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Invariant relative timing in the learning of a perceptual motor skill Stanley, Mary Louise 1989

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INVARIANT RELATIVE TIMING IN THE LEARNING OF A PERCEPTUAL MOTOR SKILL by MARY LOUISE STANLEY B.A., The University of Alberta, 1984 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENT FOR THE DEGREE OF MASTER OF PHYSICAL EDUCATION in THE FACULTY OF GRADUATE STUDIES School of Physical Education & Recreation We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA July 1989 © Mary Louise Stanley, 1989 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department The University of British Columbia Vancouver, Canada DE-6 (2/88) ABSTRACT The c o n c e p t o f i n v a r i a n t r e l a t i v e t i m i n g h a s t y p i c a l l y b e e n a s s o c i a t e d w i t h t h e c o n c e p t o f a g e n e r a l i z e d m o t o r p r o g r a m . The p r e s e n t s t u d y a p p r o a c h e s t h e phenomenon o f i n v a r i a n t r e l a t i v e t i m i n g f r o m t h e p e r s p e c t i v e o f l e a r n i n g . The u n d e r l y i n g q u e s t i o n o f c o n c e r n f o r t h i s s t u d y i s "What is learned?". The s p e c i f i c q u e s t i o n a d d r e s s e d by t h e p r e s e n t s t u d y i s w h e t h e r r e l a t i v e t i m i n g i s one o f t h e e s s e n t i a l p r o p e r t i e s o f movement t h a t i s l e a r n e d d u r i n g s k i l l a c q u i s i t i o n . I n t h e p r e s e n t e x p e r i m e n t , s u b j e c t s w e re g i v e n e x t e n s i v e p r a c t i c e i n l e a r n i n g t o v i s u a l l y t r a c k a n d r e p r o d u c e a c r i t e r i o n w a v e f o r m u s i n g a j o y s t i c k c o n t r o l f o r t h e i r r e s p o n s e . I n o r d e r t o t e s t w h e t h e r s u b j e c t s l e a r n t h e r e l a t i v e t i m i n g o f a movement, t h e y w e re t r a n s f e r r e d t o w a v e f o r m s w h i c h w ere i d e n t i c a l t o t h e c r i t e r i o n i n t e r m s o f r e l a t i v e t i m i n g , b u t d i f f e r e n t i n t e r m s o f a b s o l u t e t i m i n g . M e a s u r e m e n t s w e r e t a k e n on a l l w a v e f o r m s i n two c o n d i t i o n s : 1) i n a p u r s u i t t r a c k i n g c o n d i t i o n w here s u b j e c t s w e r e t e m p o r a l l y c o n s t r a i n e d by t h e s t i m u l u s , a n d 2) i n a r e p r o d u c t i o n c o n d i t i o n w here s u b j e c t s ' t i m i n g was n o t c o n s t r a i n e d . P u r s u i t t r a c k i n g p e r f o r m a n c e was e v a l u a t e d u s i n g t h r e e d e p e n d e n t m e a s u r e s : RMS e r r o r , l e a d - l a g i n d e x , a n d v a r i a b i l i t y . P e r f o r m a n c e i n t h e r e p r o d u c t i o n c o n d i t i o n was s u b j e c t e d t o t h r e e a n a l y s e s : 1) an h a r m o n i c a n a l y s i s , w h i c h d e s c r i b e d e a c h r e s p o n s e w a v e f o r m i n t e r m s o f i t s p h a s e , f r e q u e n c y , a m p l i t u d e , a n d p e r i o d ; 2 ) p r o p o r t i o n a l i n t e r v a l d u r a t i o n s ; a n d 3 ) p r o p o r t i o n a l i n t e r v a l d i s p l a c e m e n t s . The outcome f r o m b o t h c o n d i t i o n s g i v e s s u p p o r t t o t h e i d e a t h a t t h e i n v a r i a n t r e l a t i v e t i m i n g o f movement i s one o f t h e a s p e c t s o f a movement t h a t humans l e a r n . i v TABLE OF CONTENTS A b s t r a c t i i L i s t of Tables i v L i s t o f F i g u r e s v 1. I n t r o d u c t i o n 1 2. Methods 12 Subjects 12 Task 12 Apparatus 12 Stimulus Waveforms 14 P u r s u i t T r a c k i n g and Input B l a n k i n g 16 Procedure 17 Data A n a l y s i s 20 S t a t i s t i c a l A n a l y s i s 26 3. R e s u l t s 28 Part One - P u r s u i t T r a c k i n g 28 I. RMS E r r o r 2 8 I I . W i thin S u b j e c t V a r i a b i l i t y 35 I I I . Lead-Lag Index 38 Part Two - Input B l a n k i n g 45 I. I n t e r v a l D u r a t i o n s 45 I I . I n t e r v a l Displacements 54 I I I . P e r i o d 58 IV. RMS E r r o r 63 V. Frequency Composition 64 VI. Kinematic P r o f i l e s 65 4. D i s c u s s i o n 69 Pa r t One - P u r s u i t T r a c k i n g 69 Part Two - Input B l a n k i n g 7 4 I. I n t e r v a l D u r a t i o n s 74 I I . I n t e r v a l Displacements . 80 I I I . Cycle D u r a t i o n 81 IV. Frequency Composition and RMS E r r o r . 82 V. Kinematic P r o f i l e s . 84 Pa r t Three - C o n c l u s i o n s 8 6 Component Fr e q u e n c i e s 85 R e l a t i v e Timing 8 6 What i s Learned? 88 Appendix A: Review of L i t e r a t u r e 90 What i s Learned? 91 R e p r e s e n t a t i o n a l i s m and the Problem of Higher A u t h o r i t y 98 I n v a r i a n t R e l a t i v e t i m i n g 104 V Appendix B: P i l o t Study 117 I n t r o d u c t i o n 117 Methods 124 R e s u l t s and D i s c u s s i o n 133 Appendix C: Kinematic p r o f i l e s from i n p u t b l a n k i n g day 15 best RMS 155 Appendix D: Kinematic p r o f i l e s from input b l a n k i n g day 15 - a l l f i v e c y c l e s 162 Appendix E: Harmonic p r o f i l e s day 15 wl - w7 169 References 177 v i LIST OF TABLES T a b l e Page 1. E x p e r i m e n t a l d e s i g n 19 2. Waves * Days i n t e r a c t i o n s : R o o t Mean S q u a r e d E r r o r 33 3. ANOVA t a b l e v a r i a b i l i t y : P l a n n e d c o n t r a s t s d a y 15 38 4 . ANOVA t a b l e : I n t e r v a l d u r a t i o n s 52 5. I n t r a - i n d i v i d u a l v a r i a b i l i t y f o r i n t e r v a l d u r a t i o n d a t a a c r o s s t h e f i v e w a v e f o r m s 54 6. ANOVA t a b l e : I n t e r v a l d i s p l a c e m e n t s 55 7. I n t r a - i n d i v i d u a l v a r i a b i l i t y f o r i n t e r v a l d i s p l a c e m e n t d a t a a c r o s s t h e f i v e w a v e f o r m s . . . . 55 8 . RMS E r r o r : I n p u t b l a n k i n g d ay 15 63 9. ANOVA T a b l e : RMS E r r o r I n p u t B l a n k i n g 64 v i i LIST OF FIGURES F i g u r e Page 1. R o o t Mean S q u a r e d E r r o r as a f u n c t i o n o f p r a c t i c e . 30 2. Mean o f 512 s t a n d a r d d e v i a t i o n v a l u e s f r o m t h e d i s p l a c e m e n t t i m e p r o f i l e s o f 10 c y c l e s o f p u r s u i t t r a c k i n g f o r 7 w a v e f o r m s o v e r 6 t r a n s f e r d a y s . 37 3. The l e a d - l a g i n d e x o f t h e s u b j e c t s ' r e s p o n s e s r e l a t i v e t o t h e s t i m u l u s a s a f u n c t i o n o f p r a c t i c e f o r w l - w5. 40 4 . The l e a d - l a g i n d e x o f t h e s u b j e c t ' s r e s p o n s e s r e l a t i v e t o t h e s t i m u l u s a s a f u n c t i o n o f p r a c t i c e f o r w6 - w8. 42 5. The s t a n d a r d d e v i a t i o n s o f t h e l e a d - l a g i n d e x o f t h e s u b j e c t s ' r e s p o n s e s r e l a t i v e t o t h e s t i m u l u s f o r w l - w8. 44 6. Waveforms by i n t e r v a l s i n t e r a c t i o n f o r p r o p o r t i o n a l i n t e r v a l d u r a t i o n d a t a . 47 7 . I n t e r v a l s b y c y c l e s i n t e r a c t i o n f o r p r o p o r t i o n a l i n t e r v a l d u r a t i o n d a t a . 4 9 8. P r o p o r t i o n a l i n t e r v a l d u r a t i o n s as a f u n c t i o n o f o v e r a l l d u r a t i o n f o r s u b j e c t 2. 51 9. Waveforms b y i n t e r v a l s i n t e r a c t i o n f o r r e l a t i v e i n t e r v a l d i s p l a c e m e n t d a t a . 57 10. Mean c y c l e d u r a t i o n s ( p e r i o d ) c o l l a p s e d o v e r 5 c y c l e s o f i n p u t b l a n k i n g f r o m w l - w5. 60 11 . Mean c y c l e d u r a t i o n s ( p e r i o d ) c o l l a p s e d o v e r 5 c y c l e s o f i n p u t b l a n k i n g f r o m w6 - w8. 62 12. K i n e m a t i c p r o f i l e s f r o m s u b j e c t 2 f o r w l - w5. 67 13. K i n e m a t i c p r o f i l e s f r o m s u b j e c t 6 f o r w l - w5. 68 1 CHAPTER 1.  INTRODUCTION One o f t h e f u n d a m e n t a l q u e s t i o n s f o r t h o s e o f us who s e e k t o u n d e r s t a n d l e a r n i n g i s "what is learned?". T h i s q u e s t i o n h a s b e e n c e n t r a l t o p s y c h o l o g y a t l e a s t a s f a r b a c k as t h e i n c e p t i o n o f b e h a v i o r i s m i n t h e 1930's ( G i b s o n , 1969; Weimer, 1977; W h i t i n g , 1 9 8 0 ) . The b e h a v i o r i s t s h a v e p r o p o s e d , t h a t i t i s a s s o c i a t i o n s b e t w e e n s t i m u l i a n d r e s p o n s e s t h a t a r e l e a r n e d . The c o g n i t i v i s t s , on t h e o t h e r h a n d , h a v e a r g u e d , t h a t what Is learned a r e r e p r e s e n t a t i o n s o f movement, o b j e c t s , o r e v e n t s . T h e r e h a s b e e n much s p e c u l a t i o n a s t o t h e n a t u r e o f t h i s r e p r e s e n t a t i o n f o r l e a r n e d movements; i t h a s b e e n d e s c r i b e d i n d i f f e r e n t ways by d i f f e r e n t r e s e a r c h e r s , w i t h l a b e l s s u c h a s schema ( S c h m i d t , 1975) image o f a c h i e v e m e n t ( P r i b r a m , 1 9 7 1 ) , a n d m o t o r p r o g r a m ( K e e l e , 1 9 7 5 ) . The G i b s o n i a n s o r t h e e c o l o g i c a l g r o u p , who l i k e t h e b e h a v i o r i s t s , h a v e r e j e c t e d e x p l a n a t i o n s b a s e d on r e p r e s e n t a t i o n , h a v e e x p l a i n e d l e a r n i n g i n y e t a n o t h e r way. J . J . G i b s o n (1966, p.279) h a s d e f i n e d p e r c e p t u a l l e a r n i n g a s " c a s e s o f p e r c e i v i n g o r d e t e c t i n g an i n v a r i a n t " . J . J . G i b s o n ' s i d e a c a n be e x t e n d e d t o b o t h t h e c o g n i t i v e a n d m o t o r d o m a i n s . I n r e l a t i o n t o c o g n i t i o n , E l e a n o r G i b s o n (1969, p471) h a s a r g u e d t h a t t h e l e a r n e d p e r c e p t u a l a b i l i t y " t o d e t e c t r e g u l a r i t y , o r d e r , a n d s t r u c t u r e " p r o v i d e s t h e b a s i s f o r c o g n i t i v e a b i l i t i e s s u c h a s l e a r n i n g m a t h e m a t i c s 2 ( s e e a l s o W e r t h e i m e r , 1 9 4 5 ) . I n t h e c a s e o f movement as w e l l , t h e r e a r e c e r t a i n o f i t s f e a t u r e s t h a t become i n v a r i a n t a s i t becomes w e l l l e a r n e d . The s t u d i e s t h a t c o n s t i t u t e t h i s t h e s i s w e r e c o n d u c t e d i n o r d e r t o i n v e s t i g a t e t h e q u e s t i o n "what is learned?" i n t h e p r o c e s s o f p e r c e p t u a l - m o t o r l e a r n i n g . I n t h e f i e l d o f m o t o r l e a r n i n g a n d c o n t r o l t h e r e h a v e b e e n s e v e r a l h y p o t h e s e s p u t f o r w a r d i n an a t t e m p t t o a n s w e r t h i s q u e s t i o n . Two o f t h e s e w e re t h e f o c u s o f t h i s s t u d y . The f i r s t o f t h e s e was t h a t p e o p l e l e a r n t h e r e l a t i v e t i m i n g o f a movement. The s e c o n d o f t h e s e , a d d r e s s e d i n t h e p i l o t s t u d y ( a p p e n d i x ) , was t h a t p e o p l e l e a r n t h e component f r e q u e n c i e s o f a movement. F o r s e v e r a l y e a r s t h e r e h a s b e e n e v i d e n c e t h a t t h e r e l a t i v e t i m i n g o f t h e r e s p o n s e e l e m e n t s t h a t make up a movement r e m a i n i n v a r i a n t o v e r c h a n g e s i n a b s o l u t e t i m i n g d u r i n g t h e p e r f o r m a n c e o f m o t o r s k i l l s . M o t o r t h e o r i s t s h a v e i n f e r r e d , f r o m t h i s e v i d e n c e , t h a t r e l a t i v e t i m i n g may be an i n v a r i a n t f e a t u r e o f t h e c e n t r a l r e p r e s e n t a t i o n ( u s u a l l y m o t o r p r o g r a m ) o f t h e movement b e i n g l e a r n e d ( S h a p i r o & S c h m i d t , 1982; S h a p i r o , Z e r n i c k e , G r e g o r , & D i e s t e l , 1 9 8 1 ) . From a n o t h e r p e r s p e c t i v e , a c t i o n t h e o r i s t s , t h o u g h h a v i n g r e j e c t e d t h e n o t i o n o f r e p r e s e n t a t i o n , n e v e r t h e l e s s h a v e a r g u e d t h a t i n v a r i a n t r e l a t i v e t i m i n g i s one o f t h e e s s e n t i a l v a r i a b l e s t h a t c h a r a c t e r i z e s human s k i l l e d a c t i o n ( K e l s o , Putnam, & Goodman, 1 9 8 3 ; T u l l e r & K e l s o , 1 9 8 4 ) . 3 Most of the r e s e a r c h e r s who have s t u d i e d i n v a r i a n t r e l a t i v e t i m i n g have s t u d i e d i t i n r e l a t i o n t o the motor program. A c e n t r a l q u e s t i o n f o r those who study the motor program has been "What are i t s i n v a r i a n t f e a t u r e s ? " , and i t has been suggested (Schmidt, 1988) t h a t r e l a t i v e t i m i n g i s one o f these i n v a r i a n t f e a t u r e s . The i d e a t h a t r e l a t i v e t i m i n g i s an i n v a r i a n t f e a t u r e of the motor program i s o f t e n r e f e r r e d t o i n the l i t e r a t u r e as the proportional duration model (Gentner, 1987). The p r o p o r t i o n a l d u r a t i o n model p r e d i c t s t h a t any s k i l l e d movement performed wi t h d i f f e r e n t o v e r a l l d u r a t i o n s w i l l e x h i b i t f i x e d r e l a t i v e d u r a t i o n s . O r i g i n a l evidence f o r t h i s came from some unp u b l i s h e d s t u d i e s by Armstrong (1970, c i t e d i n Schmidt, 1988). He had h i s s u b j e c t s r e p e a t e d l y move a l e v e r through a p a r t i c u l a r u n i d i m e n s i o n a l s p a t i a l - t e m p o r a l p a t t e r n . When s u b j e c t s moved too q u i c k l y they nonetheless maintained an i n v a r i a n c e i n the r e l a t i v e t i m i n g between r e v e r s a l s . I t was proposed t h a t t h i s o c c u r r e d because r e l a t i v e t i m i n g was s t r u c t u r e d i n t o the motor program, whereas the o v e r a l l d u r a t i o n was a parameter whose va l u e c o u l d vary across i n s t a n c e s of the s k i l l . Thus, f o r each i n s t a n c e o f the s k i l l a d i f f e r e n t parameter v a l u e f o r o v e r a l l d u r a t i o n was a s s i g n e d t o the motor program. T h i s p r o p o r t i o n a l d u r a t i o n model of t i m i n g i n s k i l l e d motor performance has been widely accepted up u n t i l now. (For other e m p i r i c a l r e s e a r c h s u p p o r t i n g t h i s model see: C a r t e r & Shapiro, 1984; Shapiro, 1977; Summers, 1977; T e r z u o l o & V i v i a n i , 1979). 4 Recently, however, the concept o f i n v a r i a n t r e l a t i v e t i m i n g has come i n t o q u e s t i o n Gentner (1987). Gentner r e a n a l y z e d some of the data from past s t u d i e s on i n v a r i a n t r e l a t i v e t i m i n g . He argued t h a t the m a j o r i t y o f the data used as s u p p o r t i n g evidence f o r the p r o p o r t i o n a l d u r a t i o n model had been analyzed i m p r e c i s e l y i n t h a t r e s e a r c h e r s had analyzed mean d u r a t i o n s of a giv e n i n t e r v a l i n s t e a d of i n d i v i d u a l observed d u r a t i o n s . To overcome t h i s problem, Gentner proposed a constant p r o p o r t i o n t e s t (see Review of L i t e r a t u r e ) . A f t e r having r e a n a l y z e d the data from experiments t h a t had found evidence f o r i n v a r i a n t r e l a t i v e t i m i n g i n motor t a s k s , Gentner concluded t h a t the p r o p o r t i o n a l d u r a t i o n model was not supported. R e l a t i v e d u r a t i o n s were maintained t o some extent but not p r e c i s e l y . Since the p u b l i c a t i o n of Gentner's paper s e v e r a l r e s e a r c h e r s have begun t o q u e s t i o n the phenomenon of i n v a r i a n t r e l a t i v e t i m i n g (Heuer, 1988a; Heuer, 1988b; Heuer & Schmidt, 1988; Schmidt, 1988; Z e l a z n i k et a l . , 1986). Though human's may not exhibit r e l a t i v e t i m i n g w i t h p e r f e c t i n v a r i a n c e , one cannot r u l e out the n o t i o n t h a t they may learn i n v a r i a n t r e l a t i v e t i m i n g . One c o u l d p o s i t at l e a s t t h r e e reasons f o r a l a c k o f p e r f e c t i n v a r i a n c e e v i d e n t at the b e h a v i o r a l l e v e l . The f i r s t has been suggested by Heuer (1988), who has argued t h a t a l a c k o f i n v a r i a n c e i n r e l a t i v e t i m i n g at the b e h a v i o r a l l e v e l does not n e c e s s a r i l y i n d i c a t e a l a c k o f i n v a r i a n c e c e n t r a l l y . T h i s i s because t h e r e are n o n - l i n e a r i t i e s i n the nervous system which may 5 d i s t o r t a c e n t r a l i n v a r i a n c e i n r e l a t i v e t i m i n g , such t h a t i t would manifest p e r i p h e r a l l y ( b e h a v i o r a l l y ) i n the form of v a r i a b l e r e l a t i v e t i m i n g . The second i s t h a t humans may l e a r n r e l a t i v e t i m i n g i n a formal way (Thompson, 1952). As Bateson (1982) has p o i n t e d out i n d e s c r i b i n g morphogenesis, though t h e r e may be an "asymmetry i n s i z e " , one n e v e r t h e l e s s f i n d s "a deeper symmetry i n formal r e l a t i o n s " . In the same way t h a t symmetry of form organi z e s morphogenesis, r e l a t i v e t i m i n g may be the s t r u c t u r e around which a movement p a t t e r n i s or g a n i z e d . S e v e r a l authors have drawn p a r a l l e l s between morphogenesis and motor l e a r n i n g ( B e r k i n b l i t , Feldman, & Fukson, 1986 p.599; Turvey, 1986 p.624). L i v i n g c r e a t u r e s e x h i b i t symmetry i n terms of form, but r a r e l y i s t h i s expressed i n terms of p e r f e c t l y e q u i v a l e n t magnitudes on the r i g h t and l e f t s i d e s of the body. For i n s t a n c e , the r i g h t l e g may be s l i g h t l y longer than the l e f t ( i . e . the magnitudes are not e x a c t l y e q u i v a l e n t ) but the form i s symmetrical i n t h a t t h e r e are two l e g s , two knees, two f e e t and the form of these on the r i g h t i s the exact m i r r o r image of t h a t on the l e f t . The concept of r e l a t i v e t i m i n g can be c o n s i d e r e d i n a s i m i l a r l i g h t . Gentner (1987) has g i v e n evidence t h a t i n t e r v a l d u r a t i o n s are not always mathematically p e r f e c t p r o p o r t i o n s of o v e r a l l movement time. T h i s i s analogous t o Bateson's n o t i o n of "asymmetry i n s i z e " . Gentner a l s o has giv e n evidence t h a t on average the p r o p o r t i o n s are i n v a r i a n t , and t h i s can be thought of as 6 a n a l o g o u s t o B a t e s o n ' s n o t i o n o f t h e " d e e p e r s ymmetry i n f o r m a l r e l a t i o n s " . The t h i r d r e a s o n t h a t r e l a t i v e t i m i n g may n o t e x h i b i t p e r f e c t i n v a r i a n c e , i s t h a t f e e d b a c k may somehow be i n v o l v e d i n m o d u l a t i n g t h e e x p r e s s i o n o f r e l a t i v e t i m i n g . I n t e r v a l s t h a t a r e n o t p e r f e c t p r o p o r t i o n s o f o v e r a l l movement t i m e , c r e a t e p r o b l e m s f o r t h e p r e s e n t m o d e l o f a m o t o r p r o g r a m w i t h f i x e d r e l a t i v e t i m i n g a n d an o v e r a l l d u r a t i o n p a r a m e t e r . I n s u c h a m o d e l r e l a t i v e t i m i n g must be m a i n t a i n e d p r e c i s e l y . The d u r a t i o n p a r a m e t e r o n c e p u t i n t o t h e p r o g r a m i s n o t m o d i f i a b l e . I f , h o w e v e r , f e e d b a c k w e r e b e i n g u s e d t h r o u g h o u t t h e d u r a t i o n o f t h e movement t o c o n t r o l a b s o l u t e t i m i n g , t h i s m i g h t a c c o u n t f o r s l i g h t v a r i a t i o n s i n r e l a t i v e t i m i n g . T h e r e h a s b e e n e v i d e n c e f o r t h i s i n t r a c k i n g s t u d i e s ( F r a n k s & W i l b e r g , 1 9 8 2 ) . I n t h i s s t u d y , when v i s u a l f e e d b a c k f r o m t h e s t i m u l u s was a v a i l a b l e , s u b j e c t s m a i n t a i n e d t h e a b s o l u t e d u r a t i o n , w h e r e a s when t h i s f e e d b a c k was n o t a v a i l a b l e t h e a b s o l u t e d u r a t i o n v a r i e d . A n o t h e r r e a s o n , t h a t i n v a r i a n t r e l a t i v e t i m i n g i s n o t f o u n d i n movement p r o d u c t i o n t a s k s , i s t h a t f ew r e s e a r c h e r s h a v e c o n s i d e r e d t h e n e c e s s i t y o f p r a c t i c e i n t h e d e v e l o p m e n t o f r e l a t i v e t i m i n g . F o r i n s t a n c e , i n t h e r e c e n t s t u d y b y H e u e r a n d S c h m i d t ( 1 9 8 8 ) , i n w h i c h s u b j e c t s w e r e g i v e n o n l y 250 c y c l e s o f p r a c t i c e , i t was c o n c l u d e d t h a t r e l a t i v e t i m i n g d o e s n o t r e m a i n i n v a r i a n t i n a t r a n s f e r t a s k . H owever i t i s q u e s t i o n a b l e w h e t h e r 250 c y c l e s i s a d e q u a t e p r a c t i c e f o r t h e d e v e l o p m e n t o f i n v a r i a n t r e l a t i v e t i m i n g , 7 or f o r the development of a motor program. The development of the motor program i s presumably based on e x t e n s i v e experience with the environment such t h a t an a p p r o p r i a t e form of o r g a n i z a t i o n might develop. But, s i n c e n e i t h e r l e a r n i n g , nor the development of the motor program, are addressed, the problem of adequate p r a c t i c e i s o f t e n over-looked. With i n s u f f i c i e n t p r a c t i c e , i t i s not s u r p r i s i n g t h a t the i n v a r i a n c e t h a t i s deemed t o e x i s t w i t h i n the program has not been found. Subjects have not been gi v e n s u f f i c i e n t time t o develop t h a t i n v a r i a n c e . Thus, d e s p i t e recent c r i t i c s m by Gentner (1987) of the i n v a r i a n t r e l a t i v e t i m i n g h y p o t h e s i s , the evidence p r e s e n t e d above i n d i c a t e s t h a t i n v a r i a n t r e l a t i v e t i m i n g remains a v i a b l e t o p i c of i n v e s t i g a t i o n . The assumption u n d e r l y i n g most of the r e s e a r c h on i n v a r i a n t r e l a t i v e t i m i n g has been t h a t , i n v a r i a n t r e l a t i v e t i m i n g m a n i f e s t s on a b e h a v i o r a l l e v e l because i t i s s t r u c t u r e d i n t o the motor program. Thus r e l a t i v e t i m i n g i s i n v a r i a n t , and i s seen t o f u n c t i o n i n an open loop f a s h i o n , w h ile o v e r a l l d u r a t i o n i s a parameter l e f t f r e e t o vary. But i n motor programming theory, the way i n which the o v e r a l l d u r a t i o n parameter value i s determined and a s s i g n e d has not been addressed. The computer analogy may be m i s l e a d i n g i n t h i s case, i n t h a t i n a computer program the t a s k of a s s i g n i n g and determining parameter v a l u e s i s taken care of by the programmer. I f one assumes t h a t a s i m i l a r p r o c e s s i s o c c u r r i n g i n humans, one i s l e d to the dubious 8 c o n c l u s i o n t h a t t h e r e i s a computer programmer (or homunculus) i n ones head whose job i t i s t o determine and a s s i g n parameter v a l u e s . The c r u c i a l q u e s t i o n o f the way i n which feedback i n t e r a c t s with the program i n t i m i n g c o n t r o l i s r e l e g a t e d t o the realm of the programmer/homunculus. Because a computer does not have t h a t dynamic i n t e r a c t i o n w i t h i t s environment, t h a t i s c h a r a c t e r i s t i c o f l i v i n g systems, the computer metaphor can be both l i m i t i n g and m i s l e a d i n g ( C a r e l l o et a l . , 1984). In i n v e s t i g a t i n g r e l a t i v e t i m i n g , I am not assuming the e x i s t e n c e o f a motor program, nor t h a t r e l a t i v e t i m i n g f u n c t i o n s w i t h i n the context of a motor program. The pres e n t study was designed t o i n v e s t i g a t e the development of i n v a r i a n t r e l a t i v e t i m i n g i n s k i l l e d movement. I t was c a r r i e d out p a r t l y as a r e s u l t of the recent c o n t r o v e r s y , as t o whether i n v a r i a n t r e l a t i v e t i m i n g i s a c h a r a c t e r i s t i c of s k i l l e d movement (Gentner, 1987; Heuer, 1988; Heuer & Schmidt, 1988). As has been put forward above, the present view of i n v a r i a n t r e l a t i v e t i m i n g i n human s k i l l e d a c t i o n i s d i f f e r e n t than t h a t proposed by most motor programming t h e o r i s t s (e.g. Schmidt, 1988). Because I see s k i l l e d human a c t i o n t o be c h a r a c t e r i z e d by a continuous i n t e r a c t i o n with the environment, I chose t o i n v e s t i g a t e the development of s k i l l i n a t r a c k i n g t a s k i n which t h i s i n t e r a c t i o n i s over t and measurable. Most of the c o n f u s i o n surrounding the i s s u e o f c l o s e d and open loop c o n t r o l has t o do with the assumption t h a t a system under 9 c l o s e d l o o p c o n t r o l w i l l e x h i b i t discrete f e e d b a c k c o r r e c t i o n s . T h i s i s n o t a l w a y s t h e c a s e h o w e v e r . F e e d b a c k c a n a l s o a c t i n a c o n t i n u o u s f a s h i o n i n m o d u l a t i n g a c t i o n , s u c h t h a t r a t h e r t h a n b e i n g m o d i f i e d d i s c r e t e l y , a c t i o n i s m o d i f i e d c o n t i n u o u s l y o v e r t i m e . P i l o t d a t a g i v e s u p p o r t t o t h i s c o n t e n t i o n ( s e e a p p e n d i x ) . As P o w e r s (1973) h a s p o i n t e d o u t : " T h i s ( d i s c r e t e model) i s a n a t u r a l f i r s t a p p r o x i m a t i o n t o d e s c r i b i n g a c l o s e d l o o p o f c a u s e s a n d e f f e c t s , b u t i t i s i n c o r r e c t ... t h e r e a l o r g a n i s m b e h a v e s i n a s m o o t h l y c o n t i n u o u s manner, w i t h b o t h r e s p o n s e s a n d s t i m u l i c o n t i n u a l l y c h a n g i n g a n d c o n t i n u a l l y i n t e r a c t i n g . " (p. 42) A s y e t , no-one h a s i n v e s t i g a t e d r e l a t i v e t i m i n g i n a c o n t e x t i n w h i c h t h e r e i s a c o n t i n u o u s i n t e r a c t i o n w i t h t h e e n v i r o n m e n t , a s t h e r e i s i n a t r a c k i n g t a s k . C o m i n g o u t o f t h e t h e o r e t i c a l f r a m e w o r k a s s o c i a t e d w i t h t h e m o t o r p r o g r a m , most o f t h e s t u d i e s on i n v a r i a n t r e l a t i v e t i m i n g h a v e n o t f o c u s s e d on t h i s r e l a t i o n s h i p . By s t u d y i n g r e l a t i v e t i m i n g i n a t r a c k i n g t a s k , i t was p o s s i b l e t o g a i n an u n d e r s t a n d i n g o f t h e c o n t r i b u t i o n t h a t f e e d b a c k makes i n t i m i n g c o n t r o l . The t r a c k i n g p a r a d i g m was u s e f u l i n t h a t i t r e q u i r e d t h a t t h e s u b j e c t c o n t i n u o u s l y i n t e r a c t w i t h t h e e n v i r o n m e n t on p e r c e p t u a l a n d m o t o r l e v e l s , a n d i t a l l o w e d p r e c i s e q u a n t i f i c a t i o n o f b o t h s t i m u l u s a n d r e s p o n s e p a t t e r n s . F i v e d i f f e r e n t b u t r e l a t e d f o r m s o f movement a n a l y s i s w e r e u s e d i n t h i s s t u d y i n o r d e r t o e v a l u a t e t h e p e r f o r m a n c e 10 of the s u b j e c t s : an e r r o r measurement i n d i c a t i n g the o v e r a l l accuracy and p r e c i s i o n of the s u b j e c t (Root mean squared e r r o r ) ; a measure of the s u b j e c t ' s a b i l i t y t o reproduce the movement c o n s i s t e n t l y d u r i n g each t r i a l ( w i t h i n s u b j e c t v a r i a b i l i t y of the response p r o f i l e s ) ; a l e a d l a g index gained from a c r o s s - c o r r e l a t i o n a n a l y s i s t h a t r e p r e s e n t s the s u b j e c t ' s a b i l i t y t o produce the response at the c o r r e c t time; an harmonic a n a l y s i s t h a t o f f e r s i n f o r m a t i o n r e g a r d i n g the composition of the response; and a c a l c u l a t i o n of the p r o p o r t i o n a l d u r a t i o n of the time between movement r e v e r s a l s . The q u e s t i o n of i n v a r i a n t r e l a t i v e t i m i n g was e x p l o r e d u s i n g a t r a i n i n g \ t r a n s f e r paradigm i n which s u b j e c t s were giv e n e x t e n s i v e p r a c t i c e on t r a c k i n g a s p e c i f i c waveform ( t r a i n i n g ) and then t r a n s f e r r e d to waveforms i d e n t i c a l t o the t r a i n i n g waveform i n r e l a t i v e t i m i n g , but d i f f e r e n t i n o v e r a l l d u r a t i o n . T h i s was c a r r i e d out under two c o n d i t i o n s : a pursuit tracking c o n d i t i o n , i n which both s t i m u l u s and response i n f o r m a t i o n were v i s u a l l y a v a i l a b l e to the s u b j e c t , and an input blanking c o n d i t i o n , i n which these sources of v i s u a l i n f o r m a t i o n were removed. Three hypotheses were t e s t e d u s i n g t h i s paradigm. F i r s t l y , f o l l o w i n g e x t e n s i v e p r a c t i c e on a given waveform, s u b j e c t s are capable of t r a c k i n g , e q u a l l y w e l l , other waveforms which have the same r e l a t i v e t i m i n g as the o r i g i n a l waveform, but d i f f e r e n t base f r e q u e n c i e s . Secondly, when s u b j e c t s are r e q u i r e d t o reproduce (during input blanking) the o r i g i n a l 11 and v a r i e d base frequency waveforms, t h e i r performance w i l l e x h i b i t i n v a r i a n t r e l a t i v e t i m i n g between r e v e r s a l s i n the waveform. In a d d i t i o n , i n order t o t e s t the hy p o t h e s i s ( o r i g i n a l l y put forward i n the p i l o t study) t h a t a movement i s l e a r n e d i n terms of i t s component f r e q u e n c i e s , s u b j e c t s were a l s o t r a n s f e r r e d t o two a d d i t i o n a l waveforms: the f i r s t c o n t a i n e d i d e n t i c a l component f r e q u e n c i e s t o t h a t of the t r a i n i n g waveform, but d i f f e r e n t phase angles, and the second was an e n t i r e l y new waveform ( d i f f e r e n t frequency, amplitude and phase r e l a t i o n s h i p s ) . I f s u b j e c t s l e a r n a movement i n terms of component f r e q u e n c i e s , then one would expect t o f i n d a b e t t e r performance on the waveform which v a r i e d only the phase angles, than on an e n t i r e l y new waveform. 