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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  degree freely  at  the  available  copying  of  department publication  this  of  in  partial  fulfilment  University  of  British  Columbia,  for  this or  thesis  reference  thesis by  this  for  his thesis  and  scholarly  or for  her  Department The University of British Columbia Vancouver, Canada  I  I further  purposes  gain  the  shall  requirements  agree  that  agree  may  representatives.  financial  permission.  DE-6 (2/88)  study.  of  be  It not  is be  that  the  for  Library  an  advanced  shall  permission for  granted  by  understood allowed  the  make  extensive  head  that  without  it  of  copying my  my or  written  ABSTRACT  The  concept  of  invariant relative  been a s s o c i a t e d w i t h program.  The  invariant  relative  The is  present  underlying  essential  approaches the  for this  question  relative  given  extensive  reproduce  In the  timing  of  order  to  test  a  whether  a movement, t h e y to  relative  different  i n terms  Measurements were taken 1)  on  the  constrained  reproduction  of  a l l waveforms  three  variability.  was  subjected  phase,  stimulus, subjects'  d e p e n d e n t m e a s u r e s : RMS  to  described frequency,  Performance three each  and  track  1)  were and  control learn  i n terms  i n two  for the  subjects and  2)  in  t i m i n g was  an  of  timing.  conditions: were a not  evaluated  reproduction  response waveform  amplitude,  subjects  error, lead-lag  i n the  analyses:  during  absolute  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  and  which  the  c o n d i t i o n where  constrained. using  by  the  subjects  criterion  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 where  temporally  the  were t r a n s f e r r e d t o  identical  but  i s "What  of  visually joystick  waveforms w h i c h were timing,  i s one  of  learning.  study  experiment,  a c r i t e r i o n waveform u s i n g In  of  i s learned  practice i n learning to  response.  motor  a d d r e s s e d by  timing  present  typically  phenomenon  perspective  concern  specific  has  a generalized  p r o p e r t i e s o f movement t h a t  acquisition.  relative  of  from the  of  i s whether  skill  their  timing  The  study  concept  study  question  learned?".  present  the  timing  index,  condition  harmonic a n a l y s i s , i n terms  period;  of i t s  2)proportional  interval  durations;  displacements. support movement learn.  and 3) p r o p o r t i o n a l  The outcome  t o the idea  that  from both  the invariant  i s one o f t h e a s p e c t s  interval  conditions relative  gives timing  o f a movement t h a t  of  humans  iv  TABLE OF CONTENTS Abstract  i i  List  of Tables  List  of Figures  v  1.  Introduction  1  2.  Methods Subjects Task Apparatus S t i m u l u s Waveforms 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 Procedure Data A n a l y s i s Statistical Analysis  12 12 12 12 14 16 17 20 26  3.  Results Part  28 28 28 35 38 45 45 54 58 63 64 65  Part  4.  iv  One - P u r s u i t T r a c k i n g I . RMS E r r o r II. Within Subject V a r i a b i l i t y I I I . Lead-Lag Index Two - I n p u t B l a n k i n g I. I n t e r v a l D u r a t i o n s II. Interval Displacements III. Period IV. RMS E r r o r V. F r e q u e n c y C o m p o s i t i o n VI. Kinematic P r o f i l e s  Discussion P a r t One - P u r s u i t T r a c k i n g P a r t Two - I n p u t B l a n k i n g I. I n t e r v a l D u r a t i o n s II. Interval Displacements . III. Cycle Duration IV. F r e q u e n c y C o m p o s i t i o n and RMS V. K i n e m a t i c P r o f i l e s . P a r t Three - C o n c l u s i o n s Component F r e q u e n c i e s Relative Timing What i s L e a r n e d ?  A p p e n d i x A: Review o f L i t e r a t u r e What i s L e a r n e d ? Representationalism and t h e Problem of Higher A u t h o r i t y Invariant Relative timing  Error  69 69 74 74 80 81 . 82 84 86 85 86 88 90 91 98 104  V  A p p e n d i x B: P i l o t Study Introduction Methods R e s u l t s and D i s c u s s i o n A p p e n d i x C: Kinematic p r o f i l e s day 15 b e s t RMS  from i n p u t  References  blanking 155  A p p e n d i x D: K i n e m a t i c p r o f i l e s from i n p u t day 15 - a l l f i v e c y c l e s Appendix E: Harmonic p r o f i l e s  117 117 124 133  day  15  blanking  w l - w7  162 169 177  vi L I S T OF  TABLES  Table  Page  1.  Experimental  2.  Waves Error  3.  19  * Days i n t e r a c t i o n s :  ANOVA t a b l e day  design R o o t Mean  Squared 33  variability:  Planned contrasts  15  38  4.  ANOVA t a b l e :  5.  Intra-individual variability forinterval d u r a t i o n data a c r o s s t h e f i v e waveforms ANOVA t a b l e : Interval displacements  6. 7.  Interval  durations  Intra-individual variability f o rinterval displacement data across t h e f i v e waveforms.  8.  RMS E r r o r :  9.  ANOVA T a b l e :  Input  b l a n k i n g d a y 15  RMS E r r o r  Input  Blanking  52  54 55 . . .  55 63 64  vii L I S T OF  FIGURES  Figure 1. 2.  3.  4.  5.  6. 7.  8. 9. 10. 11.  Page  R o o t Mean S q u a r e d E r r o r a s a f u n c t i o n o f practice.  30  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 the displacement 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 waveforms over 6 t r a n s f e r days.  37  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 as 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  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 as 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  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 of t h e subjects' responses 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  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 proportional i n t e r v a l duration data.  47  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 i n t e r v a l duration data.  49  forproportional  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  Waveforms by i n t e r v a l s i n t e r a c t i o n i n t e r v a l displacement data.  57  for relative  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 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.  5  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 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.  5  60 62  12.  Kinematic  profiles  from  subject  2 f o r w l - w5.  67  13.  Kinematic  profiles  from  subject  6 f o r w l - w5.  68  1 CHAPTER 1. INTRODUCTION  One  o f t h e fundamental  seek t o understand question as  1977;  proposed,  that  of  learned by  are learned.  Gibsonians  Gibson "cases  detect  basis  l a b e l s such  a s schema  (Pribram,  o r t h e e c o l o g i c a l group,  have e x p l a i n e d  learning  or detecting  1971), and  who l i k e t h e  b a s e d on i n y e t a n o t h e r way.  perceptual  learning  an i n v a r i a n t " . J . J .  c a n be extended t o b o t h t h e c o g n i t i v e and In relation  t o cognition,  Eleanor  the learned  perceptual  (1969, p471) h a s a r g u e d t h a t "to  i n d i f f e r e n t ways  1975).  of perceiving  motor domains.  much  representation f o r  (1966, p.279) h a s d e f i n e d  idea  on t h e o t h e r  are representations  have r e j e c t e d e x p l a n a t i o n s  representation,  s t i m u l i and  i t has been described  (Keele,  behaviorists,  Gibson's  of this  with  have  There has been  1975) image o f achievement  motor program  J.J.  what Is learned  or events.  d i f f e r e n t researchers,  The  The b e h a v i o r i s t s between  back  (Gibson, 1969;  The c o g n i t i v i s t s ,  as t o t h e nature  movements;  (Schmidt,  as  that  movement, o b j e c t s ,  speculation  1980).  This  a t l e a s t as f a r  i n t h e 1930's  i t i sassociations  have argued,  o f u s who  i s "what is learned?".  o f behaviorism  Whiting,  responses that hand,  for those  has been c e n t r a l t o psychology  the inception  Weimer,  learning  questions  r e g u l a r i t y , order,  for cognitive  abilities  Gibson ability  and s t r u c t u r e " provides t h e such as l e a r n i n g  mathematics  2  (see  also  well,  there  invariant The in  as i t becomes w e l l that  constitute this  question.  Two  a movement. study  (appendix),  frequencies For  people  of these,  was t h a t  people  several  years  there  movement  remain  i n v a r i a n t over  the performance  an i n v a r i a n t  feature  (usually  motor program)  (Shapiro  & Schmidt, 1981).  though having nevertheless one  Kelso,  of this  addressed  this study.  The  timing  of  i n the pilot  l e a r n t h e component  elements that  evidence,  that  of the central  have argued t h a t  action 1984).  relative  Zernicke,  of  (Kelso,  Putnam,  timing  timing  may  representation  From a n o t h e r p e r s p e c t i v e ,  rejected the notion  make up a  Motor t h e o r i s t s  o f t h e movement b e i n g  1982; Shapiro,  that the  i n absolute  skills.  learned Gregor,  &  action theorists,  representation,  invariant relative  of the essential variables that  skilled  of  several  t o answer  changes  o f motor  i n f e r r e d , from t h i s  Diestel,  i n  In the f i e l d  has been evidence  o f the response  be  learned?"  o f a movement.  timing  have  conducted  learn the relative  relative  during  "what is  o f t h e s e were t h e f o c u s  The s e c o n d  as  become  t h e s i s were  have been  i n an a t t e m p t  o f t h e s e was t h a t  that  learning.  and c o n t r o l there  hypotheses put forward  o f movement  learned.  of perceptual-motor  learning  first  In t h e case  t o investigate the question  process  motor  1945).  are certain of i t s features  studies  order  the  Wertheimer,  characterizes  & Goodman,  1983;  timing i s human Tuller &  3 Most o f t h e r e s e a r c h e r s relative  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  program.  A central question  program has been  been s u g g e s t e d  one  o f these  (Schmidt,  invariant features.  (Gentner,  overall  that  1987).  evidence  will  subjects  relative  The i d e a t h a t  and i t  timing i s relative  relative  came f r o m some  (1970, c i t e d  the r e l a t i v e  1988).  nonetheless  When  maintained  He h a d  could vary  f o r each i n s t a n c e  subjects an i n v a r i a n c e  I t was  proposed  t i m i n g was s t r u c t u r e d  i n t o t h e m o t o r p r o g r a m , whereas t h e o v e r a l l  Thus,  different  move a l e v e r t h r o u g h a p a r t i c u l a r  because r e l a t i v e  p a r a m e t e r whose v a l u e  model  unpublished  t i m i n g between r e v e r s a l s .  occurred  duration  durations.  i n Schmidt,  spatial-temporal pattern.  moved t o o q u i c k l y t h e y  this  a s t h e proportional  exhibit fixed  repeatedly  unidimensional  skill.  t h e motor  movement p e r f o r m e d w i t h  forthis  s t u d i e s by A r m s t r o n g  that  study  The p r o p o r t i o n a l d u r a t i o n  any s k i l l e d  durations  Original  in  1988) t h a t  to i n the l i t e r a t u r e  predicts  his  who  i s an i n v a r i a n t f e a t u r e o f t h e m o t o r p r o g r a m i s o f t e n  referred model  f o r those  t o t h e motor  "What a r e i t s i n v a r i a n t f e a t u r e s ? " ,  has  timing  who have s t u d i e d i n v a r i a n t  across  d u r a t i o n was a  instances  of the s k i l l  of the  a different  parameter value  for overall  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 o f t i m i n g  in  skilled  until  now.  motor p e r f o r m a n c e has been w i d e l y (For other  model s e e : C a r t e r 1977;  d u r a t i o n was a s s i g n e d  Terzuolo  empirical research  & Shapiro,  & Viviani,  accepted  supporting  1984; S h a p i r o ,  1979).  to the  up this  1977; Summers,  4  Recently, timing  however, t h e c o n c e p t  h a s come i n t o q u e s t i o n  reanalyzed relative  some o f t h e d a t a  timing.  Gentner  (1987).  from p a s t  studies  He a r g u e d t h a t  u s e d as s u p p o r t i n g  evidence  the majority  imprecisely  analyzed  of a given  individual  observed durations.  Gentner proposed a constant Literature).  A f t e r having  experiments that timing  proportional durations Since  duration  Gentner on i n v a r i a n t o f the data duration  i n that  researchers  interval  instead of  To overcome t h i s  proportion reanalyzed  had found evidence  i n motor t a s k s ,  relative  f o r the proportional  model h a d b e e n a n a l y z e d mean d u r a t i o n s  of invariant  test  problem,  (see Review o f  the data  from  for invariant  relative  Gentner concluded t h a t t h e model was n o t s u p p o r t e d .  were m a i n t a i n e d t o some e x t e n t  Relative  but not p r e c i s e l y .  t h e p u b l i c a t i o n o f Gentner's paper s e v e r a l  researchers  have begun t o q u e s t i o n  t h e phenomenon o f i n v a r i a n t  timing  Heuer,  (Heuer,  Schmidt,  1988;  1988a;  Zelaznik  1988b;  may learn least  invariance,  reasons  at t h e b e h a v i o r a l Heuer  one c a n n o t  invariant relative  three  relative  timing  with  r u l e out the n o t i o n  that  timing.  The f i r s t  (1988), who h a s a r g u e d t h a t  relative  timing  indicate  a lack of invariance  there  H e u e r & S c h m i d t , 1988;  at the behavioral  they  One c o u l d p o s i t a t  f o r a lack of perfect  level.  relative  e t a l . , 1986).  Though human's may n o t exhibit perfect  had  invariance  evident  h a s b e e n s u g g e s t e d by  a lack of invariance i n level  centrally.  are n o n - l i n e a r i t i e s i n the nervous  does n o t n e c e s s a r i l y This  i s because  s y s t e m w h i c h may  5 distort it  a central invariance i n relative  would m a n i f e s t  variable  second  a formal pointed an  way  that  timing.  i s t h a t humans may  (Thompson,  1952).  learn relative  As B a t e s o n  out i n d e s c r i b i n g morphogenesis,  "asymmetry  such  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 t h e form o f  relative  The  timing,  i n size",  i n formal  relations".  symmetry  o f form o r g a n i z e s  (1982) h a s  though t h e r e  one n e v e r t h e l e s s  symmetry  timing i n  may be  f i n d s "a d e e p e r  I n t h e same way  morphogenesis,  that  relative  timing  may be t h e s t r u c t u r e a r o u n d w h i c h a movement p a t t e r n i s organized.  Several  authors  have drawn p a r a l l e l s  morphogenesis and motor l e a r n i n g Fukson,  1986 p.599;  exhibit  symmetry  expressed right leg  Turvey,  (Berkinblit,  1986 p . 6 2 4 ) .  i n t e r m s o f form, b u t r a r e l y  s i d e s o f t h e body.  may be s l i g h t l y  longer  than the l e f t  and  i n that there  t h e form o f these  of that  on t h e l e f t .  considered evidence  that  mathematically This  interval  The c o n c e p t light.  but t h e form i s  of relative  Gentner  durations  two f e e t  mirror  timing  image  c a n be  (1987) h a s g i v e n  a r e not always  perfect proportions  Gentner a l s o has g i v e n  proportions  the right  ( i . e . the  i s the exact  of overall  i s analogous t o Bateson's n o t i o n  size".  m a g n i t u d e s on t h e  a r e two l e g s , two k n e e s ,  on t h e r i g h t  i n a similar  creatures  i s this  For instance,  magnitudes are not e x a c t l y e q u i v a l e n t ) symmetrical  Feldman, &  Living  i n terms o f p e r f e c t l y e q u i v a l e n t  and l e f t  between  time.  o f "asymmetry i n  evidence  a r e i n v a r i a n t , and t h i s  movement  that  on a v e r a g e t h e  c a n be t h o u g h t  o f as  6  analogous t o Bateson's notion formal  perfect  third  reason that  invariance,  modulating  that  create  proportions  timing  the  program  being  control  absolute  variations this  i n relative  study,  this  studies  maintained  found  reason,  parameter  of  relative  the necessity  timing.  Heuer and Schmidt 250  cycles  timing  of practice,  does n o t remain  account  1982).  duration,  tasks,  w h e r e a s when  i s that  few  this  varied.  timing  i snot  researchers  i n t h e development  i n the recent subjects  study  were g i v e n  invariant i n a transfer whether  In this  was a v a i l a b l e ,  duration  of practice  i n which  f o r t h e development  were  for slight  i t was c o n c l u d e d t h a t  However i t i s q u e s t i o n a b l e practice  once p u t i n t o  o f t h e movement t o  & Wilberg,  For instance, (1988),  be  feedback  invariant relative  i n movement p r o d u c t i o n  have c o n s i d e r e d  must  from t h e stimulus  the absolute  that  program  duration  timing  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 Another  time,  There has been evidence f o r  (Franks  when v i s u a l f e e d b a c k  subjects  might  timing.  Intervals  o f a motor  I f , however,  the duration  timing,  i n tracking  model  relative  i s not modifiable.  involved  o f o v e r a l l movement  The d u r a t i o n  used throughout  timing.  and an o v e r a l l  I n such a model  maintained precisely.  may n o t e x h i b i t  somehow b e  of relative  f o rthe present  fixed relative  timing  f e e d b a c k may  the expression  problems  parameter.  relative  i s that  are not perfect  with  symmetry i n  relations".  The  in  o f t h e "deeper  250 c y c l e s  by only  relative task. i s adequate  of invariant relative  timing,  7  or  f o r t h e d e v e l o p m e n t o f a motor p r o g r a m .  The d e v e l o p m e n t  o f t h e m o t o r p r o g r a m i s p r e s u m a b l y b a s e d on e x p e r i e n c e w i t h the environment such t h a t form o f o r g a n i z a t i o n might d e v e l o p . learning,  that  With i n s u f f i c i e n t  sufficient  practice,  neither  timing hypothesis, invariant  invariance.  within the  Thus,  timing  remains a v i a b l e  given despite  (1987) o f t h e i n v a r i a n t  t h e e v i d e n c e p r e s e n t e d above  relative  over-  surprising  S u b j e c t s have n o t b e e n  time t o develop that  c r i t i c s m by G e n t n e r  i s often  i t i s not  i s deemed t o e x i s t  p r o g r a m has n o t b e e n f o u n d .  that  appropriate  But, s i n c e  t h e problem o f adequate p r a c t i c e  the invariance that  recent  an  n o r t h e development o f t h e motor program, a r e  addressed, looked.  extensive  relative  indicates topic  of  investigation. The a s s u m p t i o n u n d e r l y i n g most invariant  relative  timing manifests  of the research  t i m i n g has b e e n t h a t ,  on a b e h a v i o r a l  level  invariant  i n t o t h e motor program.  Thus r e l a t i v e  invariant,  and i s s e e n t o f u n c t i o n  i n an open l o o p  But  overall  duration  i s a parameter l e f t  i n m o t o r programming  overall  theory,  d u r a t i o n parameter value  t h e way  i s determined  and  misleading  i n that  task  of assigning  care  o f by t h e programmer.  process  assigned be  i n a computer program t h e  and d e t e r m i n i n g p a r a m e t e r v a l u e s  i s occurring  fashion,  i n which the  The computer a n a l o g y may  case,  timing i s  free to vary.  has not been a d d r e s s e d . in this  relative  because i t i s  structured  while  on  I f one assumes t h a t  a  i s taken similar  i n humans, one i s l e d t o t h e d u b i o u s  8 conclusion  that  homunculus)  there  i s a computer  i n ones h e a d whose j o b i t i s t o d e t e r m i n e and  a s s i g n parameter v a l u e s . which is  a computer  t h e computer  misleading  (Carello  relative  timing,  program,  nor that  context  o f a motor  The p r e s e n t development movement. recent  relative  Heuer  most m o t o r  investigate which t h i s confusion control  1984).  timing  relative  In i n v e s t i g a t i n g o f a motor  functions within the  timing  out p a r t l y  in skilled  as a r e s u l t  invariant  of s k i l l e d  movement  & Schmidt,  1988).  action  i s different theorists  I see s k i l l e d  by a continuous  c a n be b o t h l i m i t i n g and  as t o w h e t h e r  programming  Because  of l i v i n g  human  of the  relative  As h a s b e e n p u t relative  than that  (e.g. Schmidt, a c t i o n t o be  interaction  of s k i l l  i s overt  1988).  