mass be e x p l o i t e d c o m p u t a t i o n a l l y ? Many of the advantages of using analogues d e r i v e from using space, time and mass d i r e c t l y r a t h e r than attempting to model them with symbolic d e s c r i p t i o n s . In p a r t i c u l a r , with r e f e r e n c e to diagrammatic analogues, there i s no need to model two-dimensional space when i t can r i g h t f u l l y be considered to be a part of the machine i t s e l f . The only problem i s to have a device with which to look at and access t h i s space; t h i s i s the f u n c t i o n of the eye. By adding an eye as an e x t r a piece of hardware, the 'hardware' of space i t s e l f becomes a v a i l a b l e as a medium f o r r e p r e s e n t i n g and manipulating i n f o r m a t i o n . T h i s does not o b v i a t e the need f o r some other r e p r e s e n t a t i o n of s p a t i a l i n f o r m a t i o n ; i t does e l i m i n a t e the need f o r a model of space i t s e l f . An example might be i n the use of a map to plan a r o u t e from one l o c a t i o n to another. I f a map of an area that a person knew we l l were 13 not a v a i l a b l e then he l i k e l y could c o n s t r u c t one from memory. I t seems u n l i k e l y t h a t he would have a copy of the map i n h i s memory which he then redraws on a piece of paper, but r a t h e r t h a t he c o n s t r u c t s i t from a set of a s s e r t i o n s d e s c r i b i n g the r e l e v a n t s p a t i a l r e l a t i o n s h i p s . The content and s t r u c t u r i n g of t h i s i n f o r m a t i o n does not matter f o r our c u r r e n t purposes. The important t h i n g i s that he can c o n s t r u c t at l e a s t a rough approximation to a proper map. The two-dimensional t o p o l o g i c a l s t r u c t u r e of t h e paper provides a context i n which the f a c t s i n h i s memory are to be i n t e r p r e t e d . Bather than having t c have a model of two-dimensional space he can use the a l r e a d y a v a i l a b l e space of the paper. A great many more a s s e r t i o n s about s p a t i a l r e l a t i o n s h i p s can be e x t r a c t e d from the map than Here used i n c o n s t r u c t i n g i t because of the context provided by the paper. T h i s and other advantages of such a r e - r e p r e s e n t a t i o n are part of what WHISPER i s intended t o demonstrate, and they w i l l be d i s c u s s e d i n more d e t a i l as they a r i s e . For the moment, the p o i n t i s t h a t i n _ o r d e r _ t o _ u s e _ d i a ^ s t o r e images_of them in,memory! t h e r e f o r e , i f a g a i n can be made by r e - r e p r e s e n t i n g the s p a t i a l i n f o r m a t i o n s t o r e d i n memory i n diagrammatic form, then t h i s might as w e l l be done s i n c e two-dimensional space can be c o n s i d e r e d as a part of the hardware of the machine. The two-dimensional s t r u c t u r e of an a r r a y i s provided c o m p u t a t i o n a l l y . I t i s a f u n c t i o n of conventions f o r a c c e s s i n g a one-dimensicnal s t r u c t u r e , namely l i n e a r l y ordered computer 1 4 memory. S i n c e t h e r e i s no sharp d i s t i n c t i o n t c be made between diagrams s t o r e d i n a r r a y s and on paper, WHISPER 'S use of diagrams can be c o n s i d e r e d analogous t o human use of diagrams. That the diagrams are modeled i n t e r n a l l y i s p u r e l y a con v e n i e n c e i n t h a t i t was e a s i e r t o p r o v i d e a s o f t w a r e s i m u l a t i o n of t h e eye and paper c o m b i n a t i o n than to p r o v i d e the a c t u a l hardware. The a r r a y WHISPER uses i s not t o be i n t e r p r e t e d as a model f o r human v i s u a l imagery. A p r o p o s a l f o r u s i n g WHISPER's p a r a l l e l p r o c e s s i n g eye w i t h o u t an a r r a y , and i t s r e l a t i o n s h i p to imagery i s p r e s e n t e d i n Chapter V. 15 C h a p t e r I I ; _ WHISPER: fl System,Employing Analogues I n Reascninq WHISPER i s a working program. I t s e r v e s as an i n s t a n t i a t i o n of the g e n e r a l i d e a s d i s c u s s e d i n subsequent s e c t i o n s , and e s t a b l i s h e s the u t i l i t y and f e a s i b i l i t y o f i n c o r p o r a t i n g analoques i n t o problem s o l v i n g systems. WHISPEB i s not a s t u d y i n the s p e c i a l i z e d domain dependent h e u r i s t i c s p e r t a i n i n g t o a p a r t i c u l a r c l a s s of problem. Many of the mechanisms r e g u i r e d i n i n t e r p r e t i n g and m o d i f y i n g analogues i n WHISPEB *s domain s i l l a l s o be r e g u i r e d when analoques a re u t i l i z e d i n systems r e a s o n i n g on o t h e r domains. WHISPEB *s r e a s o n i n g i s e n t i r e l y q u a l i t a t i v e i n n a t u r e . I b e l i e v e t h a t i t i s n e c e s s a r y t o o b t a i n q u a l i t a t i v e s o l u t i o n s t o problems b e f o r e a t t e m p t i n g g u a n t i t a t i v e o r p r e c i s e s o l u t i o n s . A q u a l i t a t i v e s o l u t i o n p r o v i d e s a framework on which p l a n n i n g f o r a g u a n t i t a t i v e s o l u t i o n can be based. D e K l e e r 5 has i n v e s t i g a t e d some ways i n which t h i s can be a c c o m p l i s h e d . Analogues are p a r t i c u l a r l y i m p o r t a n t i n r e d u c i n g t h e c o n c e p t u a l c o m p l e x i t y i n v o l v e d i n o b t a i n i n g q u a l i t a t i v e s o l u t i o n s . The e f f e c t i v e n e s s of analoques i n c u r b i n g c o m p l e x i t y i s e v i d e n c e d by the c o n c e p t u a l s i m p l i c i t y o f the q u a l i t a t i v e knowledge of P h y s i c s which WHISPER employs i n s o l v i n g i t s problems. 16 II;l_Th§_Problej_Domain Given a stack of p h y s i c a l o b j e c t s , WHISPER e s t a b l i s h e s i t s s t a b i l i t y or i n s t a b i l i t y , and the seguence of events which w i l l ensue i f i t i s unstable. A t y p i c a l example of the kind of c o n f i g u r a t i o n that WHISPER can handle i s shown i n f i g u r e I I - 1 . The u s u a l assumptions about ' i d e a l ' environments common to i n t r o d u c t o r y P h y s i c s t e x t s have been made. The o b j e c t s are p e r f e c t l y r i g i d , of uniform d e n s i t y and t h i c k n e s s , and have f r i c t i o n l e s s s u r f a c e s . They are otherwise of a r b i t r a r y shape, not r e s t r i c t e d t o cubes, wedges, or other simple polyhedra. One f u r t h e r r e s t r i c t i o n i s t h a t the faces of the o b j e c t s must be a l i g n e d . Although t h i s g i v e s the problems a b a s i c a l l y two-dimensional c h a r a c t e r , i t i s a well precedented and f r e q u e n t l y unstated assumption, p r e v a l e n t i n Phy s i c s t e x t s and other A r t i f i c i a l I n t e l l i g e n c e systems. In p a r t i c u l a r , although a l l the problems handled by Eahlman's BOIID system are sketched as 2-D p r o j e c t i o n s of thr e e - d i m e n s i o n a l scenes, they a l l conform to these r e s t r i c t i o n s and have the same two-d i m e n s i o n a l i t y about them. Problems are in p u t to the system as an. a r r a y encoding of a two-dimensional c r o s s - s e c t i o n a l view of the scene. The a r r a y can be generated by drawing with a l i g h t p e n at a gr a p h i c s t e r m i n a l . Nonetheless, i t i s the a r r a y , not the l i g h t pen co o r d i n a t e s , t h a t forms the f i n a l i n put to the system. T h i s c l a s s of problem was chosen because i t provides a 1.0 11.0 21.0 31.0 41.0 51.0 61.0 71.0 81.0 91.0 101.0 101.01 I I I I I I I I I ! 91.0 81.0 71.0' 2 22222 2222 B 8 2 22 B B 3 3 2 2223 3 B B 3 B B2 22B 8 B B B B 8 B B2 228 B B 8 3 B 3 3 3 32 2222B B B B 8 B B B B B B 2 22223 B B B B B 8 B \ 223 8 B 3 B 3 8 S B B B 3 B 8 B 2 B 3 3 ,B 3 B2 • 2228 B S B 8 B B 3 3 B 3 8 3 B '"8 8 32 222B B 3 B 8 8 B 3 B 8 B B 8 8 B B B 3 B22 2 2 B B B B B 3 8 B 8 3 B B B B 8 8 B 8 8 3 2 2222 B B e B 8 B ' B 3 B S B B B B B B 8 8 B B 8 2 F1GURQI-1 2222222222222222222222222222222222222222222222222222 u u n u n n i n i INITIAL • 1A 1A A A A A A A A A «r < A A 1 1 SNAPSHOT 1A A A A A A A 1 1A A A A A A * i 1A A A A A A A 1 61.0- 1A A A A A A A 1 1A A A A A A A 1 1A A A A A A A 1 1A A A A A A A 1 444444444444444444444444444444444444444444444444444444444 1A A A A A A A 1 4440 D D D O D O ' D O D D D 0 0 D D D 0 D O D 0 D D D444 . 1A A A A A A A 1 444 D D D C D 0 0 O D D 0 0 D D C D D D D D D 444 51.0- ' 1A A A A A A A 1 4 O D D D D D D 0 0 O O 0 D D D D D D D 0 D 4 . 1A A A A A A A 1 444 0 D D D D D 9 D D D D D 9 D D D D 444 Y. 1A A A A A A A 1 444D D 0 D D D D O D D 0 D D D D 4 4 • 1A A A A A A A 1 4 4 D D D D 0 . 0 D 0 D 0 D 0 D 4 1A A A A A A A 1 44440 0 D O D O D O D 0 O 0 D4D444 1A A A A A A A 1 44444D4D D D 0 0 D D D D 0 0 D D D 0 D D D40444 41.0- 1A A A A A A A 1 444 D O D 0 D D O D D O D D O D 0 O O D D D O D D 444 1A A A A A A A 1 444444444444444444444444444443444444444444444444444444444 1A A A A A A A 1 333 1A A A A A A A 1 3 3 1A A A A A A A 1 3 C3 1A A A A A A A 1- 3C C33 31.0- 1A A A A A A A 1 3C C 3 1A A A A A A A 1 33C C C3 1A A A A A A A 1 3 C C C33 1A A A A A A A 1 3C C C C 3 • 1A A A A A A A 1 3C C C C C3 1A A A A A A A 1 33C C C C C33 21.0- 111 11111111 i l l ! 1 3333333333333 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 U . 0 | I I I I... | I | f ! I _ 1.0 11.0 21.0 31.0 41.0 51.0 61.0 71.0 81.0 91.0 101.0 ~ J 18 n o n - t r i v i a l domain i n which t c demonstrate many of t h e t h o u g h t s and i d e a s I had about the u t i l i z a t i o n of analogues i n r e a s o n i n g and the advantages which a system i n c o r p o r a t i n g analogues would d e r i v e from them. 6 These i d e a s w i l l be d i s c u s s e d as they a r i s e i n the d e s c r i p t i o n of WHISPEB i n t h i s c h a p t e r , and i n more g e n e r a l terms i n the f o l l o w i n g c h a p t e r . Problems i n t h i s domain a r e of i n t e r e s t because they i n v o l v e a c t i o n and the d i s c o v e r y o f c a u s a l c h a i n s of e v e n t s . They are e v e r y d a y , r e a l w o r l d problems which people l e a r n t o s o l v e a t an e a r l y age, i n c o n t r a s t t o h i g h l y i n t e l l e c t u a l and f o r m a l domains such as c h e s s or Mathematics. S u r p r i s i n g l y , problems of t h i s s o r t have e l u d e d s a t i s f a c t o r y s o l u t i o n by o t h e r methods, one of t h e main r e a s o n s being the presence o f the •frame 1 problem ( d i s c u s s e d i n s e c t i o n I I - 7 . 1 ) , a n o t h e r b e i n g t h e l a c k of an adeguate method of s t o r i n g and m a n i p u l a t i n g s p a t i a l r e l a t i o n s h i p s . The p h y s i c s i s s i m p l e enough sc t h a t i n i m p l e m e n t i n g a system one i s u n l i k e l y t o become d i s t r a c t e d from the main q u e s t i o n a t hand - the u t i l i z a t i o n o f analogues i n r e a s o n i n g - and bogged down i n a study o f i r r e l e v a n t a s p e c t s of the problem domain. Another f e a t u r e o f t h i s domain i s t h a t diagrams p r o v i d e an o b v i o u s and commonly used analogue of ' b l o c k s * w o r l d s i t u a t i o n s . These problems a l s o p r o v i d e an o p p o r t u n i t y t o s t u d y the t y p e of i n t e r a c t i o n which must take p l a c e between p r o p o s i t i o n a l knowledge of q u a l i t a t i v e a s p e c t s of P h y s i c s and the a n a l o g u e . The analogue i s r e p e a t e d l y examined t c draw f i r s t c o n c l u s i o n s , m o d i f i e d t o r e f l e c t t h e r a m i f i c a t i o n s of 19 t h e s e c o n c l u s i o n s , and re-examined t o draw f u r t h e r c o n c l u s i o n s . 20 IIz2_System_Overview I w i l l attempt t o put t h e whole WHISPER system and the q u e s t i o n of analogues i n p e r s p e c t i v e b e f o r e g o i n g i n t c g r e a t e r d e t a i l . The s i g n i f i c a n t f e a t u r e o f WHISPER i s t h a t i t uses a diagrammatic_ai)alogu_e o f the s i t u a t i o n s i t r e a s o n s about i n a d d i t i o n t o a descri£tive_re£resenta c f t h e s e s i t u a t i o n s , such as t h a t which c o u l d be p r o v i d e d by a s e t o f a s s e r t i o n s , a s e t of p r o c e d u r e s , o r a network. I t r e l i e s on t h e ana l o g y between diagrams of the s e s i t u a t i o n s and the s i t u a t i o n s t h e m s e l v e s , and m a n i p u l a t e s the analogue d u r i n g t h e problem s o l v i n g p r o c e s s . I n t h e diagrams which WHISPER uses t h e r e a re some s i m p l e and w e l l - d e f i n e d c o r r e s p o n d e n c e s o r s i m i l a r i t i e s between the t o p o l o g i c a l s t r u c t u r e of the c o n f i g u r a t i o n s i n the diagram and th o s e i n the problem domain. Shapes and p o s i t i o n s o f the c o n f i g u r a t i o n s i n the diagrams a r e analogous to the shapes and p o s i t i o n s of t h e o b j e c t s i n the r e a l w o r l d : the c o n t o u r s i n the diagram a re i d e n t i c a l (except f o r s c a l i n g ) t o the shapes of the o b j e c t s (viewed head-on); and t h e p o s i t i o n s r e l a t i v e t c one an o t h e r of the shapes i n t h e diagram and the o b j e c t s i n t h e world i s the same. Of c o u r s e i t i s p o s s i b l e t o c r e a t e n o n - a n a l o g i c a l diagrams, ones f o r which t h e r e i s no s i m p l e c o r r e s p o n d e n c e between the c o n f i g u r a t i o n s of marks i n the diagram and t h e e x t e r n a l r e a l i t y . There i s a l s o a correspondence between the changes which 21 o c c u r i n the r e a l w o r l d and the changes which WHISPER makes to i t s diagrams. S i n c e the o b j e c t s i n the problem environment are r i g i d b o d i e s , o n l y l i n e a r t r a n s f o r m a t i o n s are a p p l i e d . I t i s because of these c o r r e s p o n d e n c e s between both the s t a t i c c o n f i g u r a t i o n s o f the diagram and the s t a t i c p h y s i c a l s i t u a t i o n s , and between t h e dynamic a c t i o n s o c c u r r i n g i n t h e s e s i t u a t i o n s , t h a t the c o m b i n a t i o n of the diagram and the p r o c e d u r e s which modify i t t o g e t h e r c o n s t i t u t e an analogue o f r e a l w o r l d s i t u a t i o n s i n v o l v i n g s t a c k s of p h y s i c a l o b j e c t s . To d i s t i n g u i s h t h i s analogue from d i f f e r e n t t y p e s of analogues of o t h e r r e a l w o r l d s i t u a t i o n s i t w i l l be termed a d i a g r a m m a t i c a n a l o g u e . The medium i n which t h e marks o f the diagram a r e s t o r e d i s t h a t of v a l u e s i n a t w o - d i m e n s i o n a l a r r a y ( p r e s e n t l y 101 x 1 0 1 ) . A more common medium i s , of c o u r s e , p e n c i l marks on a p i e c e o f paper. D i f f e r e n t o b j e c t s a r e coded w i t h d i f f e r e n t v a l u e s i n t h e a r r a y . In a d d i t i o n , t h e c o n t o u r s o f o b j e c t s are coded w i t h v a l u e s which are d i f f e r e n t f r o m , but r e l a t e d t o , the v a l u e s of the o b j e c t s ' i n t e r i o r s . For a problem s o l v i n g system t o make e f f e c t i v e use o f diagrammatic analogues i t must have a method of examining and u n d e r s t a n d i n g them and a method of a l t e r i n g t h e i r c o n f i g u r a t i o n s o f marks. Human problem s o l v e r s use t h e i r eyes f o r the e x a m i n a t i o n o f diagrammatic a n a l o g u e s . WHISPER has been endowed w i t h an 'eye' a l s o . T h i s 'eye' i s a s o f t w a r e s i m u l a t i o n of some of the dominant f e a t u r e s o f the human eye. 22 The s i m u l a t e d eye l o o k s at s i m u l a t e d p a p e r , namely a t w o - d i m e n s i o n a l a r r a y . The so f tware r e t i n a has some of the b a s i c c h a r a c t e r i s t i c s o f the human r e t i n a . I t i s movable and can f i x a t e anywhere i n the d iagram; the a c u i t y v a r i e s a c r o s s i t with the c e n t e r hav ing the h i g h e s t r e s o l u t i o n and the p e r i p h e r y hav ing the l o w e s t ; i t i s composed of many ' r e c e p t o r s ' which opera te i n p a r a l l e l ; and communicat ion between ' r e c e p t o r s ' i s c o n s t r a i n e d to message £ a s s i n q _ b e t w e e n _ n e i g These f e a t u r e s p r o v i d e a new framework, p a r t l y a data s t r u c t u r e and p a r t l y a c o m p u t a t i o n a l s t r u c t u r e , i n which p r i m i t i v e p e r c e p t u a l o p e r a t i o n s can be e x p r e s s e d and implemented . Al though I w i l l use the terms ' e y e ' and ' r e t i n a ' when d i s c u s s i n g t h i s framework, there i s no d i r e c t c o r r e s p o n d e n c e between i t and any p a r t i c u l a r p h y s i c a l par t of the human e y e . The ana logy h o l d s o n l y wi th r e s p e c t to the g r o s s o r g a n i z a t i o n of some of the p r e l i m i n a r y p r o c e s s i n g s t a g e s o f the human p e r c e p t u a l s y s t e m . O b v i o u s l y , the problem o f e x t r a c t i n g i n f o r m a t i o n from diagrams i s r e l a t e d t c the q u e s t i o n s o f v i s u a l p e r c e p t i o n . However, WHISPER'S p e r c e p t i o n of diagrams i s s i m p l e r than t h a t o f human p e r c e p t i o n o f r e a l world s c e n e s because o b j e c t s i n the d iagrams are ' c o l o u r ' c o d e d , and because the o b j e c t s are p o r t r a y e d i n d r a f t s m a n ' s t w o - d i m e n s i o n a l v iews. WHISPER r e l i e s on a number of p r i m i t i v e p e r c e p t s which are p r o v i d e d by r o u t i n e s r e l y i n g on the o r g a n i z a t i o n of the so f tware r e t i n a and i t s p a r a l l e l c o m p u t a t i o n a l c a p a b i l i t i e s . R e c o g n i t i o n of 23 s y m m e t r i e s , s i m i l a r i t i e s , s c a l i n g s , r o t a t i o n s , a n d c o n t a c t p o i n t s b e t w e e n o b j e c t s a r e s o m e c f t h e p r i m i t i v e p e r c e p t s w h i c h a r e i m p l e m e n t e d . W H I S P E R ' S u s e o f d i a g r a m m a t i c a n a l o g u e s d e m o n s t r a t e s t h a t i t i s n o t n e c e s s a r y t o s o l v e a l l t h e p r o b l e m s o f v i s u a l p e r c e p t i o n b e f o r e u s i n g a p e r c e p t u a l l y o r i e n t e d s y s t e m . T h e r e a r e s o m e p e r c e p t u a l o p e r a t i o n s w h i c h a r e b o t h u s e f u l t o a s y s t e m s u c h a s W H I S P E R a n d p r i m i t i v e e n o u g h s o a s n o t t o r e q u i r e a m o r e s o p h i s t i c a t e d u n d e r s t a n d i n g o f t h e w o r l d t h a n t h a t r e q u i r e d t o s o l v e t h e p r o b l e m a t h a n d . T h e r e m u s t b e a m e c h a n i s m w h e r e b y c h a n g e s c a n b e m a d e t o d i a g r a m s t o r e f l e c t t h e c h a n g e d p o s i t i o n o f o b j e c t s i n t h e r e a l w o r l d . T h e o n l y t r a n s f o r m a t i o n s w h i c h n e e d b e c o n s i d e r e d i n t h e c u r r e n t d o m a i n a r e t h o s e o f r i g i d t r a n s l a t i o n a n d r o t a t i o n . O f c o u r s e , o t h e r n o n - l i n e a r t r a n s f o r m a t i o n s w o u l d b e n e c e s s a r y i n o t h e r d o m a i n s c o n t a i n i n g n o n - r i g i d e n t i t i e s . T h e r e i s a c o r r e s p o n d e n c e b e t w e e n t h e t r a n s f o r m a t i o n s w h i c h a r e made t o o b j e c t s i n t h e d i a g r a m s a n d t h o s e w h i c h o c c u r f o r r i g i d o b j e c t s i n t h e r e a l w o r l d . . C h a n g e i n t h e w o r l d i s r e p r e s e n t e d b y a n a l o g o u s c h a n g e i n t h e d i a g r a m . R o t a t i n g o r t r a n s l a t i n g a n o b j e c t i n t h e d i a g r a m i s a s i m p l e m a t t e r o f r e d r a w i n g t h e o b j e c t a t i t s new l o c a t i o n b y c o m p u t i n g t h e new c o o r d i n a t e s o f e v e r y p o i n t i n t h e o b j e c t , a n d b l a n k i n g o u t t h e o r i g i n a l l o c a t i o n . T r a n s f o r m a t i o n s c a n a l s o b e ' v i s u a l i z e d * o n t h e r e t i n a r a t h e r t h a n b e i n g c a r r i e d o u t d i r e c t l y i n t h e d i a g r a m . T h e s o f t w a r e r e t i n a i s e n d o w e d w i t h a o n e - l e v e l m e m o r y w i t h w h i c h 24 i t can hold the p a t t e r n imposed cn i t by the o b j e c t to be moved. The 'image' of that o b j e c t can then be t e m p o r a r i l y t r a n s l a t e d by simply f i x a t i n g the r e t i n a a t a new l o c a t i o n and superimposing the st o r e d p a t t e r n on the new p a t t e r n c r e a t e d on the r e t i n a . S i m i l a r l y , the p a t t e r n of an o b j e c t can be r o t a t e d on the r e t i n a and re-imposed on the i n p u t of the c u r r e n t f i x a t i o n . T h i s type of t e n t a t i v e t r a n s f o r m a t i o n i s very u s e f u l i n determining the l i k e l y e f f e c t s r e s u l t i n g from the motion of an o b j e c t , and i n e s t i m a t i n g the a p p r o p r i a t e parameters to pass to the redrawing t r a n s f o r m a t i o n s j u s t d i s c u s s e d . WHISPER p r o c e d u r a l l y r e p r e s e n t s i t s g u a l i t a t i v e knowledge of p h y s i c s . T h i s knowledge i s g u a l i t a t i v e i n t h a t WHISPER reasons i n terms l i k e ' i f a block i s hanging over too f a r i t w i l l t o p p l e * and * i f a block i s on a s l a n t then i t w i l l s l i d e ' , r a t h e r than i n terms of moments of i n e r t i a and vecto r components of f o r c e s . The g u a l i t a t i v e knowledge i s intended to r e f l e c t what a 'naive' person would use i n s o l v i n g these problems. To s o l v e a s t a b i l i t y problem, the q u a l i t a t i v e knowledge procedures d i r e c t the eye to focus on v a r i o u s p a r t s of the diagram t o e x t r a c t i n f o r m a t i o n r e q u i r e d f o r a d e c i s i o n on the s t a b i l i t y of the o b j e c t s . These procedures q u e s t i o n the eye about the f e a t u r e s i t sees i n the diagrammatic analogue and a s s i g n s meanings t c the p r i m i t i v e percepts i t p r o v i d e s . A t y p i c a l g u e s t i o n might be * where does o b j e c t x touch other o b j e c t s * . I f the s i t u a t i o n d e p i c t e d by the diagram i s s t a b l e 25 then the problem i s s o l v e d . I f any o b j e c t i s found t o be u n s t a b l e , then the eye i s questioned f u r t h e r to e s t a b l i s h what the o b j e c t ' s motion w i l l be. Whatever the motion - s l i d i n g , f a l l i n g , or t o p p l i n g - i t w i l l not continue i n d e f i n i t e l y . WHISPEP, uses a r e t i n a l ' v i s u a l i z a t i o n ' process (to be d e s c r i b e d i n d e t a i l i n s e c t i o n III-3.4) t o perform a very rough s i m u l a t i o n of an o b j e c t ' s motion while watching f o r a c o l l i s i o n d i s c o n t i n u i t y to a r i s e . Once the type of motion and i t s d i s c o n t i n u i t y p o i n t s are known, then a change can be made t o the diagrammatic analogue to r e f l e c t the s t a t e r e s u l t i n g from the completion of the motion. On a piece of paper t h i s change i s made by e r a s i n g the marks r e p r e s e n t i n g the moving ob j e c t and redrawing them at the new l o c a t i o n ; the ar r a y e q u i v a l e n t i n v o l v e s the a p p l i c a t i o n of a t r a n s l a t i o n or r o t a t i o n t r a n s f o r m a t i o n . The diagrammatic analogue, now i n a new s t a t e , i s ready f o r f u r t h e r c o n s i d e r a t i o n almost as i f i t were an o r i g i n a l s t a r t i n g s t a t e . Huch of the i n f o r m a t i o n e x t r a c t e d from the o r i g i n a l diagram by d i r e c t i n g the eye i s now out cf date and of l i t t l e use, but the analogue i s i n a c o n s i s t e n t s t a t e and can be f r e s h l y re-examined i n response to qu e s t i o n s posed by the q u a l i t a t i v e kno wle d ge proced ur es. D e t e r m i n i n g an_objec tj_s_ motion ,_an^ a n o t h e r _ a r e _ t w o _ o f _ t h e _ p r i n c i p a l _ b e n e f i t fSgg„a_diagrammatic analoque. 26 The g u a l i t a t i v e knowledge d i v i d e s n a t u r a l l y i n t o two p a r t s . One concerns the s t a b i l i t y of o b j e c t s , the other the motions of o b j e c t s as they f a l l . At the top l e v e l ( f i g u r e 11-2} WHISPEB loops between s t a b i l i t y t e s t i n g and moving un s t a b l e o b j e c t s . , The s t a b i l i t y t e s t c o n s i d e r s a l l the o b j e c t s i n the s t r u c t u r e , and notes a l l the i n s t a b i l i t i e s i t f i n d s i n an a s s o c i a t i v e data base. When i t i s complete, the dominant i n s t a b i l i t y i s determined, and the o b j e c t s a f f e c t e d by i t are moved. The e f f e c t s of only the one dominant i n s t a b i l i t y are d e a l t with at a time. WHISPEB outputs the updated diagram as i t s f i r s t s o l u t i o n 'snapshot*, and passes i t back t c the s t a b i l i t y t e s t . The d e s c r i p t i o n of the system w i l l be approached i n a top-down f a s h i o n and w i l l c e n t e r on some of the s o l u t i o n s obtained by WHISPEB. The f i r s t problem t o be c o n s i d e r e d i s the 'chain r e a c t i o n ' problem of f i g u r e I I - 1 . I I - 3 & 1 _ S t a b i l i t y T e s t i n g The c e n t r a l i d e a i n the s t a b i l i t y t e s t i s to d i v i d e the i n i t i a l s t r u c t u r e i n t o s m a l l e r s u b - s t r u c t u r e s which are t e s t e d f o r s t a b i l i t y as i f they were s i n g l e o b j e c t s . The s u b - s t r u c t u r e s are e i t h e r i n d i v i d u a l o b j e c t s , or conglomerates c o n s i s t i n g of two or more o b j e c t s glued t o g e t h e r . The s t a b i l i t y t e s t i s t h e r e f o r e a two part process - s u b d i v i s i o n *7 Test S t a b i l i t y of Structure by Examining Contact Relationships i n Diagram Yes -$Sa*« Finished Pick Dominant I n s t a b i l i t y Move Object i n the Diagram Output Updated Diagram as a Solution 'Snapshot' FIGURE H - i 28 of a s t r u c t u r e and s t a b i l i t y t e s t i n g of i n d i v i d u a l o b j e c t s . The s u b d i v i s i o n i s d i r e c t e d by the top l e v e l r o u t i n e , STABLE-STRUCTURE, which f i r s t c o n s t r u c t s a l i s t of the names of a l l the o b j e c t s i n the scene. The diagram i s i n t h i s case, as i n a l l other cases, accessed through the eye and never d i r e c t l y c e l l by c e l l . STABLE-STR UCTURE then t e s t s each o b j e c t to see i f i t i s UPWARDS-STABIE. An o b j e c t , 0 , i s UPWARDS-STABLE i f the conglomerate o b j e c t , C, formed by g l u i n g together 0 and e v e r y t h i n g 0 supports ( i n c l u d i n g what O's supportees s u p p o r t ) , i s s t a b l e . When t e s t i n g the s t a b i l i t y of C, 0*s supporters are assumed to to be s t a b l e . I f every o b j e c t i s UPWARDS-STABLE then the complete s t r u c t u r e w i l l be s t a b l e . Tc f i n d e v e r y t h i n g t h a t an o b j e c t supports f o r the upwards s t a b i l i t y t e s t , the cha i n of v i s u a l support l i n k s i s f o l l o w e d , and each new o b j e c t i s imagined to be glued onto i t s s u p p o r t i n g o b j e c t . In the case of the c u r r e n t example, WHISPER happened to choose o b j e c t A as the f i r s t o b j e c t t o be te s t e d f o r upwards s t a b i l i t y , and so when E i s found to be a supportee of A, the p o i n t where they touch i s con s i d e r e d to be g l u e d , r e s u l t i n g i n a new o b j e c t AB. F i n d i n g p o i n t s of co n t a c t and support between o b j e c t s i s one c f the p e r c e p t u a l p r i m i t i v e s which w i l l be d i s c u s s e d l a t e r , but o b v i o u s l y i t need not i n v o l v e the complex touch t e s t mechanism d e s c r i b e d by Fahlman, s i n c e c o n t a c t p o i n t s need o n l y be re c o g n i z e d not computed. I f there were another o b j e c t on top of AB, then the process would be repeated u n t i l e i t h e r an o b j e c t with nc supportees or an o b j e c t which a c t s as 29 a c o s u p p o r t e r of a t h i r d o b j e c t i s reached. The d o t t e d c u r v e s i n f i g u r e I I - 3 e n c i r c l e t h e s u b - s t r u c t u r e s UPWARDS-STABLE f i n d s . I n ( c ) , Q and RS are c o s u p p o r t e r s of X, so the s u b d i v i s i o n s t o p s a t X. II ; 3 ^ 2 _ O b j e c t _ A m a l g a m a t i c Combining the d e s c r i p t i o n s of two o b j e c t s i s p a r t i c u l a r l y s i m p l e i n the framework of a diagrammatic analogue. C r e a t i n g a new d e s c r i p t i o n from two o t h e r d e s c r i p t i o n s i s an i n s t a n c e of ill§_§JS§i3SJ9ii££_££2ilJiDi ID t n e case a t hand the c r e a t i o n of a new o b j e c t from two o t h e r o b j e c t s i s merely a matter c f not d i s t i n g u i s h i n g between the ' c o l o u r * v a l u e s ( i n t h i s case A and B) d e s i g n a t i n g t h e o r i g i n a l o b j e c t s . A r e d o b j e c t combined w i t h a bl u e o b j e c t i s d e s c r i b e d as t h e r e d - b l u e o b j e c t . A l l th e f e a t u r e s or p r o p e r t i e s t h a t can be seen i n t h e o r i g i n a l o b j e c t s can a l s o be seen i n the combined o b j e c t . Seme of the p r o p e r t i e s which t h e combined o b j e c t i n h e r i t s a r e : i t s shape, i t s c e n t e r of g r a v i t y , i t s mass, i t s p o s i t i o n r e l a t i v e t o o t h e r o b j e c t s , and i t s s u p p o r t r e l a t i o n s h i p s . Some of t h e s e f e a t u r e s might not be so hard to compute i n a d e s c r i p t i v e f o r m a l i s m , but t h e r e s t i l l e x i s t s the need t o compute them and more i m p o r t a n t l y , t h e need f o r p r o c e d u r e s which know how t o compute them. One p r o p e r t y which would g i v e t h e most d i f f i c u l t y i n a non - diagrammatic r e p r e s e n t a t i o n would be shape. I f , f o r 31 example, the o b j e c t s were d e s c r i b e d as polygons ( f i g u r e .11-4) then there must be some way i n which the d e s c r i p t i o n s c f the two o b j e c t s can be e d i t e d to remove the segments corresponding to the c o n t a c t , and to j o i n the segments which lead from one o b j e c t i n t o the other even though these may not n e c e s s a r i l y occur at the endpoints of the o r i g i n a l segments. I i - 3 . 3 S i n g l e Object S t a b i l i t y In the upwards s t a b i l i t y t e s t , once the o b j e c t has been glued to e v e r y t h i n g i f supports the s t a b i l i t y of t h i s combined o b j e c t i s t e s t e d independently. Thus the problem of determining the s t a b i l i t y of a whole s t r u c t u r e i s reduced at each stage t o the determination of the s t a b i l i t y of a s i n g l e o b j e c t . For a s i n g l e o b j e c t there are only three b a s i c types of i n s t a b i l i t i e s t h a t can a r i s e . An o b j e c t can e i t h e r r o t a t e about some support p o i n t , i t can s l i d e along some s u r f a c e , or i t can simply f a l l f r e e l y . I f the center of g r a v i t y o f an ob j e c t has a support v e r t i c a l l y below i t or i f there are supports of the o b j e c t on both s i d e s of the v e r t i c a l through the c e n t e r of g r a v i t y , then the o b j e c t w i l l not r o t a t e . WHISPEB t h i n k s an o b j e c t 'hangs over too f a r ' i f i t s p e r c e i v e d center of area f a l l s o u t s i d e i t s supports. Because of the r e s t r i c t i o n s o f uniform d e n s i t y and t h i c k n e s s imposed upon the c l a s s of o b j e c t s WHISPEB handles, an o b j e c t ' s diagrammatic 3 2 -AMALGAMATION OF TtfE pdY^CNAL DESCRIPTION o F TWO OBJECTS. F I G U R E nT-Zf 33 c e n t e r o f area and i t s p h y s i c a l c e n t e r of mass a r e a t c o r r e s p o n d i n g l o c a t i o n s . C e n t e r of area d e t e r m i n a t i o n i s a p e r c e p t u a l p r i m i t i v e whose i n c l u s i o n i n t h e s e t o f p r i m i t i v e s i s j u s t i f i e d by i t s i m p o r t a n c e i n t h e i m p l e m e n t a t i o n of the s i m i l a r i t y and symmetry p r i m i t i v e s i n a d d i t i o n t o i t s u t i l i t y i n t h e c u r r e n t domain. In the c u r r e n t problem ( f i g u r e I I - 1 ) , WHISPER sees t h a t t h e c e n t e r of area of the combined o b j e c t AB i s t o t h e r i g h t of the support p r o v i d e d by the t a b l e so i t n o t e s t h a t AB w i l l r o t a t e and c o n t i n u e s w i t h an a n a l y s i s c f the o t h e r o b j e c t s i n t h e scene. ( E v e n t u a l l y the s t a b i l i t y o f B a l o n e w i l l be c o n s i d e r e d i n t h e upwards s t a b i l i t y t e s t i n g , and i t too w i l l be noted as b e i n g r o t a t i o n a l l y u n s t a b l e because i t s c e n t e r of a r e a l i e s t o the r i g h t of the su p p o r t p r o v i d e d by A.) E q u i l i b r i u m s i t u a t i o n s such as t h a t of o b j e c t D o r o f M and N i n f i g u r e I I - 5 p r o v i d e a good example o f the q u a l i t a t i v e n a t u r e o f WHISPER'S r e a s o n i n g . The approximate c e n t e r of g r a v i t y of the b a l a n c i n g o b j e c t i s found by the p e r c e p t u a l r o u t i n e s , but t h i s i s i n s u f f i c i e n t f o r d e t e r m i n i n g the s t a b i l i t y of the s i t u a t i o n . S i n c e t h e s l i g h t e s t s h i f t i n the c e n t e r o f g r a v i t y would upset t h e b a l a n c e , i t s p r e c i s e l o c a t i o n must be known i n o r d e r t o e s t a b l i s h t h a t the o b j e c t i s i n a s t a t e of e q u i l i b r i u m . The c e n t e r of g r a v i t y can be e s t a b l i s h e d as b e i n g d i r e c t l y above the s u p p o r t p o i n t i f the b a l a n c i n g FIGURE IE-5" 35 object i s symmetrical (symmetry i s another perceptual primitive) about a v e r t i c a l axis through the support. If the object i s not symmetrical about that axis then WHISPER may have to report that i t cannot decide the s t a b i l i t y of the configuration. In a case such as that of figure I I - 6 , however, WHISPER determines that although the combined object PQ i s unsymmetrical, P i t s e l f i s symmetrical, and so Q, no matter how small i t i s , w i l l t i p the balance to the right. It i s only i n the case where Q i s small that the need for the symmetry testing a r i s e s , since i f i t were large enough i t would have had a s i g n i f i c a n t enough effect on the o r i g i n a l approximation to the center of gravity that PQ would have been c l e a r l y unstable. ilrlj.iAi_l2££§§_2a_£2JS£'£2iiers When two supporting objects participate together i n supporting an object then they share the , force from that object. This force may be enough to cause one cf the cosupporting objects to rotate, depending on where the supportee makes contact. As mentioned e a r l i e r , the gluing together process continues u n t i l either a top block (one with no supportees), or a cosupporting object i s reached. In the l a t t e r case an extra force i s noted as being applied to the cosuppcrters from the supported object. Thus i n the second frame, figure II-7, of the current problem WHISPER w i l l proceed to determine the s t a b i l i t y of object D i n the same manner as i n ' S i FIGURE JI 6 1 .0 1 1 . 