12 CHAPTER 2.  METHODS Sub j e c t s S i x u n i v e r s i t y students with no motor or v i s i o n d e f i c i t s v o l u n t e e r e d to p a r t i c i p a t e i n t h i s study. None had had p r e v i o u s t r a c k i n g experience. The s u b j e c t s were r i g h t hand dominant and used t h i s hand to move the j o y s t i c k . Task Subjects were r e q u i r e d to move a j o y s t i c k which c o n t r o l l e d a response c u r s o r (point l i g h t d i s p l a y ) on an o s c i l l o s c o p e screen. The s u b j e c t ' s task was to f o l l o w a s t i m u l u s c u r s o r (point l i g h t d i s p l a y ) which appeared d i r e c t l y above the response c u r s o r on the screen and moved i n a s e r i e s of h o r i z o n t a l movements across the s c r e e n . S u b j e c t s sat at a t a b l e with t h e i r r i g h t forearm comfortably supported. The o s c i l l o s c o p e screen was p l a c e d 50 cm i n f r o n t of them at a v i s u a l l y subtended angle of 11.4 degrees. The s u b j e c t s h e l d the j o y s t i c k between the index f i n g e r and thumb. The w r i s t pronated and s u p i n a t e d i n the c o r o n a l plane w h i l e the j o y s t i c k was being moved. Apparatus The j o y s t i c k , an i n d u s t r y standard p l o t t i n g j o y s t i c k (Hughes A i r c r a f t Company CONOGRAPHIC - 12 model 6110) was adapted f o r use i n the experiment by bypassing i n t e r n a l 13 e l e c t r o n i c s w i t h i n t h e j o y s t i c k . The j o y s t i c k was f e d by a f i l t e r e d 30 v o l t s p l i t p o w e r s u p p l y a n d c o n n e c t e d t o an a n a l o g t o d i g i t a l c o n v e r t e r ( L a b m a s t e r ) w i t h a 12 b i t r e s o l u t i o n , whose d a u g h t e r b o a r d was r e s i d e n t i n an IBM M i c r o c o m p u t e r . The L a b m a s t e r g a v e d i g i t a l v a l u e s r a n g i n g f r o m +2048 (+ 5 v o l t s ) t o -2048 v a l u e s (- 5 v o l t s ) , w h i l e t h e v o l t a g e r a n g e o f t h e j o y s t i c k was a p p r o x i m a t e l y + 5 v o l t s t o -5 v o l t s ( z e r o v o l t s b e i n g c e n t e r ) . V a l u e s f r o m t h e j o y s t i c k w e r e c o n v e r t e d t o o s c i l l o s c o p e d i s p l a c e m e n t v a l u e s r a n g i n g f r o m 0 - 1000. The j o y s t i c k was s p r i n g c e n t e r e d a l o n g t h e Y a x i s . The X a x i s h a d f r e e d i s p l a c e m e n t . O n l y X c o - o r d i n a t e d i s p l a c e m e n t was r e c o r d e d . The p o t e n t i o m e t e r (a B o u r n s number 3 8 5 2 A - 2 8 2 - 1 0 3 A ) , w h i c h t r a n s f o r m e d j o y s t i c k d i s p l a c e m e n t i n t o an e l e c t r i c a l s i g n a l , h a d a r e s i s t a n c e o f 10,000 Ohms, a n d was l i n e a r ( w i t h i n one p e r c e n t ) t h r o u g h o u t t h e f u l l r a n g e o f j o y s t i c k movement. The j o y s t i c k h a d a z e r o o r d e r c o n t r o l . The j o y s t i c k was t e s t e d f o r c o n s i s t e n t l i n e a r i t y e a c h d a y w i t h t h e f o l l o w i n g p r o c e d u r e . A t e m p l a t e was made i n a r a n g e o f 45 d e g r e e s w i t h t h e l e f t (0 d e g r e e s ) , t h e c e n t e r (22 1/2 d e g r e e s ) , a n d t h e r i g h t (45 d e g r e e s ) m a r k e d o f f . E a c h p o t e n t i o m e t e r t h a t was u s e d i n t h e e x p e r i m e n t was c h e c k e d t o v e r i f y t h a t t h e d i s p l a c e m e n t t o t h e l e f t o f c e n t e r was r e p r e s e n t e d b y an e q u a l number o f d i g i t a l v a l u e s a s was t h e d i s p l a c e m e n t t o t h e r i g h t o f c e n t e r . A c o m p u t e r g e n e r a t e d s t i m u l u s was p r e s e n t e d on t h e o s c i l l o s c o p e u s i n g a d i g i t a l o u t p u t e q u i v a l e n t t o t h e 14 d i g i t a l i n put of the j o y s t i c k . A second analog s i g n a l was used t o m a i n t a i n 1 cm of v e r t i c a l displacement between the s t i m u l u s and response c u r s o r s on the o s c i l l o s c o p e . Response v a l u e s were sampled every fo u r m i l l i s e c o n d s . The p r e c i s i o n of the A/D i n t e r f a c e between the j o y s t i c k and the computer was t e s t e d u s i n g the f o l l o w i n g procedure. Fourteen l o c a t i o n s across the range of the j o y s t i c k were chosen at random. At each l o c a t i o n , data was sampled at a r a t e of 250 Hz. f o r 4.096 seconds. At any of the f o u r t e e n l o c a t i o n s , the range i n the j o y s t i c k never exceeded 4 d i g i t a l v a l u e s (or 0.008 v o l t s ) and was never l e s s than 2 d i g i t a l v a l u e s (or 0.004 v o l t s ) . The standard d e v i a t i o n v a r i e d from 0.3 to 0.47 d i g i t a l v a l u e s over the f o u r t e e n l o c a t i o n s of the j o y s t i c k . The r e s o l u t i o n of the f u l l range of the j o y s t i c k was 1,000 d i g i t a l v a l u e s . The range of the j o y s t i c k was t e s t e d w i t h the experimenter h o l d i n g the j o y s t i c k at r e s t f o r 40 seconds. With the j o y s t i c k h e l d at r e s t , the recorded range of the j o y s t i c k was 0.7 m i l l i m e t e r s . Thus any r e c o r d e d movement l e s s than 0.7 mm was not c o n s i d e r e d to be i n t e n t i o n a l movement. Stimulus Waveforms Subject s were gi v e n the f o l l o w i n g e i g h t waveforms to t r a c k : Wl)The t r a i n i n g waveform was g i v e n by the e q u a t i o n : f ( t ) = A/2 + 240 cos (cot + 3/2 71) + 120 cos 2 (cot + 5/6 ic) + 60 15 c o s 4 (cot + 1 / 6 7t) . Where cot r e p r e s e n t s t h e a n g u l a r v e l o c i t y a n d t h e p h a s e a n g l e i s e x p r e s s e d i n r a d i a n s . The p e r i o d o f t h i s w a v e f o r m was 2048 ms w i t h a b a s e f r e q u e n c y o f 0.5 Hz. F o u r o f t h e t r a n s f e r w a v e f o r m s were d e s c r i b e d b y the same e q u a t i o n a s t h e t r a i n i n g w a v e f o r m , h o w e v e r t h e b a s e f r e q u e n c y was m a n i p u l a t e d s u c h t h a t t h e f o l l o w i n g w a v e f o r m s w e r e c r e a t e d : W 2 ) t h e t r a i n i n g w a v e f o r m w i t h a p e r i o d o f 3248 ms, a n d a b a s e f r e q u e n c y o f 0.3 Hz. W 3 ) t h e t r a i n i n g w a v e f o r m w i t h a p e r i o d o f 2448 ms, a n d a b a s e f r e q u e n c y o f 0.4 Hz. W 4 ) t h e t r a i n i n g w a v e f o r m w i t h a p e r i o d o f 1648 ms, a n d a b a s e f r e q u e n c y o f 0.6 Hz. W 5 ) t h e t r a i n i n g w a v e f o r m w i t h a p e r i o d o f 1448 ms, a n d a b a s e f r e q u e n c y o f 0.7 Hz. Waveform 6 was a t r a n s f o r m a t i o n o f t h e t r a i n i n g w a v e f o r m s u c h t h a t t h e p h a s e a n g l e s o f t h e f r e q u e n c y c o m p o n e n t s w e r e a l t e r e d . W 6 ) T h i s w a v e f o r m i s g i v e n b y t h e e q u a t i o n : f(t) = A/2 + 240 c o s (cot + 3/2 7C) + 120 c o s 2 (cot + 2/3 n) + 60 c o s 4 (cot + 1/4 Ji) w i t h a p e r i o d o f 2048 a n d a b a s e f r e q u e n c y o f 0.5 Hz.. W 7 ) T h i s w a v e f o r m was an e n t i r e l y new w a v e f o r m g i v e n b y the e q u a t i o n : f (t) = A/2 + 230 c o s (cot + 3/2 TC) + 130 c o s 3 (cot + 11/6 7C) + 70 c o s 4 (cot + 2/3 7C) w i t h a p e r i o d o f 2048 ms a n d a b a s e f r e q u e n c y o f 0.5 Hz.. T h i s w a v e f o r m 16 was t h e same a s t h e t r a i n i n g w a v e f o r m i n t h a t i t h a d t h e same b a s e f r e q u e n c y , t h e same number o f component f r e q u e n c i e s , a n d t h e same o v e r a l l a m p l i t u d e r a n g e . I t v a r i e d f r o m t h e t r a i n i n g w a v e f o r m i n t h e a m p l i t u d e s a n d p h a s e a n g l e s o f t h e component f r e q u e n c i e s . T h e s e were v a r i e d i n o r d e r t o c r e a t e a p e r i o d i c w a v e f o r m w i t h t h e same o v e r a l l a m p l i t u d e r a n g e as t h e t r a i n i n g w a v e f o r m , a n d a d i f f e r e n t t o p o l o g y t h a n t h e t r a i n i n g w a v e f o r m . W8)This w a v e f o r m was t e r m e d a random w a v e f o r m b e c a u s e i t n e v e r r e p e a t e d i t s e l f . I t s p e r i o d was 40960 ms. I t was made up o f component f r e q u e n c i e s w i t h an a m p l i t u d e r a n g e o f 20 mm t o 200 mm a n d f r e q u e n c i e s r a n g i n g f r o m 0.5 Hz t o 2 Hz. The same w a v e f o r m was g i v e n t o s u b j e c t s on e a c h o f t h e s i x t r a n s f e r d a y s . on e a c h t r a n s f e r d a y . B e c a u s e t h i s w a v e f o r m h a d no c y c l i c i t y a n d t h u s no p r e d i c t a b i l i t y , s u b j e c t s w e re u n a b l e t o u s e p e r c e p t u a l a n t i c i p a t i o n ( P o u l t o n , 1952) i n t r a c k i n g i t . P u r s u i t T r a c k i n g and Input B l a n k i n g E a c h t r i a l c o n s i s t e d o f two c o n d i t i o n s : p u r s u i t t r a c k i n g a n d i n p u t b l a n k i n g . A t r i a l b e g a n w i t h 20 c y c l e s o f p u r s u i t t r a c k i n g i n w h i c h b o t h t h e s t i m u l u s a n d t h e r e s p o n s e w e r e p r e s e n t e d on t h e s c r e e n , t h u s s t i m u l u s i n f o r m a t i o n , r e s p o n s e i n f o r m a t i o n , a n d e r r o r i n f o r m a t i o n w e r e a v a i l a b l e t o t h e s u b j e c t . F o l l o w i n g t h i s t h e r e w e r e two c y c l e s o f t r a c k i n g i n w h i c h o n l y t h e s t i m u l u s r e m a i n e d on t h e s c r e e n . T h i s was u s e d as a w a r n i n g t o t h e s u b j e c t 17 t h a t they would be b e g i n n i n g the input b l a n k i n g stage of the t r i a l . In the l a s t p o r t i o n of the t r i a l , the input b l a n k i n g phase, the s u b j e c t was r e q u i r e d t o reproduce the waveform t h a t had p r e v i o u s l y been t r a c k e d i n the p u r s u i t t r a c k i n g phase, t h i s b e i n g done i n the absence of s t i m u l u s , response, and e r r o r i n f o r m a t i o n . The time t o complete t h i s phase of the t r i a l was e q u i v a l e n t i n d u r a t i o n t o 12 c y c l e s of the s t i m u l u s waveform. The middle 10 c y c l e s of p u r s u i t t r a c k i n g and the middle s i x c y c l e s of input b l a n k i n g were sampled at 250 Hz. Procedure In order t o motivate s u b j e c t s t o perform at t h e i r optimum l e v e l a p r i z e was o f f e r e d f o r the s u b j e c t who achieved the best r o o t mean squared (RMS) e r r o r score by the l a s t day of the study. A f t e r each t e s t t r i a l , s u b j e c t s were giv e n feedback about t h e i r performance i n the form of an o v e r a l l RMS e r r o r score f o r t h a t t r i a l . S ubjects were a l s o asked i n f o r m a l q u e s t i o n s about the phenomenological aspects of the t r a c k i n g t h a t they were asked t o perform. Over the course of 15 days, the s u b j e c t s were gi v e n e x t e n s i v e p r a c t i c e i n t r a c k i n g the t r a i n i n g waveform (Wl). On each of the f i f t e e n days of the study, t h e i r t r a c k i n g performance was e v a l u a t e d on t h i s t r a i n i n g waveform u s i n g v a r i o u s dependent measures. In a d d i t i o n , every t h i r d day the s u b j e c t ' s t r a c k i n g performance was assessed on the seven t r a n s f e r waveforms. Each experimental s e s s i o n began wi t h a 18 p r a c t i c e o f 200 c y c l e s o f Wl. These 200 c y c l e s were d i v i d e d i n t o 4 b l o c k s o f 50 c y c l e s . The time taken t o t r a c k each b l o c k o f c y c l e s was approximately two minutes, a f t e r which s u b j e c t s r e s t e d f o r a f u r t h e r two minutes b e f o r e b e g i n n i n g the next b l o c k . The f i f t e e n days of t h i s study were made up of nine t r a i n i n g days and s i x t r a n s f e r days. (See Table 1 f o r the la y o u t o f the experimental design.) T r a i n i n g Days: On t r a i n i n g days i n a d d i t i o n t o the p r a c t i c e component, s u b j e c t s were giv e n e i g h t t e s t t r i a l s on Wl. Each t r i a l c o n s i s t e d of twenty c y c l e s o f p u r s u i t t r a c k i n g i n which both stimulus and response c u r s o r s were v i s i b l e and ten c y c l e s of input b l a n k i n g i n which n e i t h e r the s t i m u l u s nor the response were d i s p l a y e d on the screen. Data was c o l l e c t e d from the middle ten c y c l e s o f the p u r s u i t t r a c k i n g phase and from the middle f i v e c y c l e s of the i n p u t b l a n k i n g phase. In the input b l a n k i n g phase, data was c o l l e c t e d f o r the d u r a t i o n of 6 stimulus c y c l e s i n order t o ensure t h a t 5 e n t i r e response c y c l e s were c o l l e c t e d . The sampling r a t e was 250 Hz. 19 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * T a b l e 1. Experimental Design 200 p r a c t i c e 8 t e s t t r i a l s on; c y c l e s on Wl Wl W2 W3 W4 W5 W6 W7 W8 I X X X X X X X X X 2 X X 3 X X DAYS 4 X X X X X X X X X 5 X X 6 X X 7 X X X X X X X X X 8 X X 9 X X 10 X X X X X X X X X 11 X X 12 X X 13 X X X X X X X X X 14 X X 15 X X X X X X X X X One t e s t t r i a l c o n s i s t e d of 20 c y c l e s o f p u r s u i t t r a c k i n g f o l l o w e d by 25 seconds of input b l a n k i n g . T r a n s f e r days are h i g h l i g h t e d . ********************************************************** T r a n s f e r Days: On t r a n s f e r days i n a d d i t i o n t o the p r a c t i c e component, s u b j e c t s were given one t r i a l of each of the e i g h t waveforms (Wl - W8). One t r i a l of each waveform 20 was c o m p r i s e d o f t h e two p h a s e s d e s c r i b e d a b o v e i . e . p u r s u i t t r a c k i n g a n d i n p u t b l a n k i n g . Data A n a l y s i s Root mean squared error (RMS Error) was c a l c u l a t e d on t h e pursuit tracking d a t a i n o r d e r t o d e t e r m i n e r e s p o n s e a c c u r a c y . P o u l t o n (1974) d e f i n e s RMS e r r o r as t h e s q u a r e r o o t o f t h e sum o f t h e s q u a r e s o f t h e e r r o r a t e a c h s a m p l i n g i n t e r v a l , d i v i d e d by t h e number o f s a m p l i n g i n t e r v a l s . I t i s g i v e n b y t h e e q u a t i o n : RMSE = [ £ ( s - r ) 2 / p J 1 / 2 , w h e r e s i s t h e s t i m u l u s v a l u e a t t i m e i n t e r v a l t , r i s t h e r e s p o n s e v a l u e a t t i m e i n t e r v a l t , a n d p i s t h e number o f i n t e r v a l s t h a t t h e r e s p o n s e i s s a m p l e d o v e r . RMS e r r o r h a s b e e n reccommended by P o u l t o n as t h e b e s t m e a s u r e f o r e v a l u a t i n g t h e " o v e r a l l adequacy o f t r a c k i n g " (1974, p . 3 8 ) . A d e c r e a s e i n t h e v a l u e o f RMS e r r o r s c o r e s i n d i c a t e s t h a t t h e s u b j e c t h a s become more a c c u r a t e a n d p r e c i s e i n t r a c k i n g , a n d t h u s i s i n d i c a t i v e o f l e a r n i n g ( F r a n k s , W i l b e r g & F i s h b u r n e , 1985; P o u l t o n , 1 9 7 4 ) . A c o m p u t e r p r o g r a m was w r i t t e n t o c a l c u l a t e t h e RMS e r r o r f o r t h e p u r s u i t t r a c k i n g p e r f o r m a n c e o f t h i s s t u d y . I n o r d e r t o d e t e r m i n e t h e l o w e s t p o s s i b l e RMS s c o r e w i t h t h e p r e s e n t e q u i p m e n t , d a t a w e re c o l l e c t e d w i t h t h e j o y s t i c k a t r e s t f o r t h e d u r a t i o n o f two c y c l e s o f t h e s t i m u l u s w a v e f o r m (1024 d a t a p o i n t s ) . The mean o v e r t h e 1024 d a t a p o i n t s was c a l c u l a t e d . A d a t a f i l e was t h e n c r e a t e d i n w h i c h t h i s mean v a l u e was s u b s t i t u t e d f o r a l l 1024 s t i m u l u s v a l u e s . The RMS 21 program was then run on t h i s data f i l e p r o d u c i n g an RMS v a l u e of 0.3 data p o i n t s or 0.45 mm. RMS Error was a l s o c a l c u l a t e d on the input blanking data i n order t o compare performance on the v a r i o u s waveforms d u r i n g input b l a n k i n g . Each c y c l e of input b l a n k i n g was normalized i n terms of i t s o v e r a l l d u r a t i o n , and i n terms of i t s s p a t i a l symmetry. T h i s was done i n order t o account f o r the temporal and s p a t i a l d r i f t t h a t can occur when n e i t h e r stimulus nor response are v i s i b l e t o the s u b j e c t (Vossius, 1965). The normalized response was then compared t o the stimulus i n such a way as t o determine the lowest RMS v a l u e f o r t h a t c y c l e . T h i s was achieved by s h i f t i n g the response i n both the forward and backward d i r e c t i o n s f o r a t o t a l of 20 ms by i n t e r v a l s of 4 ms. The Variability of each s u b j e c t ' s response was c a l c u l a t e d w i t h i n each t r i a l f o r the p u r s u i t t r a c k i n g phase based on a procedure from Franks, W i l b e r g & Fishburne (1982). The displacement-time curves (ten from each t r i a l ) were superimposed upon one another i n order to c a l c u l a t e a w i t h i n t r i a l v a r i a b i l i t y s c o r e . At each of the 512 sampling i n t e r v a l s , a standard d e v i a t i o n (sd) of the t e n response displacements was c a l c u l a t e d u s i n g the f o l l o w i n g e q u a t i o n : S.D. = [ E (Mean r - r) ^  / 10 J 1 ^ , where r i s the response at a g i v e n time i n t e r v a l and p i s the number of i n t e r v a l s at which r i s sampled. The standard d e v i a t i o n v a l u e s were p l o t t e d a g a i n s t time y i e l d i n g a p r o f i l e o f the w i t h i n waveform v a r i a b i l i t y f o r a given s u b j e c t on a g i v e n t r i a l . 22 The mean o f t h e 512 s d ' s was c a l c u l a t e d a n d t h i s was u s e d as an i n d e x o f t h e w i t h i n s u b j e c t v a r i a b i l i t y (v) f o r a g i v e n t r i a l . V a r i a b i l i t y m e a s u r e s h a v e b e e n u s e d i n m o t o r l e a r n i n g a n d t r a c k i n g s t u d i e s t o e v a l u a t e s k i l l a c q u i s i t i o n . Many s t u d i e s h a v e f o u n d t h a t a s u b j e c t ' s r e s p o n s e becomes more c o n s i s t e n t a s a r e s u l t o f p r a c t i c e , a n d u s e o f t h i s p a r t i c u l a r m e a s u r e h a s r e f l e c t e d t h i s phenomenon i n r e c e n t s t u d i e s , ( e . g . F r a n k s , W i l b e r g , & F i s h b u r n e , 1982; G l e n c r o s s , 1979). A t e s t was made i n o r d e r t o d e t e r m i n e t h e l o w e s t v a r i a b i l i t y s c o r e p o s s i b l e g i v e n any e r r o r i n t h e s y s t e m as a ' w h o l e , i n c l u d i n g t h e v a r i a b i l i t y p r o g r a m i t s e l f , t h e A/D c o n v e r t e r , a n d t h e j o y s t i c k . D a t a c o l l e c t e d d u r i n g t e n c y c l e s i n w h i c h t h e j o y s t i c k r e m a i n e d a t r e s t . The j o y s t i c k r e m a i n e d i n t h e same l o c a t i o n f o r e a c h o f t h e t e n c y c l e s . The d u r a t i o n o f e a c h c y c l e was 2.048 s e c o n d s a n d t h e d i g i t a l v a l u e s ( s a m p l e d a t 250 Hz) t h a t w e r e c o l l e c t e d d u r i n g e a c h c y c l e w e r e c o m p i l e d i n t o d i s p l a c e m e n t t i m e p r o f i l e s w h i c h w e r e t h e n s u p e r i m p o s e d upon one a n o t h e r . F rom t h e s e v a l u e s , s t a n d a r d d e v i a t i o n v a l u e s w e re c a l c u l a t e d a t e a c h p o i n t i n t i m e . The r a n g e o f t h e s e s t a n d a r d d e v i a t i o n v a l u e s was b e t w e e n 0 a n d 1 d i g i t a l v a l u e s . The mean o f t h e s e s t a n d a r d d e v i a t i o n v a l u e s was 0.3 d i g i t a l v a l u e s . Lead-lag index was u s e d t o d e t e r m i n e t h e e x t e n t t o w h i c h t h e s u b j e c t l e d o r l a g g e d t h e s t i m u l u s d u r i n g p u r s u i t t r a c k i n g . A c r o s s - c o r r e l a t i o n c o e f f i c i e n t was c a l c u l a t e d 23 u s i n g t h e s t i m u l u s a n d t h e r e s p o n s e w a v e f o r m s ( e a c h c omposed o f 512 p o i n t s ) , w i t h t h e s t i m u l u s b e i n g h e l d c o n s t a n t a n d t h e r e s p o n s e s i g n a l b e i n g a d v a n c e d i n t i m e by i n t e r v a l s o f t e n m i l l i s e c o n d s . F o r e a c h a d v a n c e m e n t o f t h e r e s p o n s e s i g n a l a P e a r s o n p r o d u c t - m o m e n t c o r r e l a t i o n c o e f f i c i e n t b e t w e e n s t i m u l u s a n d r e s p o n s e was c a l c u l a t e d . The t i m e a t w h i c h t h e c o r r e l a t i o n b e t w e e n s t i m u l u s a n d r e s p o n s e was g r e a t e s t was u s e d t o d e t e r m i n e t h e l e a d o r l a g o f t h e r e s p o n s e w i t h r e s p e c t t o t h e s t i m u l u s . The l e a d - l a g i n d e x h a s b e e n u s e d t o e v a l u a t e t h e l a g o f t h e r e s p o n s e r e l a t i v e t o t h e s t i m u l u s d u r i n g t r a c k i n g ( B e n n e t t , 1957 ( c i t e d i n F r a n k s , 1 9 8 2 ) ; F r a n k s , 1 9 8 2 ; F r a n k s & W i l b e r g , 1 9 8 2 ) . The l i m i t a t i o n o f t h i s m e a s u r e i s t h a t i t o n l y r e f l e c t s t h e a v e r a g e l e a d o r l a g , r a t h e r t h a n t h e s p e c i f i c l o c a t i o n i n t h e w a v e f o r m a t w h i c h t h e s u b j e c t was l e a d i n g o r l a g g i n g ( P o u l t o n , 1 9 7 4 ) . Harmonic analysis was u s e d t o a n a l y z e t h e r e s p o n s e w a v e f o r m s f r o m t h e i n p u t b l a n k i n g p h a s e i n t o component f r e q u e n c i e s . The H a r m o n i c a n a l y s i s y i e l d e d t h e f o l l o w i n g i n f o r m a t i o n : i ) t h e component f r e q u e n c i e s o f t h e r e s p o n s e . i i ) t h e a m p l i t u d e v a l u e s o f t h e s e component f r e q u e n c i e s . i i i ) t h e p h a s e a n g l e v a l u e s o f t h e s e component f r e q u e n c i e s . i v ) t h e p e r i o d o f t h e w a v e f o r m . H a r m o n i c a n a l y s i s was u s e d t o d e t e r m i n e t h e f r e q u e n c y , a m p l i t u d e , a n d p h a s i n g o f a c y c l i c w a v e f o r m . B e r n s t e i n (1967) was among t h e f i r s t t o u s e h a r m o n i c a n a l y s i s i n t h e s t u d y o f human movement. I n t h e e a r l y 1 9 0 0 ' s , he p e r f o r m e d experiments i n which he f i l m e d s u b j e c t s p e r f o r m i n g v a r i o u s movements. The movement p a t t e r n s of the v a r i o u s j o i n t s were then a n a l y z e d i n t o component f r e q u e n c i e s . More r e c e n t l y t h i s a n a l y s i s has been used by Green (1971) on RT data, by Franks and W i l b e r g (1982) i n t r a c k i n g , by Marteniuk & Romanow (1983) on arm movement t r a j e c t o r i e s , and by Richardson and Pew (1968) i n measuring s t a b i l o m e t e r performance. In the present study, Harmonic a n a l y s i s was used i n the input b l a n k i n g c o n d i t i o n to determine the composition of the response waveform. The phase angles of the frequency components of the response were compared with those of the s t i m u l u s i n order to determine whether the r e l a t i v e t i m i n g of the response was e q u i v a l e n t to t h a t of the s t i m u l u s . The p e r i o d of the response was compared wi t h the p e r i o d of the stimulus i n order t o determine whether the o v e r a l l d u r a t i o n of one c y c l e of the response waveform was the same as the o v e r a l l d u r a t i o n of one c y c l e of the s t i m u l u s waveform. The harmonic a n a l y s i s was c a l c u l a t e d based on a method d e s c r i b e d i n Lowry and Hayden (1951 pp 324 - 328). The p e r i o d i c i t y of the waveform ( p e r i o d =2 7C) was determined u s i n g an a u t o c o r r e l a t i o n . T h i s waveform was d i v i d e d i n t o p equal u n i t s and each of these p o i n t s were l a b e l l e d xO, x l , x2, ... xp, w i t h t h e i r c orresponding o r d i n a t e v a l u e s being yO, y l / y2, ... yp. The t r a p e z o i d a l r u l e of i n t e g r a t i o n was a p p l i e d over the p e r i o d y i e l d i n g the f o l l o w i n g e q u a t i o n s : 1) a Q = 2/p TC y r 2) a n = 2/p n y r cos n x r 3) b n = 2/p K y r s i n n x r E q u a t i o n 2 g a v e t h e h a r m o n i c c o e f f i c i e n t s o f t h e c o s i n e component o f t h e w a v e f o r m , w h i l e e q u a t i o n 3 g a v e t h e h a r m o n i c c o e f f i c i e n t s o f t h e s i n e component o f t h e w a v e f o r m The e n t i r e w a v e f o r m was d e s c r i b e d b y t h e e q u a t i o n : f ( t ) = A 0 / 2 + 7C A n c o s n o t + B n s i n ncot T h i s e q u a t i o n was e x p r e s s e d i n t e r m s o f a c o s i n e f u n c t i o n : f ( t ) = A 0 / 2 + 7C C n c o s (ncot-(j>n) w h e r e Cn = A n 2 + B n 2 (|)n r e p r e s e n t e d t h e p h a s e a n g l e v a l u e s w h i c h p r o v i d e d t h e n e c e s s a r y t i m i n g r e l a t i o n s h i p among v a r i o u s h a r m o n i c c o m p o n e n t s . T h e s e p h a s e a n g l e v a l u e s w e r e d e t e r m i n e d u s i n g t h e f o l l o w i n g e q u a t i o n : t a n <|>n = B n / A n . I n o r d e r t o t e s t t h e a c c u r a c y o f t h e h a r m o n i c a n a l y s i s t h e s t i m u l u s w a v e f o r m i t s e l f was a n a l y z e d i n t o component f r e q u e n c i e s . T h e s e d a t a w e r e t h e n r e s y n t h e s i z e d i n t o a w a v e f o r m w h i c h was c o m p a r e d t o t h e o r i g i n a l w a v e f o r m b y c a l c u l a t i n g t h e RMS e r r o r b e t w e e n t h e two w a v e f o r m s . T h i s p r o d u c e d an RMS e r r o r o f 1.8 mm. Interval Durations were c a l c u l a t e d on t h e r e s p o n s e w a v e f o r m s t h a t t h e s u b j e c t s g e n e r a t e d d u r i n g i n p u t b l a n k i n g E a c h r e s p o n s e c y c l e was d i v i d e d i n t o i n t e r v a l s b y c a l c u l a t i n g t h e t i m e b e t w e e n a d j a c e n t r e v e r s a l s . A p r o g r a m was d e v e l o p e d i n o r d e r t o a i d t h e e x p e r i m e n t e r i n p r e c i s e l y m a r k i n g t h e s e r e v e r s a l s . The d i s p l a c e m e n t t i m e p r o f i l e o f e a c h c y c l e was p r e s e n t e d on a c o m p u t e r s c r e e n . The e x p e r i m e n t e r went t h r o u g h e a c h r e s p o n s e c y c l e m a r k i n g t h e p o i n t o f e a c h r e v e r s a l . The c o m p u t e r t h e n r e c o r d e d t h e X 26 a n d Y c o o r d i n a t e s o f t h a t p o i n t . X r e p r e s e n t e d t h e t e m p o r a l d i m e n s i o n . Y r e p r e s e n t e d t h e s p a t i a l d i m e n s i o n . I n o r d e r t o c a l c u l a t e an i n t e r v a l d u r a t i o n , t h e X c o o r d i n a t e v a l u e a t t h e b e g i n n i n g o f t h e i n t e r v a l was s u b t r a c t e d f r o m t h e X c o o r d i n a t e v a l u e a t t h e e n d o f t h a t i n t e r v a l . The i n t e r v a l d u r a t i o n was t h e n e x p r e s s e d as a p r o p o r t i o n o f t h e o v e r a l l d u r a t i o n o f t h e e n t i r e c y c l e b y d i v i d i n g t h e i n t e r v a l d u r a t i o n b y t h e o v e r a l l d u r a t i o n o f t h e c y c l e i n w h i c h t h e i n t e r v a l o c c u r r e d . Interval Displacements w e r e c a l c u l a t e d u s i n g t h e same p r o c e d u r e a s t h a t u s e d f o r t h e i n t e r v a l d u r a t i o n s . I n o r d e r t o c a l c u l a t e an i n t e r v a l d i s p l a c e m e n t , t h e Y c o o r d i n a t e v a l u e a t t h e b e g i n n i n g o f t h e i n t e r v a l was s u b t r a c t e d f r o m t h e Y c o o r d i n a t e v a l u e a t t h e e n d o f t h a t i n t e r v a l . The i n t e r v a l d i s p l a c e m e n t was t h e n e x p r e s s e d a s a p r o p o r t i o n o f t h e maximum d i s p l a c e m e n t b y d i v i d i n g t h e i n t e r v a l d i s p l a c e m e n t b y t h e maximum d i s p l a c e m e n t o f t h e c y c l e i n w h i c h t h e i n t e r v a l o c c u r r e d . S t a t i s t i c a l A n a l y s i s Pursuit Tracking: RMS e r r o r d a t a w e re s u b j e c t e d t o a Waves (8) b y Days (6) ANOVA w i t h p r e - p l a n n e d o r t h o g o n a l c o n t r a s t s a n d r e p e a t e d m e a s u r e s on b o t h f a c t o r s . C o n t r a s t s w e r e p l a n n e d f o r b o t h t h e d a y s f a c t o r ( t r e n d a n a l y s i s ) a n d t h e waves f a c t o r . The s e v e n c o n t r a s t s p e r f o r m e d on t h e waves f a c t o r w e r e a s f o l l o w s : 1) The t r a i n i n g w a v e f o r m (Wl) was c o n t r a s t e d w i t h t h e v a r i e d 27 s p e e d w a v e f o r m s (W2, W3, W4, W5) p o o l e d t o g e t h e r . 2) The s l o w w a v e f o r m s (W2 & W3) w e r e c o m p a r e d w i t h t h e f a s t w a v e f o r m s (W4 & W5). 3) The s l o w e s t w a v e f o r m (W2) was c o n t r a s t e d w i t h t h e s e c o n d s l o w e s t w a v e f o r m (W3). 4) The f a s t e s t w a v e f o r m (W5) was c o m p a r e d w i t h t h e s e c o n d f a s t e s t w a v e f o r m (W4). 5) The w a v e f o r m i n w h i c h t h e p h a s e a n g l e s o f t h e f r e q u e n c y c o m p o n e n t s w e r e a l t e r e d (W6) was c o n t r a s t e d w i t h t h e e n t i r e l y new w a v e f o r m (W7). 6) W l, W2, W3, W4 & W5 p o o l e d w e re c o n t r a s t e d w i t h W6 & W7 p o o l e d . 