characterized I chose t o  i n a tracking  and m e a s u r a b l e .  surrounding the issue of closed  h a s t o do w i t h t h e a s s u m p t i o n t h a t  timing  p r o p o s e d by  i n t e r a c t i o n with t h e environment,  t h e development  timing  ( G e n t n e r , 1987;  t h e present view o f i n v a r i a n t  skilled  interaction  program.  I t was c a r r i e d  f o r w a r d above,  control  s t u d y was d e s i g n e d t o i n v e s t i g a t e t h e  controversy,  human  et a l . ,  of invariant  1988;  dynamic  I am n o t a s s u m i n g t h e e x i s t e n c e  a characteristic  Heuer,  i n timing  i s characteristic  metaphor  o f t h e way i n  programmer/homunculus.  does n o t have t h a t  i t s environment, t h a t  systems,  in  question  feedback i n t e r a c t s w i t h t h e program  Because  is  The c r u c i a l  r e l e g a t e d t o the realm of the  with  programmer ( o r  task i n  Most  a n d open a system  of the  loop under  9 closed  loop  control will  corrections. can  also  act  such that modified this  This  i s not  rather  contention  (see  case however.  fashion  than being  discretely,  Pilot  appendix).  As  Feedback  i n modulating  modified  over time.  feedback  data  Powers  action, action  give  is  support  (1973)  to  has  out:  "This  ( d i s c r e t e model)  to  describing a closed  it  i s i n c o r r e c t ...  smoothly stimuli  As  environment,  (p.  the  as  there  on  studies this  of  the  is a  on  i t was  the  subject  continuously  quantification  were used  different  responses  but  a and  continually  continuous  timing  interaction  associated with  but  study  By  useful i n that interact and  stimulus  with  an  to  timing  control. that  evaluate  on  precise patterns.  r e l a t e d f o r m s o f movement i n order  of  not  environment  response  the  understanding  i t required  the  a  program,  have  relative  i t allowed and  with  motor  timing  gain  in  Coming out  the  studying  possible to  levels,  of both  in this  and  in  f e e d b a c k makes i n t i m i n g  t r a c k i n g p a r a d i g m was  motor  both  invariant relative  The  and  effects,  i s i n a tracking task.  contribution that  perceptual  and  organism behaves  relationship.  a tracking task,  causes  approximation  investigated relative  framework  in  Five  real  first  42)  no-one has  theoretical  focussed  of  manner, w i t h  i n which there  most o f  loop  c o n t i n u a l l y changing  yet,  context  is a natural  the  continuous  interacting."  the  always the  i n a continuous  continuously  pointed  e x h i b i t discrete  the  analysis performance  10 of the  subjects:  an  accuracy  and  overall  squared e r r o r ) ; reproduce the (within lead  p r e c i s i o n of the  a measure o f t h e  l a g index  gained  the  subject  subject's  an  regarding  a calculation  of the  of the  the  (Root mean  ability each  to  trial  response p r o f i l e s ) ;  a  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  subject's  c o r r e c t time;  information  indicating  movement c o n s i s t e n t l y d u r i n g  subject v a r i a b i l i t y  represents the  e r r o r measurement  ability  to produce the  response  harmonic a n a l y s i s t h a t  offers  the  response;  composition  of the  proportional duration  of the  at  and  time  b e t w e e n movement r e v e r s a l s . The  question  using  a training  given  extensive  (training) the  and  \ t r a n s f e r paradigm p r a c t i c e on  stimulus  and  sources  an  information  are  extensive  capable  have t h e different  base  timing  frequencies.  reproduce  two  as  both  a v a i l a b l e to  were removed.  paradigm.  a given  the  original  Three  Firstly,  waveform,  of t r a c k i n g , equally well, other  same r e l a t i v e  required to  under  in  c o n d i t i o n , i n which  information  p r a c t i c e on  to  different  were v i s u a l l y  i n p u t blanking  of v i s u a l  out  but  were  waveform  c o n d i t i o n , i n which  h y p o t h e s e s were t e s t e d u s i n g t h i s following  i n which s u b j e c t s  timing,  carried  tracking  response  subject,  these  T h i s was  a pursuit  and  explored  t h e n t r a n s f e r r e d t o waveforms i d e n t i c a l  duration.  conditions:  t i m i n g was  tracking a specific  t r a i n i n g waveform i n r e l a t i v e  overall  the  of i n v a r i a n t r e l a t i v e  subjects  waveforms waveform,  S e c o n d l y , when s u b j e c t s  (during input blanking)  which  the  but  are  original  11 and  v a r i e d base frequency  exhibit  invariant relative  waveform.  learned  put forward  performance  will  t i m i n g between r e v e r s a l s i n t h e  In a d d i t i o n , i n o r d e r  (originally is  waveforms, t h e i r  to test  i n the p i l o t  i n t e r m s o f i t s component  the  hypothesis  study) t h a t  a movement  frequencies,  subjects  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 w a v e f o r m s : t h e f i r s t contained  identical  component  frequencies  t r a i n i n g waveform, b u t d i f f e r e n t s e c o n d was an e n t i r e l y amplitude movement  and p h a s e r e l a t i o n s h i p s ) .  expect t o f i n d varied  only  waveform.  phase angles,  new waveform  i n t e r m s o f component  to that  and t h e  (different  frequency,  I f subjects  frequencies,  of the  then  learn a one w o u l d  a b e t t e r p e r f o r m a n c e on t h e waveform w h i c h  t h e phase angles,  t h a n on an e n t i r e l y  new  12  CHAPTER  2.  METHODS  Subjects Six u n i v e r s i t y deficits had  students  w i t h no  volunteered to p a r t i c i p a t e  previous  t r a c k i n g experience.  hand dominant  and  used t h i s  motor or in this  The  vision  study.  None  s u b j e c t s were  hand t o move t h e  had  right  joystick.  Task S u b j e c t s were r e q u i r e d t o move a j o y s t i c k controlled  a response  oscilloscope  screen.  stimulus  cursor  directly  above t h e  in  a series  Subjects  The  response  The while  d i s p l a y ) on  d i s p l a y ) which c u r s o r on  the  to  The  oscilloscope  right  s c r e e n was  j o y s t i c k was  moved  screen. comfortably  p l a c e d 50  supinated  being  and  forearm  subtended angle  and  follow a  screen  j o y s t i c k between t h e  w r i s t pronated the  their  an  appeared  o f h o r i z o n t a l movements a c r o s s t h e  o f them a t a v i s u a l l y  thumb.  (point l i g h t  s u b j e c t ' s t a s k was  (point l i g h t  s u b j e c t s h e l d the  plane  The  sat at a t a b l e with  supported. front  cursor  which  cm  o f 11.4 index  i n the  in degrees.  finger  and  coronal  moved.  Apparatus The  joystick,  (Hughes A i r c r a f t adapted  f o r use  an  industry standard  plotting  Company CONOGRAPHIC - 12 i n the  e x p e r i m e n t by  model  bypassing  joystick 6110)  was  internal  13 electronics filtered analog  within  30 v o l t  the  +2048  the  (+ 5 v o l t s )  joystick  along  displacement.  had  The j o y s t i c k  The X a x i s  into  the full  checked  to verify  order  from  displacement was s p r i n g  had free was  recorded. which  an e l e c t r i c a l  signal,  ( w i t h i n one movement.  control.  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 procedure.  A template  and t h e r i g h t t h a t was u s e d  (45 d e g r e e s )  was t h e d i s p l a c e m e n t  marked o f f .  to the left  output  of values  of center.  s t i m u l u s was p r e s e n t e d  using a digital  was  number o f d i g i t a l  to the right  A computer generated  the center  i n t h e experiment  that the displacement  each  w a s made i n a  (0 d e g r e e s ) ,  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  oscilloscope  + 5  Values  range o f j o y s t i c k  o f 45 d e g r e e s w i t h t h e l e f t  Each potentiometer  as  center).  to oscilloscope  displacement  had a zero  1/2 d e g r e e s ) ,  while  (a B o u r n s number 3 8 5 2 A - 2 8 2 - 1 0 3 A ) ,  joystick  joystick  ranging  (- 5 v o l t s ) ,  X co-ordinate displacement  with the following  range (22  Only  values  was a p p r o x i m a t e l y  being  0 - 1000.  the Y axis.  throughout  joystick The  day  w i t h a 12 b i t  a r e s i s t a n c e o f 1 0 , 0 0 0 Ohms, a n d w a s l i n e a r  percent) The  from  t o an  w a s r e s i d e n t i n a n IBM  t o -2048 v a l u e s  (zero v o l t s  potentiometer  transformed  board  were c o n v e r t e d  ranging  centered  (Labmaster)  of the joystick  t o -5 v o l t s  values  The  converter  was f e d b y a  and connected  The L a b m a s t e r gave d i g i t a l  v o l t a g e range  volts  The j o y s t i c k  power s u p p l y  whose d a u g h t e r  Microcomputer. from  split  to digital  resolution,  the joystick.  on t h e  equivalent t othe  14 digital  input  used to  maintain  stimulus  and  of  the  joystick.  1 cm  response cursors  and  precision  the  Fourteen  locations  chosen at rate  of  c o m p u t e r was  of  250  Hz.  locations,  the  on  four  the  A/D  tested  At  for  4.096 s e c o n d s .  0.008 v o l t s )  digital  values  (or  0.004 v o l t s ) .  locations of  the  of  to  the  0.47  j o y s t i c k was  The  digital  joystick.  range of  1,000  the  With the  joystick  joystick  was  less  than  0.7  0.7 mm  The  held  rest,  millimeters. was  not  Response  any  joystick  procedure.  joystick  was  of  the  never  of  a  4 than  2  deviation  over the  resolution  at  fourteen  less  standard  values  were  sampled  never exceeded  The  fourteen  the  full  range  values.  was  joystick  at  the  At  and  digital  joystick  experimenter h o l d i n g the  the  between the  d a t a was  joystick  (or  0.3  between  following  range of  each l o c a t i o n ,  range i n the  was  oscilloscope.  u s i n g the  values  from  the  signal  milliseconds.  digital  varied  displacement  interface  a c r o s s the  random.  second analog  of v e r t i c a l  v a l u e s were s a m p l e d e v e r y The  A  tested at  the  rest  with for  recorded  Thus any  the 40  seconds.  range of  the  r e c o r d e d movement  c o n s i d e r e d t o be  intentional  movement.  S t i m u l u s Waveforms S u b j e c t s were g i v e n t h e  following  eight  waveforms  to  track: W l ) T h e t r a i n i n g waveform was A/2  + 240  cos  (cot + 3/2  g i v e n by 71) + 120  the  cos  2  equation: (cot + 5/6  f(t) ic) +  = 60  15  cos  4  + 1/6  (cot  velocity  W h e r e cot  and t h e phase angle  The p e r i o d frequency Four  7t) .  of this o f 0.5  waveforms  as t h e t r a i n i n g  frequency  manipulated  i n radians.  with  a base  were  waveform,  such that  described however  by  the  the base  the following  waveforms  created:  W2)the  training  base W3)the  W4)the  training  training  training  Waveform waveform  o f 0.6  were  W6)This waveform  o f 0.7  a period  o f 2 4 4 8 ms,  and  a  a period  o f 1648  ms,  and  a  a period  o f 1448  ms,  and  a  Hz.  a transformation the phase angles  of the of the  training frequency  altered. by t h e e q u a t i o n :  3/2  7C) + 120  cos 2  Ji) w i t h  a period  o f 2048 and a b a s e  (cot  + 2/3  f(t)  = A/2  +  240  n) + 60 c o s 4 (cot frequency  of  Hz..  W 7 ) T h i s w a v e f o r m was equation: (cot  a  i s given  (cot +  1/4  and  Hz.  waveform w i t h  6 was  o f 3 2 4 8 ms,  Hz.  waveform w i t h  such that  components  0.5  o f 0.4  frequency  a period  Hz.  waveform w i t h  frequency  base  cos  o f 0.3  frequency  base W5)the  waveform w i t h  frequency  base  +  2 0 4 8 ms  angular  Hz.  same e q u a t i o n  were  the  i s expressed  w a v e f o r m was  of the transfer  was  represents  + 11/6  2 0 4 8 ms  f (t)  an e n t i r e l y  = A/2  + 230  7C) + 70 c o s 4  and a base  new  cos  (cot  frequency  waveform  (cot  + 2/3 o f 0.5  + 3/2  TC) + 1 3 0  7C) w i t h Hz..  given  by  cos 3  a period This  the  of  waveform  16 w a s t h e same a s t h e t r a i n i n g same b a s e  frequency,  frequencies, varied phase varied  same o v e r a l l and  a n d t h e same o v e r a l l  to create  amplitude  a different  repeated  topology  itself.  made u p o f c o m p o n e n t of  20 mm  2 Hz. the  t o 200  mm  Pursuit  than  the training  with  ranging  from  to subjects  and thus  0.5  Hz t o  on e a c h o f Because  perceptual  i n trackingi t .  Blanking  blanking.  response  A trial  began w i t h  on t h e s c r e e n ,  information,  thus  Following  two  only  o f t r a c k i n g i n which This  was u s e d  cycles  and t h e  information  this  there  the stimulus  as a w a r n i n g  20  stimulus  and e r r o r  were a v a i l a b l e t o t h e s u b j e c t .  the screen.  range  no  were u n a b l e t o use  1952)  I t was  an a m p l i t u d e  on e a c h t r a n s f e r d a y .  subjects  response were p r e s e n t e d  on  waveform,  waveform.  of p u r s u i t t r a c k i n g i n which both the stimulus  cycles  were  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  and input  information,  and  a random waveform b e c a u s e i t  and frequencies  (Poulton,  These  as t h e t r a i n i n g  frequencies  T r a c k i n g and Input  Each t r i a l tracking  frequencies.  w a v e f o r m h a d no c y c l i c i t y  anticipation  It  i n the amplitudes  T h e same w a v e f o r m w a s g i v e n  predictability,  range.  I t s p e r i o d w a s 40960 ms.  s i xt r a n s f e r days.  this  i t had t h e  a p e r i o d i c waveform w i t h t h e  range  W 8 ) T h i s w a v e f o r m was t e r m e d never  amplitude  waveform  o f t h e component  i n order  i n that  t h e same n u m b e r o f c o m p o n e n t  from t h e t r a i n i n g angles  waveform  were  remained  to the subject  17 that  they  trial.  In t h e  phase, that  w o u l d be  the  had  phase,  beginning  last  done i n t h e  and  error information.  the  trial  stimulus the  250  Hz.  was  The  equivalent  waveform. middle  trial,  required to  p r e v i o u s l y been t r a c k e d being  input blanking  p o r t i o n of the  s u b j e c t was  this  and  the  The  the  stage  input  reproduce the  i n the  waveform  pursuit tracking  time t o complete t h i s  i n duration to 10  the  blanking  absence of s t i m u l u s ,  middle  of  12  response, phase  cycles of  of  the  c y c l e s of p u r s u i t t r a c k i n g  s i x c y c l e s of input blanking  were s a m p l e d  at  Procedure In o r d e r  to motivate subjects  optimum l e v e l  a p r i z e was  achieved  the  last  of the  day  given  best  RMS  r o o t mean s q u a r e d  study.  of the  t r a c k i n g t h a t they  Over the extensive  course  trial,  of  15  days,  the  fifteen  p e r f o r m a n c e was  days o f t h e  evaluated  on  dependent measures.  subject's  this  form o f  Subjects  were  also  aspects  perform. given  t r a i n i n g waveform study, training  their  assessed  (Wl).  tracking  waveform  In a d d i t i o n , e v e r y  Each experimental  the  an  were  s u b j e c t s were  t r a c k i n g p e r f o r m a n c e was  t r a n s f e r waveforms.  by  subjects  phenomenological  were a s k e d t o  p r a c t i c e i n t r a c k i n g the  each of the  various  about the  who  e r r o r score  for that t r i a l .  questions  their  subject  (RMS)  A f t e r each t e s t  e r r o r score  asked i n f o r m a l  the  o f f e r e d f o r the  feedback about t h e i r performance i n the  overall  On  to perform at  using  third on  the  day seven  s e s s i o n began w i t h  a  18 practice into  o f 200 c y c l e s  4 blocks  block  o f 50 c y c l e s .  o f c y c l e s was  subjects  rested  the  next  block.  The  fifteen  training layout  days o f t h i s  tracking  the  consisted  and t e n c y c l e s  D a t a was  collected  eight  o f twenty c y c l e s  of input  and r e s p o n s e c u r s o r s blanking  In t h e i n p u t  f o r the duration  five  blanking  i n which  phase,  screen.  of the pursuit of the input data  cycles  was  i n order  5 e n t i r e r e s p o n s e c y c l e s were c o l l e c t e d .  r a t e was  250 Hz.  were  neither  on t h e  cycles  of 6 stimulus  on  of pursuit  n o r t h e r e s p o n s e were d i s p l a y e d  phase.  1 f o r the  test trials  c o l l e c t e d from t h e m i d d l e t e n c y c l e s  ensure that sampling  (See T a b l e  were g i v e n  t r a c k i n g phase and from t h e m i d d l e blanking  beginning  On t r a i n i n g d a y s i n a d d i t i o n t o t h e  i n which both stimulus  stimulus  a f t e r which  design.)  component, s u b j e c t s  Each t r i a l  each  s t u d y were made up o f n i n e  days and s i x t r a n s f e r days.  practice  divided  The t i m e t a k e n t o t r a c k  a p p r o x i m a t e l y two m i n u t e s ,  of the experimental  visible  T h e s e 200 c y c l e s were  f o r a f u r t h e r two m i n u t e s b e f o r e  T r a i n i n g Days:  Wl.  o f Wl.  to  The  19 ******************************************************  T a b l e 1.  Experimental  Design  200 p r a c t i c e  8 test  cycles  Wl  on Wl  I  X  2  X  X  3  X  X  DAYS 4  X  5  X  X  6  X  X  7  X  8  X  X  9  X  X  10  X  11  X  X  12  X  X  13  X  14  X  15  X  t r i a l s on;  W2  W3  W4  W5  W6  W7  W8  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  One t e s t  trial  consisted  o f 20 c y c l e s  followed  by 25 s e c o n d s o f i n p u t  of pursuit  blanking.  tracking  Transfer  days a r e  highlighted. **********************************************************  Transfer practice the  eight  Days:  component, waveforms  On t r a n s f e r d a y s i n a d d i t i o n subjects  were g i v e n  (Wl - W8).  one t r i a l  One t r i a l  t o the o f each o f  o f e a c h waveform  20  was  comprised  tracking  Data  and  of the input  two  Analysis  t h e pursuit  tracking  accuracy.  Poulton  of the  interval, is s  sum  i s the  the  value  intervals RMS  error  precise  has  response  for the  and  data  was  the  data  A  data  at each  (s-r) /  The file  substituted  p  1  2  the  number  of  Poulton  as  best  of  o f RMS  the  tracking"  error  scores  become more a c c u r a t e is indicative 1985;  written  of  Poulton, to  then  f o r a l l 1024  1024  the  RMS  study.  score with  with the  cycles of the the  1974).  of t h i s  p o s s i b l e RMS  and  learning  calculate  performance  mean o v e r  It  over.  adequacy  value  sampling  J / , where  i s the  were c o l l e c t e d  was  2  p  square  intervals.  t , and  lowest  d u r a t i o n o f two  points).  calculated.  error  t, r is  i n the  thus  the  interval  "overall  pursuit tracking  to determine  f o r the  as  been reccommended by  & Fishburne,  equipment,  [ £  on  response  error  i s sampled  s u b j e c t has  calculated  sampling  RMSE =  interval  decrease  that the  of the  at time  was  to determine  number o f  c o m p u t e r p r o g r a m was  present  value  at time  Wilberg  In order  (1024  the  in tracking,  (Franks,  rest  by  squares  f o r e v a l u a t i n g the  indicates  Error)  i n order  equation:  A  (RMS  ( 1 9 7 4 ) d e f i n e s RMS  that the  (1974, p . 3 8 ) .  A  data  stimulus value  response  measure  error  of the  divided  g i v e n by  error  i . e . pursuit  blanking.  Root mean squared  root  phases d e s c r i b e d above  joystick  stimulus data  stimulus values.  at  waveform  points  created i n which  the  this The  was mean RMS  21 p r o g r a m was value  o f 0.3 RMS  data  then  r u n on t h i s  data points  Error  was  also  data f i l e  o r 0.45  on t h e input  i n o r d e r t o compare p e r f o r m a n c e  waveforms d u r i n g i n p u t b l a n k i n g . n o r m a l i z e d i n terms  and  of i t s s p a t i a l  i n terms  order t o account  subject  (Vossius,  cycle  symmetry.  The  and  T h i s was spatial  shifting  the response  directions The  value for that  Variability  calculated within based  The  trial  intervals,  at  [ E  =  variability  a g i v e n time  which  plotted  against  interval  intervals  f o r the p u r s u i t  score.  the  then the  backward of 4  ms.  was  tracking  phase  (ten from each  The  J  i n order to c a l c u l a t e  At each  o f t h e 512  (sd) o f t h e t e n  1  trial) a  sampling  response  following equation:  ^ , where r i s t h e  response  and p i s t h e number o f i n t e r v a l s s t a n d a r d d e v i a t i o n v a l u e s were  time y i e l d i n g  waveform v a r i a b i l i t y  to  can  a c h i e v e d by  s u b j e c t ' s response  another  - r) ^ / 10  r i s sampled.  