0 2 1 . 0 3 1 . 0 4 1 . 0 5 1 . 0 6 1 . 0 7 1 . 0 8 1 . 0 91 1 0 1 . 0 ! I ! .1 I I . . I | | 1 I 91 .0-22222222 222222222222222222222222222222222222 8 B22 222222222228 3282 BB 8 8 8 8 B B B B 8 ,3 8 8 8 22 2223 B 8 8 B 8 B B B B B B B B 8 B 3 3' SB 3 82 _ , r _ _ _ 22223 B B B BB B B B B B 8 S B B B B B B 3 B 2 rlbUKt: I L - / 222223 B 3 B 3 3 B B B 8 33 8 8 3 822 1111111111111111228 3 8 8 3 83 B 8 88 8 B 3 3 38 82 1A A A A A A A 1 2222B F S 8 D 3 3 3 3 BB B B 8B2 1A A A A A A A 1 222222 B B B 8 B B B B B B 2 2 1A A A A A A A 1 223 B 3 B 8 3 B 8 B BB2 lA A A I A A A 1 22 3 B B 33 B 8 B 82 1A A A A A A A 1 22222 B 8 8 8 B 2 1A A A A A A A 1 22 B 8 BB 8 2 s 1A A A A A A A 1 222223 B 2 1A A A A A A A 1 222222 1A A A A A A A 1 / » 4 4 ^ ^ 4 ^ 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 ' » 4 4 4 ' f 44444444444444444444444 1A A A A A A A i 4440 D D D D 0 0 0 O D D D D D O D Q D D D D O D D 0444 1A A A A A A A i • 444 D O D D D D O O D D D O D D O O D D D O D 444 1A A A A A A A l . 4 D D 0 D D D 0 0 D 0 D D D 0 0 D D D . D D D 4 1A A A A A A A i • 444 D O D D O O O D O O O D O O O O ' D 444 1A A A A A A A l 4440 O D D O O D D D D D O D D O 44 1A A A A A A' A I 44D D 0 D D D 0 0 D D D 0 D 4 4 1A A A A A A A l 44440 O D D O D D D O D D D D4D444 1A A A A A A A i 44444040 O D D D D D D D D D D D D D D D 040444 1A A A A A A A l 444 D n O O D O D D D D O D O O D D O D O O O D O O 444 1A A A A A A A 444444444444444444444444444443444444444444444444444444444 1A A A. A A A A I 333 1A A A A A A A i 3 3 1A A A A A A A I 3 C3 1A A A A A A A i 3C C33 1A A A A A 4 A l 3C C 3 1A A A A A A A I 33C C C3 1A A A A A A A l 3 C C C?3 1A A A A A A A l 3C C C C 3 1A A A A A A A i 3C C C C C3 1A A A A A A A i 33C C C C C33 1111111111111111 3333333333333 9999999999999999999999999999999999999999999999999999999999999999999999 99999999999999999999999999 1 1 . 0 1 I I ! I I ! I ! . . I I 1.0 1 1 . 0 2 1 . 0 31 .0 4 1 . 0 5 1 . 0 6 1 . 0 7 1 . 0 8 1 . 0 9 1 . 0 1 0 1 . 0 -4 38 the f i r s t frame, except t h a t the extra f o r c e from B w i l l be noted. WHISPEB does not c o n s i d e r the exact magnitude of the f o r c e , but simply notes i t as a f o r c e g r e a t e r than zero a p p l i e d a t the point of c o n t a c t . The e f f e c t t h i s f o r c e w i l l have i s determined by t a k i n g the c o n t a c t p o i n t as the new center of g r a v i t y of the o b j e c t r e c e i v i n g i t . T h i s i s e q u i v a l e n t to assuming t h a t the f o r c e i s of a r b i t r a r i l y l a r g e magnitude. I f the o b j e c t with t h i s new v i r t u a l center of g r a v i t y i s s t a b l e then the e x t r a f o r c e has no e f f e c t . Thus the s t a b i l i t y of B and T i s not a f f e c t e d by S i n f i g u r e I I - 8 , whereas the s t a b i l i t y of D i s a f f e c t e d by B i n f i g u r e I I - 7 . Counterbalancing f o r c e s such as that provided by V i n f i g u r e I I - 9 r e q u i r e a g u a n t i t a t i v e s o l u t i o n and have not been c o n s i d e r e d . In ge n e r a l , people when asked about such s i t u a t i o n s r e p l y t h a t they are not sure about the s t a b i l i t y , p o i n t i n g out t h a t i t depends on the exact weight of the co u n t e r b a l a n c i n g o b j e c t . 31 FIGURE TL-S s R A F I G U R E JLS V \ A no I f the s t a b i l i t y t e s t d i s c o v e r s that a s i n g l e or conglomerate o b j e c t w i l l t o p p l e then the diagram must be updated to r e f l e c t the r e s u l t i n g s i t u a t i o n . To do t h i s the angle of r o t a t i o n must be determined. A t o p p l i n g o b j e c t w i l l r o t a t e e i t h e r u n t i l i t h i t s something or u n t i l i t begins to f a l l f r e e l y . WHISPEB v i s u a l i z e s an o b j e c t ' s r o t a t i o n with the r e t i n a t o determine the point at which i t s swing ends, and c a l l s the redrawing t r a n s f o r m a t i o n s to r o t a t e the o b j e c t to t h a t p o i n t i n the diagram. Figure 1 1 - 1 0 shows the o v e r a l l o r g a n i z a t i o n of the r o t a t i o n a l motion procedures. The t r a n s f o r m a t i o n s of the o b j e c t s i n the diagram are c a r r i e d cut a f t e r a l l of the p r i m i t i v e o b j e c t s i n the scene have been t e s t e d by UPWABDS-STABLE. In the c u r r e n t example t h i s r e q u i r e s t e s t i n g the independent s t a b i l i t y of o b j e c t s AB, B, CD, and D. When t h i s i s complete WHISPEB w i l l have noted two r o t a t i o n a l i n s t a b i l i t i e s , o b j e c t s AB and B, and no s l i d i n g or f r e e f a l l i n s t a b i l i t i e s (these w i l l be d i s c u s s e d i n s e c t i o n II-8 with r e f e r e n c e to another example). N o t i c i n g t h a t B i s a par t of AB, WHISPER decides t o r o t a t e B r a t h e r than AB. (To see t h a t combined o b j e c t s need t o be considered at a l l look at f i g u r e 1 1 - 1 1 i n which the o b j e c t which i s r o t a t i o n a l l y unstable i s RS alone, so i t i s RS which must be rotated.) Object E w i l l p i v o t around the p o i n t at which i t c o n t a c t s A nearest the ce n t e r of g r a v i t y of B. WHISPEB uses i t s eye to examine the Handling Rotational Motions 1 Find Pivot Point V i s u a l i z e Object's Rotation This p r e d i c t s : (a) Object Hit (b) Angle of Rotation Redrawing Transformations Rotate Object Through Predicted Angle Move Eye to Predicted C o l l i s i o n Point No Finished Estimate Angle of Rotation to Close Gap F I G U R E IT-SO FIGURE TL-H R s T 4 3 c o n t a c t s u r f a c e between the two o b j e c t s t c f i n d the e x t r e m i t i e s o f t h e c o n t a c t . S i n c e the c o n t a c t i s t o the l e f t of B*s c e n t e r o f g r a v i t y , i t i s the r i g h t c o n t a c t e x t r e m i t y which i s used as th e p i v o t p o i n t . I I j ; ^ 1_ F i n d i n g _ D i s c o n G i v e n the p i v o t p o i n t , i t i s s i m p l e t o s t a r t t he r o t a t i o n o f B. There i s one s e r i o u s problem r e m a i n i n g , however. When s h o u l d the r o t a t i o n be t e r m i n a t e d ? I term t h i s problem s e r i o u s o n l y because i t or a v a r i a t i o n t h e r e o f has managed t o escape any s a t i s f y i n g and r e a s o n a b l e s o l u t i o n , i n o t h e r problem s o l v i n g systems. The e s s e n t i a l element o f the problem i s the a n t i c i p a t i o n o r d e t e c t i o n of c o l l i s i o n s between a moving o b j e c t and o t h e r elements of t h e environment. Winograd's 7 SHBDLO i g n o r e d the problem; Fahlman a l s o appears t o have b a s i c a l l y i g n o r e d i t . The c l o s e s t he has come i s with h i s F i n d s p a c e P r o p o s e r which puts an o b j e c t i n t o an a r b i t r a r y p o s i t i o n and then checks whether i t t o u c h e s a n y t h i n g u s i n g h i s r a t h e r complex t o u c h t e s t a l g o r i t h m . Fahlman s u g g e s t s t h a t i t would be h o p e l e s s t o use a v a r i a n t of t h i s a l g o r i t h m f o r f i n d i n g p aths i n 3-space. 8 44 IIriiAlxJ_2hS_Il£il_SJ2ace_Problei The s o u r c e o f the d i f f i c u l t y i s i n h a n d l i n g n e g a t i v e q u e s t i o n s . The approach of most c u r r e n t systems i s t o d e s c r i b e the p o s i t i o n of each o b j e c t by the c o o r d i n a t e s o f i t s o r i g i n - some a r b i t r a r y p o i n t on i t . No mention i s made of where o b j e c t s are not l o c a t e d . Thus empty space must be found through ' p r o o f * , e i t h e r c o m p u t a t i o n a l o r d e d u c t i v e , of the st a t e m e n t * t h e r e does not e x i s t an o b j e c t a t l o c a t i o n P'. Al t h o u g h i t need n ot n e c e s s a r i l y be the c a s e , t h i s has been e f f e c t e d by u s i n g the e q u i v a l e n t statement ' f o r each o b j e c t 0, 0 i s n o t a t P', and i n d i v i d u a l l y t e s t i n g a l l the o b j e c t s i n the u n i v e r s e . The r e s u l t i s unmanageable growth of c o m p u t a t i o n a l r e g u i r e m e n t s . The f e a t u r e t h a t WHISPEB e x p l o i t s i n t h e diagrammatic analogue i s t h a t §iS£ty_space_in_the_jroblem_en^ sxp,licitly__re£resented_b analogue.. While the p r o p o s a l t h a t p h y s i c a l space be r e p r e s e n t e d by a r r a y space i s net new 9, i t seems never t o have been re g a r d e d as v i a b l e . Some r e a s o n s a r e : ( i ) I t would appear t o be very i n e f f i c i e n t and e x p e n s i v e i n terms of memory usage. T h i s o b j e c t i o n can be c o u n t e r e d i n s e v e r a l ways. I n view o f the d i s c u s s i o n on the i n t e r n a l / e x t e r n a l g u e s t i o n ( s e c t i o n 1-2), 2-space and 3-space can be viewed as p a r t o f the 'hardware' of any machine, so i t i s a m a t t e r of h a r n e s s i n g t h i s space as opposed t o a l l o c a t i n g 45 more i n the form of core s t o r a g e . In a d d i t i o n , c u r r e n t technology promises vast q u a n t i t i e s of cheap computer memory. The l i m i t s of processor speed seem much c l o s e r t o being reached than the l i m i t s c f storage c a p a c i t y . In WHISPER'S domain there i s not only a t r a d e - o f f between space and time, but one between space and conceptual s i m p l i c i t y as w e l l . I t i s reasonable to t r a d e a f i x e d , but l a r g e amount of storage f o r these two f a c t o r s of time and s i m p l i c i t y . ( i i ) The empty space comes i n too many pi e c e s to be d e a l t with by a s e q u e n t i a l process. The answer to t h i s o b j e c t i o n i s to use a p a r a l l e l process. The human eye i s a s t r o n g precedent f o r t h i s s u g g e s t i o n . Normally i n AI a p p l i c a t i o n s , the l i n e a r r e d u c t i o n i n e l a p s e d computation time acquired through p a r a l l e l i s m i s not s i g n i f i c a n t because of the f r e g u e n t l y e x p o n e n t i a l c h a r a c t e r o f the growth of computational reguirements; however, i n t h i s case the amount of computation i s a f u n c t i o n of the f i x e d array s i z e . The number of p r o c e s s o r s can be made l a r g e enough so t h a t what would be an i m p r a c t i c a l and i n e f f i c i e n t s e q u e n t i a l s o l u t i o n becomes p r a c t i c a l and e f f i c i e n t i n terms of p a r a l l e l computation. Thus the p r o p o s a l to e x p l i c i t l y r e p r e s e n t p h y s i c a l space with a r r a y space a t t a i n s a c e r t a i n v i a b i l i t y through a re-examination and r e d e f i n i t i o n of e f f i c i e n c y c r i t e r i a f o r both storage and p r o c e s s i n g . 46 11-4^ li A2_Ho w_RHIS S i n c e t h e diagram e x p l i c i t l y r e p r e s e n t s t h e empty space o f the problem s i t u a t i o n , WHISPEB c o u l d determine what happens t o moving o b j e c t s by watching them. as l o n g as an o b j e c t passes t h r o u g h unoccupied space i n the diagram, then i t w i l l not be i n v o l v e d i n a c o l l i s i o n i n t h e r e a l w o r l d . I t would be a p r o h i b i t i v e l y e x p e n s i v e c o m p u t a t i o n t o s i m u l a t e the motions by i n c r e m e n t a l movements, so i n s t e a d o f a c t u a l l y w a t c h i n g o b j e c t s move i n the diagram t h e i r motions are v i s u a l i z e d w i t h the r e t i n a . There are two t y p e s o f r o t a t i o n a l motion d i s c o n t i n u i t i e s . An o b j e c t w i l l s t o p r o t a t i n g e i t h e r when i t c o l l i d e s w i t h a n o t h e r o b j e c t o r when i t s c e n t e r c f g r a v i t y r e a c h e s a p o s i t i o n d i r e c t l y below i t s p i v o t p o i n t . At t h a t p o i n t t h e o b j e c t b e g i n s f a l l i n g f r e e l y . The check f o r t h e s e two c o n d i t i o n s i s a c c o m p l i s h e d by c e n t e r i n g the eye on t h e p i v o t p o i n t , and • v i s u a l i z i n g * t he r o t a t i o n of the o b j e c t from i t s i n i t i a l p o s i t i o n u n t i l a c o l l i s i o n o c c u r s , o r u n t i l the o b j e c t r e a c h e s the f r e e f a l l p o i n t . I I - 4 i 2 _ C h a r a c t e r i s t i c s I would l i k e t o emphasize t h a t t h e v i s u a l i z a t i o n p r o c e s s o c c u r s on the s o f t w a r e r e t i n a not on t h e diagram i t s e l f . For the f u l l 360 degree r e t i n a l f i e l d t h e r e are o n l y a s m a l l number o f d i r e c t i o n s ( i n the case o f t h e c u r r e n t r e t i n a l U7 i m p l e m e n t a t i o n , t h i r t y - s i x ) a t which the o b j e c t i s ' v i s u a l i z e d ' d u r i n g the r o t a t i o n . S i n c e an o b j e c t w i l l never r o t a t e more than h a l f a t u r n b e f o r e i t f a l l s o f f , at most h a l f of t h e s e need be c o n s i d e r e d . The mapping from the diagram t o the r e t i n a e n s u r e s t h a t n o t h i n g p r e s e n t i n the diagram i s absent on the r e t i n a , w i t h the i m p l i c a t i o n t h a t any empty space on the r e t i n a i s a l s o empty i n the diagram. Thus i f a c o l l i s i o n i s not d e t e c t e d d u r i n g t h e v i s u a l i z a t i o n p r o c e s s no c o l l i s i o n would o c c u r i n the diagram, f u r t h e r i m p l y i n g t h a t no c o l l i s i o n would have o c c u r r e d i n the r e a l w o r l d . T h i s i s t h e case even though o n l y a f i x e d number of d i f f e r e n t o r i e n t a t i o n s a r e t e s t e d . The o n l y d i s a d v a n t a g e i s t h a t some f a l s e alarms may a r i s e , because o b j e c t s are expanded s l i g h t l y i n the mapping from the diagram t o the r e t i n a . The s h i f t from one o r i e n t a t i o n t o the n e x t , and the t e s t f o r any c o l l i d i n g c o n t o u r segments are both p a r a l l e l c o m p u t a t i o n s , so t h e net s e r i a l t i m e r e g u i r e d t o t e s t f o r c o l l i s i o n by v i s u a l i z a t i o n i s s m a l l . I n a d d i t i o n , the number of p r o c e s s e s , and hence the number of p r o c e s s o r s , i s f i x e d as the number of c e l l s (not t o be c o n f u s e d w i t h r e c e p t o r s s i n c e t h e r e might w e l l be more r e c e p t o r s than p r o c e s s o r s ) composing t h e s o f t w a r e r e t i n a . In the c u r r e n t i m p l e m e n t a t i o n t h i s number i s 540, A c o l l i s i o n i s d e t e c t e d i f the c o n t o u r of t h e r o t a t i n g o b j e c t c r o s s e s a c e l l whose c u r r e n t i n p u t c o n t e n t as seen d i r e c t l y from t h e diagram i s non-empty and d i f f e r e n t from t h a t of the c o n t o u r i t s e l f . 48 IS zH A 2 i 1 _ S u r p r i s e _ C o l l i s i o i i s A n i c e f e a t u r e o f WHISPEE's use of v i s u a l i z a t i o n f c r the d e t e c t i o n o f c o l l i s i o n s i s t h a t i t i s never s u r p r i s e d by the presence c f o b j e c t s such as C i n f i g u r e 11-12. S t r a t e g i e s r e l y i n g on the c o m p u t a t i o n o f c o l l i s i o n s of o n l y p o i n t P on o b j e c t E, or o t h e r s t r a t e g i e s o f p a r t i t i o n i n g t h e c l a s s of p o s s i b l e c a n d i d a t e c o l l i s i o n o b j e c t s on t h e b a s i s of b e i n g members o f the same s t r u c t u r e or b e i n g below the c u r r e n t o b j e c t would more than l i k e l y o v e r l o o k such s i t u a t i o n s . 50 I I - 5 , O p d a t i n q The Diagram To R e f l e c t ft R o t a t i o n Once t h e t e r m i n a t i o n p o i n t c f an o b j e c t ' s r o t a t i o n i s known then the r e d r a w i n g t r a n s f o r m a t i o n p r o c e d u r e s a r e c a l l e d t o r o t a t e i t i n t h e diagram. The a n g l e of r o t a t i o n a t which, t h r o u g h v i s u a l i z a t i o n , the f i r s t c o l l i s i o n i s d e t e c t e d i s an a p p r o x i m a t i o n of t h e a c t u a l a n g l e t h r o u g h which th e o b j e c t must be r o t a t e d i n t h e diagram. The t r a n s f o r m a t i o n p r o c e d u r e s are c a l l e d w i t h a s l i g h t l y c a u t i o u s e s t i m a t i o n o f t h i s a n g l e so t h a t the r o t a t i n g o b j e c t w i l l not o v e r s h o o t i t s c o l l i s i o n p o i n t . The r e s u l t o f t h i s f i r s t r o t a t i o n i n the c h a i n r e a c t i o n problem i s shown i n f i g u r e 11-13. A f t e r t h i s r o t a t i o n has been made, t h e eye i s moved t o t h e p r e d i c t e d c o l l i s i o n p o i n t . The s p a c i n g between the moving o b j e c t and the one w i t h which i t i s t o c o l l i d e i s measured w i t h the e y e , and t h i s measurement i s used t c compute the e x t r a t w i s t n e c e s s a r y t o c l o s e t h e gap ( f i g u r e 11-14). A l t h o u g h i t i s not u s u a l l y n e c e s s a r y , the eye i s used t o recheck the s p a c i n g . The r o t a t i o n i s c omplete. I I r 5 . 1 _ G r i g e _ S i t u a t i o n s The one s i t u a t i o n i n which t h e gap would s t i l l e x i s t i s d e p i c t e d i n f i g u r e 11-15. A f a c i l i t y f o r h a n d l i n g t h i s s i t u a t i o n has not yet been i n c l u d e d i n WHISPER, but i t i s a s i m p l e matter t o see how a c o m p l a i n t message (Fahlman termed t h e s e messages ' g r i p e s ' ) c o u l d be s e n t back t o .the v i s u a l i z a t i o n p rocedures r e q u e s t i n g the g e n e r a t i o n of t h e next 1.0 1 0 1 . 0 1 . . 1 1 . 0 2 1 . 0 3 1 . 0 • • I • • • 4 1 . 0 5 1 . 0 6 1 . 0 7 1 . 0 8 1 . 0 9 1 . 0 1 0 1 . 0 22 2 2 2 2 2 2222 2 2 22 2 \ 2 2 22232222S222B2 22B3 B B , 83 BB B22 222 B22223 2 B2B2 BB B B BB BB B 3 B 8 B BB B 2 2223 B 3 8 8 B B 8 3 B 3 B 2 22223 B B B 83 B B B B B 8 B B 8 B 83 B2 22222B B B B B B B8 B B B B B B B B 2 1111111111111111223 B B B B B B B B2 2222B B B 8 BB BB B B B 8 B B B 2 222222 8 B B 8 B 3 BB 8 32 22 B B B B B 2 2222 3GB B B BB B2 22222 3 B 3 8 2 222B 3 8 2 222 1*0 1A A A A A A A 1 1A A A A A A A 1 1A A A A A A A 1 1A A A A A A A 1 1A A A A A A A 1 1A A A A A A A 1 1A A A A A A A I 1A A A A A A A 1 1A A A A A A A 1 1A A A A A A A 1 1A A A A A A A 1 1A A A A A A A 1 1A A A A A A A 2. 1A A A A A A A 1 I 1 1A A A A A A A i 1A A A A A A A 1 1A A A A A A A 1 1A A A A A A A 1 1A A A A A A A 1 1A A A A A A A 1 1A A A A A A A 1 IA A A A A A A 1 1A A A A A A A 1 1A A A A A A A 1 1A A A A A A A 1 1A A A A A A A 1 1A A A A A A A 1 1A A A A A A A 1 F I G U R E JT-13. SLIGHT "GAP 1111111111111111 4440 D D D D 0 D D D O 0 O D 0 0 0 O D 0 D 0 D 0 D C444 444 D D D D O D D D D D D D O D O O D D D D O 444 4 D D D D 0 0 D 0 D D 0 D D D D D D D D 0 4 444 O O D D D O D O D D D O D D O D D 444 4440 O D D 0 O D O O O D D O O D 4 4 440 D 0 D D O 0 D D 0 D D D 4 4 4444D D D D D O O D D O O O 04D444 4444404D 0 D D D O D D O D D D D D O D D 040444 444 O D D D O O O O D O D O O D O D D D D D D D D 444 4444<,4444i ,^444444444444444443444444444444444444444444444 333 3 3 3 C3 3C C33 3C C 3 • 33C C C3 . 3 C C C33 3C C C C 3 3C C C C C3 33C C C C C33 3333333333333 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 52_ —« O rH o o o 4s •H Id D LD LL CM *\J f\l f\| f \J N N (\l N D z o u LU in • (M CO CO CO CM CO IM CM CO CM CO CO cu CO (M CO CM fM CM o • fNj CO CD CO CO CO CO CM if PH • • eg co CO CD CO CD CO *v*y rH CM CM co m CO CO CO CO <M""& in • CM CM tO CO CO CO CO CO CM -r • CM CO CO CO CO CO CO co r-j <r • CM CO CO co cn r.j c\j vJ-• CM . CO CO CO CO CO CO CM vT • CM CO CD CO CO CO CM • CM m CO CO CO CD CO CO CM • CM CO CO C U CO o • CM CO cu CO CO CO CM • r • • CM CO CD CO CO CM •3-rH — CM CO CO CO CO cO CM <• CM CO CO cO CO fM • CM CO CO CO CO CM • CM CO CO CO CO CO ro • CM CO CO CO CD CM • CM CO CO CO CO CM CM CO CO CD CO CO CM • CM CO CO co CM o t CM CO CO CO EC IM c n (O ro ro m ro o o co ro co ro u o o o o ro o u o o o o o o o o o o o o ro ro ro ro ro o o o ro co ro ro C* Cf O ro c* ro Cf <o Cf CO Cr ro Cf ro Cf ro Cf ro cr ro Cf ro Cf ro Cf ro cr ro o» o o .4--3- O sj-•4- *r Cf o Cf ro co CM CM CO CM CO CO , CM CO fM • CD CM CM CM CO CO CM CO i CM CD > CM CO CO CM 1 ro co co ro i ro co co ro CO CM CM o O Cf o o o CM i CO CO ro rH < <l < < <. <l < < < <l < <l < < <l < < < < <L ro CM r-4 CM CO CO CM rH <I < < < < < < < < < •c < < < < < < < < < <l < < < ro CM rH CM co CM —4 < < < < < < < < < < < <t < < < < < < <l < < <t < < < CM CM r~i CM CO CM CO CO rH < < < < < < < < < < < < < < •< < ro ro CM CM r-t < < < < < < < < < < < < < < < < < < < < < < < < CM CM r-4 < < < < < <t < < < < < < < < < < < < < < < < < CM »H < < < < < < < < < < < < < < < < <I < < < < •< < *"* rH r-4 rH rH rH rH r-l r-4 rH rH rH rH rH rH -H rH rH rH rH rH rH —4 rH rH o rH Cf wt Cf rH Cf rH Cf rH Cf rH Cf rH Cf rH O - I Cf rH O r-l Cf rH Cf r-l Cf r< Cf rH Cf o rH? o CO rH • Q F I G U R E 31-15". 54 c o l l i s i o n p o i n t . T h i s i s a q u a l i t a t i v e l y d i f f e r e n t t y pe o f g r i p e s i t u a t i o n than those a r i s i n g i n Fahlman 1s BOTLD system. The g r i p e here i s not computable i n advance b u t _ a r i s e s ^ r . u r e 1 y out of .the.experiment„,sith mthe_analoguej; q r i p e s i n BUILD a r i s e because the code was more c o n v e n i e n t l y w r i t t e n i n a form which put o f f e r r o r c h e c k i n g as l o n g as p o s s i b l e . A l l g r i p e s i n BUILD c o u l d be e l i m i n a t e d , t h a t i s they c o u l d be p r e d i c t e d and th u s a v o i d e d , by e x e c u t i n g t h e same code i n d i f f e r e n t sequence. F o r example, F a h l m a n 1 0 d i s c u s s e s t h e example of a r o u t i n e named MOVE, f i n d i n g an o b j e c t a l r e a d y i n the s p o t where i t i s r e q u e s t e d t o p l a c e a n other o b j e c t . I n t h i s case MOVE g e n e r a t e s a g r i p e i n d i c a t i n g t h a t t h e two o b j e c t s have c o l l i d e d . The d i s c o v e r y t h a t the spo t i s o c c u p i e d i s made by e x e c u t i n g some of BUILD'S code to e x p l i c i t l y t e s t f o r the presence c f the g r i p e c o n d i t i o n . T h i s t e s t c o u l d have been executed e a r l i e r , b e f o r e MOVE was c a l l e d upon t o perfor m an i m p o s s i b l e t a s k . I n our example t h e g r i p e s i t u a t i o n i s n o t p r e d i c t a b l e t h r o u g h the e x e c u t i o n o f any o f IHISPER's code i n any o r d e r . The g r i p e a r i s e s e x p e r i m e n t a l l y i n the analogue and i s o n l y r e c o g n i z e d , not computed, by SHISPER. I I z 5 A 2_Advantaqes_Of_The_Feedback_Method I t i s t h i s feedback from SHISPER's e x p e r i m e n t s w i t h t he diagrammatic analogue t h a t p r o v i d e s c o n c e p t u a l s i m p l i c i t y i n d i s c o v e r i n g r o t a t i o n a l t e r m i n a t i o n p o i n t s . Both v i s u a l i z a t i o n 55 and gap c l o s u r e r e l y on feedback. These two methods i n c o m b i n a t i o n r e p r e s e n t WHISPER 'S p r a g m a t i c e g u i v a l e n t t o the e x p e r i m e n t o f r e p e a t e d l y r o t a t i n g t h e o b j e c t i n the diagram by s m a l l i n c r e m e n t s u n t i l t h e f i r s t c o l l i s i o n o c c u r s . U s i n g f e e d b a c k i n t h i s manner has g e n e r a l l y been spoken of i n terms o f a r o b o t immersed i n a r e a l w o r l d environment. Here i t i s b e i n g o b t a i n e d not from the r e a l w o r l d of f a l l i n g o b j e c t s , but from an analogue of the r e a l w o r l d s i t u a t i o n , namely t h e c o m b i n a t i o n of a diagram and a p p r o p r i a t e t r a n s f o r m a t i o n p r o c e d u r e s . B e l i a n c e on t h i s feedback from e x p e r i m e n t s w i t h the d i a g r a m m a t i c analogue e l i m i n a t e s the n e c e s s i t y f o r e g u a t i o n s of motion and touch t e s t s f o r a r b i t r a r y shapes. WHISPER i s not f o r c e d t o use " s o p h i s t i c a t e d * number-crunching• t e c h n i q u e s i n e s t a b l i s h i n g t h e p o i n t s a t which an o b j e c t ' s motion w i l l change. T h i s i s a p p r o p r i a t e because the hard p a r t o f the problem, the p a r t which i n v o l v e s t h e g u a l i t a t i v e p h y s i c s , i s p r e d i c t i n g what the motion w i l l be, not when i t w i l l t e r m i n a t e . 56 II-6_The_Eie_aov§i§nt_Pr As t h e problem s o l v i n g p r o c e s s proceeds the r e t i n a c o n s t a n t l y moves from p l a c e t c p l a c e i n the diagram. A t r a c e o f the eye movements i s g i v e n by t h e c i r c l e d numbers i n f i g u r e 11-16, f i g u r e 11-13, and f i g u r e 11-14. Each c i r c l e r e p r e s e n t s a f i x a t i o n of t h e r e t i n a a t i t s l o c a t i o n i n the diagram. The numbers g i v e t h e o r d e r i n which t h e f i x a t i o n s o c c u r r e d . A number w i t h the l e t t e r C a t t a c h e d to i t i n d i c a t e s t h a t t h e c e n t r a l p o r t i o n o f the r e t i n a was f i x a t e d a t the l o c a t i o n ; a number w i t h o u t a l e t t e r i n d i c a t e s t h a t the p e r i p h e r y of t h e r e t i n a was f i x a t e d a t the l o c a t i o n . The s t r u c t u r e of the r e t i n a i s d i s c u s s e d i n s e c t i o n I I I - 2 . A l t h o u g h moving t h e two p a r t s of the r e t i n a s e p a r a t e l y would be u n n e c e s s a r y i f t h e r e a c t u a l l y were many p r o c e s s o r s o p e r a t i n g i n p a r a l l e l , i t saves a c o n s i d e r a b l e amount of c o m p u t a t i o n i n the p s e u d o - p a r a l l e l s i m u l a t i o n . A l i s t of t h e f i x a t i o n s p l o t t e d on t h e diagrams w i t h reasons the g u a l i t a t i v e Knowledge d i r e c t e d them f o l l o w s : (1) Move t o c e n t e r of diagram; r e t u r n names of a l l t h e o b j e c t s i n the scene. (2-4) F i n d the c e n t e r of g r a v i t y of A; f i n d s u p p o r t e e s o f A. (5-6) F i n d the c e n t e r o f g r a v i t y of E; f i n d s u p p o r t e e s and s u p p o r t e r s of E. (7) Move c e n t r a l s e c t i o n of r e t i n a ; f i n d e x a c t c o n t a c t p o i n t o f A and B. 57 o r-l -r l LU K D LU CM f\J IN INI CM CO CD CO IM CM f\J co co co co co c\l rsj r\j r\j CM CM CM CM CMCMCOCOCOCOCOCM CM CM C O c O C O C O c O C O C O C M eg C O c O C O C O c O c O C O r M fM C M C O C O C O C O C O C O C O C O C O C O C O C O C M CM c D c o c o c o c o c n c o f M CM c o c o c o c o c o c o c a r g CM co eo~£0 cn co cc co CM CO CO CO to co^F) 0 ( N | CM CO CO CO CO I CM CM CO CO CO CO < CM CM CO CO CO I CM CO CO CO ro CM CO CO CM CO CO IM IM CO e o c o e o c o c o c o c o r M co Q^/WYO GD CO £D <M eo c o y U U o CO CO CO CM •J V ^ CM J C O C O C O C Q C O C O C O C M CM CM f M C O c O C O C Q C O c a c M CM CO fMcacococococorM CM CJ CM CO CO CO CO CO CM CM CM CM eo co eo co cn CM CM CM •4" <4" -4" •4- -4" * <f •4- <t *t o *r •4- <r c 0 <t-O Q *4" sr *4-a a *t *f -4-*f 4-•* *4" •* -1 -.4- o <J-•4" O O CI v* «4" sfr •4" Q O O -4" <t d o o a - 4 - 4 • 4 - O O O O O v J - O O O - r ^- - 4 -4- "4" «4- <r > j - Q o o o c n o c o o - 4 -v f o n 0 . 0 t-'fPjrj o o -4- F «4" _ -4" CO i -4- o o o «£ip o o o o-t m m o i •4- C y / ^ V ro rn . 4 - 0 0 o r r « o o t'**r ro m o 0 o o < «4- IrVXV l«T ^  «4- o o r.^ TpPi o c/jc- I —V m to ro «_> t_> o * •4- o C / T N AS / O C V ? -4- I S ) -4- o o V I / o o o 0 a o -4-•4" *4" ^ O O O C O O O O O v r -4-^ • o Q o o c n o o O o ^ -4" -4" ,4- o t 3 o n o o o o o - f •4- <r •4- -4" NJ- «4 <r -4- -4- .4->J- Q O O O ^  - 4 O O 4 " <T >4- -4" -4-•4 Q O O -4- O O - * •4* •4" «4 -4" •4" O O O *4" J-O-tf-•4" -4" *4" «4* >r o ^ -d- o -4--4" >4" -4-•4- a <r * <t •4- ** - 4 <r -4* -4- <r •4/ *4- «4-c a m r o ro 1 CM co co co cn CM CM CM CO cO CO ca eo cn * //Ir^ CM r-4 < <, <I CM CO CO CM r-t [ <T < <I E < <* < cv c r T n rg rg H < < < CsJ fM_r-4 < < < . a I r-h~*\ Cf < i < < i < i < r < < < < < - a < i < i < i < < ( < i « a < < l ^ < l < < £ < <t < < <r * i < <t Q-^p}) < @ f < < < < < < < < t < < < < ^ cf -1 o -« c -H Cf Cf o • — 58 (8-9) f i n d c e n t e r of g r a v i t y of AB; f i n d s u p p o r t e r s of AB. (10) Move c e n t r a l s e c t i o n ; f i n d e x a c t c o n t a c t p o i n t o f AB w i t h t a b l e . (11-12) Move c e n t r a l s e c t i o n ; f i n d e x t r e m i t i e s of c o n t a c t s u r f a c e . (13) F i n d t h e s l o p e o f the c o n t a c t s u r f a c e . (14) Move t o c e n t e r of g r a v i t y of B3 l o o k a t c o n t a c t between A and B. (15-16) Move c e n t r a l s e c t i o n ; f i n d e x t r e m i t i e s o f c o n t a c t s u r f a c e between A and E; (5 , 72) and (19 , 72) are r e t u r n e d . (17) Determine the s l o p e c f the c o n t a c t s u r f a c e . (18-20) F i n d c e n t e r o f g r a v i t y of D; l o o k f o r s u p p o r t e r s and s u p p o r t e e s . (21-22) Move both the c e n t r a l s e c t i o n and the p e r i p h e r y ; f i n d the e x a c t p o i n t of c o n t a c t w i t h C. D i s c o v e r s t h a t s u p p o r t i s a p o i n t not a s u r f a c e i n d i c a t i n g p o s s i b l e e q u i l i b r i u m s i t u a t i o n . (23) Move back t c c e n t e r of g r a v i t y of D t o check f o r symmetry of D; e q u i l i b r i u m i s found t o be ok. (24) F i n d i n g c e n t e r o f g r a v i t y of C; l o o k f o r s u p p o r t e e s of C. (25-26) F i n d i n g c e n t e r of g r a v i t y of CD; f i n d s u p p o r t e r s c f CD; f i n d s the t a b l e . (27) Move c e n t r a l s e c t i o n ; f i n d e x a c t p o i n t of c o n t a c t of CD w i t h t a b l e . (28-29) Move c e n t r a l s e c t i o n ; f i n d e x t r e m i t i e s of c o n t a c t s u r f a c e ; r e t u r n s (64 , 22) and (76 , 21) . (30) Determine t h e type o f c o n t a c t and i t s s l o p e . 59 (31) Move t o the p i v o t p o i n t of t h e r o t a t i o n o f B t o v i s u a l i z e t h e r o t a t i o n , ****The r o t a t i o n i s then c a r r i e d out i n the d i a g r a m , see f i g u r e 1 1 - 1 3 . * * * * (32) Move c e n t r a l s e c t i o n t o e s t i m a t e d p o i n t of c o l l i s i o n between B and A t o see i f they t o u c h ; the gap i s s e e n ; the amount o f the next r o t a t i o n i s e s t i m a t e d . ****Another r o t a t i o n i s c a r r i e d out i n the d i a g r a m , see f i g u r e n - m . * * * * (33) Move c e n t r a l s e c t i o n t c e s t i m a t e d p o i n t of c o l l i s i o n between E and A; now they are seen t o t o u c h . 60 Il22_Subseauent_Sna£sh In the problem s o l v i n g process thus f a r , the s t a t e of the world has been considered by examination of the diagrammatic analogue, and i t was concluded that o b j e c t B would r o t a t e , fiotating an o b j e c t i s an a c t i o n which changes the s t a t e of the world; the e f f e c t s of t h i s change must be r e f l e c t e d i n WHISPER'S world model i f i t i s to s u c c e s s f u l l y continue with the problem s o l v i n g process. The a c t i o n i s represented by the a p p l i c a t i o n of a r o t a t i o n a l t r a n s f o r m a t i o n t o B i n the diagrammatic analogue, and the new s t a t e of the analogue r e p r e s e n t s the s t a t e of the world r e s u l t i n g from the a c t i o n . The problem of updating a system's r e p r e s e n t a t i o n of the s t a t e of the world t o r e f l e c t the e f f e c t s of a c t i o n s performed i n the world i s the 'frame* problem. In i l l u s t r a t i n g t h i s problem R a p h a e l 1 1 used the example of a s i t u a t i o n with a robot a t p o s i t i o n A, a box ET at p o s i t i o n B, and another box B2 on top of B1. I f the robot moves to a new p o s i t i o n , C, then the statement d e s c r i b i n g fl as the robot's p o s i t i o n has to be r e p l a c e d by one s t a t i n g t h at the robot i s at C, while a l l the other statements must be l e f t unchanged. If the robot pushes / box B1 t o C, then both the d e s c r i p t i o n s of the p o s i t i o n of the ro b o t and the p o s i t i o n of B1 must be changed. In a d d i t i o n , f a c t s d e r i v e d from the i n i t i a l s i t u a t i o n , such as B2 i s at E, 61 may no longer h o l d . In order to make these t r a n s i t i o n s from an i n i t i a l s t a t e to the s t a t e which r e s u l t s from an a c t i o n , the c a u s a l connections between a c t i o n s and p r o p e r t i e s of s t a t e s must be s p e c i f i e d . One aspect of the * frame' problem i s the n e c e s s i t y to e x p l i c i t l y know which p r o p e r t i e s remain u n a f f e c t e d by which a c t i o n s . I f t h i s i s not known, then i t i s r o t p o s s i b l e to i n f e r t h a t these p r o p e r t i e s s t i l l hold a f t e r an a c t i o n by which they are a c t u a l l y u n a f f e c t e d . 1 2 Another aspect i s t h a t t h e r e must be some way to s t a t e t h a t the problem d e s c r i p t i o n e x h a u s t i v e l y d e s c r i b e s a l l the c a u s a l connections which e x i s t between o b j e c t s . For example, i t i s p o s s i b l e t h a t E2 i s connected by a wire t o the c e i l i n g so t h a t when B1 i s moved, B2 a c t u a l l y remains a t p o s i t i o n B i n s t e a d o f moving with B1. Even i f these d i f f i c u l t i e s are surmounted, the problem remains of e f f e c t i v e l y o r g a n i z i n g an i n f e r e n c e mechanism t c e f f i c i e n t l y reason about and d i s c o v e r the chains of c a u s a l c o n n e c t i o n along which the s i d e e f f e c t s of a c t i o n s propagate. The t r a n s i t i o n between WHISPER'S snapshots i s e x a c t l y the type o f s i t u a t i o n i n which the 'frame' problem would t r o u b l e a system based e n t i r e l y on a d e s c r i p t i v e r e p r e s e n t a t i o n . I t i n v o l v e s the r e p r e s e n t a t i o n of a c t i o n , the e f f e c t s of a c t i o n , the i s s u e of exhaustiveness, and chains of c a u s a l i t y . Because WHISPEB r e l i e s cn a diagrammatic analogue as a r e p r e s e n t a t i o n of the s t a t e of the world i n s t e a d of a d e s c r i p t i o n i t i s not t r o u b l e d by the u b i g u i t o u s 'frame' problem. I h e _ s t a t e _ o f _ f h e 62 w o r l d _ i s _ r € P r g s g n t e iQ-^hg-goSJ-4_Jr§^,giB¥§§§gtg^ feJ..