7) The random w a v e f o r m (W8) was c o n t r a s t e d w i t h W1-W7 p o o l e d . Input Blanking: B o t h t h e i n t e r v a l displacement a n d i n t e r v a l d u r a t i o n d a t a f r o m d a y f i f t e e n w e r e s u b j e c t e d t o a waves (5) by i n t e r v a l s (5) b y c y c l e s (3) r e p e a t e d m e a s u r e s ANOVA w i t h t r e n d a n a l y s i s on a l l f a c t o r s . The w a v e f o r m s u s e d i n t h i s a n a l y s i s w e r e waves one t h r o u g h f i v e . 28 CHAPTER 3.  RESULTS Part One - Pursuit Tracking S u b j e c t s were given e x t e n s i v e p r a c t i c e d a i l y i n t r a c k i n g a s p e c i f i c p e r i o d i c waveform (the t r a i n i n g waveform, wl) which had a base frequency of 0.4 9 Hz.. Under i n v e s t i g a t i o n was the q u e s t i o n "would s u b j e c t s be able t o perform e q u a l l y w e l l on waveforms which maintained the r e l a t i v e t i m i n g of the t r a i n i n g waveform, but were transformed i n terms of t h e i r base frequency?" In order t o answer t h i s q u e s t i o n , p u r s u i t t r a c k i n g performance was e v a l u a t e d u s i n g t h r e e dependent measures: RMS e r r o r ; w i t h i n s u b j e c t v a r i a b i l i t y ; and l e a d - l a g index ( c a l c u l a t e d u s i n g a c r o s s - c o r r e l a t i o n f u n c t i o n ) . I . RMS E r r o r RMS data were s u b j e c t e d t o a Waves(8) by Days(6) ANOVA w i t h planned orthogonal c o n t r a s t s and repeated measures on both f a c t o r s . C o n t r a s t s were planned f o r both the days f a c t o r (trend a n a l y s i s ) and the waves f a c t o r . A) Dav 15 Of the RMS data, the f i r s t t o be c o n s i d e r e d w i l l be the RMS v a l u e s on the l a s t day, day 15. Seven planned o r t h o g o n a l c o n t r a s t s were performed on the RMS v a l u e s of a l l e i g h t waveforms from day 15: F i g u r e 1. Root Mean Squared E r r o r as a f u n c t i o n of p r a c t i c e . RMS ERROR AS A FUNCTION OF PRACTICE 2 0 0 1 4 7 10 13 15 Transfer Days RMS Error in units of 1/10 mm W A V E F O R M S W1 . 4 9 H z -4- W 2 .31 H z -*- W 3 .41 H z - B - W 4 .61 H z W 5 . 6 9 H z 0 W 6 . 4 9 H z W 7 . 4 9 H z W 8 R a n d o m o 31 In t h e f i r s t contrast, RMS v a l u e s on t h e t r a i n i n g wave (wl) were compared w i t h t h e v a r i e d speed waves (w2, w3, w4, w5) p o o l e d . T h i s c o n t r a s t was s i g n i f i c a n t F(1,5)=32.3, p=0.002. S u b j e c t s , t h e r e f o r e , p e r f o r m e d s i g n i f i c a n t l y worse on v a r i o u s speeds o f t h e t r a i n i n g waveform (M = 36) c o n s i d e r e d t o g e t h e r , t h a n t h e y d i d on t h e o r i g i n a l i t s e l f (M = 3 0 ) . However, i n t a k i n g a c l o s e r l o o k a t t h e RMS d a t a on t h i s l a s t day (see F i g u r e 1 ) , i t i s e v i d e n t t h a t t h e s l o w e r waves had t h e same RMS v a l u e as t h e o r i g i n a l wave. Thus t h e o r i g i n a l and s l o w e r waves were t h e same as each o t h e r but d i f f e r e n t t h a n t h e f a s t e r waveforms; s u b j e c t s p e r f o r m e d as w e l l on t h e two s l o w e r waveforms (on w h i c h t h e y had m i n i m a l p r a c t i c e ) as t h e y d i d on w l , on w h i c h t h e y had e x t e n s i v e t r a i n i n g The second contrast compared w2 and w3 (the slow waves) w i t h w4 and w5 (the f a s t waves). The slow waves (M = 30.5) were found t o be s i g n i f i c a n t l y d i f f e r e n t t h a n t h e f a s t waves (M = 41.5) F ( l , 5 ) = 8 . 7 , p=0.032, meaning t h a t s u b j e c t s p e r f o r m e d s i g n i f i c a n t l y b e t t e r on t h e slow waves t h a n t h e y d i d on t h e f a s t waves (as measured by RMS e r r o r ) . The t h i r d contrast compared w2 (the s l o w e s t wave) w i t h w3 (the second s l o w e s t wave). There were no d i f f e r e n c e s i n RMS v a l u e s on t h e two waveforms F ( l , 5 ) < 1.0.. The fourth contrast compared w4 w i t h w5. RMS v a l u e s on w5, t h e f a s t e s t waveform (M = 45), were s i g n i f i c a n t l y h i g h e r t h a n t h o s e on w4, t h e second f a s t e s t waveform (M = 38), F ( l , 5 ) = 8 . 0 , p=0.036. 32 The f i f t h contrast c o m p a r e d w l - w5 p o o l e d ( t h e v a r i e d s p e e d w a v e f o r m s ) w i t h w6 & w7 p o o l e d ( t h e c o n s t a n t s p e e d w a v e f o r m s ) . RMS v a l u e s on t h e f i r s t g r o u p w e r e s i g n i f i c a n t l y l o w e r t h a t RMS v a l u e s on t h e s e c o n d g r o u p F ( l , 5 ) = 6 6 . 7 , p<0.001. Thus s u b j e c t s p e r f o r m e d more a c c u r a t e l y w h i l e t r a c k i n g t h e w a v e f o r m s t h a t v a r i e d o n l y i n b a s e f r e q u e n c y ( w l - w5) t h a n w h i l e t r a c k i n g t h e w a v e f o r m s t h a t v a r i e d t h e p h a s e r e l a t i o n s h i p s among t h e component f r e q u e n c i e s (w6) o r v a r i e d t h e component f r e q u e n c i e s t h e m s e l v e s (w7). A s c a n be s e e n i n F i g u r e 1, n o t o n l y d i d s u b j e c t s p e r f o r m b e t t e r on t h e t r a i n i n g wave (wl) a n d t h e two s l o w e r waves (w2 & w3) t h a n t h e y d i d on w6 a n d w7, t h e y a l s o p e r f o r m e d b e t t e r on t h e two f a s t e r s p e e d s , w4 & w5, w h i c h h a d b a s e f r e q u e n c i e s o f 0.61 a n d 0.69 Hz r e s p e c t i v e l y , t h a n t h e y p e r f o r m e d on W6 a n d w7, w h i c h b o t h h a d b a s e f r e q u e n c i e s o f 0.49 Hz. The s i x t h contrast c o m p a r e d w6 w i t h w7. RMS v a l u e s on W6 a n d W7 w e r e n o t d i f f e r e n t F ( 1 , 5 ) = 0 . 1 , p < 1.0, i n d i c a t i n g t h a t s u b j e c t s do n o t f i n d w6 (a w a v e f o r m t h a t c o n t a i n s t h e same component f r e q u e n c i e s as t h e t r a i n i n g w a v e f o r m ) any e a s i e r t o t r a c k t h a n w7 (an e n t i r e l y new w a v e f o r m ) . The seventh contrast c o m p a r e d w8 ( t h e random w a v e f o r m ) w i t h w l - w7 ( t h e p e r i o d i c w a v e f o r m s ) p o o l e d . A s e x p e c t e d RMS v a l u e s on w8 w e re s i g n i f i c a n t l y h i g h e r t h a n t h o s e on wl - w7 p o o l e d F ( 1 , 5 ) = 4 9 7 . 2 , p<0.001. T a b l e 2 Waves * Days I n t e r a c t i o n s : RMS E r r o r . SOURCE SS SS% DF MS F P W * D 26, 944.1 100.0% 35, 175 769.8 7.15 0.001 W , * W * DQ 453.4 898.6 1.7% 2.9% 1, 1, 5 5 453.4 898.6 4.04 6. 61 0.101 0.050 W * W o * D L DQ 6510.5 1507.7 24.2% 5.6% 1, 1, 5 5 6510.5 1507.7 104 .5 11. 6 0.001 0.019 W , * VVC3 w * C^3 DL DQ 525.7 452.7 1.9% 1.7% 1, 1, 5 5 525.7 452.7 30.17 31.47 0.003 0.002 w * ^04 w * D L DQ 774.7 0.4 2.9% 0.0% 1, 1, 5 5 774 .7 0.35 6.83 0.00 0.047 0.948 w c 5 * WC5 * D L DQ 85.9 3698.4 0.3% 13.7% 1, 1, 5 5 85. 9 3698.4 0.39 35.9 0.560 0.002 WC6 * WC6 * D L DQ 1992.8 94.8. 7.4% 0.4% 1, 1, 5 5 1992.8 94.8 6.56 0.27 0.051 0.625 W o * w * D L DQ 4905.7 908.8 18.2% 3.4% 1, 1, 5 5 4905.7 908.8 17.8 4.21 0.008 0.095 cx = c o n t r a s t one D L = days l i n e a r D Q = days q u a d r a t i c 34 B) Day 1 t h r o u g h Day 15 I n o r d e r t o d e t e r m i n e t h e d i f f e r e n c e s i n t h e r a t e s o f i m p r o v e m e n t amongst t h e v a r i o u s w a v e f o r m s , t h e waves by d a y s i n t e r a c t i o n s w i l l be e x a m i n e d . T a b l e 21 g i v e s a d e t a i l e d a c c o u n t o f t h e s e i n t e r a c t i o n s . O n l y t h e s i g n i f i c a n t i n t e r a c t i o n s w i l l be a d d r e s s e d i n t h e t e x t o f t h e r e s u l t s . The i n t e r a c t i o n o f c o n t r a s t 2 ( t h e s l o w waves c o m p a r e d t o t h e f a s t waves) w i t h days l i n e a r was s i g n i f i c a n t F ( 1 , 5 ) = 1 0 4 . 5 , p=0.001 i n d i c a t i n g t h a t t h e f a s t w a ves i m p r o v e d a t a f a s t e r r a t e t h a n t h e s l o w w a v e s . T h i s d i f f e r e n c e i n s l o p e b e t w e e n t h e f a s t a n d s l o w waves i s a l s o e v i d e n t i n F i g u r e 1, b u t a p p e a r s t o be p r i m a r i l y due t o t h e s t e e p e r s l o p e f r o m day 1 t o day 10. The i n t e r a c t i o n o f c o n t r a s t 2 w i t h days q u a d r a t i c was s i g n i f i c a n t F ( 1 , 5 ) = 1 1 . 6 , p=0.019 r e v e a l i n g t h a t t h e q u a d r a t i c component o f t h e d a y s e f f e c t was d i f f e r e n t b e t w e e n t h e s l o w a n d f a s t w a v e s . The s t r o n g e r q u a d r a t i c component o f t h e d a y s e f f e c t f o r t h e f a s t w aves i s a p p a r e n t i n F i g u r e 1. As c a n be s e e n , t h e r e was a g r e a t e r c h a n g e i n s l o p e o v e r d a y s f o r t h e f a s t waves t h a n t h e r e was f o r t h e s l o w w a v e s . The i n t e r a c t i o n o f c o n t r a s t 5 ( w l - w5 p o o l e d c o m p a r e d t o w6 & w7 p o o l e d ) w i t h days q u a d r a t i c was s i g n i f i c a n t F ( 1 , 5 ) = 3 5 . 9 , p=0.002. I t i s a p p a r e n t f r o m F i g u r e 1 t h a t t h e d a y s e f f e c t on w l t h r o u g h w5 h a s a s t r o n g q u a d r a t i c c o m p o n e n t . On t h e s e waves t h e r e i s a l a r g e d r o p i n RMS f r o m d a y one t o day f o u r . W6 a n d w7 show no s u c h d r o p . T h e i r p r o g r e s s i s f a i r l y l i n e a r f r o m day one t o d a y f i f t e e n . 35 The i n t e r a c t i o n o f c o n t r a s t 7 (w8 c o m p a r e d t o w l - w7 p o o l e d ) w i t h days l i n e a r was s i g n i f i c a n t F ( 1 , 5 ) = 1 7 . 8 , p=0.008. O v e r t h e f i f t e e n d a y s , s u b j e c t s ' p e r f o r m a n c e showed g r e a t e r i m p r o v e m e n t on t h e p e r i o d i c w a v e f o r m s t h a n on t h e random w a v e f o r m ; as F i g u r e 1 i l l u s t r a t e s , t h e random w a v e f o r m (w8) h a d a more s h a l l o w s l o p e t h a n d i d t h e p e r i o d i c w a v e f o r m s ( w l - w 7 ) . I I . W i t h i n S u b j e ct V a r i a b i l i t y V a r i a b i l i t y s c o r e s w e re s u b j e c t e d t o a r e p e a t e d m e a s u r e s ANOVA on a l l w a v e f o r m s ( w l , w2, w3, w4, w5, w6, w7, a n d w8) f r o m d ay 15, u s i n g t h e same p l a n n e d o r t h o g o n a l c o n t r a s t s t h a t w e r e u s e d i n t h e RMS ANOVA. ( V a r i a b i l i t y s c o r e s w e r e c a l c u l a t e d b y t a k i n g t h e mean o f 512 s t a n d a r d d e v i a t i o n v a l u e s f r o m t h e d i s p l a c e m e n t t i m e p r o f i l e s o f 10 c y c l e s o f p u r s u i t t r a c k i n g . ) R e s u l t s f r o m t h e ANOVA on t h e v a r i a b i l i t y d a t a p a r a l l e l e d c l o s e l y t h e r e s u l t s f r o m t h e ANOVA on t h e RMS d a t a ( s e e T a b l e 3 ) . The o n l y c o n t r a s t t h a t d e v i a t e d f r o m t h i s p a t t e r n was c o n t r a s t 2 i n w h i c h t h e s l o w waves were c o n t r a s t e d w i t h t h e f a s t w a v e s . I n t h e c a s e o f t h e v a r i a b i l i t y d a t a t h i s c o n t r a s t was n o t s i g n i f i c a n t F ( 1 , 5 ) = 4 . 2 , p=0.095. Thus t h e s l o w waves a r e n o t s i g n i f i c a n t l y d i f f e r e n t f r o m t h e f a s t waves on t h e v a r i a b i l i t y m e a s u r e . A s F i g u r e 2 i l l u s t r a t e s , s u b j e c t s ' r e s p o n s e s on a l l e i g h t w a v e f o r m s w e r e more v a r i a b l e e a r l y i n l e a r n i n g (day 1) t h a n t h e y w e r e l a t e r i n l e a r n i n g (day 1 5 ) . I n c o n s i d e r i n g 36 F i g u r e 2. Mean of 512 standard d e v i a t i o n v a l u e s from the displacement time p r o f i l e s of 10 c y c l e s of p u r s u i t t r a c k i n g f o r 7 waveforms over 6 t r a n s f e r days. VARIABILITY AS A FUNCTION OF PRACTICE 38 b o t h t h e v a r i a b i l i t y a n d t h e RMS r e s u l t s , i t i s e v i d e n t t h a t as s u b j e c t s became more a c c u r a t e t h e y a l s o became l e s s v a r i a b l e i n t h e i r r e s p o n s e . T a b l e 3 ANOVA Tabl e V a r i a b i l i t y Planned C o n t r a s t s Day 15 CONTRAST F DF P 1) Wl v s W2-W5 20.29 1, 5 0.006 2) W2 & W3 v s W4 & W5 4 .23 1, 5 0.095 3) W2 v s W3 1.66 1, 5 0.254 4) W4 v s W5 8.87 1/ 5 0.031 5) W1-W5 v s W6 & W7 26.23 1, 5 0.004 6) W6 v s W7 2.03 1/ 5 0.213 7) W8 v s W1-W7 169.47 1/ 5 0.001 I I I . Lead-Lag Index A s i s e v i d e n t f r o m F i g u r e s 3 a n d 4, on d a y one t h e s u b j e c t s ' r e s p o n s e s l a g g e d b e h i n d t h e s t i m u l u s d u r i n g t h e p u r s u i t t r a c k i n g o f a l l w a v e f o r m s ( w l , w2, w3, w4, w5, w6, w7, a n d w 8 ) . On t h e f a s t e r w a ves, t h e r e s p o n s e s l a g g e d b e h i n d t h e s t i m u l u s b y t h e g r e a t e s t amount. O v e r t h e f i f t e e n d a y s o f t r a i n i n g , s u b j e c t s ' r e s p o n s e s on a l l f i v e o f t h e v a r i o u s s p e e d w a v e f o r m s ( w l - w5) moved n e a r e r t h e z e r o l a g p o i n t . By day 15, t h e r e s p o n s e s on w l , w2, a n d w3 ( t h e t r a i n i n g a n d s l o w e r w a v e f o r m s ) were a t t h e z e r o l a g p o i n t . R e s p o n s e s on t h e two f a s t e r waves ,w4 a n d w5, l a g g e d t h e s t i m u l u s b y 7 a n d 5 m i l l i s e c o n d s on day 15. The v a r i a b i l i t y o f t h e l a g o f t h e s u b j e c t s ' r e s p o n s e s f o r a l l w a v e f o r m s ( F i g u r e 5) d e c r e a s e d a s l e a r n i n g p r o g r e s s e d , m a k i n g t h e mean l a g v a l u e s f r o m day 15 more 39 F i g u r e 3. The l e a d - l a g index of the s u b j e c t s ' responses r e l a t i v e t o the s t i m u l u s as a f u n c t i o n of p r a c t i c e f o r wl - w 5 . LEAD-LAG AS A FUNCTION OF PRACTICE 41 F i g u r e 4 . The l e a d - l a g index of the s u b j e c t s ' respones r e l a t i v e t o the st i m u l u s as a f u n c t i o n fo p r a c t i c e f o r w 6 - w 8 . LEAD-LAG AS A FUNCTION OF PRACTICE 43 F i g u r e 5 . The s t a n d a r d d e v i a t i o n s o f t h e l e a d - l a g i n d e x o f t h e s u b j e c t s ' r e s p o n s e s r e l a t i v e t o t h e s t i m u l u s f o r w l - w 8 . VARIABILITY OF LEAD-LAG SCORES 1 4 7 10 13 15 T r a n s f e r D a y s 45 r e l i a b l e than the mean va l u e s from day 1. Responses on the random waveform e x h i b i t e d much g r e a t e r v a r i a b i l i t y throughout and showed the g r e a t e s t decrease i n v a r i a b i l i t y over the f i f t e e n days of t r a i n i n g . Part Two - Input Blanking S e v e r a l dependent v a r i a b l e s were used i n order t o ev a l u a t e performance on the input b l a n k i n g data on Day 15. I) I n t e r v a l d u r a t i o n s expressed as a p r o p o r t i o n o f the o v e r a l l d u r a t i o n (an index o f r e l a t i v e t i m i n g ) . II) I n t e r v a l displacements expressed as a p r o p o r t i o n o f the maximum displacement (an index o f r e l a t i v e d i s p l a c e m e n t ) . I I I ) C y c l e d u r a t i o n or p e r i o d o f the response waveforms from wl - w7 (the p e r i o d i c waveforms). IV) Root Mean Squared E r r o r . V) Frequency composition o f the response waveforms ( c a l c u l a t e d u s i n g Harmonic a n a l y s i s ) . VI) Kinematic p r o f i l e s o f the response waveforms. I. I n t e r v a l D u r a t i o n s I n t e r v a l d u r a t i o n s from the input b l a n k i n g data (day 15) were analyzed i n order t o determine whether s u b j e c t s maintained a c o n s i s t e n t p r o p o r t i o n a l d u r a t i o n a c r o s s repeated i n s t a n c e s o f a giv e n movement i n t e r v a l . In t h i s experiment, a movement i n t e r v a l was d e f i n e d as the time from one r e v e r s a l t o an adjacent r e v e r s a l (or stop) o f the 46 F i g u r e 6. Waveforms by i n t e r v a l s i n t e r a c t i o n f o r p r o p o r t i o n a l i n t e r v a l d u r a t i o n data. Di/T as a function of Waveforms (collapsed over cycles) -X • X m -• v — 6 - a -+ JJC J ^ . . yp? W1 .5Hz W2 ,3Hz W3 ,4Hz W4 ,6Hz W5 .7Hz W a v e f o r m s — — In te rva l 1 —I— In te r va l 2 I n t e r v a l 3 • _ a _ I n te rva l 4 I n te rva l 5 48 F i g u r e 7 . I n t e r v a l s by c y l e s i n t e r a c t i o n f o r p r o p o r t i o n a l i n t e r v a l d u r a t i o n data. Di/T as a function of Cycles (collapsed over waveforms) -a/ ^ ffl My 1 A 1 1 d c2 c3 C y c l e s ~~*~ I n te rva l 1 ~ B ~ In te rva l 4 — r — I n te r va l 2 - x - I n te r va l 5 I n t e r v a l 3 50 F i g u r e 8 . P r o p o r t i o n a l i n t e r v a l d u r a t i o n s as a f u n c t i o n of o v e r a l l d u r a t i o n f o r s u b j e c t 2 . Subject 2 Day 15 Waves 1 - 5 D i / T ( interval as p ropo r t i on of T in % 100r 80 60 40 20 - - j y £ x-^iC-X Pff- T L j » ^ D - ^ - - ^ g -x < x X • x x__ ^ i r * ^ F T T T T ^ • • 0 1300 1800 2300 2800 3300 3800 T (overal l dura t ion in ms) — i n t e r v a M — I n t e r v a l 2 " * " I n t e r v a l s - ° - Interval 4 Interval 5 Cn 52 movement p a t t e r n . Each o f the stimulus waves 1 to 5 con t a i n e d f i v e such i n t e r v a l s with p r o p o r t i o n a l d u r a t i o n s o f 21%, 17%, 10%, 16% & 35% of the o v e r a l l d u r a t i o n . The p r o p o r t i o n a l d u r a t i o n of a response i n t e r v a l was c a l c u l a t e d by d i v i d i n g the i n t e r v a l d u r a t i o n by the o v e r a l l d u r a t i o n o f t h a t c y c l e i n which the i n t e r v a l o c c u r r e d . T a b l e 4 ANOVA Table I n t e r v a l D u r a t i o n s SOURCE F DF P WAVES 1 .58 4, 16 0.227 INTERVALS 95. 60 4, 16 0.001 Wl 0.79 16, 64 0.693 Wl (1,1) 0 .44 1, 4 0 .544 Wl (1,2) 0.06 1, 4 0.821 Wl (1,3) 0.07 1, 4 0.805 Wl(1,4) 0.54 1, 4 0 .504 CYCLES 0.82 2, 8 0.475 WC 1.33 8, 32 0.266 IC 0.89 8, 32 0.534 WIC 0.95 32, 128 0 .557 The p r o p o r t i o n a l i n t e r v a l d u r a t i o n s on day 15 were s u b j e c t e d t o a waves(5) * i n t e r v a l s ( 5 ) * c y c l e s ( 3 ) repeated measures ANOVA with t r e n d a n a l y s i s on a l l f a c t o r s . The waves main e f f e c t (see Table 4) was n o n - s i g n i f i c a n t F(4,16)=1.58, p=0.23, as expected. Because a l l i n t e r v a l d u r a t i o n s were taken as p r o p o r t i o n s of the o v e r a l l d u r a t i o n , when the data were c o l l a p s e d over the f i v e i n t e r v a l s , the mean i n t e r v a l d u r a t i o n became i n a l l cases 20% of the t o t a l d u r a t i o n . A n o n - s i g n i f i c a n t main e f f e c t was expected no matter what the a c t u a l i n t e r v a l d u r a t i o n s v a l u e s . For t h i s reason, i t was the waves by i n t e r v a l s i n t e r a c t i o n t h a t was of concern i n e v a l u a t i n g the r e l a t i v e t i m i n g h y p o t h e s i s (see I n t r o d u c t i o n p.2). The waves by i n t e r v a l s i n t e r a c t i o n was 53 not s i g n i f i c a n t F(16,64)=0.79, p=0.693. The p r o p o r t i o n a l i n t e r v a l d u r a t i o n s , t h e r e f o r e , appear to be i n v a r i a n t . (For a g r a p h i c a l r e p r e s e n t a t i o n of the waves by i n t e r v a l s i n t e r a c t i o n see F i g u r e 6). In a d d i t i o n , both the w a v e s ( l i n e a r ) and waves(quadratic) by i n t e r v a l s i n t e r a c t i o n s were n o n - s i g n i f i c a n t ( i n both cases p > 0.50), thus l e n d i n g support to the i n v a r i a n t r e l a t i v e t i m i n g h y p o t h e s i s . The c y c l e s main e f f e c t F(2,8)=0.82, p=0.475 was non-s i g n i f i c a n t i n d i c a t i n g t h a t when the p r o p o r t i o n a l i n t e r v a l d u r a t i o n data were c o l l a p s e d over waveforms and i n t e r v a l s , the mean p r o p o r t i o n a l i n t e r v a l d u r a t i o n s from the t h r e e c y c l e s were the same. The waves by c y c l e s i n t e r a c t i o n was n o n - s i g n i f i c a n t F(8,32)=1.33, p=0.266 i n d i c a t i n g t h a t when the p r o p o r t i o n a l i n t e r v a l d u r a t i o n data were c o l l a p s e d over i n t e r v a l s , the d i f f e r e n c e s between waveforms ( a c t u a l l y e q u a l i t y ) was constant over the t h r e e c y c l e s . The i n t e r v a l s by c y c l e s i n t e r a c t i o n was n o n - s i g n i f i c a n t F(8,32)=0.89, p=0.534 i n d i c a t i n g t h a t when the p r o p o r t i o n a l i n t e r v a l d u r a t i o n data were c o l l a p s e d over waveforms, the d i f f e r e n c e s among the f i v e i n t e r v a l s under each of the t h r e e c y c l e s were constant over the t h r e e c y c l e s . For a g r a p h i c a l r e p r e s e n t a t i o n of t h i s i n t e r a c t i o n see F i g u r e 7. Although i t has been suggested (Gentner, 1987) t h a t i t i s necessary t o c a l c u l a t e r e g r e s s i o n l i n e s f o r each s u b j e c t f o r each i n t e r v a l , t h i s i s not necessary p r o v i d e d t h a t the w i t h i n s u b j e c t v a r i a b i l i t y i s low enough. (For an example 54 of r e g r e s s i o n l i n e s f i t t e d t o the data o f an i n d i v i d u a l s u b j e c t see F i g u r e 8). In the present study, the w i t h i n s u b j e c t v a r i a b i l i t y ( c o e f f i c i e n t o f v a r i a t i o n ) was c a l c u l a t e d and i s pres e n t e d i n the f o l l o w i n g t a b l e : T a b l e 5 I n t r a - i n d i v i d u a l V a r i a b i l i t y f o r I n t e r v a l D u r a t i o n s a c r o s s the F i v e Waveforms. SD 1 5 V I n t e r v a l 1 2.4 0.10 I n t e r v a l 2 1.7 0.10 I n t e r v a l 3 1.4 0.15 I n t e r v a l 4 1.7 0.10 I n t e r v a l 5 2.6 0.07 SD = standard d e v i a t i o n over f i f t e e n c y c l e s V = c o e f f i c i e n t of v a r i a t i o n I I . I n t e r v a l Displacements The i n t e r v a l displacement data were analyzed u s i n g a th r e e way ANOVA which was i d e n t i c a l t o t h a t used on the i n t e r v a l d u r a t i o n data. The dependent measure was a r e l a t i v e i n t e r v a l displacement. In a giv e n c y c l e , each i n t e r v a l displacement was d i v i d e d by the maximum displacement t h a t o c c u r r e d i n t h a t c y c l e , thus g i v i n g an i n t e r v a l displacement expressed as a p r o p o r t i o n o f the maximum displacement. The f i v e p r o p o r t i o n a l i n t e r v a l displacement v a l u e s f o r the stimulus (or c r i t e r i o n ) were 50%, 20%, 9%, 38%, 100%. 55 T a b l e 6 ANOVA Table I n t e r v a l Displacements SOURCE F DF P WAVES 0.50 4, 16 0.737 INTERVALS 412.52 4, 16 0.000 Wl 0.56 16, 64 0.899 Wl (1,1) 0.89 1, 4 0.340 Wl (1,2) 0.17 1, 4 0.705 Wl (1,3) 1.29 1, 4 0.319 Wl (1,4) 2.33 1, 4 0 .202 CYCLES 0.03 2, 8 0.967 WC 0.97 8, 32 0.476 IC 0.37 8, 32 0.931 WIC 1.63 32, 128 0.030 (0.075)* * Huynh-Feldt a d j u s t e d p val u e T a b l e 7 I n t r a - i n d i v i d u a l V a r i a b i l i t y f o r I n t e r v a l Displacements a c r o s s the F i v e Waveforms • SD 1 5 V I n t e r v a l 1 5.5 0.10 I n t e r v a l 2 4.4 5. 67 I n t e r v a l 3 4.3 3.00 I n t e r v a l 4 4.2 0.12 I n t e r v a l 5 5.7 0.06 SD = standard d e v i a t i o n over f i f t e e n c y c l e s V = c o e f f i c i e n t o f v a r i a t i o n The i n t e r v a l displacement data (see Table 6) p a r a l l e l c l o s e l y the i n t e r v a l d u r a t i o n data. (For a g r a p h i c a l r e p r e s e n t a t i o n of the waves by i n t e r v a l s i n t e r a c t i o n f o r the i n t e r v a l displacement data see F i g u r e 9). The i n t e r v a l displacement and i n t e r v a l d u r a t i o n data were d i f f e r e n t only i n the w i t h i n s u b j e c t v a r i a b i l i t y ( i n d i c a t e d by the e r r o r term). The v a r i a b i l i t y of the displacement data was l a r g e r 56 F i g u r e 9. Waveforms by i n t e r v a l s i n t e r a c t i o n f o r r e l a t i v e i n t e r v a l displacement data. r e I a t i v e s P I a c e m e n t Relative Displacement as a Function of Waveforms (collapsed over cycles) 120 100 8 0 6 0 40 2 0 0 -• -I • n D + i T i - r 1 I * 1 1 i W1 ,5Hz W 2 .3Hz W 3 .4Hz W 4 .6Hz W 5 .7Hz w a v e f o r m s Interval 1 Interval 4 -*— Interval 2 •~x— Interval 5 Interval 3 01 ^3 58 than t h a t o f the d u r a t i o n data. However the displacement data v a l u e s were l a r g e r than the d u r a t i o n data v a l u e s . D u r a t i o n data v a l u e s were l i m i t e d t o a range of 100 p o i n t s , whereas, displacement data i n t e r v a l v a l u e s were l i m i t e d t o a range of 230 p o i n t s . I I I . P e r i o d On a l l waveforms (wl - w7) s u b j e c t s reproduced a response waveform whose p e r i o d was longer than the sti m u l u s p e r i o d (see F i g u r e s 10 & 11). For the slower waveforms on day one, the s u b j e c t s reproduced waveforms whose p e r i o d was lon g e r than the sti m u l u s p e r i o d , by 73 ms f o r w2, and by 166 ms f o r w3. By day 15, the p e r i o d s of the response waveforms of w2 and w3 were longer than the stimulus p e r i o d s by 327 and 24 8 ms r e s p e c t i v e l y . On the f a s t e r and t r a i n i n g waveforms, s u b j e c t s became more ac c u r a t e i n rep r o d u c i n g the stimulus p e r i o d w i t h p r a c t i c e . As wi t h the slower waveforms, response p e r i o d s on the f a s t e r and t r a i n i n g waveforms were lo n g e r than the st i m u l u s p e r i o d s on day one. However wit h p r a c t i c e , these response p e r i o d s became s h o r t e r such t h a t by day 15 the response p e r i o d s of wl, w2 and w3 were c l o s e r t o those of the s t i m u l u s p e r i o d s than they had been on day 1. In the case of w6 and w7 ( j u s t as f o r wl - w5) the p e r i o d s of the response waveforms were always longer than those o f the s t i m u l u s . Thus d u r i n g input b l a n k i n g , s u b j e c t s 59 F i g u r e 1 0 . Mean p e r i o d o v e r f i v e c y c l e s o f i n p u t b l a n k i n g w l - w 5 . Period Waves 1-5 —*— Wave 1 — f - Wave 2 Wave 3 - B - Wave 4 - O - Wave 5 S t i m u l u s 1 ••+•• S t i m u l u s 2 S t i m u l u s 3 • B - S t i m u l u s 4 ••-€>• S t i m u l u s 5 4 7 10 13 T r a n s f e r D a y s F i g u r e 1 1 . M e a n p e r i o d o v e r f i v e c y c l e s o f i n p u t b l a n k i n g w6 & w 7 . Period Waves 6 & 7 Stimulus Wave 6 Wave 7 4 7 10 13 T r a n s f e r D a y s 15 63 reproduced responses on a l l waveforms (wl - w7) t h a t were c o n s i s t e n t l y slow. IV) RMS E r r o r In order t o o b t a i n a q u a n t i t a t i v e comparison of performance on the v a r i o u s waveforms i n input b l a n k i n g f o r day f i f t e e n , an RMS e r r o r score was c a l c u l a t e d f o r each of the f i v e c y c l e s from input b l a n k i n g . The sti m u l u s was s h i f t e d backward and forward i n time i n order t o f i n d the lowest RMS e r r o r score between stimulus and response f o r a g i v e n c y c l e . Of the RMS v a l u e s c a l c u l a t e d f o r each of the f i v e c y c l e s , the c y c l e with the lowest RMS va l u e i s p r e s e n t e d i n Table 8. (For kinematic r e p r e s e n t a t i o n s of these responses p l o t t e d a g a i n s t the stimulus f o r the t r a i n i n g waveform (wl) on day 15, see Appendix C. See a l s o Appendix D f o r i n d i v i d u a l s u b j e c t p l o t s of the v a r i a b i l i t y o f the i n p u t b l a n k i n g responses from the t r a i n i n g waveform (wl) on day 15.) Tabl e 8 - RMS E r r o r Input B l a n k i n g Day 15 (u n i t s i n 1/10 mm) wl w2 w3 w4 w5 w6 w7 s i 68 41 31 91 74 56 41 s2 40 26 29 20 32 57 86 s3 84 85 91 106 103 108 109 s4 45 4 0 75 40 38 51 74 s5 33 57 53 39 48 75 88 s6 52 31 42 62 63 70 113 Mean 54 47 53 60 60 69 85 There were no s t a t i s t i c a l l y s i g n i f i c a n t d i f f e r e n c e s among the RMS e r r o r scores t h a t were d e r i v e d from the input 64 b l a n k i n g d a t a . However t h e d e s c r i p t i v e d a t a i n d i c a t e t h a t t h e s u b j e c t s p e r f o r m e d b e t t e r on t h e t r a i n i n g a n d v a r i e d s p e e d w a v e f o r m s (wl - w5) t h a n t h e y d i d on t h e p h a s e s h i f t e d w a v e f o r m (w6). I n a d d i t i o n , s u b j e c t s seemed t o p e r f o r m b e t t e r on t h e p h a s e s h i f t e d w a v e f o r m (w6) t h a n on t h e e n t i r e l y new w a v e f o r m (w7). Th e s e RMS e r r o r s c o r e s w e r e s u b j e c t e d t o a r e p e a t e d m e a s u r e s ANOVA u s i n g t h e o r t h o g o n a l c o n t r a s t s a s p r e s e n t e d i n T a b l e 9 b e l o w . T a b l e 9 ANOVA Tabl e RMS I n p u t B l a n k i n g Orthogonal C o n t r a s t s Day 15 CONTRAST F DF P 1) Wl v s W2-W5 0.06 1/ 5 0 . 809 2) W2 & W3 v s W4 & W5 0.91 1, 5 0.385 3) W2 v s W3 1.14 1, 5 0.334 4) W4 v s W5 0.01 1, 5 0. 999 5) W1-W5 v s W6 & W7 6.85 1, 5 0 . 