that  as t o d e t e r m i n e  c a l c u l a t e d u s i n g the r  drift  f o r w a r d and  by  a standard deviation  (Mean  done i n  from F r a n k s , W i l b e r g & F i s h b u r n e  upon one  d i s p l a c e m e n t s was S.D.  each t r i a l  duration,  are v i s i b l e  T h i s was  displacement-time curves  were s u p e r i m p o s e d within  o f 20 ms  o f each  on a p r o c e d u r e  (1982).  cycle.  i n both the  for a total  input  n o r m a l i z e d r e s p o n s e was  compared t o t h e s t i m u l u s i n s u c h a way l o w e s t RMS  of  of i t s o v e r a l l  s t i m u l u s nor response 1965).  blanking  on t h e v a r i o u s  Each  f o r the temporal  o c c u r when n e i t h e r  RMS  mm.  calculated  b l a n k i n g was  p r o d u c i n g an  a profile  for a given subject  of the  within  on a g i v e n  trial.  at  22 The an  mean o f t h e index  512  of the  sd's  was  calculated  and  this  within subject v a r i a b i l i t y  (v)  was  used  for a  as  given  trial. Variability and  tracking  studies  measures have been used  studies to evaluate  have  found  that  consistent  as  particular  measure has  studies,  (e.g.  Glencross, A  The  score  and  cycle  the  the  i n the  duration of  values  (sampled  standard time.  use  of  & Fishburne,  more  this  phenomenon i n  recent  1982;  joystick  program  Data  collected  remained  at  250  Hz)  into  rest.  of these  1 digital was  index  0.3 was  l e d or  time  another.  values.  The  digital used to lagged  cross-correlation  The ten  and  A/D  ten  cycles. the  digital  during  profiles  at  each  which values,  each p o i n t  deviation values mean o f t h e s e  as  joystick  From t h e s e  were c a l c u l a t e d standard  the  during  t h a t were c o l l e c t e d displacement  system  itself,  2.048 s e c o n d s  at  lowest  e r r o r i n the  e a c h c y c l e was  subject A  any  the  f o r each of the  values  Lead-lag  tracking.  Many  becomes  same l o c a t i o n  range  0 and  which the  this  variability  deviation values  deviation  and  to determine  s u p e r i m p o s e d u p o n one  The  between  Wilberg,  joystick.  were compiled  were then  reflected  possible given  i n which the  remained  of p r a c t i c e ,  made i n o r d e r  including  converter,  a s u b j e c t ' s response  Franks,  was  variability a'whole,  acquisition.  1979).  test  cycles  a result  skill  i n motor l e a r n i n g  in  was standard  values. determine the  the  extent  to  stimulus during pursuit  coefficient  was  calculated  23 using of  the  512  s t i m u l u s and  points),  with  the  response  ten  milliseconds.  signal  a Pearson  between which  the  response  with  The  For  to determine  i n d e x has  & Wilberg, 1982). reflects  specific leading  the  location or  waveforms  from  analysis the  input  The  information:  i)the  the  iii) iv)  analysis  amplitude,  and  (1967)  among t h e  was  was  the  l a g of  1982;  measure  i s that i t  than  the  Franks  the  subject  was  1974). to analyze the  blanking  phase  into  yielded  response  component the  following  frequencies of the component  angle values of these  Harmonic  at  tracking  or l a g , rather  used  component  of the  time  l a g of  Franks,  of this  Harmonic a n a l y s i s  the period  The  to evaluate the  1982);  amplitude values of these  the phase  study  lead  was  coefficient  stimulus during  limitation  (Poulton,  frequencies.  ii)  or  of  response  response  i n the waveform at which  lagging  Harmonic  lead  been used  i n Franks,  average  intervals  calculated.  the  and  stimulus.  to the  The  i n t i m e by  s t i m u l u s and  composed  constant  correlation  was  between  (cited  (each  advancement o f t h e  response  relative  1957  (Bennett,  each  respect to the  lead-lag  waveforms  stimulus being held  product-moment  used  response  response  b e i n g advanced  correlation was  only  the  s t i m u l u s and  greatest  the  signal  the  response.  frequencies.  component  frequencies.  waveform. was  used  to determine  phasing of a c y c l i c first  o f human movement.  t o use  the  waveform. harmonic  In the e a r l y  frequency,  Bernstein  analysis  1900's,  he  i n the  performed  experiments  i n w h i c h he  movements.  The  then analyzed this  movement p a t t e r n s  i n t o component  a n a l y s i s has  F r a n k s and Romanow  (1983) on and  performance.  present  input blanking  composition  of the  those  relative  timing  stimulus.  the  p e r i o d of the  the  The  duration  same as  stimulus The  the  Marteniuk  overall  and  by  &  by  The  was  the  phase angles  of  r e s p o n s e were compared t o determine whether  p e r i o d of the stimulus  were  data,  Harmonic a n a l y s i s  r e s p o n s e was  o f one  RT  c o n d i t i o n to determine  i n order  of the  joints  stabilometer  r e s p o n s e waveform.  stimulus  the  overall  study,  components o f t h e  of the  (1971) on  (1968) i n m e a s u r i n g  In t h e  frequency  Green  various  More r e c e n t l y  movement t r a j e c t o r i e s ,  used i n the  the  various  (1982) i n t r a c k i n g , by arm  Pew  of the  frequencies.  b e e n u s e d by  Wilberg  Richardson  filmed subjects performing  equivalent  r e s p o n s e was  i n order  the  to that  of  compared  with  t o determine whether  c y c l e of the duration  with  r e s p o n s e waveform  o f one  c y c l e of  the  was  the  waveform. h a r m o n i c a n a l y s i s was  described  i n Lowry and  periodicity  of the  using  an  equal  u n i t s and  Hayden  waveform  autocorrelation.  ...  xp,  yO,  y l / y2,  was  a p p l i e d over the  equations:  with ...  1)  their yp.  a  Q  (1951  324 7C)  a method  - 328). was  T h i s waveform was  The  determined divided into p  p o i n t s were l a b e l l e d  corresponding  The  xO,  xl,  ordinate values  being  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  period yielding  = 2/p  pp  ( p e r i o d =2  each of these  x2,  c a l c u l a t e d b a s e d on  TC y  r  2)  a  n  the = 2/p  following n y  r  cos  nx  r  3)  component harmonic  entire  = A /2  f(t)  = A /2 0  + 7C C  n  angle  These phase  following order  to test  frequencies. waveform which calculating  the accuracy  a n RMS  error  error  n  calculating  marking  reversals.  these  experimenter o f each  into  went t h r o u g h reversal.  analysis  component a  waveform by  into  on t h e  This  response  during input blanking intervals  by  reversals.  t o a i dt h e experimenter  c y c l e was p r e s e n t e d  using  resynthesized into  between adjacent  i n order  harmonic  o f t h e harmonic  were c a l c u l a t e d  was d e v e l o p e d  provided the  mm.  c y c l e was d i v i d e d  t h e time  2 n  n  waveforms t h a t t h e s u b j e c t s generated Each response  B  between t h e two waveforms.  o f 1.8  Durations  +  2 n  B /A .  was a n a l y z e d  were then  function:  were determined  was c o m p a r e d t o t h e o r i g i n a l  t h e RMS  Interval  values n  These data  s i n ncot  among v a r i o u s  t a n <|> =  itself  n  values which  angle  equation:  s t i m u l u s waveform  point  3 gave t h e  w h e r e Cn = A  n  timing relationship  components.  each  of the cosine  i n terms o f a cosine  c o s (ncot-(j> )  t h e phase  n  produced  cos not + B  n  was e x p r e s s e d  (|) r e p r e s e n t e d  the  coefficients  o f t h e s i n e component o f t h e waveform  + 7C A  0  equation  necessary  r  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 :  This  In  s i nnx  r  o f t h e waveform, w h i l e e q u a t i o n coefficients  f(t)  the  = 2/p K y  n  2 gave t h e harmonic  Equation  The  b  The d i s p l a c e m e n t on a computer each response  time  screen.  A  program  i n precisely profile The  c y c l e marking  The c o m p u t e r t h e n  of  recorded  the  the X  26  and  Y coordinates of that point.  dimension. to the  Y represented  calculate  an i n t e r v a l  beginning  coordinate  was t h e n  duration  of the entire  duration  by t h e o v e r a l l  interval  occurred.  procedure to  value the  the  Pursuit Waves  (8)  contrasts  the  waves  waves  durations.  displacement,  In order  the Y coordinate was s u b t r a c t e d  a t t h e end o f that i n t e r v a l . was t h e n  expressed  by d i v i d i n g  from The  as a p r o p o r t i o n o f  the interval of the cycle i n  occurred.  Tracking: (6)  and repeated f o rboth  factor.  factor  u s i n g t h e same  Analysis  by Days  were p l a n n e d  the interval  calculated  b y t h e maximum d i s p l a c e m e n t  which t h e i n t e r v a l  Statistical  were  of the interval  maximum d i s p l a c e m e n t  displacement  interval  as a p r o p o r t i o n o f t h e o v e r a l l  f o rt h e i n t e r v a l  an i n t e r v a l  displacement  The  duration of the cycle i n which the  Displacements  Y coordinate value  interval  was s u b t r a c t e d f r o m t h e X  c y c l e by d i v i d i n g  at the beginning  In order  duration, the X coordinate value at  expressed  as t h a t used  calculate  dimension.  a t t h e end o f that i n t e r v a l .  duration  Interval  the spatial  of the interval  value  X represented t h e temporal  were  1) T h e t r a i n i n g  RMS  error  were  ANOVA w i t h p r e - p l a n n e d measures on b o t h t h e days  The s e v e n as  data  factor  subjected to a orthogonal  factors.  Contrasts  (trend a n a l y s i s ) and  contrasts performed  on t h e  follows:  waveform  (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  speed waveforms 2)  The s l o w w a v e f o r m s  waveforms  slowest  5)  The f a s t e s t  pooled were  together.  compared w i t h  the fast  (W2) w a s c o n t r a s t e d  with  t h e second  (W3).  waveform  (W5) w a s c o m p a r e d w i t h  t h e second  w a v e f o r m (W4).  The w a v e f o r m  components entirely  W5)  (W2 & W3)  waveform  waveform  fastest  W4,  (W4 & W 5 ) .  3) T h e s l o w e s t  4)  (W2, W3,  i n which t h e phase angles  were  altered  of the  (W6) w a s c o n t r a s t e d  frequency  with the  new w a v e f o r m (W7).  6) W l , W2,  W3,  W4  & W5 p o o l e d  were  contrasted  with  W6  & W7  pooled. 7)  The random  waveform  (W8) w a s c o n t r a s t e d  with  W1-W7  pooled. Input Blanking: interval waves  duration data  (5) b y i n t e r v a l s  ANOVA w i t h used  trend  i n this  Both the interval from day f i f t e e n (5) b y c y c l e s  analysis  analysis  displacement were  subjected  (3) r e p e a t e d  on a l l f a c t o r s .  and to a  measures  The w a v e f o r m s  were waves one t h r o u g h  five.  28 CHAPTER 3. RESULTS  Part  One - Pursuit  Tracking  S u b j e c t s were g i v e n e x t e n s i v e p r a c t i c e tracking  a specific  waveform,  wl) w h i c h h a d a b a s e  i n v e s t i g a t i o n was perform  p e r i o d i c waveform  (the t r a i n i n g  frequency  o f 0.4 9 Hz..  t h e q u e s t i o n "would s u b j e c t s be  e q u a l l y w e l l on waveforms  relative  daily in  i n terms o f t h e i r base f r e q u e n c y ? "  answer  question, pursuit  within using  I.  subject v a r i a b i l i t y ; a cross-correlation  (calculated  function).  RMS  d a t a were s u b j e c t e d t o a Waves(8) by D a y s ( 6 ) orthogonal  factors.  ANOVA  c o n t r a s t s and r e p e a t e d m e a s u r e s  C o n t r a s t s were p l a n n e d  ( t r e n d a n a l y s i s ) and t h e waves  A) Dav  f o r both  on  t h e days  factor.  15  Of t h e RMS values  orthogonal eight  and l e a d - l a g i n d e x  error;  Error  factor  RMS  RMS  was  RMS  with planned both  In o r d e r t o  t r a c k i n g performance  e v a l u a t e d u s i n g t h r e e dependent measures:  the  b u t were  transformed this  able to  which maintained  t i m i n g o f t h e t r a i n i n g waveform,  Under  data,  on t h e l a s t  the f i r s t  t o be c o n s i d e r e d w i l l  day, d a y 15.  Seven  planned  c o n t r a s t s were p e r f o r m e d on t h e RMS  waveforms  f r o m day  15:  be t h e  values  of a l l  Figure R o o t Mean S q u a r e d E r r o r  1.  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 200  WAVEFORMS W1  .49  Hz  -4-  W2  .31  Hz  -*-  W3  .41  Hz  - B -  W4  .61  Hz  W5  .69  Hz  W6  .49  Hz  W7  .49  Hz  W8  Random  0  1 R M S Error in u n i t s of  1/10 mm  4  7 10 Transfer Days  13  15 o  31 In t h e f i r s t  c o n t r a s t , RMS  v a l u e s on t h e t r a i n i n g  (wl) w e r e c o m p a r e d w i t h t h e v a r i e d s p e e d waves w5)  pooled.  p=0.002.  T h i s c o n t r a s t was  significant  Subjects, t h e r e f o r e , performed  on v a r i o u s s p e e d s o f t h e t r a i n i n g  (w2,  this  w3,  significantly  waveform  (M =  original  and  different  data  wave.  w e l l on t h e two  faster  waveforms;  s l o w e r waveforms  Thus t h e  as t h e y d i d on w l , on w h i c h  but  s u b j e c t s performed  (on w h i c h  t h e y had  t h e y had  on  slower  s l o w e r waves w e r e t h e same as e a c h o t h e r  than the  practice)  v a l u e as t h e o r i g i n a l  (M  itself  (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  waves h a d t h e same RMS  worse  36)  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  l a s t day  w4,  F(1,5)=32.3,  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 = 30).  wave  as  minimal  extensive  training The w i t h w4  second c o n t r a s t c o m p a r e d w2 and w5  (the f a s t  w e r e f o u n d t o be (M = 41.5) performed did  The w3 RMS  waves  The  (as m e a s u r e d by RMS  s l o w e s t wave).  F(l,5)=8.0,  than the fast  waves  they  error).  T h e r e w e r e no d i f f e r e n c e s i n 1.0..  w i t h w5.  RMS  values  (M = 4 5 ) , w e r e s i g n i f i c a n t l y  the second  p=0.036.  30.5)  ( t h e s l o w e s t wave) w i t h  waveforms F ( l , 5 ) <  waveform  t h a n t h o s e on w4,  waves)  (M =  b e t t e r on t h e s l o w waves t h a n  f o u r t h c o n t r a s t c o m p a r e d w4  the fastest  s l o w waves  different  t h i r d c o n t r a s t c o m p a r e d w2  v a l u e s on t h e two  (the slow  p=0.032, m e a n i n g t h a t s u b j e c t s  significantly  (the second  The w5,  significantly  F(l,5)=8.7,  on t h e f a s t  waves).  and w3  fastest  waveform  (M =  on  higher  38),  32 The  fifth  contrast  speed waveforms)  with  waveforms).  values  RMS  significantly F(l,5)=66.7, accurately  lower  base  frequency  that  v a r i e d the  frequencies  subjects two  had  The  that  of  W7  to  The  -  be  wl  (w2  & w3)  pooled  than  on  two  of  W6  they  0.61  and  w7,  waveforms  component  1,  d i d on  and  in  not (wl)  w6  did  and  and  speeds, 0.69  only  the  w7,  w4  &  they w5,  Hz r e s p e c t i v e l y ,  which both  had  base  RMS  values  Hz. c o m p a r e d w6  different  not  find  w7  were  the  p  training  entirely  new  c o m p a r e d w8  significantly  F(1,5)=497.2,  w7. <  (a w a v e f o r m t h a t  as  (an  with  F(1,5)=0.1,  w6  frequencies  w8  varied only  wave  faster  group  frequencies  i n Figure  training  speed  more  t r a c k i n g the  (the p e r i o d i c waveforms)  on  second  performed  component  seen  the  seventh c o n t r a s t - w7  while  the  frequencies  do  the  varied  were  waveforms t h a t  than  can  t r a c k than  values w7  As  were not  on  (the  constant  group  subjects  v a r i e d the  0.49  (the  first  values  pooled  r e l a t i o n s h i p s among t h e  sixth contrast  subjects  easier  RMS  or  performed  same c o m p o n e n t  with  RMS  Thus  phase  waves  base  they  and  the  p e r f o r m b e t t e r on  frequencies  W6  that  p e r f o r m e d b e t t e r on  which than  on  - w5  pooled  t r a c k i n g the  (w7).  slower  also  & w7  ( w l - w5)  (w6)  themselves  w6  p<0.001.  while  compared wl  p<0.001.  1.0,  on  indicating  contains  waveform)  the any  waveform).  (the  random  pooled.  higher  than  As  waveform) expected  those  on  wl  Table 2 Waves * Days I n t e r a c t i o n s : SOURCE  SS  * D  W  RMS  Error.  DF  SS%  35,  MS  F  P  769.8  7.15  0.001  26, 944.1  100.0% 1.7% 2.9%  1, 5 1, 5  453.4 898.6  4.04 6. 61  0.101 0.050  24.2% 5.6%  1, 5 1, 5  6510.5 1507.7  104 .5 11. 6  0.001 0.019  175  W ,  *  W  *  DQ  453.4 898.6  W  *  D DQ  6510.5 1507.7  DL DQ  525.7 452.7  1.9% 1.7%  1, 5 1, 5  525.7 452.7  30.17 31.47  0.003 0.002  L  W o * W , *  C3 w ^C3 w ^04 w w VV  * * D DQ * * D C5 * DQ  774.7 0.4  2.9% 0.0%  1, 5 1, 5  774 .7 0.35  6.83 0.00  0.047 0.948  85.9 3698.4  0.3% 13.7%  1, 5 1, 5  85. 9 3698.4  0.39 35.9  0.560 0.002  C6 * D C6 * DQ  1992.8 94.8.  7.4% 0.4%  1, 5 1, 5  1992.8 94.8  6.56 0.27  0.051 0.625  18.2% 3.4%  1, 5 1, 5  4905.7 908.8  17.8 4.21  0.008 0.095  D  quadratic  L  c5  W  W W  W o *  w  L  L  D * DQ L  c  x  4905.7 908.8  = contrast  one  D  L  = days l i n e a r  Q  = days  34  B)  Day  1 t h r o u g h Day  In  order to determine  improvement  account  will  of these  interactions The the  be  will  be  improved  faster  i n slope  evident  i n Figure  steeper  slope 2  from  with  was  stronger waves  between the but  day  there  w6  quadratic  was The  to  different  change  days  effect  component. day  one  progress  i n Figure  slow  pooled)  over  days  of contrast  to  interaction  of  and  days can  i s also  due  component fast  be  of the  days  waves.  The  f o r the  seen, fast  the  F(1,5)=11.6,  effect  f o r the  5  ( w l - w5  I t i s apparent  On  t h e s e waves t h e r e  is fairly  primarily  days q u a d r a t i c was  wl  t h r o u g h w5  four.  slow waves  The  slow  As  on  t o day  and  there waves  fast  was  a  than  waves.  with  p=0.002.  This  significant  of the  compared  slow waves.  10.  1.  results.  significant  the  t o be  between the  of the  waves  quadratic  component  interaction  F(1,5)=35.9,  the  detailed  fast  fast  1 t o day  i n slope  f o r the  & w7  that  appears  a  days  significant  text  d a y s l i n e a r was  of  t h e waves by  gives  the  rates  (the slow waves  d a y s q u a d r a t i c was  i s apparent  greater  2  rate than the  1,  21  i n the  indicating  p=0.019 r e v e a l i n g t h a t effect  Only  o f contrast  p=0.001  contrast  Table  addressed  waves) w i t h  at a  waveforms,  interactions.  F (1,5)=104.5,  difference  differences i n the  examined.  interaction  fast  the  amongst t h e v a r i o u s  interactions  to  15  W6  linear  and  has  w7  from  from  a strong  pooled  significant Figure  day  one  1 that  the  quadratic  i s a l a r g e drop show no  compared  such t o day  i n RMS  drop.  from  Their  fifteen.  35  The pooled)  interaction  o f contrast 7  (w8 c o m p a r e d t o w l - w7  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.  Over t h e f i f t e e n  days,  subjects'  performance  showed g r e a t e r improvement on t h e p e r i o d i c the  random waveform; as F i g u r e 1 i l l u s t r a t e s ,  waveform  (w8) h a d a m o r e s h a l l o w s l o p e t h a n  waveforms  II.  Within  w8) f r o m  s c o r e s were  cycles  were used  values  variability  from  data p a r a l l e l e d  from  this  pattern  closely  F(1,5)=4.2,  p=0.095.  significantly variability  data this  contrast  from  than  o f 10  t h e ANOVA o n t h e from t h e  The o n l y c o n t r a s t  waves.  that  t h e slow  I n t h e case o f  was n o t s i g n i f i c a n t  Thus t h e s l o w waves  different  profiles  was c o n t r a s t 2 i n w h i c h  the fast  are not  waves  on t h e  measure.  As F i g u r e 2 i l l u s t r a t e s , eight  time  the results  3).  were c o n t r a s t e d w i t h t h e f a s t  the v a r i a b i l i t y  (Variability  R e s u l t s from  (seeTable  orthogonal  t h e mean o f 5 1 2 s t a n d a r d  the displacement  tracking.)  ANOVA o n t h e RMS d a t a  waves  ( w l , w2, w3, w4, w5, w6, w7,  i n t h e RMS ANOVA.  c a l c u l a t e d by t a k i n g  of pursuit  deviated  d i d the periodic  subjected t o a repeated  d a y 1 5 , u s i n g t h e same p l a n n e d  that  s c o r e s were deviation  t h e random  Subject V a r i a b i l i t y  m e a s u r e s ANOVA o n a l l w a v e f o r m s  contrasts  on  (wl - w7).  