£°££^§£2S^isg-g^t|op_in_ the aSSlSaSSi. T h e c o r r e s p o n d i n g a c t i o n i s the a p p l i c a t i o n cf the a p p r o p r i a t e t r a n s f o r m a t i o n , and the e f f e c t s of the a c t i o n are c o r r e c t l y r e p r e s e n t e d by the r e s u l t i n g s t a t e of the analogue. In WHISPER'S c u r r e n t problem the g u a l i t a t i v e knowledge procedures know t h a t the a c t i o n of B's r o t a t i o n i s represented by c a l l i n g the r o t a t i o n t r a n s f o r m a t i o n procedure to redraw B at i t s new l o c a t i o n i n the diagram. Almost a l l of the i n f o r m a t i o n t h a t i t needs t o continue i t s problem s o l v i n g i s c o r r e c t l y r e p resented by the updated diagram. I t can proceed j u s t as i f the new snapshot were i t s o r i g i n a l i n p u t and i t were s t a r t i n g a brand new problem. The most important i n f o r m a t i o n which has changed i n the t r a n s i t i o n between the s t a t e s as a r e s u l t of the r o t a t i o n i s : the p o s i t i o n and o r i e n t a t i o n of o b j e c t B; the p o s i t i o n of i t s center of area; the c o n t a c t s i t makes with other o b j e c t ; and the shape of the areas of empty space. There are a l s o a multitude of t h i n g s which have not changed and are c o r r e c t l y l e f t unchanged by the r o t a t i o n a l t r a n s f o r m a t i o n , such as the p o s i t i o n of a l l the other o b j e c t s , the shape of a l l o b j e c t s , the area of a l l o b j e c t s , and the c o n t a c t r e l a t i o n s h i p s of other o b j e c t s not i n v o l v i n g B. A l l of these t h i n g s work out c o r r e c t l y without the need of any deduction or i n f e r e n c e on WHISPER'S p a r t . A l l t h a t i t need do i s t o use i t s r e t i n a t o look at the diagrammatic analogue and e x t r a c t whatever i n f o r m a t i o n i t needs. 63 The v i s u a l i z a t i o n process works because of the exhaustive nature of the diagrammatic analogue. A l l the o b j e c t s which c o u l d a f f e c t the motion c f B are i n t h e i r proper p o s i t i o n s i n the diagram. None i s missing. He could add some e x t e r n a l f o r c e such as a st r o n g magnetic f i e l d which would i n t e r f e r e with B, but there i s no problem i n expressing the assumption t h a t such a f o r c e dees not e x i s t i n the c u r r e n t s i t u a t i o n . The d i s c o v e r y of c a u s a l chains i s a l s o f a c i l i t a t e d by the diagrammatic analogue. In p a r t i c u l a r , what causes t e r m i n a t i o n of B's r o t a t i o n - i t s c o l l i s i o n with D - i s e a s i l y found by the v i s u a l i z a t i o n process. A f t e r the r o t a t i o n a l t r a n s f o r m a t i o n i s a p p l i e d , a l l i t s s i d e e f f e c t s are immediately propagated throughout the diagrammatic analogue. WHISPER i s i n a good p o s i t i o n t c apply i t s g u a l i t a t i v e p r o c e d u r a l knowledge to determine what e f f e c t s w i l l f o l l o w from t h i s new s t a t e . In f o l l o w i n g the c a u s a l chain from the i n i t i a l i n p u t snapshot through the i n t e r v e n i n g seguence of snapshots to the f i n a l snapshot, t h e r e i s c o n t i n u a l i n t e r a c t i o n between the higher l e v e l p r o c e d u r a l l y represented g u a l i t a t i v e knowledge and the more mundane though voluminous i n f o r m a t i o n contained i n the diagrammatic analogue. An expanded WHISPER system c o u l d net completely avoid the p i t f a l l s of the 'frame' problem because not a l l of the i n f o r m a t i o n about the c u r r e n t s t a t e c f the world can be represented by the s t a t e of the analogue. For example, once an 64 o b j e c t s t a r t s moving i t a c q u i r e s some momentum and t h i s momentum w i l l cause a f o r c e g r e a t e r than that r e s u l t i n g from the f o r c e of g r a v i t y alone t o be a p p l i e d to the su p p o r t e r s of the moving o b j e c t i n the subsequent snapshot a n a l y s i s . V e l o c i t i e s are not par t of the s t a t e of diagrammatic analogues and thus v e l o c i t i e s i n the world are not represented by them. For the g u a l i t a t i v e s o l u t i o n s which WHISPER c u r r e n t l y o b t a i n s , a c o n s i d e r a t i o n of the v e l o c i t y and momentum of o b j e c t s i s not necessary. Although the 'frame' problem cannot be t o t a l l y e l i m i n a t e d , WHISPER demonstrates t h a t i t can be circumvented to the e xtent t h a t the system need not be hampered i n i t s search f o r a g u a l i t a t i v e s o l u t i o n by the many messy d e t a i l s i n v o l v e d i n propagating the e f f e c t s of simple c a u s a l i t y . l l . z l s. 2 ^  Jfeg .„, % fell §.. ftp d.Fjn al.. Snapshots WHISPEE begins t h i n k i n g about the second snapshot as a new problem and proceeds through some of the same c o n s i d e r a t i o n s as f o r the f i r s t stage. Object D i s found to balance on C except t h a t there i s an e x t r a f o r c e on D from B and t h i s f o r c e l i e s o u t s i d e the supports of D. Therefore D i s noted as r o t a t i o n a l l y u n s t a b l e . Object B i s at f i r s t expected to s l i d e to the r i g h t except that t h i s i s based on the assumption t h a t i t s s u p p o r t e r s are s t a b l e . Supporter D i s not s t a b l e , however. The r o t a t i o n a l i n s t a b i l i t y of D i s given precedence over the s l i d i n g i n s t a b i l i t y of B, and D i s r o t a t e d about i t s c o n t a c t 65 with C u n t i l i t h i t s the t a b l e . As with B t o p p l i n g , D i s v i s u a l i z e d as r o t a t i n g with the eye centered on the p i v o t p o i n t , an approximate angle of r o t a t i o n i s o b t a i n e d , D i s r o t a t e d i n the diagram by t h i s amount ( f i g u r e 11-17}, and then the eye i s moved to the gap t o measure i t f o r the computation of the f i n a l t w i s t . The r e s u l t i s the t h i r d snapshot, f i g u r e 11-18. Again, t h i s t h i r d snapshot i s taken as a new problem. Object B i s found t o be r o t a t i o n a l l y u n s t a b l e , and i s r o t a t e d u n t i l i t h i t s D agai n , f i g u r e 11-19. T h i s i s the point at which HHISPEE's a n a l y s i s stopped. Seme of i t s f i r s t order approximations to s i m u l t a n e i t y and v e l o c i t y are simply no longer v i a b l e . The e s s e n t i a l elements of the a c t i o n i n v o l v e d i n the c o l l a p s e of the i n i t i a l s t r u c t u r e are portrayed by the four snapshots t h a t 1HISPEB produced. The i n i t i a l i n s t a b i l i t y of B i s shown to r e s u l t , as B h i t s D, i n the subseguent t o p p l i n g of D, and t h e i r e v e n t u a l tumble to the f a b l e . The a c t i o n c o u l d be s p e c i f i e d somewhat more p r e c i s e l y by i n c l u d i n g the two snapshots of f i g u r e 11-20 between the c u r r e n t second and t h i r d snapshots. These two e x t r a ones could be determined by r o t a t i n g D only p a r t way to the t e r m i n a t i o n point c f the r o t a t i o n and then s t a r t i n g the s t a b i l i t y t e s t i n g procedure over a g a i n . 1.0 1 0 1 . 0 1 . . 11.0 21.0 31.0 41.0 51.0 61.0 7 1 . 0 81.0 91.0 101.0 A 2 2 2 2 2 2 222B2222B222 2 22822 8 2228 2 B B22 222 822228/2 B2B2 BB B B B 8 8 B B B 3 B 8 8 B 22 2228 B E B B B B B B B BB 2 2222B E B B 3B B B B B B 8 B B B B B B B 8 B 2 22222B B B B B B B B B BBB B B B 322 1111111111111111228 3 3 B 8 FIGURE TI-IT; B B B 1A A A A A A A l 2222B B B B 8 8 B B SB BB 8B2 1A A A A A A A 1 222222 BB 8 B B 8 8 B 8 B 22 444 1A A A A A A A 1 22 B B B 62 4 4 1A A A A A A A 1 22 B 8 B BB B B B B2 4444 04 1A A A A A A A 1 22222 B B 8 B B 2 444 0 044 1A A A A A A A 1 22 8 B 2 4 . D 1A A A A A A A 1 22222B B 2 4440 D 0044 1A A A A A & A i 222222 44440 0 D DO 44 1A A A A A A A 1 4 0 0 1A A A A A A A 1 O D D 00 004 4 4444 1A A A A A 4 A 1 444 0 00 0 0 DO 0 4 44 44044444 1A A A A A A A 1 44 0 0 0 0 •044 4 0 44 1A A A A A A A 1 444 0 D D 0 0 D DO 0 ODD 4444 1A A A A A A A 1 444 0 0 D DO D D DO D ODD 0 4444 1A A A A A A A 1 4 0 DO D O D 4 1A A A A A A A 1 444400 0 0 DO D D DO D 0444 1A A A A A A A 1 44 D 0 D 0 00 0 ODD 0 DO 444 1A A A A A A A 1 44 0 0 DO 0 D 0 44 1A A A .A A A A 1 444 0 DO D 0 DO 0 DO D DD 443 1A A A A A A A 1 444 4444 4444 4 4444 000 0 444 333 1A A A A A A A 1 0 0 44 3 3 " 1A A A A A A A 1 440 0 44 3 C3 1A A A A A A A 1 44 0 4444 3C C33 1A A A A A A A 1 0 44 3C C 3 1A A A A A A A 4 4 4 4 4 4 4 33C C C3 1A 1A A A A A A A A A A A A A 1 1 SLIGHT GAP 4 4 V " 3 c c c ; J 3C C C C 3 1A A A A A A A 1 _ 44 3C C C C C3 1A A A A A A A 1 ^ ^ ^ » 33C C C C C33 1111111111111111 3333333333333 999999999999 999999999999999999999999999999999999999999999999999999999999999999999999999999999999 1 1 . 0 1 . . 1.0 11.0 21.0 31.0 4 1 . 0 »•!••• 51.0 61.0 71.0 81.0 91.0 1 0 1 . 0 6^ 1.0 11.0 21.0 101.01..........! |... 31.0 » • I • • • 41. 0 51.0 61.0 71.0 81.0 91.0 101.0 THIRD 5NAPSHOT. FIGURE JT-IS. 2 ^ 2 2 222822228222 2 2 2 2 2 22B22 B 2228 2 8 B22 222 B22228 2V'*B2B2 38 B B 8 B 8 8 8 8 B B;-:.B B 8 22 2228 B B B B 8 8 8 B B BB 2 2222B B B B BB B B BBB B B B B 3 B 3 B B B 2 222228 8 3 B 8 B B B 8 BB8 B B B B22 HHH1111111U122B 8 B B B B B B B 2 22228 B B B 3 B 8 8 BB B B B32 222222 B B B B B B B B B B 22 22 8 8 8 B2 83 B B B B2 3 B 8 B B 2 22 3 B 2 22222B B 2 222222 1A A A A A A A 1 1A A A A A A A 1 14 A A A A A A 1 1A A A A A A A 1 1A A A A A A A 1 1A A A 4 A A A 1 1A A A A A A A i 1A A A A A A A i 1A A A 4 A A A i 1A A A A A A A I 1A A A A A 4 A I 1A A A A A A A I 1A A A A A A A I 1A A A A A A A I 1A A A A A A A i 1A A A A A A A I 1A A A A A A A 1A A A A A A A i 1A A A A A A A i 1A A A A A A A I 14 A A A A A A l 1A A A A A A A l 1A A A A A A A i 1A A A A A A A I 1A A A A A A A l 1A A A A A A A l 1A A A A A A A l 1A A A A A A A l 1A A A A A A A i 22 B 3 22222 44 4444 44 4 444 0 4 44 0D . 44 4 0 4 444D DO 0D4 4440 DO D 44 4 0 D 04 . 444 D 0 D DO 044 44 DO DD CO 044 4440 4444 44 0 D D D 0 0 4 44 0 DOO 0 0 000 DO D 44 444 D 0 DD DO 0 0 0 444 4 D D D DD D D 4 4440 D ODD D O D O 0 44 44D0 D 0 DD 0 0 00 44 44 0 00 0 0 D 44 44 DD D 000 D OD 0 0 443 444 DD 0 D DD 0 0 D D.044 333 4 444 4D44444 4 444 4 4 ' 1111111111111111 D D D D D D 4 3 3 44 444 4 4444 00 0 444 3 C3 440 444 3C C33 4 44 3C C 3 40 044 33C C C3 4 4 4 4 4 4 4 3 C C C33 4 3C C C C 3 4444 3C C C C C3 4 33C C C C C33 4 3333333333333 99 9999999999 99999999999999999999999999999999999999999999999999 9999999999999999999999999999999999 11.0|.. 1.0 21.0 31.0 4 1 . 0 51. 0 61.0 71.0 81.0 91.0 ..I .101.0 i o , oT° z}'° 4r*° 51*° 61«° 71«° 8i«° 9i.o loi.o 101.01. . . . . . . . . ! . . . . . . . . . . . . . . . | I I I 1 1 I 91.0 81.0 71.0 61.0 51.0 41. 0 31.0 21.0 FINAL SNAPSHOT. 22 I2|Y2 FIGURE IE-19-23 22 28 822 22 B 23 33 22 28 8 322 2 1111111111111121 B B B 2B2 A 2 B B2 A2B BBB B 22 1A A A A A A 1A A A A A A 1A A A A A A 1A A A A A A 1A A A A A A 1A A A A A A 1A A A A A A 1A A A A A A 1A A A A A A 1A A A A A A 14 A A A A A 1A A A A A A 1A A A A A A 1A A A A A A 1A A A A A A 1A A A A A A 1A A A A A A 1A A A A A A 1A A A A A A 1A A A A A A 1A A A A A A 1A A A A A A 1A A A A A A 1A A A A A A 14 A A A A A 1A A A A A A 1 1A A A A A A 14 A A A A A 44 4444 A 2 2 B 8 B B 2 44 4 A 12 BBB B 82 4 4 4 D 4 A 12B B B3B 32 44 0 0 44 A 1 28 3 B 3 BB 22 4 D 4 A 1 2B 8 83 3 B B 82 4440 00 004 A 1 22 BB B B 2 /" 4440 0 D 0 '44 4 A l 22 8 B B B B S B 2 4 0 D 04 4 444 A l 29 B 8 B 8 B 8 8 8 22 2 444 0 0 0 DO 044 4044444 A 1 2 B B 3 8 3 8 8 2 44 D D DD DO 044 444D 4444 A 1 2 B B 88 2 44 0 0 0 0 0 D 4 A 1 2B3B 8 B 8 B 8 88 BS22 44 0 000 0 0 ODD DD 0 44 A l 28 8 B B 8 B B 3 B 3222 444 D 0 DD DD 0 D D 444 A l 2 B 3 3 2 2 2 4 O D D D D 0 0 4 4 1 22 8 8 B 83 8 B222 2 444D 0 000 0 0 0 0 0 44 A 1 2B 8 B B B 822 44DD 0 0 DD D 0 DO 44 A 1 2 B22 44 D DO D 0 0 44 A 1 222 B 8 2222 44 DD D 000 0 DO 0 0 443 A 1 2B 2 22 444 00 0 0 DO D D 0 D 044 333 A l 23 4 0 0 0 0 0 D 4 3 3 4 1 2 444 4 44 444 4 4444 DD 0 444 3 C3 A 1 4 44D 444 3C C33 A 'l 4 44 3C C 3 A 1 40 044 33C C C3 A 1 4444444 3 C C C33 1 4 : 3C C C C 3 A 1 4444 3C C C C C3 A 1 4 33C C C C C33 • 1111111111111111 4 3333333333333 9999999999999999999999999999999999999999999999999999999999999999999999 99999999999999999999999999 11.01 I I DO F I G U R E T T - a o ROTATE TO cftrtM OP 70 The c h a i n r e a c t i o n problem d i d not i n v o l v e any t r a n s l a t i o n a l l y u n s t a b l e o b j e c t s . The example of f i g u r e 11-21 w i l l be used t o i l l u s t r a t e how WHISPEB d e t e r m i n e s whether an o b j e c t w i l l s l i d e , and i f i t s l i d e s , how f a r i t w i l l t r a v e l . As d e s c r i b e d e a r l i e r ( s e c t i o n I I - 3 . 1 ) , the s t a b i l i t y o f a complete s t r u c t u r e i s t e s t e d by s u b d i v i d i n g i t i n t o c o nglomerate o b j e c t s whose s t a b i l i t y i s t e s t e d s e p a r a t e l y . The t r a n s l a t i o n a l s t a b i l i t y of these conglomerate o b j e c t s i s t e s t e d a t the same time as t h e i r r o t a t i o n a l s t a b i l i t y . WHISPEB d e c i d e s on t r a n s l a t i o n a l s t a b i l i t y of an o b j e c t by ex a m i n i n g i t s c o n t a c t s . There are t h r e e t y p e s of c o n t a c t t h a t a r e c o n s i d e r e d : s u r f a c e - t o - s u r f a c e , s u r f a c e - t o - p c i n t , and p o i n t - t o - s u r f a c e . The s t a b i l i t y c r i t e r i o n f o r a p a r t i c u l a r c o n t a c t i s whether or not t h e tan g e n t t o t h e s u r f a c e i n v o l v e d i n t h e c o n t a c t i s h o r i z o n t a l a t t h e p o i n t of c o n t a c t . (Tangent f i n d i n g i s another p e r c e p t u a l p r i m i t i v e . ) I f t h e t a n g e n t i s not h o r i z o n t a l , then t h e d i r e c t i o n of downward t i l t i s t a k e n as the r e s u l t a n t d i r e c t i o n of motion of t h e o b j e c t . I f a c o n f l i c t i n the d i r e c t i o n a r i s e s , one c o n t a c t i n d i c a t i n g l e f t w a r d motion and a n o t h e r i n d i c a t i n g r i g h t w a r d motion, then WHISPEB r e p o r t s i t s i n a b i l i t y t o d e c i d e on what t h e motion w i l l be. T h i s i l l u s t r a t e s t he need a r i s i n g i n some s i t u a t i o n s f c r a g u a n t i t a t i v e i n v e s t i g a t i o n i n o r d e r t o r e s o l v e the g u a l i t a t i v e a m b i g u i t y . ( E e s o l v i n g g u a l i t a t i v e a m b i g u i t i e s by g u a n t i t a t i v e 1.0 11.0 21.0 31.0 41.0 101.01 I I I I... 51.0 61.0 71.0 81.0 91.0 101.0 91.0 81.0 71.0 61.0 51.0 Y 41.0 31.0 21.0 1 1 1 1A 1A 1A 1A 11A 1 A 11 A 1A A 1A A A A A A A A A A A & A A A 1 A 111A A 111 A A A A A A A A A A A A 11 11A A1A11 1A1A A A A A1A11 A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A l H U l l l l H l Al 11 1 22 111111111A 111111111 2 2 2 2B 28 223 2 S 2 32 B B 8 2 B22 B B2 B B 2 A H A A l l H H U l l l l i i l A A A A A A A A 1111 A A A A A A A . A A A A A A A A A A ' ; A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A -A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A 11111A A 1 A1A1 A A A l l 11111111111 A l l A Al 11111111111 1 Al A l l A 1 FIGURE I L - 2 ± I Al Al 41 A l l 28 2B B B 3 3 8 8 B B B B B B 3 8 B B 322 B 32 B B 2 8 B B22 3 8 B 82 11111111-33333333333333333333334444444444444444444444444 2B B B 8 B B B 8 3 8 2 3 C c c c c c c c c C34 0 0 0 0 D 0 D D D 0 0 4 22 B B B B 8 8 B 8 8 8 B2 3 C c c c c c c c c C34 0 0 0 D 0 0 0 D 0 0 0 4 2 B 6 B 8 3 8 B B B B B 8 2 3 C c c c c c c c c C34 D D 0 D D 0 0 D D D 0 4 28 B 8 B 8 B 8 B B B B B 8 B2 3 c c c c c c c c c C34 0 0 0 0 0 D 0 0 D 0 0 4 2B B 8 B 3 B B B 8 B B 3 3 822 3 c c c c c c c c c C34 D D D 0 0 0 0 0 0 0 0 4 2B B 3 B B B 3 B B B B B B B 32 3 c c c c c c c c c C34 0 D D 0 0 D 0 0 0 0 0 4 23 8 B 3 B B 8 B B 8 B 8 B 8 B2 3 c c c c c c c c c C34 0 D 0 D D 0 D 0 0 0 0 4 2 B B B B 8 B B B 8 B B B B B2 3 c c c c c c c c c C34 0 D 0 0 D 0 0 D D D 04 2 B 3 B B B B B B B B B B B 2 3 c c c c c c c c c C34 0 D 0 D D 0 0 0 D 0 44 2 B B B' B 8 B B 8 B B 8 B B 2 3 c c c c c c c c c C34 D 0 0 0 D 0 D 0 0 0 4 22B 8 B 8 3 B 8 B B 8 B B 8 2 3 c c c c c c c c c C?4 D D D D D D 0 D 0 0 4 . 22 8 B B B 8 B B 8 B B B B2 3 c c c c c c c c c C34 0 0 D D D 0 D 0 0 04 2 8 B 3 8 B B B B B 3 B 82 3 c c c c c c c c c C34 0 D D 0 D 0 D 0 0 04 2B B B 8 3 B B B B 8 B 82 3 c c c r r c c c c C34 0 0 0 n 0 c 0 0 0 4 2 B B 8 B B 8 3 B B S 2 . 3 c c c c c c c c c C34 D D D 0 D D 0 D 044 22222222222222222 22222 33 3 33333332 33333333 33344444444444444 444444 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 11.01 I I ! I I, 72 reasoning i s d i s c u s s e d by D e K l e e r ) . There i s , of course, no c o n f l i c t between a h o r i z o n t a l c o n t a c t slope and a n o n - h o r i z o n t a l contact s l o p e , the former simply does not c o n t r i b u t e to the motion. In the example of f i g u r e 11-21 o b j e c t fl r o t a t e s u n t i l i t h i t s o b j e c t C, f i g u r e 11-22, j u s t as i n the p r e v i o u s example. at t h i s p o i n t the eye i s moved s e p a r a t e l y to each of the c o n t a c t s . The s u r f a c e - t o - p o i n t c o n t a c t between A and B i s noted as i s the r i g h t w a r d t i l t of the s u r f a c e of A at the c o n t a c t , and the p o i n t - t o - s u r f a c e c o n t a c t between A and C with the h o r i z o n t a l s l o p e of C at the c o n t a c t . The A-to-B contact i s c l a s s i f i e d as s u r f a c e - t o - p o i n t , with the rightward t i l t of the s u r f a c e of A at the c o n t a c t noted as c o n t r i b u t i n g to a rightward motion f o r A. S i m i l a r l y , the A-to-C c o n t a c t i s c l a s s i f i e d as p o i n t - t c - s u r f a c e with no c o n t r i b u t i o n to the motion of A because of the h o r i z o n t a l nature of the s l o p e of C at the c o n t a c t p o i n t . Thus WHISPEB concludes that A w i l l s l i d e to the r i g h t along the s u r f a c e of B. 1.0 . 11.0 21.0 31.0 41.0 51.0 61.0 71.0 31.0 91.0 101.0 101.01 ! I I I I ,.| | | | | 91.0 81.0 71.0-61.0 51.0 Y 41.0 31.0 21.0-i A i m 11A1A A A A l l 11A A A 11 111 A A A A A A AAA A l l l 111A A A A A A A A A A A A A l l l l • 1A A A ^ A A A A A 111111 HA A A A Xs AA A A A A A A A A A A A A l l l l l „ n I D C T T _ £ > 9 1 A A A A A A A A A A A A A A A A A A A A-A 11 r l b U K t i L ctoC. 1 A A A A A A A A A A . A A 11 1A A A A A A A A A A A A A A A A A A A A A A A 1 1 . 1A A A 1 A 1A A A . 1A A A 1A A 11A A • Ali 111111A 1 111 i A A A A A A A A A A AA A A A A A A A A A A Al A A A A A A A A A A A A 11 A A A A A A A A A A A A A A A A A A A A A A A A 1 A1111111A A A A A A A A A A A A A A A A A A A A A1A1 r , 11111 A A A A A AA A A A A 1 Al 1 i 22 1111 e. A A A A A A A A A A A A A A A A l l / i S 2B2 11111 A A AA A A A A A A A A A A A Al / / 2 3 2 11 A A A A A A A 1 / j / 2 a B 22 11111 A A A A A A A A A AA A 11 / 2 B 3 B2 111111 A A A A A A A A A Al Cl 2 B B 3 2 111A A A A A A A A Al ca 2B R B B B22 H i l l A A A AA A 11 J r 22B 3 B B B B2 111111 A A Al / 2 B B 8 B B 3 2 11 A A 23 3-3 B B B S 822 1111 1 > r 28 3 B B 8 8 B 8 B B2 33? 323333333333332 33334444444444444444444444444 2B 3 B B 8 B B 3 B B 2 3 C C r u C C C C C C C34 D D 0 D 0 0 D 0 0 D D 4 22 8 B B B B R 3 B B B 82 3 C C c C C C c C C C34 D 0 0 0 0 D 0 0 0 0 0 4 2 8 8 B 8 B B B B B B B 3 2 3 C C c C C C c C C C34 0 D 0 0 D 0 D 0 0 0 0 4 28 3 8 B 3 B B B 8 B B 8 B 82 3 C C c C c C c c C C34 0 D D 0 0 0 0 0 D 0 4 2B B 8 B B B B B B 8 8 B 8 B22 3 c c C c C c c C C34 0 • 0 0 0 0 D 0 0 0 0 4 28 B 8 B 8 B 8 B B B 3 B B B 82 3 c c c C c C c c c C34 D D 0 D 0 0 D 0 D 0 0 4 23 B B B B 8 B B 8 B B 8 B B 82 3 c c c C c C c c c C34 0 0 0 D 0 0 D 0 0 D 0 4 2 8 8 B B B B B 8 8 B B B 8 B2 3 c c c c c c c c c C34 0 D 0 0 0 D 0 0 D 0 04 2 8 B 3 3 3 B B 8 8 B 8 B B 2 3 c c c c c c c c C34 D D a 0 0 0 D D 0 D 44 2 3 8 8 •8 B 3 B B B 3 B B B 2 3 c c c c c c c c c C34 D 0 D 0 0 D D 0 D 0 4 223 8 B 8 3 B B 8 B B B B B . 2 3 c c c c c c c c c C34 D 0 0 D D D D 0 o 0 4 22 B B B B B B B 8 B B 8 B2 3 c c C c c c c c c C34 D 0 D 0 D D D 0 0 04 2 B B B B B B 8 B 8 8 B B2 3 c c C c c c c c c C34 D D D 0 0 D D 0 n D4 2B B B B B B B B B B 8 82 3 c c C c c c c c c C34 0 D 0 0 0 0 D D 0 4 2 8 B 8 B 8 B 8 B B B 2 3 c c C c c c c c c C34 0 D D 0 0 D D D D44 2222222222222222222222 333333333333333333333344444444444444444444 9999999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999 74 An o b j e c t ' s s l i d i n g motion, u n l i k e a r o t a t i o n a l mcticn, cannot be v i s u a l i z e d on the r e t i n a , because the o b j e c t ' s path i s not e a s i l y found, WHISPER's method of performing s l i d e s i s o u t l i n e d i n f i g u r e 11-23 . Instead of v i s u a l i z i n g s l i d i n g motions, WHISPER examines the c o n t a c t i n g s u r f a c e s of the o b j e c t and i t s suppo r t e r s f o r a circumstance causing the o b j e c t to st o p . The st o p p i n g p o i n t i s c a l l e d an i n t e r r u p t i o n point,. To update the diagram the o b j e c t i s t r a n s l a t e d to the nearest i n t e r r u p t i o n p o i n t . A f t e r the t r a n s l a t i o n , a r o t a t i o n g e n e r a l l y i s r e g u i r e d to make the s u r f a c e s touch a t a l l t h e i r proper l o c a t i o n s . To f i n d the c o r r e c t o r i e n t a t i o n of the o b j e c t , i t s r o t a t i o n i s v i s u a l i z e d to see the angle at which the r i g h t support r e l a t i o n s h i p s between the s u r f a c e s occur. £XZ2A1_ Surface_Examination There are two elements to the examination of the s l i d i n g s u r f a c e s f o r t e r m i n a t i o n p o i n t s . E x a c t l y what p o r t i o n s of which s u r f a c e s are to be examined, and what f e a t u r e s of the s u r f a c e s are important? The b a s i c o b j e c t i v e i s both to examine those s u r f a c e s on the moving o b j e c t which w i l l s l i d e past a p o i n t on a s t a t i o n a r y o b j e c t , and those on a s t a t i o n a r y o b j e c t which w i l l have a point of the moving o b j e c t r i d e over them. Thus i n the c u r r e n t example ( f i g u r e 11-22) the s u r f a c e of A w i l l be examined from C1 to the l e f t , and the s u r f a c e of C and Examine Surfaces for Interruption Point 7 Redraw Object Translated to Interruption Point I Do a l l O r i g i n a l Support Conditions Hold? Yes EB»'" Finished No V i s u a l i z e Rotation About Interruption Point. Watch for Support Condition to be re-Established. C a l l Redrawing Transformations to Perform Rotation • Center Eye on Expected Support Point Finished Estimate Gap Closing Rotation F & G - U R E m-sa 76 p o s s i b l y D w i l l be examined from C2 to t h e r i g h t . S u r f a c e - t o - s u r f a c e c o n t a c t s i n v o l v e t h e e x a m i n a t i o n of both the c o n t a c t i n g s u r f a c e s i n t h i s manner. I t i s o n l y t h e f i r s t o c c u r r e n c e o f a t e r m i n a t i o n c o n d i t i o n t h a t i s of i n t e r e s t , s i n c e i t i s the one which w i l l s t o p the o b j e c t ' s s l i d i n g m otion. Thus WHISPER can c o n s t r a i n i t s e x a m i n a t i o n o f s u r f a c e s subseguent t o the d i s c o v e r y of cne t e r m i n a t i o n c o n d i t i o n t o o n l y t h a t p o r t i o n of them which would cause a p r i o r t e r m i n a t i o n c o n d i t i o n t o a r i s e . The second element - what i s t o be l o o k e d f o r w h i l e e x a m i n i n g a s u r f a c e - i s dependent upon whether t h e s u r f a c e under c o n s i d e r a t i o n i s an upper or a lo w e r s u r f a c e . For example, i t i s n e c e s s a r y t o l o o k f o r o b j e c t s s i t t i n g on a lo w e r s u r f a c e w i t h which the s l i d i n g o b j e c t might c o l l i d e , whereas t h i s i s not n e c e s s a r y f o r an upper s u r f a c e . The o t h e r c o n d i t i o n s which c o u l d be r e l e v a n t t c t h e o b j e c t ' s motion a r e : a s h a r p bend i n a s u r f a c e ; a h i l l which i s h i g h e r than the o b j e c t ' s i n t i t i a l p o s i t i o n ; r e a c h i n g the end of a s u r f a c e i n the d i r e c t i o n of motion; and as mentioned, an o b j e c t on t h e s u r f a c e c r c l o s e enough t o the s u r f a c e t h a t a c o l l i s i o n between i t and t h e moving o b j e c t would o c c u r . These c o n d i t i o n s a re i l l u s t r a t e d i n f i g u r e 11-24. C u r r e n t l y , WHISPER examines s u r f a c e s f o r any of thes e c o n d i t i o n s i n one f i x a t i o n by c e n t e r i n g t h e eye on t h e r e l e v a n t s t a r t i n g c o n t a c t p o i n t . The d e t e c t o r s f o r t h e s e c o n d i t i o n s are b u i l t i n at the l e v e l of p e r c e p t u a l p r i m i t i v e s ( s e c t i o n I I I - 3 ) . However, because o f SHARP BEND A HILL END OF SURFACE (e) COLLISION ON SURFACE SURPRISE COLLISION 78 t h e i r s p e c i a l i z e d nature f o r t h i s problem domain, I would h e s i t a t e to c a l l any but the sharp bend and c o l l i s i o n d e t e c t o r s t r u l y p r i m i t i v e . I t would be p o s s i b l e and d e s i r a b l e i n terms of accuracy to use the c u r r e n t d e f e c t o r s to propose f u r t h e r f i x a t i o n l o c a t i o n s to which the eye could be moved to t e s t more p r e c i s e l y f o r the f u l f i l l m e n t of a p a r t i c u l a r c o n d i t i o n . HHISPEB must make m u l t i p l e f i x a t i o n s along the s u r f a c e i f i t i s to d e t e c t the ' s u r p r i s e 1 c o l l i s i o n of f i g u r e .11-24 (e) . Although i t does not c u r r e n t l y handle t h i s case, i t i s c l e a r how i t e a s i l y could by f i x a t i n g the r e t i n a a t r e g u l a r i n t e r v a l s a long the s u p p o r t i n g s u r f a c e . T h i s i s i l l u s t r a t e d by f i g u r e 11-25 i n which v an x i n d i c a t e s a f i x a t i o n p o i n t , a s e m i - c i r c l e i n d i c a t e s the area of the diagram to be checked by the r e t i n a at each f i x a t i o n (checking a c i r c u l a r r e g i o n i s easy because of the r e t i n a ' s r i n g s t r u c t u r e ) , and the space between dashed l i n e and the s u r f a c e i n d i c a t e s a c l e a r ' c o r r i d o r * f o r o b j e c t . The r a d i u s of the s e m i - c i r c l e i s a f u n c t i o n of the o b j e c t ' s s i z e and the f i x a t i o n i n t e r v a l . The same s i z e d c o r r i d o r can be examined with fewer f i x a t i o n s by using a l a r g e r r a d i u s . The only disadvantage i s t h a t the p r o b a b i l i t y of f a l s e alarms i n c r e a s e s , because the d i s t a n c e between the dashed l i n e and the c i r c u m f e r e n c e of the s e m i - c i r c l e s i s g r e a t e r . F a l s e alarms can be handled by making more f i x a t i o n s i n the r e g i o n where they occur. This method of d e t e c t i n g c o l l i s i o n s i s very good f o r two reasons: (i) because the r e t i n a can check l a r g e segments of space i n a s i n g l e g l a n c e , the number of f i x a t i o n s 7^ 80 r e g u i r e d t o examine the space near the s u r f a c e i s r e l a t i v e l y s m a l l ; ( l i ) a c o l l i s i o n w i l l never be m issed, I I - 9 i 2 _ A d y a n t a 3 e s _ O f _ T h There are s e v e r a l r e s p e c t s i n which WHISPER*s a n a l y s i s of the t e r m i n a t i o n c o n d i t i o n s f o r s l i d i n g motions i s s i m p l i f i e d by the analogue. One i s t h a t t h e r e i s no need f o r the a p p l i c a t i o n o f n u m e r i c a l methods i n f i n d i n g the c u r v e f e a t u r e s . The f e a t u r e s are found by i n s p e c t i o n o f t h e diagram. Of c o u r s e , t h e r e i s c o m p u t a t i o n i n v o l v e d i n t h i s p r o c e s s , but i t i s a c o m p a r a t i v e l y s m a l l amount because WHISPER i s working w i t h t h e c u r v e i t s e l f r a t h e r than an e g u a t i o n a l d e s c r i p t i o n c f the c u r v e . A d d i t i o n a l l y , such a d e s c r i p t i v e e q u a t i o n o f t e n i s not a v a i l a b l e , and may i t s e l f have t o be computed through a c u r v e - f i t t i n g p r o c e s s . Another i m p o r t a n t r e s p e c t i n which WHISPER 'S s l i d e a n a l y s i s i s s i m p l i f i e d i s i n d e t e c t i n g c o i n c i d e n t a l a l i g n m e n t s of two or more o b j e c t s whose s u r f a c e s form one c o n t i n u o u s c u r v e over which an o b j e c t c o u l d s l i d e ; s u ch c o i n c i d e n c e s a l s o r e s u l t i n smooth c u r v e s i n the diagram. N o t i c e t h a t i n f i g u r e 11-22 o b j e c t A w i l l s l i d e a l o n g t h e s u r f a c e of both C and D. The s u r f a c e e x a m i n a t i o n t e s t i n g s h o u l d t h u s be c a r r i e d out a l o n g o n l y the upper edges of C and D. The f a c t t h a t C and D t o g e t h e r form a smooth s u r f a c e i s a p r o p e r t y which emerges from t h e c o i n c i d e n c e t h a t they have the same h e i g h t and t h a t t h e y 81 a r e t o u c h i n g . I t w o u l d be v e r y d i f f i c u l t f o r a s y s t e m r e l y i n g o n s e p a r a t e e n c o d i n g s o f t h e s h a p e s o f o b j e c t s t o d i s c o v e r t h i s effi§£2®Bi_£E2JBS£Sljt 1 ° f i n d i f w o u l d f i r s t o f a l l r e q u i r e t h e b u i l t i n e x p e c t a t i o n t h a t i t m i g h t h a p p e n . T h e n i t s e x i s t e n c e w o u l d h a v e t o b e c o n t i n u a l l y c h e c k e d . T h i s c h e c k w o u l d i n v o l v e e s t a b l i s h i n g a l l t h e c o n t a c t r e l a t i o n s h i p s o f t h e o b j e c t o n w h i c h t h e s l i d i n g o b j e c t i s i n i t i a l l y r e s t i n g w i t h a l l t h e o t h e r o b j e c t s i n t h e u n i v e r s e , a l r e a d y a d i f f i c u l t p r o b l e m , f o l l o w e d b y t h e a m a l g a m a t i o n o f t h e d e s c r i p t i o n s o f t h e t w o s e p a r a t e c u r v e d e s c r i p t i o n s i n t o a new c u r v e d e s c r i p t i o n . E s t a b l i s h i n g t h e c o n t a c t r e l a t i o n s o f t h e s u p p o r t i n g o b j e c t c a n n o t b e s i m p l i f i e d b y a s s e r t i n g t h e m a s p a r t o f t h e i n i t i a l p r o b l e m d e s c r i p t i o n , b e c a u s e i t m i g h t h a v e r o l l e d o r s l i d i n t o i t s c u r r e n t l o c a t i o n . I n a d d i t i o n , n o t o n l y m u s t t o u c h i n g o b j e c t s be c o n s i d e r e d , b u t a l s o o b j e c t s w h i c h a r e a l m o s t t o u c h i n g , s i n c e a s m a l l g a p may n o t i n h i b i t t h e s l i d i n g m o t i o n o f a n o b j e c t . I t i s u n n e c e s s a r y f o r H H I S P E R t c c o n c e r n i t s e l f w i t h q u e s t i o n s o f how c o n t o u r s a n d e t h e r p r o p e r t i e s m i g h t h a v e c o m b i n e d t o p r o d u c e a s m o o t h c u r v e . T h i s i s a n o t h e r i n s t a n c e o f t h e a m a l g a m a t i o n p r o b l e m d i s c u s s e d i n s e c t i o n I V - 4 . 1 . 3 . S i n c e a s m o o t h c u r v e i n t h e r e a l w o r l d i s m o d e l e d b y a s m o o t h c u r v e i n t h e a n a l o g u e , W H I S P E R r e g u i r e s o n l y a r e c o g n i z e r o f s m o o t h c u r v e s . T h e a m a l g a m a t i o n o f c o n t o u r d e s c r i p t i o n s i s s o l v e d b y s i m p l y i g n o r i n g t h e d i s t i n g u i s h i n g c o l o u r i n g o f a l l o b j e c t s e x c e p t t h e s l i d i n g o n e . T h e t o u c h i n g f a c e s o f C a n d D 82 thus become i n s i d e p o i n t s o f the combined CD, and hence are not seen as par t o f the c o n t o u r . The r e s u l t i n g c o n t o u r and i t s shape a r i s e d i r e c t l y i n the d i a g r a m , not as the net product of a complex c h a i n of d e d u c t i v e c r c o m p u t a t i o n a l i n f e r e n c e s about the p r o p e r t i e s of the independent o b j e c t s . 83 II-lP_U£datin3_The_piag Using feedback from the diagram, WHISPER can avoid having to e s t a b l i s h the exact l o c u s of motion of a s l i d i n g o b j e c t . The l o c u s f o l l o w e d by each contact i s known to be the same as the s u r f a c e s over which i t s l i d e s which i s why those s u r f a c e s were examined; nonetheless, the motion of the o b j e c t i t s e l f i s a composite of the l o c i of the s u r f a c e s i n v o l v e d . I t i s of s u b s t a n t i a l b e n e f i t to WHISPER t h a t i t can avoid the c a l c u l a t i o n of t h i s composite. The t e r m i n a t i o n point of the s l i d e has already been found; what remains i s t o move the o b j e c t to that p o i n t . The f i r s t stage i s simply to t r a n s l a t e the o b j e c t so t h a t the s p e c i f i e d point on i t i s a l i g n e d with the s p e c i f i e d p o i n t on the c o n t a c t s u r f a c e . T h i s i s shown i n the change from f i g u r e 11-22 to f i g u r e 11-26 i n which p o i n t X i s a l i g n e d with C1. This t r a n s l a t i o n i s accomplished by simple matrix m u l t i p l i c a t i o n much the same as f o r r o t a t i o n s . A f t e r t h i s t r a n s l a t i o n , WHISPER checks t h a t the con t a c t r e l a t i o n s h i p s which e x i s t e d b e f o r e the t r a n s l a t i o n s t i l l e x i s t . T h i s examination i n the example of f i g u r e 11-26 r e v e a l s t h a t the c o n t a c t , C2, e x i s t i n g i n f i g u r e 11-22 has changed. A r o t a t i o n about the t e r m i n a t i o n p o i n t w i l l c o r r e c t the problem. With the eye centered on t h i s p i v o t p o i n t a r o t a t i o n i s v i s u a l i z e d u n t i l the contact i s r e - e s t a b l i s h e d . The amount of t h i s r o t a t i o n i s used to perform a r o t a t i o n i n the diagram ( f i g u r e 11-27). As with the purely r o t a t i o n a l examples, another gap c l o s i n g 1.0 101.01.. 1 1 . 0 21 .0 3 1 . 0 t • I • • • 4 1 . 0 • • 1 • • * 5 1 . 0 6 1 . 0 7 1 . 0 8 1 . 0 9 1 . 0 • • ! • • • 1 0 1 . 0 1111 1 A 11 11 A l A A A A H 11 111A A A A A A A1A11 1 A A A Aa 1 111A A A A A A A A A A A A A 1 H 1 11A A A A A A A A A A A ' A A A A A l l l l l l l 1 A A A A A A A A A A 1111 1 A A A A A A A A A A A . A A A A A A A A A A 1 1 FIGURE J£-£.6> H A A A A A A A A A A A A A A A A A A A A A A A l l 1 A A A A A A A A A A A 1 1A A A A A A A A A A A A A AA A A A A A A A A A A A l 1A A A 4 A 4 A A A A A A 4 A A A A A A A A A 4 A A A A l l 1 A A A A A A A A A A A A A 1A A A A1211111A A A A A A A A A A A A A A A A A A A A A l A l H A A A A1B2 11111 A A A A A A A A A A AA A A A A A A A l l 1 A A 12 B 2 1111 A A A A A 4 A A A A 1 111111A 12 8 322 11111 A A AA A A A A A A A A A A A 41 1112 B 3 32 H i l l A A A A / i A A A A A A A A 1 23 B 3 B 2 11 4 A 4 A 4 \ A 4 1 2S 8 3 3 822 11111 1 I I A A A A A A A A 41 223 3 3 8 B 32 m i AA A A A - A A A l OYgRl/tPPIHG 2 3 B 3 ES 8 B 2 111 A A A 1 X 23 B 8 3 B 8 3 B22 111111 A A A l 28 3 B 3 3 B 8 B 8 B2 3333333333333333333 3311 AAAl44444444444444444444 23 8 B 8 8 B B 3 B 8 2 3 C C c C C C C C C C34 1 1 D D D D D D D 0 D 4 22 3 B B B 3 3 B 8 8 B B2 3 C c c C C C C c C C34 • ID D D D D D D 0 0 0 4 2 B B 8 8 3 B 3 3 B B B B 2 3 c c c c C C C c C C34 D D 0 D D D D D D D D 4 2 B 8 B B 8 8 B 8 3 B B B 8 B2 3 c c c c c C C c C C34 D D D b D D D D D Q 0 4 2B B B 8 B B B 8 B 3 B B B 822 3 c c c c c C c c C C34 D D D 0 0 D D D D D D 4 2 B B B B B S 3 8 B 8 B 3 B 8 B2 3 c c c c c C c c c C34 D 0 D 0 D 0 D D D D 0 4 28 B 8 B B 3 3 S 6 B B 8 B 8 32 3 c c c c c C c c c C34 D D D 0 D D D 0 D D 0 4 2 B B 3 8 B B B 3 S 3 8 8 B 82 c c c c c C c c c C34 0 D D D D D D D D D 04 2 8 B 3 B 8 3 8 B B 8 8 3 8 2 3 c c c c c c c r c C34 D D D D D D D D D 0 44 2 8 8 8 B B 3 B 8 B B B B B 2 3 c c c c c c c c c C34 D D D D D D D D D 0 4 22B 8 8 3 B 8 B B B B B 8 8 2 3 c c c r c c c c c C34 0 0 D D D D D D 0 D 4 22 8 B B 8 B 3 8 5 B B 8 82 3 c c c C c c c c c C 3 4 D D D D 0 D D D D 04 2 3 3 B B 8 B 3 B B 3 8 82 3 c c c C c c c c c C34 D 0 D D 0 D 0 D D 04 23 B B B 8 3 8 8 B . B B B2 3 c c c C c c c c c C34 D D 0 D D D 0 D 0 4 2 B B B 3 8 8 8 B B 8 2 3 c c c c c c r c c C34 C D D 0 D D D D D44 2 222222 222222 2222 22222 33333 3 333333 333333333344444444444444444444 99999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999 11.01.. 