047 6) W6 v s W7 3.44 1, 5 0.123 V Frequency Composition I n p u t b l a n k i n g d a t a f r o m d a y 15 were s u b j e c t e d t o an h a r m o n i c a n a l y s i s i n o r d e r t o d e t e r m i n e t h e f r e q u e n c y c o m p o s i t i o n o f t h e r e s p o n s e w a v e f o r m s o f w l - w7. T h i s a n a l y s i s g a v e a more d e t a i l e d d e s c r i p t i o n o f t h e w a v e f o r m s t h a n c o u l d be d e r i v e d f r o m t h e RMS E r r o r r e s u l t s . F i g u r e s 1 - 7 ( A p p e n d i x E) r e p r e s e n t t h e mean v a l u e s o f t h e h a r m o n i c c o m p o n e n t s c o n t a i n e d i n t h e r e s p o n s e s o f t h e s i x s u b j e c t s p l o t t e d b e s i d e c r i t e r i o n s t i m u l u s v a l u e s . Though t h e r e i s no s i m p l e way t o make q u a n t i t a t i v e c o m p a r i s o n s amongst t h e f r e q u e n c y p r o f i l e s d e r i v e d f r o m t h e 65 v a r i o u s waveforms through harmonic a n a l y s i s , these frequency p r o f i l e s can h e l p i n determining what u n d e r l i e s the d i f f e r e n c e s found i n the RMS e r r o r r e s u l t s . In comparing w6 (the phase s h i f t e d waveform) and w7 (the new waveform) i t seems t h a t w6 and w7 (whose s t i m u l i both c o n t a i n e d t h r e e component fr e q u e n c i e s ) are of s i m i l a r accuracy w i t h the e x c e p t i o n of the f o u r t h harmonic. The amplitude of the f o u r t h harmonic of w7 i s 3.6 mm l a r g e r than t h a t of the s t i m u l u s , whereas the amplitude of the f o u r t h harmonic of w6 i s o n l y 1.1 mm l a r g e r than the s t i m u l u s . The l a r g e r amplitude of the f o u r t h harmonic may have c o n t r i b u t e d to the l a r g e r RMS E r r o r v a l u e i n w7 as compared wi t h w6. A d d i t i o n a l l y , w7 a l s o had h i g h e r amplitude v a l u e s f o r most of i t s r e s i d u a l component f r e q u e n c i e s ( i . e . comparing 2 to 3, 5 t o 5, and 6 to 6) than d i d w6. Waveforms which c o n t a i n h i g h e r amplitude v a l u e s on the r e s i d u a l component f r e q u e n c i e s w i l l be l e s s a c curate r e p r o d u c t i o n s of the s t i m u l u s than those which have lower amplitude v a l u e s on the r e s i d u a l component f r e q u e n c i e s . T h i s may a l s o have c o n t r i b u t e d t o the h i g h e r RMS e r r o r v a l u e on w7 as compared wit h w6. VI) Kinematic P r o f i l e s F i g u r e s 12 & 13 c o n t a i n the p l o t s of two i n d i v i d u a l s u b j e c t s a c r o s s the f i v e waveforms. These p l o t s g i v e a k i n e m a t i c r e p r e s e n t a t i o n of the movement be i n g made i n the i n p u t b l a n k i n g s i t u a t i o n . A f t e r f i f t e e n days of e x t e n s i v e p r a c t i c e on the t r a i n i n g waveform (wl), these s u b j e c t were extremely c o n s i s t e n t i n producing t h i s p a r t i c u l a r waveform. There was a l s o a g r e a t d e a l of s i m i l a r i t y i n response p r o d u c t i o n not only w i t h i n a p a r t i c u l a r t r i a l , but a l s o between t r i a l s t h a t r e q u i r e d responses of d i f f e r e n t speeds. One other i n t e r e s t i n g p o i n t to note about a s u b j e c t s c o n s i s t e n c y of response, i s t h a t a l l s u b j e c t s produced a r e q u i r e d response t h a t approximated the s t i m u l u s ( t h i s approximation was more accurate as l e a r n i n g progressed) but s u b j e c t s produced t h e i r own p a r t i c u l a r brand of e r r o r , or c a r i c a t u r e of the movement. And t h i s c a r i c a t u r e was r e l i a b l e both w i t h i n and across waveforms of d i f f e r e n t base f r e q u e n c i e s . Take f o r example the f i r s t t o p o l o g i c a l element i n the response waveform of s u b j e c t 6 . T h i s s u b j e c t c o n s i s t e n t l y f a b r i c a t e d a r e v e r s a l i n the response, t h a t d i d not e x i s t i n the s t i m u l u s . In comparing these i n s t a n c e s with the other s u b j e c t s , i t seems t h a t each s u b j e c t developed h i s or her own unique c a r i c a t u r e of the movement. Each s u b j e c t seems to have made c e r t a i n s y s t e m a t i c d i s t o r t i o n s i n the s t i m u l u s waveform i n attempting t o reproduce i t . F i g u r e 13. Kinematic p r o f i l e s from s u b j e c t 6 (wl - w5). 69 CHAPTER 4.  DISCUSSION The u n d e r l y i n g purpose of t h i s t h e s i s was to i n v e s t i g a t e the q u e s t i o n what is learned. Two p o s s i b l e answers t o t h i s q u e s t i o n were the focus o f t h i s study. The f i r s t o f these was t h a t humans l e a r n a movement i n terms of the relative timing of the response elements t h a t make up t h a t movement. The second of these was t h a t humans l e a r n a movement i n terms o f the frequency composition of t h a t movement. The r e s u l t s generated from t h i s study speak not only t o these s p e c i f i c aspects of the q u e s t i o n what is learned but t o other f a c e t s as w e l l . PART ONE - PURSUIT TRACKING Two s p e c i f i c q u e s tions, with r e s p e c t t o what is learned, were put forward i n r e l a t i o n t o the s u b j e c t s ' performance i n the p u r s u i t t r a c k i n g phase o f t h i s study. These were: One, would s u b j e c t s perform e q u a l l y w e l l w hile t r a c k i n g s t i m u l u s waveforms which maintained the r e l a t i v e t i m i n g of the t r a i n i n g waveform, but were transformed i n terms o f t h e i r base frequency? Two, would s u b j e c t s perform b e t t e r w hile t r a c k i n g a stimulus waveform which c o n t a i n e d the same component f r e q u e n c i e s as the t r a i n i n g waveform (but d i f f e r e n t phase angles) than they would on an e n t i r e l y new sti m u l u s waveform? 70 S u b j e c t s p e r f o r m a n c e o v e r t h e f i f t e e n d a y s o f t h e s t u d y on w a v e f o r m s one t o f i v e ( t h e t r a i n i n g w a v e f o r m s a n d t h e v a r i e d s p e e d w a v e f o r m s ) e x h i b i t e d a s i m i l a r p a t t e r n o f i m p r o v e m e n t on e a c h o f t h e t h r e e d e p e n d e n t m e a s u r e s (RMS e r r o r , v a r i a b i l i t y , a n d r e s p o n s e l a g ) . P e r f o r m a n c e , as m e a s u r e d b y RMS e r r o r a n d v a r i a b i l i t y showed a q u a d r a t i c d e c r e a s e t y p i c a l o f most l e a r n i n g s t u d i e s ( F r a n k s , W i l b e r g , & F i s h b u r n e , 1982; M a r t e n i u k & Romanow, 1 9 8 3 ) . By t h e l a s t d ay o f t h e s t u d y , day 15, s u b j e c t s w e r e p e r f o r m i n g more a c c u r a t e l y (as m e a s u r e d b y RMS e r r o r s c o r e s ) w h i l e t r a c k i n g t h e w a v e f o r m s t h a t v a r i e d o n l y i n b a s e f r e q u e n c y o r s p e e d (wl - w5) t h a n w h i l e t r a c k i n g t h e w a v e f o r m s t h a t v a r i e d t h e p h a s e r e l a t i o n s h i p s among t h e component f r e q u e n c i e s (w6) o r v a r i e d t h e component f r e q u e n c i e s t h e m s e l v e s (w7). The f a c t t h a t s u b j e c t s p e r f o r m e d b e t t e r on t h e two f a s t e r s p e e d s (w4 & w5) t h a n t h e y d i d on t h e o t h e r two p e r i o d i c w a v e f o r m s (w6 & w7) i s e s p e c i a l l y i n t e r e s t i n g b e c a u s e t y p i c a l l y i t i s more d i f f i c u l t , a s e v i d e n t f r o m RMS e r r o r s c o r e s , f o r a s u b j e c t t o t r a c k f a s t e r w a v e f o r m s ( N o b l e , F i t t s , & W a r r e n , 1955; Pew, D u f f e n d a c k , & F e n s c h , 1 9 6 7 ) . D e s p i t e t h i s f a c t s u b j e c t s w e r e a b l e t o more a c c u r a t e l y t r a c k t h e s e two f a s t e r w a v e f o r m s (w4 a n d w5) t h a n t h e y w e re a b l e t o t r a c k t h e new a n d p h a s e s h i f t e d w a v e f o r m s (w7 a n d w 6 ) . T h e s e d a t a , t h e r e f o r e , l e n d s u p p o r t t o t h e h y p o t h e s i s t h a t s u b j e c t s l e a r n a movement i n t e r m s o f i t s r e l a t i v e t i m i n g r a t h e r t h a n i n t e r m s o f i t s a b s o l u t e t i m i n g . 71 The h y p o t h e s i s t h a t movement i s l e a r n e d i n terms of i t s frequency composition was not supported by the RMS e r r o r r e s u l t s f o r the p u r s u i t t r a c k i n g phase of t h i s experiment. I f s u b j e c t s l e a r n a movement i n terms of i t s component f r e q u e n c i e s , they would be expected t o perform b e t t e r on a waveform which c o n t a i n e d the same component f r e q u e n c i e s as the t r a i n i n g waveform (such as w6) than they would on an e n t i r e l y new waveform (such as w7). However t h i s was not the case; s u b j e c t s performed no b e t t e r on w6 than they d i d on w7 . In examining performance on the random waveform (w8) over the p e r i o d of a c q u i s i t i o n , i t i s ev i d e n t t h a t s u b j e c t s improved s l i g h t l y . Improvement on t h i s waveform was i n d i c a t i v e o f a s u b j e c t ' s a b i l i t y t o t r a c k without the p e r i o d i c i t y t h a t e x i s t e d i n the other waveforms, and was r e f l e c t i v e of l e a r n i n g the c o n t r o l f u n c t i o n s of the t a s k . The c o n t r o l f u n c t i o n s o f the ta s k c o u l d be summed up as the f o l l o w i n g : 1) l e a r n i n g the r e l a t i o n s h i p between the movement produced with the j o y s t i c k and the consequent movement of the response c u r s o r on the screen 2) l e a r n i n g the maximum amplitude range of the stimulus c u r s o r . As i s ev i d e n t from F i g u r e 1, waveforms 1 t o 5 d i s p l a y e d a g r e a t e r r a t e o f t r a c k i n g improvement than w6 and w7. The days e f f e c t on a l l of the v a r i e d speed waveforms (w2 - w5) co n t a i n e d a q u a d r a t i c component s i m i l a r t o t h a t o f the t r a i n i n g waveform (wl). W6 and w7 had no such q u a d r a t i c component and e x h i b i t e d only a l i n e a r decrease i n RMS E r r o r . 72 Thus t h e r e was t r a n s f e r o f l e a r n i n g b e t w e e n t h e t r a i n i n g w a v e f o r m (wl) a n d t h e v a r i e d s p e e d w a v e f o r m s (w2 - w 5 ) . What c h a r a c t e r i s t i c s do t h e t r a i n i n g w a v e f o r m a n d t h e v a r i e d s p e e d w a v e f o r m s h a v e i n common? The v a r i e d s p e e d a n d t r a i n i n g w a v e f o r m s were i d e n t i c a l i n t e r m s o f t h e i r r e l a t i v e t i m i n g a n d i n t e r m s o f t h e i r s p a t i a l c h a r a c t e r i s t i c s . T h e s e w a v e f o r m s w e r e two d i m e n s i o n a l w a v e f o r m s , t h e two d i m e n s i o n s b e i n g t e m p o r a l d u r a t i o n a n d s p a t i a l d i s p l a c e m e n t . The r e l a t i v e t i m i n g a n d t h e r e l a t i v e d i s p l a c e m e n t d e f i n e d t h e t o p o l o g y o f t h e s e w a v e f o r m s , a n d w o u l d be what G e l ' f a n d a n d T s e t l i n (1962, 1971, c i t e d i n K u g l e r e t a l . , 1980) h a v e c a l l e d e s s e n t i a l v a r i a b l e s . T h e s e w a v e f o r m s were d i f f e r e n t i n t e r m s o f t h e i r o v e r a l l t i m i n g o r b a s e f r e q u e n c y , w h i c h i s what G e l ' f a n d a n d T s e t l i n w o u l d c a l l a n o n - e s s e n t i a l o r s c a l a r v a r i a b l e . N o n - e s s e n t i a l v a r i a b l e s do n o t i n f l u e n c e t o p o l o g y . The f a c t t h a t s u b j e c t s showed a s i m i l a r t r e n d o f i m p r o v e m e n t on t h e s e w a v e f o r m s w o u l d i n d i c a t e t h a t t h e y l e a r n a movement i n t e r m s o f i t s t o p o l o g y r a t h e r t h a n i n t e r m s o f i t s s c a l a r c h a r a c t e r i s t i c s s u c h a s o v e r a l l t i m i n g . The p a t t e r n o f i m p r o v e m e n t f o u n d i n t h e RMS r e s u l t s , i s a l s o f o u n d i n t h e v a r i a b i l i t y r e s u l t s , i n d i c a t i n g t h a t a s s u b j e c t s become more a c c u r a t e , t h e y a l s o become l e s s v a r i a b l e i n t h e i r , r e s p o n s e s . The i n c r e a s e i n c o n s i s t e n c y t h a t o c c u r e d d u r i n g t h e a c q u i s i t i o n o f t h i s t r a c k i n g t a s k h a s b e e n f o u n d i n many s t u d i e s on l e a r n i n g a n d s k i l l a c q u i s i t i o n ( B u r g e t t , 1970; F r a n k s & W i l b e r g , 1984; G l e n c r o s s , 1 9 7 9 ; L e w i s , 1956; M a r t e n i u k & Romanow, 1 9 8 3 ) . 73 The pr o c e s s e s u n d e r l y i n g such a decrease have been the s u b j e c t of s p e c u l a t i o n . I t may be t h a t e a r l y i n l e a r n i n g , s u b j e c t s were u s i n g a v a r i e t y of d i f f e r e n t s t r a t e g i e s i n attempting t o t r a c k the stim u l u s , whereas l a t e r i n l e a r n i n g they seem t o have adopted a more c o n s i s t e n t t r a c k i n g s t r a t e g y . In i n v e s t i g a t i n g t y p i n g , Lundervold (1958) found t h a t d u r i n g the process of s k i l l a c q u i s t i o n t y p i s t s developed a more e f f i c i e n t p a t t e r n of muscular c o n t r a c t i o n as measured by EMG. Fewer motor u n i t s were r e c r u i t e d t o execute the t y p i n g t a s k . Glencross (1979) found a s i m i l a r change i n EMG over the course of l e a r n i n g , and found a l s o t h a t t h i s change i n EMG c o i n c i d e d w i t h a decrease i n ki n e m a t i c v a r i a b i l i t y . F i g u r e s 3 and 4 d e p i c t how s u b j e c t s a d j u s t e d the time of responding w i t h r e s p e c t t o l e a d i n g or l a g g i n g the s t i m u l u s . The response t o a l l waveforms e a r l y on i n l e a r n i n g was t e m p o r a l l y r e t a r d e d , but as l e a r n i n g on wl progressed, responses t o a l l waveforms moved toward a c o i n c i d e n t response. By day 15, the s u b j e c t s ' responses t o wl, w2 and w3 were t e m p o r a l l y a l i g n e d with the s t i m u l u s . On w4 and w5 the s u b j e c t s ' responses s l i g h t l y lagged the st i m u l u s by 7 & 5 ms r e s p e c t i v e l y . On waveforms w4 and w5 the s u b j e c t s may have been p r o v i d i n g a response t h a t was ac c u r a t e i n terms of i t s r e l a t i v e t i m i n g c h a r a c t e r i s t i c s , but because of the speed of the stim u l u s , they were not able to keep up with the s t i m u l u s . In a d d i t i o n response e r r o r s become exaggerrated at the f a s t e r speeds because the s t i m u l u s s p e e d makes i t more d i f f i c u l t f o r s u b j e c t s t o b r i n g t h e r e s p o n s e c u r s o r b a c k i n a l i g n m e n t w i t h t h e m o v i n g s t i m u l u s . PART TWO - INPUT BLANKING Two s p e c i f i c h y p o t h e s e s , w i t h r e s p e c t t o what is learned, w e r e p u t f o r w a r d i n r e l a t i o n t o t h e s u b j e c t s ' p e r f o r m a n c e i n t h e i n p u t b l a n k i n g p h a s e o f t h i s s t u d y . T h e s e w e r e : One, s u b j e c t s w o u l d r e p r o d u c e w2 - w5 ( t h e v a r i o u s s p e e d w a v e f o r m s ) a s w e l l a s t h e y r e p r o d u c e d w l ( t h e t r a i n i n g w a v e f o r m ) . Two, s u b j e c t s w o u l d r e p r o d u c e a w a v e f o r m w h i c h c o n t a i n e d t h e same component f r e q u e n c i e s as t h e t r a i n i n g w a v e f o r m p h a s e s h i f t e d (w6) b e t t e r t h a n t h e y w o u l d r e p r o d u c e an e n t i r e l y new w a v e f o r m (w7). I. Interval Durations A s d e s c r i b e d i n t h e r e s u l t s , t h e ANOVA p e r f o r m e d on t h e p r o p o r t i o n a l i n t e r v a l d u r a t i o n s y i e l d e d a n o n - s i g n i f i c a n t e f f e c t f o r t h e waves b y i n t e r v a l s i n t e r a c t i o n . Thus t h e p r o p o r t i o n a l i n t e r v a l d u r a t i o n s a p p e a r t o be i n v a r i a n t , a n d t h e i n v a r i a n t r e l a t i v e t i m i n g h y p o t h e s i s s u p p o r t e d . I t i s i n t e r e s t i n g , t h e r e f o r e , t o c o n s i d e r t h i s r e s u l t i n l i g h t o f f i n d i n g s a n d c o n t e n t i o n s f r o m s e v e r a l r e c e n t p a p e r s , a n d i n l i g h t o f o t h e r d a t a f r o m t h e p r e s e n t e x p e r i m e n t . G e n t n e r (1987) h a s c r i t i c i z e d t h e p r o c e d u r e ( f o l l o w e d i n t h e p r e s e n t s t u d y ) o f t a k i n g means a c r o s s s u b j e c t s a n d a c r o s s i n s t a n c e s w i t h i n a g i v e n s u b j e c t . However, i f t h e 75 w i t h i n s u b j e c t v a r i a b i l i t y scores are examined i n c o n j u n c t i o n w i t h the ANOVA, t h i s p r o v i d e s an adequate t e s t of c o n s i s t e n c y (or i n v a r i a n c e ) . From the c o e f f i c i e n t of v a r i a t i o n t a b l e s i n the r e s u l t s , i t i s e v i d e n t t h a t compared to other motor behaviors (such as r e a c t i o n time) the w i t h i n s u b j e c t v a r i a b i l i t y of the p r o p o r t i o n a l i n t e r v a l d u r a t i o n data i s low. To date, i t has not been determined how c o n s i s t e n t scores must be i n order t o be c o n s i d e r e d i n v a r i a n t . In comparison to other motor b e h a v i o r s such as r e a c t i o n time the p r o p o r t i o n a l i n t e r v a l d u r a t i o n s from the p r e s e n t study e x h i b i t very low v a r i a b i l i t y . A recent study conducted by Heuer and Schmidt (1988) seemed to g i v e evidence a g a i n s t the t r a n s f e r of i n v a r i a n t r e l a t i v e t i m i n g between movement p a t t e r n s . However, i n Heuer and Schmidt's study s u b j e c t s were gi v e n l i t t l e p r a c t i c e (250 c y c l e s ) . T h i s amount of p r a c t i c e may have been i n s u f f i c i e n t t o a l l o w s u b j e c t s t o l e a r n the r e l a t i v e t i m i n g of the t r a i n i n g p a t t e r n . In examining the power s p e c t r a of the s u b j e c t s ' responses i t i s c l e a r t h a t s u b j e c t s were unable to reproduce even the r e l a t i v e t i m i n g of the p a t t e r n they had t r a i n e d on with any degree of accuracy. Thus i t i s not s u r p r i s i n g t h a t t h e r e was no d i f f e r e n c e i n t r a n s f e r between p a t t e r n s which shared the r e l a t i v e t i m i n g of the t r a i n i n g p a t t e r n and those which d i d not. Perhaps i f s u b j e c t s i n the Heuer and Schmidt study had been gi v e n more p r a c t i c e , t h e r e would have been a b e t t e r t r a n s f e r t o the p a t t e r n which shared the r e l a t i v e t i m i n g of 76 the t r a i n i n g p a t t e r n . By the l a s t day of the presen t study, day 15, s u b j e c t s had had 5740 c y c l e s of p r a c t i c e on the t r a i n i n g waveform, and had thus been gi v e n more time t o l e a r n the r e l a t i v e t i m i n g p a t t e r n of the t r a i n i n g waveform. T h i s may e x p l a i n the apparent d i s c r e p a n c y i n the r e s u l t s of the two s t u d i e s . Two hypotheses i n r e f e r e n c e t o r e l a t i v e t i m i n g have been put forward by Heuer (1988). The f i r s t i s t h a t " d i f f e r e n t temporal p a t t e r n s are c a t e g o r i c a l l y d i f f e r e n t " , and c o n t r o l l e d by d i f f e r e n t motor programs. The second i s t h a t "temporal p a t t e r n s d i f f e r on one or more c o n t i n u a " such t h a t movements f a l l i n g at d i f f e r e n t p l a c e s along these c o n t i n u a are c o n t r o l l e d by d i f f e r e n t parameters w i t h i n the same motor program. The c a t e g o r i c a l \ c o n t i n u a l hypotheses were not r e l e v a n t t o the present study because, the presen t study d i d not address the q u e s t i o n of whether r e l a t i v e t i m i n g i s an i n v a r i a n t f e a t u r e o f a motor program, but whether s u b j e c t s l e a r n i n v a r i a n t r e l a t i v e t i m i n g . In the context o f the present experiment, r e l a t i v e t i m i n g i s seen as an i n v a r i a n t t h a t i s l e a r n e d or a b s t r a c t e d out of movement, r a t h e r than as a f i x e d s t r u c t u r e of a motor program. Thus the t h e o r e t i c a l context out of which the present experiment was developed i s d i f f e r e n t than t h a t surrounding the motor program. Heuer and Schmidt (1988) i n d i s c u s s i n g r e l a t i v e t i m i n g have made the d i s t i n c t i o n between processes t h a t are mandatory and those t h a t are s t r a t e g i c . They suggest t h a t 77 r e l a t i v e t i m i n g i s s t r a t e g i c and not mandatory. From the p e r s p e c t i v e o f the c u r r e n t study, i n v a r i a n t r e l a t i v e t i m i n g i s not mandatory i n the sense t h a t i t i s i m p o s s i b l e t o change i t , but then again most l e a r n e d b e h a v i o r s are m a l l e a b l e . L i v i n g nervous systems ( e s p e c i a l l y the human nervous system) are p l a s t i c and by t h e i r nature designed t o adapt t o change. From the p e r s p e c t i v e o f l e a r n i n g , i n v a r i a n t r e l a t i v e t i m i n g i s seen as an aspect o f movement t h a t i s l e a r n e d by the s u b j e c t and by t h a t f a c t a l s o capable of b e i n g changed ( i . e . m a l l e a b l e ) . The i n t e r v a l d u r a t i o n data can be c o n s i d e r e d i n l i g h t o f some of the i n f o r m a l o b s e r v a t i o n s and s e l f r e p o r t data from both p i l o t and t h e s i s experiments. T h i s data supports the n o t i o n t h a t people may l e a r n movement i n terms of i t s rhythmic p a t t e r n , the rhythmic p a t t e r n b e i n g e s s e n t i a l l y an a b s t r a c t i o n o f the r e l a t i v e t i m i n g p a t t e r n of the movement. Over the course o f s k i l l a c q u i s i t i o n , s u b j e c t s l e a r n e d t o express the rhythm of the movement p a t t e r n t h a t they were t r a i n i n g on, i n other sensory m o d a l i t i e s and wit h other body p a r t s . S u b j e c t s seemed t o encode the rhythm of the movement p a t t e r n i n the a u d i t o r y modality. Many s u b j e c t s r e p o r t e d t h a t they would hum or tap the rhythm of the st i m u l u s t o themselves. In a d d i t i o n some of the s u b j e c t s would move t h e i r head i n the p a t t e r n o f the stimulus both while t r a c k i n g and while input b l a n k i n g . T h e r e f o r e i t may be t h a t one aspect of l e a r n i n g movement i s l e a r n i n g i t s rhythmic p a t t e r n , and encoding t h i s p a t t e r n i n v a r i o u s m o d a l i t i e s . 78 T h i s e x p r e s s i o n of rhythm i s found not only i n movement and a u d i t i o n , but a l s o i n the development of anatomical s t r u c t u r e . Bateson (1982) has observed the occurrence of rhythm d u r i n g the process of morphogenesis: The anatomy of the crab i s r e p e t i t i v e and r h y t h m i c a l . I t i s , l i k e music, r e p e t i t i v e with modulation. Indeed, the d i r e c t i o n from head toward t a i l corresponds t o a sequence i n time. L i v i n g systems then seem to d i s p l a y rhythm not on l y i n movement but a l s o i n s t r u c t u r e . Rhythm may be a p r o p e r t y shared by a l l l i v i n g systems and m a n i f e s t i n g i n v a r i o u s ways. For i n s t a n c e rhythm i s found i n the c a r d i a c and r e s p i r a t o r y p a t t e r n s of a l l animals as w e l l as i n t h e i r c i r c a d i a n rhythms of r e s t and a c t i v i t y . Common t o a l l human c u l t u r e s i s the e x p r e s s i o n of rhythm i n poetry, music and dance. The e x p r e s s i o n of rhythm m a n i f e s t i n g i n more than one mo d a l i t y t h a t was d e s c r i b e d above, can be e x p l a i n e d by what Schmidt (1988) and others have c a l l e d a b s t r a c t i o n . R a i b e r t (1977) and Merton (1973) have pr e s e n t e d f i n d i n g s , s i m i l a r t o those of the present study, f o r han d w r i t i n g . When hand w r i t i n g was t r a n s f e r r e d t o the non-dominant hand, to the arm (by i m m o b i l i z i n g the w r i s t ) , t o the mouth, and to the f o o t , the w r i t i n g i n a l l s i t u a t i o n s e x h i b i t e d a c o n s i s t e n t t o p o l o g i c a l form, though i t was v a r i a b l e i n i t s s c a l a r c h a r a c t e r i s t i c s . From t h i s i t was suggested t h a t s u b j e c t s might have encoded an a b s t r a c t r e p r e s e n t a t i o n of the 79 movement t h a t they produced. An a b s t r a c t code of movement would al l o w f o r the v a r i o u s m a n i f e s t a t i o n s of the movement i n the v a r i o u s m o d a l i t i e s . Another way of i n t e r p r e t i n g t h i s evidence i s t h a t a movement t h a t i s w e l l l e a r n e d becomes redundantly encoded i n the nervous system, and t h a t p a r t of t h i s redundant encoding might i n v o l v e an encoding i n other m o d a l i t i e s . Pribram (1971) and La s h l e y (1950) have gi v e n evidence f o r such a d i s t r i b u t e d system f o r memory. Pribram, u s i n g the analogy of the hologram, has suggested t h a t as a movement becomes w e l l l e a r n e d , the b r a i n encodes the movement at a f i n e r r e s o l u t i o n i n the same way t h a t a complete h o l o g r a p h i c p l a t e s t o r e s a f i n e r r e s o l u t i o n image than a p i e c e o f t h a t p l a t e i s capable o f s t o r i n g . Bateson (1982) has suggested t h a t one of the p r o p e r t i e s t h a t l i v i n g systems e x h i b i t i s an i n v a r i a n c e i n u n d e r l y i n g formal r e l a t i o n s . As Bateson has p o i n t e d out i n d e s c r i b i n g v e r t e b r a t e morphology, though t h e r e may be an "asymmetry i n s i z e " , one n e v e r t h e l e s s f i n d s "a deeper symmetry i n formal r e l a t i o n s " . In the same way t h a t symmetry of form o r g a n i z e s morphogenesis, r e l a t i v e t i m i n g may be the s t r u c t u r e around which a movement p a t t e r n i s or g a n i z e d . S e v e r a l authors have drawn p a r a l l e l s between morphogenesis and motor l e a r n i n g ( B e r k i n b l i t , Feldman, & Fukson, 1986 p. 5 9 9 ; Turvey, 1986 p . 6 2 4 ) . L i v i n g c r e a t u r e s e x h i b i t symmetry i n terms of form, but r a r e l y i s t h i s expressed i n terms of p e r f e c t l y e q u i v a l e n t magnitudes on the r i g h t and l e f t s i d e s o f the 80 body. For i n s t a n c e , the r i g h t l e g may be s l i g h t l y l o n g e r than the l e f t ( i . e . the magnitudes are not e x a c t l y e q u i v a l e n t ) but the form i s symmetrical i n t h a t t h e r e are two l e g s , two knees, two f e e t and the form of these on the r i g h t i s the exact m i r r o r image of t h a t on the l e f t . The concept of r e l a t i v e t i m i n g can be c o n s i d e r e d i n a s i m i l a r l i g h t , and the process of a b s t r a c t i o n can be c o n s i d e r e d as a proc e s s of deter m i n i n g the u n d e r l y i n g formal r e l a t i o n s . J J . Interval Displacements The p r o p o r t i o n a l i n t e r v a l displacements ( i n t e r v a l s taken as a p r o p o r t i o n of the maximum displacement t h a t o c c u r r e d i n t h a t c y c l e ) were i n v a r i a n t across c y c l e s and waveforms w i t h i n a gi v e n s u b j e c t . Thus i t seems t h a t both the relative s p a t i a l and the relative temporal c h a r a c t e r i s t i c s o f the response waveforms remained i n v a r i a n t across c y c l e s and waveforms w i t h i n a gi v e n s u b j e c t . I t was these two c h a r a c t e r i s t i c s t h a t d e f i n e d the topology of the p a r t i c u l a r t r a c k i n g waveforms t h a t were used i n t h i s experiment. Therefore the topology of the response waveforms f o r a giv e n s u b j e c t remained i n v a r i a n t , w h i l e the s c a l a r c h a r a c t e r i s t i c s of those response waveforms v a r i e d t o some ex t e n t . The s c a l a r c h a r a c t e r i s t i c of o v e r a l l d u r a t i o n v a r i e d g r e a t l y across waveforms. Subjects were able t o vary t h i s s c a l a r c h a r a c t e r i s t i c while m a i n t a i n i n g the r e l a t i v e t i m i n g and the o v e r a l l topology. T h i s g i v e s support t o the i d e a t h a t one of the aspects o f a movement t h a t s u b j e c t s 81 l e a r n i s the t o p o l o g i c a l p r o p e r t i e s of a movement. B e r n s t e i n (1967) has suggested t h a t we encode movement i n terms of i t s t o p o l o g i c a l p r o p e r t i e s . Pribram (1971) has m o d i f i e d B e r n s t e i n ' s i d e a s u g g e s t i n g t h a t we encode movement i n terms of a n t i c i p a t e d f o r c e p a t t e r n s . However, more rece n t s t u d i e s by Soechting & L a c q u a n t i (1981) g i v e evidence t h a t humans p l a n and c o n t r o l the k inematics of the movement t r a j e c t o r y r a t h e r than the f o r c e s used t o produce the movement t r a j e c t o r y . Perhaps t h i s d i s c r e p a n c y e x i s t s because both c o n t e n t i o n s are c o r r e c t depending on which l e v e l of a n a l y s i s one i s a d d r e s s i n g . Whiting and Den B r i n k e r (1982) i n i n t e g r a t i n g these two p o s i t i o n s suggests j u s t t h i s , t h a t both c o n t e n t i o n s are c o r r e c t , i n t h a t f o r c e i s what we are r e q u i r e d t o produce, but t h a t at a h i g h e r l e v e l i n the system we encode topology. Present data supports Whiting's c o n t e n t i o n . III. Cycle Duration From the r e s u l t s of t h i s experiment i t seems t h a t s u b j e c t s o r g a n i z e d t h e i r movement p a t t e r n s i n terms of r e l a t i v e t i m i n g r a t h e r than i n terms of o v e r a l l d u r a t i o n . Subjects were more accurate at r e p r o d u c i n g the r e l a t i v e t i m i n g p a t t e r n of the stimulus waveforms than they were at r e p r o d u c i n g the o v e r a l l d u r a t i o n of the s t i m u l u s waveforms. These r e s u l t s can be c o n s i d e r e d i n l i g h t of an i d e a put forward by Kugler et a l . (1980) t h a t the nervous system encodes i n f o r m a t i o n i n a way t h a t i s system s c a l e d and 82 d i m e n s i o n l e s s . O v e r a l l d u r a t i o n i m p l i e s some k i n d of e x t e r n a l o b j e c t i v e time c l o c k , whereas i f Kugler et a l are c o r r e c t , the nervous system would only "understand" time i n a r e l a t i v i s t i c sense. In order f o r the organism t o tune i t s response t i m i n g c h a r a c t e r i s t i c s t o c o n i n c i d e w i t h events i n the environment, the organism would u t i l i z e feedback from the environment. Then i t would not be the o v e r a l l d u r a t i o n , but r a t h e r the immediate t i m i n g c h a r a c t e r i s t i c s i n the environment, t h a t would be of r e l e v a n c e to the organism i n moving. In r e l a t i o n t o t i m i n g , Pribram (1971) has suggested t h a t r a t h e r than encoding absolute time i n the b r a i n , humans encode p a t t e r n s of frequency i n f o r m a t i o n . Movement i t s e l f , a c c o r d i n g to Pribram, i s encoded i n terms of a F o u r i e r transform, which d e s c r i b e s movement i n terms of i t s p a t t e r n of frequency composition. F o u r i e r transforms f o r movement p a t t e r n s which have d i f f e r e n t o v e r a l l t i m i n g , but have the same r e l a t i v e t i m i n g are i d e n t i c a l . Thus i f movement i s encoded i n t h i s way, only i t s r e l a t i v e t i m i n g c h a r a c t e r i s t i c s would be important. IV. Frequency Composition & Root Mean Squared Error The movement p a t t e r n s reproduced d u r i n g input b l a n k i n g f o r w6 (the phase s h i f t e d waveform) were more acc u r a t e as measured by RMS e r r o r than those generated f o r w7 (the e n t i r e l y new waveform), though t h i s d i f f e r e n c e was not s t a t i s t i c a l l y s i g n i f i c a n t . I t seems t h a t i n i n p u t b l a n k i n g , s u b j e c t s may t r a n s f e r to w6 (a waveform which c o n t a i n s 83 i d e n t i c a l component f r e q u e n c i e s t o the t r a i n i n g waveform) more e a s i l y than they t r a n s f e r to w7 (a new waveform). This data lends some support to the c o n j e c t u r e t h a t has been put forward by Pribram (1971), Franks and W i l b e r g (1982), and Marteniuk and Romanow (1983) t h a t s u b j e c t s may o r g a n i z e memory f o r movement i n terms of the component f r e q u e n c i e s of t h a t movement. In p u r s u i t t r a c k i n g , s u b j e c t s performed e q u a l l y w e l l on w6 and w7, and performed worse on these than they d i d on wl - W5. Subjects may have performed d i f f e r e n t l y i n p u r s u i t t r a c k i n g than i n input b l a n k i n g on w6 and w7, because b e i n g d r i v e n v i s u a l l y d u r i n g p u r s u i t t r a c k i n g , s u b j e c t s may have been more attuned to the topology of the s t i m u l u s , whereas d u r i n g input b l a n k i n g when s u b j e c t s were not d r i v e n v i s u a l l y they may have been attuned to the frequency composition of the s t i m u l u s p a t t e r n . In a d d i t i o n , d u r i n g p u r s u i t t r a c k i n g s u b j e c t s were l e s s dependent on t h e i r memory of the movement because the s t i m u l u s was p r e s e n t e d b e f o r e them. In input b l a n k i n g , however, with no stimulus a v a i l a b l e , s u b j e c t s were r e q u i r e d to r e l y on t h e i r memory f o r the movement. In t h i s case, they f e l l back on what they had l e a r n e d from wl. Because wl and w6 c o n t a i n e d i d e n t i c a l component f r e q u e n c i e s , s u b j e c t s were able t o generate a b e t t e r r e p r o d u c t i o n of w6 than they were of w7 (an e n t i r e l y new waveform). I f memory i s o r g a n i z e d i n terms of component f r e q u e n c i e s , t h i s would make i t e a s i e r f o r s u b j e c t s to reproduce w6 than i t would f o r them t o reproduce w7. 