Variability  and  waveforms than  subjects'  w a v e f o r m s were more v a r i a b l e t h e y were  later  i n learning  early  responses  on a l l  i n learning  (day 1 5 ) .  ( d a y 1)  In considering  36  Figure Mean o f 512  standard deviation  time p r o f i l e s  o f 10  cycles  waveforms o v e r  2. v a l u e s from the  of pursuit 6 transfer  displacement  tracking days.  for 7  VARIABILITY AS A FUNCTION OF PRACTICE  38 both that  the v a r i a b i l i t y  a n d t h e RMS  as s u b j e c t s became more a c c u r a t e  variable  i n their  Table  3  III.  w7,  from  responses  tracking  and w8).  behind  20.29 4 .23 1.66 8.87 26.23 2.03 169.47  On  Figures  lagged  5 5 5 5 5 5 5  1, 1, 1, 1/ 1, 1/ 1/  3 a n d 4,  behind  o f a l l waveforms the faster  days o f t r a i n i n g ,  0.006 0.095 0.254 0.031 0.004 0.213 0.001  on d a y one t h e  the stimulus during the ( w l , w2,  waves,  w3,  v a r i o u s speed waveforms  lag  point.  training Responses stimulus  By  day  at the zero  waves  ,w4  a n d w5,  7 and 5 m i l l i s e c o n d s on day  The v a r i a b i l i t y a l l waveforms  lagged  moved n e a r e r  waveforms) were faster  m a k i n g t h e mean l a g v a l u e s  zero  a n d w3  (the  lag point. the  15.  as  responses  learning  from  day  of  the  lagged  of the l a g of the subjects'  ( F i g u r e 5) d e c r e a s e d  w6,  on a l l f i v e  o n w l , w2,  on t h e two  progressed,  ( w l - w5)  w5,  Over t h e  15, t h e r e s p o n s e s  and slower  by  w4,  the responses  subjects' responses  the  for  P  t h e s t i m u l u s by t h e g r e a t e s t amount.  fifteen  less  Index  i s evident  subjects'  a l s o became  DF  F  Lead-Lag  pursuit  they  ANOVA T a b l e V a r i a b i l i t y Planned Contrasts Day 15  Wl vs W2-W5 W2 & W3 vs W4 & W5 W2 vs W3 W4 vs W5 W1-W5 vs W6 & W7 W6 vs W7 W8 vs W1-W7  As  i t i s evident  response.  CONTRAST 1) 2) 3) 4) 5) 6) 7)  results,  15  more  39  Figure The  lead-lag the  index  stimulus  as  of the  3.  subjects'  a function  responses r e l a t i v e  o f p r a c t i c e f o r wl  -  w5.  to  LEAD-LAG AS A FUNCTION OF PRACTICE  41  Figure The  lead-lag  index of the  stimulus  4.  subjects'  as a f u n c t i o n  respones  relative  fo p r a c t i c e f o r w6  -  w8.  to  the  LEAD-LAG AS A FUNCTION OF PRACTICE  43  Figure The  standard  subjects'  deviations  responses  of  relative  5. the  to  lead-lag  the  index  stimulus  for  of wl  the -  w8.  VARIABILITY OF LEAD-LAG SCORES  1  4  7  Transfer  10  Days  13  15  45 reliable  than  t h e mean v a l u e s  f r o m day 1.  random waveform e x h i b i t e d much g r e a t e r throughout  variability  a n d showed t h e g r e a t e s t d e c r e a s e  over  the f i f t e e n  Part  Two - Input Several  R e s p o n s e s on t h e  in variability  days o f t r a i n i n g .  Blanking  d e p e n d e n t v a r i a b l e s were u s e d  i n order t o  e v a l u a t e p e r f o r m a n c e on t h e i n p u t b l a n k i n g d a t a I)  I n t e r v a l durations expressed overall  II)  duration  (an i n d e x  I n t e r v a l displacements maximum d i s p l a c e m e n t  on Day 15.  as a p r o p o r t i o n o f t h e  of relative  expressed (an i n d e x  timing).  as a p r o p o r t i o n o f t h e  of relative  displacement). III)  C y c l e d u r a t i o n or p e r i o d o f the response wl  - w7  (the p e r i o d i c  IV)  R o o t Mean S q u a r e d  V)  Frequency composition  I.  Kinematic  Interval  Error. o f the response  repeated  analysis).  o f the response  waveforms.  f r o m t h e i n p u t b l a n k i n g d a t a (day  i n o r d e r t o determine whether  a consistent proportional duration  subjects  across  i n s t a n c e s o f a g i v e n movement i n t e r v a l .  experiment, one  durations  were a n a l y z e d  maintained  waveforms  Durations  Interval 15)  profiles  from  waveforms).  ( c a l c u l a t e d u s i n g Harmonic VI)  waveforms  reversal  a movement i n t e r v a l t o an a d j a c e n t  In t h i s  was d e f i n e d a s t h e t i m e  reversal  (or stop)  of the  from  46  Figure Waveforms by  intervals  6.  interaction duration  for proportional  data.  interval  Di/T as a function of Waveforms (collapsed over cycles)  X X  -  •  m  •  v  -  — 6  + JJC  W1 .5Hz  - a -  .  J^.  yp?  W2 ,3Hz  W3 ,4Hz  W4 ,6Hz  W5 .7Hz  Waveforms ——  Interval 1  —I— I n t e r v a l 2  •  Interval 4  Interval 5  _  a  _  Interval 3  48  Figure 7 . Intervals  by  cyles  interaction for proportional duration  data.  interval  Di/T as a function of Cycles (collapsed over waveforms)  -  ffl ^  a/  A  1  1  d  c2  My  1  c3  Cycles ~~*~  Interval 1  —  ~ ~  Interval 4  - x  B  r— -  Interval 2 Interval 5  Interval 3  50  Figure Proportional  interval  durations  duration  8. as  a function  for subject  2.  of  overall  Subject 2  Day 15  Waves 1 - 5  D i / T (interval a s p r o p o r t i o n of T in % 100r x -  x-^iC-X<  - j y £  80  x  x  x__  X  • Pff-  T L j »  ^  D  -  ^  -  -  ^  g  -  60 40  ^  ir*  ^ F T T  TT  ^  20  •  0 1300  1800  2300  2800  3300  •  3800  T ( o v e r a l l d u r a t i o n in m s ) —  intervaM  - ° -  Interval 4  —Interval  2  "*"  Intervals  Interval 5  Cn  52 movement p a t t e r n . contained 21%,  five  such i n t e r v a l s with  duration  o f a response  dividing the interval  that  duration  cycle  i n which t h e i n t e r v a l  Table  4  ANOVA T a b l e  The subjected  interval  t o a waves(5)  m e a s u r e s ANOVA w i t h waves main e f f e c t  The  duration o f  occurred. Durations DF  1 .58 95. 60 0.79 0 .44 0.06 0.07 0.54 0.82 1.33 0.89 0.95 proportional  P  4, 4, 16, 1, 1, 1, 1, 2, 8, 8, 32,  durations  16 16 64 4 4 4 4 8 32 32 128  0.227 0.001 0.693 0 .544 0.821 0.805 0 .504 0.475 0.266 0.534 0 .557  on d a y 15 were  * intervals(5) * cycles(3)  trend  a n a l y s i s on a l l f a c t o r s .  (see Table  repeated The  4) was n o n - s i g n i f i c a n t  F ( 4 , 1 6 ) = 1 . 5 8 , p=0.23, as e x p e c t e d .  Because a l l i n t e r v a l  durations  of the overall  were t a k e n a s p r o p o r t i o n s  when t h e d a t a  were c o l l a p s e d o v e r t h e f i v e  mean i n t e r v a l  duration  duration.  duration,  intervals, the  became i n a l l c a s e s 20% o f t h e t o t a l  A n o n - s i g n i f i c a n t main e f f e c t  m a t t e r what t h e a c t u a l i n t e r v a l reason,  of  was c a l c u l a t e d  by t h e o v e r a l l  F  WAVES INTERVALS Wl Wl (1,1) Wl (1,2) Wl (1,3) Wl(1,4) CYCLES WC IC WIC  durations  duration.  interval  Interval  SOURCE  waves 1 t o 5  proportional  17%, 10%, 16% & 35% o f t h e o v e r a l l  proportional by  Each o f t h e stimulus  durations  was e x p e c t e d no values.  For this  i t was t h e 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 evaluating  Introduction  p.2).  the relative  timing  h y p o t h e s i s (see  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  significant  interval  F ( 1 6 , 6 4 ) = 0 . 7 9 , p=0.693.  durations,  therefore,  a graphical  representation  interaction  see  waves(linear)  Figure  and  to the  The  the  invariant.  invariant relative  i n d i c a t i n g that  the  intervals interactions > 0.50), t h u s  timing  when t h e  d a t a were c o l l a p s e d  lending  hypothesis.  c y c l e s were t h e  proportional  o v e r waveforms and  interval  (For  intervals  In a d d i t i o n , b o t h  (in both cases p  mean p r o p o r t i o n a l  The  proportional  c y c l e s main e f f e c t F ( 2 , 8 ) = 0 . 8 2 , p=0.475 was  significant duration  waves by  w a v e s ( q u a d r a t i c ) by  were n o n - s i g n i f i c a n t support  a p p e a r t o be  of the  6).  The  durations  non-  interval  intervals,  from the  three  same.  waves by  cycles  i n t e r a c t i o n was  non-significant  F ( 8 , 3 2 ) = 1 . 3 3 , p=0.266 i n d i c a t i n g t h a t  when t h e  interval  over i n t e r v a l s , the  duration  differences constant The  d a t a were c o l l a p s e d  between waveforms  over the  three  i n t e r v a l s by  proportional  (actually equality)  was  cycles.  cycles  i n t e r a c t i o n was  non-significant  F ( 8 , 3 2 ) = 0 . 8 9 , p=0.534 i n d i c a t i n g t h a t  when t h e  interval  o v e r waveforms,  duration  differences  d a t a were c o l l a p s e d  among t h e  c y c l e s were c o n s t a n t representation Although is for  i t has  three  been s u g g e s t e d  this  cycles.  i n t e r a c t i o n see  calculate regression  each i n t e r v a l , subject  i n t e r v a l s under each of the  over the  of t h i s  necessary to  within  five  i s not  variability  proportional  For  Figure  (Gentner, lines  a  enough.  three  graphical  7. 1987)  that i t  f o r each  necessary provided  i s low  the  (For  an  subject  that  the  example  54 of r e g r e s s i o n l i n e s  fitted  subject  see F i g u r e 8 ) .  subject  variability  calculated  Table 5  In t h e p r e s e n t  (coefficient  and i s p r e s e n t e d  1 2 3 4 5  Interval The  i n the following  2.4 1.7 1.4 1.7 2.6  table:  0.10 0.10 0.15 0.10 0.07  interval  displacement  duration data.  relative  interval  interval  displacement  displacement  d a t a were a n a l y z e d u s i n g a  that  values  u s e d on t h e  In a g i v e n c y c l e ,  each  was d i v i d e d by t h e maximum  occurred i n that  maximum d i s p l a c e m e n t .  to that  The d e p e n d e n t measure was a  displacement.  displacement  displacement  cycles  Displacements  interval  50%,  was  V  15  t h r e e way ANOVA w h i c h was i d e n t i c a l  interval  the within  of variation)  SD = s t a n d a r d d e v i a t i o n o v e r f i f t e e n V = coefficient of variation  II.  study,  Intra-individual Variability f o r Interval D u r a t i o n s a c r o s s t h e F i v e Waveforms. SD  Interval Interval Interval Interval Interval  t o t h e d a t a o f an i n d i v i d u a l  expressed  cycle,  thus  as a p r o p o r t i o n o f t h e  The f i v e p r o p o r t i o n a l  f o rthe stimulus  20%, 9%, 38%, 100%.  g i v i n g an  interval  (or c r i t e r i o n )  were  55  Table 6  ANOVA T a b l e  Interval  SOURCE  F  WAVES INTERVALS Wl Wl (1,1) Wl (1,2) Wl (1,3) Wl (1,4) CYCLES WC IC WIC  4, 4, 16, 1, 1, 1, 1, 2, 8, 8, 32,  closely  1 2 3 4 5  interval  0.10 5. 67 3.00 0.12 0.06  displacement  the interval  data  duration data.  data  (see T a b l e  and i n t e r v a l  The v a r i a b i l i t y  6) p a r a l l e l  (For a g r a p h i c a l interaction  see F i g u r e 9 ) .  f o r the  The i n t e r v a l  d u r a t i o n d a t a were d i f f e r e n t  the within subject v a r i a b i l i t y  term).  cycles  o f t h e waves by i n t e r v a l s  displacement  displacement in  0.737 0.000 0.899 0.340 0.705 0.319 0 .202 0.967 0.476 0.931 0.030 (0.075)*  V  15  5.5 4.4 4.3 4.2 5.7  representation interval  16 16 64 4 4 4 4 8 32 32 128  adjusted p value  SD = s t a n d a r d d e v i a t i o n o v e r f i f t e e n V = coefficient of variation  The  P  Intra-individual Variability for Interval D i s p l a c e m e n t s a c r o s s t h e F i v e Waveforms • SD  Interval Interval Interval Interval Interval  DF  0.50 412.52 0.56 0.89 0.17 1.29 2.33 0.03 0.97 0.37 1.63  * Huynh-Feldt  Table 7  Displacements  only  ( i n d i c a t e d by t h e e r r o r  of the displacement  d a t a was  larger  56  Figure Waveforms by  intervals  9.  interaction  displacement  for relative  data.  interval  Relative Displacement as a Function of Waveforms (collapsed over cycles) r e  I a t  i  v e  120 100 80 60  s P  I  a c e m e n t  •  40  •  n -I  20  D  + i  T  i  -r  1  *  0 W1 ,5Hz  I  1  1  i  W 2 .3Hz  W 3 .4Hz  W 4 .6Hz  W 5 .7Hz  waveforms Interval 1  -*— Interval 2  Interval 4  •~  x—  Interval 3  Interval 5  01 ^3  58 than  that  data  values  Duration  of the duration data. were l a r g e r t h a n  data values  However t h e  the duration data  displacement values.  were l i m i t e d t o a r a n g e o f 100 p o i n t s ,  whereas, d i s p l a c e m e n t  data  interval  values  were l i m i t e d  to a  r a n g e o f 230 p o i n t s .  III.  Period On a l l waveforms  (wl - w7)  subjects reproduced  r e s p o n s e w a v e f o r m whose p e r i o d was period day  (see F i g u r e s  the stimulus  f o r w3.  o f w2 and  than  By day 15, t h e p e r i o d s  24 8 ms  than  more a c c u r a t e  the stimulus  and t r a i n i n g waveforms, s u b j e c t s  i n reproducing  the stimulus  periods  the slower  period  a n d t r a i n i n g waveforms were l o n g e r on day one.  response periods  became  response periods  o f w l , w2  stimulus  periods  In t h e case  those  a n d by  p e r i o d s by  the  periods  was 166  o f t h e r e s p o n s e waveforms  As w i t h  the  waveforms on  f o r w2,  practice.  stimulus  stimulus  327  respectively.  On t h e f a s t e r  faster  the  waveforms whose p e r i o d  p e r i o d , by 73 ms  and w3 were l o n g e r  than  F o r the slower  one, t h e s u b j e c t s r e p r o d u c e d  longer ms  10 & 1 1 ) .  longer  a  waveforms, r e s p o n s e p e r i o d s  However w i t h  on  than the  practice,  a n d w3 were c l o s e r they  these  and w7  t o those  of  h a d b e e n on day 1. (just  as f o r wl - w5) t h e  o f t h e r e s p o n s e waveforms were a l w a y s  of the stimulus.  with  s h o r t e r s u c h t h a t by day 15 t h e  than  o f w6  became  Thus d u r i n g  longer  input blanking,  than subjects  59  Figure Mean p e r i o d  over  five  cycles  10. of  input  blanking  wl  -  w5.  Period  Waves 1 - 5  —*—  Wave 1  — f -  Wave 2 Wave 3  -B-  Wave 4  -O-  Wave 5 Stimulus 1  ••+••  Stimulus 2 Stimulus  4  7  Transfer  10  Days  13  3  •B-  Stimulus 4  ••-€>•  Stimulus  5  Figure Mean  period  over  five  cycles  11. of  input  blanking  w6  &  w7.  Period Waves 6 & 7  Stimulus Wave 6 Wave 7  4  7  Transfer  10  Days  13  15  63 reproduced  r e s p o n s e s on a l l waveforms  consistently  IV)  RMS  day  fifteen,  the  five  t o o b t a i n a q u a n t i t a t i v e comparison o f  an RMS  e r r o r s c o r e was  RMS  Of t h e RMS  i n time  values  cycles, the cycle with i n Table  The s t i m u l u s i n order  8.  the lowest  RMS  Table  for a  value i s  representations of f o r the  (wl) on day 15, s e e A p p e n d i x C.  of the input blanking on day  to f i n d the  c a l c u l a t e d f o r each o f the  (For k i n e m a t i c  Appendix D f o r i n d i v i d u a l  was  and r e s p o n s e  responses p l o t t e d against the stimulus  t r a i n i n g waveform  (wl)  c a l c u l a t e d f o r each o f  e r r o r s c o r e between s t i m u l u s  cycle.  presented these  i n input blanking f o r  c y c l e s from i n p u t b l a n k i n g .  s h i f t e d b a c k w a r d and f o r w a r d  five  were  Error  p e r f o r m a n c e on t h e v a r i o u s waveforms  given  that  slow.  In o r d e r  lowest  (wl - w7)  See a l s o  subject p l o t s of the v a r i a b i l i t y  responses  from t h e t r a i n i n g  waveform  15.) 8 - RMS  Error  I n p u t B l a n k i n g Day ( u n i t s i n 1/10 mm)  15  wl  w2  w3  w4  w5  w6  w7  si s2 s3 s4 s5 s6  68 40 84 45 33 52  41 26 85 40 57 31  31 29 91 75 53 42  91 20 106 40 39 62  74 32 103 38 48 63  56 57 108 51 75 70  41 86 109 74 88 113  Mean  54  47  53  60  60  69  85  T h e r e were no s t a t i s t i c a l l y among t h e RMS  e r r o r scores  significant differences  t h a t were d e r i v e d  from t h e i n p u t  64 blanking the  data.  However  the descriptive  subjects performed  ( w l - w5) t h a n  waveform  In addition,  better  on t h e p h a s e  entirely  shifted  new w a v e f o r m  t o a repeated  contrasts  as presented  9  they  waveform  error  m e a s u r e s ANOVA i n Table  DF  1) 2) 3) 4) 5) 6)  0.06 0.91 1.14 0.01 6.85 3.44  1/ 1, 1, 1, 1, 1,  harmonic  analysis than -  7  blanking data  from  i n order  o f t h e response  gave  (Appendix  plotted  contained  beside  Though comparisons  E) r e p r e s e n t  waveforms  were  P 5 5 5 5 5 5  0 . 809 0.385 0.334 0. 9 9 9 0 . 047 0.123  t h e RMS  o f w l - w7.  This  o f t h e waveforms  Error results.  t h e mean v a l u e s  Figures  o f t h e harmonic  of the s i xsubjects  stimulus values.  i s no s i m p l e  amongst  s u b j e c t e d t o an  t h e frequency  description  i n t h e responses  criterion  there  d a y 15 w e r e  t o determine  a more d e t a i l e d  c o u l d be d e r i v e d from  components  scores  Composition  analysis  composition  on t h e  Blanking Day 15  F  Input  perform  using the orthogonal  CONTRAST  V Frequency  shifted  9 below.  ANOVA T a b l e RMS I n p u t Orthogonal Contrasts  Wl v s W2-W5 W2 & W3 vs W4 & W5 W2 vs W3 W4 vs W5 W1-W5 v s W6 & W7 W6 vs W7  to  (w6) t h a n  T h e s e RMS  that  and v a r i e d  d i d on t h e p h a s e  s u b j e c t s seemed  (w7).  subjected  Table  indicate  b e t t e r on t h e t r a i n i n g  speed waveforms (w6).  data  way t o make  the frequency  profiles  quantitative d e r i v e d from t h e  1  65 v a r i o u s waveforms t h r o u g h profiles  can  differences (the phase  help  harmonic a n a l y s i s ,  i n determining  found  i n t h e RMS  and  w7  error  results.  w7  frequencies)  exception  of the  both  are of s i m i l a r  f o u r t h harmonic.  In c o m p a r i n g  ( t h e new  (whose s t i m u l i  component  frequency  what u n d e r l i e s t h e  s h i f t e d waveform) and  seems t h a t w6  these  waveform) i t  contained  accuracy  The  three  with  amplitude  the  of  the  that of  the  f o u r t h h a r m o n i c o f w7  i s 3.6  mm  larger  than  stimulus,  amplitude  of the  f o u r t h harmonic of  is  only  whereas t h e  1.1  amplitude  mm  l a r g e r than  of the  l a r g e r RMS  w7  of i t s r e s i d u a l 3,  5 t o 5,  and  component 6 to  frequencies w i l l  be  less  those  component  VI)  have c o n t r i b u t e d t o  frequencies d i d w6.  on t h e  values  f o r most 2 to  Waveforms w h i c h c o n t a i n component  accurate reproductions of  frequencies.  the  w6.  ( i . e . comparing  residual  w h i c h have l o w e r  w6  larger  as compared w i t h  c o n t r i b u t e d t o t h e h i g h e r RMS with  The  higher amplitude  6) t h a n  values  residual  i n w7  a l s o had  higher amplitude  stimulus than  stimulus.  f o u r t h h a r m o n i c may  Error value  Additionally,  the  w6  amplitude  T h i s may  error value  the  values  also  have  on w7  as  on  the  compared  w6.  Kinematic Figures  subjects kinematic  12  Profiles & 13  across the  contain the p l o t s f i v e waveforms.  o f two  individual  These p l o t s  give  a  r e p r e s e n t a t i o n o f t h e movement b e i n g made i n t h e  input blanking practice  on  situation.  the  After fifteen  t r a i n i n g waveform  extremely  consistent i n producing  T h e r e was  also a great  production  not  between t r i a l s One  other  only within that  of response,  response that  a p p r o x i m a t i o n was  reliable  in  the  Take  with  exist  own  the  other  and  as  distortions  across  stimulus.  subjects,  reproduce i t .  also  own  a  (this  brand of e r r o r , caricature  first 6.  but or  was  waveforms o f d i f f e r e n t  base  t o p o l o g i c a l element This  subject  response,  In c o m p a r i n g t h e s e  i t seems t h a t  each  that  did  instances  subject  unique c a r i c a t u r e of the  stimulus  speeds.  subjects  stimulus  seems t o have made c e r t a i n i n the  but  l e a r n i n g progressed)  this  f o r example t h e  developed h i s or her Each s u b j e c t  waveform.  a l l subjects produced  particular And  a  were  response  trial,  f a b r i c a t e d a r e v e r s a l i n the  i n the  in  t o note about  r e s p o n s e waveform o f s u b j e c t  consistently not  a particular  i s that  movement.  both within  frequencies.  subject  particular  of s i m i l a r i t y  more a c c u r a t e  of the  this  approximated the  subjects produced t h e i r caricature  (wl), these  extensive  r e q u i r e d responses of d i f f e r e n t  interesting point  consistency required  deal  days o f  movement.  systematic  waveform i n a t t e m p t i n g  to  Figure  13.  Kinematic p r o f i l e s  from  subject  6  (wl -  w5).  