1.0 1 1 . 0 2 1 . 0 3 1 . 0 4 1 . 0 5 1 . 0 • • 1 • • • 61.0 • • I • • * 7 1 . 0 8 1 . 0 9 1 . 0 1 0 1 . 0 OO 11 $k 1 A A A A . 111A A A A A A A 1A A A A A AA A 1A A A A A 1 A A A A A A A A 1 A A A A A A A 1 A A A A 11A A A A A A A A 1 A A A A A A A A A 1A A A A A 1A A A A121111111H1 1A A A A12 1 1 B 2 1 A A A 1 3 B22 11111112 B 8 32 1111 1 A A1A1 111 A 1 1 UA A A A A A A1A1U 1 A A A A AA A A A l l l l U U U A A A A A A A A A A H i l l AA A A A A 11 AA AA A A A A AA A A A A A A A A A A A A A A A A A A A A A A A AA A A AAA A A A A A A A A A A A A A A A A A A A A A A AA A A A A A A A A A A A A A A A A AAA A A A A l l l A A 1 A A A A A A l l l A A A A A l A A A A A A l l l A A A A A A A A A l l AA A A A A A A Al A A A A 1 A AA A A A A A A FlGUREir:-a7 23 8 3 B 2 23 B 3 B 822 223 3 8 3 3 32 2 3 8 3 8 8 3 2 23 3 g 3 B 8 B 822 28 B B B 3 8 8 8 3 82 23 B B B B 8 3 3 B B 2 22 B B 3 B 8 B B B B 8 82 2 3 B 3 3 3 3 8 3 B 8 3 3 2 23 8 B B B B B B 3 B 3 B B 82 2B B B 8 B 8 3 B B 3 B B 3 B22 23 3 B B B 8 B B 8 3 8 3 B B 32 28 B 3 B B 3 B 8 B 8 3 B 3 8 82 2 3 8 3 B B 8 8 B 8 8 B B 8 B2 ?. 8 B 8 3 B 8 B B 8 8 B 8 8 2 2 B 8 B B 3 8 B 3 B B 8 B 3 2 22B B 3 B B B 8 B B 8 B B B 2 22 3 B 3 8 3 3 8 B 8 8 8 82 2 3 3 B 3 3 3 B 3 8 B 8 82 2B B 8 B 8 B 3 8 8 8 8 B2 2 8 B B B B B 3 3 8 B 2 11111A 1 A A AA A A A A A AA A AA A 1 U U A A A A A A A Al l U l l i l l l A A A A A A A A A A A 1 11111UAA A, A A A Al U l 1 A 1 11 11111 UA 1 1 U l 333333 333333333333333 „„„„ 2222222222222222222222 33333333333333333333334444444444^444444444 99999999999999999999999999999999999999999999999999999999999999g9999999999999999999999g999g9999gg 3 C c c c c c c c c C34 0 D 0 D 0 D D D D 0 D 4 3 C c c c c c r c c C34 D 0 0 0 0 D D 0 D 0 0 4 3 c c c c c c c c c C34 D D D D D 0 0 D D 0 0 4 3 c c c c c c c c c C34 D D 0 0 0 0 0 0 D 0 0 4 3 c c c c c c c c c C34 D 0 D D D 0 D D D 0 D 4 3 c c c c c c c c c C34 0 D D 0 C D 0 D D D 0 4 3 c c c c c r c c c C34 D 0 D D 0 D 0 D 0 0 4 3 c c c c c c c c c C34 D D 0 D 0 0 n 0 0 0 04 3 c c c r c c c c c C34 D D D 0 D 0 0 D D 0 -44 3 c c c c c c c c c C34 0 0 0 D D 0 D 0 D 0 4 3 c c c c c c c c c C34 D • D D 0 D D 0 0 D 4 3 c c c c c c c c c C34 D 0 D D D D D D D 04 3 c c c c c c c c c C34 0 0 D 0 D 0 D 0 D 04 3 c c c c c c c c c C34 0 0 0 0 0 0 D 0 0 4 3 c c c c c c c c c C34 D D 0 0 D 0 D D 044 3  486 r o t a t i o n may be r e g u i r e d ( f i g u r e 11-28} because of the approximate nature of v i s u a l i z a t i o n . I t should be noted t h a t the above two-step method -t r a n s l a t i o n t o a l i g n the o b j e c t with i t s i n t e r r u p t i o n p o i n t f o l l o w e d by a c o r r e c t i n g r o t a t i o n - works f o r curved as well as s t r a i g h t s u r f a c e s ( f i g u r e 11-29). T h i s c o n c e p t u a l l y simple approach, i n c o r p o r a t i n g experimental feedback from the analogue, i s a very n a t u r a l form of g u a l i t a t i v e reasoning embodying a f i r s t order theory of the motion of s l i d i n g o b j e c t s . 1.0 . 11.0 21.0 31.0 41.0 51.0 61.0 71.0 81.0 91.0 101.0 101.01 I | | | | | | , . | | | A l l l l 1111 A A l H A A A A A A H A H • 11 1 A A A A A AA4 A 11 .^ 1 A A A A l l 1 x X 111A A A A A A A A A A A A A-A1411111111111 0 0 1 A A A A A A A A A A A A A A A A A A A A 1 1 H b U K f c lX~cL<J. 1 A A A A A A A A A A A A A A A 11 H A A A A A A A A A A A A A A A A A A A A A A A 1 1 1 A A A A A A A A A A A A A A A A A A A A A A AA1 1 A A A A A A A 1 1 H A A A A A A AA A A A A A A AA A A A A A A A A A 1 1 A A A A A A A A A A A A A A A A A A A A A A A A A A A A1A1 1 A A A A A A A A A A A A A A A A A A A 1 1A A A A121111111A A A A A A A A A A A A •AA A A -A A A A A l 1A A A A12 111 11HAAAA AA A A A AA A AA A A A AA A 1 11 1 3 2 11 1 A A A A A 1 1 A A A 1 3 822 11 H l l l A A A A A A A A AAA A AA A 1 11111112 B B 8 2 111111 A A A A A A A A A A A l 2 8 8 8 2 11 11A A A A A l 2B B 8 B B22 1 11111A A A A A l 22B 8 3 8 B B2 111111 A A A l i 2 B B 3 B B B 2 11 11 1 28 a B 3 B 5 B B22 1 111 28 8 8 5 8 B 3 B B B2 333333333333333333333 44 44444444444444444444 2B B 3 3 3 B B 3 B B 2 3 C c c r c C c C C C34 0 D 0 0 0 0 0 0 0 0 0 4 22 B 8 S 8 B B B 3 B B 82 3 C c c C c C c r c C34 0 0 0 D 0 D 0 0 D 0 0 4 . 2 8 3 3 8 8 B B B 8 B 8 8 2 3 c c c c c C c c c C34 0 D 0 D D D D 0 D D D 4 23 B 8 B B 8 B 8 B 8 B 3 B 82 3 c c c c c c c c «*> C34 0 D D D D 0 0 0 D 0 0 4 2B B B B B B 3 PI B 3 B 8 B B22 3 c c c c c c c c c C34 0 D D D D 0 D D 0 0 0 4 28 8 B B 8 8 8 8 B B B 8 3 8 B2 3 c c c c c c c c c C34 0 0 0 0 D 0 0 D 0 0 0 4 28 B 8 B B B B 8 8 3 B 8 8 B 82 3 c c c c c c c c c C34 0 o D 0 0 0 D D 0 0 0 4 2 B B 8 8 8 8 B 8 3 8 8 8 B B2 3 c c c c c c c c c C34 0 0 D D 0 0 0 0 D 0 04 2 3 3 B B B B B 8 B B 8 B 8 2 3 c c c c c c c c c C34 0 0 0 0 0 D 0 0 D 0 44 2 6 8 8 B B 3 B B B 8 B B B 2 ? c c c c c c c c c C34 0 D D D 0 0 0 0 D 0 4 22B B 3 8 3 3 8 8 B B B 8 B 2 3 c c c c r c c c c C34 0 0 D D 0 0 0 0 D 0 4 22 B 8 B 8 B B B 8 B B B 82 3 c c c c c c c c c C34 0 0 0 0 D D D 0 D 04 2 3 B B 3 B B B B B B 8 B2 3 c c c c c c c c c C34 0 D 0 D 0 0 D 0 0 04 28 B B B B B 3 B B B 8 82 3 c c c c c c c c c C34 0 0 D 0 D D D D 0 4 2 8 8 B B B 8 B 8 B B 2 3 c c c c c c c c c C34 0 0 0 D D 0 0 0 04 4 22222 22222222 2222 22 22 2 333333 3333333333333 33344444444444444444444 999999999999999 999999999999999999999 9999999999999999 9999999999999999 9999999999 999999999999999999 11.0! I I I I I I .1 I I j 1-0 H.O 21.0 31.0 41.0 51.0 61.0 71.0 81.0 91;0 101.0 °0 F I G U R E JT-Q3 89 I n c o n c l u d i n g t h i s s e c t i o n on g u a l i t a t i v e r e a s o n i n g I w o u l d l i k e t c s u m m a r i z e a few p o i n t s . T a k e n t o g e t h e r , t h e d i a g r a m , and t h e s e t o f t r a n s f o r m a t i o n s t h a t a r e a p p l i e d t o i t , i s an a n a l o g u e o f t h e r e a l w o r l d o b j e c t s . F u t u r e m o t i o n s o f t h e s e o b j e c t s u n d e r t h e f o r c e o f g r a v i t y a r e p r e d i c t e d by WHISPEB. C o n n e c t i o n w i t h t h e a n a l o g u e i s m a i n t a i n e d v i a c o n t i n u e d i n t e r a c t i o n u s i n g t h e e y e a n d i t s p e r c e p t u a l p r i m i t i v e s , a n d ' v i a t h e t r a n s f o r m a t i o n p r o c e d u r e s . P r o b l e m s a r e s o l v e d by i n t e r a c t i o n c f t h e p r o c e d u r a l l y e n c o d e d g u a l i t a t i v e k n o w l e d g e o f b l o c k s w o r l d p h y s i c s w i t h t h e d i a g r a m m a t i c a n a l o g u e . T h i s i n t e r a c t i o n i s t h r o u g h e x p e r i m e n t s d i r e c t e d by t h e g u a l i t a t i v e k n o w l e d g e , p e r f o r m e d i n t h e a n a l o g u e , a nd a c c e s s e d by t h e s i m u l a t e d r e t i n a . When an e x p e r i m e n t , s u c h a s t h e r o t a t i o n o f an o b j e c t , i s c o m p l e t e , WHISPEB o n l y n e e d s t o * l o o k ' a t t h e r e s u l t i n g d i a g r a m t o d e t e r m i n e t h e new s t a t e o f t h e w o r l d . I f ,_is_fa^g^5^§§_W^ISP^B n e e d _ o n ^ y _ b e _ a d e p t _ a t _ d i r ^ i n s t e a d o f ^ b e c o m i n g _ b o g g e y e x p l o d i n g compjjt a t i o n s , _ i t _ i s _ a b l e _ t o S 2 i S t i o n s _ t o _ s i m p , l e t h o u g h n o n - t r i v i a l , ^ p r o b l e m s . 90 Cha£ter_.IIIi_The 111 -J_In troduction The eye i s the primary connection between WHISPER and i t s diagrammatic analogues. The perceptual primitives provide answers to the basic questions that WHISPER can ask of the eye. These guestions concern topological features of configurations i n 2-space, and are independent of any interpretation that the diagram might have as an analogue. Interpretations are assigned to the topological features perceived by WHISPER in accordance with the analogy that exists between the diagram and the p a r t i c u l a r domain of in t e r e s t . T h f _ p e r c e p t u a l ^ r i m i t i y e s ^Cf .tfeu5-§-li£f .,of ..gBiEations, ..applicable _ tg_ a_variety of dif f e r e n t domains. The s i g n i f i c a n c e of the eye and i t s perceptual primitives for the u t i l i t y of analogues i s that they provide a new set of £2££§£iM2 primitives. The world i s d i v i s i b l e , rather a r b i t r a r i l y , into many di f f e r e n t conceptual categories; the choice of a conceptual segmentation i s primarily a function of the available conceptual primitives. High l e v e l programming languages provide an example of the influence of d i f f e r e n t sets of conceptual primitives. Some may guarrel, but i t seems reasonable to suggest that there have been programs written i n , say CONNIVES or PLANNER, which would never have been written 91 i n , s a y , FORTRAN, ( l e t i m p l e m e n t a t i o n s of COSN.IVE.B i n FOBTRAN be r u l e d out) even though t h e r e i s no t h e o r e t i c a l r e a s o n why they c o u l d not have been. The c o n c e p t u a l c o m p l e x i t y of a program i s r e l a t e d t o the i n t e r w e a v i n g of t h e c o n c e p t u a l p r i m i t i v e s i n i t s c o n s t r u c t i o n . I f t h e c o n c e p t u a l p r i m i t i v e s a r e l e s s p o w e r f u l , t h a t i s t o say l e s s s u i t e d t o the problem a t hand, then the r e s u l t i n g c o n c e p t u a l c o m p l e x i t y of the s o l u t i o n w i l l be g r e a t e r . I n p r o v i d i n g WHISPEB w i t h an eye and a s s o c i a t e d p e r c e p t u a l p r i m i t i v e s I have endeavoured t o expand t h e a v a i l a b l e s e t c f c o n c e p t u a l p r i m i t i v e s t o i n c l u d e some which a r e t a i l o r e d t o s p a t i a l problems, A new s e t of machine i n s t r u c t i o n s o r a new language i s e s t a b l i s h e d . There i s an i m p r e s s i v e p h y s i c a l and c o m p u t a t i o n a l s t r u c t u r e imposed by t h e senses on human c o n c e p t u a l p r i m i t i v e s . Our v i s u a l p e r c e p t u a l u n d e r s t a n d i n g s would be ve r y d i f f e r e n t i f we were endowed w i t h x-ray v i s i o n , f o r example, or i f we had a t h i r d eye i n t h e back of our heads, o r any of t h e o t h e r m u l t i t u d i n o u s p o s s i b i l i t i e s . E x p r e s s i n g such examples of expanded c o n c e p t u a l i z a t i o n i n terms of our f a m i l i a r p e r c e p t s would p r o b a b l y be as d i f f i c u l t as e x p r e s s i n g the con c e p t of c o l o u r t o a b l i n d man. Communicating shapes i n s t e a d o f c o l o u r s would not be so d i f f i c u l t i f , r a t h e r than s t a t i n g f a c t s about t h e geometry or t o p o l o g y of t h e shapes, they a re s i m p l y m a n i p u l a t e d and understood by t o u c h . The argument t h a t the s t r u c t u r e imposed by our senses i n f l u e n c e s o u r t h i n k i n g about the w o r l d i s n o t new, I r a i s e i t here merely t o h i g h l i g h t the 9 2 n e c e s s i t y f o r an e n l a r g e d s e t of c o n c e p t u a l p r i m i t i v e s i n A l systems and t o j u s t i f y t he s i m u l a t i o n of some o f the c o m p u t a t i o n a l and s t r u c t u r a l p r o p e r t i e s o f the human eye as a s e n s i b l e approach t o t h i s e x p a n s i o n . 93 WHISPEB's eye i s based on t h e s i m u l a t i o n of the s t r u c t u r a l and c o m p u t a t i o n a l a s p e c t s of the human r e t i n a ' s most pronounced f e a t u r e s , m o d i f i e d and guided by pragmatic c o n s i d e r a t i o n s of c o m p u t a t i o n a l expense on the a v a i l a b l e hardware, and ease o f i m p l e m e n t a t i o n both of the s i m u l a t i o n i t s e l f and of the p e r c e p t u a l p r i m i t i v e s dependent on i t . I t i s not to be i n t e r p r e t e d as a model of t h e o p e r a t i o n of t h e human r e t i n a or th e e a r l y p e r c e p t u a l p r o c e s s i n g s t a g e s . I n o r d e r t o e s t a b l i s h t h e c o m p u t a t i o n a l f e a s i b i l i t y of u t i l i z i n g d iagrammatic a n a l o g u e s , a c o m p u t a t i o n a l l y f e a s i b l e i m p l e m e n t a t i o n o f the p e r c e p t u a l p r i m i t i v e s which examine them must be p r o v i d e d . A s i m u l a t i o n o f some a s p e c t s o f the human e y e , e s p e c i a l l y i t s p a r a l l e l o p e r a t i o n , p r o v i d e s t h e framework i n which th e s e p r i m i t i v e s can be implemented. 111; 2_j. J _ Be t i n a 1_ Ge c me t r y - The_ P e r i p h e r y The o v e r a l l s t r u c t u r e o f t h e p e r i p h e r y of the r e t i n a i s shown i n f i g u r e 111-1, Each ' c i r c l e ' r e p r e s e n t s one ' r e c e p t o r ' p r o c e s s o r , and i s c a l l e d a bubble.. S i n c e t h e di a m e t e r of the b u b b l e s i n c r e a s e s w i t h i n c r e a s i n g d i s t a n c e from the c e n t e r of t h e r e t i n a , t h e a c u i t y i s a d e c r e a s i n g f u n c t i o n o f t h i s d i s t a n c e . The s i z e of the bubble i s dependent on the f u n c t i o n which maps t h e a r r a y v a l u e s of t h e diagram onto the r e t i n a . T h i s f u n c t i o n i s e g u i v a l e n t t o the p r o c e s s of o v e r l a y i n g the 95 b u b b l e s o f f i g u r e I I I - 1 on the diagram which the eye i s t o l o o k a t , and s h a d i n g i n each bubble w i t h t h e c o l o u r under i t as i n f i g u r e I I I - 2 . A bubble can be a s s i g n e d m u l t i p l e v a l u e s i f i t c o v e r s more than cne c o l o u r . (Only s i n g l e v a l u e s would be r e g u i r e d i f t h e r e were more bubbles t h a n can c u r r e n t l y be a f f o r d e d due t o t h e expense of the p s e u d o - p a r a l l e l mode o f o p e r a t i o n . ) The r e t i n a i s a c i r c u l a r a r r a y of b u b b l e s , each bubble c o n s i s t i n g of a p r o c e s s o r , some memory, and a d d r e s s a b l e i n terms of i t s wedge and r i n g c o o r d i n a t e s . A wedge i s one l i n e of b u b b l e s r a d i a t i n g outwards from the c e n t e r , as shown by the s o l i d l i n e i n f i g u r e a r i n g i s one c i r c l e o f bub b l e s e q u i d i s t a n t from the c e n t e r , as shown by t h e dashed l i n e . The r i g i d a l i g n m e n t of t h e bubbles was chosen so t h e l o c a t i o n of a bubble c e n t e r r e l a t i v e t c t h e r e t i n a l c e n t e r c o u l d be c a l c u l a t e d from i t s wedge and r i n g c o o r d i n a t e s . I t i s i m p o r t a n t to r e a l i z e t h a t the r e t i n a i s not c o n f i n e d t o a s i n g l e p o s i t i o n over t h e diagram, but i s f r e e t o move and be r e f i l l e d w i t h a f r e s h view of the diagram under commands from a h i g h e r l e v e l p r o c e s s . T h i s r e f i l l i n g p r o c e s s i s assumed t o be a c c o m p l i s h e d i n p a r a l l e l , a l l the bub b l e s r e c e i v i n g new v a l u e s s i m u l t a n e o u s l y . A l l t h e r e c e p t o r s on t h e human r e t i n a o b v i o u s l y r e c e i v e new i n p u t s i n u n i s o n a f t e r a saccade t o a new f i x a t i o n p o i n t . I n a d d i t i o n t o t h e a d d r e s s a b i l i t y o f t h e b u b b l e s as an a r r a y , each bubble has d i r e c t p o i n t e r s t o each of i t s f o u r FIGURE H - ' a 97 nearest neighbours, the two i n the same r i n g and the two i n the same wedge, as d e p i c t e d by the arrows i n f i g u r e I l l - t , These p o i n t e r s are software e g u i v a l e n t s of what would be d i r e c t communication l i n k s between p r o c e s s o r s i n a hardware implementation. In ether words the r e t i n a i s a c i r c u l a r a r r a y c o n s i s t i n g of bubbles, each bubble a l i s t composed of a two l e v e l s t a c k of c u r r e n t and previous values, p o i n t e r s to i t s f o u r n e a r e s t neighbours, and i t s own c o o r d i n a t e s . Each wedge and r i n g i s addressable as a l i s t of bubbles as a r e s u l t of the l i n k a g e s from each bubble t o i t s nearest neighbours. These l i s t s f a c i l i t a t e the use of the LISP mapping f u n c t i o n s which apply a s i n g l e LISP f u n c t i o n u n i f o r m l y to each l i s t element. The uniform a p p l i c a t i o n of a s i n g l e f u n c t i o n to a l l the bubbles i s a form of p s e u d o - p a r a l l e l p r o c e s s i n g . As lo n g as the a p p l i e d f u n c t i o n has no s i d e e f f e c t s , then there i s no time or order dependence between i t s i n v o c a t i o n s . Thus i f m u l t i p l e p r o c e s s o r s are a v a i l a b l e then a l l the separate i n v o c a t i o n s can be executed s i m u l t a n e o u s l y . I t i s i n t h i s sense that a processor i s considered to be a s s o c i a t e d with every bubble. In the c e n t r a l area of the r e t i n a the diameter of the bubbles becomes l e s s than the width of the squares of the a r r a y g r i d i n which the diagram i s encoded. Thus, p a r a d o x i c a l l y , i n 98 c o n t r a s t to the human eye where the c e n t r a l s e c t i o n , the fovea, i s very important, the c e n t r a l area of the simulated r e t i n a becomes i n many r e s p e c t s l e s s i n t e r e s t i n g than the periphery because i t s r e s o l u t i o n begins to exceed the r e s o l u t i o n of the diagram i t i s viewing. T h i s problem stems from the poor r e s o l u t i o n of the diagram r a t h e r than the c o n s t r u c t i o n of the r e t i n a , and c o u l d be s o l v e d simply by i n c r e a s i n g the s i z e of the diagram g r i d . I t would not be bothersome except t h a t the c u r r e n t s i m u l a t i o n operates only i n p s e u d o - p a r a l l e l mode so the e x t r a bubbles i n the c e n t r a l area must be paid f o r i n terms of i n c r e a s e d t o t a l computation time. In the i n t e r e s t of economy the c e n t r a l r e g i o n was separated from the p e r i p h e r y a l l o w i n g the two s e c t i o n s to be moved and r e f i l l e d i n d i v i d u a l l y . I t was p o s s i b l e t c implement many of the p e r c e p t u a l p r i m i t i v e s u s i n g the p r o c e s s o r s from only one of the two r e t i n a l a r e a s , r e d u c i n g the amount of computation r e g u i r e d to simulate the r e t i n a ' s p a r a l l e l p r o c e s s i n g . Since the r e t i n a ' s c e n t r a l area operates i n d e p e n d e n t l y , i t does not c o n t i n u a l l y slow down the s i m u l a t i o n . Thus f o r u n i f o r m i t y , the r e t i n a ' s c e n t e r has the same c i r c u l a r a r r a y s t r u c t u r e as the p e r i p h e r y even though i t s r e s o l u t i o n then exceeds the diagram's. The blank area i n the middle of f i g u r e I.II-1 i s covered with more bubbles i n the same pa t t e r n as those on the p e r i p h e r y . The remaining s m a l l blank area i n the a b s o l u t e c e n t e r of the r e t i n a i s covered with a separate c e n t r a l bubble. I t i s l i k e l y t h a t a d i f f e r e n t o r g a n i z a t i o n of 99 t h e c e n t r a l b u b b l e s would be r e q u i r e d i f the r e s o l u t i o n o f the a r r a y diagram ( c u r r e n t l y 101 by 101 u n i t s ) were improved. £II~2A;3^$he^Betina fls A Data S t r u c t u r e The s i m u l a t e d r e t i n a d i s t i n g u i s h e s i t s e l f as both a data s t r u c t u r e and a c o m p u t a t i o n a l s t r u c t u r e . C o n s i d e r f i r s t i t s p r o p e r t i e s as a data s t r u c t u r e , The r e t i n a l a r r a y i n c o n j u n c t i o n w i t h t h e d i a g r a m - t o - r e f i n a mapping which f i l l s t h e bubble v a l u e s l o t s , p o s s e s s e s t h e v a r y i n g a c u i t y p r o p e r t y of t h e human eye. T h i s p r o p e r t y i s i m p o r t a n t i n the p r o v i s i o n of a f o c u s of a t t e n t i o n and a v a r y i n g degree of c o n c e n t r a t i o n on d e t a i l . The c u r r e n t r e s o l u t i o n o f t h e eye, poor but w o r k a b l e , i s p r o v i d e d by a t o t a l o f 540 b u b b l e s (15 r i n g s by 36 wedges) on t h e p e r i p h e r y and a n o t h e r 540 on the c e n t r a l r e g i o n . The c o m p l e x i t y of the human eye i s of a d i f f e r e n t o r d e r of magnitude w i t h an approximate 116.5-131.5 m i l l i o n r e c e p t o r s (6.5 m i l l i o n cones and 110-125 m i l l i o n rods) on each r e t i n a , a l t h o u g h t h e number of b u b b l e s might more r e a s o n a b l y be compared w i t h t h e one m i l l i o n f i b e r s i n t h e o p t i c n e r v e . 1 3 The mapping from the diagram t o the r e t i n a i s i n e f f e c t a r e - r e p r e s e n t a t i o n o f the diagram i n which some d e t a i l i s b l u r r e d . The t o p o l o g i c a l s t r u c t u r e of t h e diagram i s p r e s e r v e d i n t r a n s f e r r i n g t o the r e t i n a . In p a r t i c u l a r , w i t h i n the c o n s t r a i n t s of t h e r e s o l u t i o n of t h e s i m u l a t e d r e t i n a , t h e b u b b l e - f i l l mapping ens u r e s t h a t no o b j e c t d e p i c t e d i n the 100 diagram i s missed on the r e t i n a . The c h o i c e o f c i r c u l a r b u b b l e s r e s u l t s i n an e q u a l degree of b l u r r i n g i n both the r a d i a l and c i r c u m f e r e n t i a l d i r e c t i o n s . Other r e t i n a l d e s i g n s were c o n s i d e r e d such as t h a t of f i g u r e I I J - 3 i n which the r a d i u s o f the r i n g s i n c r e a s e s as t h e tan g e n t of t h e i r d i s t a n c e from the c e n t e r , but the unegual s p r e a d i n g i n t h e two d i r e c t i o n s r e s u l t e d i n such a s e v e r e d i s t o r t i o n of the diagram t h a t i t became alm o s t u n r e c o g n i z a b l e . I I I - 2 A i _ I h e _ B e t i n a l s _ C g m p u P a r a l l e l i s m i s t h e o v e r r i d i n g c h a r a c t e r i s t i c of the r e t i n a when viewed as a c o m p u t a t i o n a l s t r u c t u r e . T h i s i s a c h a r a c t e r i s t i c s h a r ed w i t h a t l e a s t t h e i n i t i a l p r o c e s s i n g s t a g e s of the human p e r c e p t u a l system. I n the c u r r e n t i m p l e m e n t a t i o n , each c f the p r o c e s s o r s has been g i v e n the f u l l power of the LISP e v a l u a t o r . A l l o f t h e bub b l e s a re f i l l e d i n p a r a l l e l from t h e diagram and then t h e _ i n d i v i d u a l _ p r o c e s §ach_simultaneously_e A s u p e r v i s o r y s e q u e n t i a l p r o c e s s , c a l l e d t h e r e t i n a l , s u p e r v i s o r , c o n s t r u c t s t h e common program and i n i t i a t e s t he p a r a l l e l e x e c u t i o n . An i m p o r t a n t c h a r a c t e r i s t i c of the r e t i n a l p a r a l l e l i s m i s t h a t t h e number c f p r o c e s s o r s i s f i x e d . There i s no need f o r the i n t r o d u c t i o n of new p r o c e s s e s and t h e c r e a t i o n o r hook-up of new p r o c e s s o r s as t h e co m p u t a t i o n proceeds, as Fahlman's system r e q u i r e s . A l t hough i t i s p o s s i b l e t o e n v i s i c n the F I G U R E . Iff - 3 10 2 growth o f new p r o c e s s o r s , from a hardware s t a n d p o i n t i t would be much l e s s c o m p l i c a t e d t o be a b l e t c c o n s t r u c t a f i x e d number of p r o c e s s o r s i n a p r e d e f i n e d and f i x e d c o n f i g u r a t i o n . The c o m p u t a t i o n a l s t r u c t u r e of the r e t i n a i s a l s o a f f e c t e d by t h e d e c i s i o n (again w i t h a view t o a f e a s i b l e hardware i m p l e m e n t a t i o n ) t h a t egmm a n i c a t i o n _ b e t w e e n _ p r g c e s s o r s _ b e r e s t r i c t e d _ t g _ t h e i r . n e a r e s t . n e i g h b o u r s . The o n l y e x c e p t i o n i s a l i n k from each p r o c e s s o r v i a a common data bus t o the r e t i n a l s u p e r v i s o r . Eecause o f the l o c a l s p a t i a l n a t u r e o f t h e p e r c e p t u a l l y p r i m i t i v e o p e r a t i o n s , e.g. c o n t a c t p o i n t f i n d i n g , n eighbourhood communication i s a l l t h a t i s g e n e r a l l y r e q u i r e d . The c o m p u t a t i o n a l assumption of p a r a l l e l i s m w i t h neighbourhood communication i s j u s t i f i e d by the f e a s i b i l i t y of i m p l e m e n t i n g p e r c e p t u a l p r i m i t i v e s . Without p a r a l l e l i s m t h e i r c o m p u t a t i o n would be t o o i n e f f i c i e n t . The g u e s t i o n of e f f i c i e n c y f o r the purposes of A r t i f i c i a l I n t e l l i g e n c e i s t o be d e c i d e d not on the t o t a l amount of com p u t a t i o n i n v o l v e d , but on the t o t a l amount of e l a p s e d time r e g u i r e d . The r e d u c t i o n i n t o t a l e l a p s e d time which can be e f f e c t e d by u s i n g p a r a l l e l i s m i s p r o p o r t i o n a l t o t h e number of s i m u l t a n e o u s p r o c e s s e s . I n the c u r r e n t s i t u a t i o n t h i s r e d u c t i o n i s s i g n i f i c a n t even though i n many problem s o l v i n g systems where the c o m p u t a t i o n a l r e g u i r e m e n t s grow e x p o n e n t i a l l y i t would not be. I t i s s i g n i f i c a n t here because p e r c e p t u a l p r i m i t i v e s can be i n c o r p o r a t e d i n a new programming language as p r i m i t i v e o p e r a t i o n s w i t h e x e c u t i o n t i m e s o f t h e same o r d e r of magnitude 103 as f o r o t h e r more c o n v e n t i o n a l language c o n s t r u c t s . The number of p r o c e s s o r s r e g u i r e d i s f i x e d ( i n the c u r r e n t i m p l e m e n t a t i o n t h e r e are 1080) and l a r g e . Perhaps as many as one m i l l i o n c o u l d be used i n o b t a i n i n g the r e s o l u t i o n of the human eye. Here, s a v i n g a l a r g e c o n s t a n t f a c t o r i s i m p o r t a n t . The r e t i n a l s t r u c t u r e and i t s use of p a r a l l e l i s m i s not t h e same as t h a t o f a p e r c e p t r o n (Minsky and P a p e r t 1 4 ) ; and t h e t h e o r e t i c a l l i m i t a t i o n s o f p e r c e p t i o n s do not d i r e c t l y a p p l y . JSinsky and P a p e r t imposed v a r i o u s r e s t r i c t i o n s on the d e v i c e s they were s t u d y i n g t o e l i m i n a t e any a s p e c t s of s e q u e n t i a l c o m p u t a t i o n i n o r d e r t h a t a n o n - t r i v i a l t h e o r y of p u r e l y p a r a l l e l c o m p u t a t i o n and i t s l i m i t a t i o n s c o u l d be e s t a b l i s h e d . T h i s i s v e r y d i f f e r e n t from the i n t e n t here which i s t o i n t e r m i x p a r a l l e l c o m p u t a t i o n w i t h s e q u e n t i a l c o m p u t a t i o n t o as g r e a t an e x t e n t as p o s s i b l e i n an attempt t o i n c r e a s e the c o m p u t a t i o n a l f e a s i b i l i t y of e f f i c i e n t l y computing th e p e r c e p t u a l p r i m i t i v e s . The main d i f f e r e n c e s between r e t i n a l and p e r c e p t r o n c o m p u t a t i o n a r e : (a) The r e t i n a l s u p e r v i s o r , which p l a y s an a n a l o g o u s r o l e to t h a t o f the p e r c e p t r o n * s l i n e a r t h r e s h o l d f u n c t i o n , can perform a r b i t r a r y c o m p u t a t i o n s , not merely weighted summations. (b) The bubbles can t a l k t o each o t h e r . (c) The r e t i n a can s e q u e n t i a l l y f i x a t e a t numerous l o c a t i o n s i n 104 the diagram during a s i n g l e computation. I I I - 2 f 6 Comparison S i t h Baker's Baching B a k e r 1 S has proposed what he terms a ' s p a t i a l l y - o r i e n t e d i n f o r m a t i o n p r o c e s s o r ' which performs v i s u a l i z a t i o n s of motions. His machine i s a v a r i a n t on the c e l l u l a r a u t o m a t a 1 6 c o n s i s t i n g of a sguare f i n i t e g r i d of f i n i t e s t a t e p r o c e s s o r s connected t o t h e i r n e a r e s t neighbours. Each processor holds a s i n g l e p o i n t , and to si m u l a t e smooth motions i t computes the ' l o c a l c o o r d i n a t e s * of t h a t p o i n t r e l a t i v e to the p r o c e s s o r s ' ' c e l l c o o r d i n a t e s ' . I f the ' l o c a l c o o r d i n a t e * of the po i n t f a l l s o u t s i d e the c e l l boundary then i t i s communicated t c the a p p r o p r i a t e neighbour. There are two d i f f e r e n c e s between WHISPER'S r e t i n a and Baker's processor. The f i r s t concerns the geometry of the pro c e s s o r g r i d , WHISPER'S r e t i n a i s c i r c u l a r r a t h e r than sguare, and the s i z e of the b u b b l e s / c e l l s v a r i e s . The e f f e c t t h i s has i s t h a t r o t a t i o n s can be v i s u a l i z e d without the need o f e x t r a p r o c e s s i n g . A second important d i f f e r e n c e i s t h a t Baker's processor has no method of e x t r a c t i n g f e a t u r e s from the diagram r e p r e s e n t e d by the p a t t e r n of values h e l d by the p r o c e s s o r s , 105 The implementation o f the p e r c e p t u a l p r i m i t i v e s i s reasonably s t r a i g h t f o r w a r d . T h e i r implementation g e n e r a l l y adheres to the computational r e s t r i c t i o n s imposed by the r e t i n a l s t r u c t u r e . Although the c u r r e n t s e t of p r i m i t i v e s i s adequate f o r WHISPEB i n i t s problem domain, i t c o u l d c e r t a i n l y be extended. The u l t i m a t e g o a l would be to expand the c u r r e n t s e t of p r i m i t i v e s to i n c l u d e a l l the p e r c e p t u a l o p e r a t i o n s performed by the human p e r c e p t u a l system, although as yet we do not know the c o n s t i t u e n t s of t h i s s e t . Each of the p e r c e p t u a l p r i m i t i v e s w i l l now be d i s c u s s e d i n t u r n . I l l r i i i - £ § D £ e r _ 0 f _ f l r e a C a l c u l a t i n g the c e n t e r of area of a c l o s e d f i g u r e i s a p a r t i c u l a r l y simple p a r a l l e l computation. Each bubble f i r s t checks to see i f i t s value i s the ' c o l o u r 1 of e i t h e r the i n t e r i o r or contour of the o b j e c t whose c e n t e r of area i s to be found; i f so, i t r e t u r n s to the r e t i n a l s u p e r v i s o r the p a i r of v a l u e s r e p r e s e n t i n g the x and y components of the c o n t r i b u t i o n of i t s area to the c e n t e r of area, i . e . (xA,yA) where A i s the area of the diagram mapped onto the bubble. The s u p e r v i s o r sums i n p a r a l l e l a l l the component p a i r s i t r e c e i v e s and d i v i d e s by the t o t a l area of the o b j e c t . The t o t a l area cf the o b j e c t i s obtained by summing the areas of a l l the c o r r e c t l y 106 c o l o u r e d bubbles. T h i s i s the usual n o t i o n of the ce n t e r of g r a v i t y of a body. The f i n a l r e s u l t i s the c o o r d i n a t e cf the ce n t e r of area r e l a t i v e to the c u r r e n t c e n t e r of the r e t i n a . I f the r e t i n a i s centered f a r from the o b j e c t then t h i s r e s u l t , because of the b l u r r i n g of the p e r i p h e r a l bubbles, w i l l be only a rough approximation to the a c t u a l c e n t e r of area. I t i s improved by c e n t e r i n g the r e t i n a at t h i s estimated l o c a t i o n of the c e n t e r of area and computing the c e n t e r of area a g a i n . The c u r r e n t implementation g e n e r a l l y converges to an accept a b l e r e s u l t i n th r e e i t e r a t i o n s . An o b j e c t ' s diagrammatic c e n t e r of area provides a c a n o n i c a l p o i n t which i s used as a f o c a l p o i n t f o r many cf the other p r i m i t i v e s . I t helps e s t a b l i s h the presence of symmetries, s i n c e i f an o b j e c t i s symmetrical, the center of area must l i e cn the a x i s of symmetry, thereby p r o v i d i n g a c l u e as t o where t o look f o r symmetries. The s i m i l a r i t y t e s t p r i m i t i v e uses i t to a l i g n two o b j e c t s f o r comparison. Another more minor f e a t u r e of the cente r cf area i s t h a t except f o r o b j e c t s with h o l e s or l a r g e c o n c a v i t i e s , i t l i e s w i t h i n the boundaries of the o b j e c t at a r e l a t i v e l y c e n t r a l l o c a t i o n . I t i s thus a good p o i n t on which t c focus the eye when l o c k i n g f o r co n t a c t p o i n t s . The c e n t e r of area p r i m i t i v e i s not simply an ad hoc a d d i t i o n made i n response to a p a r t i c u l a r requirement unigue to WHISPER'S problem domain. The above f e a t u r e s provide independent j u s t i f i c a t i o n of i t s i n c l u s i o n as a p e r c e p t u a l 107 p r i m i t i v e a p a r t from i t s u t i l i t y i n t h e c u r r e n t domain. I l l - 3 ^ 2 _ C o n t a c t _ F i n d i n g F i n d i n g t h e p o i n t s at which c o n t a c t i s made between o b j e c t s i s a c c o m p l i s h e d by a s k i n g each bubble t o check whether i t s v a l u e d i f f e r s from t h a t of any o f i t s n e i g h b o u r s . The p o i n t s a t which a p a r t i c u l a r o b j e c t c o n t a c t s o t h e r o b j e c t s are e a s i l y s i n g l e d o u t by h a v i n g each bubble check t h a t i t s v a l u e i s t h a t of the d e s i r e d o b j e c t b e f o r e t e s t i n g f o r i t s p a r t i c i p a t i o n as a c o n t a c t . These t e s t s a r e performed on the p e r i p h e r a l b u b b l e s a f t e r the eye has been f o c u s e d on the c e n t e r o f a r e a of t h e o b j e c t . The d i f f e r e n c e amongst c o n t a c t s i n v o l v i n g t h e s u p p o r t o f another o b j e c t , the s u p p o r t c f the c u r r e n t o b j e c t , or s i m p l e t o u c h i n g w i t h o u t s u p p o r t i s de t e r m i n e d by a comparison o f t h e c o o r d i n a t e s of the bubb l e s as t o t h e i r r e l a t i v e v e r t i c a l p o s i t i o n w i t h r e s p e c t t o 'up 1, as d e f i n e d by the diagram. T h i s i n v o l v e s an i n t e r a c t i o n between t h e g u a l i t a t i v e knowledge and the p r i m i t i v e c o n t a c t f i n d i n g s i n c e t h e assignment o f a v e r t i c a l i s a f u n c t i o n of the problem domain and the correspondence between i t and the diagrams b e i n g used. Once t h e i n d i v i d u a l c o n t a c t i n g bubbles have been found they must be grouped t o g e t h e r . Even though t h e r e w i l l be many s e p a r a t e c o n t a c t i n g b u b b l e s , t h e r e w i l l o n l y be a few d i s t i n c t a r e a s of c o n t a c t between t h e o b j e c t s . To form the groups 108 r e q u i r e s s e q u e n t i a l l y f o l l o w i n g the neighbourhood l i n k s from one c o n t a c t bubble to another. As the chain of neighbouring c o n t a c t bubbles i s f o l l o w e d , each bubble i n the cha i n i s recorded as being a member of the same group. I f no neighbouring bubble i s a co n t a c t bubble, then the chain i s broken. The l e n g t h of the c h a i n i s used i n c l a s s i f y i n g a co n t a c t as e i t h e r a s u r f a c e of con t a c t or a point of c o n t a c t . The c o o r d i n a t e s of the bubbles at the ends of the c h a i n provide the e x t r e m i t i e s of a contact s u r f a c e . Averaging the c o o r d i n a t e s of a l l the bubbles i n the group y i e l d s a r e p r e s e n t a t i v e c o o r d i n a t e f o r the whole group to which the eye can be moved f o r more d e t a i l e d a n a l y s i s . When the eye has been moved t h e r e , the c e n t r a l p o r t i o n of the r e t i n a i s examined f o r c o n t a c t i n g bubbles, the c o o r d i n a t e s of which w i l l be the p r e c i s e p o i n t s of c o n t a c t between the o b j e c t s . Although the l e s s a c c u r a t e p e r i p h e r a l d e t e r m i n a t i o n of the co n t a c t p o i n t s i s s u f f i c i e n t f o r e s t a b l i s h i n g support r e l a t i o n s h i p s , exact c o n t a c t f i n d i n g i s necessary when a c o n t a c t i s the p i v o t p o i n t f o r a r o t a t i o n , or when the center of g r a v i t y cf an o b j e c t i s near the b a l a n c i n g p o i n t . I t i s a l s o used i n the feedback method of r o t a t i o n to check whether a gap has been c l o s e d and c o n t a c t e s t a b l i s h e d . 