84 V. Kinematic Profiles The k i n e m a t i c r e p r e s e n t a t i o n s of the responses generated d u r i n g input b l a n k i n g on wl - w5, day 15, g i v e evidence f o r t o p o l o g i c a l c o n s i s t e n c y w i t h i n s u b j e c t s . A l l s u b j e c t s were c o n s i s t e n t i n producing the f i v e c y c l e s w i t h i n a g i v e n waveform. There was a l s o a great d e a l of s i m i l a r i t y i n response p r o d u c t i o n across the v a r i e d speed waveforms. A d d i t i o n a l l y , though s u b j e c t s produced a r e q u i r e d response t h a t approximated the stimulus, they a l s o produced t h e i r own p a r t i c u l a r brand of e r r o r , or what Gibson (1969) has l a b e l l e d a " c a r i c a t u r e " of the movement. T h i s c a r i c a t u r e was r e l i a b l e both w i t h i n and across waveforms of d i f f e r e n t base f r e q u e n c i e s . For example the f i r s t t o p o l o g i c a l element generated by s u b j e c t s i x i s a r e v e r s a l t h a t d i d not e x i s t i n the s t i m u l u s . Subject s i x generated t h i s element f o r each c y c l e on each of the f i v e waveforms. Gibson (1969) found s i m i l a r d i s t o r t i o n s i n her s u b j e c t s ' drawings of o b j e c t s t h a t they were r e q u i r e d to remember: ...(they) were i n f a c t exaggerations of those f e a t u r e s which made one plane d i s t i n g u i s h a b l e from o t h e r s , so t h a t the composites are i n a sense c a r i c a t u r e s . I t seems, t h e r e f o r e , t h a t memory images or schematic r e p r e s e n t a t i o n s of the a i r c r a f t were indeed based on d i s t i n c t i v e f e a t u r e s d e t e c t e d while l o o k i n g f o r d i f f e r e n c e s . (Gibson 1969, pp.146-147) In comparing topology across the s i x s u b j e c t s , i t seems t h a t each s u b j e c t developed h i s or her own unique c a r i c a t u r e of 85 t h e movement. E a c h s u b j e c t seems t o h a v e made some s y s t e m a t i c d i s t o r t i o n s i n t h e s t i m u l u s w a v e f o r m i n a t t e m p t i n g t o r e p r o d u c e i t . An i n t e r e s t i n g c o m p a r i s o n c a n be made b e t w e e n t h e s e f i n d i n g s a n d f i n d i n g s r e p o r t e d b y B a r t l e t t (1932). He f o u n d t h a t s u b j e c t s , i n r e c a l l i n g s t o r i e s , w o u l d d i s t o r t t h e d e t a i l s t o f i t t h e i r own c u l t u r a l c o n t e x t . More r e c e n t l y T v e r s k y (1981) i n h e r r e s e a r c h on memory f o r s p a t i a l l o c a t i o n s , h a s f o u n d t h a t i n r e c a l l i n g g e o g r a p h i c a l l o c a t i o n s s u b j e c t s made s y s t e m a t i c d i s t o r t i o n s o f s p a c e . I t a p p e a r s t h a t s u b j e c t s s y s t e m a t i c a l l y d i s t o r t p h y s i c a l r e a l i t y i n f a v o u r o f a p s y c h o l o g i c a l r e a l i t y t h a t i s i n f l u e n c e d o r b i a s e d b y p r e v i o u s e x p e r i e n c e . I n t h e c a s e o f t h i s p a r t i c u l a r e x p e r i m e n t t h e d i s t o r t i o n s i n t h e t o p o l o g y o f t h e w a v e f o r m s were d i f f e r e n t f o r e a c h s u b j e c t a n d c o n s i s t e n t w i t h i n a g i v e n s u b j e c t . . PART THREE - CONCLUSIONS  Component Fr e q u e n c i e s The i d e a t h a t s u b j e c t s l e a r n a n d o r g a n i z e a movement i n t e r m s o f i t s component f r e q u e n c i e s was n o t s u p p o r t e d b y t h e p u r s u i t t r a c k i n g r e s u l t s , b u t was p a r t i a l l y i n d i c a t e d b y t h e i n p u t b l a n k i n g r e s u l t s . D u r i n g p u r s u i t t r a c k i n g s u b j e c t s e x h i b i t e d e q u i v a l e n t l e v e l s o f a c c u r a c y on t h e new a n d t h e o u t o f p h a s e w a v e f o r m , a n d t h u s seem n o t t o o r g a n i z e a movement i n t e r m s o f i t s component f r e q u e n c i e s d u r i n g p u r s u i t t r a c k i n g . However d u r i n g i n p u t b l a n k i n g , s u b j e c t s 86 seem t o have performed b e t t e r on w6 than they d i d on w7. The previous s t u d i e s (Franks & Wilberg, 1980; Marteniuk & Romanow, 1983) tha t gave evidence t h a t subjects l e a r n movement i n terms of component frequencies measured subjects during input b l a n k i n g r a t h e r than p u r s u i t t r a c k i n g . Thus evidence from the present study i s c o n s i s t e n t w i t h evidence from these e a r l i e r s t u d i e s . R e l a t i v e Timing The hypothesis that subjects l e a r n a movement i n terms of r e l a t i v e t i m i n g was supported by t h i s experiment i n both the p u r s u i t t r a c k i n g and input b l a n k i n g c o n d i t i o n s . With p r a c t i c e i n t r a c k i n g the t r a i n i n g waveform (wl), there was p o s i t i v e t r a n s f e r t o the var i o u s speed waveforms (w2, w3, w4, w5). For p u r s u i t t r a c k i n g , i f the t r a n s f e r waveform was slower (w2 or w3) than the t r a i n i n g waveform (wl), there was almost p e r f e c t t r a n s f e r i n terms of response accuracy. When t r a n s f e r r e d t o f a s t e r waveforms (w4 and w5), the response accuracy was somewhat diminished. Nevertheless, subjects performed f a r more a c c u r a t e l y on the f a s t e r t r a n s f e r waveforms (w4 and w5) than they d i d on the new waveform (w7) and the phase s h i f t e d waveform (w6). For input b l a n k i n g , the i n t e r v a l durations t h a t were c a l c u l a t e d revealed that the p r o p o r t i o n a l i n t e r v a l durations were i n v a r i a n t across the f i v e v a r i e d speed waveforms, thus supporting the not i o n t h a t s k i l l e d movement i s c h a r a c t e r i z e d by i n v a r i a n t r e l a t i v e t i m i n g . 87 T y p i c a l l y i n the f i e l d o f motor l e a r n i n g and c o n t r o l i n v a r i a n t r e l a t i v e t i m i n g has been thought of as an i n v a r i a n t f e a t u r e of a motor program. I f s u b j e c t s i n the present study had achieved i d e n t i c a l RMS e r r o r scores f o r wl - w5, the c o n t e n t i o n t h a t r e l a t i v e t i m i n g i s f i x e d i n the motor program, and t h a t o v e r a l l d u r a t i o n i s a parameter whose va l u e can vary might have been supported. However the data from t h i s experiment d i d not t u r n out e x a c t l y as p r e d i c t e d . One reason f o r t h i s i s t h a t f a s t e r waveforms are more d i f f i c u l t t o t r a c k , and thus as present r e s u l t s show, one f i n d s h i g h e r RMS scores on these waveforms. A d d i t i o n a l l y , i n the case of p u r s u i t t r a c k i n g , s u b j e c t s used feedback t o c o n t i n u o u s l y modulate t h e i r response, making the n o t i o n of a d i s c r e e t parameter value u n l i k e l y . For p u r s u i t t r a c k i n g i t i s l i k e l y t h a t the o v e r a l l (or absolute) t i m i n g i s c o n t i n u o u s l y modulated by feedback. From both the input b l a n k i n g and the p u r s u i t t r a c k i n g data, t h e r e i s evidence t h a t r e l a t i v e t i m i n g i s one of the aspects o f a movement t h a t people l e a r n d u r i n g the process of s k i l l a c q u i s i t i o n . The evidence t h a t a p a t t e r n o f i n v a r i a n t r e l a t i v e t i m i n g was l e a r n e d d u r i n g the process of s k i l l a c q u i s i t i o n need not be taken t o mean t h a t i n v a r i a n t r e l a t i v e t i m i n g i s an i n v a r i a n t f e a t u r e of a g e n e r a l i z e d motor program. I t can j u s t as w e l l be taken as support f o r the i d e a t h a t r e l a t i v e t i m i n g i s one of the i n v a r i a n c e s t h a t i s l e a r n e d d u r i n g motor s k i l l a c q u i s i t i o n , perhaps i n a 88 s i m i l a r way t o the p i c k up of i n v a r i a n t s d u r i n g p e r c e p t u a l l e a r n i n g (Gibson, 1966; Gibson, 1969). What i s Learned? Both t h e s i s and p i l o t experiments l e n d support t o the i d e a t h a t r e l a t i v e t i m i n g (of the response elements t h a t make up a movment) i s one of the aspects of movement t h a t i s l e a r n e d . T h i s f i n d i n g i s l i m i t e d t o c y c l i c movements of two k i n d s : those i n which v i s u a l feedback i s i n v o l v e d i n the c o n t r o l of the movement such as i n p u r s u i t t r a c k i n g , and those i n which both k i n e s t h e t i c feedback and memory are i n v o l v e d i n the c o n t r o l o f movement such as i n in p u t b l a n k i n g . These r e s u l t s a l s o g i v e some i n d i c a t i o n t h a t d u r i n g response r e p r o d u c t i o n a movement may be o r g a n i z e d i n terms of i t s component f r e q u e n c i e s . T h i s f i n d i n g i s l i m i t e d t o t a s k s such as input b l a n k i n g i n which the c o n t r o l o f movement i s based on k i n e s t h e t i c feedback and memory. Both the r e l a t i v e t i m i n g and the component f r e q u e n c i e s of a movement can be seen t o be a way of o r g a n i z i n g movement, such t h a t as l e a r n i n g progresses the person moves toward a hi g h e r s t a t e o f o r g a n i z a t i o n , i n the same way t h a t as morphogenesis progresses the system reaches a more complex form of o r g a n i z a t i o n . Though l e a r n i n g i s i t s e l f a process t h a t occurs i n l i v i n g systems, i t has o f t e n been c o n s i d e r e d as a "higher" f u n c t i o n t h a t i s somehow removed from the r e s t of the b i o l o g i c a l world, and t h e r e f o r e not governed by the same laws. In c o n t r a s t , the view of l e a r n i n g put forward i n 89 t h i s t h e s i s has been t h a t l e a r n i n g i s a process r o o t e d i n b i o l o g y , r a t h e r than one removed from i t . L e a r n i n g can be c o n s i d e r e d as an e x p r e s s i o n of l i f e and governed by the same laws. In t h i s t h e s i s p a r a l l e l s have been drawn between p r i n c i p l e s of l e a r n i n g and p r i n c i p l e s of l i f e . The most emphasized p a r a l l e l has been t h a t of the e v o l u t i o n toward a h i g h e r s t a t e of o r g a n i z a t i o n . Both i n l e a r n i n g and i n morphogenesis the human or organism goes through a p r o c e s s whereby the entropy g r a d i e n t i s r e v e r s e d and the organism c o n t i n u a l l y achieves a h i g h e r and h i g h e r order o r g a n i z a t i o n . The development of the c o o r d i n a t i v e s t r u c t u r e i s an example of such a p r o c e s s . I t can be thought of as a form of i n t e r n a l o r g a n i z a t i o n , which, becomes both more d i f f e r e n t i a t e d and more i n t e g r a t e d throughout the l e a r n i n g process, i n the same way t h a t the nervous system d u r i n g i t s morphogenesis becomes more d i f f e r e n t i a t e d and i n t e g r a t e d (Schacher, 1985). Le a r n i n g then, can be c o n s i d e r e d as a s p e c i a l i n s t a n c e of the l a r g e r process of l i f e . 90 APPENDIX A  REVIEW OF LITERATURE A simple but e s s e n t i a l q u e s t i o n f o r those who seek t o understand l e a r n i n g i s what is learned. Or from the movement s c i e n t i s t ' s p e r s p e c t i v e "What changes w i t h i n a person b r i n g about more s k i l l e d motor performance?" T h i s q u e s t i o n has been c e n t r a l t o psychology s i n c e the i n c e p t i o n of b e h a v i o r i s m i n the 1930's (Gibson, 1969; Weimer, 1977; Whiting, 1980). The b e h a v i o r i s t s have proposed, t h a t i t i s a s s o c i a t i o n s between s t i m u l i and responses t h a t are l e a r n e d . The c o g n i t i v i s t s , on the other hand, have argued, t h a t what is learned are r e p r e s e n t a t i o n s of movement, o b j e c t s , or events. There has been much s p e c u l a t i o n as t o the nature of the r e p r e s e n t a t i o n f o r s k i l l e d movement; i t has been d e s c r i b e d i n d i f f e r e n t ways by d i f f e r e n t r e s e a r c h e r s , w i t h l a b e l s such as schema (Schmidt, 1975) image of achievement (Pribram), and motor program (Keele, 1975). The Gibsonians or the e c o l o g i c a l group, who l i k e the b e h a v i o r i s t s , have r e j e c t e d e x p l a n a t i o n s based on r e p r e s e n t a t i o n , have e x p l a i n e d l e a r n i n g i n yet another way. J . J . Gibson (1966, p.279) has d e f i n e d p e r c e p t u a l l e a r n i n g as "cases o f p e r c e i v i n g or d e t e c t i n g an i n v a r i a n t " . J . J . Gibson's i d e a have be extended t o both the c o g n i t i v e and motor domains. In r e l a t i o n t o c o g n i t i o n , E l e a n o r Gibson (1969, p471) has argued t h a t the l e a r n e d p e r c e p t u a l a b i l i t y "to d e t e c t r e g u l a r i t y , order, and s t r u c t u r e " p r o v i d e s the b a s i s f o r c o g n i t i v e a b i l i t i e s such as l e a r n i n g mathematics (see a l s o Wertheimer, 1 9 4 5 ) . In the case of movement as w e l l , t h e r e are c e r t a i n of i t s f e a t u r e s t h a t become i n v a r i a n t as i t becomes w e l l l e a r n e d . "What is Learned?" S e v e r a l r e s e a r c h e r s ( B a r t l e t t , 1 9 3 2 ; Head, 1 9 2 0 ; G a l l i s t e l , 1 9 8 0 ; Schmidt, 1975) have proposed t h a t d u r i n g l e a r n i n g we develop a schema as a r e p r e s e n t a t i o n of a g i v e n s k i l l e d a c t . T h i s schema i s a set of r u l e s used to d e f i n e and generate movement. B a r t l e t t , one of the f i r s t t o have c o n c e p t u a l i z e d the n o t i o n of a schema, has i n c l u d e d i n i t , a d a p t a t i o n t o a changing environment through feedback: In a world of c o n s t a n t l y changing environment, l i t e r a l r e c a l l i s e x t r a o r d i n a r i l y unimportant. I t i s w i t h remembering as i t i s with the s t r o k e i n a s k i l l e d game. We may fancy t h a t we are r e p e a t i n g a s e r i e s of movements l e a r n e d a long time b e f o r e from a text-book or from a t e a c h e r . But motion study shows t h a t i n f a c t we b u i l d up the s t r o k e a f r e s h on the b a s i s of the immediately p r e c e d i n g balance of postures and the momentary needs of the game. Every time we make i t , i t has i t s own c h a r a c t e r i s t i c s . ( 1 9 3 2 , p. 2 0 4 . ) The other important p o i n t t h a t B a r t l e t t has made i s t h a t memory or r e p r o d u c t i o n of movement r a r e l y i n v o l v e s r o t e r e c a p i t u l a t i o n . Because the environment i s always changing, any s k i l l e d a c t i o n must be adapted t o the immediate 92 e n v i r o n m e n t . A n d o f c o u r s e t h i s c a n o n l y be a c c o m p l i s h e d t h r o u g h f e e d b a c k . A n o t h e r v e r s i o n o f t h e r e p r e s e n t a t i o n f o r s k i l l e d movement i s t h e c o n c e p t o f t h e image o f a c h i e v e m e n t ( P r i b r a m , 1971) w h i c h i s b a s e d on b o t h n e u r o p h y s i o l o g i c a l a n d b e h a v i o r a l e v i d e n c e . P r i b r a m h a s s u g g e s t e d t h a t t h e image o f a c h i e v e m e n t i s e n c o d e d i n t h e m o t o r c o r t e x a s a F o u r i e r t r a n s f o r m o f t h e l e a r n e d a n t i c i p a t i o n s o f f o r c e r e q u i r e d t o e x e c u t e an a c t i o n , a n d t h a t i t e m p l o y s f e e d f o r w a r d , t u n i n g , a n d i n t e r a c t i o n w i t h t h e e n v i r o n m e n t . P r i b r a m h a s g i v e n p h y s i o l o g i c a l e v i d e n c e f o r t h e image o f a c h i e v e m e n t a n d f o r t h e n o t i o n t h a t we e n c o d e t h e f r e q u e n c y c o m p o n e n t s o f movement. F r a n k s & W i l b e r g (1982) h a v e a l s o g i v e n s u p p o r t t o t h e n o t i o n t h a t we l e a r n a n d o r g a n i z e a movement i n t e r m s o f i t s component f r e q u e n c i e s . I n t h e i r s t u d y , s u b j e c t s l e a r n e d t o t r a c k a w a v e f o r m w h i c h c o n s i s t e d o f t h r e e component f r e q u e n c i e s w i t h a b a s e f r e q u e n c y o f 0.5 Hz. I n a d d i t i o n , s u b j e c t s r e p r o d u c e d t h i s w a v e f o r m i n an i n p u t b l a n k i n g s i t u a t i o n i n w h i c h b o t h s t i m u l u s a n d r e s p o n s e c u r s o r s w e r e r e m o v e d f r o m t h e d i s p l a y . The r e s p o n s e was m e a s u r e d t h r o u g h a F o u r i e r a n a l y s i s w h i c h d e t e r m i n e d t h e component f r e q u e n c i e s , a m p l i t u d e s a n d p h a s e a n g l e s t h a t made up t h e r e s p o n s e w a v e f o r m . I t was f o u n d t h a t e a r l y i n l e a r n i n g s u b j e c t s o n l y r e p r o d u c e d t h e f u n d a m e n t a l f r e q u e n c y . H owever, as l e a r n i n g p r o g r e s s e d s u b j e c t s a d d e d h i g h e r f r e q u e n c y c o m p o n e n t s t o t h e i r r e s p o n s e s u g g e s t i n g t h a t s u b j e c t s may s y s t e m a t i c a l l y o r g a n i z e t h e c o n t i n u o u s 93 movements t h a t they l e a r n i n terms of the component f r e q u e n c i e s t h a t make up the movement. Other s t u d i e s have a l s o g i v e n evidence t h a t support t h i s i n t e r p r e t a t i o n ( B e r n s t e i n , 1967; Marteniuk & Romanow, 1983). Yet another v e r s i o n o f the r e p r e s e n t a t i o n f o r s k i l l e d movement i s the motor program (Keele, 1975) or g e n e r a l i z e d motor program (Schmidt, 1988). A c c o r d i n g t o Schmidt (1988), the motor program e x i s t s at a lower l e v e l i n the system than the schema, and i s i n v o l v e d i n the e x e c u t i o n of pre-planned movement sequences. Since i t s i n c e p t i o n i n the e a r l y 60's the motor program has undergone some m o d i f i c a t i o n s . Keele's (1968) d e f i n i t i o n perhaps best c h a r a c t e r i z e s the e a r l y v e r s i o n s of the motor program concept. At t h a t time Keele d e f i n e d i t as "... a set of muscle commands t h a t are s t r u c t u r e d b e f o r e a movement sequence begins, and t h a t allows the e n t i r e sequence t o be c a r r i e d out u n i n f l u e n c e d by p e r i p h e r a l feedback." T h i s i s an open loop e x p l a n a t i o n o f motor c o n t r o l i n which feedback p l a y s no r o l e . Since t h a t time the concept of the motor program has developed such t h a t some forms of feedback are now accounted f o r . The motor program i s p r e s e n t l y thought t o be an open loop mechanism, which though i t i s s t r u c t u r e d i n advance of movement, can be m o d i f i e d with feedback at lower l e v e l s i n the system (e.g. the r e f l e x l e v e l (Schmidt, 1988)). Thus the motor program i s a h i g h e r l e v e l open loop s t r u c t u r e which has embedded w i t h i n i t lower l e v e l c l o s e d loop p r o c e s s e s , which are capable of adapting t o minor 9 4 p e r t u r b a t i o n s , but are not capable of changing the e n t i r e a c t i o n . From an a l t e r n a t i v e p e r s p e c t i v e , the l e a r n i n g of movement can be e x p l a i n e d i n terms of the n o t i o n o f a coordinative structure. As T u l l e r , Turvey, & F i t c h (1982, p.255) have e x p l a i n e d : "One of the t h i n g s you are t r y i n g t o d i s c o v e r i n l e a r n i n g (a movement) ... i s a way of l i n k i n g or c o n s t r a i n i n g those muscles i n v o l v e d so they become j u s t a s i n g l e e n t i t y " . Kugler, Kelso, & Turvey (1980, p.17) have f o r m a l l y d e f i n e d the c o o r d i n a t i v e s t r u c t u r e as "a group of muscles o f t e n spanning a number of j o i n t s t h a t i s c o n s t r a i n e d t o act as a s i n g l e f u n c t i o n a l u n i t " . Thus the c o o r d i n a t i v e s t r u c t u r e serves i n e x p l a i n i n g the c o n t r o l o f a c t i o n which i n v o l v e s a c o o r d i n a t i o n of s e v e r a l body p a r t s ( i . e . multi-movement c o o r d i n a t i o n ) . The c o o r d i n a t i v e s t r u c t u r e , l i k e the motor program, has undergone i t s own conceptual e v o l u t i o n . The term was c o i n e d by Easton (1972). Turvey (1977), borrowing Easton's term, developed the n o t i o n o f the c o o r d i n a t i v e s t r u c t u r e based on B e r s t e i n ' s (1967) concept of muscle s y n e r g i e s . At t h a t p o i n t , i n 1977, Turvey s t i l l allowed f o r an e x e c u t i v e as a c o n t r o l l i n g agent, though one t h a t i n t e r v e n e d m i n i m a l l y . By 1980, however, Kugler et a l (1980) had begun t o see " c o n t r o l " as an in h e r e n t process of the s e l f - o r g a n i z i n g system, and had t h e r e f o r e removed the need f o r any recourse to an " e x e c u t i v e " or t o r e p r e s e n t a t i o n a l i s m . From a compatible t h e o r e t i c a l p e r s p e c t i v e t o t h a t out 95 of which the c o o r d i n a t i v e s t r u c t u r e developed, are J . J . Gibson's (1966) s p e c u l a t i o n s on l e a r n i n g . In a d i s c u s s i o n on the nature of memory, he has c o n s i d e r e d the q u e s t i o n of what is learned: An observer l e a r n s with p r a c t i c e t o i s o l a t e more s u b t l e i n v a r i a n t s d u r i n g t r a n s f o r m a t i o n and t o e s t a b l i s h more e x a c t l y the permanent f e a t u r e s o f an a r r a y . (1966, p.265) In p e r c e p t i o n , humans l e a r n t o d e t e c t i n v a r i a n t s . In movement l e a r n i n g ( s p e c i f i c a l l y t r a c k i n g ) s u b j e c t s may l e a r n t o d e t e c t the i n v a r i a n t s of the stim u l u s t h a t they are f o l l o w i n g . An example of such an i n v a r i a n t i s the r e l a t i v e t i m i n g o f response elements w i t h i n a complex motor a c t . In order t o ma i n t a i n the topology of such a movement, one must mai n t a i n i t s r e l a t i v e t i m i n g . One can however, vary the ab s o l u t e t i m i n g , w hile s t i l l m a i n t a i n i n g the to p o l o g y . B e r n s t e i n (1967, pl77) i n r e f e r e n c e t o topology, has p o i n t e d out t h a t "a f u n c t i o n i s w e l l o r g a n i z e d i f i t s arguments can be separated i n t o : 1 ) e s s e n t i a l v a r i a b l e s and 2 ) n o n - e s s e n t i a l v a r i a b l e s " . E s s e n t i a l v a r i a b l e s are those t h a t p r e s e r v e the t o p o l o g i c a l p r o p e r t i e s o f movement; these would p a r a l l e l Gibson's i n v a r i a n t s . N o n - e s s e n t i a l v a r i a b l e s are s c a l a r changes, f o r example the o v e r a l l r a t e or speed of a movement. Thus, i n the l e a r n i n g of movement, what is learned are the e s s e n t i a l v a r i a b l e s (or i n v a r i a n t s ) i . e . those v a r i a b l e s t h a t are r e s p o n s i b l e f o r p r e s e r v i n g the topo l o g y of movement. 96 The e s s e n c e o f l e a r n i n g ( a n d e v e n l i f e i t s e l f ) may be p u l l i n g i n v a r i a n t s ( o r o r d e r ) o u t o f a p p a r e n t c h a o s . S c h r o d i n g e r (1944) h a s a r g u e d t h a t t h i s i s t h e e s s e n c e o f a l l l i v i n g s y s t e m s . Many o f o u r e x p l a n a t i o n s i n m o t o r c o n t r o l a n d l e a r n i n g h a v e t o do w i t h t h e i n t e r p l a y o f v a r i a n c e ( e n t r o p y ) a n d i n v a r i a n c e ( o r d e r ) . F o r e x a m p l e , schema t h e o r y ( S c h m i d t , 1975) h a s e x p l a i n e d l e a r n i n g i n t e r m s o f f i n d i n g i n v a r i a n c e a n d d e v e l o p i n g an e q u a t i o n t h a t e x p r e s s e s what i s v a r i a b l e a n d what i s n o t v a r i a b l e . F rom a n o t h e r p e r s p e c t i v e , t h e a c t i o n t h e o r i s t s h a v e p o s t u l a t e d an e q u a t i o n o f c o n s t r a i n t , w h i c h a l s o d e f i n e s what i s i n v a r i a n t a n d what i s v a r i a b l e . F rom b o t h p e r s p e c t i v e s , two s i m u l t a n e o u s p r o c e s s e s a r e o c c u r r i n g . 