69  CHAPTER 4. DISCUSSION  The  u n d e r l y i n g purpose  investigate  the that  relative  timing  movement.  humans l e a r n  o f t h e response  The s e c o n d  learned  Two p o s s i b l e  The r e s u l t s  generated  study.  The  a movement i n t e r m s o f elements  o f t h e s e was t h a t  movement i n t e r m s o f t h e frequency  only t o these  was t o  q u e s t i o n were t h e f o c u s o f t h i s  o f t h e s e was t h a t  movement.  thesis  t h e q u e s t i o n what is learned.  answers t o t h i s first  of this  that  humans l e a r n a  composition from t h i s  make up  of that  study  speak n o t  s p e c i f i c a s p e c t s o f t h e q u e s t i o n what is  but t o other  PART ONE - PURSUIT  facets  as w e l l .  TRACKING  Two s p e c i f i c q u e s t i o n s , w i t h r e s p e c t t o what is learned,  were p u t f o r w a r d  performance T h e s e were: tracking timing  i n the pursuit  base  same component  equally well  while  the relative  Two, w o u l d s u b j e c t s  a s t i m u l u s waveform w h i c h  f r e q u e n c i e s as t h e t r a i n i n g  phase angles) waveform?  study.  waveform, b u t were t r a n s f o r m e d i n  frequency?  better while tracking  stimulus  t r a c k i n g phase o f t h i s  s t i m u l u s waveforms w h i c h m a i n t a i n e d  of the training  different  t o thesubjects'  One, w o u l d s u b j e c t s p e r f o r m  terms o f t h e i r  the  i n relation  perform  contained waveform (but  t h a n t h e y w o u l d on an e n t i r e l y new  70 Subjects on  waveforms  varied  performance one t o f i v e  error,  m e a s u r e d b y RMS  By  the last  performing while  day o f t h e study,  more a c c u r a t e l y  o r speed  waveforms t h a t component  varied  frequencies  frequencies  performed better  studies  difficult,  as evident  Pew, D u f f e n d a c k , subjects  were able  1967).  (w4 a n d w5)  and  s h i f t e d waveforms  therefore, learn in  lend  a movement  terms  than they  support  of i t s absolute  i n base  (w4 & w5)  (w7 a n d w 6 ) .  of i t s relative timing.  (w6 & w7) i s  for a  subject  & Warren, 1955; this  track  were a b l e  than  i t i s more  Despite  t o the hypothesis  i n terms  scores)  subjects  scores,  Fitts,  t o more a c c u r a t e l y  waveforms phase  error  (Noble,  & Fensch,  error  tracking the  two p e r i o d i c waveforms  f a s t e r waveforms  were  t h e component  i n t e r e s t i n g because t y p i c a l l y  track  only  The f a c t t h a t  f r o m RMS  Wilberg,  r e l a t i o n s h i p s among t h e  especially  to  quadratic  (Franks,  on t h e two f a s t e r s p e e d s  d i d on t h e o t h e r  as  1983).  varied  (w6) o r v a r i e d (w7).  (RMS  day 15, s u b j e c t s  than while  t h e phase  themselves  showed a  ( a s m e a s u r e d b y RMS  ( w l - w5)  of  Performance,  & Romanow,  t r a c k i n g t h e waveforms t h a t  frequency  they  lag).  learning  Marteniuk  and t h e  a similar pattern  and v a r i a b i l i t y  o f most  1982;  of the study  dependent measures  and response  error  decrease t y p i c a l & Fishburne,  exhibited  on e a c h o f t h e t h r e e  variability,  days  (the t r a i n i n g waveforms  speed waveforms)  improvement  over the f i f t e e n  fact  these  two  to track These that timing  faster  t h e new  data, subjects rather  than  71 The  hypothesis  frequency results If  t h a t movement i s l e a r n e d  composition  was n o t s u p p o r t e d  subjects  training  entirely  they  experiment.  w o u l d be e x p e c t e d t o p e r f o r m b e t t e r on a t h e same component  waveform  (such  as w6) t h a n t h e y  new waveform  (such  as w7).  case;  error  l e a r n a movement i n t e r m s o f i t s component  waveform w h i c h c o n t a i n e d  the  by t h e RMS  f o r t h e p u r s u i t t r a c k i n g phase o f t h i s  frequencies,  the  i n terms o f i t s  frequencies  as  w o u l d on an  However t h i s  was n o t  s u b j e c t s p e r f o r m e d no b e t t e r on w6 t h a n t h e y d i d  on w7 . I n e x a m i n i n g p e r f o r m a n c e on t h e random waveform over the p e r i o d o f a c q u i s i t i o n ,  i t i s evident  improved  on t h i s  slightly.  indicative  of a subject's  periodicity reflective The  Improvement  that  ability  maximum a m p l i t u d e i s evident  a greater  and t h e consequent  on t h e s c r e e n  range o f t h e s t i m u l u s  from F i g u r e  2) l e a r n i n g  cursor.  1, waveforms 1 t o 5 d i s p l a y e d  on a l l o f t h e v a r i e d s p e e d waveforms  a quadratic  t r a i n i n g waveform component  of the task.  r a t e o f t r a c k i n g improvement t h a n w6 a n d w7.  days e f f e c t contained  a n d was  c o u l d be summed up as t h e  the joystick  movement o f t h e r e s p o n s e c u r s o r  As  the  1) l e a r n i n g t h e r e l a t i o n s h i p b e t w e e n t h e  movement p r o d u c e d w i t h  the  waveforms,  of learning the control functions  following:  subjects  waveform was  t o t r a c k without  e x i s t e d i n the other  c o n t r o l functions of the task  that  (w8)  component  (wl).  W6  and e x h i b i t e d o n l y  similar  to that  and w7 h a d no s u c h a linear  decrease  The  (w2 - w5) of the  quadratic i n RMS  Error.  72  Thus t h e r e waveform What  was t r a n s f e r  (wl) and t h e v a r i e d  characteristics  training  speed waveforms  i n common?  waveforms were  and i n terms  of their  temporal  duration  spatial  relative  timing  topology  o f these waveforms,  Tsetlin  (1962,  called in  essential  terms  and T s e t l i n  variable.  topology.  overall  improvement  a movement  terms  of i t s scalar  also  pattern  found  timing would  i n the variability  i n their, responses.  found  acquisition  variables  (Burgett,  Glencross,1979;  1970;  Lewis,  become  1956;  of this  on l e a r n i n g  Franks  they  that  i s  as  less  i n consistency tracking and  & Wilberg,  Marteniuk  timing.  results,  indicating  also  of  than i n  i n t h e RMS  The i n c r e a s e  studies  that  rather  or  trend  such as o v e r a l l  found  they  which i s  influence  showed a s i m i l a r  the acquisition  i n many  different  do n o t  indicate  and  have  a non-essential  results,  variable  been  call  characteristics  become more a c c u r a t e ,  has  defined the  frequency,  of i t s topology  o f improvement  occured during  The  e t a l . , 1980)  or base  subjects  i n terms  dimensions  These waveforms were  subjects  that  displacement  on t h e s e waveforms w o u l d  learn  The  that  t h e two  These  and w o u l d be what G e l ' f a n d  Non-essential  The f a c t  relative  displacement.  i n Kugler  variables.  of their  what G e l ' f a n d scalar  1971, c i t e d  of their  characteristics.  waveforms,  and t h e r e l a t i v e  varied  speed and  i n terms  and s p a t i a l  (w2 - w 5 ) .  waveform and t h e  The v a r i e d  identical  waveforms were two d i m e n s i o n a l being  between t h e t r a i n i n g  do t h e t r a i n i n g  speed waveforms have  timing  of learning  task  skill 1984;  & Romanow,  1983).  73 The p r o c e s s e s u n d e r l y i n g  s u c h a d e c r e a s e have b e e n t h e  subject  I t may  of speculation.  subjects  were  using  during  the process  execute the t y p i n g change  i n EMG  this  coincident  the  but  coincided  found  contraction  recruited to found a s i m i l a r and f o u n d  also  with a decrease i n  how  subjects  to leading  adjusted  or lagging  retarded,  response.  the subjects' by 7 & 5 ms may  moved t o w a r d a  respectively.  i n terms o f i t s r e l a t i v e  On  lagged the  On waveforms  have b e e n p r o v i d i n g  w4  a response that  and  w5  was  timing c h a r a c t e r i s t i c s ,  because o f t h e speed o f the s t i m u l u s ,  become e x a g g e r r a t e d  responses to  aligned with the stimulus.  responses s l i g h t l y  t o k e e p up w i t h t h e s t i m u l u s .  the  e a r l y on i n  By day 15, t h e s u b j e c t s '  were t e m p o r a l l y  the time  b u t as l e a r n i n g on wl  r e s p o n s e s t o a l l waveforms  subjects  accurate  (1979)  over the course of l e a r n i n g ,  temporally  and w3  stimulus  of muscular  The r e s p o n s e t o a l l waveforms  progressed,  and w5  (1958)  acquistion typists  pattern  3 and 4 d e p i c t  l e a r n i n g was  w2  tracking  Lundervold  Glencross  responding with respect  stimulus.  w4  task.  i n learning  variability.  Figures  wl,  i n learning,  later  Fewer m o t o r u n i t s were  change i n EMG  kinematic  of  of s k i l l  a more e f f i c i e n t  m e a s u r e d by EMG.  that  whereas  In i n v e s t i g a t i n g t y p i n g ,  developed as  the stimulus,  seem t o have a d o p t e d a more c o n s i s t e n t  strategy. that  early  a variety of d i f f e r e n t strategies i n  attempting to track they  be t h a t  In a d d i t i o n  t h e y were n o t response  at t h e f a s t e r speeds because t h e  able  errors  stimulus the  s p e e d makes  response  cursor  i t more d i f f i c u l t back  i n alignment  f o rsubjects  to bring  with  t h e moving  respect  t o what is  stimulus.  PART TWO  - INPUT BLANKING  Two s p e c i f i c h y p o t h e s e s , learned,  were p u t forward  performance These were: various  i n the input  training  waveform).  waveform which the  training  would  I.  effect  would  shifted  light  reproduced wl reproduce  (the  a  frequencies  as  they  new w a v e f o r m ( w 7 ) .  Durations i ntheresults,  interval  interval  durations  durations  therefore,  and contentions  o f other Gentner  t h epresent  across  study.  (w6) b e t t e r t h a n  t h e ANOVA p e r f o r m e d  interaction.  data  supported. result  several recent  (1987) h a s c r i t i c i z e d  instances  this  from t h e present  study)  I t i s  i n light of  papers,  and i n  experiment.  t h eprocedure  o f t a k i n g means  within a given  Thus t h e  appear t o be i n v a r i a n t , and  t o consider from  on t h e  yielded a non-significant  invariant r e l a t i v e timing hypothesis  findings  of this  r e p r o d u c e w2 - w5 ( t h e  f o rt h e waves by i n t e r v a l s  interesting,  in  phase  t h e same c o m p o n e n t  an e n t i r e l y  described  proportional the  would  t o the subjects'  as w e l l as they  waveform phase  Interval  proportional  blanking  Two, s u b j e c t s  contained  reproduce  As  i nrelation  One, s u b j e c t s  speed waveforms)  with  across  subject.  (followed  subjects and  However,  i f the  75 within  subject v a r i a b i l i t y  conjunction  with  of consistency variation to  other  the  results,  motor b e h a v i o r s  (such  consistent  present A  study  (250  cycles).  of the  were u n a b l e t o p a t t e r n they  of the  durations  been g i v e n  to  However,  the  any  those  have  relative  timing  degree of was  no  the  power  Heuer and  of  subjects the  accuracy.  difference in relative  which d i d  in  little  l e a r n the  relative  which shared  i n the  as  (1988)  i t i s clear that  s u r p r i s i n g that there  more p r a c t i c e , t h e r e  to the  from  Schmidt  In e x a m i n i n g t h e  t r a i n e d on w i t h  Perhaps i f s u b j e c t s  such  t r a n s f e r of i n v a r i a n t  subjects  and  how  amount o f p r a c t i c e may  r e p r o d u c e even the  training pattern  transfer  the  responses  between p a t t e r n s  within  duration  motor b e h a v i o r s  Heuer and  pattern.  subjects'  had  Thus i t i s n o t  This  compared  considered  s u b j e c t s were g i v e n  to allow  training  of the  transfer  t o be  of  variability.  against  Schmidt's study  been i n s u f f i c i e n t  spectra  low  c o n d u c t e d by  evidence  that  been d e t e r m i n e d  t i m i n g between movement p a t t e r n s .  Heuer and  timing  not  test  coefficient  r e a c t i o n time) the  proportional interval  study  seemed t o g i v e  practice  as  i n order  e x h i b i t very  recent  adequate  proportional interval  i t has  must be  an  i t i s evident  In comparison t o o t h e r  time the  relative  of the  date,  scores  invariant. reaction  To  examined i n  From t h e  t a b l e s i n the  i s low.  are  ANOVA, t h i s p r o v i d e s  (or i n v a r i a n c e ) .  subject v a r i a b i l i t y data  scores  timing  not.  Schmidt  study  had  w o u l d have b e e n a b e t t e r  p a t t e r n which shared  the  relative  timing  of  76 the  training pattern.  day  15, s u b j e c t s  By t h e l a s t  day o f t h e p r e s e n t  h a d h a d 5740 c y c l e s o f p r a c t i c e on t h e  t r a i n i n g waveform,  and h a d t h u s b e e n g i v e n  learn  timing pattern  the r e l a t i v e  T h i s may e x p l a i n t h e a p p a r e n t the  more t i m e t o  of the t r a i n i n g  discrepancy  waveform.  i n the results of  two s t u d i e s . Two h y p o t h e s e s  been p u t forward "different and  i n reference  by Heuer  c o n t r o l l e d by d i f f e r e n t "temporal p a t t e r n s  that  movements f a l l i n g  continua  motor programs.  differ  different",  The s e c o n d i s  on one o r more c o n t i n u a "  at different  places  along  such  these  parameters w i t h i n the  The c a t e g o r i c a l \ c o n t i n u a l h y p o t h e s e s study  d i d not address the question  because, t h e present  o f whether  relative  i s an i n v a r i a n t f e a t u r e o f a m o t o r p r o g r a m , b u t  whether s u b j e c t s context  learn invariant relative  of the present  an i n v a r i a n t t h a t  experiment,  i s learned  r a t h e r t h a n as a f i x e d  program.  Thus t h e t h e o r e t i c a l  t h e motor  H e u e r and S c h m i d t  and those  timing  In t h e i s seen  out o f  s t r u c t u r e o f a motor out o f which t h e  i s different  than  that  program. (1988) i n d i s c u s s i n g r e l a t i v e  have made t h e d i s t i n c t i o n mandatory  relative  context  e x p e r i m e n t was d e v e l o p e d  surrounding  timing.  or abstracted  movement,  present  have  i s that  are c a t e g o r i c a l l y  were n o t r e l e v a n t t o t h e p r e s e n t  timing  timing  The f i r s t  a r e c o n t r o l l e d by d i f f e r e n t  same m o t o r p r o g r a m .  study  to relative  (1988).  temporal patterns  that  as  study,  that  between p r o c e s s e s are s t r a t e g i c .  timing  that are  They s u g g e s t  that  77  relative  timing  perspective is  i s strategic  of the current  and n o t m a n d a t o r y .  study,  not mandatory i n t h e sense t h a t  change i t , b u t t h e n malleable. nervous  Living  invariant  changed  The  timing  notion  nature  designed  and by t h a t  data  o f movement  fact  also  c a n be c o n s i d e r e d  observations  and s e l f  and t h e s i s e x p e r i m e n t s .  abstraction  i n light  report  This data  the rhythmic p a t t e r n being  of the r e l a t i v e  Over t h e c o u r s e  data supports  of s k i l l  timing pattern  acquisition,  essentially  on, i n o t h e r  sensory  subjects  modalities  parts.  Subjects  pattern  i n the auditory modality.  they  learned to  one  Many s u b j e c t s  I n a d d i t i o n some o f t h e s u b j e c t s  and w h i l e  aspect  pattern,  other  body  seemed t o e n c o d e t h e r h y t h m o f t h e movement  head i n t h e p a t t e r n  tracking  and w i t h  were  reported  w o u l d hum o r t a p t h e r h y t h m o f t h e s t i m u l u s t o  themselves. their  an  o f t h e movement.  e x p r e s s t h e r h y t h m o f t h e movement p a t t e r n t h a t t h e y  that  capable  t h a t p e o p l e may l e a r n movement i n t e r m s o f i t s  rhythmic pattern,  training  to  of learning,  i s s e e n a s an a s p e c t  duration  o f some o f t h e i n f o r m a l  the  and by t h e i r  t h e human  (i.e. malleable).  interval  from b o t h p i l o t  (especially  From t h e p e r s p e c t i v e  relative  timing  i t i s impossible to  nervous systems  i s l e a r n e d by t h e s u b j e c t  of being  invariant relative  most l e a r n e d b e h a v i o r s a r e  system) a r e p l a s t i c  adapt t o change.  that  again  From t h e  of the stimulus  input blanking.  both  Therefore  w o u l d move while i t may be t h a t  o f l e a r n i n g movement i s l e a r n i n g i t s r h y t h m i c  and e n c o d i n g t h i s  pattern  i n various  modalities.  78 This expression  o f rhythm  i s found  not only  and a u d i t i o n , b u t a l s o i n t h e d e v e l o p m e n t structure.  Bateson  (1982)  rhythm d u r i n g t h e p r o c e s s The It the  music,  direction  sequence Living  i s repetitive  r e p e t i t i v e with  of  and  rhythmical. Indeed,  corresponds  to a  i n time. seem t o d i s p l a y r h y t h m n o t o n l y i n  movement b u t a l s o i n s t r u c t u r e . shared  by  ways.  F o r i n s t a n c e rhythm  a l l living  respiratory  cultures  the occurrence  modulation.  from head toward t a i l  systems then  circadian  anatomical  of morphogenesis:  anatomy o f t h e c r a b i s , like  has o b s e r v e d  of  i n movement  patterns  rhythms  Rhythm may  s y s t e m s and m a n i f e s t i n g i s found  property  i n various and  as w e l l as i n t h e i r  and a c t i v i t y .  i s the expression  a  i n the c a r d i a c  of a l l animals  of rest  be  o f rhythm  Common t o a l l human  i n poetry,  music  and  dance. The modality Schmidt (1977) those  expression t h a t was (1988)  arm  d e s c r i b e d above,  and o t h e r s  and M e r t o n  (1973)  of the present  handwriting  was  have  called  form, t h o u g h i t was  characteristics. m i g h t have  From t h i s  Raibert  findings, similar  hand,  to the  exhibited a consistent  variable in i t s scalar  i t was  suggested  to  When  t o t h e mouth, and t o t h e  the w r i t i n g i n a l l s i t u a t i o n s  topological  abstraction.  f o r handwriting.  the w r i s t ) ,  one  c a n be e x p l a i n e d by what  have p r e s e n t e d  study,  i n more t h a n  t r a n s f e r r e d t o t h e non-dominant  (by i m m o b i l i z i n g  foot,  o f rhythm m a n i f e s t i n g  that  subjects  e n c o d e d an a b s t r a c t r e p r e s e n t a t i o n o f t h e  79 movement t h a t would a l l o w in  they produced.  f o r the various  the various  An a b s t r a c t manifestations  movement t h a t nervous  might  i s well  system,  involve  (1971)  learned  and t h a t  an e n c o d i n g  and L a s h l e y  distributed  system  (1950)  learned,  part  of this  i n other  resolution stores is  encoding  Pribram f o r such a  using  the analogy  as a movement becomes  e n c o d e s t h e movement a t a  finer  a complete h o l o g r a p h i c  r e s o l u t i o n image t h a n a p i e c e  of that  plate plate  capable of s t o r i n g . Bateson  that  living  formal  size",  (1982)  has s u g g e s t e d t h a t  As B a t e s o n h a s p o i n t e d  morphology, though t h e r e  one n e v e r t h e l e s s  relations".  finds  relative  timing  w h i c h a movement p a t t e r n drawn p a r a l l e l s (Berkinblit,  out i n d e s c r i b i n g  may be an "asymmetry i n  symmetry  Feldman,  rarely i s this  Several  1986 p.599;  e x h i b i t symmetry  expressed  organizes  may be t h e s t r u c t u r e  i s organized.  & Fukson,  i n formal  o f form  between m o r p h o g e n e s i s a n d m o t o r  L i v i n g creatures  equivalent  i n underlying  "a d e e p e r symmetry  I n t h e same way t h a t  morphogenesis,  p.624).  one o f t h e p r o p e r t i e s  s y s t e m s e x h i b i t i s an i n v a r i a n c e  relations.  vertebrate  but  a  encoded i n  redundant  evidence  Pribram,  i n t h e same way t h a t  a finer  i s that  modalities.  have g i v e n  f o r memory.  the brain  evidence  becomes r e d u n d a n t l y  of t h e hologram, has suggested t h a t well  o f t h e movement  modalities.  A n o t h e r way o f i n t e r p r e t i n g t h i s  the  code o f movement  around  authors learning  Turvey,  1986  i n t e r m s o f form,  i n terms o f p e r f e c t l y  m a g n i t u d e s on t h e r i g h t and l e f t  have  sides  of the  80  body. than  For instance, the right the l e f t  equivalent) two  b u t t h e form i s s y m m e t r i c a l  i s the exact  concept light,  JJ.  mirror  of relative  of determining  Interval  and t h e f o r m o f t h e s e  image o f t h a t  the underlying  i n that  relative  c y c l e ) were  spatial  characteristics across these  relations.  