1 0 9 I I I - 3 i 3 _ f i n d i n 3 _ N e a r e s t I t i s f r e q u e n t l y necessary t o f i n d the l o c a t i o n nearest or f a r t h e s t r e l a t i v e to the r e t i n a l c e n t e r which s a t i s f i e s an a r b i t r a r y c o n d i t i o n . For example, i n e s t i m a t i n g the f i n a l amount of t w i s t i n r o t a t i o n s , the s i z e o f the gap between the o b j e c t s must be determined. Io do so i t i s necessary to focus the eye on the gap and then f i n d the nearest bubbles whose val u e s are those of the o b j e c t s i n v o l v e d . The o r g a n i z a t i o n of the r e t i n a i n t o r i n g s , each an i n c r e a s i n g d i s t a n c e from the c e n t e r , f a c i l i t a t e s the search f o r the r e g u i r e d nearest and f a r t h e s t bubbles. For example, to f i n d the nearest bubble s a t i s f y i n g c o n d i t i o n C, the r e t i n a l s u p e r v i s o r executes the f o l l o w i n g a l g o r i t h m : ( 1 ) D i r e c t each bubble to t e s t C and save the r e s u l t ( e i t h e r • t r u e ' or ' f a l s e ' ) . (2) For n = 1 to the number of r i n g s on the r e t i n a do steps (3) and (4) . (3) D i r e c t each bubble to r e p o r t i t s wedge and r i n g c o o r d i n a t e s as a message to the r e t i n a l s u p e r v i s o r i f the f o l l o w i n g h o l d : (a) i t belongs to r i n g n, (b) i t s saved value i s ' t r u e * . (4) I f there i s a message pending, r e t u r n the c o o r d i n a t e s s p e c i f i e d by i t as those of the nearest bubble, and stop. T h i s a l g o r i t h m i s a good example of the d i f f e r e n c e between e f f i c i e n c y i n s e q u e n t i a l and p a r a l l e l computation. Since t e s t i n g C c o u l d be an a r b i t r a r i l y long computation, i t i s more 110 e f f i c i e n t i n t e r m s o f e l a p s e d t i m e t o s i m u l t a n e o u s l y t e s t C on a l l b u b b l e s a s i n s t e p (1) , t h a n t o t e s t i t f o r o n l y t h o s e b u b b l e s i n t h e s c a n n e d r i n g s o f s t e p ( 3 ) . On a s e g u e n t i a l p r o c e s s o r i t w o u l d be b e s t t o t e s t C a s few t i m e s a s p o s s i b l e ; w h e r e a s , on a p a r a l l e l p r o c e s s o r t h e t o t a l number o f times c i s t e s t e d i s i r r e l e v a n t ( i f we assume t h a t t h e t i m e t o c o m p u t e C on f a i l i n g b u b b l e s i s n e v e r l o n g e r t h a n t h e t i m e t c c o m p u t e C on s u c c e s s f u l b u b b l e s ) . I t i s t h e number o f t i m e s C i s t e s t e d s e g u e n t i a l l y w h i c h i s i m p o r t a n t . I l l z i i i i - I i s u a l i z a t i o n The r e t i n a l v i s u a l i z a t i o n c f r o t a t i o n s i s a l s o an e x e r c i s e i n n e i g h b o u r c o m m u n i c a t i o n . I h a v e u s e d t h e te rm v i s u a l i z a t i o n b e c a u s e t h e _ p r o c e s s _ i s _ o c c u r r i n S 2 i _ d i r e c t l y _ o n _ t h e _ d i a g r a m i T h i s p r o c e s s i s f a s t e r , bu t b e c a u s e o f t h e l a r g e s i z e o f t h e p e r i p h e r a l b u b b l e s , l e s s p r e c i s e t h a n r o t a t i o n i n t h e d i a g r a m . An o b j e c t c a n be r o t a t e d u n i f o r m l y on t h e r e t i n a a r o u n d t h e r e t i n a l c e n t e r u s i n g n e i g h b o u r c o m m u n i c a t i o n b e c a u s e t h e a n g u l a r s h i f t b e t w e e n b u b b l e c e n t e r s i n n e i g h b o u r i n g wedges i s t h e same f c r a l l r i n g s . G e n e r a l l y , a s t h e r o t a t i o n i s t a k i n g p l a c e , t h e r e i s a p r e d i c a t e P, f o r e x a m p l e a t e s t f o r c o l l i s i o n , w h i c h e a c h bubble i s t o t e s t . I f t h e p r e d i c a t e s u c c e e d s t h e n t h e b u b b l e i n t e r r u p t s t h e r e t i n a l s u p e r v i s o r w i t h a message i n d i c a t i n g t h a t a c o l l i s i o n h a s been d e t e c t e d a t t h e b u b b l e ' s l o c a t i o n . 111 During the v i s u a l i z a t i o n process each bubble executes the f o l l o w i n g steps: (1) Save a copy of i t s current value on i t s two - l a v e l stack. (2) I f i t s current value i s the same as the »colour' of the r o t a t i n g o b j e c t , send i t to i t s r i n g neighbour i n the clockwise or counterclockwise d i r e c t i o n depending on the d i r e c t i o n of r o t a t i o n . (3) Set the current value to the value expressed i n the incoming message; NIL i f there i s no message. (4) Pass the p a i r cf current and saved values to P as arguments. (5) I f P succeeds, re p o r t t h i s to the r e t i n a l s u p e r v i s o r ; i f i t f a i l s , repeat from (2). The process repeats u n t i l e i t h e r the predicate succeeds or u n t i l i t has been executed as many times as there are wedges. The second c o n d i t i o n i n d i c a t e s that the object has been rotated through a f u l l c i r c l e . Because of the coarseness of the r e t i n a l r e s o l u t i o n , the v i s u a l i z a t i o n process i s much f a s t e r than the a l t e r n a t i v e of r o t a t i n g the object by sm a l l increments d i r e c t l y on the diagram. This speed i s gained at the expense of the p o s s i b i l i t y of f a l s e alarms generated by the predicate succeeding during the v i s u a l i z a t i o n when i t would not succeed f o r the a c t u a l c o n d i t i o n s i n the diagram. In p a r t i c u l a r t h i s i s t r u e f o r c o l l i s i o n d e t e c t i o n . Although f a l s e alarms may a r i s e i n which the c o l l i s i o n p r e d i c t e d succeeds f o r the r e t i n a 1 1 2 when i t would not f o r t h e di a g r a m , i t w i l l , however, never be the c a s e t h a t i t succeeds f o r t h e diagram but f a i l s f o r t h e r e t i n a . T h i s i s a r e s u l t o f the s l i g h t e x p a n s i o n i n the s i z e o f o b j e c t s which o c c u r s i n the mapping from the diagram to the r e t i n a , because p o i n t s i n t h e diagram are b l u r r e d i n t o l a r g e r a r e a s o f the r e t i n a . F a l s e a l a r m s cannot be d e t e c t e d o r ha n d l e d on the r e t i n a a l o n e . The v i s u a l i z e d r o t a t i o n must f i r s t be c a r r i e d out i n the diagram. I t i s then examined by moving the r e t i n a o v e r i t t o det e r m i n e whether or not the s i t u a t i o n i s as p r e d i c t e d . I f i t i s not as a n t i c i p a t e d then a f a l s e a l a r m was generated d u r i n g t h e v i s u a l i z a t i o n . V i s u a l i z a t i o n i s a q u i c k , h i g h l y p a r a l l e l , method of a n t i c i p a t i n g t h e r a m i f i c a t i o n s of r o t a t i n g an o b j e c t through a segment c f space. I I l 2 3 i 5 _ S y m m e t r y The symmetry p r i m i t i v e t e s t s f o r symmetry about a d e s i g n a t e d v e r t i c a l a x i s by comparing t h e v a l u e s of s y m m e t r i c a l l y p o s i t i o n e d b u b b l e s . An o b j e c t i s s y m m e t r i c a l (WHISPBH t e s t s f o r v e r t i c a l and h o r i z o n t a l r e f l e c t i v e symmetry, but o t h e r t y p e s c o u l d e a s i l y be i n c l u d e d ) about a g i v e n a x i s i f each bubble h a v i n g i t s ' c o l o u r * as v a l u e has. a s y m m e t r i c a l l y l o c a t e d bubble h a v i n g the same v a l u e . In the t e s t of the v e r t i c a l r e f l e c t i v e symmetry o f a b l u e o b j e c t , f o r example, i f , sa y , t h e bubble i n the t h i r d wedge c l o c k w i s e from t h e v e r t i c a l 1 1 3 a x i s and i n the f o u r t h r i n g from the c e n t e r has the v a l u e ' b l u e ' , then t h e v a l u e of the bubble i n the t h i r d wedge c o u n t e r c l o c k w i s e from the v e r t i c a l a x i s and i n the f o u r t h r i n g must be checked t o see i f i t i s a l s o ' b l u e ' . I f i t i s not then p o s s i b l y the d i s c r e p a n c y can be r u l e d out as i n s i g n i f i c a n t , o r e l s e t h e o b j e c t i s a s y m m e t r i c a l . I n a d d i t i o n to t h e comparison o f s y m m e t r i c a l l y l o c a t e d b u b b l e s , t h e r e i s an 'excuse* mechanism whereby a non-matching p a i r o f b u b b l e s can query t h e i r n e i g h b o u r s * v a l u e s i n an attempt t o r e s o l v e a c o n f l i c t . The 'excuses' which can be g e n e r a t e d h e l p t o e l i m i n a t e f a i l u r e s of the symmetry t e s t on o b j e c t s which are a c t u a l l y s y m m e t r i c a l but whose shape on the r e t i n a l a c k s t o t a l symmetry because of r o u n d - o f f e r r o r a r i s i n g i n r e p r e s e n t i n g t h e diagram as an a r r a y . The type of asymmetry which r e s u l t s i s u s u a l l y due t o a s i n g l e bubble c o v e r e d by the o b j e c t not h a v i n g a c o r r e s p o n d i n g s y m m e t r i c a l l y p l a c e d matching b u b b l e , but h a v i n g a l l o f i t s neighbour b u b b l e s s u c c e s s f u l l y match. T h i s i s t h e o n l y type of asymmetry which WHISPEB c u r r e n t l y knows how t o excuse. To determine i f a mismatch i s e x c u s a b l e the n e i g h b o u r s of t h e t r o u b l e s o m e bubble a r e checked. A l l h a v i n g t h e same v a l u e must have s u c c e s s f u l l y matched, and a t l e a s t one o f them must be a neighbour i n the same wedge. The ' e x c u s e s ' have been d e s i g n e d t o d e a l w i t h the anomalous s i t u a t i o n s which arose f o r WHISPEB*s r e t i n a ; d i f f e r e n t e x c u s a b l e asymmetries would a r i s e f o r d i f f e r e n t r e t i n a l g e o m e t r i e s . 114 The 'excuse* mechanism i s e a s i l y i mpleraentable w i t h i n the bounds o f neighbourhood communication; however, t h e symmetry comparison i t s e l f would be more e a s i l y i mplementable i f communication l i n k s a l s o e x i s t e d between the s y m m e t r i c a l l y l o c a t e d b u b b l e s . Only one such s e t o f e x t r a l i n k s would have t o e x i s t i n o r d e r t o handle both v e r t i c a l and h o r i z o n t a l r e f l e c t i v e symmetries (or any o t h e r a x i s f o r t h a t m a t t e r ) , s i n c e t h e v i s u a l i z a t i o n p r o c e s s c o u l d be used t o r o t a t e the r e t i n a l p r o j e c t i o n of the o b j e c t i n t o a t e s t a b l e o r i e n t a t i o n . Such e x t r a l i n k s a r e not e s s e n t i a l f o r the o r g a n i z a t i o n of symmetry compar i s o n s . fl workable t e c h n i q u e would be t o use the n e i g h b o u r l i n k s t o cause whole wedges t o s h i f t i n a manner perhaps b e s t d e s c r i b e d as analogous to the c l o s i n g o f a Japanese hand f a n . As two wedges come t o g e t h e r the bubbles i n c o r r e s p o n d i n g r i n g s a r e compared. The symmetry t e s t must be s u p p l i e d a proposed a x i s of symmetry. As mentioned e a r l i e r the c e n t e r of a r e a o f f e r s p a r t i a l i n f o r m a t i o n on d e t e r m i n i n g t h i s a x i s . The c e n t e r of a r e a must l i e on any a x i s o f symmetry of an o b j e c t . T h i s does n o t , however, p r o v i d e the o r i e n t a t i o n of t h e a x i s . Although t h e s i m p l e s t s o l u t i o n may be t o t e s t the o b j e c t i n a l l c f the wedge o r i e n t a t i o n s by u s i n g the r o t a t i o n a l v i s u a l i z a t i o n , i f one more p o i n t on the a x i s o f symmetry c o u l d be found the a x i s would be u n i g u e l y d e t e r m i n e d . Such a p o i n t i s the c e n t e r of t h e c i r c u m s c r i b i n g c i r c l e o f t h e o b j e c t . The o n l y problem i s 115 t h a t t h u s f a r I have not managed to d e v i s e a g u i c k p a r a l l e l a l g o r i t h m f o r f i n d i n g t h i s c e n t e r . A l t h o u g h i n some c a s e s they c o u l d be c o i n c i d e n t , i n g e n e r a l I expect the c e n t e r of area and the c e n t e r o f t h e c i r c u m s c r i b i n g c i r c l e t o be d i s t i n c t f o r o b j e c t s w i t h o n l y a s i n g l e a x i s of symmetry. I I I - 3 A 6 _ S i j i l a r i t y _ T e s t i The s i m i l a r i t y t e s t seems t o be an i m p o r t a n t p r i m i t i v e n e c e s s a r y f o r domains such as geometry, the f i n d s p a c e problem, space p l a n n i n g , j i g s a w p u z z l e s , and o t h e r P h y s i c s problems, a l t h o u g h so f a r WHISPER has not had an o p p o r t u n i t y t o use i t . The purpose o f the s i m i l a r i t y t e s t i s t o determine whether two o b j e c t s , A and B, are s i m i l a r under any c o m b i n a t i o n o f t r a n s l a t i o n , r o t a t i o n and s c a l i n g , and i f so t o r e t u r n the a n g l e o f r o t a t i o n , d i r e c t i o n and d i s t a n c e o f t r a n s l a t i o n , and s c a l e f a c t o r . To t e s t s i m i l a r i t y cne o b j e c t i s t r a n s l a t e d , s c a l e d , and r o t a t e d t o match w i t h the o t h e r . S i n c e the c e n t e r of area of an o b j e c t i s u n i q u e , the c e n t e r s c f a r e a of the two o b j e c t s must be made t o c o i n c i d e . The parameters of t r a n s l a t i o n a re s i m p l y t h o s e r e q u i r e d t o a l i g n them. To t e s t f o r s c a l i n g and r o t a t i o n the t r a n s l a t i o n i s f i r s t ' v i s u a l i z e d ' by h a v i n g every b u bble c o v e r e d by A save i t s v a l u e w h i l e the eye i s f o c u s e d on t h e c e n t e r c f a r e a o f A, t h e n r e f o c u s i n g t h e eye on the c e n t e r o f a r e a of B. A f t e r the t r a n s l a t i o n i s ' v i s u a l i z e d * the 116 * image• of o b j e c t fl on the r e t i n a i s s c a l e d (see next s e c t i o n ) by a f a c t o r egual to the sguare root of the r a t i o of the areas of the two o b j e c t s ( i . e . s c a l e f a c t o r = s g r t (area ( A ) / a r e a ( B ) ) . (The t o t a l area of an o b j e c t can be e a s i l y obtained as a by-product of the c a l c u l a t i o n of the center of area.) C l e a r l y , i f the o b j e c t s are s i m i l a r t h i s w i l l y i e l d the c o r r e c t s c a l i n g . A f t e r t r a n s l a t i o n and s c a l i n g , r e t i n a l v i s u a l i z a t i o n can be a p p l i e d t o f i n d the angle of r o t a t i o n and thereby f i n i s h the s i m i l a r i t y t e s t . Some c l u e s t c the most l i k e l y angle of r o t a t i o n could be u t i l i z e d , although WHISPEB c u r r e n t l y t r i e s a l l the p o s s i b l e wedge o r i e n t a t i o n s u n t i l one y i e l d s an ac c e p t a b l e match. An excuse mechanism s i m i l a r to t h a t used i n the symmetry t e s t s can again be employed here (although WHISPEB does not) to handle the cases of o b j e c t s which are s i m i l a r but which do not appear p r e c i s e l y s i m i l a r on the r e t i n a . The s i m i l a r i t y t e s t , l i k e the symmetry t e s t , only provides r e s u l t s which are wi t h i n the r e s o l u t i o n of the r e t i n a . The parameters of the t r a n s l a t i o n , r o t a t i o n and s c a l i n g are approximate; the s i m i l a r i t y t e s t s p e c i f i e s o n l y t h a t a match i s probable a f t e r the designated t r a n s f o r m a t i o n . Although WHISPER does not, f u r t h e r t e s t i n g of the s i m i l a r i t y of the o b j e c t s c o u l d be c a r r i e d out by moving the eye to other l o c a t i o n s on the contours of the o b j e c t s and making f u r t h e r comparisons. 117 I I I " j A 2 _ l S i i n a l _ S c a l i n 3 An unexpected and i n t e r e s t i n g property of the r e t i n a l geometry leads t o a simple s o l u t i o n , employing neighbourhood communication, to the problem of s c a l i n g the r e t i n a l 'image' of an o b j e c t . An o b j e c t i s s c a l e d c o r r e c t l y { i.e. without d i s t o r t i n g i t s shape) i f each bubble having i t s val u e , sends t h i s value to a bubble i n the same wedge, but a f i x e d number c f r i n g s away. As long as each value i s moved the same number of r i n g s e i t h e r inwards or outwards from the bubble which o r i g i n a l l y holds i t , the s i z e of the 'image' of the o b j e c t i s changed but i t s shape i s preserved ( f i g u r e I I I - 4 ) . The reason t h i s i s the case i s t h a t the c o n s t r a i n t s imposed by the alignment of the bubbles i n t o wedges and the touching of each bubble to a l l of i t s immediate neighbours are s a t i s f i e d by having the diameters c f the bubbles i n c r e a s e by a constant f a c t o r from r i n g to r i n g , A proof of the s c a l i n g property i s given i n f i g u r e .1X1-5, S c a l i n g an o b j e c t by neighbourhood communication i s implemented by having each bubble s i m u l t a n e o u s l y send i t s value as a message to i t s neighbour i n the same wedge i n e i t h e r the a p p r o p r i a t e inwards c r outwards d i r e c t i o n , and r e p e a t i n g t h i s message passing process s e g u e n t i a l l y as many times as necessary to b r i n g about the r e q u i r e d s c a l i n g . IIS PROOF OF THE RETINAL SCALING PROPERTY Let: r. be the radius of the k*"^ 1 c i r c l e , k th be the distance from 0 to the center of the k c i r c l e . r k + l C = — which i s a constant from the construction of the k r e t i n a . The Scaling Property Hypothesis i s : +n constant for a l l k. By s i m i l a r t r i a n g l e s r k + l = C r k hence r, , = C r, k+n k \+n \ "k+n R, ^ r , tc+n k+n „n and — = = C which i s independent of k. F & G U R E W~5. 1 2 0 I I ! ; ; 3 . 8 _ C u r y e _ F e a t u r e s I n o r d e r t o e s t a b l i s h the f e a t u r e s of a c u r v e i t i s f i r s t n e c e s s a r y t o d e t e r m i n e which bubbles are p a r t of t h e c u r v e . G i v e n one bubble on t h e c u r v e , t h e o t h e r s can be found by f o l l o w i n g the c h a i n o f b u b b l e s each h a v i n g t h e same v a l u e . One o f the c o n d i t i o n s imposed upon HHISPEfi's diagrams was t h a t the c o n t o u r s of t h e o b j e c t s were ' c o l o u r e d ' a d i f f e r e n t shade from t h e i r i n t e r i o r s . T h i s p r e v e n t s t h e c u r v e f o l l o w i n g p r o c e s s from g e t t i n g l o s t t r a c i n g c h a i n s of b u b b l e s which are p a r t of an o b j e c t ' s i n t e r i o r . I f i s not n e c e s s a r y to d i s t i n c t l y code t h e c o n t o u r s o f the o b j e c t s , s i n c e i t i s p o s s i b l e to determine c o n t o u r p o i n t s by the type o f n e i g h b o u r s s u r r o u n d i n g them, but i t i s cheaper and e a s i e r . Once t h e s e t o f bubbles which are on t h e curve i s f o u n d , t h e n each bubble i n t h e s e t can i n d i v i d u a l l y t e s t i n p a r a l l e l f o r the o c c u r r e n c e of a p a r t i c u l a r f e a t u r e . Sharp bends i n a c u r v e are d e t e c t a b l e as an imbalance i n t h e number of bubble n e i g h b o u r s on o p p o s i t e s i d e s of the c u r v e which are themselves n o t members of the c u r v e . T h i s i s i l l u s t r a t e d by f i g u r e I I I - 6 i n which bubble A has t h r e e n e i g h b o u r s on each s i d e of the c u r v e i n d i c a t i n g t h a t t h e c u r v e i s smooth a t t h a t p o i n t i n c o n t r a s t t o bubble B which has s i x n e i g h b o u r s on one s i d e and o n l y one on the o t h e r . A bubble can t e s t f o r bends by s i m p l y a s k i n g i t s n e i g h b o u r s to respond whether or not they a r e a l s o members of the c u r v e , and c o u n t i n g the r e s p o n s e s from the two I 2- I 1 2 2 s i d e s of the c u r v e . For a simple c l o s e d curve, i f i t i s known which of the bubbles are i n t e r i o r and which are e x t e r i o r , then the bend can a d d i t i o n a l l y be c l a s s i f i e d as convex or concave. The slope of a curve at any curve bubble i s determined as the p e r p e n d i c u l a r to the b i s e c t o r of the angle between the c e n t e r s of i t s neighbouring bubbles cn the curve. T h i s y i e l d s a rough approximation to the a c t u a l s l o p e , but i t i s s u f f i c i e n t f o r t e s t i n g d r a s t i c changes i n the slope of the curve over i t s whole l e n g t h . A more accurate determination of the s l o p e at a p a r t i c u l a r p o i n t on a curve i s obtained by r e - c e n t e r i n g the eye on t h a t p o i n t and then u t i l i z i n g the higher r e s o l u t i o n c e n t r a l p o r t i o n of the r e t i n a . The p e r p e n d i c u l a r to the b i s e c t c r of the angle between the wedges most densely covered with p o i n t s from the curve i s the tangent t o the curve a t that p o i n t . The angle between wedges can be used because they emanate d i r e c t l y from the c e n t e r of the r e t i n a , j u s t as the curve must when the eye i s centered on i t . T h i s i s more accurate than measuring the angle between neighbouring bubbles because there are more wedges than neighbours. T h i s more accurate s l o p e determination i s used to measure the slope of s u r f a c e s a t c o n t a c t p o i n t s to decide whether or not they are h o r i z o n t a l . A s l i d i n g o b j e c t cannot s l i d e over a h i l l which i s higher than i t s i n i t i a l l o c a t i o n . The high spots of a curve are found by each bubble on the curve comparing i t s v e r t i c a l c o o r d i n a t e with the h e i g h t of the i n i t i a l l o c a t i o n . The f i n a l c o n d i t i o n which WHISPEB must know how to check 123 i s whether there are o b j e c t s r e s t i n g on a s u r f a c e with which an o b j e c t s l i d i n g along the s u r f a c e might c o l l i d e . O b j e c t s on a s u r f a c e are found by having each curve bubble t e s t t h a t ncne of i t s neighbours are e i t h e r empty space, the i n t e r i o r of the o b j e c t of which the curve i s the contour, or part of the curve. 124 jr^-S . u g l.§rY - Q l - , S S g - i§t3-Sa.,4,g^ ,rI|§„„g§?cf ptual„ P r i m i t i v e s WHISPEB uses t h e r e t i n a and i t s p e r c e p t u a l p r i m i t i v e s t o e x t r a c t i n f o r m a t i o n from a diagram. The p e r c e p t u a l p r i m i t i v e s p r o v i d e a domain independent s e t of diagrammatic f e a t u r e s which a r e i n t e r p r e t e d r e l a t i v e t o t h e c u r r e n t problem domain. The r e t i n a i s a p a r a l l e l p r o c e s s o r w i t h r e s t r i c t e d communication between p r o c e s s o r s . The p e r c e p t u a l p r i m i t i v e s a re the a l g o r i t h m s t h a t i t e x e c u t e s . I t i s moveable, and when i t i s f o c u s e d on a p o i n t i n the diagram each of i t s p r o c e s s o r s r e c e i v e s an i n p u t s i m u l t a n e o u s l y . The f u n c t i o n mapping p o i n t s i n t h e diagram onto p r o c e s s o r i n p u t s d e f i n e s t h e t c p c l c g y o f t h e r e t i n a . A l t h o u g h t h e r e c o u l d be many o t h e r r e t i n a l t o p o l o g i e s , t h e c u r r e n t one has u s e f u l p r o p e r t i e s , flotations and s c a l i n g s can be v i s u a l i z e d by a neighbourhood communication p r o c e s s , and i t s r e s o l u t i o n d e c r e a s e s w i t h i n c r e a s i n g d i s t a n c e from t h e r e t i n a l c e n t e r . 125 I I I - 5 A J _ I a j n 3 u a 3 e s The languages used i n WHISPER 'S i m p l e m e n t a t i o n a r e : L I S P , a s u b s e t o f CONNI7ER, and FORTRAN. The q u a l i t a t i v e p h y s i c a l knowledge and t h e p e r c e p t u a l p r i m i t i v e s a re p r i m a r i l y w r i t t e n i n LISP w i t h some c a l l s t o CONNIVER's p a t t e r n matcher. CONNIVER's 1 7 a s s o c i a t i v e database i s used t o s t o r e a s s e r t i o n s p e r t a i n i n g t o f e a t u r e s e x t r a c t e d from the diagram. Each s p e c i a l i s t r e g u i r i n g i n f o r m a t i o n from the diagram f i r s t checks th e database f o r a r e l e v a n t a s s e r t i o n made by an e a r l i e r s p e c i a l i s t b e f o r e i t c a l l s t h e r e t i n a l s u p e r v i s o r t o l o o k a t the diagram. The a r r a y diagram i s s t o r e d i n a FORTRAN a r r a y , and t h e d i a g r a m - t o - r e t i n a mapping i s a LISP c a l l a b l e FORTRAN s u b r o u t i n e . The r e d r a w i n g t r a n s f o r m a t i o n s a r e a l s o w r i t t e n i n FORTRAN. FORTRAN was chosen f o r t h e s e t a s k s because t h e y r e q u i r e n u m e r i c a l c a l c u l a t i o n s , and because i t i s LISP c a l l a b l e . lIIz5i2_Timinqs The t i m i n g s which can be g i v e n a re af b e s t very a p p r o x i m a t e , and h i g h l y dependent on machine speed and language i m p l e m e n t a t i o n . Running L I S P / M T S 1 8 i n t e r p r e t i v e l y under the H i c h i g a n T e r m i n a l System on an IBH 370/168, WHISPER took 126 a p p r o x i m a t e l y 2 minutes of p r o c e s s o r time f o r each snapshot. The amount of memory r e q u i r e d i n c l u d i n g space f o r LISP i n t e r p r e t e r was a p p r o x i m a t e l y 250 K words (3 2 h i t s per word). The time t o f i l l t h e r e t i n a a t each f i x a t i o n i s 1.4 seconds f o r th e p e r i p h e r y and 0.6 seconds f o r the c e n t r a l s e c t i o n . These t i m e s wculd be i n c o n s e q u e n t i a l i n t h e t o t a l problem s o l v i n g p r o c e s s i f t h e r e were t r u e p a r a l l e l i s m . S i n c e t h e c e n t r a l s e c t i o n and t h e p e r i p h e r y each have 540 b u b b l e s , each complete f i x a t i o n would r e q u i r e (1.4 + 0.6)/540 =0.0037 seconds. I n p r o d u c i n g t h e f i r s t snapshot t o t h e c h a i n r e a c t i o n problem WHISPER made 33 f i x a t i o n s (10 c e n t r a l s e c t i o n , 2.3 p e r i p h e r y ) r e q u i r i n g 10 x 0.6 + 23 x 1.4= 38.2 seconds. V i r t u a l l y a l l of t h i s t i m e (3 8.2/54 0 = 0.07) c o u l d be f a c t o r e d out from the 125 seconds r e q u i r e d f o r t h e f i r s t s napshot. I would e s t i m a t e from i s o l a t i n g p o r t i o n s o f a t r a c e of WHISPER's b e h a v i o u r d u r i n g the f i r s t snapshot t h a t a p p r o x i m a t e l y 40 p l u s o r minus 15 seconds were s p e n t i n the q u a l i t a t i v e p h y s i c s s p e c i a l i s t s . The r e s t of th e t i m e i s spent f i x a t i n g and computing t h e p e r c e p t u a l p r i m i t i v e s , and would be s u b s t a n t i a l l y reduced by p a r a l l e l i s m . The t i m e spent i n t h e q u a l i t a t i v e p h y s i c s s p e c i a l i s t s would be s i g n i f i c a n t l y r educed by c o m p i l a t i o n (LISP/MTS does not s u p p o r t a c o m p i l e r ) . 127 I V - 1 _ I n t r o d u c t i o n The use of analogues as a i d s i n human problem s o l v i n g i s very common. I t i s a c e n t r a l aim of t h i s t h e s i s t o demonstrate how computer programs can d e r i v e some o f these same b e n e f i t s from the use o f analogues i n problem s o l v i n g as do p e o p l e . The i m p o r t a n c e of the r o l e o f analogues i n human problem s o l v i n g has been u n d e r r a t e d . T h i s i s p a r t i c u l a r l y t r u e w i t h r e s p e c t t c di a g r a m s , which a r e g e n e r a l l y r e g a r d e d as s i m p l y an a d d i t i o n t o th e memory c a p a c i t y o f the b r a i n . When viewed from t h i s p e r s p e c t i v e t h e r e i s no sense i n u s i n g diagrams i n machine r e a s o n i n g because t h e r e are more c o n v e n i e n t ways of e x t e n d i n g computer memory. C u r r e n t l y AI systems are not s e v e r e l y c o n s t r a i n e d by memory c a p a c i t y l i m i t a t i o n s , but r a t h e r by the l a c k of good methods of o r g a n i z i n g t h e i n f o r m a t i o n which can a l r e a d y be s t o r e d . I t i s t h e purpose of t h i s c h a p t e r to e x p l o r e some of those a s p e c t s of analogu e s which a r e more i m p o r t a n t than t h e i r p o s s i b l e use as memory e x t e n s i o n s . A b a s i c premise u n d e r l y i n g my e x a m i n a t i o n o f the b e n e f i t s o f analogues i n problem s o l v i n g i s t h a t t h e r e i s no e s s e n t i a l d i f f e r e n c e i n the way people u t i l i z e them and the way machines s h o u l d be a b l e t o u t i l i z e them. T h i s i n t r o d u c e s a p r i o r and un s o l v e d problem c o n c e r n i n g the i n t e r a c t i o n o f a computer w i t h 128 i t s e n v i r o n m e n t ; WHISPER s e r v e s as a d e m o n s t r a t i o n t h a t t h i s problem can be overcome i f i t i s ac c e p t e d t h a t a hardware i n c a r n a t i o n of i t s s o f t w a r e s i m u l a t i o n i s r e a l i z a b l e . T h i s p remise a l s o r a i s e s the g u e s t i o n d i s c u s s e d i n s e c t i o n 1-2, namely, what i s t o be c o n s i d e r e d the c o m p u t a t i o n a l s t r u c t u r e of a machine. To say t h a t a computer not be a l l o w e d t o u t i l i z e such d i a g r a m m a t i c a i d s i n problem s o l v i n g as diagrams, would be comparable t o r e q u i r i n g a s t u d e n t t o w r i t e a P h y s i c s exam w i t h o u t a l l o w i n g him t o draw any diagrams. Why would t h i s be a ha n d i c a p ? The p o s s i b l e r e p l y t h a t i t i s a r e s u l t o f human s h o r t term memory l i m i t a t i o n i s a p a r t i a l , though i n s u f f i c i e n t answer t o t h e q u e s t i o n . The advantages t h a t WHISPER d e r i v e s from u s i n g a diagrammatic analogue and t h e f u r t h e r i s s u e s r a i s e d i n t h i s c h a p t e r a re e v i d e n c e t h a t diagrams may pla y a more fundamental r o l e i n the s t u d e n t ' s r e a s o n i n g , I would l i k e to p o i n t out a few i s s u e s t h a t t h e use of an a l o g u e s does not c o n c e r n . One i s t h a t the a b i l i t y t o d i s c o v e r a n a l o g i e s i s not p r e r e q u i s i t e t o the use of a n a l o g u e s ; t h e use o f analogu e s i s not concerned w i t h t h e i r d i s c o v e r y . There a r e many a n a l o g i e s which have been d i s c o v e r e d and t r a n s m i t t e d t o subsequent g e n e r a t i o n s . S e c o n d l y , analogues have no s p e c i a l c o n n e c t i o n w i t h the p r o p e r t y of c o n t i n u o u s n e s s . C e r t a i n l y , a p r o p e r t y of a p a r t i c u l a r analogue may be t h a t i t i s c o n t i n u o u s , but t h i s i s net a p r e r e q u i s i t e c o n d i t i o n . S i m i l a r i l y , a l t h o u g h the emphasis i n t h i s t h e s i s i s on a n a l o g u e s which have as one o f t h e i r p r o p e r t i e s 129 t w o - d i m e n s i o n a l i t y , t h i s i s not a necessary c h a r a c t e r i s t i c of an analogue. F i n a l l y , reasoning with analogues i s not intended as a replacement f o r other kinds of more a b s t r a c t r e a s o n i n g , nor i s i t claimed from a t h e o r e t i c a l s t a n d p o i n t that the use of analogues i s e s s e n t i a l or necessary i n the sense of there being something which can be computed with analogues which could not otherwise be computed. 130 Q ~ i _ £ n a logy,And-&SilSg"§.§ When there i s an analogy between two e n t i t i e s then they are each analogues of the other. Polya d e f i n e s analogy: "Analogy i s a s o r t of s i m i l a r i t y . . . . s i m i l a r o b j e c t s agree with each other i n seme aspect. I f you i n t e n d to reduce the aspect i n which they agree to d e f i n i t e concepts, you regard those s i m i l a r o b j e c t s as analogous. ...two systems are analogous, i f they &aE^,i^.Sl§§!VlJ^^%ti'U^}i>^..I.§l%%i9U§^Qi iJ^M£_ISS£ectiye_jarts A 2 ( o r i g i n a l e m p h a s i s ) . 1 9 Although almost a l l t h i n g s are analogous on a t r i v i a l l e v e l , some th i n g s are s t r o n g l y analogous i n that there are numerous r e l a t i o n s h i p s i n v o l v i n g t o t a l or l a r g e subsets of t h e i r r e s p e c t i v e p a r t s which agree. The i n g r e d i e n t s of P o l y a 1 s d e f i n i t i o n are present i n Sloman's d i s c u s s i o n of a n a l o g i c a l r e p r e s e n t a t i o n s : " i f R i s an a n a l o g i c a l r e p r e s e n t a t i o n of T, then (a) there must be p a r t s of R r e p r e s e n t i n g p a r t s of T, as dots and s q u i g g l e s on a map r e p r e s e n t towns and r i v e r s i n a country... and (b) i t must be p o s s i b l e to s p e c i f y some s o r t of correspondence, p o s s i b l y context-dependent, between p r o p e r t i e s or r e l a t i o n s of parts of R and p r o p e r t i e s or r e l a t i o n s of p a r t s of T..." 2 0 Another way to d e s c r i b e analogy would be as a correspondence i n the s t r u c t u r e of the analogous e n t i t i e s . T h i s i s simply a r e f o r m u l a t i o n of the above ' d e f i n i t i o n s ' i n t h a t the s t r u c t u r e of an e n t i t y corresponds to the p r o p e r t i e s of i t s p a r t s and the r e l a t i o n s amongst i t s p a r t s . Thus, as 131 Hayes says i n h i s d i s c u s s i o n of d i r e c t ( h i s term f o r a n a l o g i c a l ) r e p r e s e n t a t i o n s , " . . . t h e r e p r e s e n t a t i o n i s a s t r u c t u r a l homcmorph c f the r e a l i t y . " 2 1 N o t i c e t h a t so f a r t h i s d i s c u s s i o n has f o c u s e d on the r e l a t i o n s h i p between a n a l o g u e s , even though some of the q u o t a t i o n s have been concerned w i t h the r e l a t i o n s h i p of an a n a l o g i c a l r e p r e s e n t a t i o n t o t h e r e a l i t y i t r e p r e s e n t s . These two i s s u e s are r e l a t e d i n t h a t the s i m i l a r i t i e s o r c o r r e s p o n d e n c e s d e f i n i n g the analogy p r o v i d e t h e b a s i s f o r d e f i n i n g what P y l y s h y n 2 2 terms a SIF (semantic i n t e r p r e t a t i o n f u n c t i o n ) . There are many examples of a n a l o g u e s : a map i s an analogue o f t h e geography o f an a r e a ; water waves are an analogue of l i g h t waves; th e c i r c u i t s i m u l a t i o n i n the SOPHIE system of Brown, B u r t o n and B e l l 2 3 i s an analogue of a r e a l e l e c t r i c a l c i r c u i t ; a t w o - d i m e n s i o n a l a r r a y i s an analogue of a p i e c e o f paper; the diagrams used by WHISPEB are an analogue of a b l o c k s w o r l d . I n t h e case c f water v e r s u s l i g h t waves and i n the case of c i r c u i t s i m u l a t i o n , the c o r r e s p o n d e n c e s c o n s t i t u t i n g the a n a l o g y a r e not between s t a t i c a s p e c t s o f t h e e n t i t i e s but r a t h e r between a s p e c t s of t h e i r b e h a v i o u r . Thus th e ' p a r t s ' r e f e r e d t o i n t h e above d e f i n i t i o n s , p a r t i c u l a r l y i n P o l y a ' s , must be i n t e r p r e t e d v ery b r o a d l y t o encompass a n o t i o n of a • p a r t ' of b e h a v i o u r . For example, d i f f r a c t i o n i s a p a r t of the b e h a v i o u r of l i g h t f o r which t h e r e i s a c l e a r l y d e f i n a b l e c o r r e s p o n d e n c e t o the d i f f r a c t i o n of water waves. 