1) c e r t a i n t h i n g s i n movement v a r y , a n d 2) c e r t a i n t h i n g s i n movement a r e i n v a r i a n t . L e a r n i n g i s b a s e d on e s t a b l i s h i n g an o r g a n i z a t i o n i n w h i c h c e r t a i n r e l a t i o n s h i p s become i n v a r i a n t , w h i l e o t h e r s a r e l e f t f r e e t o v a r y . An a l t e r n a t i v e t o t h e n o t i o n o f r e p r e s e n t a t i o n , t h e n , i s o r g a n i z a t i o n . As s u c h , l e a r n i n g w o u l d c o n s i s t o f a p r o c e s s o f s h i f t s i n t h e i n t e r n a l s t a t e o f o r g a n i z a t i o n t o w a r d a h i g h e r f o r m o f o r g a n i z a t i o n . T h e r e h a s b e e n e v i d e n c e t o i n d i c a t e t h a t b o t h p r o c e s s e s o f l e a r n i n g a n d p r o c e s s e s o f l i f e i n v o l v e o r g a n i z a t i o n a l s h i f t s t o w a r d a h i g h e r o r d e r o r g a n i z a t i o n . S c h r o d i n g e r (1944) h a s d i f f e r e n t i a t e d t h e l i v i n g f r o m t h e non l i v i n g i n t e r m s o f o r d e r a n d e n t r o p y . He h a s s u g g e s t e d t h a t " l i v i n g o r g a n i s m s d r i n k o r d e r o u t o f t h e i r e n v i r o n m e n t " a n d i n s o d o i n g , d e f y 97 entropy. As l i v i n g organisms evolve they progress to higher order l e v e l s of o r g a n i z a t i o n . G e n t i l e & Nacson (1976) have a l s o suggested that t h i s i s the b a s i s of l e a r n i n g . Though i n t h i s paper, they d i d not consider the concept of o r g a n i z a t i o n , as an a l t e r n a t i v e to r e p r e s e n t a t i o n , the paper was nonetheless one of the f i r s t t o apply the concept of o r g a n i z a t i o n t o the f i e l d of motor s k i l l s . They contended tha t the o r g a n i z a t i o n that develops w i t h p r a c t i c e i s i n the form of v a r i o u s " r u l e s f o r encoding input" and tha t what i s learned are "contextual r e l a t i o n s h i p s among p o s i t i o n s " ( G e n t i l e & Nacson, 1976, p.16) There i s a l s o evidence from t r a c k i n g s t u d i e s f o r such a process o c c u r r i n g i n l e a r n i n g . Fuchs (1962) found t h a t subjects moved to higher order c o n t r o l systems over the course of l e a r n i n g a t r a c k i n g task such t h a t w i t h l e a r n i n g , subjects developed a higher l e v e l of perceptual motor o r g a n i z a t i o n . Fuchs had subjects t r a c k a complex waveform. In modelling t h e i r behavior mathematically, he found t h a t e a r l y i n l e a r n i n g , performance could be modelled i n terms of displacement and v e l o c i t y c o n t r o l . Further on i n l e a r n i n g , the weighting s h i f t e d t o the increased u t i l i z a t i o n of a c c e l e r a t i o n , and l a t e r d e l t a a c c e l e r a t i o n i n f o r m a t i o n . In a d d i t i o n , when subjects were given the added s t r e s s of having t o co n c u r r e n t l y perform another task, they regressed t o an e a r l i e r stage i n which they were using lower d e r i v a t i v e i n f o r m a t i o n . This progression during l e a r n i n g , and r e g r e s s i o n during s t r e s s , was termed the p r o g r e s s i o n -98 r e g r e s s i o n h y p o t h e s i s . R e c e n t l y , J a g a c i n s k i a n d Hah (1988) h a v e r e p l i c a t e d t h i s f i n d i n g . The m o r p h o g e n e s i s o f t h e n e r v o u s s y s t e m a l s o p r o v i d e s u s w i t h n umerous e x a m p l e s o f t h e p r o g r e s s i o n t o w a r d h i g h e r o r d e r f o r m s o f o r g a n i z a t i o n . B o t h p r o c e s s e s o f l e a r n i n g and p r o c e s s e s o f e v o l u t i o n , i n v o l v e s u c h a p r o g r e s s i o n . A n d one c a n d r a w a p a r a l l e l b e t w e e n t h e s e p r o c e s s e s a s F o w l e r & T u r v e y (1978, p.3) h a v e d o n e : " I n s o f a r a s a s p e c i e s i s s a i d t o be a p a r t i c u l a r b i o l o g i c a l a t t u n e m e n t t o a p a r t i c u l a r n i c h e , we may w i s h t o s a y , p e r h a p s c u r i o u s l y , t h a t t h e i n d i v i d u a l a n i m a l , as s k i l l e d p e r f o r m e r , i s a p a r t i c u l a r a t t u n e m e n t t o t h e p a r t i c u l a r t a s k i t p e r f o r m s s k i l l f u l l y . " Representationalism and the Problem of Higher Authority. . When l e a r n i n g i s c o n c e i v e d o f i n t e r m s o f o r g a n i z a t i o n , i t becomes u n n e c e s s a r y t o i n v o k e r e p r e s e n t a t i o n a n d h i g h e r a u t h o r i t y i n e x p l a i n i n g t h e p r o c e s s o f l e a r n i n g . The n o t i o n s o f r e p r e s e n t a t i o n a n d h i g h e r a u t h o r i t y a r e r e l a t e d i n t h a t any e x p l a n a t i o n w h i c h i n v o k e s r e p r e s e n t a t i o n n e c e s s a r i l y " i m p l i e s an a n i m a l a n a l o g u e w h i c h i n t u r n i m p l i e s an i n f i n i t e r e g r e s s " ( K u g l e r e t a l . , 1980). I n o t h e r w o r d s when one s p e a k s o f r e p r e s e n t i n g movement, one i m p l i e s a r e p r e s e n t a t i o n to some e n t i t y ( s u c h a s t h e h o m u n c u l u s , e x e c u t i v e , o r s o u l ) . R e p r e s e n t a t i o n a l i s m i s one o f t h e c e n t r a l i s s u e s t h e m o t o r a c t i o n c o n t r o v e r s y ( s e e B eek & M e i j e r , 1988; M e i j e r e t a l . , 1988). I n a t t e m p t i n g t o 99 understand l e a r n i n g , one comes face t o face with t h i s i s s u e . As the c o g n i t i v e n e u r o s c i e n t i s t s , Maturana and V a r e l l a , have s t a t e d : "Indeed, i f the nervous system does not operate - and cannot operate - w i t h a r e p r e s e n t a t i o n o f the surrounding world, what b r i n g s about the e x t r a o r d i n a r y f u n c t i o n a l e f f e c t i v e n e s s of man and animal and t h e i r enormous c a p a c i t y t o l e a r n and manipulate the world?" (p.133, 1987) They have proposed a s o l u t i o n t o the problem of r e p r e s e n t a t i o n a l i s m . Though l e a r n i n g may not i n v o l v e r e p r e s e n t a t i o n of movement, i t does i n v o l v e changes i n the b r a i n , which b r i n g about more s k i l l f u l movement. Ins t e a d of c o n c e i v i n g of these changes as r e p r e s e n t a t i o n s , they can be thought of as s t a t e s of i n t e r n a l o r g a n i z a t i o n , which t r a n s f o r m w i t h l e a r n i n g such t h a t the i n t e r a c t i o n s between the person/organism and the environment are d i f f e r e n t . Maturana and V a r e l l a (1987) have suggested, t h a t these i n t e r n a l changes be thought of i n terms of i n t e r n a l c o r r e l a t i o n s between sensory and motor p r o c e s s e s . Consider an experiment conducted by Sperry (1945) as an i l l u s t r a t i o n o f t h i s i d e a . A f r o g when pre s e n t e d with a f l y i n h i s v i s u a l f i e l d , w i l l s t i c k h i s tongue out and c a t c h the f l y . Sperry s u r g i c a l l y r o t a t e d the eyes of a f r o g by 90 degrees. A f t e r the surgery, when he pre s e n t e d the f r o g w i t h a f l y , the f r o g stuck i t s tongue i n a d i r e c t i o n e x a c t l y 90 degrees away from the a c t u a l l o c a t i o n o f the f l y . Thus the f r o g ' s 1 0 0 nervous system seems t o have c o r r e l a t e d sensory and motor events, r a t h e r than to have r e p r e s e n t e d the e x t e r n a l environment i n i t s b r a i n . S k i l l e d human movement would encompass a h i g h l y complex and i n t e g r a t e d a r r a y of such c o r r e l a t i o n s , f a c i l i t a t i n g a h i g h l y e f f i c i e n t i n t e r a c t i o n w i t h the environment. The problem of r e p r e s e n t a t i o n a l i s m versus s o l i p s i s m has been a p e r e n n i a l problem f o r those attempting t o understand c o g n i t i o n , and i t s r o o t s extend as f a r back as the c l a s s i c a l p e r i o d (Maturana & V a r e l l a , 1988). C u r r e n t l y , the f i e l d of motor l e a r n i n g and c o n t r o l i s dominated by a r e p r e s e n t a t i o n a l i s t ' s p e r s p e c t i v e , t h i s having been i n h e r i t e d from motor l e a r n i n g ' s parent d i s c i p l i n e , c o g n i t i v e psychology. At t h i s p o i n t i n h i s t o r y then, r e p r e s e n t a t i o n a l i s m i s f a v o r e d over s o l i p s i s m . At other times i n h i s t o r y , the r e v e r s e has been the case. P a r t of the reason f o r c o g n i t i v e s c i e n c e ' s tendency t o embrace r e p r e s e n t a t i o n a l i s m , has been i t s a s s o c i a t i o n w i t h the f i e l d of a r t i f i c i a l i n t e l l i g e n c e . There i s however a c e r t a i n i r o n y i n h e r e n t i n t h i s p a r t i c u l a r borrowing of i d e a s . Dreyfus (1985), f o l l o w i n g ideas developed by the French p h i l o s o p h e r Merleau Ponty, has argued t h a t as humans, we have no need t o r e p r e s e n t our bodies to o u r s e l v e s , as a computer would have t o do, because we are embodied. Dreyfus, then, i s a monist who sees mind and body as a u n i t y . In these terms, h i s approach can be d i s t i n g u i s h e d from the t r a d i t i o n a l t h e o r i z i n g i n motor c o n t r o l (and i t s 101 parent s c i e n c e , c o g n i t i v e psychology) which i s based on d u a l i s t i c assumptions which not only separate mind and body, but conceive of mind as c a u s a l l y primary. C o g n i t i v e psychology has attempted to e x p l a i n c o g n i t i o n i n i s o l a t i o n from the body, and from the sensory motor i n t e r a c t i o n s w i t h the environment. However, t h i s has p r e s e n t e d a problem i n t h a t human c o g n i t i v e a b i l i t y develops out of e a r l y sensori-motor i n t e r a c t i o n s w i t h the world (Piaget, 1963). Thus c o g n i t i o n cannot be i s o l a t e d from the body. In borrowing from the present c o g n i t i v i s t paradigm, movement s c i e n t i s t s have p i c k e d up the wrong end of the s t i c k (Kuhn, 1962). The i d e a t h a t our c o g n i t i v e a b i l i t i e s are i n t r i n s i c a l l y m o t o r i c i s not e n t i r e l y new, and has been proposed b e f o r e b y a s m a l l group of p s y c h o l o g i s t s ( B a r t l e t t , 1958; Klapp, 1976; Weimer, 1977), n e u r o p h y s i o l o g i s t s (Pribram, 1971; Young, 1975), and a n t h r o p o l o g i s t s (Sapir, 1921). The a n t h r o p o l o g i s t Edward S a p i r b e l i e v e d the a p p r e c i a t i o n of a r t to be a m o t o r i c f u n c t i o n . Along s i m i l a r l i n e s , B a r t l e t t (1958, pl99) has proposed t h a t t h i n k i n g i s an advanced form of s k i l l e d b e h a v i o r i n t h a t " i t has grown out of these e a r l i e r forms of f l e x i b l e a d a p t a t i o n t o the environment". From Pribram's (1971) n e u r o p h y s i o l o g i c a l evidence t h a t the motor c o r t e x i s sensory i n nature, i t can be concluded t h a t the mind i s a generator not only of i t s own output but a l s o i t s i n p u t " (Weimer, 1977). I r o n i c a l l y , movement s c i e n t i s t s have borrowed 1 0 2 i n f o r m a t i o n p r o c e s s i n g models from psychology which a r t i f i c i a l l y separates p e r c e p t i o n and a c t i o n , and then i g n o r e s and degrades a c t i o n . Thus movement s c i e n t i s t s have tended t o i g n o r e the f a c t of embodiment. Perhaps i t has been e a s i e r to e x p l a i n movement c o n t r o l i n terms of a deus ex machina (Kelso et a l . , 1980) than i n terms of processes w i t h i n the embodied organism i t s e l f . D u a l i s t i c assumptions may w e l l have l e d t o e x p l a n a t i o n s based upon a "god o u t s i d e of the machine". Tamboer (1988 p . 4 4 5 ) , i n c o n s i d e r i n g the q u e s t i o n of d u a l i s m and embodiment, has w r i t t e n : " I f a t e n a b l e and comprehensive i n t e r p r e t a t i o n of the ' f a c t s ' , d i s c o v e r e d i n the f i e l d o f human movement beha v i o r i s sought, the images of the human body, which l i e at the r o o t of the v a r i o u s approaches by which t h a t f i e l d i s s c i e n t i f i c a l l y d e f i n e d , cannot be n e g l e c t e d " . In having borrowed the s c i e n t i f i c paradigm of c o g n i t i v e psychology, movement s c i e n t i s t s have been l e d away from embodiment. Because of t h i s , they have o f t e n c r e a t e d e x p l a n a t i o n s of motor c o n t r o l i n which the " e x e c u t i v e " i s deemed to be the " c o n t r o l l i n g e n t i t y " which "commands" the lower l e v e l s . T h i s problem seems not t o be unique t o psychology and movement s c i e n c e . "The nature and power of h i g h e r / c e n t r a l / commanding / c o n t r o l l i n g e n t i t i e s , has been a problem f o r western s c i e n c e i n g e n e r a l ever s i n c e the seventeenth c e n t u r y . The quest t o a v o i d s u p e r i o r a u t h o r i t y , then, appears to 103 have had - and s t i l l has - c o n s i d e r a b l e r a m i f i c a t i o n s . " (Meijer, 1988 p.171) T h i s p a r t i c u l a r problem may have an even deeper o r i g i n than M e i j e r suggests. Fox (1983) and Merchant (1980) d i s c u s s the lo n g - s t a n d i n g r e l i g i o u s , p h i l o s o p h i c a l and c u l t u r a l r o o t s of the problem of s u p e r i o r a u t h o r i t y , and i t s r e l a t i o n s h i p t o the problem of embodiment. These companion problems have t h e i r r o o t s i n the c u l t u r a l / r e l i g i o u s context out of which modern western s c i e n c e has emerged. Modern s c i e n c e i n i t s i n c e p t i o n was wed t o r e l i g i o n . P r i g o g i n e and Stengers (1984, p.50) have p o i n t e d out the consequences of t h i s marriage: Man i s e m p h a t i c a l l y not p a r t of the nature he o b j e c t i v e l y d e s c r i b e s ; he dominates i t from the o u t s i d e . Indeed f o r G a l i l e o , the human s o u l , c r e a t e d i n God's image, i s capable o f g r a s p i n g the i n t e l l i g i b l e t r u t h s u n d e r l y i n g the p l a n o f c r e a t i o n ... t h a t God h i m s e l f possessed. For the s c i e n c e s o f psychology and motor beh a v i o r t h i s has pr e s e n t e d an i n t e r e s t i n g dilemma. How can we who study human behavior, d i s s o c i a t e o u r s e l v e s from t h a t which we " o b j e c t i v e l y d e s c r i b e " , when we are o u r s e l v e s the o b j e c t s of t h a t d e s c r i p t i o n . T h i s problem has been d e a l t with by s a v i n g a p a r t of the human as the s o u l , though s c i e n c e has r a r e l y l a b e l l e d i t as such. Rather i t has been gi v e n t i t l e s such as the homunculous or the e x e c u t i v e . I n t e r e s t i n g l y i t has been 104 t h i s p a r t o f the human t h a t has u s u a l l y been seen t o be the p a r t t h a t i s " i n c o n t r o l " . Thus i n the same way t h a t G a l i l e o b e l i e v e d man was able t o both dominate and f u l l y understand nature, so the e x e c u t i v e has been seen t o be able t o both dominate and f u l l y understand the "lower" l e v e l s of the motor system. The n o t i o n o f r e p r e s e n t a t i o n , as i t has g e n e r a l l y been conceived, has i n e v i t a b l y l e d t o the problem of 'higher a u t h o r i t y ' ( C a r e l l o , Turvey, Kugler, & Shaw, 1984; Maturana & V a r e l l a ; M e i j e r , 1988; Reed, 1988). Invariant Relative Timing F o r s e v e r a l years t h e r e has been evidence t h a t the r e l a t i v e t i m i n g o f the components of a giv e n s k i l l e d movement remain i n v a r i a n t over changes i n the o v e r a l l d u r a t i o n o f t h a t movement. Motor t h e o r i s t s have i n f e r r e d from t h i s t h a t r e l a t i v e t i m i n g may t h e r e f o r e be an i n v a r i a n t f e a t u r e of the c e n t r a l r e p r e s e n t a t i o n ( u s u a l l y motor program) of the movement be i n g l e a r n e d (Shapiro & Schmidt, 1982; Shapiro, Zernicke, Gregor, & D i e s t e l , 1981). From another p e r s p e c t i v e , a c t i o n t h e o r i s t s , though they have r e j e c t e d the n o t i o n of r e p r e s e n t a t i o n , n e v e r t h e l e s s have argued t h a t r e l a t i v e t i m i n g i s one of the i n v a r i a n t s of a movement t h a t humans l e a r n ( T u l l e r & Kelso, 1984; Kelso, Putnam, & Goodman, 1983). Thus i n v a r i a n c e b r i n g s t o g e t h e r both motor and a c t i o n p e r s p e c t i v e s . At l e a s t two ques t i o n s can be asked with r e f e r e n c e t o i n v a r i a n t r e l a t i v e t i m i n g . They are: 105 1) Is i n v a r i a n t r e l a t i v e t i m i n g a c h a r a c t e r i s t i c o f w e l l l e a r n e d movement? 2) Is r e l a t i v e t i m i n g an i n v a r i a n t f e a t u r e of a motor program? In a s k i n g the second q u e s t i o n one makes a l e a p o f f a i t h , i n t h a t one must assume the e x i s t e n c e of the motor program. Most of the t r a d i t i o n a l r e s e a r c h on i n v a r i a n t r e l a t i v e t i m i n g has addressed the second of these q u e s t i o n s . The present experiment i s designed t o address the f i r s t o f these q u e s t i o n s . However the second q u e s t i o n i s important on t h e o r e t i c a l grounds. In order t o c o n s i d e r the r a m i f i c a t i o n s of the second q u e s t i o n , one might frame i t from an a l t e r n a t e p e r s p e c t i v e . Thus a t h i r d q u e s t i o n might go something l i k e t h i s : 3) Is r e l a t i v e t i m i n g one of the i n v a r i a n c e s i n the movement a r r a y t h a t humans l e a r n . Most of the r e s e a r c h e r s who have s t u d i e d i n v a r i a n t r e l a t i v e t i m i n g have s t u d i e d i t i n r e l a t i o n t o the motor program. A c e n t r a l q u e s t i o n f o r those who have s t u d i e d the motor program has been "What are i t s i n v a r i a n t f e a t u r e s ? " , and i t has been suggested (Schmidt, 1988) t h a t r e l a t i v e t i m i n g i s one of those i n v a r i a n t f e a t u r e s . The i d e a t h a t r e l a t i v e t i m i n g i s an i n v a r i a n t f e a t u r e of the motor program has been r e f e r r e d t o i n the l i t e r a t u r e as the g e n e r a l i z e d motor program wi t h a m u l t i p l i c a t i v e r a t e parameter or the p r o p o r t i o n a l d u r a t i o n model. The p r o p o r t i o n a l d u r a t i o n model p r e d i c t s t h a t any s k i l l e d movement performed wi t h 106 d i f f e r e n t o v e r a l l d u r a t i o n s w i l l e x h i b i t f i x e d r e l a t i v e d u r a t i o n s . O r i g i n a l evidence f o r t h i s came from some unp u b l i s h e d s t u d i e s by Armstrong (1970, c i t e d i n Schmidt, 1988). He had h i s s u b j e c t s r e p e a t e d l y move a l e v e r through a p a r t i c u l a r u n i d i m e n s i o n a l s p a t i a l - t e m p o r a l p a t t e r n . When s u b j e c t s moved too q u i c k l y they n e v e r t h e l e s s maintained i n v a r i a n t r e l a t i v e t i m i n g . I t has been proposed t h a t t h i s o c c u r r e d because r e l a t i v e t i m i n g i s s t r u c t u r e d i n t o the motor program, whereas the o v e r a l l d u r a t i o n i s a parameter whose v a l u e can vary across i n s t a n c e s o f the s k i l l . Thus, f o r each i n s t a n c e of the s k i l l a d i f f e r e n t parameter v a l u e f o r o v e r a l l d u r a t i o n i s a s s i g n e d t o the motor program. The p r o p o r t i o n a l d u r a t i o n model of t i m i n g i n s k i l l e d motor performance has been widely accepted up u n t i l now. (For e m p i r i c a l r e s e a r c h s u p p o r t i n g t h i s model see: C a r t e r & Shapiro, 1984; Shapiro, 1977; Summers, 1977; Te r z u o l o & V i v i a n i , 1979). R e c e n t l y Gentner (1987) has r e - e v a l u a t e d the s u p p o r t i n g evidence f o r the p r o p o r t i o n a l d u r a t i o n model. From h i s review i t seems t h a t much of the observed performance does not p e r f e c t l y f i t the model. Gentner has argued t h a t the m a j o r i t y o f the data used as s u p p o r t i n g evidence f o r the p r o p o r t i o n a l d u r a t i o n model was analyzed i m p r e c i s e l y i n t h a t r e s e a r c h e r s analyzed mean d u r a t i o n s o f a g i v e n i n t e r v a l i n s t e a d o f the a c t u a l i n d i v i d u a l observed d u r a t i o n s . To overcome t h i s problem, Gentner has proposed a constant proportion test. Assume t h a t D i i s the d u r a t i o n o f the i - t h 107 component of a complex movement and T i s the t o t a l d u r a t i o n . Then the r e l a t i v e p r o p o r t i o n of D i with r e s p e c t t o T should remain constant over changes i n T. T h i s i s an e x p r e s s i o n of the p r o p o r t i o n a l d u r a t i o n model i n mathematical terms. For a g i v e n i n t e r v a l Gentner has taken the r a t i o of Di/T and p l o t t e d i t a g a i n s t T. I f the slope o f the r e s u l t i n g f u n c t i o n was zero the p r o p o r t i o n a l d u r a t i o n model was supported. A f t e r having r e a n a l y z e d the data from experiments t h a t found evidence f o r an i n v a r i a n t r e l a t i v e t i m i n g f e a t u r e w i t h i n a motor program, Gentner has concluded t h a t the p r o p o r t i o n a l d u r a t i o n model i s not supported. R e l a t i v e d u r a t i o n s are maintained t o some extent but not p r e c i s e l y . But as Heuer & Schmidt (1988) have p o i n t e d out: These d e v i a t i o n s might s t i l l be c o n s i d e r e d as a c c e p t a b l e d i s c r e p a n c i e s between nature and human c o n c e p t u a l i z a t i o n s of i t , and one can argue t h a t they are o f minor importance as compared wit h the conspicuous tendency toward i n v a r i a n c e . (p. 241) Though humans may not e x h i b i t r e l a t i v e t i m i n g w i t h p e r f e c t i n v a r i a n c e , one can not r u l e out the n o t i o n t h a t they may l e a r n i n v a r i a n t r e l a t i v e t i m i n g . One c o u l d p o s i t at l e a s t f o u r reasons f o r a l a c k of p e r f e c t i n v a r i a n c e on the b e h a v i o r a l l e v e l . The f i r s t has been suggested by Heuer (1987), who has argued t h a t a l a c k of i n v a r i a n c e i n r e l a t i v e t i m i n g on the b e h a v i o r a l l e v e l , does not n e c e s s a r i l y i n d i c a t e a l a c k o f i n v a r i a n c e c e n t r a l l y . T h i s i s because 108 t h e r e are n o n - l i n e a r i t i e s i n the nervous system which may d i s t o r t a c e n t r a l i n v a r i a n c e i n r e l a t i v e t i m i n g , such t h a t i t would manifest p e r i p h e r a l l y ( b e h a v i o r a l l y ) i n the form of v a r i a b l e r e l a t i v e t i m i n g . The second i s t h a t humans may l e a r n r e l a t i v e t i m i n g i n a formal way (Thompson, 1952). As Bateson (1982) has p o i n t e d out i n d e s c r i b i n g morphogenesis, though t h e r e may be an "asymmetry i n s i z e " , one n e v e r t h e l e s s f i n d s "a deeper symmetry i n formal r e l a t i o n s " . In the same way t h a t symmetry of form organi z e s morphogenesis, r e l a t i v e t i m i n g may be the s t r u c t u r e around which a movement p a t t e r n i s or g a n i z e d . S e v e r a l authors have drawn p a r a l l e l s between morphogenesis and motor l e a r n i n g ( B e r k i n b l i t , . Feldman, & Fukson, 1986 p.599; Turvey, 1986 p.624). L i v i n g c r e a t u r e s e x h i b i t symmetry i n terms of form, but r a r e l y i s t h i s expressed i n terms of p e r f e c t l y e q u i v a l e n t magnitudes on the r i g h t and l e f t s i d e s of the body. For i n s t a n c e , the r i g h t l e g may be s l i g h t l y longer than the l e f t ( i . e . the magnitudes are not e x a c t l y e q u i v a l e n t ) but the form i s symmetrical i n t h a t t h e r e are two l e g s , two knees, two f e e t and the form of these on the r i g h t i s the exact m i r r o r image of t h a t on the l e f t . The concept of r e l a t i v e t i m i n g can be c o n s i d e r e d i n a s i m i l a r l i g h t . Gentner (1987) has giv e n evidence t h a t i n t e r v a l d u r a t i o n s are not always math e m a t i c a l l y p e r f e c t p r o p o r t i o n s o f o v e r a l l movement time. T h i s i s analogous t o Bateson's n o t i o n of "asymmetry i n s i z e " . Gentner's (1987) review a l s o i l l u s t r a t e s t h a t on 109 average the p r o p o r t i o n s are i n v a r i a n t ; t h i s c o u l d be thought of as analogous t o Bateson's n o t i o n of the "deeper symmetry i n formal r e l a t i o n s " . The t h i r d reason t h a t i n v a r i a n t t i m i n g may not e x h i b i t p e r f e c t i n v a r i a n c e , i s t h a t feedback may somehow be i n v o l v e d i n modulating the e x p r e s s i o n of r e l a t i v e t i m i n g . Because the i n t e r v a l s aren't p e r f e c t p r o p o r t i o n s of o v e r a l l movement time, i t seems u n l i k e l y t h a t the present model of a program wit h f i x e d r e l a t i v e t i m i n g and an o v e r a l l d u r a t i o n parameter i s c o r r e c t . In such a model r e l a t i v e t i m i n g must be maintained p r e c i s e l y . The d u r a t i o n parameter, once put i n t o the program, i s not m o d i f i a b l e . I f , however, feedback were b e i n g used throughout the d u r a t i o n of a movement t o c o n t r o l i t s a b s o l u t e t i m i n g , t h i s might b r i n g about s l i g h t v a r i a t i o n s i n r e l a t i v e t i m i n g . The f o u r t h reason t h a t i n v a r i a n t r e l a t i v e t i m i n g i s not found i s t h a t few r e s e a r c h e r s have c o n s i d e r e d the n e c e s s i t y of p r a c t i c e i n the development of r e l a t i v e t i m i n g . For i n s t a n c e , i n a r e c e n t study by Heuer & Schmidt (1988), i n which s u b j e c t s were gi v e n only 250 c y c l e s of p r a c t i c e , i t was concluded t h a t r e l a t i v e t i m i n g does not remain i n v a r i a n t i n a t r a n s f e r t a s k . However i t i s q u e s t i o n a b l e whether 250 c y c l e s i s adequate p r a c t i c e f o r the development of i n v a r i a n t r e l a t i v e t i m i n g , or f o r the development of a motor program. The development of the motor program i s presumably based on e x t e n s i v e experience with the environment such t h a t an a p p r o p r i a t e form of o r g a n i z a t i o n might develop. But, s i n c e 110 n e i t h e r l e a r n i n g , nor the development of the motor program, are addressed, the problem of adequate p r a c t i c e i s o f t e n o v e r-looked. S c i e n t i s t s from both s i d e s of the motor a c t i o n c o n t r o v e r s y , have r e c o g n i z e d the importance of f l e x i b i l i t y i n movement c o n t r o l , and both s i d e s have attempted t o s o l v e the problem of f l e x i b i l i t y by d e v e l o p i n g models of motor c o n t r o l i n which t h e r e i s an i n t e r p l a y between t h a t which v a r i e s and t h a t which remains i n v a r i a n t . I t would be un f o r t u n a t e t o r e j e c t a phenomenon such as i n v a r i a n t r e l a t i v e t i m i n g simply because i t s data do not f i t the c u r r e n t motor programming p e r s p e c t i v e . The data, though they may r e f u t e the i d e a t h a t i n v a r i a n t r e l a t i v e t i m i n g i s f i x e d i n the motor program, c e r t a i n l y do not r e f u t e the i d e a t h a t r e l a t i v e t i m i n g i s one of the aspects o f a movement t h a t humans l e a r n . These two p o s s i b i l i t i e s must be d i f f e r e n t i a t e d otherwise we may f a l l prey t o n e g l e c t i n g an important phenomenon simply because we are wearing the wrong t h e o r e t i c a l s p e c t a c l e s . The p r o p o r t i o n a l d u r a t i o n model, as a p a r t o f the theo r y o f the g e n e r a l i z e d motor program, i s a the o r y o f motor c o n t r o l t h a t emphasizes open-loop pr o c e s s e s , though i t allows f o r feedback at lower l e v e l s i n the system. One need not accept the e x i s t e n c e of the g e n e r a l i z e d motor program i n order t o accept t h a t r e l a t i v e t i m i n g i s an i n v a r i a n t c h a r a c t e r i s t i c o f s k i l l e d a c t i o n . Two c r i t i c i s m s can be made of the g e n e r a l i z e d motor I l l program th e o r y as i t stands t o date. Both p o i n t out the n e c e s s i t y o f ac c o u n t i n g f o r feedback, which the the o r y has f a i l e d t o do adequately. The theory has accounted f o r feedback i n the sense t h a t the program has been seen t o be a h y b r i d system assembled from both open and c l o s e d loop p r o c e s s e s (Schmidt, 1988). N e v e r t h e l e s s , the the o r y has n e g l e c t e d two important aspects of feedback. F i r s t l y , the theory has i g n o r e d the way i n which s k i l l e d movement i s c h a r a c t e r i z e d by a c o o r d i n a t i o n of movement of the v a r i o u s j o i n t s . Such an i n t e g r a t i o n of body p a r t s r e q u i r e s t h a t i n f o r m a t i o n about the r e l a t i o n s h i p s amongst the v a r i o u s j o i n t s be used i n motor c o n t r o l . S e v e r a l authors have gr a p p l e d w i t h t h i s problem (e.g. Abbs, 1984; MacKenzie & Marteniuk, 1985; T u l l e r et a l . , 1982). In a study on movement c o o r d i n a t i o n d u r i n g i n s e c t f l i g h t , Altman (1982 ( c i t e d i n MacKenzie & Marteniuk, 1985)) d i s c o v e r e d t h a t a f f e r e n t input from v a r i o u s p a r t s o f the body of the i n s e c t i s i n v o l v e d i n modulating the e f f e r e n t output t o the wings. T h i s g i v e s evidence of the way i n which movement at one j o i n t can i n v o l v e an i n t e g r a t i o n o f i n f o r m a t i o n from v a r i o u s j o i n t s . Secondly, the theory has not accounted f o r the way i n which the o v e r a l l d u r a t i o n parameter v a l u e i s determined nor the way i n which i t i s assigned. In a computer program, i t i s the programmer who both determines and a s s i g n s the parameter v a l u e s . Can we assume t h a t a s i m i l a r process i s o c c u r r i n g i n humans? I f we do, we are l e f t w i t h a l i t t l e 112 computer programmer i n our head a s s i g n i n g parameter v a l u e s to the motor programs t h a t c o n t r o l our movement. T h i s i s simply an homunculus theory which serves t o e x p l a i n n o t h i n g . The c r u c i a l q u e s t i o n of the way i n which feedback i n t e r a c t s w i t h the program i n t i m i n g c o n t r o l has been r e l e g a t e d to the realm of the homunculus. Because a computer does not have t h a t dynamic i n t e r a c t i o n w i t h i t s environment, t h a t i s c h a r a c t e r i s t i c of a l l l i v i n g organisms, the computer metaphor can be both l i m i t i n g and m i s l e a d i n g . I t i s q u e s t i o n a b l e whether the metaphor of a program i s a p p r o p r i a t e f o r use i n e x p l a i n i n g human movement ( C a r e l l o et a l , 1984). T r a c k i n g s t u d i e s p r o v i d e an experimental context i n which the c o n t r i b u t i o n s of feedback to t i m i n g c o n t r o l can be examined. In t r a c k i n g (and other t a s k s i n v o l v i n g an i n t e r a c t i o n w i t h the environment) t h e r e are at l e a s t two forms of r e l a t i v e t i m i n g t h a t can be i d e n t i f i e d : 1) r e l a t i v e t i m i n g w i t h i n the response i t s e l f ; and 2) the t i m i n g of the response r e l a t i v e t o the s t i m u l u s . Feedback and feedforward mechanisms are i n v o l v e d i n t h i s second form of t i m i n g . In p u r s u i t t r a c k i n g , the two forms of t i m i n g i n f l u e n c e one another, f o r , w i t h a p r e d i c t a b l e s t i m u l u s , the b e t t e r the s u b j e c t ' s i n t e r n a l r e l a t i v e t i m i n g , the b e t t e r a s u b j e c t w i l l be able t o time the response r e l a t i v e t o the s t i m u l u s (Pew, 1974). In the case of t r a c k i n g , s u b j e c t s seem to be u s i n g feedback to determine the immediate d u r a t i o n r a t h e r than the o v e r a l l d u r a t i o n . 