displacements  (intervals  and t h e relative  characteristics  the topology subject  The s c a l a r  I t was  in this  while the  r e s p o n s e waveforms v a r i e d t o of overall  Subjects  duration  were a b l e t o v a r y  while  maintaining  topology.  This gives  one o f t h e a s p e c t s  of the  of the response  characteristic  characteristic  and t h e o v e r a l l  idea that  subject.  remained i n v a r i a n t ,  of those  both  remained i n v a r i a n t  that defined the topology  g r e a t l y a c r o s s waveforms.  scalar  timing  Therefore  c y c l e s and  temporal  o f t h e r e s p o n s e waveforms  f o r a given  some e x t e n t . varied  as a  that  Thus i t seems t h a t  t r a c k i n g waveforms t h a t were u s e d  experiment.  scalar  i n v a r i a n t across  subject.  two c h a r a c t e r i s t i c s  waveforms  similar  formal  c y c l e s a n d waveforms w i t h i n a g i v e n  particular  this  in a  The  Displacements  waveforms w i t h i n a g i v e n the  on t h e l e f t .  as 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  occurred  on t h e  o f a b s t r a c t i o n c a n be c o n s i d e r e d  The p r o p o r t i o n a l i n t e r v a l taken  i n that there are  t i m i n g c a n be c o n s i d e r e d  and t h e p r o c e s s  process  longer  ( i . e . t h e magnitudes a r e not e x a c t l y  l e g s , two k n e e s , two f e e t  right  l e g may be s l i g h t l y  the r e l a t i v e support  o f a movement t h a t  t o the  subjects  81 learn  i s the  Bernstein  topological properties  (1967) has  o f a movement.  suggested that  we  terms of  i t s topological properties.  modified  Bernstein's  in  idea  Pribram  suggesting  that  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 .  recent that  s t u d i e s by  humans p l a n  trajectory  Soechting and  rather  & Lacquanti  c o n t r o l the  than the  both contentions analysis  one  are  forces  i n t e g r a t i n g t h e s e two  required  are  to produce,  s y s t e m we  (1981) g i v e  and  i n that  but  at  Den  force  a higher  Present  evidence movement  the  e x i s t s because  which l e v e l  suggests  correct,  encode t o p o l o g y .  of the  discrepancy  positions  has  e n c o d e movement  used to produce  Whiting  that  (1971)  in  However, more  c o r r e c t d e p e n d i n g on  i s addressing.  both contentions  we  kinematics  movement t r a j e c t o r y . P e r h a p s t h i s  in  e n c o d e movement  Brinker  of (1982)  just this,  that  i s what we  are  level  in  the  data  supports  Whiting's  experiment  i t seems  that  contention.  III.  Cycle  Duration  From t h e  r e s u l t s of t h i s  subjects  organized  relative  timing  Subjects  were more a c c u r a t e  timing  pattern  reproducing  the  rather  of the  than  i n terms o f at  stimulus  be  Kugler et  encodes i n f o r m a t i o n  considered  of  duration.  the  relative  waveforms t h a n t h e y were of the in light  a l . (1980) t h a t i n a way  i n terms  overall  reproducing  overall duration  T h e s e r e s u l t s can f o r w a r d by  t h e i r movement p a t t e r n s  that  the  stimulus of  an  waveforms.  idea  nervous  at  put  system  i s system s c a l e d  and  82 dimensionless.  Overall duration  implies  some k i n d  external  o b j e c t i v e t i m e c l o c k , whereas i f K u g l e r  correct,  the  nervous  a relativistic  sense.  response timing environment,  the  environment.  but  r a t h e r the  moving. that  the  t h a t w o u l d be  In r e l a t i o n  frequency  to Pribram,  transform,  are  encoded i n t h i s  way,  characteristics  w o u l d be  IV.  Frequency The  f o r w6  only  (the p h a s e s h i f t e d  entirely  new  statistically s u b j e c t s may  overall  identical.  in  from  the  organism  i n the  in  suggested  brain,  Movement  humans  itself,  i t s pattern  f o r movement  timing,  but  have  the  Thus i f movement i s  i t s relative  timing  important.  Composition  RMS  time  in  duration,  (1971) has  F o u r i e r transforms  & Root Mean Squared  movement p a t t e r n s  m e a s u r e d by  overall  to the  information.  w h i c h have d i f f e r e n t timing  the  Pribram  in  events  feedback  movement i n t e r m s o f  composition.  same r e l a t i v e  are  i s encoded i n terms of a F o u r i e r  which d e s c r i b e s  frequency  patterns  of  be  with  characteristics  absolute  al  organism t o tune i t s  to conincide  of relevance  to timing,  r a t h e r than encoding  according  f o r the  Then i t w o u l d n o t  et  "understand" time  organism would u t i l i z e  immediate t i m i n g  encode p a t t e r n s  of  In o r d e r  characteristics  the  environment,  system would only  of  reproduced during  Error  input  blanking  waveform) were more a c c u r a t e  e r r o r than those  generated  waveform), though t h i s significant. t r a n s f e r t o w6  f o r w7  d i f f e r e n c e was  I t seems t h a t  i n input  (a waveform w h i c h  as  (the not blanking,  contains  83  identical  component  more e a s i l y data  lends  forward  frequencies  than they  t r a n s f e r t o w7  some s u p p o r t  by  Pribram  M a r t e n i u k and  t o the  to the  conjecture  (1983) t h a t  w6  waveform).  that  Wilberg  has  been  (1982),  component  and  organize  In p u r s u i t t r a c k i n g , s u b j e c t s p e r f o r m e d e q u a l l y w e l l  on  movement.  and  w7,  and  p e r f o r m e d w o r s e on  Subjects  may  they  input  may  to the  blanking  blanking,  fell  B e c a u s e wl  and  w7,  on  was  on  d i d on  presented  because  no  their  stimulus  contained  had  identical  visually  composition  were o f w7  organized  (an e n t i r e l y  i n t e r m s o f component  make i t e a s i e r f o r s u b j e c t s them t o  reproduce  w7.  new  of  pursuit tracking  them.  movement  In  input  subjects  movement.  learned  from  component  In  waveform).  frequencies,  t o r e p r o d u c e w6  than  were this  wl.  frequencies,  s u b j e c t s were a b l e t o g e n e r a t e a b e t t e r r e p r o d u c t i o n than they  have  whereas  driven  available,  memory f o r t h e  being  may  memory o f t h e  before  wl  in pursuit  stimulus,  frequency  their  b a c k on what t h e y w6  of the  In a d d i t i o n , d u r i n g  however, w i t h  they  to the  dependent  stimulus  required to r e l y case,  and  when s u b j e c t s were n o t  pattern.  s u b j e c t s were l e s s because the  on w6  topology  have b e e n a t t u n e d  stimulus  than they  during pursuit tracking, subjects  b e e n more a t t u n e d during  these  have p e r f o r m e d d i f f e r e n t l y  i n input blanking  driven visually  for  put  of  t r a c k i n g than  is  This  frequencies  - W5.  the  waveform)  s u b j e c t s may  memory f o r movement i n t e r m s o f t h e that  (a new  (1971), F r a n k s and  Romanow  training  of  w6  I f memory this  would  i t would  84  V.  Kinematic The  Profiles  kinematic  generated during  representations  input blanking  of the  on  wl  evidence  for topological consistency  subjects  were c o n s i s t e n t  a given in  waveform.  response production  Additionally, that  - w5,  day  within  i n producing  T h e r e was  responses 15,  subjects.  the  five  cycles  also a great  deal  of  across  the  stimulus,  All within  similarity  v a r i e d speed waveforms.  though s u b j e c t s produced a r e q u i r e d  approximated the  give  they  response  also produced t h e i r  particular  b r a n d o f e r r o r , o r what G i b s o n  (1969)  labelled  " c a r i c a t u r e " of the  This c a r i c a t u r e  was  a  reliable  base  both within  frequencies.  g e n e r a t e d by the  on  similar that  subject  stimulus.  cycle  example t h e  Subject  were i n f a c t  w h i c h made one the  plane  composites  seems, t h e r e f o r e , representations distinctive  d i d not  element  (1969)  s u b j e c t s ' drawings of  in  found  objects  remember:  exaggerations  are  exist  f o r each  of those  features  d i s t i n g u i s h a b l e from o t h e r s ,  of the  i n a sense c a r i c a t u r e s .  aircraft  features detected  In comparing t o p o l o g y  different  t o p o l o g i c a l element  Gibson  t h a t memory images o r  differences.  each subject  first  f i v e waveforms.  were r e q u i r e d t o  has  waveforms o f  s i x generated t h i s  d i s t o r t i o n s i n her  ...(they)  across  six i s a reversal that  each of the  they  that  For  and  movement.  own  (Gibson across  1969, the  developed h i s or her  It  schematic  were i n d e e d  while  so  based  looking  on  for  pp.146-147) six subjects, own  unique  i t seems t h a t  c a r i c a t u r e of  85 the  movement.  Each  subject  systematic  distortions  attempting  t o reproduce i t .  An  interesting  findings that  s e e m s t o h a v e made  i nthestimulus  comparison  and findings reported  subjects,  i nrecalling  to f i ttheir  Tversky  (1981) i n h e r r e s e a r c h  locations, locations  subjects  appears that reality  influenced this of  by previous  experiment  within a given  found  recently  spatial  geographical  distortions  systematically distort  f o r each  o f space.  I t  physical that i s  experience.  thedistortions  t h e waveforms were d i f f e r e n t  consistent  More  o n memory f o r  i nrecalling  He  distort the  of a psychological reality  or biased  particular  would  these  (1932).  context.  made s y s t e m a t i c  subjects  i n favour  by B a r t l e t t  own c u l t u r a l  has found that  waveform i n  c a n b e made b e t w e e n  stories,  details  some  I n t h e case o f  i nt h e topology  subject and  subject..  PART THREE - CONCLUSIONS Component The terms  idea  subjects  blanking  results.  equivalent  movement i n t e r m s pursuit  tracking.  During  subjects  o n t h e new a n d t h e  seem n o t t o o r g a n i z e  o f i t s component However d u r i n g  frequencies input  by t h e  i n d i c a t e d by t h e  pursuit tracking  o f accuracy  and thus  a movement i n  was n o t s u p p o r t e d  b u t was p a r t i a l l y  levels  o f phase waveform,  l e a r n and organize  frequencies  tracking results,  exhibited out  that  o f i t s component  pursuit input  Frequencies  a  during  blanking,  subjects  86  seem t o have p e r f o r m e d b e t t e r on w6 t h a n t h e y d i d on w7. The  previous  studies  (Franks & W i l b e r g ,  1980; M a r t e n i u k &  Romanow, 1983) t h a t gave e v i d e n c e t h a t s u b j e c t s movement i n terms o f component f r e q u e n c i e s  learn  measured  subjects  during input b l a n k i n g rather than p u r s u i t t r a c k i n g .  Thus  e v i d e n c e from t h e p r e s e n t study i s c o n s i s t e n t w i t h e v i d e n c e from t h e s e e a r l i e r s t u d i e s .  Relative  The  Timing  hypothesis  t h a t s u b j e c t s l e a r n a movement i n terms  o f r e l a t i v e t i m i n g was s u p p o r t e d by t h i s experiment i n b o t h t h e p u r s u i t t r a c k i n g and i n p u t 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 t h e t r a i n i n g waveform ( w l ) , t h e r e was p o s i t i v e t r a n s f e r t o t h e v a r i o u s speed waveforms (w2, w3, w4, w5). F o r p u r s u i t t r a c k i n g , i f t h e t r a n s f e r waveform was slower  (w2 o r w3) t h a n t h e t r a i n i n g waveform ( w l ) , t h e r e was  almost p e r f e c t t r a n s f e r i n terms o f response a c c u r a c y . t r a n s f e r r e d t o f a s t e r waveforms (w4 and w5), a c c u r a c y was somewhat d i m i n i s h e d .  When  t h e response  Nevertheless,  subjects  p e r f o r m e d f a r more a c c u r a t e l y on t h e f a s t e r t r a n s f e r waveforms (w4 and w5) than t h e y d i d on t h e new waveform (w7) and t h e phase s h i f t e d waveform (w6).  For input  blanking,  the i n t e r v a l d u r a t i o n s t h a t were c a l c u l a t e d r e v e a l e d 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 were i n v a r i a n t t h e f i v e v a r i e d speed waveforms, t h u s s u p p o r t i n g  that across  the notion  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 timing.  87 Typically  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  invariant  relative  invariant  f e a t u r e o f a motor p r o g r a m .  present - w5,  study  had achieved  the contention  motor program, whose v a l u e data  that  and t h a t  can vary  from t h i s  predicted.  Additionally,  duration  i t i s likely  i s that  on t h e s e  aspects  skill  i s evidence  acquisition.  invariant  relative  acquisition  relative  timing  motor program. the is  idea that learned  i s a parameter However t h e  results  show,  waveforms.  response,  unlikely.  that the overall  m o d u l a t e d by  o f a movement  of s k i l l  i n the  f a s t e r waveforms a r e  modulate t h e i r  used  making t h e  For pursuit  (or a b s o l u t e )  timing  feedback.  From b o t h t h e i n p u t b l a n k i n g there  i s fixed  f o r wl  i n the case o f p u r s u i t t r a c k i n g , s u b j e c t s  continuously  data,  i n the  e r r o r scores  timing  of a d i s c r e e t parameter value  tracking is  RMS  and t h u s as p r e s e n t  scores  feedback t o c o n t i n u o u s l y notion  I f subjects  d i d n o t t u r n o u t e x a c t l y as  for this  to track, RMS  relative  o f as an  m i g h t have b e e n s u p p o r t e d .  One r e a s o n  finds higher  identical  overall  experiment  more d i f f i c u l t one  t i m i n g has b e e n t h o u g h t  that  and t h e p u r s u i t t r a c k i n g  relative  that people  timing  i s one o f t h e  learn during  The e v i d e n c e  that  t i m i n g was l e a r n e d  the process  a pattern of  during  the process  of  n e e d n o t be t a k e n t o mean t h a t i n v a r i a n t  i s an i n v a r i a n t f e a t u r e o f a g e n e r a l i z e d I t can j u s t  relative  as w e l l be t a k e n as s u p p o r t f o r  timing  d u r i n g motor s k i l l  i s one o f t h e i n v a r i a n c e s acquisition,  perhaps  in a  that  88  s i m i l a r way t o t h e p i c k learning  (Gibson,  up o f i n v a r i a n t s d u r i n g  1966;  Gibson,  perceptual  1969).  What i s L e a r n e d ? B o t h t h e s i s and p i l o t idea that  r e l a t i v e timing  make up a movment) learned. two  This  kinds:  control those  experiments  lend  i s one o f t h e a s p e c t s  that  o f movement t h a t i s  i n which v i s u a l feedback  o f t h e movement  t o the  (of t h e response elements  finding i s limited to cyclic  those  support  movements o f  i s involved  s u c h as i n p u r s u i t  t r a c k i n g , and  i n w h i c h b o t h k i n e s t h e t i c f e e d b a c k a n d memory a r e  involved  i n t h e c o n t r o l o f movement s u c h as i n i n p u t  blanking. during  These r e s u l t s a l s o g i v e  response reproduction  frequencies.  to tasks  blanking  s u c h as i n p u t  some i n d i c a t i o n t h a t  a movement may be o r g a n i z e d  t e r m s o f i t s component  This  relative  timing  i n which the c o n t r o l o f  and t h e component  frequencies  movement c a n be s e e n t o be a way o f o r g a n i z i n g such t h a t higher  state  of organization,  form o f o r g a n i z a t i o n .  as  occurs  in living  a "higher"  of a  movement,  i n t h e same way t h a t  Though l e a r n i n g systems,  function that  of the b i o l o g i c a l same l a w s .  Both  as l e a r n i n g p r o g r e s s e s t h e p e r s o n moves t o w a r d a  morphogenesis p r o g r e s s e s t h e system reaches  that  in  finding i s limited  movement i s b a s e d on k i n e s t h e t i c f e e d b a c k a n d memory. the  i n the  world,  In c o n t r a s t ,  i s somehow  and t h e r e f o r e  a more complex  is itself  i t has o f t e n  as  been  a process considered  removed f r o m t h e r e s t n o t g o v e r n e d by t h e  t h e view o f l e a r n i n g put forward i n  89 this  t h e s i s has  biology,  rather  considered laws.  been t h a t  as  an  In t h i s  principles  t h a n one  of  state  removed f r o m i t .  expression  of  l e a r n i n g and has  entropy gradient  continually  achieves  of  development  such a p r o c e s s .  internal  organization,  differentiated process,  and  i n the  g o v e r n e d by  the  same  of the  life.  be  special  instance  and  higher  and  the  order  structure  thought  o f as  a  a  in process  organism  organization. i s an  a form  more i n t e g r a t e d t h r o u g h o u t that  Learning of the  toward  example of  w h i c h , becomes b o t h more  same way  1985).  most  evolution  the  nervous  then,  can  larger process  be of  the  learning  system d u r i n g  m o r p h o g e n e s i s becomes more d i f f e r e n t i a t e d and (Schacher,  The  B o t h i n l e a r n i n g and  coordinative  I t can  be  i s reversed  a higher  of the  can  o r g a n i s m goes t h r o u g h  whereby t h e  in  have b e e n drawn b e t w e e n  been t h a t  human o r  and  rooted  Learning  p r i n c i p l e s of  of o r g a n i z a t i o n .  morphogenesis the  The  life  thesis parallels  emphasized p a r a l l e l higher  learning i s a process  its  integrated  considered life.  as  a  90  APPENDIX A REVIEW OF LITERATURE  A  simple  understand  but e s s e n t i a l question  f o r those  l e a r n i n g i s what is learned.  movement s c i e n t i s t ' s  perspective  who s e e k t o  Or f r o m t h e  "What c h a n g e s w i t h i n a  p e r s o n b r i n g a b o u t more s k i l l e d m o t o r p e r f o r m a n c e ? " question  has been c e n t r a l t o p s y c h o l o g y  of behaviorism Whiting,  i n t h e 1930's  1980).  (Gibson,  The is  cognitivists, learned  events. the  i ti s  are learned. t h a t what  o f movement, o b j e c t s , o r  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 for skilled  i n different  s u c h a s schema  (Pribram), The  Gibsonians  "cases  Gibson's  (Schmidt,  i t has been researchers,  with  1975) image o f a c h i e v e m e n t  (Keele,  1975).  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  have r e j e c t e d e x p l a n a t i o n s  representation, Gibson  movement;  ways by d i f f e r e n t  a n d motor p r o g r a m  behaviorists,  as  that  hand, have a r g u e d ,  are representations  described  J.J.  1969; Weimer, 1977;  and r e s p o n s e s t h a t  on t h e o t h e r  representation  labels  since the inception  The b e h a v i o r i s t s have p r o p o s e d ,  a s s o c i a t i o n s between s t i m u l i  This  have e x p l a i n e d  b a s e d on  l e a r n i n g i n y e t a n o t h e r way.  (1966, p.279) h a s d e f i n e d p e r c e p t u a l  learning  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 . i d e a have 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  motor domains.  In r e l a t i o n  t o cognition, Eleanor  Gibson  (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 "to detect  regularity,  order,  ability  and s t r u c t u r e " p r o v i d e s t h e  basis (see  for cognitive a b i l i t i e s a l s o Wertheimer,  well,  there  are  as  "What is  Learned?"  l e a r n i n g we skilled and  researchers  to  In a w o r l d  the  may  But  stroke  preceding the  i t i s with  t h a t we  game.  motion  are  the  balance Every  of postures t i m e we  that  other  skilled  It i s  literal  game.  the  from we  a  build  immediately  momentary n e e d s its  of  own  p.204.)  point that Bartlett  a c t i o n must be  in i t ,  with  i n fact  of the  (1932,  has  o f movement r a r e l y  Because the  have  a s e r i e s o f movements  make i t , i t has  memory o r r e p r o d u c t i o n  recapitulation. any  important  and  define to  in a skilled  shows t h a t basis  given  feedback:  from a t e x t - b o o k or  the  characteristics. The  stroke  repeating  study  a f r e s h on  first  included  through  during  of a  changing environment,  a long time before  teacher. the  of the  i s e x t r a o r d i n a r i l y unimportant.  