132 L e t us c o n s i d e r more c l o s e l y the SOPHIE c i r c u i t s i m u l a t i o n . G i v e n a p a r t i c u l a r c i r c u i t t h e r e i s a c o r r e s p o n d e n c e between i t s p a r t s - t h e components, r e s i s t o r s , c a p a c i t o r s , e t c . - and the parameters o f the s i m u l a t i o n , f o r each c i r c u i t component t h e r e i s a c o r r e s p o n d i n g parameter whose n u m e r i c a l v a l u e c o r r e s p o n d s t o the p h y s i c a l v a l u e c f t h a t component. I n a d d i t i o n , t h e r e i s a c o r r e s p o n d e n c e between t h e b e h a v i o u r of t h e c i r c u i t when the v a l u e o f a component i s changed, as e v i d e n c e d by i n s t r u m e n t s measuring t h e c u r r e n t s and v o l t a g e s a t v a r i o u s p o i n t s i n the c i r c u i t , and the b e h a v i c u r of t h e s i m u l a t i o n when t h e v a l u e of the c o r r e s p o n d i n g parameter i s changed, as i n d i c a t e d by t h e r e s u l t s i t p r e d i c t s f o r the c u r r e n t s and v o l t a g e s a t t h o s e p o i n t s . The b e h a v i o u r of the c i r c u i t s i m u l a t i o n i s a t t r i b u t a b l e t o t h e b e h a v i o u r c f the machine e x e c u t i n g a program which i s based on d e s c r i p t i o n s ( e q u a t i o n s ) of the b e h a v i o u r of e l e c t r i c a l c i r c u i t s . The s i m i l a r i t y i n t h e b e h a v i o u r of the s i m u l a t i o n and o f the c i r c u i t i s p r o v i d e d by c o m p u t a t i o n ; the c o r r e s p o n d e n c e between the p h y s i c a l s t r u c t u r e o f t h e c i r c u i t and the s i m u l a t i o n i s p r o v i d e d by the o r g a n i z a t i o n of the parameters i n t o a d a t a s t r u c t u r e which i s p a r t o f the p h y s i c a l s t o r a g e s t r u c t u r e of t h e machine. Thus a composite of both c o m p u t a t i o n and p h y s i c a l s t r u c t u r e c o n s t i t u t e s the t o t a l s t r u c t u r e of the s i m u l a t i o n . There i s an a n a l o g y between the s t r u c t u r a l a s p e c t s of t h i s s i m u l a t i o n and t h e a c t u a l c i r c u i t . 133 The SOPHIE s i m u l a t i o n i s an example of an analogue c o n s t r u c t e d from a complete mathematical d e s c r i p t i o n of the b e h a v i o u r o f e l e c t r i c a l c i r c u i t s and r e l i e s on the a r b i t r a r y symbol m a n i p u l a t i o n power o f a T u r i n g machine. I t i s s i m i l a r l y p o s s i b l e , g i v e n an a p p r o p r i a t e d e s c r i p t i o n , t o s i m u l a t e any o t h e r b e h a v i o u r and hence c o n s t r u c t a system which i s an analogue of the d e s c r i b e d e n t i t y . The p r i m a r y d i f f i c u l t y i s t h a t i t i s g e n e r a l l y n o n - t r i v i a l t o p r o v i d e the r e g u i s i t e d e s c r i p t i o n . S i m u l a t i o n s a re analogues and can thus be used as an a i d t o problem s o l v i n g j u s t as any o t h e r analogue which has no dependence on computation,, but t h e r e i s the problem of p r o v i d i n g i t s u n d e r l y i n g d e s c r i p t i v e model and the c o m p u t a t i o n a l expense o f p e r f o r m i n g the s i m u l a t i o n based on i t . P y l y s h y n 2 4 comments t h a t t h e use of analogues i s an attempt to g e t f o r " f r e e " t h o s e e f f e c t s which o c c u r n a t u r a l l y i n t h e environment and which t h e r e f o r e happen w i t h o u t the need of c o m p u t a t i o n . The two f a c t o r s o f p r o v i d i n g an adequate d e s c r i p t i o n and o f computing the b e h a v i o u r of the d e s c r i b e d e n t i t y from i t s d e s c r i p t i o n a re net f r e e . A l o t of the murkiness s u r r o u n d i n q q u e s t i o n s of the use of a n a l o g u e s , e s p e c i a l l y t h e i r e f f i c i e n c y , d e r i v e s from c o n f u s i n g t h e i s s u e s of t h e c o n s t r u c t i o n of t h e analogue w i t h t h e i s s u e s o f i t s use. Once an analogue e x i s t s i t can be u t i l i z e d i n d e p e n d e n t l y of i t s o r i g i n . A c e n t r a l g u e s t i o n then i s whether i t i s p o s s i b l e t o o b t a i n more r e s u l t s from the analogue than a r e §xplicitly_described i n the c o n s t r u c t i o n of t h a t 134 system. The answer to t h i s g u e s t i o n i s yes on two grounds. The f i r s t i s that the analogue need not be s t r i c t l y i n t e r n a l to a machine, i . e . i t need not take the form of a s i m u l a t i o n . T h i s i s the case f o r analogues such as maps, diagrams, and s c a l e models. For example, i f we wish t o determine the s t a b i l i t y of a p i l e of b l o c k s i n a blocks world s i t u a t i o n on the s u r f a c e of the moon, then we c c u l d c o n s t r u c t a s i m i l a r p i l e o f bl o c k s on ea r t h and determine the r e s u l t by experiment. The experimental r e s u l t i s a c g u i r e d f o r f r e e i n t h a t there i s no need to d e s c r i b e the behaviour of the blocks on ea r t h i n order f o r them to behave c o r r e c t l y . However, s i n c e the behaviour of the two s i t u a t i o n s i s not i d e n t i c a l , the experimental r e s u l t s must be i n t e r p r e t e d on the b a s i s of the analogy. I n t e r p r e t i n g the r e s u l t s (e.g. c o n v e r t i n g a c c e l e r a t i o n s ) r e q u i r e s e s t a b l i s h i n g and executing a method to handle d i s c r e p a n c i e s . C l e a r l y , i n t e r p r e t i n g the experimental r e s u l t s i s g e n e r a l l y e a s i e r than d e r i v i n g the f i n a l ones from b a s i c p r i n c i p l e s . The second reason f o r answering yes i s demonstrated by WHISPEB. The two-dimensional s t r u c t u r e of a pie c e of paper i s p a r t i a l l y simulated by a two-dimensional a r r a y . Thus i t i s necessary to d e s c r i b e some of the aspects of two-dimensional space and to simulate these aspects c o m p u t a t i o n a l l y . A l l that t h i s s i m u l a t i o n c o n s i s t s of i s the u s u a l f u n c t i o n , mapping c o o r d i n a t e p a i r s i n t o p o s i t i o n s i n the storage v e c t o r . I t i s not necessary to d e s c r i b e any of the other t o p o l o g i c a l 135 p r o p e r t i e s c f 2-space. I n a d d i t i o n , t h e r e are procedures f o r r o t a t i o n a l and t r a n s l a t i o n a l t r a n s f o r m a t i o n s of p o i n t s i n the a r r a y . The r e s u l t i n g system of the a r r a y and the r e d r a w i n g t r a n s f o r m a t i o n s i s analogous (when o b j e c t s a r e r e p r e s e n t e d by s e t s c f p o i n t s ) t o t h e b l o c k s world w i t h r e s p e c t to the b e h a v i o u r of o b j e c t s i n terms o f t h e i r p o s s i b l e motions. Thus we do not get motions f o r f r e e s i n c e i t i s both n e c e s s a r y t o d e s c r i b e them and t o compute them. However, when an o b j e c t i s moved t h e r e a r e many t h i n g s t h a t a re o b t a i n e d w i t h o u t the need o f e x p l i c i t d e s c r i p t i o n or c o m p u t a t i o n ( i . e . f o r f r e e ) some of which have been s t u m b l i n g b l o c k s f o r many A r t i f i c i a l I n t e l l i g e n c e systems. When WHISPEB moves an o b j e c t none of the o t h e r o b j e c t s move; the shape o f t h e o b j e c t i s p r e s e r v e d ; the t o t a l amount o f empty space i s c o n s e r v e d ; the ar e a s o f empty space a r e updated p r o p e r l y ; i t s c o n t a c t s w i t h o t h e r o b j e c t s a re updated; and the shapes formed by groups of o b j e c t s change. These p r o p e r t i e s a r e updated i r r e s p e c t i v e of t h e e x i s t e n c e of p r o c e d u r e s f o r t h e i r r e c o g n i t i o n . T h e s e _ a s p e c t s _ g f _ t h e b e h a y i c u r _ o f _ t h e _ a n a l T h i s i s a r e s u l t of e x p l o i t i n g t h e o n e - d i m e n s i o n a l space i n h e r e n t i n the p h y s i c a l s t r u c t u r e of memory (an o r d e r e d sequence of b i t s ) t o p r o v i d e an analogue o f t w o - d i m e n s i o n a l s p a ce. T h i s e x p l o i t a t i o n d i d not r e g u i r e a d e s c r i p t i o n of t w o - d i m e n s i o n a l space o r , i n d e e d , of o n e - d i m e n s i o n a l s p a c e , but o n l y a method of c o n v e r s i o n between them. E s s e n t i a l l y , _ w h a t 136 k a s _ b e e n _ a v o i d e d _ i s _ a d a t a _ s t r u c t u r e j . N o n e t h e l e s s , i t i s t h e s e p r o p e r t i e s which are r e s p o n s i b l e f o r the p r o p a g a t i o n of the a p p r o p r i a t e s i d e e f f e c t s o f an o b j e c t ' s m o t i o n . 137 U s i n g an analogue i n r e a s o n i n g i n v o l v e s i n t e r a c t i n g w i t h i t t h r o u g h e x p e r i m e n t a t i o n . To f i n d the outcome of a g i v e n change i n s i t u a t i o n S, an experiment can be conducted i n an analogous s i t u a t i o n a , a c o r r e s p o n d i n g change made t o A, and the r e s u l t o f t h i s experiment i n t e r p r e t e d i n terms c f the o r i g i n a l s i t u a t i o n S. The c l a s s of mea n i n g f u l e x p e r i m e n t s and t h e i r i n t e r p r e t a t i o n s i s det e r m i n e d by t h e c o r r e s p o n d e n c e s d e f i n i n g t h e analogy between S and fl. S i n c e t h e analogy p r o v i d e s a means o f i n t e r p r e t i n g s t a t e s and events of A as i n d i c a t i n g the o c c u r r e n c e of p a r t i c u l a r s t a t e s and e v e n t s o f S, A r e p r e s e n t s S. The analogy d e f i n e s the s e m a n t i c s of the a n a l o g u e . A, as a r e p r e s e n t a t i o n of S. I n a d d i t i o n t o a s t a t i c s t a t e o f t h e analogue A d e n o t i n g a s t a t e of S, A can a l s o r e p r e s e n t t h e dynamic b e h a v i o u r of S. T h i s i s a r e s u l t of the two modes o f / e x p e r i m e n t a t i o n : measurement of a s p e c t s of the c u r r e n t s t a t e , and measurement o f a s p e c t s of t h e subseguent s t a t e o r seguence of s t a t e s a r i s i n g from some change i n the i n i t i a l s i t u a t i o n . These w i l l be c a l l e d g g n f i g u r a t i o n a l and b e h a v i o u r a l modes of e x p e r i m e n t a t i o n . An e x p e r i m e n t , t h e r e f o r e , e i t h e r d e t e r m i n e s t h e c u r r e n t p h y s i c a l c o n f i g u r a t i o n o r i t d e t e r m i n e s the subseguent b e h a v i o u r d e r i v i n g from a change i n the c u r r e n t c o n f i g u r a t i o n . I t i s because an analogy can s p e c i f y c o r r e s p o n d e n c e s between s i t u a t i o n s i n terms of t h e i r s t a t i c 138 c o n f i g u r a t i o n s , as w e l l as i n terms o f t h e i r b e h a v i o u r , t h a t t h e s e two modes o f e x p e r i m e n t a t i o n a r i s e , and t h a t an analogue can r e p r e s e n t both the s t a t i c s t a t e and t h e dynamic b e h a v i o u r of a s i t u a t i o n . An example of a c o n f i g u r a t i o n a l experiment i s measuring t h e d i s t a n c e between two p o i n t s on a map. The i n t e r p r e t a t i o n o f t h i s measurement i s made on the b a s i s of t h e ana l o g y between the map and the geography i t r e p r e s e n t s . An example of an exper i m e n t i n the b e h a v i o u r a l mode i s i n c r e a s i n g t h e v e l o c i t y of the wind i n a wind t u n n e l c o n t a i n i n g a model a i r p l a n e . Changing the v e l o c i t y i s a change i n the s t a t e of the s i t u a t i o n from which many o t h e r e f f e c t s o f t h e b e h a v i o u r of the wind-model system f o l l o w , such as an i n c r e a s e i n l i f t of the wings. These r e s u l t a n t e f f e c t s a re i n t e r p r e t e d as i n d i c a t i v e o f s i m i l a r e f f e c t s which would occur as the r e s u l t of i n c r e a s i n g the v e l o c i t y o f a f u l l s i z e d a i r p l a n e i n f l i g h t . The i n t e r p r e t a t i o n may, however, not i n v o l v e s i m p l e l i n e a r s c a l i n g as i n t h e case o f the map, but a more complex c o n v e r s i o n . A l t h o u g h a n a l o g u e s can be used as r e p r e s e n t a t i o n s t h i s does n o t i m p l y t h a t they i m m e d i a t e l y s e r v e as r e p r e s e n t a t i o n s m a n i p u l a b l e i n t e r n a l l y by a computer. A r e p r e s e n t a t i o n i s u s e f u l , n o n e t h e l e s s , i f i t i s more m a n i p u l a b l e t h a n t h a t which i t r e p r e s e n t s . Thus a p i l e o f b l o c k s on e a r t h , r e p r e s e n t i n g a p i l e o f b l o c k s on the moon, i s a u s e f u l r e p r e s e n t a t i o n s i n c e d e t e r m i n a t i o n s about the b l o c k s on the moon can be made wi t h o u t 139 v i s i t i n g t h e moon to observe them. Such r e p r e s e n t a t i o n s are u s e f u l t c people a t l e a s t , "and I see no r e a s o n shy they s h o u l d not be c o n s i d e r e d t o be u s e f u l t o a machine. The advantages of analogues to WHISPEB a r i s e p r i m a r i l y d u r i n g problem s o l v i n g r a t h e r than i n the l o n g term s t o r a g e o f i n f o r m a t i o n . A problem s o l v i n g program need not be a b l e t o i n v e n t t h e a p p r o p r i a t e analogue. The method of c o n s t r u c t i n g an analogue from a d e s c r i p t i v e r e p r e s e n t a t i o n can be d e f i n e d i n advance f o r the program. Thus a program does not need t o s t o r e a l a r g e i n v e n t o r y o f • p i c t u r e s ' . T h i s i s s i m i l a r t o t h e g r a p h i c s metaphor which K o s s l y n 2 5 has advanced as a t h e o r y f o r the s t o r a g e and c o n s t r u c t i o n c f v i s u a l images which humans s u b j e c t i v e l y e x p e r i e n c e . B i s a n a l o g y i s t h a t o f a computer g r a p h i c s t e r m i n a l d i s p l a y i n g p i c t o r i a l i n f o r m a t i o n p r e s e n t e d t o i t i n terms which are very n o n - p i c t o r i a l i n n a t u r e ( u s u a l l y i n terms of the c o o r d i n a t e s o f two p o i n t s between which a l i n e segment i s t o be drawn). I f some s o r t o f e q u i v a l e n t e x i s t s which i s the ' s c r e e n ' f o r v i s u a l i m a g e r y , then i t i s not n e c e s s a r y t o l i t e r a l l y s t o r e a p i c t u r e i n o r d e r t o have t h e s u b j e c t i v e e x p e r i e n c e o f v i s u a l imagery. S i m i l a r l y , i t i s not n e c e s s a r y t c s t o r e p i c t o r i a l diagrams i n o r d e r t o u t i l i z e d i agrammatic a n a l o g u e s . T h i s i s s u e w i l l be d i s c u s s e d a t g r e a t e r l e n g t h i n Chapter V where I propose an a l t e r n a t i v e t o the a r r a y encoding o f diagrams. The b e h a v i o u r a l and c o n f i g u r a t i o n a l modes o f e x p e r i m e n t a t i o n and the r e p r e s e n t a t i o n o f the s t a t e s and events 140 of one s i t u a t i o n by the analogous s t a t e s and events of another s i t u a t i o n r e s u l t i n two advantages (behavioural advantages and c o n f i g u r a t i o n a l advantages) which a system can d e r i v e from i n t e r a c t i o n with an analogue. These advantages w i l l now be d i s c u s s e d . 141 i l ~ i i _ l d y a i i t a 2 g s _ 0 f _l2alg<jues I want now to c l a s s i f y the b e n e f i t s d e r i v a b l e from a n a l o g u e s i n terms o f the twc modes - b e h a v i o u r a l and c o n f i g u r a t i o n a l - of e x p e r i m e n t a t i o n d i s c u s s e d e a r l i e r as t h e b a s i s of t h e i n t e r a c t i o n between a system and analogue. The WHISPER system r e l i e s upon and demonstrates t h e u s e f u l n e s s o f many of these b e n e f i t s . There a r e , however, f u r t h e r a s p e c t s which have not been touched upon by WHISPER, and a l s o f u r t h e r examples of problems whose s o l u t i o n s a r e s i m p l i f i e d by a p p e a l i n g t o a n a l o g u e s . D i f f e r e n t a s p e c t s o f analogues a r e , of c o u r s e , a p p l i c a b l e t o d i f f e r e n t problem domains; t h i s i s one re a s o n they a re not a l l demonstrated by WHISPER. To t a k e f u r t h e r advantage o f a n a l o g u e s , as w e l l as t o a p p l y them f o o t h e r domains, would r e q u i r e e x t e n s i o n s and m o d i f i c a t i o n s t o th e c u r r e n t system. On the b a s i s of the c u r r e n t i m p l e m e n t a t i o n i t s h o u l d be c l e a r t h a t o n l y r e a s o n a b l e e x t e n s i o n s to the p e r c e p t u a l p r i m i t i v e s would be r e g u i r e d i n o r d e r to handle the examples d i s c u s s e d below. The g u a l i t a t i v e knowledge i s the domain dependent p a r t of the system, and as a r e s u l t would r e q u i r e almost complete replacement w i t h the knowledge r e l e v a n t t o any new domain. The f e a s i b i l i t y of u s i n g analogues i n problem s o l v i n g has been demonstrated, I b e l i e v e , by t h e WHISPER system; the g e n e r a l i t y of u s i n g a n a l o g u e s , e s p e c i a l l y d i a grammatic a n a l o g u e s , f e l l o w s from the examples below. 142 I V - 4 x l _ E e h a y i o u r a l _ A d y a n t a ges One of the main advantages of ana logues i s t h a t i t i s p o s s i b l e t o r e p r e s e n t a c t i o n by ana logous a c t i o n . There i s a d i f f e r e n c e between the d e s c r i p t i v e e n c a p s u l a t i o n of a c t i o n i n laws of b e h a v i o u r , and the r e p r e s e n t a t i o n o f a c t i o n by analogy t o dynamic b e h a v i o u r . I t i s c o m p u t a t i o n a l l y e a s i e r to reason about a c t i o n by analogy t o some p r i m i t i v e behav iour than to r e a s o n wi th d e n o t a t i v e d e s c r i p t i o n s of a c t i o n . In a g iven s i t u a t i o n the e f f e c t s o f an a c t i o n propagate u n t i l a l l the r a m i f i c a t i o n s of the a c t i o n are f e l t . I f t h i s s i t u a t i o n i s used as an analogue to r e p r e s e n t another s i t u a t i o n , and i f the a n a l o g y i s s t r o n g enough, then the e f f e c t s which are propagated i n the analogue w i l l c o r r e s p o n d to e f f e c t s which f o l l o w from an a n a l o g o u s a c t i o n performed i n the r e p r e s e n t e d s i t u a t i o n . The • f r a m e ' problem i s concerned p r e c i s e l y wi th t h i s p r o p a g a t i o n of the s i d e e f f e c t s o f a c t i o n s , which i s why analogues overcome ( f o r those s i t u a t i o n s i n which an analogue can be found) the ' .frame* prob lem. IHISPEfi has a l r e a d y demonstrated some of the b e h a v i o u r a l advantages which r e s u l t from the use of a n a l o g u e s . ahen the a c t i o n of moving an o b j e c t i s performed i n the d iagrammat ic ana logue the s i d e e f f e c t s of the chang ing c o n t a c t and suppor t r e l a t i o n s h i p s , the changing shape of s u r f a c e s over which o b j e c t s might s l i d e , the chang ing shape of empty s p a c e , and the unchanging s h a p e s , a r e a s , and p o s i t i o n s of the unmoved o b j e c t s , 143 a r e a l l p r o p a g a t e d c o r r e c t l y and i n an a n a l o g o u s manner t o t h e way i n w h i c h t h e s e r e l a t i o n s h i p s c h a n g e o r r e m a i n u n c h a n g e d i n t h e p h y s i c a l w o r l d t h e d i a g r a m r e p r e s e n t s . A d i s c u s s i o n o f t h r e e o t h e r t y p e s c f b e h a v i o u r a l a d v a n t a g e s - s t i c k i n e s s , i m p l i c i t d e r i v a t i o n , and a m a l g a m a t i o n - f o l l o w s . l I z i j . l i J _ S t i c k i n e s s B e c a u s e o f t h e s t r u c t u r a l c o n n e c t i o n b e t w e e n e l e m e n t s i n an a n a l o g u e , a c h a n g e made t o one o f i t s e l e m e n t s a u t o m a t i c a l l y e f f e c t s i t s o t h e r e l e m e n t s . I f an a n a l o g u e i s u s e d t o r e p r e s e n t some s i t u a t i o n S , t h e n an a c t i o n i n S i s r e p r e s e n t e d by mak ing a c o r r e s p o n d i n g c h a n g e t o t h e a n a l o g u e ; s i n c e t h e e f f e c t s o f t h e c h a n g e p r o p a g a t e i n t h e a n a l o g u e , t h e s i d e e f f e c t s o f t h e a c t i o n i n S a r e p r o p e r l y r e p r e s e n t e d by i t . The p r o p e r t y o f c o r r e c t l y r e p r e s e n t i n g t h e s i d e e f f e c t s o f an a c t i o n I c a l l s t i c k i n e s s , b e c a u s e o f t h e a p p a r e n t b o n d e x i s t i n g b e t w e e n d i f f e r e n t e l e m e n t s i n t h e r e p r e s e n t a t i o n . U n d e r c e r t a i n c o n d i t i o n s t h e y b e h a v e a s i f t h e y ware ' s t u c k ' t o g e t h e r i n s u c h a way t h a t a c h a n g e t o one a u t o m a t i c a l l y c a u s e s a c h a n g e t c a n o t h e r . T h e s t i c k i n e s s p r o p e r t y h a s a d i r e c t b e a r i n g on t h e • f r a m e ' p r o b l e m d i s c u s s e d i n s e c t i o n I I - 7 . 1 . The e x a m p l e d i s c u s s e d b e l o w i s v e r y s i m i l a r t o fiaphael's e x a m p l e o f a r o b o t p u s h i n g a b o x w h i c h h a s a n o t h e r box r e s t i n g on t o p o f i t . When t h e l o w e r box i s p u s h e d t h e u p p e r one moves a s w e l l . T h i s i s 144 e s s e n t i a l l y the same as an example given by Hayes^ "Consider, f o r i n s t a n c e , a cup on a saucer. I f we move the sauce r , the cup moves t o o : but i f we move the cup, the saucer s t a y s where i t i s . I t i s not d i f f i c u l t t c inv e n t a r b i t r a r i l y complicated examples of t h i s k i n d . " 2 6 For the present, l e t us c o n s i d e r a method f o r an example of t h i s complexity. The s i t u a t i o n d e p i c t e d i n the diagram of f i g u r e I V - 1 , an a e r i a l view of a c o l l e c t i o n of boxes, might g u i t e p o s s i b l y be represented by the s e t of a s s e r t i o n s (IN E A) (IN C B) (IN Y X) (IN X fi) (IN C A) (IN Y fl) (IN H G ) . 2 7 Hoving box B from A t o G would i n t h i s r e p r e s e n t a t i o n i n v o l v e the removal of the a s s e r t i o n (IN B A) and the a d d i t i o n of the a s s e r t i o n (IN B G). The problem with t h i s scheme i s that C has been l e f t behind. A t y p i c a l s o l u t i o n to t h i s d i f f i c u l t y i s the i n t r o d u c t i o n of a demon procedure which would be invoked whenever an a s s e r t i o n of the form (IN A B) i s e i t h e r added or removed from the data base. T h i s s o l u t i o n has s e v e r a l disadvantages. To begin with i t i s necessary t o f o r e s e e that the d i f f i c u l t y w i l l a r i s e , A demon procedure must be w r i t t e n which can determine i f th e r e are any extraneous boxes whose containment r e l a t i o n s h i p s r e g u i r e t i d y i n g up, and which knows how t c a p p r o p r i a t e l y modify c o n t e n t s of the database. Given the e x i s t e n c e of such a demon, i t i s necessary t h a t i t be invoked every time a containment r e l a t i o n i n the database i s changed. Often t h i s w i l l be done t o t a l l y u n n e c e s s a r i l y when a box c o n t a i n s no ether boxes. 146 These problems can be avoided by basing a r e p r e s e n t a t i o n of the containment r e l a t i o n s on an analogy with the n e s t i n g s t r u c t u r e of a LISP l i s t . Thus the l i s t : (SCENE (A (X (I)) <E (C)}) (G (H) ) ) would represent the i n i t i a l s i t u a t i o n . The CDS of any element of the l i s t r e p r e s e n t s the s e t of elements c o n t a i n e d by that element which i s the CAR of the l i s t . The l i s t and the procedures which operate on i t together are an analogue of the containment r e l a t i o n f o r the boxes. In t h i s r e p r e s e n t a t i o n moving an o b j e c t i s represented by a corresponding rearrangement of the p o i n t e r s to the l i s t of which the o b j e c t i s the f i r s t element. A f t e r B i s moved the s i t u a t i o n i s r e p r e s e n t e d by the l i s t : (SCENE (A (X (Y) ) (G (B (C) ) (H) ) ) . In moving B no e x p l i c i t r e f e r e n c e need be made to C. A knowledge of C*s e x i s t e n c e i s not even necessary. In comparison to the demon s o l u t i o n there are s e v e r a l advantages. There i s no need to foresee the need f o r a s p e c i a l s i d e e f f e c t procedure or to execute i t . Furthermore, the amount of computation i n v o l v e d i n moving E does not i n c r e a s e as a f u n c t i o n of the number of o b j e c t s i t c o n t a i n s as i t does with the demon method. Thus there i s a s u b s t a n t i a l d i f f e r e n c e between the way i n which C a u t o m a t i c a l l y moves i n the analogue and the way i n which i t must be e x p l i c i t l y moved i n the d e s c r i p t i v e r e p r e s e n t a t i o n . 147 HZHXIJL 2_I J J j l i c i t _ Pg£,ivation F i g u r e IV-2 d e p i c t s a geometry example. Two r e p r e s e n t a t i o n s of the t r i a n g l e ABC are g i v e n , one diagrammatic, the other i n terms of i t s vertex c o o r d i n a t e s . An advantage t o using the diagrammatic r e p r e s e n t a t i o n a r i s e s i f one makes a geometric c o n s t r u c t i o n , e.g. j o i n i n g p o i n t s A and D. The new p o i n t , 1, c r e a t e d by i n t e r s e c t i n g AD and EC, i s a u t o m a t i c a l l y present i n the diagram, whereas i t must be e x p l i c i t l y computed i n the c o o r d i n a t e r e p r e s e n t a t i o n . The c o n s t r u c t i o n would be represented by the simple a d d i t i o n of the a s s e r t i o n (SEGMENT A D ) , but t h i s does not produce the new p o i n t . Adding the a s s e r t i o n t r i g g e r s a demon which computes any p o s s i b l e i n t e r s e c t i o n t h a t AD might make with a l l other l i n e s {curved or s t r a i g h t ) . T h i s has s e v e r a l disadvantages. The p o s s i b i l i t y t h a t a new p o i n t w i l l be c r e a t e d by the c o n s t r u c t i o n of a l i n e segment must be a n t i c i p a t e d i n order t h a t the demon be w r i t t e n . The demon must be reasonably complex i n t h a t i t must know how to c a l c u l a t e the i n t e r s e c t i o n of a l i n e segment with any p o s s i b l e curve which can occur . I f a new curve type i s i n t r o d u c e d , the demon must be expanded to handle i t . When a l i n e segment i s c o n s t r u c t e d the demon procedure may be c a l l e d t o t a l l y u n n e c e s s a r i l y i f the segment does not i n t e r s e c t any ether curves. More important, however, i s t h a t the p o s s i b l e i n t e r s e c t i o n of the new segment with each W8 (Coordinates A 0 0) (Coordinates B 5 1) (Coordinates C 6 -4) (Segment A B) (Segment A C) (Segment B C) (Coordinates D 9 -3) FIG-URE BT-a 149 of the ether curves must be considered separately. In the diagram the new point i s derived i m p l i c i t l y through the two-dimensional structure of the diagram, and the e x p l i c i t representation of a l l the points constituting the curves. The new point must of course be recognized as such, but i t exists without the need of additional computation, i r r e s p e c t i v e cf the existence of a procedure for i t s recognition. A procedure which recognizes i n t e r s e c t i o n points could be written using the WHISPEB re t i n a . It i s not necessary that the point be recognized when i t f i r s t appears and continually re-established every time a change i s made tc the diagram. I t i s possible that a construction could have some other effect which would in the proof of some theorem lead to other constructions. Only then would the f i r s t i n t e r s e c t i o n point become s i g n i f i c a n t . The point can be ignored u n t i l such time as the examination of the diagram for the set of a l l points i s motivated by a reguirement of the proof process. The point w i l l s t i l l c o r r e c t l y exist even though no computation has been expended to update i t . IV - 4^ .1^  3_ T h e_ A male} am at i c n_ P r c b 1 e m A common problem i s the description of a s i t u a t i o n which r e s u l t s from the combination of the descriptions of two or more other situations. The o r i g i n a l descriptions must be amalgamated i n some way to form a new one. For example, what 150 i s the shape of the f i g u r e formed by a l i g n i n g p o i n t s A with Y and B with Z of the f i g u r e s ABC and 1XYZ such t h a t C l i e s o u t s i d e 8XYZ where the c o o r d i n a t e s of the p o i n t s are: A (0,0), B(3,0), C{3,2), W (9.9,3), X(7,4.2), Y(3,6), and Z{9.6,2)? Combining the two d e s c r i p t i o n s shown i n f i g u r e IV-3 i s a simple matter of p l a c i n g the designated s i d e s t o g e t h e r . T h i s i s the f i n a l d e s c r i p t i o n . I t i s not necessary to r e c o g n i z e t h i s shape as a sguare. The shape i s i t s own d e s c r i p t i o n . The two d e s c r i p t i o n s have been amalgamated and are ready f o r f u r t h e r p r o c e s s i n g . One r e s u l t which might he computed from i t i s that i t belongs t o the c l a s s of sguares. Another example of the amalgamation problem a r i s e s i n the space planning problems d e s c r i b e d by Eastman 2 8 i n which f u r n i t u r e c r machinery i s to be placed i n a room so as to s a t i s f y a g i v e n s e t cf c o n s t r a i n t s . The o r i g i n a l s p e c i f i c a t i o n of these c o n s t r a i n t s has the form: 'the s o f a must be a g a i n s t the w a l l * and * i t must be p o s s i b l e to see out the window from the s o f a * . To f i n d the s e t of a l l p o s i t i o n s s a t i s f y i n g these c o n s t r a i n t s i t i s necessary to combine the c o n s t r a i n t s i n some way which i s mere meaningful than t h e i r simple c o n j u n c t i o n . Eastman suggests a technigue which he d i d not implement c a l l e d £L22S£^il^-l2£^i:9Q-2SE§I.^H2^» which i s based on the use of a diagrammatic analogue of the room, o b j e c t s , and c o n s t r a i n t s . His suggestion i s to d i s p l a y a schematic of the room at a g r a p h i c s t e r m i n a l , and then to shade that space i n which the next o b j e c t to be l o c a t e d i s c o n s t r a i n e d to l i e . The shaded / 5 | 152 area r e p r e s e n t s the c o n s t r a i n t on the o b j e c t ' s p o s s i b l e p o s i t i o n s , and the c o n j u n c t i o n of one or more c o n s t r a i n t s i s represented by the g r e a t e r screen i n t e n s i t y r e s u l t i n g i n the areas where the shading o v e r l a p s . The c o n s t r a i n t space i s thus represented by space on the scree n , and the way i n which c o n s t r a i n t s i n t e r a c t i s represented by the analogous way i n which m u l t i p l e shading of the screen r e s u l t s i n i n c r e a s e d i n t e n s i t y . Amalgamating the c o n s t r a i n t s on the o b j e c t s to be placed i n the room i s t h e r e f o r e very easy. Eastman's p r o p o s a l f a c i l i t a t e s human i n t e r a c t i o n with the problem s o l v i n g program. The r e p r e s e n t a t i o n o f the c o n s t r a i n t space, by space on the gr a p h i c s t e r m i n a l screen would be very u s e f u l t o a human problem s o l v e r ; there i s no reason why i t should not be as u s e f u l t o a problem s o l v i n g program i f a r r a y space were used i n s t e a d of gr a p h i c s screen space. Greater screen i n t e n s i t y c o u l d be represented by ar r a y elements of gr e a t e r magnitude, and the array c o u l d be examined by WHISPEB's eye. I t i s easy f o r WHISPEB to amalgamate the d e s c r i p t i o n s of i t s o b j e c t s . I t r e f e r s to the o b j e c t s by the array values which compose them, so combining two o b j e c t s i n t o a new o b j e c t o n l y r e g u i r e s the c o n s t r u c t i o n of a name which i s the union of t h e i r v a l u e s . The combined set of p o i n t s of both o b j e c t s i s the complete d e s c r i p t i o n of the new o b j e c t . A l l the p r o p e r t i e s which are needed i n d e c i d i n g i t s s t a b i l i t y are d e r i v a b l e from t h i s d e s c r i p t i o n . The amalgamation of the d e s c r i p t i o n s cf the 153 c o n t o u r of o b j e c t s i s e s s e n t i a l l y a by - p r o d u c t o f the amalgamation o f o b j e c t d e s c r i p t i o n s . I V - 4 A 2 _ C o n f i g u r a t i o n a l _ A d y a n t a g e s The c o n f i g u r a t i o n a l advantages d e r i v e from the r e p r e s e n t a t i o n o f r e l a t i o n s by analogous r e l a t i o n s , i n c o n t r a s t t o the b e h a v i o u r a l advantages which d e r i v e from the r e p r e s e n t a t i o n o f a c t i o n by analogous a c t i o n . S t a t i c s t a t e s or c o n f i g u r a t i o n s of an analog u e . A, of a s i t u a t i o n , S, c o r r e s p o n d i n a s i m p l e way to c o n f i g u r a t i o n s of S. P a r t s of A c o r r e s p o n d t o p a r t s o f S, and r e l a t i o n s between p a r t s c f A cor.respc.nd to r e l a t i o n s between p a r t s of S. As S l o m a n 2 9 has p o i n t e d o u t t h i s means t h a t r e l a t i o n s h i p s o f S are r e p r e s e n t e d by A wi t h o u t b e i n g e x p l i c i t l y named i n A. An i m p o r t a n t conseguence of not havi n g t o name the r e l a t i o n s h i p s i s t h a t an analogue can e x p l i c i t l y r e p r e s e n t many more o f them t h a n would o t h e r w i s e be f e a s i b l e . For example, t h e d i s t a n c e r e l a t i o n s h i p s between a l l p a i r s o f g e o g r a p h i c a l p o i n t s i s e x p l i c i t l y r e p r e s e n t e d by the d i s t a n c e r e l a t i o n s h i p s between c o r r e s p o n d i n g p a i r s o f p o i n t s on a map. I t would not be p o s s i b l e t o s t o r e t h i s p o t e n t i a l l y i n f i n i t e s e t o f r e l a t i o n s h i p s i f each had t o be e x p l i c i t l y s t a t e d . Some examples i n which t h e r e p r e s e n t a t i o n of such r e l a t i o n s h i p s i s i m p o r t a n t are d i s c u s s e d below. 154 I V-4_. 