113 Gentner (1987) i n h i s c r i t i c i s m o f the p r o p o r t i o n a l d u r a t i o n model has p o i n t e d out t h a t one of the most remarkable c h a r a c t e r i s t i c s o f s k i l l e d motor be h a v i o r i s i t s a d a p t a b i l i t y and f l e x i b i l i t y . I f f l e x i b i l i t y i s a c h a r a c t e r i s t i c of s k i l l e d b e h a v i o r then i t would seem obvious t h a t feedback i s being u t i l i z e d i n i t s c o n t r o l . The work of Abbs and h i s c o l l e a g u e s (Abbs et a l . , 1984) has i l l u s t r a t e d t h i s p o i n t . They found t h a t when the lower l i p was p e r t u r b e d d u r i n g speech, t h e r e was an adjustment t o the p e r t u r b a t i o n i n both the upper and lower l i p s . The adjustment i n the upper l i p served t o p r e s e r v e the speech o b j e c t i v e o f the u t t e r a n c e . In order t o respond t o a p e r t u r b a t i o n i n t h i s way a motor program must u t i l i z e feedback and feedforward mechanisms. T h i s example of s k i l l e d motor a c t i v i t y i l l u s t r a t e s the way i n which feedback can be c l o s e l y i n t e g r a t e d with motor program e x e c u t i o n . Current motor programming t h e o r i e s have de-emphasized the importance o f feedback i n t i m i n g c o n t r o l . T h i s may be one o f t h e i r major flaws. Gentner has used t h i s c r i t i c i s m t o r e j e c t the p r o p o r t i o n a l d u r a t i o n model. However, i t i s p o s s i b l e t h a t the p r o p o r t i o n a l d u r a t i o n model i s c o n s i s t e n t w i t h a mode of motor c o n t r o l which i n v o l v e s feedback. R e l a t i v e t i m i n g may c h a r a c t e r i z e such c l o s e d loop s k i l l s as t r a c k i n g . There has been evidence f o r t h i s i n s t u d i e s by Franks & Wi l b e r g (1982). In t h i s study, as l e a r n i n g p r o g r e s s e d the phase angles of the frequency components approached those o f the stimulus such t h a t the r e l a t i v e 114 t i m i n g of the response became i d e n t i c a l t o t h a t of the st i m u l u s , whereas the o v e r a l l d u r a t i o n of the waveform v a r i e d , and tended t o be longer than t h a t of the s t i m u l u s . The focus of the present study i s l e a r n i n g . Few of the s t u d i e s on i n v a r i a n t r e l a t i v e t i m i n g have g i v e n e x t e n s i v e enough p r a c t i c e t o address the q u e s t i o n of l e a r n i n g , nor have they g i v e n s u f f i c i e n t p r a c t i c e f o r s u b j e c t s t o develop a motor program ( i f one e x i s t s ) . I t seems t h a t one of the b l i n d spots f o r many of those i n v o l v e d i n t r a d i t i o n a l motor c o n t r o l r e s e a r c h and t h e o r i z i n g has been the l a c k of c o n s i d e r a t i o n of movement ontogeny and l e a r n i n g . In such a context, the problem of i n s u f f i c i e n t p r a c t i c e i s h a r d l y s u r p r i s i n g . Even l e a r n i n g r e s e a r c h e r s such as G e n t i l e (1972) have argued t h a t we must move away from motor l e a r n i n g i n t o motor c o n t r o l u n t i l we have a b e t t e r understanding of the "mechanisms u n d e r l y i n g movement c o n t r o l " . But as Reed (1988) has p o i n t e d out, i t i s i n s t u d y i n g l e a r n i n g i t s e l f we can ga i n a b e t t e r understanding of c o n t r o l . Arguments such as G e n t i l e ' s are i n some sense r e d u c t i o n i s t i c . Because most s t u d i e s on r e l a t i v e t i m i n g have avoided the q u e s t i o n of the ontogeny of the motor program, l i t t l e p r a c t i c e has been g i v e n . But i f one c o n s i d e r s the motor program i n l i g h t of ontogeny, one i s f o r c e d t o q u e s t i o n whether a motor program can be developed i n 20 t r i a l s . With such i n s u f f i c i e n t p r a c t i c e , i t i s not s u r p r i s i n g t h a t the i n v a r i a n c e t h a t i s deemed to e x i s t w i t h i n the program has not been found. Subjects have not 115 been g i v e n s u f f i c i e n t time t o develop t h a t i n v a r i a n c e . A l s o most s t u d i e s on i n v a r i a n t r e l a t i v e t i m i n g have been based on the premise (with the e x c e p t i o n of Armstrong's study) t h a t i n v a r i a n t r e l a t i v e t i m i n g operates i n a context i n which a continuous i n t e r a c t i o n w i t h the environment i s not important, and have thus p o s t u l a t e d a motor program which f u n c t i o n s i n a p r i m a r i l y open-loop f a s h i o n i n terms of i t s t i m i n g c o n t r o l . As I have argued above, t h e r e are problems wi t h t h i s assumption. In c h o s i n g a t r a c k i n g t a s k f o r the p r e s e n t study, the i n t e n t i o n was t o i n v e s t i g a t e the human-environment r e l a t i o n s h i p d u r i n g l e a r n i n g . Most of the s t u d i e s on i n v a r i a n t r e l a t i v e t i m i n g have n e g l e c t e d t h i s r e l a t i o n s h i p by c h o s i n g t a s k s i n which t h e r e i s no continuous i n t e r a c t i o n between human and environment. The present study was designed t o i n v e s t i g a t e the development of r e l a t i v e t i m i n g . By s t u d y i n g r e l a t i v e t i m i n g i n a t r a c k i n g task, i t was p o s s i b l e t o g a i n an understanding of the c o n t r i b u t i o n of feedback i n t i m i n g c o n t r o l . In t h i s review on l e a r n i n g , I have put focus on the q u e s t i o n "what i s l e a r n e d " . T h i s i s an e s s e n t i a l q u e s t i o n w i t h a long h i s t o r y i n the f i e l d s of psychology and motor be h a v i o r . One of the answers to t h i s q u e s t i o n , t h a t has been d i s c u s s e d h e r e i n , i s t h a t humans l e a r n the r e l a t i v e t i m i n g of a movement. However, the view of l e a r n i n g t h a t has been put forward i n the present paper, i s d i f f e r e n t than t h a t behind most of the r e s e a r c h on r e l a t i v e t i m i n g , i n t h a t 116 i t emphasizes o r g a n i z a t i o n r a t h e r than r e p r e s e n t a t i o n . In t h i s view, as has been suggested above, p a r a l l e l s can be drawn between processes of l i v i n g systems (such as morphogenesis) and processes of l e a r n i n g , i n t h a t both i n v o l v e the e v o l u t i o n o f the organism toward a more complex s t a t e o f o r g a n i z a t i o n . Though l e a r n i n g i s i t s e l f a process t h a t occurs i n l i v i n g systems, i t has o f t e n been c o n s i d e r e d as a "h i g h e r " f u n c t i o n t h a t i s somehow removed from the r e s t of the b i o l o g i c a l world, and t h e r e f o r e not governed by the same laws. T h i s assumption i s based on a d u a l i s t i c view o f the human i n which mind and body are seen as separate e n t i t i e s . In c o n t r a s t , the view of l e a r n i n g put forward i n t h i s review has been one i n which l e a r n i n g i s seen as a process r o o t e d i n b i o l o g y , r a t h e r than one removed from i t . 117 APPENDIX B  PILOT STUDY INTRODUCTION Indeed, i f the nervous system does not operate - and cannot operate - w i t h a r e p r e s e n t a t i o n of the surrounding world, what b r i n g s about the e x t r a o r d i n a r y f u n c t i o n a l e f f e c t i v e n e s s of man and animal and t h e i r enormous c a p a c i t y t o l e a r n and manipulate the world? Maturana & Varella (1987, p.133) . A simple but e s s e n t i a l q u e s t i o n f o r those who seek to understand l e a r n i n g i s "What i s l e a r n e d ? " . T h i s q u e s t i o n has been c e n t r a l t o psychology s i n c e the i n c e p t i o n of b e h a v i o r i s m i n the 1930's (Gibson, 1969; Weimer, 1977). One answer t h a t has been put forward invokes the development of some k i n d of memorial (or c e n t r a l ) r e p r e s e n t a t i o n . W i t h i n the area of motor l e a r n i n g , t h i s c e n t r a l r e p r e s e n t a t i o n has been d e s c r i b e d i n many d i f f e r e n t ways and has been g i v e n many d i f f e r e n t l a b e l s such as: schema ( B a r t l e t t , 1932; Schmidt, 1975), image of achievement (Pribram, 1971), and motor program (Keele, 1975; Schmidt, 1988). Although the h i s t o r i c a l development of these concepts has been a s s o c i a t e d most o f t e n w i t h open loop c o n t r o l processes, the r o l e t h a t feedback p l a y s i n t h i s l e a r n i n g process cannot be underestimated. Indeed, Marteniuk and h i s co-workers (MacKenzie & Marteniuk, 1985; Proteau, Marteniuk, Girouard, & Dugas, 1987; Proteau, Marteniuk, & Levesque, 1988) b e l i e v e t h a t what is learned are the d e v e l o p i n g r e l a t i o n s h i p s between the a c t i o n and the i n f o r m a t i o n t h a t i s 118 produced as a consequence of such a c t i o n s . I t i s not the i n t e n t o f t h i s paper t o pursue the c e n t r a l i s t - p e r i p h e r a l i s t debate but i n s t e a d t o address the q u e s t i o n of what is learned v i a the concept of o r g a n i z a t i o n , i n such a way as to marry both feedback and r e p r e s e n t a t i o n . But, f i r s t l e t us s t a r t by ar g u i n g t h a t o r g a n i z a t i o n i s perhaps a more a p p r o p r i a t e term t o use than i s r e p r e s e n t a t i o n . The n o t i o n of r e p r e s e n t a t i o n , as i t i s g e n e r a l l y conceived, i n e v i t a b l y leads t o the problem of 'higher a u t h o r i t y ' ( C a r e l l o , Turvey, Kugler, & Shaw, 1984; M e i j e r , 1988; and Reed, 1988). Maturana & V a r e l l a (1987) have proposed a s o l u t i o n t o the problem of r e p r e s e n t a t i o n a l i s m . Though l e a r n i n g may not i n v o l v e r e p r e s e n t a t i o n of movement, i t does i n v o l v e changes i n the b r a i n , which b r i n g about more s k i l l f u l movement. Instead of c o n c e i v i n g of these changes as r e p r e s e n t a t i o n s , they can be thought of as s t a t e s o f i n t e r n a l o r g a n i z a t i o n , which t r a n s f o r m with l e a r n i n g , such t h a t the i n t e r a c t i o n s between the person/organism and the environment are d i f f e r e n t . Maturana and V a r e l l a suggest t h a t we t h i n k o f these i n t e r n a l changes i n terms of i n t e r n a l c o r r e l a t i o n s between sensory and motor p r o c e s s e s . Consider an experiment conducted by Sperry (1945) as an i l l u s t r a t i o n o f t h i s i d e a . A f r o g when pres e n t e d with a f l y i n h i s v i s u a l f i e l d , w i l l s t i c k h i s tongue out and c a t c h the f l y . Sperry s u r g i c a l l y r o t a t e d the eyes of a f r o g by 90 degrees. A f t e r the surgery, when he pr e s e n t e d the f r o g w i t h a f l y , the f r o g stuck i t s tongue i n a d i r e c t i o n e x a c t l y 90 degrees 119 away from where the f l y a c t u a l l y was. Thus the f r o g ' s nervous system seems t o have c o r r e l a t e d sensory and motor events, r a t h e r than t o have r e p r e s e n t e d the e x t e r n a l environment i n i t s b r a i n . S k i l l e d human movement encompasses a h i g h l y complex and i n t e g r a t e d a r r a y of such c o r r e l a t i o n s , f a c i l i t a t i n g a h i g h l y e f f i c i e n t i n t e r a c t i o n w i t h the environment. An a l t e r n a t i v e t o the n o t i o n of r e p r e s e n t a t i o n , then, i s o r g a n i z a t i o n (which c o u l d i n v o l v e both open and c l o s e d loop c o n t r o l p r o c e s s e s ) . Thought of i n t h i s way, l e a r n i n g c o n s i s t s of s h i f t s i n i n t e r n a l s t a t e s of o r g a n i z a t i o n . There i s evidence t o i n d i c a t e t h a t both p r o c e s s e s of l e a r n i n g and processes of l i f e i n v o l v e o r g a n i z a t i o n a l s h i f t s toward a h i g h e r order o r g a n i z a t i o n . Schrodinger (1944) d i f f e r e n t i a t e s the l i v i n g from the non l i v i n g i n terms of order and entropy. " L i v i n g organisms" he w r i t e s " d r i n k order out of the environment" and i n so doing, defy entropy. As l i v i n g organisms evolve they p r o g r e s s t o h i g h e r order l e v e l s o f o r g a n i z a t i o n . G e n t i l e & Nacson (1976) have suggested t h a t o r g a n i z a t i o n i s a l s o the b a s i s of l e a r n i n g , and t h e r e i s b e h a v i o r a l evidence f o r such a p r o c e s s i n motor l e a r n i n g . Fuchs (1962) found t h a t s u b j e c t s developed a h i g h e r l e v e l of p e r c e p t u a l motor o r g a n i z a t i o n , w h i l e l e a r n i n g a t r a c k i n g t a s k and he based h i s p r o g r e s s i o n -r e g r e s s i o n h y p o t h e s i s on the f a c t t h a t s u b j e c t s change t h e i r c o n t r o l s t r a t e g y over the course of l e a r n i n g . T h i s experiment d i d p r o v i d e evidence f o r a p r o g r e s s i o n i n 120 l e a r n i n g t o w a r d a h i g h e r o r d e r o r g a n i z a t i o n . W i t h s u c h a p r o g r e s s i o n i t seems u n n e c e s s a r y t o make r e c o u r s e t o any k i n d o f r e p r e s e n t a t i o n i n o r d e r t o e x p l a i n l e a r n i n g . A s i m i l a r p r o g r e s s i o n may b e o c c u r r i n g i n t h e d e v e l o p m e n t o f t h e c o o r d i n a t i v e s t r u c t u r e . The c o o r d i n a t i v e s t r u c t u r e h a s b e e n f o r m a l l y d e f i n e d by K u g l e r e t . a l . (1980, p.17) a s "a g r o u p o f m u s c l e s o f t e n s p a n n i n g a number o f j o i n t s t h a t i s c o n s t r a i n e d t o a c t a s a s i n g l e f u n c t i o n a l u n i t " . The c o o r d i n a t i v e s t r u c t u r e i n c o r p o r a t e s f e e d b a c k a n d f e e d f o r w a r d c o m m u n i c a t i o n s amongst t h e v a r i o u s j o i n t s a n d b o d y p a r t s , s u c h t h a t t h e s e f u n c t i o n as an i n t e g r a t e d w h o l e . W i t h l e a r n i n g , t h e s e f e e d b a c k r e l a t i o n s h i p s become more r e f i n e d a n d o r g a n i z e d . As an i l l u s t r a t i o n o f t h i s c o n s i d e r t h e c o m p a r i s o n b e t w e e n t h e d e v e l o p m e n t o f t h e c o o r d i n a t i v e s t r u c t u r e d u r i n g l e a r n i n g a n d t h e p r o c e s s o f m o r p h o g e n e s i s . M o r p h o g e n s i s i n v o l v e s o n g o i n g a n d c o m p l e m e n t a r y p r o c e s s e s of d i f f e r e n t i a t i o n a n d i n t e g r a t i o n w h i c h l e a d t o h i g h e r o r d e r f o r m s o f o r g a n i z a t i o n . A s i m i l a r p r o c e s s may be o c c u r r i n g i n t h e d e v e l o p m e n t o f t h e c o o r d i n a t i v e s t r u c t u r e d u r i n g l e a r n i n g . I n t h e e a r l y s t a g e s o f l e a r n i n g a m o t o r t a s k , t h e b o d y o f t e n moves i n a r i g i d a n d u n d i f f e r e n t i a t e d f a s h i o n . F o r i n s t a n c e , a n o v i c e b a t t e r w i l l f r e e z e o u t t h e d e g r e e s of f r e e d o m by h o l d i n g t h e b o d y r i g i d l y . An e x p e r t on t h e o t h e r h a n d h a s l e a r n e d t h e t a s k a p p r o p r i a t e c o n s t r a i n t s t h a t d e f i n e t h e r e l a t i o n s h i p s amongst b o d y p a r t s ( T u l l e r , T u r v e y & F i t c h , 1 9 8 2 ) . Whereas e a r l y i n l e a r n i n g t h e r e l a t i o n s h i p s a r e e i t h e r random o r r i g i d , l a t e r i n l e a r n i n g t h e y become 121 more d e f i n e d and o r g a n i z e d . Thought of i n t h i s way, the c o o r d i n a t i v e s t r u c t u r e i s not a f i x e d s t r u c t u r e , but r a t h e r an ongoing process of d i f f e r e n t i a t i o n and i n t e g r a t i o n which m a n i f e s t s i n c e r t a i n ways at c e r t a i n stages of l e a r n i n g ; i t s development i n v o l v e s a p r o g r e s s i o n toward a h i g h e r order o r g a n i z a t i o n . Such a s y s t e m a t i c p r o g r e s s i o n of o r g a n i z a t i o n i n l e a r n i n g a motor s k i l l has been e v i d e n t i n t r a c k i n g s t u d i e s (Franks & Wilberg, 1982; J a g a c i n s k i & Hah, 1988), and movement r e p r o d u c t i o n t a s k s (Marteniuk & Romanow, 1983) . T h i s p r o g r e s s i o n appears to manifest i t s e l f through the s y s t e m a t i c a c q u i s i t i o n of h i g h e r order component f r e q u e n c i e s of a movement. Over the course of l e a r n i n g , the movements t h a t are produced r e v e a l a f i n e r r e s o l u t i o n . In the study by Franks & W i l b e r g (1982), s u b j e c t s were gi v e n e x t e n s i v e p r a c t i c e i n p u r s u i t t r a c k i n g a complex p e r i o d i c waveform composed of t h r e e component f r e q u e n c i e s and then r e q u i r e d to reproduce the waveform p a t t e r n i n the absence of any v i s u a l s t i m u l u s or response i n f o r m a t i o n (a method of input b l a n k i n g f i r s t developed by V o s s i u s , 1965). E a r l y i n l e a r n i n g , s u b j e c t s were able t o reproduce only the g e n e r a l f e a t u r e s of t h i s complex movement p a t t e r n . T h e i r response c o n t a i n e d the major fundamental frequency of the s t i m u l u s , and thus was o n l y an approximation of the o r i g i n a l . Only a f t e r l o n g p e r i o d s o f p r a c t i c e d i d the s u b j e c t s g a i n an o v e r a l l mastery of the whole waveform and begin c o n s t r u c t i n g the d e t a i l s t h a t were i n h e r e n t i n the s t i m u l u s . T h i s was achieved by 122 the a d d i t i o n of h i g h e r order harmonics t o the response waveform, s u g g e s t i n g t h a t people may l e a r n and o r g a n i z e movement i n terms of component f r e q u e n c i e s . The h y p o t h e s i s put forward was t h a t s k i l l e d performers can produce a response t h a t c l o s e l y maps the c r i t e r i o n movement and t h e r e f o r e reduces the r e l i a n c e of the system upon i t s feedback c o n t r o l p r o c e s s e s . Few c o r r e c t i v e a c t i o n s need t o be undertaken i f the response i s d e t a i l e d and a c c u r a t e . However, novi c e performers t h a t produce o n l y a l i m i t e d but g e n e r a l approximation of the c r i t e r i o n need to invoke the feedback and feedforward processes more f r e q u e n t l y i n d e a l i n g with d e t a i l s of the movement. Although t h i s h y p o t h e s i s was c o n s i d e r e d p l a u s i b l e g i v e n the data, the s u b j e c t s ' responses were only submitted t o a F o u r i e r a n a l y s i s d u r i n g the input b l a n k i n g stage of the experiment, and no account was taken of the s u b j e c t ' s response composition d u r i n g the p u r s u i t t r a c k i n g phase of the experiment, when both the s t i m u l u s and response c u r s o r s were v i s i b l e . C e r t a i n c o n c l u s i o n s t h e r e f o r e , r e g a r d i n g the s u p e r i m p o s i t i o n of feedback c o n t r o l p rocesses upon the produced response d u r i n g the p u r s u i t t r a c k i n g phase of the experiment were at best only s p e c u l a t i v e . The p r e s e n t study was undertaken, t h e r e f o r e , t o address the g e n e r a l q u e s t i o n of what is learned and the s p e c i f i c h y p o t h e s i s t h a t the process of l e a r n i n g a p u r s u i t t r a c k i n g t a s k i n v o l v e s a nested process of response g e n e r a t i o n w i t h superimposed c o n t r o l . That i s , i n order to f u l f i l l the 123 requirements of the task (maintain alignment between st i m u l u s and response with zero lag) the s u b j e c t must generate a movement. The observed e r r o r between the s t i m u l u s and t h i s generated response i s d e a l t w i t h by a feedback c o n t r o l system t h a t operates upon t h i s e r r o r . S e v e r a l s p e c i f i c q u e s t i o n s were addressed i n t h i s study. F i r s t l y , i t was f e l t t h a t f u r t h e r evidence was needed t o v e r i f y the hypothesis t h a t s u b j e c t s do i n f a c t l e a r n t o produce the h i g h e r frequency components of a complex waveform d u r i n g the l a t e r stages of s k i l l a c q u i s i t i o n . Secondly, i n order t o g a i n an understanding of the way i n which feedback i n f l u e n c e s the e x p r e s s i o n of component f r e q u e n c i e s over the course of l e a r n i n g , t h r e e input b l a n k i n g c o n d i t i o n s (which i n v o l v e d a m a n i p u l a t i o n of v i s u a l feedback) were i n t r o d u c e d . These were c o n d i t i o n s i n which the s t i m u l u s was withdrawn, the response was withdrawn and both s t i m u l u s and response were withdrawn from the v i s u a l d i s p l a y . T h i r d l y , a r e t e n t i o n t e s t was g i v e n t o the s u b j e c t s . Subjects were r e t e s t e d a f t e r a r e t e n t i o n p e r i o d of t h r e e months i n order t o i n v e s t i g a t e the s t a b i l i t y and l o n g e v i t y of t h e i r t r a c k i n g a b i l i t y , and t h e i r a b i l i t y t o reproduce the l e a r n e d waveform. I f s u b j e c t s l e a r n t o produce complex responses by s y s t e m a t i c a l l y adding h i g h e r frequency components t o t h e i r response, are they a l s o able t o produce these same h i g h e r harmonics a f t e r a p e r i o d of r e t e n t i o n . F o u r t h l y , at the time of the r e t e n t i o n t e s t , s u b j e c t s were t r a n s f e r r e d t o f o u r waveforms which v a r i e d i n 124 base frequency, and two waveforms which v a r i e d the phase angles o f the component f r e q u e n c i e s . The f i r s t t r a n s f e r c o n d i t i o n was g i v e n i n order t o t e s t whether s u b j e c t s l e a r n a movement i n terms of the r e l a t i v e t i m i n g of the response elements of the movement, or i n terms of the o v e r a l l d u r a t i o n of the movement. The second t r a n s f e r c o n d i t i o n was give n i n order t o determine whether s u b j e c t s l e a r n movement i n terms of component f r e q u e n c i e s or i n terms of t o p o l o g i c a l f e a t u r e s . In t h i s c o n d i t i o n , the t r a n s f e r waveforms are composed of the same component f r e q u e n c i e s as t h a t o f the t r a i n i n g waveform. In v a r y i n g the phase angles o f these component f r e q u e n c i e s one c r e a t e s a waveform w i t h d i f f e r e n t t o p o l o g i c a l f e a t u r e s METHOD  Sub j e c t s Four u n i v e r s i t y students w i t h a r i g h t hand p r e f e r e n c e and no motor or v i s i o n d e f i c i t s r e c e i v e d course c r e d i t f o r t h e i r p a r t i c i p a t i o n i n t h i s study. None of these s u b j e c t s had p r e v i o u s t r a c k i n g e x p e r i e n c e . Task Subjects were r e q u i r e d t o move a j o y s t i c k which c o n t r o l l e d a response c u r s o r (point l i g h t d i s p l a y ) on an o s c i l l o s c o p e screen. The s u b j e c t ' s task was to f o l l o w a st i m u l u s c u r s o r (point l i g h t d i s p l a y ) which appeared 125 d i r e c t l y above the response c u r s o r on the screen and moved i n a s e r i e s of h o r i z o n t a l movements acr o s s the s c r e e n . Subjects sat at a t a b l e with t h e i r r i g h t forearm comfortably supported. The o s c i l l o s c o p e screen was p l a c e d 50 cm i n f r o n t of them at a v i s u a l l y subtended angle of 11.4 degrees. The s u b j e c t s h e l d the j o y s t i c k between the index f i n g e r and thumb. The w r i s t pronated and s u p i n a t e d i n the c o r o n a l plane while the j o y s t i c k was b e i n g moved. Apparatus An i n d u s t r y standard p l o t t i n g j o y s t i c k (Hughes A i r c r a f t Company CONOGRAPHIC - 12 model 6110) w i t h zero order c o n t r o l , was adapted f o r use i n the experiment by b y p a s s i n g i t s i n t e r n a l e l e c t r o n i c s . T h i s j o y s t i c k was f e d by a f i l t e r e d 30 v o l t s p l i t power supply and connected t o an analog to d i g i t a l c o n v e r t e r (Techmar Labmaster), whose daughter board was r e s i d e n t i n an IBM Microcomputer. The d i g i t a l v a l u e s g i v e n by the A/D c o n v e r t e r of the Labmaster ranged from +32767 (+10 v o l t s ) t o -32768 d i g i t a l v a l u e s (-10 v o l t s ) , w h i le the v o l t a g e range of the j o y s t i c k was approximately + 5 v o l t s t o -5 v o l t s (zero v o l t s b e i n g dead c e n t e r ) . The j o y s t i c k was s p r i n g c e n t e r e d along the Y a x i s and the X a x i s had f r e e displacement, t h e r e f o r e only X co-o r d i n a t e displacement was recorded. The potentiometer (a Bourns number 3852A-282-103A), which transformed j o y s t i c k displacement i n t o an e l e c t r i c a l s i g n a l , had a r e s i s t a n c e of 10,000 Ohms, and was l i n e a r ( w i t h i n one percent) throughout 126 the f u l l range of j o y s t i c k movement. A computer generated s t i m u l u s was p r e s e n t e d on the o s c i l l o s c o p e u s i n g a d i g i t a l output e q u i v a l e n t t o the d i g i t a l i n p u t of the j o y s t i c k . A second analog s i g n a l was used t o m a i n t a i n 1 cm of v e r t i c a l displacement between the s t i m u l u s and response c u r s o r s on the o s c i l l o s c o p e . Response v a l u e s were sampled every f o u r m i l l i s e c o n d s . Waveform The s t i m u l u s waveform was g i v e n by e q u a t i o n (1): f ( t ) = A/2 + C cos cot + C/2 cos 2cot + C/4 cos 4cot. The p e r i o d of one c y c l e of the stimulus was 2048 ms. 127 Procedure I. T r a i n i n g Phase T h i s p h a s e o f t h e e x p e r i m e n t t o o k p l a c e o v e r f i v e c o n s e c u t i v e d a y s . E a c h e x p e r i m e n t a l s e s s i o n c o n s i s t e d o f 200 c y c l e s o f p r a c t i c e i n p u r s u i t t r a c k i n g t h e s t i m u l u s w a v e f o r m . T h i s was f o l l o w e d b y 10 t e s t t r i a l s . The 200 p r a c t i c e c y c l e s w e r e b r o k e n down i n t o f o u r b l o c k s o f 50 c y c l e s . The f i r s t f i v e t e s t t r i a l s c o n s i s t e d o f t h r e e p h a s e s : 1) p u r s u i t t r a c k i n g (PT) i n w h i c h b o t h s t i m u l u s a n d r e s p o n s e c u r s o r s r e m a i n e d on t h e s c r e e n ; 2) p a r t i a l i n p u t b l a n k i n g I (PIB1) i n w h i c h o n l y t h e movements o f t h e s t i m u l u s c u r s o r w e r e shown on t h e s c r e e n ; 3) t o t a l i n p u t b l a n k i n g (TIB) i n w h i c h n e i t h e r t h e s t i m u l u s n o r t h e r e s p o n s e w e r e shown on t h e s c r e e n . E a c h o f t h e s e f i r s t f i v e t r i a l s c o n s i s t e d o f 15 c y c l e s o f PT, f o l l o w e d b y 7 c y c l e s o f P I B 1 , f o l l o w e d b y 8 c y c l e s o f T I B . D a t a was s a m p l e d f r o m t h e m i d d l e 2 c y c l e s o f e a c h o f t h e s e t h r e e p h a s e s . The second f i v e t e s t t r i a l s c o n s i s t e d o f two p h a s e s : 1) p u r s u i t t r a c k i n g (PT) as a b o v e ; 2) p a r t i a l i n p u t b l a n k i n g I I (PIB2) i n w h i c h o n l y t h e r e s p o n s e was shown on t h e s c r e e n . E a c h o f t h e s e s e c o n d f i v e t r i a l s c o n s i s t e d o f 15 c y c l e s o f PT, f o l l o w e d b y 15 c y c l e s o f P I B 2 . D a t a was s a m p l e d f r o m t h e m i d d l e two c y c l e s o f b o t h p h a s e s . 128 I I . R e t e n t i o n Phase The same fou r s u b j e c t s t h a t were used i n the t r a i n i n g phase of the experiment r e t u r n e d t o the l a b o r a t o r y a f t e r a p e r i o d of 3 months. The task i n t h i s phase of the experiment was i d e n t i c a l t o t h a t used i n the f i r s t phase except t h a t s e v e r a l d i f f e r e n t s t i m u l u s waveforms were used. The s u b j e c t s were gi v e n 200 c y c l e s of p r a c t i c e on the o r i g i n a l waveform (see F i g u r e 1 and equation 1) and then t e s t e d f o r two t r i a l s o f each of 10 waveforms d e s c r i b e d below. Each t r i a l c o n s i s t e d of 10 c y c l e s of PT, f o l l o w e d b y 10 c y c l e s of PIB1, f o l l o w e d by 10 c y c l e s of PIB2, f o l l o w e d by 10 c y c l e s of TIB. Subjects were t e s t e d on t h e i r a b i l i t y t o t r a c k the f o l l o w i n g t e n waveforms: 1) the o r i g i n a l waveform from the t r a i n i n g phase of the experiment at i t s o r i g i n a l base frequency of 0.4 9 Hz.; 2) the o r i g i n a l waveform at a base frequency of 0.31 Hz.; 3) the o r i g i n a l waveform at a base frequency of 0.41 Hz.; 4) the o r i g i n a l waveform at a base frequency of 0.61 Hz.; 5) the o r i g i n a l waveform at a base frequency of 0.69 Hz.; 6) t r a n s f o r m a t i o n of the o r i g i n a l waveform w i t h the component f r e q u e n c i e s s h i f t e d out of phase by 90, 30, and 60 degrees and g i v e n by equation (2): f ( t ) = A /2 + C cos (cot + TC/2) + C/2 cos (2cot + 7T./6) + C/4 cos (4cot + 71/3) . 7) t r a n s f o r m a t i o n of the o r i g i n a l 0.5 Hz waveform wi t h the component f r e q u e n c i e s s h i f t e d out of phase by 30, 60, 129 and 45 degrees and g i v e n by equation (3): f ( t ) = A / 2 + C cos (cot + 7C/6) + C/2 cos (2cot + JC /3) + C/4 cos (4cot + 71/4) . 