learned  up  one  o f a schema, has  of c o n s t a n t l y  fancy  1920;  Head,  a representation  a changing environment  r e m e m b e r i n g as We  1932;  have p r o p o s e d t h a t  Bartlett,  notion  as  become  schema i s a s e t o f r u l e s u s e d t o  g e n e r a t e movement.  recall  1975)  d e v e l o p a schema as  conceptualized  c a s e o f movement  learned.  (Bartlett,  Schmidt,  act. This  adaptation  In the  i t becomes w e l l  1980;  Gallistel,  1945).  l e a r n i n g mathematics  c e r t a i n of i t s features that  invariant  Several  s u c h as  environment  adapted t o the  made i s  involves  i s always immediate  rote  changing,  92 environment. through  And o f course  (Pribram,  1971) w h i c h  behavioral  Fourier  transform  required  Pribram  Pribram  i s encoded  movement i n t e r m s  Hz.  learned  component  blanking  cursors  were removed  component up  frequencies,  that  we  f o r t h e image o f  (1982)  frequency  have  also  l e a r n and organize frequencies.  consisted  a base  frequency  reproduced t h i s  waveform  stimulus  a  In their  a waveform which  with  o f 0.5 i n an  and response  The r e s p o n s e  was  a n a l y s i s which determined the  amplitudes  and phase  I t was  learning  subjects  However,  as l e a r n i n g p r o g r e s s e d  frequency  components t o t h e i r may  only  the environment.  we e n c o d e t h e  from t h e d i s p l a y .  t h e response waveform.  subjects  with  i n which both  a Fourier  as a  i t employs  & Wilberg  to track  situation  measured through  that  frequencies  cortex  anticipations of force  o f i t s component  In addition, subjects  input  i n t h e motor  Franks  to the notion  subjects  neurophysiological  p h y s i o l o g i c a l evidence  and f o r t h e n o t i o n  support  for skilled  has suggested t h a t t h e  and i n t e r a c t i o n  components o f movement.  three  on b o t h  an a c t i o n , and t h a t  tuning,  has given  achievement  i s based  of the learned  t o execute  feedforward,  of  accomplished  o f t h e image o f achievement  evidence.  image o f achievement  study,  be  of the representation  movement i s t h e c o n c e p t  given  can only  feedback.  Another version  and  this  reproduced  found that  angles  that  early i n  the fundamental  subjects  response  systematically organize  added  frequency.  higher  suggesting  the  made  that  continuous  93 movements t h a t  they  frequencies that also  learn  make up t h e movement.  given evidence that  (Bernstein, Yet  1967;  (Keele,  sequences.  Since  A c c o r d i n g t o Schmidt  i t s inception  definition  versions defined  perhaps best  o f t h e motor p r o g r a m  some m o d i f i c a t i o n s . characterizes  concept.  structured before  a movement  allows the e n t i r e  s e q u e n c e t o be c a r r i e d  motor  feedback." This  control  of pre-planned  i n the early  Keele's  time  Keele  that are  sequence b e g i n s ,  i s an open  60's  the early  At that  i t as "... a s e t o f m u s c l e commands  peripheral  (1988),  i n t h e system than  i n the execution  t h e motor program has undergone (1968)  for skilled  1975) o r g e n e r a l i z e d  a t a lower l e v e l  schema, a n d i s i n v o l v e d  movement  have  interpretation  of the representation  (Schmidt, 1988).  t h e motor program e x i s t s the  Other s t u d i e s  support t h i s  i s t h e motor p r o g r a m  motor program  component  M a r t e n i u k & Romanow, 1 9 8 3 ) .  another v e r s i o n  movement  i n terms o f t h e  and t h a t  out u n i n f l u e n c e d b y  loop explanation o f  i n w h i c h f e e d b a c k p l a y s no r o l e .  Since  that  t i m e t h e c o n c e p t o f t h e motor p r o g r a m h a s d e v e l o p e d s u c h that  some f o r m s o f f e e d b a c k a r e now a c c o u n t e d f o r .  motor program  i s presently  t h o u g h t t o be an open  mechanism, w h i c h t h o u g h i t i s s t r u c t u r e d movement, the  system  c a n be m o d i f i e d w i t h (e.g. the r e f l e x  t h e motor program  w h i c h h a s embedded w i t h i n processes,  loop  i n advance o f  feedback at lower l e v e l s i n  level  i s a higher  The  (Schmidt, 1 9 8 8 ) ) .  level  open  i t lower l e v e l  loop  Thus  structure  closed  loop  which are capable o f a d a p t i n g t o minor  94  perturbations,  but are not capable of changing the e n t i r e  action. From an a l t e r n a t i v e p e r s p e c t i v e , movement  c a n be e x p l a i n e d  coordinative  structure.  discover  i n learning  constraining single  defined  muscles o f t e n constrained  (a movement)  Kugler,  multi-movement  serves  coordinative  Easton  (1972).  structure,  Turvey  developed the notion Berstein's point,  1980,  i n 1977, T u r v e y  parts  like  t h e motor program, has  evolution.  The t e r m was  (1977), b o r r o w i n g E a s t o n ' s  o f muscle  still  a g e n t , t h o u g h one t h a t  term,  s t r u c t u r e b a s e d on  synergies.  allowed  coined  At that  f o r an e x e c u t i v e  intervened  as a  minimally.  By  however, K u g l e r e t a l (1980) h a d begun t o s e e  "control" system, to  the control of  o f s e v e r a l body  of the coordinative  (1967) c o n c e p t  controlling  Thus t h e  coordination).  u n d e r g o n e i t s own c o n c e p t u a l by  as "a g r o u p o f  that i s  i n explaining  a coordination  just a  (1980, p.17) h a v e  structure  s p a n n i n g a number o f j o i n t s  structure  (1982,  you a r e t r y i n g t o  so t h e y become  & Turvey  the coordinative  a c t i o n which i n v o l v e s  The  & Fitch  ... i s a way o f l i n k i n g o r  involved  Kelso,  of a  t o a c t as a s i n g l e f u n c t i o n a l u n i t " .  coordinative  (i.e.  Turvey,  "One o f t h e t h i n g s  those muscles  entity".  formally  i n terms o f t h e n o t i o n As T u l l e r ,  p.255) have e x p l a i n e d :  the learning of  as an i n h e r e n t  and had t h e r e f o r e  an " e x e c u t i v e "  or t o  process  of the s e l f - o r g a n i z i n g  removed t h e n e e d f o r any  recourse  representationalism.  From a c o m p a t i b l e 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 t h e c o o r d i n a t i v e Gibson's on  structure  (1966) s p e c u l a t i o n s  developed,  on l e a r n i n g .  In a d i s c u s s i o n  t h e n a t u r e o f memory, he h a s c o n s i d e r e d  what is An  are J . J .  the question  learned:  observer  invariants exactly  learns with p r a c t i c e to i s o l a t e during  transformation  t h e permanent  features  more  In p e r c e p t i o n , movement  learning  o f an  array.  detect  order  o f response elements w i t h i n t o maintain the topology i t s relative  absolute  timing,  Bernstein pointed  timing.  while  still  (1967, p l 7 7 )  out t h a t  2)non-essential  would p a r a l l e l  variables".  Gibson's  s c a l a r changes,  learned  that  In  may  learn  they are  Thus,  maintaining  one must  i s well  the topology. t o t o p o l o g y , has  organized  i fi t s  i n t o : 1 ) e s s e n t i a l v a r i a b l e s and Essential variables  invariants.  are the essential variables are responsible  are those  o f movement;  Non-essential  i n t h e l e a r n i n g o f movement,  o f movement.  In  One c a n however, v a r y t h e  f o r example t h e o v e r a l l r a t e  those v a r i a b l e s that topology  subjects  o f s u c h a movement,  preserve the t o p o l o g i c a l properties  a movement.  invariants.  a complex m o t o r a c t .  i n reference  "a f u n c t i o n  a r g u m e n t s c a n be s e p a r a t e d  are  p.265)  An example o f s u c h an i n v a r i a n t i s t h e r e l a t i v e  maintain  that  tracking)  the i n v a r i a n t s of the stimulus  following. timing  humans l e a r n t o d e t e c t (specifically  subtle  and t o e s t a b l i s h more  (1966,  to  of  these  variables o r speed o f  what is  (or i n v a r i a n t s ) i . e . f o r preserving the  96 The  essence  pulling  invariants  Schrodinger all  living  control  (and even  (or order)  (1944) h a s a r g u e d t h a t systems.  (entropy)  schema t h e o r y  and i n v a r i a n c e  (Schmidt,  what  this  of constraint, which  and  i s variable.  chaos.  i n motor  F o r example,  and developing  equation  be  the interplay of  1975) h a s e x p l a i n e d  the action  may  i s the essence o f  (order).  i s v a r i a b l e and what  another perspective,  what  itself)  Many o f o u r e x p l a n a t i o n s  of finding invariance  expresses  life  out o f apparent  a n d l e a r n i n g h a v e t o do w i t h  variance  terms  of learning  learning i n an e q u a t i o n  that  i s not variable.  From  t h e o r i s t s have p o s t u l a t e d  also  defines  what  From b o t h p e r s p e c t i v e s ,  i s invariant two  simultaneous processes  are occurring.  1) c e r t a i n  in  2) c e r t a i n t h i n g s  i n movement a r e  movement v a r y ,  invariant.  Learning  organization invariant, An is  and  i n which  while  are l e f t  As such,  of shifts a higher  evidence processes higher  on e s t a b l i s h i n g an  alternative to the notion  process  order  involve  organization.  differentiated  the living  order  and entropy.  drink  order  to  vary.  of representation,  state  of organization.  to indicate that of life  free  l e a r n i n g would  i n the internal  form  things  c e r t a i n r e l a t i o n s h i p s become  others  organization.  toward  i s based  an  of  of a  organization  There has been  both processes  o f l e a r n i n g and  organizational  shifts  Schrodinger  from t h e non l i v i n g  environment"  toward  a  (1944) h a s  He h a s s u g g e s t e d t h a t  out of t h e i r  consist  then,  i n terms o f  "living  organisms  and i n so doing,  defy  97  entropy. order  As l i v i n g organisms e v o l v e t h e y p r o g r e s s t o h i g h e r  levels of organization.  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, t h e y d i d n o t c o n s i d e r t h e concept o f 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 t o r e p r e s e n t a t i o n , t h e paper was n o n e t h e l e s s one o f t h e f i r s t t o a p p l y t h e concept o f organization t o the f i e l d  o f motor s k i l l s .  They contended  that the o r g a n i z a t i o n that develops with p r a c t i c e i s i n the form o f v a r i o u s  " r u l e s f o r e n c o d i n g i n p u t " and t h a t what i s  l e a r n e d a r e " c o n t e x t u a l 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 e v i d e n c e from t r a c k i n g s t u d i e s f o r such a process occurring i n learning. s u b j e c t s moved t o h i g h e r  Fuchs (1962) found t h a t  o r d e r c o n t r o l systems over t h e  c o u r s e o f l e a r n i n g a t r a c k i n g t a s k such t h a t w i t h l e a r n i n g , subjects developed a higher organization. In m o d e l l i n g  l e v e l of perceptual  motor  Fuchs had s u b j e c t s t r a c k a complex waveform. 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 c o u l d be m o d e l l e d i n terms o f d i s p l a c e m e n t and v e l o c i t y c o n t r o l . the weighting  F u r t h e r on i n l e a r n i n g ,  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 s u b j e c t s were g i v e n t h e added s t r e s s o f having t o c o n c u r r e n t l y perform another task, they t o an e a r l i e r s t a g e i n which t h e y were u s i n g derivative information. and  This progression  regressed  lower  during  learning,  r e g r e s s i o n d u r i n g s t r e s s , was termed t h e p r o g r e s s i o n -  98  regression have  order  processes  of  the  of  evolution,  (1978, p.3)  "Insofar  as  biological to  say  as  skilled  the  a  i s said to to  performer,  of  in  any  that  implies other  an  i t performs  and  the  implies  a  of &  the  and  regress" speaks  executive,  1988;  Meijer  learning  as  and  And  Fowler  one  &  or the et  to  particular we  may  individual  wish  animal,  attunement  of  to  the  of  invokes  (Kugler  and  higher The related  representation  et  which  in  turn  a l . , 1980).  representing  In  movement,  (such  as  action controversy In  one  the  Representationalism  a l . , 1988).  .  organization,  a u t h o r i t y are  some e n t i t y  motor  of  learning.  analogue  soul).  Authority.  representation  higher  of  Higher  i n terms  process  animal  an  of  invoke  "implies  central issues  Meijer,  to  representation  homunculus,  the  Problem  which  w o r d s when one  of  higher  skillfully."  explanation  infinite  provides  toward  niche,  is a particular  representation  necessarily  a  a particular  i n e x p l a i n i n g the  notions  (1988)  a progression.  be  curiously, that  becomes u n n e c e s s a r y  also  progression  such  When l e a r n i n g i s c o n c e i v e d  authority  Hah  done:  attunement  Representationalism  it  system  between these processes  species  task  and  Both processes  involve  have  , perhaps  particular  of  nervous  organization.  draw a p a r a l l e l  Turvey  of  numerous examples  forms  Jagacinski  finding.  morphogenesis  with  can  Recently,  replicated this The  us  hypothesis.  attempting  is  (see to  one Beek  99 understand As  learning,  the cognitive  one comes f a c e  neuroscientists,  t o face  with t h i s  issue.  Maturana and V a r e l l a ,  have  stated: "Indeed, cannot  i f t h e n e r v o u s s y s t e m does n o t o p e r a t e  operate - with a representation  s u r r o u n d i n g w o r l d , what b r i n g s functional  effectiveness  enormous c a p a c i t y  - and  of the  about t h e  extraordinary  o f man a n d a n i m a l a n d t h e i r  t o l e a r n and m a n i p u l a t e t h e w o r l d ? " (p.133,  1987)  They h a v e p r o p o s e d a s o l u t i o n t o t h e p r o b l e m o f representationalism. representation brain,  thought  o f as s t a t e s  of internal organization,  which  such t h a t  c o r r e l a t i o n s between s e n s o r y  of t h i s idea.  Sperry  surgically rotated  will  the surgery,  frog stuck  are d i f f e r e n t . that  these  and m o t o r p r o c e s s e s . (1945) as an  Consider  illustration  A f r o g when p r e s e n t e d w i t h a f l y i n h i s  field,  the  c a n be  o f i n terms o f i n t e r n a l  c o n d u c t e d by S p e r r y  visual  After  of  t h e i n t e r a c t i o n s between  (1987) have s u g g e s t e d ,  c h a n g e s be t h o u g h t  experiment  Instead they  p e r s o n / o r g a n i s m and t h e environment  internal  changes i n t h e  c h a n g e s as r e p r e s e n t a t i o n s ,  learning  Maturana and V a r e l l a  an  i t does i n v o l v e  a b o u t more s k i l l f u l movement.  of these  transform with the  o f movement,  which b r i n g  conceiving  Though l e a r n i n g may n o t i n v o l v e  s t i c k h i s tongue out and c a t c h  the f l y .  t h e e y e s o f a f r o g by 90 d e g r e e s .  when he p r e s e n t e d t h e f r o g w i t h a f l y ,  i t s tongue i n a d i r e c t i o n e x a c t l y  away f r o m t h e a c t u a l  location of the f l y .  90 d e g r e e s  Thus t h e f r o g ' s  100  nervous  s y s t e m seems t o have c o r r e l a t e d s e n s o r y  events,  r a t h e r t h a n t o have r e p r e s e n t e d  environment  in i t s brain.  Skilled  encompass a h i g h l y complex and correlations, with  facilitating  integrated array  a highly  The  problem of r e p r e s e n t a t i o n a l i s m  cognition, period  and  solipsism to  has  understand  the  classical  (Maturana & V a r e l l a , 1988).  Currently,  the  field  inherited  c o n t r o l i s d o m i n a t e d by  At  this point  representationalism  reason  of a r t i f i c i a l  Dreyfus  unity. from the  has  represent  our  traditional  At  case.  tendency to  other Part  of  embrace  of  the  field  ideas.  d e v e l o p e d by  argued t h a t bodies to  b e c a u s e we  i s a m o n i s t who  In t h e s e t e r m s ,  cognitive  T h e r e i s however a c e r t a i n  M e r l e a u P o n t y , has  then,  been the  following ideas  c o m p u t e r w o u l d have t o do, Dreyfus,  been  discipline,  i n t h i s p a r t i c u l a r borrowing  (1985),  need t o  having  been i t s a s s o c i a t i o n w i t h  intelligence.  inherent  philosopher  reverse  has  a  over s o l i p s i s m .  for cognitive science's  representationalism,  of  i n h i s t o r y then,  i s favored  i n h i s t o r y , the  h a v e no  this  from motor l e a r n i n g ' s p a r e n t  psychology.  irony  such  f a r b a c k as  representationalist's perspective,  the  of  e x t e n d as  m o t o r l e a r n i n g and  times  versus  f o r those attempting  i t s roots  would  efficient interaction  environment.  problem  motor  external  human movement  the  been a p e r e n n i a l  the  and  as  French  humans,  ourselves,  are  we  as  a  embodied.  s e e s m i n d and  h i s a p p r o a c h can  the  be  body as  a  distinguished  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  science,  dualistic but  assumptions which not  c o n c e i v e o f m i n d as Cognitive  in  c o g n i t i v e psychology) which i s based  isolation  i n t e r a c t i o n s with the presented a problem out  of  body,  body.  1963).  movement s c i e n t i s t s  The  from the  present  that  our  group o f p s y c h o l o g i s t s  1976;  Weimer,  Young,  1975),  entirely  cognitive  a  and  earlier  develops  world  isolated  from  the  paradigm,  wrong end  new,  and  abilities has  of  the  anthropologists  function.  has  proposed that  behavior  forms o f  From P r i b r a m ' s  Along  i n that  thinking  i s sensory  the  mind i s  a g e n e r a t o r not  its  input"  (Weimer,  i n nature, only  1958;  1921).  lines, i s an  grown out t o the  i t can of  1971; The of  advanced of  i t s own  form  these  environment".  evidence that be  art  Bartlett  concluded output but  1977).  movement s c i e n t i s t s  by  Klapp,  appreciation  (1971) n e u r o p h y s i o l o g i c a l  motor c o r t e x  Ironically,  the  similar  f l e x i b l e adaptation  intrinsically  (Pribram,  (Sapir,  " i t has  are  been p r o p o s e d b e f o r e  (Bartlett,  Edward S a p i r b e l i e v e d  a motoric  skilled  the  has  ability  cognitivist  1977), n e u r o p h y s i o l o g i s t s  anthropologist  of  up  cognition  1962).  idea  (1958, p l 9 9 )  c a n n o t be  have p i c k e d  body,  motor  However, t h i s  i n t e r a c t i o n s with the  i s not  t o be  sensory  human c o g n i t i v e  motoric small  from the  Thus c o g n i t i o n  In b o r r o w i n g  (Kuhn,  attempted to e x p l a i n  and  i n that  s e p a r a t e m i n d and  primary.  environment.  e a r l y sensori-motor  (Piaget,  stick  causally  p s y c h o l o g y has  from the  only  on  have b o r r o w e d  the that also  102  information  processing  artificially ignores  and  tended to  models from p s y c h o l o g y  separates  perception  degrades a c t i o n .  ignore  the  fact  and  which  a c t i o n , and  then  Thus movement s c i e n t i s t s  o f embodiment.  Perhaps i t  have  has  b e e n e a s i e r t o e x p l a i n movement c o n t r o l i n t e r m s o f a deus ex  (Kelso et a l . , 1980)  machina  within may  the  embodied o r g a n i s m  than  dualism  (1988  and  p.445),  assumptions  b a s e d upon a  i n c o n s i d e r i n g the  embodiment, has  I f a tenable  and  discovered  i n the  behavior  i s sought,  the  at the  field  root  of the  psychology,  images o f t h e  c a n n o t be  scientific  movement s c i e n t i s t s  human body,  a p p r o a c h e s by  defined,  borrowed the  have been  explanations  o f motor c o n t r o l i n which the  deemed t o be  the  "controlling  This problem  psychology  movement  and  nature  controlling science  and  i n general  quest  to  they  avoid  have o f t e n  seems n o t  t o be  which that  neglected".  l e d away  e n t i t y " which  cognitive from  created  "executive" "commands" unique  is the  to  science.  power o f h i g h e r  entities,  of  the  which  paradigm of  Because of t h i s ,  lower l e v e l s .  