2 A J _ F i r s t _ A PJDT oximat i on _ B i agrams One of the h e u r i s t i c s t h a t Polya emphasizes ahcut s o l v i n g problems i s to draw a f i g u r e i l l u s t r a t i n g the data, A problem he d i s c u s s e s to which I w i l l g ive a r e l a t e d but somewhat d i f f e r e n t approach i s : "He are given three p o i n t s A # E, and C. Draw a l i n e through A which passes between B and C and i s at egual d i s t a n c e s from E and c . " 3 0 The s o l u t i o n to c o n s t r u c t i o n problems of t h i s s o r t i s not r e a l l y the f i n a l diagram but an a l g o r i t h m f o r i t s c o n s t r u c t i o n , A d e t a i l e d account of a computer program which s o l v e s g e o m e t r i c a l c o n s t r u c t i o n problems i s given by F u n t 3 1 A diagram of the problem would a c t as a model and c o u l d be used i n the same f a s h i o n as G e l e r h t e r ' s Geometry M a c h i n e 3 2 d i d f o r the proof of theorems. G e l e r n t e r ' s system i s provided with the diagrams i t uses as models i n the form of a c o o r d i n a t e s p e c i f i c a t i o n of t h e i r p o i n t s ; however, c r e a t i n g the diagrams from the hypotheses of a theorem or the statement of a problem i s g e n e r a l l y a n o n - t r i v i a l task. V i s u a l feedback from the diagrams as they are being c o n s t r u c t e d can be used to bootstrap from a diagram on l y p a r t i a l l y f u l f i l l i n g the c o n d i t i o n s of the problem to one which completely s a t i s f i e s them. A p a r t i a l diagram f o r Polya*s example would be j u s t the three p o i n t s as i n f i g u r e IV-4. A l i n e can then be drawn through A i n any d i r e c t i o n and then r o t a t e d ( f i g u r e IV - 5 ) about A u n t i l the d i s t a n c e s between i t and the p o i n t s B and C are egua l . Measurement i s the b a s i s of I 55* A c F I G U R E TSL-5. 156 t h i s t e s t . The r o t a t i o n could be accomplished by WHISPEB's v i s u a l i z a t i o n process or i t could be done by the systematic generation of new l i n e s . The main point i s that feedback from the diagram i s used both to t e s t f o r the c o n d i t i o n and to suggest a b e t t e r o r i e n t a t i o n f o r the l i n e ; c o n s t r u c t i n g a diagram which looks c o r r e c t i n t h i s way i s e a s i e r than s o l v i n g the o r i g i n a l problem. In the f i n a l diagram, f i g u r e I V - 6 , a l l the r e l a t i o n s h i p s expressed i n the problem statement are e x p l i c i t l y represented. I t i s an analogue of the more general e n t i t y described by the c o n d i t i o n s of the problem. A l l the r e l a t i o n s h i p s between the g e n e r a l i z e d points fl,E,and C, and the generalized l i n e passing through A hold i n the diagram between the s p e c i f i c points marked by the dots on the paper. Thus, i n t h i s case at l e a s t , an analogue i s a model of the problem. I t i s necessary to d i s t i n g u i s h two analogues i n t h i s example. These a r e : the a n a l o g i c a l r e p r e s e n t a t i o n of the three points and a random l i n e used to help i n the c o n s t r u c t i o n of the f i n a l model, and the f i n a l model i t s e l f , also an analogue. A f t e r the approximate o r i e n t a t i o n of the l i n e i s determined by feedback the problem i s e a s i l y solved using the a n a l o g i c a l p r o p e r t i e s of the diagram. Connecting points E and C r e s u l t s i n the i n t e r s e c t i o n point D. An i n s p e c t i o n of the diagram now r e v e a l s that BD and CD are of egual length { f i g u r e IV-7); t h i s i s the key to the problem. The diagram i s e s s e n t i a l to i t s discovery. '57 FIGURE T f f - 7 158 S t r o n g c l u e s t o the d e r i v a t i o n of the f i n a l s o l u t i o n are p r o v i d e d by a p p r o x i m a t i o n d iagrams, s i n c e r e l a t i o n s h i p s between p a r t s i n t h e s p e c i a l i z e d s i t u a t i o n s they d e p i c t have s t r o n g a n a l o g i c a l c o r r e s p o n d e n c e s w i t h t h e g e n e r a l r e l a t i o n s h i p s i n t h e a b s t r a c t g e o m e t r i c a l s i t u a t i o n . These c o r r e s p o n d e n c e s p r o v i d e some j u s t i f i c a t i o n f o r t u r n i n g a s p e c i f i c r e l a t i o n s h i p i n t h e diagram i n t o a g e n e r a l h y p o t h e s i s about the g e n e r a l v a l i d i t y of the r e l a t i o n s h i p . P r o v i n g t h i s h y p o t h e s i s becomes a s u b g o a l of t h e o r i g i n a l problem. I n the c u r r e n t example, e s t a b l i s h i n g BD=CD as a w o r t h w h i l e h y p o t h e s i s i s t h e most f o r m i d a b l e p a r t of the problem; p r o v i n g t h i s h y p o t h e s i s i s not d i f f i c u l t . iXr i i * 2* 2_ Ch a ng,i n g _ l ey e l _ G f _ D e t a i l 8e are a l l f a m i l i a r w i t h t h e e x p e r i e n c e of b e i n g so near t o a p i c t u r e t h a t i t i s u n i n t e l l i g i b l e , w h i l e s t a n d i n g back from i t makes i t s u d d e n l y u n d e r s t a n d a b l e . T h i s i s p a r t i c u l a r l y common w i t h d i g i t a l l y produced p i c t u r e s on a l i n e p r i n t e r . F i n e d e t a i l seen c l o s e t o the p i c t u r e , e.g. t h e i n d i v i d u a l c h a r a c t e r s i n t h e p r i n t o u t , or p a t t e r n s or words they might f o r m , i s i r r e l e v a n t t o the i n t e r p r e t a t i o n o f the p i c t u r e . The p i c t u r e must be examined a t a g r o s s e d l e v e l o f d e t a i l as some v i s i o n systems ( K e l l y 3 3 and S h i r a i 3 * ) have done. The e x t r a n e o u s d e t a i l cannot j u s t be i g n o r e d , i t must be smoothed o r b l u r r e d i n such a way t h a t the i m p o r t a n t g u a l i t i e s of the 159 next l e v e l of d e t a i l axe not s i m u l t a n e o u s l y e l i m i n a t e d . The amazing t h i n g i s t h a t the pxocess of moving away from the p i c t u r e c r e a t e s e x a c t l y the r i g h t kind of t r a n s i t i o n from one l e v e l of d e t a i l t c another. T h i s smoothing i s a f u n c t i o n of the o p t i c s of the s i t u a t i o n and the f i x e d r e s o l v i n g power of the eye. The d e t a i l e l i m i n a t e d and t h a t r e t a i n e d i s a consequence of the p h y s i c s of the s i t u a t i o n , not of the e x e c u t i o n of any f i l t e r i n g a l g o r i t h m . The p h y s i c s of the s i t u a t i o n d i c t a t e s t h a t p r o x i m i t y i s the b a s i s of the b l u r r i n g . Thus, neighbouring elements meld. Part of the e f f e c t of b l u r r i n g i s to t u r n d i g i t a l data i n t o a form which has more of the c h a r a c t e r i s t i c s of continuous data. Smoothing reduces the number of d i s c r e t e f a c t s which have t o be d e a l t with. Formal r e p r e s e n t a t i o n s have a d i g i t a l or d i s c r e t e q u a l i t y i n that they are composed of a l a r g e number of d i s t i n c t axioms or a s s e r t i o n s . The problem i s t h a t there i s no easy way to b l u r an axiom or a group of axioms. The problem o f b l u r r i n g axioms i s M i n s k y ' s 3 5 nearness problem: I f we know Near (A,B) and Near(B,C) then under c e r t a i n circumstances i t would be c o r r e c t to deduce Near (A,C); but t h i s cannot continue i n d e f i n i t e l y f o r Near(C,D) and so on, because at some p o i n t i t w i l l not be the case t h a t A i s near X where X i s r e l a t e d to A by a s u f f i c i e n t l y l o n g c h a i n of nearness l i n k s . The proximity of p o i n t s i n a diagram i s not e x p l i c i t l y c h a r a c t e r i z e d by statements of t h i s k i n d , but i s a f u n c t i o n of the diagram's t o p o l o g i c a l s t r u c t u r e . The r e s u l t i s a smooth t r a n s i t i o n of 160 the r e l a t i o n s h i p between p o i n t s as the context and l e v e l of d e t a i l i n viewing them changes. B l u r r i n g which i s based on pr o x i m i t y may or may not be a u s e f u l t r a n s f o r m a t i c n of d e t a i l , depending cn what i s r e p r e s e n t e d by the diagram's proxi m i t y s t r u c t u r e . In many cases p h y s i c a l p r o x i m i t y i n a diagram does seem to i n d i c a t e a k i n d of o r g a n i z a t i o n a l p r o x i m i t y i n the domain represented. A l s o grouping on the b a s i s of p r o x i m i t y i s f r e q u e n t l y a b e n e f i c i a l r e o r g a n i z a t i o n of the s i t u a t i o n r epresented. For example, c l u s t e r s of boxes on a f l o w c h a r t or components i n a c i r c u i t diagram are o f t e n i n d i c a t i v e of a c l u s t e r i n g on the f u n c t i o n a l l e v e l . Elements r e l a t e d by t h e i r p h y s i c a l proximity f u n c t i o n together c l o s e l y as part of a l a r g e r g l o b a l module. The c o l o u r spectrum produced by a prism has p r o x i m i t y of frequency represented by s p a t i a l p r o x i m i t y . In normal musical n o t a t i o n p r o x i m i t y i n the v e r t i c a l corresponds to proximity i n freguency while p r o x i m i t y i n the h o r i z o n t a l corresponds to p r o x i m i t y i n time. Although i t i s not the case i n a l l of these examples that a p p r o p r i a t e c l u s t e r i n g w i l l a u t o m a t i c a l l y occur simply by moving away from the diagram, the e x p l i c i t r e p r e s e n t a t i o n of a proximity r e l a t i o n s h i p i n the s i t u a t i o n of i n t e r e s t by analogy to the s p a t i a l p r o x i m i t y of marks i n a diagram f r e q u e n t l y means t h a t changing the l e v e l of d e t a i l at which the diagram i s viewed r e s u l t s i n an a p p r o p r i a t e and c o r r e s p o n d i n g change i n the l e v e l of d e t a i l at which the represented s i t u a t i o n i s c o n s i d e r e d . I f the proximity 161 i n f o r m a t i o n of a s i t u a t i o n i s not contained i n a r e p r e s e n t a t i o n , then i t i s very d i f f i c u l t to vary the l e v e l of d e t a i l at which the s i t u a t i o n i s to be c o n s i d e r e d . S i n c e the r e s o l u t i o n of the eye decreases with the d i s t a n c e from the c e n t e r of the r e t i n a , f i x a t i n g the eye at a d i f f e r e n t l o c a t i o n while maintaining i t a t a f i x e d d i s t a n c e from the diagram a l s o r e s u l t s i n a r e s t r u c t u r i n g of d e t a i l . The b l u r r i n g e f f e c t i s s i m i l a r t o t h a t a l r e a d y discussed except i n t h i s case the r e s o l u t i o n i s v a r y i n g while the d i s t a n c e remains f i x e d , whereas i n the previous case the d i s t a n c e was v a r i e d while the r e s o l u t i o n remained f i x e d . Changing the f i x a t i o n point changes the r e l a t i v e a t t e n t i o n paid to the d e t a i l i n d i f f e r e n t p a r t s of the diagram. The c o a r s e r d e t a i l of the surrounding area provides a context f o r the f i n e r d e t a i l a t the f i x a t i o n p o i n t . In a sense the diagram i s being viewed s i m u l t a n e o u s l y from v a r y i n g d i s t a n c e s . The s t r u c t u r e which remains a f t e r b l u r r i n g on the p e r i p h e r y e s t a b l i s h e s a context f o r i n t e r p r e t i n g the s t r u c t u r e of the d e t a i l e d unblurred i n f o r m a t i o n on the c e n t r a l p o r t i o n of the r e t i n a , ' I1ZB.JL2± 3_Planning An obvious example of p l a n n i n g i s d i s c o v e r i n g a path between two p o i n t s along which a given o b j e c t can be moved. A s t r a i g h t l i n e j o i n i n g the two p o i n t s i s a f i r s t order p l a n . I f t h i s p l a n i s represented a n a l o g i c a l l y as a l i n e i n a diagram, 16 2 then the plan can be examined to f i n d the bugs i n i t . I t i s easy t c a n t i c i p a t e c o l l i s i o n s by simply l o o k i n g at the amount of empty space near the path. I f at some p o i n t the d i s t a n c e between the path and another o b j e c t i s l e s s than the ' r a d i u s ' of the o b j e c t to be moved, then a c o l l i s i o n w i l l r e s u l t . The c o l l i s i o n p o i n t s can be d e a l t with i n the order they a r i s e on the path and be e l i m i n a t e d by i n t r o d u c i n g detours. I t i s important t h a t a d e t a i l e d a n a l y s i s of p o s s i b l e c o l l i s i o n s i s r e g u i r e d at only a few p o i n t s , and not a t a l l (or even a f i n i t e approximation to a l l ) p o i n t s along the path. a d d i t i o n a l l y , i t i s g e n e r a l l y s t r a i g h t f o r w a r d to determine a detour which w i l l circumvent the d i f f i c u l t y without much t r o u b l e , because i t can be seen whether or not the c o l l i s i o n i s a r e s u l t of o b j e c t s on only one s i d e of the proposed path. Without the e x p l i c i t r e p r e s e n t a t i o n of empty space and the p r o x i m i t y r e l a t i o n s h i p of the path to o b j e c t s i n the environment, these two advantageous f a c t o r s would not r e s u l t . C l e a r l y , the t h r e e - d i m e n s i o n a l v e r s i o n of t h i s problem i s more d i f f i c u l t than the two-dimensional case j u s t d i s c u s s e d . There are two s o l u t i o n s : use a t h r e e - d i m e n s i o n a l analogue such as a s c a l e model, or decompose the t h r e e - d i m e n s i o n a l case i n t o a sequence of two-dimensional problems. I t h i n k t h a t most of the problems which people are able fo s o l v e e a s i l y can be handled by the decomposition method. I f a problem i s d i f f i c u l t , then o f t e n a 3-D s c a l e model i s b u i l t or the problem i s d i r e c t l y present i n the world, so the world serves as i t s 163 own r e p r e s e n t a t i o n . The type of planning which can be accomplished i s very s i m i l a r to the two-dimensional case whichever method i s used. As an example of a problem whose ease of s o l u t i o n i s h i g h l y dependent on the c o n f i g u r a t i o n a l a spects of analogues, I w i l l d i s c u s s the problem d e p i c t e d i n f i g u r e IV-8, o r i g i n a l l y proposed by Sloman as an example of a n a l o g i c a l i n f e r e n c e . The diagram r e p r e s e n t s the usual i d e a l s i t u a t i o n of most Ph y s i c s problems: two r i g i d rods, attached fo an u n s t r e t c h a b l e s t r i n g p assing over a f r i c t i o n l e s s p u l l e y . Sloman suggests t h a t i f the arrows r e p r e s e n t the d i r e c t i o n of motion of the ends of the r i g i d rods, the i n f e r e n c e from f i g u r e IV-8 to f i g u r e IV-9 i s v a l i d and t h a t anyone who does not understand t h i s can be helped by i n t r o d u c i n g e x t r a arrows as i n f i g u r e IV-10. He then poses the problem of how these i n t e r m e d i a t e arrows are i n s e r t e d . I w i l l sketch how a 5JHISPEE-like system might s o l v e t h i s problem. For c o n t r a s t , I s h a l l f i r s t o u t l i n e how a system r e l y i n g e n t i r e l y on a d e s c r i p t i v e r e p r e s e n t a t i o n , and not on any analogue of t h e problem, might proceed. The problem s i t u a t i o n c o u l d be d e s c r i b e d by the statements l i s t e d i n f i g u r e I?-11 i n a d d i t i o n t o a scheme f o r d e s c r i b i n g the shapes and p o s i t i o n s of the r i g i d o b j e c t s . Notice t h a t the s t r i n g has been d e s c r i b e d F I G U R E TST-8 R J 1 » I A ' ( R i g i d Rod R l ) ( R i g i d Rod R2) ,:, (Wedge Wl) (Wedge W2) ( P u l l e y P) ( S t r i n g S) (Length S i s d) (Fastened S to R l ) (Fastened S to R2) (Runs-thru P S) / / ? (Endpoints-of S (X2,Y2) (X3,Y3) ) (Radius P i s r ) ( P i v o t P (X5.Y5) ) (Endpoints-of R l (XI,YI) (X2,Y2) ) (Endpoints-of R2 (X3,Y3) (X4,Y4) ) F I G U R E E T - r t l 166 by i t s l e n g t h and the o b j e c t s w i t h which i t i n t e r a c t s , r a t h e r than by i t s shape. The problem can then be s t a t e d : what happens t o the r i g h t end of r o d E2 when the l e f t end cf E1 moves upwards. The type of p h y s i c a l knowledge r e g u i r e d would i n v o l v e p r o c e d u r e s f o r : d e t e r m i n i n g t h a t t h e rods p i v o t about t h e i r s u p p o r t i n g wedges; t h a t as one end o f a p i v o t e d r o d goes up, the o t h e r goes down; t h a t when one end o f a t a u t s t r i n g i s p u l l e d , t h e o t h e r end moves an e g u a l d i s t a n c e o r e x e r t s an e g u a l f o r c e ; and t h a t a f r i c t i o n l e s s , f i x e d p o s i t i o n p u l l e y does not a f f e c t a s t r i n g i n any way o t h e r t h a n by changing i t s shape and d i r e c t i o n . When the problem s o l v i n g p r o c e s s b e g i n s , t h e r e i s no immediate c o n n e c t i o n between the two r o d s ; t h e r e i s n o t h i n g which g i v e s any h i g h e r p r i o r i t y t o a c o n s i d e r a t i o n of t h e s t r i n g as the c a u s a l c o n n e c t i o n between the rods than t o a c o n s i d e r a t i o n of the p o s s i b i l i t y of one rod h i t t i n g t h e e t h e r , o r any o t h e r p o s s i b l e c a u s a l c o n n e c t i o n between them. Thus many of t h e problems o f f o l l o w i n g u n f r u i t f u l s e a r c h paths and ha v i n g t o b a c k t r a c k and e x p l o r e a l t e r n a t e paths w i l l a r i s e . An even more s e r i o u s problem w i l l a r i s e , however, i n f o l l o w i n g the c o n n e c t i o n v i a the s t r i n g when i t i s c o n s i d e r e d . I n o r d e r f o r t h e s t r i n g s p e c i a l i s t t o work i t must know whether o r not t h e s t r i n g i s t a u t b e f o r e i t can d e c i d e what f o r c e w i l l o c c u r a t the t a i l end of the s t r i n g . The problem s o l v e r must be on the a l e r t f o r a s i t u a t i o n such as t h a t c f f i g u r e IV-12. A t a u t n e s s s p e c i a l i s t might know t h a t a s t r i n g i s t a u t when the l e n g t h of t h e s h o r t e s t p a t h between the s t r i n g ' s ends p a s s i n g 168 around a l l t h e o b s t a c l e s the s t r i n g goes around e q u a l s the l e n g t h of the s t r i n g i t s e l f . I f t h e s h o r t e s t path i s s h o r t e r than t h e s t r i n g , t h e r e must be an e x t r a w i g g l e i n the s t r i n g which i m p l i e s seme s l a c k n e s s . I n many r e s p e c t s d e t e r m i n i n g whether or not the s t r i n g i s t a u t appears t o be a geometry problem of the same o r d e r o f d i f f i c u l t y as t h e o r i g i n a l problem. I n the c u r r e n t example i t r e q u i r e s f i n d i n g the d i s t a n c e from each r o d t o t h e p u l l e y and the d i s t a n c e around the p u l l e y . Without changing t h e p h y s i c s of the s i t u a t i o n a t a l l , t h e problem would become mere d i f f i c u l t i f the s i n g l e p u l l e y was r e p l a c e d by two o r more p u l l e y s , or by an o b s t a c l e o f more complex shape { f i g u r e I V - 1 3 ) . I n a d d i t i o n t o knowing i f the s t r i n g i s t a u t , i t i s a l s o n e c e s s a r y t o know the o r i e n t a t i o n o f the s t r i n g a t i t s e n d p o i n t s , s i n c e the f o r c e e x e r t e d by the s t r i n g i s a l o n g i t s t a n g e n t a t e v e r y p o i n t . Thus t h e s i t u a t i o n i n f i g u r e IV-14 i s ver y d i f f e r e n t from the o r i g i n a l problem. The d i r e c t i o n of t h e s t r i n g c o u l d p r o b a b l y be determined as a by-product c f the s h o r t e s t path c a l c u l a t i o n . However, s i n c e knowing the o r i e n t a t i o n o f t h e s t r i n g ' s ends i s a l s o e s s e n t i a l , s i m p l y a d d i n g t h a t t h e s t r i n g i s t a u t , t o the o r i g i n a l problem d e s c r i p t i o n would not s u c c e s s f u l l y c i r c u m v e n t the d i f f i c u l t i e s i n h e r e n t i n t h i s approach. An a l t e r n a t i v e would be t o d e s c r i b e t h e shape o f the c u r v e t h a t t h e s t r i n g forms as p a r t of the i n i t i a l problem d e s c r i p t i o n . While t h i s i s r e a s o n a b l e , i t i n t r o d u c e s s e v e r a l F I G U R E ! 131-13 171 problems. The f i r s t i s that i f t h i s process of i n c r e a s i n g the d e t a i l c f the i n i t i a l d e s c r i p t i o n i s kept up, then at some po i n t t h e r e i s almost no problem l e f t t o s o l v e . To exaggerate somewhat, the d e s c r i p t i o n might take the form: two see-saws connected by a taut s t r i n g over a p u l l e y such that when the end att a c h e d to the s t r i n g of one see-saw goes down the end attac h e d to the s t r i n g of the other see-saw goes up. I f the d e s c r i p t i o n of the s t r i n g ' s shape as an ordered seguence of s t r a i g h t and curved segments i s admitted, then i t would be reasonable not to i n c l u d e the statement t h a t the s t r i n g runs over the p u l l e y s i n c e t h i s can now be determined from the shape of the s t r i n g and the l o c a t i o n o f the p u l l e y . In t h i s case th e r e i s a s e r i o u s problem of matching the shape of the curve to the shape of the o b s t a c l e s i t passes over. To determine i f the s t r i n g i s t a u t , every wiggle i n the s t r i n g must match an o b s t a c l e ; and to e s t a b l i s h that a wiggle i m p l i e s t h a t the s t r i n g i s s l a c k , r e g u i r e s a proof t h a t i f does not match with any o b j e c t i n the domain s i n c e any o b j e c t i s a p o t e n t i a l o b s t a c l e d i v e r t i n g the s t r i n g . Even i g n o r i n g t h i s problem of determining t a u t n e s s , having the d e s c r i p t i o n of the s t r i n g shape a v a i l a b l e would mean th a t i t would have to be updated i f the s t r i n g were moved. T h i s process would be g u i t e complicated even f o r simple motions. In the c u r r e n t p u l l e y problem when the s t r i n g i s p u l l e d down i t i s a l s o p u l l e d s l i g h t l y sideways by the l e v e r so t h a t not only do the l e n g t h s of the segments to the p u l l e y change, but the slope 172 o f the segments and the f r a c t i o n of the s t r i n g which i s curved t o go arcund the p u l l e y changes as w e l l . The problem of updating the curve d e s c r i p t i o n could e a s i l y r e - i n t r o d u c e a l l the problems of determining the tautness of the s t r i n g which the p r o v i s i o n of the curve d e s c r i p t i o n was intended to avo i d . U t i l i z i n g a WHISPEB l i k e r e t i n a , a diagram of the problem, some a d d i t i o n a l t r a n s f o r m a t i o n procedures, and a g u a l i t a t i v e knowledge of the p h y s i c s o f s t r i n g s and p u l l e y s , these problems can be s o l v e d i n a s t r a i g h t f o r w a r d manner. The WHISPEB r o u t i n e s are alre a d y capable of d e a l i n g with the see-saw part of the problem, A rough o u t l i n e of the knowledge about s t r i n g s which would be r e g u i r e d f o r t h i s c l a s s of problem i s given i n f i g u r e IV-15. Most r e l e v a n t t o the p u l l e y problem i s t h a t a f i x e d p u l l e y simply changes the d i r e c t i o n of the f o r c e t r a n s m i t t e d along the s t r i n g so t h a t whatever occurs at one end of the s t r i n g occurs a t the other. S t r i n g t a u t n e s s i s e a s i l y determined by using the r e t i n a t o look at the curve i n the diagram. Bends i n the curve are d e t e c t a b l e i n the same way as were o b j e c t ' s s u r f a c e i r r e g u l a r i t i e s which WHISPEB needed to f i n d i n order to know i f an o b j e c t would s l i d e smoothly. As l o n g as t h e r e are no bends i n the s t r i n g where the s t r i n g i s not i n c o n t a c t with an o b s t a c l e , then the s t r i n g i s t a u t . Since proximity r e l a t i o n s h i p s h o l d i n the diagrammatic analogue, a bend i n the s t r i n g which i s not i n co n t a c t with an o b s t a c l e i s e a s i l y s p o t t e d by the empty space which surrounds the bend. This i n PHYSICS OF UNSTRETCHABLE STRING 1. A force applied to one end of a s t r i n g i n a d i r e c t i o n along i t s length causes the s t r i n g to act l i k e a r i g i d rod. The force i s transmitted along the s t r i n g . 173 e.g. 2. A force not i n the s t r i n g d i r e c t i o n e.g. eventually causes a s h i f t to s i t u a t i o n (1) 3. A force to a slack s t r i n g causes i t to straighten before any force i s transmitted to i t s f a r end. 4. A force i s transmitted around a f r i c t i o n l e s s b a r r i e r . Whatever happens before the b a r r i e r happens a f t e r i t . 5. Pushing on a s t r i n g makes i t s l a c k F I G U R E 35T - 1 5 : 174 s h a r p c o n t r a s t t o t h e problem mentioned e a r l i e r of t e s t i n g the p o s s i b l e c o n t a c t o f t h e s t r i n g w i t h e v e r y o b j e c t . The s o l u t i o n sequence which I e n v i s i o n b e g i n s w i t h the s t a t e m e n t of the problem as a c o m b i n a t i o n of the s t y l i z e d diagram and the s e t of a s s e r t i o n s g i v e n i n f i g u r e IV-16. A WHISPEB l i k e a n a l y s i s o f the r i g i d r o d and i t s s u p p o r t y i e l d s t h e f i r s t s t e p i n the s o l u t i o n p r o c e s s , f i g u r e IV-17. When t h i s new diagram i s examined t h e c o n d i t i o n s o f s u p p o r t and c o n n e c t i o n f c r t h e r i g i d rod are checked and i t i s n o t i c e d t h a t the c o n n e c t i o n between the r o d and the s t r i n g has been broken. T h i s i s very s i m i l a r to the way i n which WHISPEB c a r r i e s out s l i d e s by s i m p l e t r a n s l a t i o n f o l l o w e d by a r o t a t i o n t o c o r r e c t f o r any s u p p o r t c o n d i t i o n s which may have changed as a r e s u l t o f t he t r a n s l a t i o n ( s e c t i o n 11-10). To conn e c t the s t r i n g back t o t he r o d a g a i n , i t w i l l have t o be p u l l e d i n t h e d i r e c t i o n c o n n e c t i n g the end of the s t r i n g and the end of the r o d . The analogue has so f a r p r o v i d e d t h e s o l u t i o n t o two of the problems which plagued t h e p r e c e d i n g system. F i r s t , t h e r e i s no f l o u n d e r i n g about f o l l o w i n g dead end s o l u t i o n paths because o n l y t h o s e c o n d i t i o n s which a c t u a l l y change i n a r e a l p u l l e y system change i n the diagram. Thus i n f i g u r e IV-18 when the r o d B1 i s p i v o t e d , the c o n n e c t i o n between i t and the s t r i n g i s not s e v e r e d ; t h e r e t i n a l v i s u a l i z a t i o n p r o c e s s w i l l d e t e c t t h e c o l l i s i o n w i t h rod B2. The second problem which has been a v o i d e d i s d e t e r m i n i n g the o r i e n t a t i o n o f t h e s t r i n g a t i t s e n d p o i n t s . S i n c e t h e shape of t h e cu r v e i n the diagram i s the < 7 5 * ( F r i c t i o n l e s s P u l l e y P) (Unstretenable St r i n g S) (Rigid Body A) (Rigid Body B) 71 F l & U R E WT/ (Connected-to S A) (Rigid Body C) (Rigid Body D) (Connected-to S B) 176 same as the shape of the a c t u a l s t r i n g , the tangents at the curve's endpcints are the same as the tangents at the corresp o n d i n g endpcints of the s t r i n g . The curve tangents can be found by the WHISPEH r e t i n a . The s o l u t i o n process c o n t i n u e s with an examination of the s t r i n g , s i n c e i t s t a u t n e s s i s c r u c i a l t o the c h o i c e of the t r a n s f o r m a t i c n which must be a p p l i e d to i t . Since there are no bends i n the curve other than f o r that around the p u l l e y , and s i n c e a p u l l e y i s a f r i c t i o n l e s s o b s t a c l e , the s t r i n g s p e c i a l i s t ( i . e . a procedure which knows about the p h y s i c s of s t r i n g s ) knows that any motion of the s t r i n g at the l e f t hand s i d e w i l l cause a corresponding motion of the same magnitude but d i f f e r e n t d i r e c t i o n on the r i g h t hand s i d e . N o tice that i t i s no more d i f f i c u l t t c solve the two p u l l e y problem of f i g u r e IV-13 than the s i n g l e p u l l e y problem. The r e g u i r e d t r a n s f o r m a t i o n lengthens the s t r i n g at one end and shortens i t at the e t h e r . T h i s i s a si m p l e r t r a n s f o r m a t i o n than the e q u i v a l e n t one of s h i f t i n g every point of the curve so as • to s i m u l a t e the a c t u a l motion of the s t r i n g , but has the same net e f f e c t . The r e s u l t i s shown i n f i g u r e IV-19. The c o n d i t i o n s which the s t r i n g must s a t i s f y are then checked, and t h i s time the gap between the s t r i n g and the second rod i s found. T h i s i m p l i e s t h a t a f o r c e i n the d i r e c t i o n of the s t r i n g must be a p p l i e d to t h a t rod, causing i t to r o t a t e . The r o t a t i o n can be ' v i s u a l i z e d ' to determine the angle r e g u i r e d t o remake the connect i o n with the s t r i n g ( f i g u r e IV-20) . The problem i s F I G U R E 178 s o l v e d . A l t h o u g h i t i s not c o m p l e t e l y c l e a r how i t might be done, i t s h o u l d be p o s s i b l e t o u t i l i z e t h e s i m i l a r i t y of the l e f t and r i g h t h a l v e s of f i g u r e IV-21 t o c o n c l u d e , a f t e r f i n d i n g the c l o c k w i s e motion o f t h e c e n t e r r o d , t h a t the r i g h t m o s t r o d w i l l a l s o swing c l o c k w i s e . The s y n t a c t i c s i m i l a r i t y of the two h a l v e s of the c o n f i g u r a t i o n t r i g g e r s the h y p o t h e s i s t h a t the complete problem i s a c o m b i n a t i o n of two i d e n t i c a l subproblems. The s o l u t i o n t o t h e f i r s t subproblem i s then u s e a b l e as the s o l u t i o n to the second subproblem w i t h o u t f u r t h e r a n a l y s i s . The d e t e c t i o n o f t h e s i m i l a r i t y i n t h e problem i s a r e s u l t of t h e e x p l i c i t r e p r e s e n t a t i o n of the s t r u c t u r e o f the s i t u a t i o n i n the c o n f i g u r a t i o n a l s t r u c t u r e of t h e diagram sc t h a t a s p e c i a l s i m i l a r i t y t e s t does not have t o be t a i l o r - m a d e t o t h e problem domain; i n s t e a d , one a p p l i c a b l e to diagrams i n g e n e r a l , such as WHISPEB's s i m i l a r i t y t e s t , can be employed. I t i s much l e s s l i k e l y t h a t t h e s i m i l a r i t y of t h e two subproblems would be r e c o g n i z e d , or even t h a t the problem would be s u b d i v i d e d i n t o subproblems a t a l l , i n a p u r e l y a s s e r t i o n a l system o p e r a t i n g w i t h o u t an analogue of t h e problem s i t u a t i o n . 180 There i s a spectrum of analogues with r e s p e c t t c the complexity of t h e i r u n d e r l y i n g d e s c r i p t i o n s . In s e c t i o n IV-2 I d i s c u s s e d hew an analogue could have components of both p h y s i c a l and computational s t r u c t u r e . The computation i s based on the u n d e r l y i n g d e s c r i p t i v e model, A decrease i n the s t r u c t u r a l s i m i l a r i t y between the p h y s i c a l a spects of the analogue and the s i t u a t i o n to which i t corresponds leads to an i n c r e a s e i n the complexity of the r e q u i s i t e d e s c r i p t i o n . At one end of the spectrum i s the world i t s e l f . The world s i m u l a t e s i t s e l f and does not operate by f o l l o w i n g an u n d e r l y i n g d e s c r i p t i o n of i t s own behaviour. The next point on the spectrum corresponds to s c a l e models, l i k e maps or model a i r p l a n e s . In these there i s a strong s i m i l a r i t y between the p h y s i c a l s t r u c t u r e of the analogue and the p h y s i c a l s t r u c t u r e of the r e a l i t y they r e p r e s e n t . A l l t h a t i s r e g u i r e d i n d e s c r i p t i v e terms are r e l a t i v e l y simple r u l e s f o r d i s c r e p a n c i e s due to s c a l i n g . S i m u l a t i o n s such as SOPHIE, which are eguation based, l i e a t the f a r end o f the spectrum. They are t o t a l l y dependent upon an u n d e r l y i n g d e s c r i p t i v e model. I t i s necessary to be a b l e to completely d e s c r i b e the domain before s i m u l a t i n g i t c o m p u t a t i o n a l l y . Also t h i s f i n a l point cn the spectrum corresponds to analogues which r e l y on deduction and a x i o m a t i z a t i o n . A theorem prover w i l l s imulate any domain d e s c r i b e d by the a x i o m a t i z a t i o n s u p p l i e d t o i t . Again, . i t i s 181 necessary t o completely d e s c r i b e the domain of i n t e r e s t . Formulating a s u f f i c i e n t a x i o m a t i z a t i o n i s o f t e n a very d i f f i c u l t t ask. In g e n e r a l formal d e s c r i p t i o n s of s i t u a t i o n s are incomplete, and more than one s i t u a t i o n w i l l f i t the d e s c r i p t i o n . (The axioms have more than one model.) I t i s d i f f i c u l t t o design a d e s c r i p t i o n such t h a t a unigue s i t u a t i o n w i l l f i t i t . Often we are i n t e r e s t e d i n a s i n g l e s i t u a t i o n , so i t would be advantageous to c o n s t r u c t d e s c r i p t i o n s which are exhaustive i n the sense t h a t they do c o n s t r a i n the set of p o s s i b l e s i t u a t i o n s to j u s t t h a t one of i n t e r e s t . Shen a d e s c r i p t i o n admits more than one s i t u a t i o n c r model the c o n c l u s i o n s drawn are of grea t e r g e n e r a l i t y , Any c o n c l u s i o n i s v a l i d f o r a l l the s i t u a t i o n s which f i t the d e s c r i p t i o n not j u s t the s i t u a t i o n of i n t e r e s t , I t seems s e l f - e v i d e n t that g e n e r a l i t y c o s t s . A reasonable goal would be then t o reason i n no more g e n e r a l i t y than necessary. Consider again the spectrum cf analogues. Although i t i s t h e o r e t i c a l l y p o s s i b l e to provide adeguate d e s c r i p t i o n s f o r the d e n o t a t i v e model, i t i s seldom the case that they are provided. At the end of the spectrum r e g u i r i n g the l e a s t formal d e s c r i p t i o n , the r e g u i s i t e i n f o r m a t i o n i s co n t a i n e d i m p l i c i t l y i n the p h y s i c a l medium or data s t r u c t u r e . The medium a c t s as a complete d e s c r i p t i o n of i t s e l f . F u r t h e r along i n the spectrum, the p r o p e r t i e s of the medium have t o be d e s c r i b e d as w e l l , and i t i s o f t e n p r e c i s e l y some of these p r o p e r t i e s which are 1 8 2 overlooked or taken f o r granted when f o r m a l i z i n g a domain. Thus in 1 n y p k i ng m analogues _ at_ the_ wor Id _ e n d _ c f _n t h e _ s p ec t r u ro „ i s _ a * a y _ o f _ u t i i i : z j ^ j 2 _ i ^ £§££§sen t ing,_med i u m , _ Jb u t _ w h i c h _ i s _ n o t _y e t_ su f f i c i e n t l y as d e r s t o o d_ t o_ ch a r a c t erize_descri£tivelyj. Admitting i n f o r m a t i o n i n t o the problem s o l v i n g process i n t h i s way avoids two problems. The f i r s t i n v o l v e s reasoning with o n l y p a r t i a l i n f o r m a t i o n ; hence, reasoning i n g r e a t e r g e n e r a l i t y and a t greater c o s t . The second i n v o l v e s s o l v i n g subproblems which r e g u i r e deducing r e s u l t s about the medium which are harder t c o b t a i n than a s o l u t i o n to the o r i g i n a l problem appears to be. In a v o i d i n g t h i s second problem i t i s o f t e n necessary to give such t a i l c r - m a d e d e s c r i p t i o n s that the s o l u t i o n i s v i r t u a l l y contained i n the d e s c r i p t i o n . T h i s i s the case, f o r example, i n the 'monkey and bananas' problem where u s u a l l y i t i s given that i f the monkey stands on the box, then i t w i l l be able to grasp the bananas. I f t h i s i s not given, how i s the monkey to deduce that standing on the box w i l l s o l v e i t s problem? A r e a l monkey i n a r e a l s i t u a t i o n c o u l d simply t r y the experiment of standing on the box; an a b s t r a c t monkey t h i n k i n g about the a b s t r a c t s i t u a t i o n would have to be given f u r t h e r i n f o r m a t i o n about i t s h e i g h t , the l e n g t h of i t s arm, the height of the box, and the height cf the bananas. I f any of t h i s i n f o r m a t i o n i s omitted, i t w i l l not be a b l e t o so l v e the problem. In a d d i t i o n , the subproblems of determining the d i s t a n c e from the top of the box to the bananas 183 and the l e n g t h of the monkey's reach are nos becoming more d i f f i c u l t problems than the main problem of h y p o t h e s i z i n g the box as the p o s s i b l e key to the s o l u t i o n . The advantage of using analogues i s , t h e r e f o r e , t h a t they provide a way i n which t c b r i n g the i n f o r m a t i o n present as p r o p e r t i e s of the medium i n t o the problem s o l v i n g process without e x p l i c i t l y knowing and d e s c r i b i n g what these p r o p e r t i e s are. Furthermore, the presence of t h i s i n f o r m a t i o n i s important i n both (a) reducing the g e n e r a l i t y of the reasoning by e l i m i n a t i n g the u n a n t i c i p a t e d matching of one s i t u a t i o n ' s d e s c r i p t i o n by other s i t u a t i o n s , and (b) e l i m i n a t i n g the need t o deduce r e s u l t s about the medium i t s e l f from a d e s c r i p t i o n of i t s p r o p e r t i e s . T h i s i s true whether the medium i s a p h y s i c a l one e x i s t i n g o u t s i d e the c o n v e n t i o n a l c o n f i n e s of a machine, or e x i s t i n g w i t h i n through s i m u l a t i o n . A medium can be si m u l a t e d , as i n the case of the s i m u l a t i o n of two-dimensional media by two-dimensional a r r a y s , without f i r s t d e s c r i b i n g i t s p r o p e r t i e s . Thus even i n the case of a simulated medium, when i t i s used as the b a s i s f o r an analogue, i t s p r o p e r t i e s s t i l l become part of the problem s o l v i n g process without the need of p r i o r d e s c r i p t i c n or f o r m a l i z a t i o n . 