8) an e n t i r e l y new waveform gi v e n by equation ( 6 ) : f ( t ) = A / 2 + 170 cos cot + 65 cos 2cot + 45 cos 4cot 9) a randomly generated waveform v a r y i n g i n frequency between 0.391 Hz and 1.904 Hz. 10) a waveform with the same amplitude and frequency v a l u e s as the o r i g i n a l , but with those amplitude v a l u e s a s s o c i a t e d w i t h d i f f e r e n t f r e q u e n c i e s g i v e n by equation (5) : f (t) = A / 2 + C/4 cos cot + C cos 2 cot + C/2 cos 4 cot. Data A n a l y s i s Root mean squared error (RMS Error) was c a l c u l a t e d on the p u r s u i t tracking data i n order to determine response accuracy. P o u l t o n (1974) d e f i n e s RMS e r r o r as the square ro o t of the sum of the squares of the e r r o r at each sampling i n t e r v a l , d i v i d e d by the number of sampling i n t e r v a l s . I t i s g i v e n by the e q u a t i o n : RMSE = [ L ( s - r ) 2 / p I1/2, where s i s the s t i m u l u s v a l u e at time i n t e r v a l t , r i s the response v a l u e at time i n t e r v a l t , and p i s the number of i n t e r v a l s t h a t the response i s sampled over. RMS e r r o r has been recommended by P o u l t o n as the best measure f o r e v a l u a t i n g the " o v e r a l l adequacy of t r a c k i n g " (1974, p.38 ) . A decrease i n the v a l u e of RMS e r r o r scores i n d i c a t e s t h a t the s u b j e c t has become more ac c u r a t e and 130 p r e c i s e i n t r a c k i n g , and thus i s i n d i c a t i v e o f l e a r n i n g (Franks, W i l b e r g & Fishburne, 1985; Poulton, 1974). Variability of each s u b j e c t ' s response was c a l c u l a t e d w i t h i n each b l o c k of f i v e t r i a l s f o r the p u r s u i t t r a c k i n g phase based on a procedure from Franks, Wilberg, & Fishburne (1982). Two c y c l e s from each of the f i v e t r i a l s were sampled ( f o r a t o t a l o f ten c y c l e s ) . The displacement-time curves from these ten c y c l e s were superimposed upon one another i n order t o c a l c u l a t e a w i t h i n s u b j e c t v a r i a b i l i t y s c o r e . At each of the 512 sampling i n t e r v a l s a standard d e v i a t i o n (sd) of the ten response displacements was c a l c u l a t e d u s i n g the f o l l o w i n g e q u a t i o n : S.D. = [ £ (Mean r - r ) 2 / 10 j 1 / 2 , where r i s the response at a g i v e n time i n t e r v a l and p i s the number of i n t e r v a l s at which r i s sampled. The mean of these 512 sd's was used as the index of w i t h i n s u b j e c t v a r i a b i l i t y f o r a g i v e n t r i a l . I t a l s o allowed a p r o f i l e o f w i t h i n waveform v a r i a b i l i t y t o be c a l c u l a t e d f o r each s u b j e c t on each set of f i v e t r i a l s , thus i n d i c a t i n g d i f f e r e n t i a l i n t r a - s u b j e c t v a r i a b i l i t y throughout the waveform. Lead-lag index was used t o determine the extent t o which the s u b j e c t ' s response l e d or lagged the s t i m u l u s d u r i n g p u r s u i t t r a c k i n g . A c r o s s - c o r r e l a t i o n c o e f f i c i e n t was c a l c u l a t e d u s i n g the st i m u l u s and the response waveforms (each composed of 512 p o i n t s ) , w i t h the s t i m u l u s b e i n g h e l d constant and the response s i g n a l b e i n g advanced i n time by i n t e r v a l s of t e n m i l l i s e c o n d s . For each advancement of the 131 response s i g n a l a Pearson product-moment c o r r e l a t i o n c o e f f i c i e n t between stimulus and response was c a l c u l a t e d . The time at which the c o r r e l a t i o n between s t i m u l u s and response was g r e a t e s t was used t o determine the l e a d or l a g of the response w i t h r e s p e c t t o the s t i m u l u s . The l e a d - l a g index has p r e v i o u s l y been used as an i n d i c a n t o f the changing response s t r a t e g i e s used by s u b j e c t s d u r i n g t r a c k i n g (Franks, 1 9 8 2 ; Franks & Wilberg, 1 9 8 2 ) . The l i m i t a t i o n o f t h i s measure i s t h a t i t only r e f l e c t s the average l e a d or l a g , r a t h e r than the s p e c i f i c l o c a t i o n i n the waveform at which the s u b j e c t was l e a d i n g o r l a g g i n g (Poulton, 1 9 7 4 ) . Harmonic analysis was used t o analyze the response waveforms i n t o component f r e q u e n c i e s . The Harmonic a n a l y s i s y i e l d e d the f o l l o w i n g i n f o r m a t i o n : i ) the component f r e q u e n c i e s o f the response; i i ) the amplitude v a l u e s o f these component f r e q u e n c i e s ; i i i ) the phase angle v a l u e s o f these component f r e q u e n c i e s ; and iv) the p e r i o d o f the waveform; B e r n s t e i n (1967) was among the f i r s t t o use harmonic a n a l y s i s i n the study of human movement. In the e a r l y 1 9 0 0 ' s , he performed experiments i n which s u b j e c t s were f i l m e d p e r f o r m i n g v a r i o u s everyday movement t a s k s such as f i l i n g or hammering. The movement kinematics of the v a r i o u s l i n k segments were then analyzed i n t o component f r e q u e n c i e s . More r e c e n t l y t h i s a n a l y s i s has been used by Green (1971) on RT data, by Franks & Wilbe r g (1982) i n t r a c k i n g , by 132 Marteniuk & Romanow (1983) on arm movement t r a j e c t o r i e s , and by Richardson & Pew (1968) i n measuring s t a b i l o m e t e r performance. In the present study, Harmonic a n a l y s i s was used i n order t o determine the composition o f the s u b j e c t ' s response, d u r i n g movement p r o d u c t i o n , i n a l l f o u r feedback c o n d i t i o n s (PT, PIB1, PIB2, and TIB). The harmonic a n a l y s i s was c a l c u l a t e d based on a method d e s c r i b e d i n Lowry and Hayden (1951 pp 324 - 328). The p e r i o d i c i t y o f the waveform ( p e r i o d = 2 7t) was determined u s i n g an a u t o c o r r e l a t i o n . T h i s waveform was then d i v i d e d i n t o p equal u n i t s and each of these p o i n t s were l a b e l l e d xO, x l , x2, ... xp, with t h e i r c o r r e s p o n d i n g o r d i n a t e v a l u e s b e i n g yO, y l , y2, ... yp. The t r a p e z o i d a l r u l e of i n t e g r a t i o n was a p p l i e d over the p e r i o d y i e l d i n g the f o l l o w i n g e q u a t i o n s : 1) a D = 2/p % y r 2) a n = 2/p 7t y r cos n x r 3) b n = 2/p 7C y r s i n n x r Equation 2 gave the harmonic c o e f f i c i e n t s of the c o s i n e • component of the waveform, while equation 3 gave the harmonic c o e f f i c i e n t s o f the s i n e component of the waveform. The e n t i r e waveform was d e s c r i b e d by the eq u a t i o n : f (t) = A Q/2 + K A n cos ncot + B n s i n ncot T h i s equation was expressed i n terms of a c o s i n e f u n c t i o n : f ( t ) = A 0/2 + 7t C n cos (nu)t-(j)n) where Cn = A n 2 + B n 2 (j)n r e p r e s e n t e d the phase angle v a l u e s which p r o v i d e d the necessary t i m i n g r e l a t i o n s h i p among v a r i o u s harmonic components. These phase angle v a l u e s were determined u s i n g 133 the f o l l o w i n g e q u a t i o n : t a n <|>n = B n/A n In order t o t e s t the accuracy o f the harmonic a n a l y s i s , the s t i m u l u s waveform i t s e l f was analyzed i n t o component f r e q u e n c i e s . These data were then r e s y n t h e s i z e d i n t o a waveform which was compared t o the o r i g i n a l waveform by c a l c u l a t i n g the RMS e r r o r between the two waveforms. T h i s produced an RMS e r r o r o f 1.8 mm. RESULTS and DISCUSSION P u r s u i t T r a c k i n g As expected, i n the p u r s u i t t r a c k i n g c o n d i t i o n performance improved wi t h p r a c t i c e . Subjects became l e s s e r r o r f u l as measured by RMS e r r o r (see F i g u r e 1 ) . They a l s o became more c o n s i s t e n t i n t h e i r response as measured by a w i t h i n b l o c k v a r i a b i l i t y score (see F i g u r e 2 ) . In a d d i t i o n , the l e a d l a g index as measured by a c r o s s c o r r e l a t i o n f u n c t i o n not only approached zero but became more c o n s i s t e n t w i t h i n each t r i a l b l o c k as l e a r n i n g p r o g r e s s e d . From the beginning, s u b j e c t s were both l e a d i n g the s t i m u l u s and l a g g i n g i t , s u g g e s t i n g t h a t s u b j e c t s d i d not use a wait and move s t r a t e g y i n p u r s u i t t r a c k i n g . Rather i t i s l i k e l y t h a t feedback was be i n g used c o n t i n u o u s l y t o modify the s u b j e c t ' s response (see F i g u r e 3) . 134 F i g u r e 1. Root Mean' Squared E r r o r as a f u n c t i o n of p r a c t i c e f o r t r a i n i n g and r e t e n t i o n days. RMS ERROR R m s 6 0 5 0 E 4 o r r 30 o r 20 1 2 '3 4 Tra in ing D a y s 3 M 0 n t h s o phase A new X .69 .49 £ .31 m .61 .4 1 R e t e n t i o n .49 Hz wave + .31 Hz wave * .41 Hz wave • .61 Hz wave x .69 Hz wave 0 p h a s e s h i f t e d A new * R M S Er ro r 6 4 0 un i t s = 10.0 c m CO Cn 136 F i g u r e 2. Mean of 512 standard d e v i a t i o n v a l u e s from the displacement time p r o f i l e s of 10 c y c l e s of p u r s u i t t r a c k i n g f o r r a i n i n g and r e t e n t i o n days. Variability v a r i I a b t y 3 M o n t h s 0 phase A new X .69 • .6 1 • .49 * .4 1 + .31 R e t e n t i o n 1 2 3 4 Tra in ing D a y s . 4 9 H z w a v e + .31 H z w a v e * .41 H z w a v e D .61 H z w a v e x . 6 9 H z w a v e 0 p h a s e s h i f t e d A n e w * V a r i a b i l i t y 6 4 0 u n i t s = 10 .0 c m £ 138 F i g u r e 3 . The standard d e v i a t i o n of the l e a d - l a g index of the s u b j e c t s ' responses r e l a t i v e t o the s t i m u l u s over the f i v e t r a i n i n g days. Variability of Lead-Lag D a y s * a v e r a g e d o v e r t h e f o u r s u b j e c t s 140 When s u b j e c t s r e t u r n e d a f t e r a 3 month p e r i o d f o r 2 f u r t h e r days of t e s t i n g ( r e t e n t i o n days), i t was found t h a t s u b j e c t s r e t a i n e d a l e v e l of performance e q u i v a l e n t t o t h a t of days t h r e e and four (experiment one) as measured by RMS and v a r i a b i l i t y scores (see F i g u r e s 1 and 2). In order to determine whether s u b j e c t s l e a r n r e l a t i v e t i m i n g , s u b j e c t s , on these r e t e n t i o n days, were t r a n s f e r r e d t o v a r i o u s speeds of the o r i g i n a l waveform. They maintained RMS and v a r i a b i l i t y scores e q u i v a l e n t to those a c h i e v e d on the o r i g i n a l waveform f o r a l l speeds of the waveform, wit h the e x c e p t i o n of the f a s t e s t waveform which had both h i g h e r RMS and v a r i a b i l i t y scores (see F i g u r e s 1 and 2 ) . In order t o determine whether s u b j e c t s l e a r n a movement i n terms of i t s component f r e q u e n c i e s or i n terms of i t s t o p o l o g i c a l f e a t u r e s , s u b j e c t s were t r a n s f e r r e d t o two waveforms c o n t a i n i n g the component f r e q u e n c i e s of the o r i g i n a l waveform at d i f f e r e n t phase angles than the o r i g i n a l . Performance on these waveforms was compared wi t h performance on an e n t i r e l y new waveform which c o n t a i n e d d i f f e r e n t component f r e q u e n c i e s . A l l t h r e e waveforms had d i f f e r e n t t o p o l o g i c a l p r o p e r t i e s than the o r i g i n a l . Performance on these waveforms was e q u i v a l e n t as measured by RMS and v a r i a b i l i t y s c ores, i n d i c a t i n g t h a t s u b j e c t s do not l e a r n a movement i n terms of i t s component f r e q u e n c i e s but seem r a t h e r t o l e a r n a movement i n terms of i t s t o p o l o g i c a l f e a t u r e s (see F i g u r e s 1 and 2). 141 T r a c k i n g under V a r i o u s Feedback C o n d i t i o n s The r e s p o n s e w a v e f o r m s f r o m e a c h o f t h e f o u r f e e d b a c k c o n d i t i o n s w e r e c o m p a r e d a n d a n a l y z e d u s i n g an H a r m o n i c a n a l y s i s . W i t h p r a c t i c e a t t h e t r a c k i n g t a s k , s u b j e c t s l e a r n e d t o p r o d u c e a r e s p o n s e ( i n a l l c o n d i t i o n s ) whose p h a s e , f r e q u e n c y a n d a m p l i t u d e more c l o s e l y a p p r o x i m a t e d t h a t o f t h e s t i m u l u s , t h a n t h o s e o f t h e i r e a r l i e r r e s p o n s e s h a d ( s e e F i g u r e s 4 - 6 ) . T h i s i s i n l i n e w i t h e v i d e n c e f r o m s t u d i e s b y F r a n k s & W i l b e r g (1982) a n d M a r t e n i u k & Romanow (1983) . I n c o m p a r i n g t h e h a r m o n i c p r o f i l e s o f t h e s u b j e c t s ' r e s p o n s e s w i t h t h o s e o f t h e s t i m u l u s , two a s p e c t s w i l l be c o n s i d e r e d : one, how t h o s e f r e q u e n c y c o m p o n e n t s t h a t a r e c o n t a i n e d i n t h e s t i m u l u s a r e m a t c h e d b y e q u i v a l e n t c o m p o n e n t s i n t h e r e s p o n s e , t w o , how t h o s e r e s i d u a l f r e q u e n c i e s n o t c o n t a i n e d i n t h e s t i m u l u s ( b u t e x p r e s s e d i n t h e r e s p o n s e ) m a n i f e s t i n t h e f o u r f e e d b a c k c o n d i t i o n s w i t h d i f f e r e n t amounts o f p r a c t i c e . S u b j e c t s p e r f o r m e d b e s t i n t h e p u r s u i t t r a c k i n g c o n d i t i o n (as c o m p a r e d t o t h e o t h e r f e e d b a c k c o n d i t i o n s ) i n t e r m s o f a c c u r a t e l y p r o d u c i n g t h e a m p l i t u d e v a l u e s o f t h o s e component f r e q u e n c i e s c o n t a i n e d i n t h e s t i m u l u s ( F i g u r e s 4 -6). W i t h p r a c t i c e ( i . e . b y day f i v e ) t h e a m p l i t u d e v a l u e s o f t h e r e s p o n s e c o m p o n e n t s became c l o s e r i n v a l u e t o t h o s e o f t h e s t i m u l u s , a n d t h i s was m a i n t a i n e d o v e r t h e t h r e e m o nth r e t e n t i o n i n t e r v a l . F o r t h e s t i m u l u s o n l y c o n d i t i o n , h o w e v e r ( s e e F i g u r e s 4 - 6 ), s u c h an i m p r o v e m e n t w i t h 142 F i g u r e 4 . The amplitudes of the harmonic components t h a t comprised the response waveforms under the f o u r feedback c o n d i t i o n s on d a y 1. Pursuit Tracking Day 1 1 2 3 < S ( 1 8 component frequencies Response Only Day 1 Response Waveform component frequencies 144 F i g u r e 5. The amplitudes of the harmonic components t h a t comprised the response waveforms under the four feedback c o n d i t i o n s on day 5. Pursuit Tracking Day 5 component frequencies Response Only Day 5 Response Waveform 1 2 3 4 5 ( 1 1 component frequencies Stimulus Only Day 5 component frequencies Input Blanking Day 5 Response Waveform component frequencies 146 F i g u r e 6 . The amplitudes of the harmonic components t h a t comprised the response waveforms under the f o u r feedback c o n d i t i o n s on the r e t e n t i o n day. Response Only Retention 1 2 3 4 S ( 7 component frequencies Pursuit Tracking Retention component frequencies Input Blanking Retention Response Waveform 1 2 3 4 5 ( 7 6 component frequencies Stimulus Only Retention Response Waveform 1 2 3 4 5 ( 7 1 component frequencies 148 p r a c t i c e was n o t e v i d e n t . I n c o m p a r i n g p e r f o r m a n c e f r o m t h e s t i m u l u s o n l y a n d p u r s u i t t r a c k i n g c o n d i t i o n s on d a y one, one f i n d s t h a t s u b j e c t s seem t o p r o d u c e a b e t t e r r e s p o n s e i n t h e s t i m u l u s o n l y c o n d i t i o n t h a n t h e y do i n t h e p u r s u i t t r a c k i n g c o n d i t i o n . T h i s may b e b e c a u s e e a r l y i n l e a r n i n g , when s u b j e c t s h a v e a more l i m i t e d a t t e n t i o n a l c a p a c i t y t h a n t h e y do l a t e r i n l e a r n i n g ( N e i s s e r , 1 9 8 0 ) , t h e y p e r f o r m b e t t e r i n a s i t u a t i o n ( l i k e t h e s t i m u l u s o n l y c o n d i t i o n ) i n w h i c h t h e r e i s l e s s i n f o r m a t i o n t o a t t e n d t o . I n t h e s t i m u l u s o n l y c o n d i t i o n s u b j e c t s a r e o n l y r e q u i r e d t o a t t e n d t o t h e s t i m u l u s , w h e r e a s i n p u r s u i t t r a c k i n g t h e y a r e g i v e n i n f o r m a t i o n a b o u t t h e s t i m u l u s , t h e r e s p o n s e a n d t h e e r r o r . E a r l y i n l e a r n i n g a t t e m p t i n g t o a t t e n d t o t h e s e t h r e e f o r m s o f i n f o r m a t i o n seems t o c a u s e p e r f o r m a n c e d e c r e m e n t s . The component f r e q u e n c i e s o f t h e r e s p o n s e w a v e f o r m d u r i n g t h e r e s p o n s e o n l y c o n d i t i o n c o m p a r e d more f a v o r a b l y t o t h e s t i m u l u s t h a n t h e i n p u t b l a n k i n g c o n d i t i o n . T h i s was t h e c a s e b o t h e a r l y a n d l a t e r i n l e a r n i n g . V i s u a l i n f o r m a t i o n o f t h e i r own r e s p o n s e a p p e a r e d t o be c r i t i c a l i n o r d e r f o r t h e s u b j e c t s t o p r o d u c e an a c c u r a t e a p p r o x i m a t i o n o f t h e s t i m u l u s . When s u b j e c t s r e t u r n a f t e r a 3 month b r e a k , t h e c o n d i t i o n s t h a t show t h e g r e a t e s t d e c r e m e n t i n p e r f o r m a n c e a r e t h o s e i n w h i c h t h e v i s u a l r e s p o n s e i n f o r m a t i o n h a s b e e n r e m o v e d . Thus i t a p p e a r s t h a t t h e s u b j e c t s may f o r g e t t h e c o r r e s p o n d e n c e b e t w e e n t h e v i s u a l i n f o r m a t i o n on t h e s c r e e n a n d t h e movement o f t h e i r h a n d . T h i s s u g g e s t s t h a t FB a b o u t o n e s own r e s p o n s e i s c r i t i c a l i n 149 o r d e r t o p r o d u c e a c c u r a t e movement. T h i s i s i n l i n e w i t h P r i b r a m ' s (1971) c o n t e n t i o n t h a t movement i s r e p r e s e n t e d i n s e n s o r y t e r m s . F o r a l l f o u r f e e d b a c k c o n d i t i o n s , t h e r e s i d u a l n o i s e i n t h e r e s p o n s e d i s s i p a t e d s u c h t h a t b y d a y f i v e t h e a m p l i t u d e s o f t h e r e s i d u a l f r e q u e n c i e s w e r e d i m i n i s h e d , t h u s c r e a t i n g a r e s p o n s e w h i c h more c l o s e l y a p p r o x i m a t e d t h e s t i m u l u s . T h i s l e v e l o f a c c u r a c y was c a r r i e d o v e r t h e 3 month r e t e n t i o n i n t e r v a l i n a l l f o u r f e e d b a c k c o n d i t i o n s . I n t h e p u r s u i t t r a c k i n g c o n d i t i o n f e w e r r e s i d u a l f r e q u e n c i e s w e r e p r e s e n t a s c o m p a r e d w i t h t h e o t h e r c o n d i t i o n s . A n d b y d a y f i v e v i r t u a l l y n one o f t h e h i g h e r f r e q u e n c y r e s i d u a l c o m p o n e n t s w e r e p r e s e n t i n t h e p u r s u i t t r a c k i n g c o n d i t i o n . The f a c t t h a t f e w e r h i g h f r e q u e n c y c o m p o n e n t s w e r e f o u n d i n t h e p u r s u i t t r a c k i n g c o n d i t i o n t h a n w e r e f o u n d i n t h e o t h e r c o n d i t i o n s i s c o n t r a r y t o what was e x p e c t e d . I t was p r e d i c t e d t h a t r e s p o n s e s made i n t h e p u r s u i t t r a c k i n g c o n d i t i o n w o u l d c o n t a i n more r e s i d u a l h i g h e r f r e q u e n c y c o m p o n e n t s t h a n t h e o t h e r c o n d i t i o n s . I t was t h o u g h t t h a t s u b j e c t s w o u l d make more d i s c r e t e c o r r e c t i o n s i n p u r s u i t t r a c k i n g w h e r e t h e y w e re g i v e n f e e d b a c k a b o u t t h e d i s c r e p a n c y b e t w e e n s t i m u l u s a n d r e s p o n s e t h a n t h e y w o u l d i n o t h e r c o n d i t i o n s i n w h i c h t h i s d i s c r e p a n c y i n f o r m a t i o n was n o t a v a i l a b l e . T h i s p r e d i c t i o n was b a s e d on t h e a s s u m p t i o n t h a t when f e e d b a c k a b o u t e r r o r i s a v a i l a b l e , s u b j e c t s w i l l r e s p o n d t o e r r o r by m a k i n g d i s c r e t e c o r r e c t i o n s . However i t seems f r o m t h e p r e s e n t f i n d i n g s t h a t r a t h e r t h a n m a k i n g any 150 F i g u r e 7 . Mean c y c l e d u r a t i o n (period) under the f o u r feedback c o n d i t i o n s d u r i n g t r a i n i n g and r e t e n t i o n . Period of Training Wave p e r r I 0 d m s e c 2 2 0 0 2 1 0 0 2 0 0 0 1 2 3 Tra in ing D a y s P u r s u i t T r a c k i n g R e s p o n s e On ly R2 R e t e n t i o n + S t i m u l u s O n l y D Input B l a n k i n g 152 k i n d o f d i s c r e t e c o r r e c t i o n s , s u b j e c t s u s e d t h e v i s u a l f e e d b a c k t o m o d u l a t e t h e i r r e s p o n s e i n a more c o n t i n u o u s f a s h i o n . As r e g a r d s t i m i n g c o n t r o l , i n t h e s t i m u l u s o n l y a n d p u r s u i t t r a c k i n g c o n d i t i o n s , s u b j e c t s p r o d u c e d movement c y c l e s t h a t w e r e o f t h e same b a s e f r e q u e n c y a s t h o s e o f t h e s t i m u l u s . I n t h e r e s p o n s e o n l y a n d i n p u t b l a n k i n g c o n d i t i o n s , s u b j e c t s p r o d u c e d movement c y c l e s w i t h l o w e r b a s e f r e q u e n c i e s ( i . e . l o n g e r p e r i o d s ) t h a n t h e s t i m u l u s . Thus i t seems t h a t s t i m u l u s i n f o r m a t i o n i s i m p o r t a n t i n d e t e r m i n i n g t h e o v e r a l l t i m i n g o f a movement c y c l e ( s e e F i g u r e 7 ). I t seems f r o m t h e p r e s e n t r e s u l t s t h a t t h e c l o s e d l o o p p r o c e s s e s o f r e s p o n s e m o d i f i c a t i o n a r e u t i l i z e d i n d e t e r m i n i n g a b s o l u t e ( o r i m m e d i a t e ) t i m i n g . T h i s p r o c e s s o f r e s p o n s e m o d i f i c a t i o n i s u t i l i z e d e a r l y i n l e a r n i n g i n t h e p u r s u i t t r a c k i n g c o n d i t i o n , a s w e l l as l a t e i n l e a r n i n g i n t h e r e s p o n s e o n l y c o n d i t i o n , s u c h t h a t t h e a b s o l u t e t i m i n g o f t h e s u b j e c t s r e s p o n s e becomes i d e n t i c a l t o t h a t o f t h e s t i m u l u s . When n e i t h e r s t i m u l u s n o r r e s p o n s e i n f o r m a t i o n a r e a v a i l a b l e t o t h e s u b j e c t t h e o v e r a l l d u r a t i o n o f t h e s u b j e c t ' s r e s p o n s e i s t y p i c a l l y l o n g e r t h a n t h a t o f t h e s t i m u l u s . Thus f e e d b a c k f r o m t h e e n v i r o n m e n t seems t o be i m p o r t a n t i n d e t e r m i n i n g a b s o l u t e t i m i n g . E a r l y i n l e a r n i n g s t i m u l u s i n f o r m a t i o n i s n e c e s s a r y , w h e r e a s l a t e i n l e a r n i n g r e s p o n s e i n f o r m a t i o n i s s u f f i c i e n t . The p r e s e n t e v i d e n c e i n d i c a t e s t h a t s u b j e c t s d e v e l o p some k i n d o f o r g a n i z a t i o n o f movement i n w h i c h t h e r e seems 153 t o b e , a s B a r t l e t t (1932) h a s s u g g e s t e d f o r h i s schema, an i n t e r p l a y b e t w e e n FB a n d t h e schema i t s e l f . The movements f r o m t h i s s t u d y t h a t w e r e r e p r o d u c e d f r o m memory a l s o e x h i b i t e d c e r t a i n s y s t e m a t i c d i s t o r t i o n s . T h i s i s i n l i n e w i t h B a r t l e t t ' s (1932) s t u d i e s on memory i n w h i c h he f o u n d t h a t i n r e c a l l i n g s t o r i e s s u b j e c t s w o u l d d i s t o r t t h e d e t a i l s t o f i t t h e i r own c u l t u r a l c o n t e x t . M o r e r e c e n t l y r e s e a r c h on memory f o r s p a t i a l l o c a t i o n s ( T v e r s k y , 1981) i l l u s t r a t e s t h a t i n r e c a l l i n g g e o g r a p h i c a l l o c a t i o n s s u b j e c t s make s y s t e m a t i c d i s t o r t i o n s o f s p a c e . F o r e x a m p l e , when s u b j e c t s a r e a s k e d t o r e c a l l t h e l o c a t i o n o f M i a m i w h i c h i s on t h e e a s t c o a s t o f N o r t h A m e r i c a r e l a t i v e t o L i m a w h i c h i s on t h e w e s t c o a s t o f S o u t h A m e r i c a , t h e y d i s t o r t t h e r e l a t i o n s h i p o f t h e two c o n t i n e n t s p u t t i n g S o u t h A m e r i c a d i r e c t l y s o u t h o f N o r t h A m e r i c a . Thus t h o u g h M i a m i i s i n f a c t w e s t o f L i m a , p e o p l e t h i n k o f i t b e i n g e a s t o f L i m a . T h i s k i n d o f d i s t o r t i o n i s a l s o f o u n d i n t h e b r a i n ' s s e n s o r i - m o t o r h o m u n c u l u s . A s i m i l a r p r o c e s s may be o c c u r r i n g i n t h e r e p r o d u c t i o n o f t h e w a v e f o r m s i n t h i s s t u d y . T h a t i s , i n t h e i n p u t b l a n k i n g c o n d i t i o n t h e l o c a t i o n s o f t h e r e v e r s a l s a n d t h e c h a n g e s o f s p e e d seem to be s y s t e m a t i c a l l y d i s t o r t e d i n s p a c e d u r i n g movement r e p r o d u c t i o n o r "memory". The h y p o t h e s i s t h a t s u b j e c t s s y s t e m a t i c a l l y a c q u i r e the component f r e q u e n c i e s o f a movement was n o t s u p p o r t e d b y the p r e s e n t d a t a . R a t h e r i n t h i s s t u d y , s u b j e c t s seemed t o s y s t e m a t i c a l l y d i m i n i s h the r e s i d u a l f r e q u e n c i e s over the course of l e a r n i n g . I t i s p o s s i b l e t h a t the p r o g r e s s i v e a c q u i s i t i o n o f component f r e q u e n c i e s p r e v i o u s l y found (Franks & Wilberg, 1982; Marteniuk & Romanow, 1983) was tas k s p e c i f i c i n the sense t h a t both these s t u d i e s used a l a r g e amplitude movement which i n v o l v e d the whole arm. The p r e s e n t study on the other hand used a s m a l l e r w r i s t movement. 155 APPENDIX C KINEMATIC PROFILES INPUT BLANKING DAY 15 (BEST RMS) F i g u r e Page 1. Displacement-time p r o f i l e of stimulus and response d u r i n g input b l a n k i n g f o r s u b j e c t 1 on day 15 wl 157 2. Displacement-time p r o f i l e of stimulus and response d u r i n g input b l a n k i n g f o r s u b j e c t 2 on day 15 wl 158 3. Displacement-time p r o f i l e of stimulus and response d u r i n g input b l a n k i n g f o r s u b j e c t 3 on day 15 wl 159 4. Displacement-time p r o f i l e o f stimulus and response d u r i n g input b l a n k i n g f o r s u b j e c t 4 on day 15 wl 160 5. Displacement-time p r o f i l e o f stimulus and response d u r i n g input b l a n k i n g f o r s u b j e c t 5 on day 15 wl 161 6. Displacement-time p r o f i l e of stimulus and response d u r i n g input b l a n k i n g f o r s u b j e c t 6 on day 15 wl 162 162 APPENDIX D KINEMATIC PROFILES INPUT BLANKING DAY 15  VARIABILITY AMOUNGST THE FIVE CYCLES F i g u r e P a g e 1. V a r i a b i l i t y a c r o s s f i v e c y c l e s d u r i n g i n p u t b l a n k i n g f o r s u b j e c t 3 on d a y 15 w l 164 2. V a r i a b i l i t y a c r o s s f i v e c y c l e s d u r i n g i n p u t b l a n k i n g f o r s u b j e c t 3 on d a y 15 w l 165 3. V a r i a b i l i t y a c r o s s f i v e c y c l e s d u r i n g i n p u t b l a n k i n g f o r s u b j e c t 3 on d a y 15 w l 166 4. V a r i a b i l i t y a c r o s s f i v e c y c l e s d u r i n g i n p u t b l a n k i n g f o r s u b j e c t 4 on d a y 15 w l 167 5. V a r i a b i l i t y a c r o s s f i v e c y c l e s d u r i n g i n p u t b l a n k i n g f o r s u b j e c t 5 on d a y 15 w l 168 6. V a r i a b i l i t y a c r o s s f i v e c y c l e s d u r i n g i n p u t b l a n k i n g f o r s u b j e c t 6 on d a y 15 w l 169 169 APPENDIX E  HARMONIC PROFILES DAY 15 (Wl - W7) F i g u r e s Page 1. A m p l i t u d e s o f h a r m o n i c c o m p o n e n t s t h a t c o m p r i s e d w l on d a y 15 171 2. A m p l i t u d e s o f h a r m o n i c c o m p o n e n t s t h a t c o m p r i s e d w2 on d a y 15 172 3. A m p l i t u d e s o f h a r m o n i c c o m p o n e n t s t h a t c o m p r i s e d w3 on d a y 15 173 4. A m p l i t u d e s o f h a r m o n i c c o m p o n e n t s t h a t c o m p r i s e d w4 on d a y 15 174 5. A m p l i t u d e s o f h a r m o n i c c o m p o n e n t s t h a t c o m p r i s e d w5 on d a y 15 175 6. A m p l i t u d e s o f h a r m o n i c c o m p o n e n t s t h a t c o m p r i s e d w6 on d a y 15 17 6 7. A m p l i t u d e s o f h a r m o n i c c o m p o n e n t s t h a t c o m p r i s e d w7 on d a y 15 177 Day 15 Wave 1 350 300 1 2 3 4 5 6 7 8 component f requenc ies Day 15 Wave 2 350 300 1 2 3 4 5 6 7 8 c o m p o n e n t f r e quen c i e s Day 15 Wave 3 I S t a n d a r d D e v i a t i o n WW S t i m u l u s ZH R e s p o n s e 4 2 3 4 6 7 8 component frequencies Day 15 Wave 4 350 300 1 2 3 4 5 6 7 8 c o m p o n e n t f r e q u e n c i e s Day 15 Wave 5 350 300 component f requenc ies Day 15 Wave 6 I S t a n d a r d D e v i a t i o n H i S t i m u l u s ZZI R e s p o n s e 2 3 4 5 6 component f requenc ies 7 8 Day 15 Wave 7 350 300 a m 250 1 2 3 4 5 6 7 8 component frequencies 177 REFERENCES A b b s , J . H . , G r a c c o , V . L . , & C o l e , K . J . ( 1 9 8 4 ) . C o n t r o l o f m u l t i m o v e m e n t c o o r d i n a t i o n : S e n s o r i m o t o r m e c h a n i s m s i n s p e e c h p r o g r a m m i n g . Journal of Motor Behavior, 16, 195- 2 3 1 . A r m s t r o n g , T.R. ( 1 9 7 0 ) . Training for the production of memorized movement patterns (Tech. Rep. No. 26). Ann A r b o r : U n i v e r s i t y o f M i c h i g a n , Human P e r f o r m a n c e C e n t r e . B a r t l e t t , F.C. ( 1 9 3 2 ) . Remembering: A study in experimental and social psychology. C a m b r i d g e : C a m b r i d g e U n i v e r s i t y P r e s s . B a r t l e t t , F.C. ( 1 9 5 8 ) . Thinking. New Y o r k : B a s i c B o o k s . B a t e s o n , G. ( 1 9 8 2 ) . Mind and Nature: a Necessary Unity. New Y o r k : Bantam. B e e k , P . J . & M e i j e r , O . G . ( 1 9 8 8 ) . On t h e N a t u r e o f t h e M o t o r A c t i o n C o n t r o v e r s y . I n O . G . M e i j e r & K . R o t h (Eds.) Complex Movement Behavior: The Motor Action Controversy. 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