184 Cha£ter_Vi_VisuaJL_Iffia^ V - J _ I n t r e d u c t i o n WHISPER'S use of array diagrams p a r a l l e l s human use of diagrams; i t can a l s o use analogues without an array diagram, and c r e a t e 'images' on i t s r e t i n a p a r a l l e l i n g human v i s u a l imagery. The r e t i n a can 'look' at and process i n f o r m a t i o n r e p r e s e n t e d i n a n o n - p i c t o r i a l form. Analogues very s i m i l a r to those provided by the ar r a y diagrams can be c r e a t e d and used d i r e c t l y on WHISPER'S r e t i n a , because i t a l s o has two-dimensional s t r u c t u r e . The r e t i n a i s b a s i c a l l y a two-dimensional array of p r o c e s s o r s ; although i n c o n t r a s t to the diagram a r r a y , i t i s c i r c u l a r , not sguare. The l i n k i n g of each processor t o i t s neighbours and the manner i n which the value of each processor i s set i s r e s p o n s i b l e f o r the two-dimensional c h a r a c t e r of the r e t i n a . Of cou r s e , the pr o c e s s o r s themselves do not a c t u a l l y have to be a l i g n e d i n a plane as they are dep i c t e d i n the p i c t u r e of WHISPER * s r e t i n a l bubbles, f i g u r e IV-21. The diagram can be e l i m i n a t e d and the a n a l o g i c a l nature of u s i n g diagrams r e t a i n e d , i f th e r e i s a method of f i l l i n g the r e t i n a from an u n d e r l y i n g r e p r e s e n t a t i o n other than the diagram. Since a l l of WHISPER'S i n t e r a c t i o n with the diagram was through, the r e t i n a , i t i s only dependent on the r e t i n a and 185 not on the diagram i t s e l f . As long as there i s a mechanism whereby the r e t i n a i s f i l l e d c o r r e c t l y , SHISPEH w i l l be unaware of the removal of the diagram. The method c f f i l l i n g the r e t i n a from the u n d e r l y i n g r e p r e s e n t a t i o n must be f a s t , however, because the r e t i n a i s r e f i l l e d every time i t f i x a t e s a t a new l o c a t i o n . 186 V - 2_ F i 11 i n g_ T h e _ B e t i n a The r e t i n a ' s p a r a l l e l i s m can be e x p l o i t e d i n mapping from an u n d e r l y i n g r e p r e s e n t a t i o n to the r e t i n a . Assume that the u n d e r l y i n g r e p r e s e n t a t i o n i s i n the form of a l i n e drawing, s p e c i f i e d by the c o o r d i n a t e s of the endpcints of i t s l i n e segments. For each l i n e segment, the r e t i n a l s u p e r v i s o r would determine the equation of the l i n e and broadcast i t and i t s endpoint c o o r d i n a t e s to a l l the bubbles, asking them each to execute the f o l l o w i n g simple a l g o r i t h m : (1) Let D equal the p e r p e n d i c u l a r d i s t a n c e from the c e n t e r of the bubble to the l i n e . (2) I f D i s l e s s than the r a d i u s of the bubble, then s e t the bubble value 'on'. (3) Otherwise, do n o t h i n q . The time taken t o map from the u n d e r l y i n q l i n e seqment d e s c r i p t i o n to the r e t i n a would be d i r e c t l y p r o p o r t i o n a l to the number of l i n e segments. The same method i s a p p l i c a b l e t o mapping d e s c r i p t i o n s based upon other types of p r i m i t i v e s (other curves, s u r f a c e s , or volumes) f o r which there i s a simple way each bubble can determine i f i t i s w i t h i n the s e c t i o n of the r e t i n a a f f e c t e d by the presence of a p r i m i t i v e element. I r r e g u l a r l y shaped areas c o u l d be d e s c r i b e d by t h e i r decomposition i n t o t r i a n g u l a r l y shaped p i e c e s ( f i g u r e v -1). In f i l l i n g the r e t i n a , each bubble would only have to answer the question as to i t s presence 188 w i t h i n the area d e f i n e d by a t r i a n g l e . The time r e g u i r e d would again be p r o p o r t i o n a l to the number of t r i a n g l e s i n the decomposition. In the case of a 3-D p r i m i t i v e , each bubble would be r e g u i r e d t o determine whether i t was i n the s e c t i o n of the r e t i n a l y i n g under i t s 2-D p r o j e c t i o n . 189 V-3_advantages The above scheme has s e v e r a l advantages over the ar r a y r e p r e s e n t a t i o n of diagrams. There i s a s i g n i f i c a n t s aving i n storage space. D e s c r i b i n g s u r f a c e s i n terms of p r i m i t i v e segments of area i s much more compact than saving a l l the p o i n t s which are on the s u r f a c e . A second advantage i s t h a t the r e s o l u t i o n i s l e s s l i m i t e d . The r e t i n a c o u l d zoom i n on any s e c t i o n o f the represented e n t i t y to whatever extent i t wished. In the case of the a r r a y , i t c o u l d not o b t a i n b e t t e r r e s o l u t i o n than t h a t of the a r r a y i t s e l f . Using the proposed scheme the r e s o l u t i o n i s l i m i t e d only by the number of p r i m i t i v e s which are used i n d e s c r i b i n g the e n t i t y . T h i s number can be i n c r e a s e d i n d e f i n i t e l y when the d e s c r i p t i o n i s c o n s t r u c t e d . I f they are s u i t a b l y o r g a n i z e d , then only a subset of these need be p r o j e c t e d onto the r e t i n a a t any one time, and more can be p r o j e c t e d i f g r e a t e r r e s o l u t i o n i s r e g u i r e d at a p a r t i c u l a r p o i n t . A t h i r d advantage i s the p o s s i b i l i t y o f u t i l i z i n g 3-D e n t i t i e s . Each f i x a t i o n would only provide a 2-D p r o j e c t i o n , but the f i x a t i o n s could be made from viewpoints a l l around the e n t i t y . In a d d i t i o n , the p o s s i b l e mappings are not r e s t r i c t e d to p e r s p e c t i v e p r o j e c t i o n s . They may a l s o i n c l u d e p r o j e c t i o n s which c r e a t e diagrams l i k e those c u r r e n t l y used. The primary d i f f i c u l t y which a r i s e s i n r e p l a c i n g the array diagram with a d i f f e r e n t type of d e s c r i p t i o n i s i n a p p l y i n g 190 t r a n s f o r m a t i o n s to i t . Non-linear t r a n s f o r m a t i o n s would cause the g r e a t e s t d i f f i c u l t y because the shape of p r i m i t i v e elements would be changed. For l i n e a r t r a n s f o r m a t i o n s , the t r a n s f o r m a t i o n would be a p p l i e d i d e n t i c a l l y to each of the p r i m i t i v e elements. In l i n e segment d e s c r i p t i o n s , f o r example, the recomputation of the endpcints of each segment a c c o r d i n g to the t r a n s f o r m a t i o n i s a l l t h a t i s necessary. I f the p r i m i t i v e elements are s o l i d s , d e s c r i b e d i n terms such as Fahlman 1s AT a r r a y s which u t i l i z e a homogeneous c o o r d i n a t e r e p r e s e n t a t i o n , then t r a n s f o r m a t i o n can again be a p p l i e d u n i f o r m l y to each element. 191 Employing t h e c o m b i n a t i o n of a WHISPER-like r e t i n a f i l l e d from a n o n - p i c t o r i a l u n d e r l y i n g r e p r e s e n t a t i o n agrees w i t h K o s s l y n ' s t h e o r y o f human v i s u a l imagery. "A computer g r a p h i c s metaphor: A v i s u a l image i s c o n s i d e r e d t o bear t h e same b a s i c r e l a t i o n s h i p t o i t s u n d e r l y i n g s t r u c t u r e as a p i c t o r i a l d i s p l a y on a cathode ray tube (CRT) does to the computer program t h a t g e n e r a t e s i t . The u n d e r l y i n g 'deep' s t r u c t u r e i s a b s t r a c t and not e x p e r i e n c e d d i r e c t l y , whereas t h e image i t s e l f seems p i c t o r i a l i n n a t u r e . He are not c l a i m i n g , however, t h a t t h e p s y c h o l o g i c a l analogue t o the CRT d i s p l a y s p i c t u r e s as su c h ; r a t h e r , t h i s s t r u c t u r e i s c h a r a c t e r i z e d as s u p p o r t i n g i n t e r n a l r e p r e s e n t a t i o n s (whatever they may be l i k e ) s i m i l a r t o those t h a t engender the e x p e r i e n c e c f p e r c e i v i n g a p i c t u r e when a person i s v i e w i n g o n e . " 3 6 The v a l u e c e l l s o f t h e bub b l e s of WHISPEB 1s r e t i n a s e r v e the r o l e o f the d i s p l a y s c r e e n , and t h e f u n c t i o n of the e l e c t r o n beam i s r e p l a c e d w i t h p a r a l l e l e x e c u t i o n of the r e t i n a l p r o c e s s o r s i n f i l l i n g t h i s • s c r e e n ' . The r e t i n a l s t r u c t u r e does s u p p o r t an i n t e r n a l r e p r e s e n t a t i o n s i m i l a r t o t h a t produced by v i e w i n g one of WHISPEB's a r r a y diagrams (the c l o s e s t t h i n g t o v i e w i n g a p i c t u r e ) . K o s s l y n a l s o s u g g e s t s t h a t " s u b r o u t i n e s f o r d i s p l a y i n g l i n e s , a r c s , and a s e t of b a s i c p a t t e r n s might s e r v e as p r i m i t i v e s " ( o r i g i n a l emphasis) i n a " h i e r a r c h i c a l r e p r e s e n t a t i o n " from which t h e d i s p l a y would be g e n e r a t e d . 3 7 T h i s i s a l s o s i m i l a r t o what has been suggested above. A s i g n i f i c a n t d i f f e r e n c e between u s i n g WHISPEB•s r e t i n a l s t r u c t u r e as t h e d i s p l a y ' s c r e e n ' and K o s s l y n ' s g r a p h i c s metaphor i s t h a t t h e l a t t e r i m p l i e s the e x i s t e n c e of a ' s c r e e n ' 192 on which the image i s represented with uniform r e s o l u t i o n as i t i s i n WHISPEE's a r r a y s . T h i s i m p l i c a t i o n i s a l s o present i n h i s f o l l o w i n g comments: " ' F o c u s i n g ' on part of an image may be thought of i n terms of s e l e c t i v e l y a l l o c a t i n g d i s p l a y c a p a c i t y to a p a r t i c u l a r p o r t i o n of an image. 'Scanning' an image may i n v o l v e s e q u e n t i a l f o c u s i n g , which s h i f t s s e r i a l l y and c o n t i n u o u s l y a c r o s s an image." 3 8 Using the r e t i n a l s t r u c t u r e as the ' s c r e e n ' e l i m i n a t e s the need f o r an a d d i t i o n a l d i s p l a y 'screen'. In a d d i t i o n to being i n t u i t i v e l y more a p p e a l i n g , t h i s s o l v e s s e v e r a l problems. Since there i s no obvious e q u i v a l e n t i n the b r a i n to the e l e c t r o n gun which draws l i n e s on a CBT, i t s e l v e s the problem of how the image would be d i s p l a y e d . Of c o u r s e , i t c o u l d be generated using the p a r a l l e l a l g o r i t h m s put forward f o r f i l l i n g WHISPEB's r e t i n a , but t h i s has the disadvantage t h a t a much l a r g e r number of processors would be r e g u i r e d , because of the uniform g u a l i t y of the image out to i t s boundaries. Another problem i s how some e q u i v a l e n t to the BHISPEB r e t i n a would be f i l l e d from t h i s image. I t i s d i f f i c u l t to e n v i s i o n how the numerous connections c c u l d be made and broken q u i c k l y enough to provide p a r a l l e l i n p u t s to the many sepa r a t e processors as they 'scan' a c r o s s the image. Although these problems do not r u l e out the e x i s t e n c e cf an image of uniform g u a l i t y , ' d i s p l a y i n g ' the i n f o r m a t i o n d i r e c t l y onto the r e t i n a l p r o cessors circumvents them e n t i r e l y . One hypothesis Kosslyn i s l e a d to by the g r a p h i c s metaphor i s t h a t there would be c a p a c i t y l i m i t a t i o n s . There might be 193 l i m i t a t i o n s on how d e t a i l e d the g e n e r a t i n g d e s c r i p t i o n could be, and l i m i t a t i o n s on the amount of i n f o r m a t i o n that the d i s p l a y i t s e l f c o u l d hold at one time. T h i s l a t t e r l i m i t a t i o n , he suggests, might be l i k e the f l i c k e r o c c u r r i n g i n CRT d i s p l a y s when they are r e f r e s h e d with i n s u f f i c i e n t freguency. T h i s happens when t h e r e i s a l a r g e number of l i n e s t o be drawn on the screen. WHISPER 1s r e t i n a suggests a d i f f e r e n t source of • f l i c k e r * than the simple f a d i n g suggested by analogy to the phosphor of a CRT. As the number of p r i m i t i v e s to be d i s p l a y e d i n c r e a s e s , so does the time which i t takes to d i s p l a y them. Sin c e WHISPER i s dependent on f i x a t i n g the r e t i n a at many d i f f e r e n t l o c a t i o n s an extreme i n c r e a s e i n f i x a t i o n time would cause the system to become bogged down i n the overhead of moving the r e t i n a . Thus, there i s a l i m i t on what i s a p r a c t i c a l amount of i n f o r m a t i o n to d i s p l a y . Kosslyn t e s t s the metaphor e x p e r i m e n t a l l y by asking s u b j e c t s to c o n s t r u c t a p a r t i c u l a r mental image, and then a s k i n g them to respond when they have picked out a s p e c i f i c f e a t u r e i n the image. The time the s u b j e c t takes to respond i s measured. He found: t h a t i t takes longer f o r s u b j e c t s to d i s c e r n f e a t u r e s of s u b j e c t i v e l y s m a l l images than s u b j e c t i v e l y l a r g e ones; t h a t as the complexity of the image i n c r e a s e s , the time to d i s c e r n f e a t u r e s i n c r e a s e s ; t h a t i t takes longer to c o n s t r u c t a more complex image than a simple image; t h a t there i s a maximal s i z e to which images can be s u b j e c t i v e l y expanded before they appear to overflow. A d e t a i l e d comparison of the 194 performance o f WHISPER * s r e t i n a and the s e r e s u l t s i s unnecessary s i n c e WHISPER 'S r e t i n a v i o l a t e s many o t h e r p h y s i o l o g i c a l and p s y c h o l o g i c a l c o n s t r a i n t s . S u f f i c e i t to say t h a t K o s s l y n ' s e x p e r i m e n t s p r o v i d e e v i d e n c e t h a t the g r a p h i c s metaphor a l s o a p p l e s t o WHISPER 'S r e t i n a , w i t h o u t drawing s t r o n g c o n c l u s i o n s about any d i r e c t r e l a t i o n s h i p between WHISPEB's r e t i n a and human v i s u a l imagery, K o s s l y n b a s i c a l l y approached h i s work from the p e r s p e c t i v e o f e x p l a i n i n g how human v i s u a l imagery works, and what i t s u n d e r l y i n g mechanisms must be i n o r d e r t o e x p l a i n the e x p e r i m e n t a l d a t a . I have approached t h e q u e s t i o n o f what c o m p u t a t i o n a l advantage can be o b t a i n e d by u s i n g a n a l o g u e s - p a r t i c u l a r l y diagrams - i n r e a s o n i n g . By d e m o n s t r a t i n g t h i s advantage we are c l o s e r t o answering the g u e s t i o n of why imagery e x i s t s at a l l . 195 I I z l _ I i i : J 5 i i a i i : 2 i J S _ i n d _ | uture_Dir€ction£ IIzJiJ_£ty;sical_Ki|0Mljd3e As p r e v i o u s l y i n d i c a t e d WHISPER*s knowledge of P h y s i c s i s f a r from comprehensive. The 'snapshot* by i t s very n a t u r e p o r t r a y s a l l o b j e c t s as s t a t i o n a r y , whereas some may be moving. To t a k e v e l o c i t i e s i n t o account r e g u i r e s the a d d i t i o n o f a g u a n t i t a t i v e r e a s o n i n g component t o i t s c u r r e n t q u a l i t a t i v e knowledge. WHISPER c u r r e n t l y does not i n t e g r a t e knowledge of v e l o c i t y , a c c e l e r a t i o n , momentum c r moments o f i n e r t i a . These would have t o be r e p r e s e n t e d i n terms o f e q u a t i o n s which c o u l d be a p p l i e d a f t e r WHISPER makes i t s c u r r e n t p r e d i c t i o n s . WHISPER a p p r o x i m a t e s s i m u l t a n e i t y by moving o b j e c t s one a f t e r a n o t h e r . T h i s p r o c e s s works f o r the problems d i s c u s s e d i n C h a pter I I ; however, c a s e s e x i s t f o r which t h i s a p p r o x i m a t i o n i s i n s u f f i c i e n t . I n f i g u r e V I - 1 , f o r example, i f B i s moved a f t e r A i s moved, then they w i l l not c o l l i d e ; however, i f they a r e moved s i m u l t a n e o u s l y they w i l l c o l l i d e . The d i a g r a m m a t i c analogue can be used t o overcome t h i s problem by s h a d i n g t h e space swept out by each o b j e c t as i t moves. The shaded a r e a s o f the diagram c o u l d be examined f o r o v e r l a p , B / A ' A FIGURE m-A 197 t h e r e b y i n d i c a t i n g t h a t a c o l l i s i o n might o c c u r . I f t h e a r e a s do not o v e r l a p then t h e r e w i l l d e f i n i t e l y not be a c o l l i s i o n , but i f th e y do then f u r t h e r g u a n t i t a t i v e a n a l y s i s c f the a n g u l a r v e l o c i t i e s of both o b j e c t s i s n e c e s s a r y t o determine whether t h e y w i l l occupy the o v e r l a p p i n g s e c t i o n of space a t th e same t i m e . 1 iz 1 s. 2. _ 1 feg ^. J g % % s a _ B s a* . I g I g§ B% H 3 1 ^ ? £ A14 % 4 y f § The r e s t r i c t e d r e s o l u t i o n of the r e t i n a i s i t s main l i m i t a t i o n . The r e s o l u t i o n c o u l d be i n c r e a s e d by a d d i n g more b u b b l e s , but t h i s would n ot make a t h e o r e t i c a l d i f f e r e n c e i n t h e type o f p e r c e p t u a l p r i m i t i v e s i t c o u l d compute. There are two main d i r e c t i o n s f o r f u r t h e r r e s e a r c h r e l a t i n g t o t h e r e t i n a . The f i r s t i s replacement of the s o f t w a r e s i m u l a t i o n w i t h p a r a l l e l p r o c e s s i n g hardware. The second i s e x p e r i m e n t a t i o n w i t h o t h e r r e t i n a l g e o m e t r i e s and communication l i n k s . The r o t a t i o n a l v i s u a l i z a t i o n and the s c a l i n g p r o p e r t y a r e a r t i f a c t s of t h e c u r r e n t geometry. Other g e o m e t r i e s o r e x t r a communication l i n k s might f a c i l i t a t e t h e v i s u a l i z a t i o n of t r a n s l a t i o n s or r o t a t i o n s o f 3-D o b j e c t s . A d i f f e r e n t geometry would a l s o a f f e c t t h e r a t e a t which r e s o l u t i o n d e c r e a s e s w i t h i n c r e a s i n g d i s t a n c e from the r e t i n a l c e n t e r . A r e t i n a whose r e s o l u t i o n d e c r e a s e s a t t h e same r a t e as t h e a c u i t y o f t h e human eye d e c r e a s e s might be a good c h o i c e . The way r e s o l u t i o n d e c r e a s e s c o u l d be i m p o r t a n t i n the 198 i m p l e m e n t a t i o n of p e r c e p t u a l p r i m i t i v e s f o r t h e r e c o g n i t i o n of o b j e c t s . The c u r r e n t s e t o f p e r c e p t u a l p r i m i t i v e s i s adequate f o r WHISPER'S t w o - d i m e n s i o n a l domain. A s i g n i f i c a n t e x t e n s i o n t o the p e r c e p t u a l p r i m i t i v e s would be the a d d i t i o n of p r i m i t i v e s t h a t e x t r a c t f e a t u r e s from t w o - d i m e n s i o n a l p r o j e c t i o n s of t h r e e - d i m e n s i o n a l s c e n e s . The c l a i m here i s not t h a t a n a l o g u e s are good i n a l l s i t u a t i o n s ; t h e y do have l i m i t a t i o n s . I n s e c t i o n IV-5 how ana l o g u e s h e l p reduce t h e l e v e l c f g e n e r a l i t y was d i s c u s s e d . I t i s not always b e s t t o r e a s o n about a s p e c i f i c r a t h e r than a g e n e r a l s i t u a t i o n . Sloman g i v e s an e x c e l l e n t example: " I f I s t a r t i n room A and then move back and f o r t h between room A and room B, which room w i l l I be i n a f t e r e x a c t l y 377 mo v e s ? " 3 9 Se do n o t want t o perfo r m an experiment i n an analogue o f t h i s s i t u a t i o n t o f i n d the answer, a l t h o u g h some e x p e r i m e n t a t i o n w i t h an analogue c o u l d h e l p f o r m u l a t e o r s u b s t a n t i a t e a g e n e r a l h y p o t h e s i s about t h e l o c a t i o n a f t e r an odd number of moves. I n s e c t i o n IV-4.2.1 and IV-4.2.4 examples were g i v e n o f how a n a l o g u e s can e s t a b l i s h a reason o r e v i d e n c e f o r an h y p o t h e s i s . T h i s does n o t , however, guarantee t h a t the h y p o t h e s i s i s v a l i d , a l o t o f e f f o r t c o u l d be expended i n v a i n a t t e m p t s t o prove i t . Thus r e l a t i o n s h i p s i n the analogue may 199 be m i s l e a d i n g . For example, i f two a n g l e s o f a t r i a n g l e appeared e g u a l i n a geometry diagram the h y p o t h e s i s t h a t i t i s i s o s c e l e s i s s u b s t a n t i a t e d , but u n f o r t u n a t e l y s o , i f the e g u a l i t y of t h e a n g l e s i s c o i n c i d e n t a l . Some f e a t u r e s of the analogue may not be g e n e r a l i z a b l e at a l l , and i f t h e ones which do n o t g e n e r a l i z e a r e not known, the analogue can be d e t r i m e n t a l . For example, WHISPER knows t h a t an o b j e c t which i s s y m m e t r i c a l about a v e r t i c a l a x i s t h r o u g h i t s s u p p o r t p o i n t w i l l b a l a n c e ( s e c t i o n I I - 3 . 3 . 1 ) . However, i f the o b j e c t s were not o f u n i f o r m d e n s i t y the symmetry of an o b j e c t c o u l d be taken as e v i d e n c e t h a t i t would b a l a n c e , but i t would be p u r e l y c o i n c i d e n t a l i f t h i s h y p o t h e s i s were v a l i d . ft f r u i t l e s s s e a r c h f o r a p r o o f might be i n i t i a t e d by t h i s h y p o t h e s i s based on, i n t h i s c a s e , an i r r e l e v a n t f e a t u r e of t h e analogue. VI-1.4 P s y c h o l o g i c a l C o r r e l a t i o n S i n c e WHISPER* s r e t i n a f i x a t e s at a seguence o f p o i c t s on a diagram u n d e r s t a n d a b l e by a human, an o p p o r t u n i t y i s p r o v i d e d f o r c omparison of human and machine problem s o l v i n g b e h a v i o u r . One o f WHISPER*s eye movement p r o t o c o l s was g i v e n i n s e c t i o n I I - 6 . The eye movement p r o t o c o l of a human s u b j e c t c o u l d be o b t a i n e d by p r e s e n t i n g him w i t h one of WHISPER 'S diagrams and r e c o r d i n g h i s eye movements. T h i s has n o t been done, but c o u l d be an i n t e r e s t i n g e x p l o r a t o r y a r e a . U s i n g WHISPER as a model f o r i n t e r p r e t i n g t h e r e s u l t s of human eye movement might r e v e a l 2 0 0 something of the human s u b j e c t ' s knowledge of P h y s i c s , h i s problem s o l v i n g s t r a t e g y , and h i s s e t of p e r c e p t u a l p r i m i t i v e s . 201 VI-2_Key_Ideas A b r i e f summary o f t h e i m p o r t a n t i d e a s p r e s e n t e d i n t h i s t h e s i s i s g i v e n below. V I - 2 i j _ T h e _ A n a l o g u e WHISPER reas o n s by e x p e r i m e n t i n g w i t h an analogue o f b l o c k s w o r l d s i t u a t i o n s . The analogue c o n s i s t s of t h e diagram and the t r a n s f o r m a t i o n p r o c e d u r e s which modify i t . The s t a t i c c o n f i g u r a t i o n s of marks i n the diagram a re analogous i n terms o f s p a t i a l r e l a t i o n s t o the c o n f i g u r a t i o n s o f o b j e c t s i n t h e problem, and t h e b e h a v i o u r o f o b j e c t s i n the diagram under the l i n e a r t r a n s f o r m a t i o n s i s analogous to the b e h a v i o u r of p h y s i c a l o b j e c t s . The i n t e r a c t i o n o f t h e p a r t s of WHISPEB w i t h t h e analogue i s shown i n f i g u r e VI-2. 2Iz2i2_Be^efits_Cf_The_Ana (a) A r b i t r a r y _ O b J e c t _ S h a p e s j . There are no o b j e c t d e s c r i p t i o n s e x c e p t f o r t h e o b j e c t i t s e l f as i t appears i n t h e diagram. As a r e s u l t WHISPEB h a n d l e s o b j e c t s o f a r b i t r a r y t w o - d i m e n s i o n a l shape. (b) Ng.frame,Problem: The diagram c o n t a i n s a l l the i n f o r m a t i o n c o n c e r n i n g the shapes and p o s i t i o n s c f o b j e c t s which WHISPEB needs t o c o n t i n u e i t s r e a s o n i n g a f t e r a change i n the s i t u a t i o n . Only the p o s i t i o n s and support r e l a t i o n s h i p s of FIGURE. HI-Si 203 o b j e c t s which s h o u l d be a f f e c t e d by a change are a f f e c t e d . (c) Ajalc[afflation2 Eecause t h e o n l y d e s c r i p t i o n of the shape of an o b j e c t i s the o b j e c t i t s e l f , amalgamating the shapes of two o b j e c t s i s s i m p l y a matter of i g n o r i n g t h e i r ' c o l o u r ' d i f f e r e n c e . (d) E m e r g e n t _ P r o p e r t i e s : These r e l a t e t o the amalgamation problem. When twc o b j e c t s are combined, c o i n c i d e n t a l a l i g n m e n t s may cause the combined o b j e c t t o have an i n t e r e s t i n g o r u s e f u l p r o p e r t y . For WHISPER t h e u s e f u l p r o p e r t y i s t h a t two o r more o b j e c t s may a l i g n so t h a t t h e i r s u r f a c e s p r o v i d e a c o n t i n u o u s smooth c u r v e f o r a s l i d i n g o b j e c t . (e) D e s c r i p t i o n , O f Empty.Space: Space i s r e p r e s e n t e d by space i n t h e diagram. There i s no d i f f i c u l t y d e s c r i b i n g t h e a r e a s of empty space. T h i s i s i m p o r t a n t when f i n d i n g a c l e a r path f o r an o b j e c t . There i s no need t o prove t h a t a p a r t i c u l a r p o i n t i n space i s u n o c c u p i e d . (f) P§l§g^i;S2-^9t-3;9g„.£4§S9^liDJj^^ig§l R e t i n a l v i s u a l i z a t i o n can be used f o r d e t e c t i n g c o l l i s i o n s d u r i n g r o t a t i o n s . D i s c o n t i n u i t i e s i n s l i d i n g motions a r e found by examining the s l i d i n g s u r f a c e s f o r bumps, h i l l s , c l i f f s , and o b j e c t s i n the way. The diagram h e l p s because empty space i s r e p r e s e n t e d and because t h e shapes of the s u r f a c e s i n v o l v e d i n a s l i d e a r e r e p r e s e n t e d by c o r r e s p o n d i n g shapes i n t h e diagram. The r e t i n a can l o c k a t l a r g e s e c t i c n s of t h e s e c u r v e s i n p a r a l l e l . 204 VI-2 i3_The_Betina ( a) g a x a l l e l P r o c e s s i n g : The r e t i n a c o n s i s t s of a l a r g e number of p r o c e s s o r s o p e r a t i n g i n p s e u d o - p a r a l l e l . There i s no need to spawn new p r o c e s s o r s . (b) B e t i n a l _ S u p e r v i s o r : 1 s i n g l e s e g u e n t i a l p r o c e s s o r which d i r e c t s the p a r a l l e l p r o c e s s o r s . (c) Ue i g hb ourhood.Message _ P a s s i n g i Each pro c e s s o r exchanges messages with i t s immediate neighbours and with the r e t i n a l s u p e r v i s o r . The r e s t r i c t i o n to neighbourhood communication i s important i n f a c i l i t a t i n g a f u t u r e hardware implementation of the r e t i n a . (d) 8etinal_Topology._: The c u r r e n t r e t i n a l l a y o u t has s e v e r a l p r o p e r t i e s : (i) The r e s o l u t i o n decreases from the r e t i n a l c e n t e r . ( i i ) O b j e c t s can be s c a l e d by message passing along wedge l i n k s . ( i i i ) Objects can be r o t a t e d about the r e t i n a l c e n t e r by message pa s s i n g along r i n g l i n k s . (e) Domai n_I.nde pendent .Percept u The p e r c e p t u a l p r i m i t i v e s e x t r a c t f e a t u r e s from diagrams. The f e a t u r e s are a s s i g n e d d i f f e r e n t i n t e r p r e t a t i o n s depending upon the problem domain. The c u r r e n t s e t of percepts i n c l u d e s : s i m i l a r i t y , c e n t e r of area, symmetry, c o n t a c t p o i n t s , v i s u a l i z a t i o n of r o t a t i o n s to d i s c o v e r c o l l i s i o n s , nearest and f a r t h e s t l o c a t i o n s s a t i s f y i n g an a r b i t r a r y p r e d i c a t e , and curve t a n g e n t s , c o n v e x i t i e s and c o n c a v i t i e s . 2 0 5 V 1 - 3 ^ 1 osing_Remaj:ks The work p r e s e n t e d here has demonstrated a computer problem s o l v i n g system which d e r i v e s r e s u l t s by r e l y i n g upon e x p e r i m e n t a l f e e d b a c k from an analogue. WHISPER'S r e t i n a and r e d r a w i n g t r a n s f o r m a t i o n s p r o v i d e one example of a mechanism which makes i t p o s s i b l e t o o b t a i n t h e feedback from a diagr a m m a t i c a n a l o g u e . fi h i g h l e v e l r e a s o n i n g component i n t e r p r e t s the e x p e r i m e n t a l r e s u l t s on the b a s i s o f the s i m i l a r i t i e s between the analogue and the c o r r e s p o n d i n g r e a l i t y . I t need o n l y know how r e s u l t s a r e i n t e r p r e t e d i n o r d e r t o i n c l u d e t h e i n f o r m a t i o n p r e s e n t i n the s t r u c t u r e of t h e analogue i n i t s problem s o l v i n g . The i n f o r m a t i o n i s i n t r o d u c e d i n t o t h e problem s o l v i n g system w i t h o u t need o f p r i o r f o r m a l i z a t i o n and d e s c r i p t i o n . The r e s u l t i s a system which b e n e f i t s from the analogue i n o b t a i n i n g a p p r o p r i a t e l y s i m p l e s o l u t i o n s t o problems posed by t h e everyday p h y s i c a l e nvironment. 206 F o o t n o t e s 1. M a r v i n Minsky and Seymour P a p e r t , A x t i f i c i a l _ I n t e l l i g e n c e ££2a£sss_Beport# Cambridge, Mass.: M a s s a c h u s e t t s I n s t i t u t e of T e c h n o l o g y ! AI~Hemo No. 252, 1972. 2. G. P o l y a , Mathj2matical_Di^ L e a r n i n g , _ a n d _ T e a c h i n g _ P r o b l e f f i New York: John Wiley S Sons, v o l . I I , p.8. 3. L o c . C i t . 4. S c o t t E. Fahlman, J L g l a n n i n g _ S y s t e m _ f o r _ R o b o t C o n s t r u c t i o n _ T a s k s , Cambridge, Mass.: M a s s a c h u s e t t s I n s t i t u t e of T e c hnology, AI T e c h n i c a l Report No. 283, 1973. 5. Johan d e K l e e r , Q u a l i t a t i v e ^ a n d _ Q u a n t i t a t i y e ^ K n o w l e d g e ^ i n C l a s s i c a l _ M e c h a n i c s , Cambridge, Mass.: M a s s a c h u s e t t s I n s t i t u t e o f T e c h n o l o g y , M.Sc. T h e s i s , 1975. 6. WHISPER'S problem domain was suggested by A l a n Mackworth i n d i s c u s s s i o n w i t h Raymond R e i t e r . 7. T e r r y Winograd, P£ocedures_as_a_Repre a_Computer_Prggram _ f o r Understanding„Natural Language, Cambridge, Mass.: M a s s a c h u s e t t s I n s t i t u t e o f Tec h n o l o g y , PhD, T h e s i s , MAC T e c h n i c a l Report No. 84. 8, S c o t t E. Fahlman, op., c i t . . , p. 134-135. 9. C h a r l e s M. Eastman, "Automated Space P l a n n i n g , " A r t i f i c i a l _ I n t e l l i g e n c e , v o l . 4(1973), pp.41-64. 10. S c o t t E. Fahlman, op.. c i t . , p. 100. 11. B. R a p h a e l , "The Frame Problem i n P r o b l e m - S o l v i n g Systems," M t i l i g i a l _ l n t e l l i g e n c e ^ a n d _ H e u r i s t i c _ P r o g r a m m i n g , ed. N.V. F i n d l e r and B, M e l t z e r , E d i n b u r g h : Edinburgh U n i v e r s i t y P r e s s , 1971, pp.159-169. 207 1 2 . P . H a y e s , " A L o g i c o f A c t i o n s , " M a c h i n e _ I n t e l l i g e n c e _ 6 , e d . B . M e l t z e r and D. M i c h i e , New Y o r k : A m e r i c a n E l s e v i e r P u b l i s h i n g , 1 9 7 1 , p p . 4 9 5 - 5 2 0 . 1 3 . M . H . P i r e n n e , l i s i o n _ a n d _ t h e _ E y e , L o n d o n ; Chapman S H a l l , 1 9 6 7 , p . 3 2 . 14. M a r v i n M i n s k y and Seymour P a p e r t , P e r ^ e £ t r o n s i _ A n i S l £2^ S g J i 9 S m ^ g - £ g I £ B l § t i 9 B a I „. G e o m e t r y , C a m b r i d g e , M a s s . : MTITTT" iress7~196 9. 1 5 . R i c h a r d B a k e r , " A S p a t i a l l y - O r i e n t e d I n f o r m a t i o n P r o c e s s o r w h i c h S i m i u l a t e s t h e M o t i o n s o f R i g i d O b j e c t s , " A r t i f i c i a l _ I n t e l l i g e n c e , v o l . 4 ( 1 9 7 3 ) , p p . 2 9 - 4 0 . 1 6 . E . F . C o d d , C e l l u l a r _ A u t o m a t a , New Y o r k : A c a d e m i c P r e s s , 1 9 6 8 . 1 7 . D . V . M c D e r m o t t , £ 0 N N I V E R _ B e f e r e n c e _ M a n u a l , C a m b r i d g e , M a s s . : M a s s a c h u s e t t s I n s t i t u t e o f T e c h n o l o g y , A l Memo N o . 2 5 9 , 1972 . 1 8 . B.Wilcox and G . J.Sussman, L ISP^MTS_U s€rJ.s_G u i de, Ann aRbor, M i c h i g a n : M e n t a l H e a l t h Research I n s t i t u t e , 1 9 7 3 . 1 9 . G . P o l y a , I n d u c t i o n _ a n d _ A n a l o 2 y _ i o£JM§^feli!S^ig§-§S^-Elay§4fe2g-Igg§5SAsg» P r i n c e t o n , N . J . : P r i n c e t o n U n i v e r s i t y P r e s s , 1 9 5 4 , p . 1 3 . 20.. 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