question  o f human movement  embodiment.  The  outside  i n t e r p r e t a t i o n of  field  various  is scientifically  In h a v i n g  "The  "god  written:  comprehensive  'facts',  lie  Dualistic  machine".  Tamboer  "  processes  itself.  w e l l have l e d t o e x p l a n a t i o n s  of the  i n terms o f  has  ever  / c e n t r a l / commanding  been a p r o b l e m  s i n c e the  f o r western  seventeenth  s u p e r i o r a u t h o r i t y , then,  century. appears  to  /  103  have h a d - a n d 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,  This p a r t i c u l a r Meijer  p r o b l e m may have an e v e n d e e p e r o r i g i n  suggests.  long-standing  1988 p.171)  F o x (1983) a n d M e r c h a n t  religious,  than  (1980) d i s c u s s t h e  p h i l o s o p h i c a l and c u l t u r a l  roots of  the  p r o b l e m o f 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  p r o b l e m o f embodiment.  their  roots  i n the c u l t u r a l / r e l i g i o u s  modern w e s t e r n  consequences o f t h i s  (1984, p.50) have p o i n t e d  out t h e  marriage:  Man i s e m p h a t i c a l l y  not part  of the nature  he  d e s c r i b e s ; he d o m i n a t e s i t f r o m t h e o u t s i d e .  Indeed  for Galileo,  image,  i s capable  underlying  out o f which  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 .  and S t e n g e r s  objectively  context  have  s c i e n c e h a s emerged.  Modern s c i e n c e Prigogine  T h e s e companion p r o b l e m s  t h e human s o u l , c r e a t e d  of grasping  the plan  i n God's  the i n t e l l i g i b l e  of creation  ... t h a t  truths  God h i m s e l f  possessed. For  the sciences  presented  o f psychology  an i n t e r e s t i n g  human b e h a v i o r , "objectively  and motor b e h a v i o r  dilemma.  How c a n we who  dissociate ourselves  describe",  t h i s has study  f r o m t h a t w h i c h we  when we a r e o u r s e l v e s  the objects of  that description. T h i s p r o b l e m has been d e a l t w i t h the as  human a s t h e s o u l , t h o u g h s c i e n c e such.  Rather  i t has been g i v e n  homunculous o r t h e e x e c u t i v e .  by s a v i n g has r a r e l y  titles  a part of labelled i t  such as t h e  I n t e r e s t i n g l y i t has been  104 this  part  o f t h e human t h a t h a s u s u a l l y b e e n s e e n t o be t h e  part  that  i s " i ncontrol".  Thus i n t h e same way  that  G a l i l e o b e l i e v e d man was a b l e t o b o t h d o m i n a t e a n d understand nature, to the  so t h e e x e c u t i v e  b o t h dominate and f u l l y motor system.  g e n e r a l l y been conceived, of  'higher  1984;  authority'  Maturana  Invariant For  (Carello,  timing  Turvey,  Meijer,  able  levels of as i t h a s  l e d t o the problem Kugler,  1988;  & Shaw,  Reed,  1988).  Timing  several years  relative  of representation,  has i n e v i t a b l y  & Varella;  Relative  h a s b e e n s e e n t o be  understand t h e "lower"  The n o t i o n  fully  there  has been e v i d e n c e  o f t h e components o f a g i v e n  that the skilled  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 t h e o v e r a l l duration  o f t h a t movement.  from t h i s feature  that  relative  M o t o r t h e o r i s t s have  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  of the c e n t r a l representation  program) o f t h e movement b e i n g 1982;  Shapiro,  Zernicke,  another p e r s p e c t i v e , rejected the notion argued t h a t  learned  Gregor,  action theorists,  timing  ( u s u a l l y motor (Shapiro  & Diestel,  of representation,  relative  inferred  & Schmidt,  1981).  though they nevertheless  (Tuller  Putnam,  Thus i n v a r i a n c e b r i n g s  1983).  have have  i s one o f t h e i n v a r i a n t s o f a  movement t h a t humans l e a r n & Goodman,  From  & Kelso,  1984; K e l s o , together  b o t h motor and a c t i o n p e r s p e c t i v e s . At  least  invariant  two q u e s t i o n s  relative  timing.  c a n be a s k e d w i t h They a r e :  reference to  105 1)  Is i n v a r i a n t r e l a t i v e learned  2)  timing  a characteristic  of well  movement?  Is r e l a t i v e  timing  an i n v a r i a n t f e a t u r e  o f a motor  program? In a s k i n g  t h e second q u e s t i o n  that  one must  Most  of the t r a d i t i o n a l  timing  one makes a l e a p  assume t h e e x i s t e n c e research  of faith, i n  o f t h e motor program.  on i n v a r i a n t  relative  has addressed t h e second o f these q u e s t i o n s .  present  experiment  i s designed t o address the f i r s t  questions.  However t h e s e c o n d q u e s t i o n  theoretical  grounds.  In order  of t h e second question, perspective.  The  Thus a t h i r d  i s important  t o consider  one m i g h t  o f these on  the ramifications  frame i t f r o m an a l t e r n a t e  question  m i g h t go s o m e t h i n g  like  this: 3)  Is r e l a t i v e  timing  movement a r r a y  one o f t h e i n v a r i a n c e s  that  humans  Most o f t h e r e s e a r c h e r s relative program.  timing  have s t u d i e d  A c e n t r a l question  motor program has been and  timing  i s one o f t h o s e  relative has  timing  learn.  who have s t u d i e d i n v a r i a n t i t in relation  f o r t h o s e who have s t u d i e d t h e  (Schmidt,  1988) t h a t  invariant features.  i s an i n v a r i a n t f e a t u r e  been r e f e r r e d t o i n t h e l i t e r a t u r e  motor program w i t h proportional  features?", relative  The i d e a  o f t h e motor  that program  as t h e g e n e r a l i z e d  a m u l t i p l i c a t i v e r a t e parameter or the  duration  model p r e d i c t s t h a t  t o t h e motor  "What a r e i t s i n v a r i a n t  i t has been s u g g e s t e d  i n the  model.  The p r o p o r t i o n a l  any s k i l l e d  duration  movement p e r f o r m e d  with  106  different  overall  durations  will  durations.  Original  unpublished  s t u d i e s by A r m s t r o n g  1988).  evidence  He h a d h i s s u b j e c t s  a particular  unidimensional  for this  occurred  relative  timing.  because r e l a t i v e  (1970, c i t e d  can vary  for  each i n s t a n c e  for  overall  proportional  across  Viviani,  1979).  Recently  Gentner  When  maintained this  i s a parameter  of the s k i l l .  a different  Thus,  parameter  value  t o t h e motor program.  accepted  supporting  1984; S h a p i r o ,  evidence  duration  instances  i s assigned  Shapiro,  through  i s structured into the  d u r a t i o n model o f t i m i n g  research  i n Schmidt,  move a l e v e r  nevertheless  timing  performance has been w i d e l y empirical  some  I t has been p r o p o s e d t h a t  of the s k i l l  duration  relative  spatial-temporal pattern.  m o t o r p r o g r a m , whereas t h e o v e r a l l whose v a l u e  fixed  came f r o m  repeatedly  s u b j e c t s moved t o o q u i c k l y t h e y invariant  exhibit  in skilled up u n t i l  The  motor  now.  (For  t h i s model s e e : C a r t e r &  1977; Summers,  1977; T e r z u o l o  (1987) h a s r e - e v a l u a t e d  f o r t h e p r o p o r t i o n a l d u r a t i o n model.  &  the supporting From h i s  r e v i e w i t seems t h a t much o f t h e o b s e r v e d p e r f o r m a n c e not  perfectly  majority  o f the data  proportional researchers instead  f i t t h e model.  Gentner has argued t h a t t h e  used as s u p p o r t i n g  d u r a t i o n model was a n a l y z e d analyzed  mean d u r a t i o n s  of the actual individual  overcome t h i s proportion  problem,  test.  does  evidence  f o r the  imprecisely  of a given  i n that  interval  observed durations.  Gentner has p r o p o s e d a  To  constant  Assume t h a t D i i s t h e d u r a t i o n  of the i - t h  107  component  o f a complex movement a n d T i s t h e t o t a l  Then t h e r e l a t i v e remain constant the  proportion  of D i with  o v e r c h a n g e s i n T.  proportional duration  a given  interval  plotted  i t against  respect  This  f u n c t i o n was z e r o  to T  should  i s an e x p r e s s i o n  model i n m a t h e m a t i c a l t e r m s .  Gentner has taken t h e r a t i o T.  duration.  I f the slope  of  For  o f D i / T and  of the r e s u l t i n g  the proportional duration  model was  supported. After  having  found evidence within  durations  from e x p e r i m e n t s  f o r an i n v a r i a n t r e l a t i v e  duration  timing  model i s n o t s u p p o r t e d .  a r e m a i n t a i n e d t o some e x t e n t  as Heuer & Schmidt  discrepancies  still  a s compared w i t h  invariance,  behavioral  reasons level.  timing.  with  One c o u l d  f o r a lack of perfect The f i r s t  on t h e b e h a v i o r a l  indicate  timing  one c a n n o t r u l e o u t t h e n o t i o n  (1987), who h a s a r g u e d t h a t timing  they  (p. 241)  t h e y may l e a r n i n v a r i a n t r e l a t i v e four  acceptable  the conspicuous  Though humans may n o t e x h i b i t r e l a t i v e  least  as  o f i t , and one c a n a r g u e t h a t  o f minor importance  perfect  Relative  but not p r e c i s e l y .  be c o n s i d e r e d  tendency toward i n v a r i a n c e .  the  feature  between n a t u r e and human  conceptualizations  at  that  (1988) have p o i n t e d o u t :  These d e v i a t i o n s might  are  the data  a motor program, Gentner has c o n c l u d e d t h a t t h e  proportional  But  reanalyzed  a lack of invariance  posit  i n v a r i a n c e on  h a s b e e n s u g g e s t e d by H e u e r  a lack  level,  that  of invariance  i n relative  does n o t n e c e s s a r i l y  centrally.  This  i s because  108 there  a r e n o n - l i n e a r i t i e s i n t h e nervous system which  distort it  a central invariance i n relative  would m a n i f e s t  variable  a  pointed  timing.  s e c o n d i s t h a t humans may  formal  way  (Thompson,  1952).  i n size",  As B a t e s o n  i n formal  relations".  symmetry  o f form o r g a n i z e s  organized.  Several  morphogenesis  a n d motor  Fukson,  1986 p.599;  exhibit  symmetry  expressed  leg  and l e f t  Turvey,  magnitudes symmetrical  relative  (Berkinblit,.  1986 p . 6 2 4 ) .  s i d e s o f t h e body.  are not e x a c t l y equivalent) i n that there  The c o n c e p t o f r e l a t i v e  evidence  that  mathematically This  interval  durations  i s the exact  Gentner  perfect proportions  Gentner's  (1987)  two f e e t  mirror  timing  (1987)  image  c a n be  has g i v e n  a r e not always of overall  i s analogous t o Bateson's n o t i o n  size".  the right  a r e two l e g s , two k n e e s ,  light.  on t h e  but t h e form i s  of that  i n a similar  i s this  ( i . e . the  on t h e r i g h t  considered  &  creatures  magnitudes  and t h e f o r m o f t h e s e on t h e l e f t .  Feldman,  For instance,  than the l e f t  between  Living  o f form, b u t r a r e l y  longer  timing  a movement p a t t e r n i s  of p e r f e c t l y equivalent  may be s l i g h t l y  that  drawn p a r a l l e l s  learning  i n terms  i n terms  have  may be  f i n d s "a d e e p e r  morphogenesis,  authors  (1982) h a s  I n t h e same way  may be t h e s t r u c t u r e a r o u n d w h i c h  timing i n  though t h e r e  one n e v e r t h e l e s s  symmetry  right  learn relative  out i n d e s c r i b i n g morphogenesis,  an "asymmetry  such t h a t  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 t h e form o f  relative  The  timing,  may  movement t i m e .  o f "asymmetry i n  review a l s o i l l u s t r a t e s  t h a t on  109 average t h e o f as in  proportions  The perfect  third  reason  invariance,  intervals  time,  is  fixed  expression  aren't  timing  i s not  absolute  in relative  f o u r t h reason  i s that  instance,  this  few  timing,  that  study  development  extensive  experience  appropriate  parameter be  feedback  into were  o f a movement t o c o n t r o l slight  by  have c o n s i d e r e d of r e l a t i v e  timing the  Heuer & Schmidt 250  timing  f o r the  is  For  (1988),  in  c y c l e s of p r a c t i c e , i t does n o t  remain i n v a r i a n t  development  development  whether  the  250  of i n v a r i a n t  o f a motor program.  motor program i s presumably b a s e d  with  not  necessity  timing.  However i t i s q u e s t i o n a b l e  of the  movement  once put  invariant relative  only  relative  or  t i m i n g must  I f , however,  i s adequate p r a c t i c e f o r the  relative  duration  might b r i n g about  development  a t r a n s f e r task.  cycles  The  that  Because  timing.  w h i c h s u b j e c t s were g i v e n concluded  involved  model o f a p r o g r a m  overall  duration  exhibit  of o v e r a l l  d u r a t i o n parameter,  researchers  i n a recent  not  timing.  present  an  modifiable.  timing,  of p r a c t i c e i n the  in  of r e l a t i v e  and  The  used throughout the  found  thought  symmetry  somehow be  perfect proportions  precisely.  variations  was  f e e d b a c k may  In s u c h a model r e l a t i v e  program,  The  "deeper  i n v a r i a n t t i m i n g may  i s that  relative  correct.  being its  that  i t seems u n l i k e l y t h a t t h e  maintained the  of the  c o u l d be  relations".  i n modulating the  with  invariant; this  analogous to Bateson's notion  formal  the  are  environment  such t h a t  form o f o r g a n i z a t i o n might d e v e l o p .  But,  on  an since  110 neither are  learning,  addressed,  n o r t h e development  o f t h e motor program,  t h e problem o f adequate p r a c t i c e i s o f t e n  over-looked. Scientists controversy, in  from b o t h s i d e s  have r e c o g n i z e d  o f t h e motor  t h e importance  movement c o n t r o l , a n d b o t h s i d e s  the  problem o f f l e x i b i l i t y  control varies  i n which there and t h a t  action of  flexibility  have a t t e m p t e d t o s o l v e  by d e v e l o p i n g  models o f motor  i s an i n t e r p l a y b e t w e e n t h a t  which remains i n v a r i a n t .  which  I t w o u l d be  u n f o r t u n a t e t o r e j e c t a phenomenon s u c h as i n v a r i a n t relative current  timing  simply  b e c a u s e i t s d a t a do n o t f i t t h e  motor programming p e r s p e c t i v e .  t h e y may r e f u t e t h e i d e a fixed  i n t h e motor program,  that  relative  that  humans l e a r n .  timing  differentiated important  The theory  T h e s e two p o s s i b i l i t i e s  timing i s  fall  o f a movement must be  prey t o n e g l e c t i n g  an  b e c a u s e we a r e w e a r i n g t h e wrong  spectacles.  proportional  duration  of the generalized  model,  as a p a r t  motor program,  of the  i s a theory  emphasizes open-loop p r o c e s s e s ,  the existence  t o accept  characteristic  that  of the generalized  relative  of skilled  timing  of  though i t  f o r feedback at lower l e v e l s i n t h e system.  accept  order  though  c e r t a i n l y do n o t r e f u t e t h e i d e a  o t h e r w i s e we may  motor c o n t r o l t h a t allows  invariant relative  i s one o f t h e a s p e c t s  phenomenon s i m p l y  theoretical  not  that  The d a t a ,  One n e e d  motor program i n  i s an i n v a r i a n t  action.  Two c r i t i c i s m s c a n be made o f t h e g e n e r a l i z e d  motor  Ill program t h e o r y necessity failed  as i t s t a n d s  of accounting  hybrid  processes  (Schmidt,  neglected  The t h e o r y  has a c c o u n t e d f o r  has i g n o r e d  Nevertheless,  aspects  t h e way i n w h i c h s k i l l e d  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 o f movement joints.  Such an i n t e g r a t i o n o f body p a r t s  information  with  Marteniuk, movement (cited  is  this  problem  1985; T u l l e r  e t a l . , 1982).  coordination during  input  Several  ( e . g . Abbs,  F i r s t l y , the movement i s of the various  requires  from v a r i o u s  authors  parts  gives  joint  evidence  have  In a study Altman  1985)) d i s c o v e r e d  on (1982 that  o f t h e body o f t h e i n s e c t  i n v o l v e d i n modulating t h e e f f e r e n t output  This  that  1984; M a c K e n z i e &  insect flight,  i n MacKenzie & Marteniuk,  afferent  has  a b o u t t h e r e l a t i o n s h i p s amongst t h e v a r i o u s  j o i n t s be u s e d i n m o t o r c o n t r o l . grappled  loop  the theory  o f feedback.  has  s e e n t o be a  f r o m b o t h open a n d c l o s e d  1988).  two i m p o r t a n t  out the  which t h e theory  i n t h e sense t h a t t h e program has been  system assembled  theory  Both p o i n t  f o r feedback,  t o do a d e q u a t e l y .  feedback  t o date.  t o t h e wings.  o f t h e way i n w h i c h movement  c a n 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  a t one from  various  joints. Secondly,  the theory  which t h e o v e r a l l the is  has not a c c o u n t e d  d u r a t i o n parameter value  way i n w h i c h i t i s a s s i g n e d .  f o r t h e way i n i s determined nor  In a computer program, i t  t h e programmer who b o t h d e t e r m i n e s and a s s i g n s t h e  parameter values. occurring  Can we assume t h a t  i n humans?  a s i m i l a r process i s  I f we do, we a r e l e f t  with  a  little  112 c o m p u t e r programmer  i n our  head a s s i g n i n g parameter  to the  motor programs t h a t  simply  an  The  the  realm that  homunculus t h e o r y  crucial  with  question  of the  homunculus.  questionable  whether the  appropriate  both  f o r use  to explain  is  nothing.  been r e l e g a t e d t o  Because a computer does not i t s environment, organisms,  limiting  and  the  that  the  have  is  computer  misleading.  It i s  metaphor o f a program i s  i n e x p l a i n i n g human movement  ( C a r e l l o et  1984). Tracking  which the examined.  studies provide  In t r a c k i n g the  forms o f r e l a t i v e 1)  relative  2)  the  (and  timing that  of the  of timing  i n f l u e n c e one  stimulus,  the  tracking,  can  response  another,  will  be (Pew,  seem t o be  immediate d u r a t i o n  are  at  least  itself; to the  two  and stimulus.  involved in  internal  1974).  two  relative  forms  In t h e  overall  timing,  response case  feedback to  rather than the  this  a predictable  able t o time the  using  be  i n v o l v i n g an  for, with  subject's  in  c o n t r o l can  In p u r s u i t t r a c k i n g , t h e  stimulus  subjects  context  identified:  mechanisms a r e  b e t t e r the  to the  be  response r e l a t i v e  feedforward  better a subject  tasks  environment) t h e r e  form o f t i m i n g .  relative  experimental  other  t i m i n g w i t h i n the  timing  F e e d b a c k and second  an  c o n t r i b u t i o n s of feedback to t i m i n g  i n t e r a c t i o n with  the  This  i n which feedback i n t e r a c t s  c o n t r o l has  of a l l l i v i n g  be  the  way  dynamic i n t e r a c t i o n w i t h  metaphor can  movement.  which serves  of the  program i n t i m i n g  characteristic  al,  c o n t r o l our  values  of  determine duration.  113 Gentner duration  (1987) i n h i s c r i t i c i s m  model has p o i n t e d  out t h a t  of the proportional one o f t h e 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 adaptability  and f l e x i b i l i t y .  characteristic obvious that  If flexibility  of s k i l l e d behavior then  feedback  i s being  utilized  work o f Abbs a n d h i s c o l l e a g u e s illustrated  this  was p e r t u r b e d perturbation adjustment objective  point.  during  They  found t h a t  speech, t h e r e  can  i n this  In order  illustrates  one  of their  o f feedback  major  flaws.  reject the proportional  possible  that  t o respond t o a  This  tracking. Franks  duration  have  duration  may c h a r a c t e r i z e  (1982).  de-emphasized  control.  model.  In t h i s  This  criticism i t is  model i s c o n s i s t e n t feedback.  forthis  loop  skills  i n s t u d i e s by  as l e a r n i n g  p r o g r e s s e d t h e phase angles o f t h e frequency approached those o f t h e stimulus  may be  However,  such c l o s e d  study,  feedback  execution.  Gentner has used t h i s  There has been e v i d e n c e  & Wilberg  utilize  example o f  w i t h a mode o f m o t o r c o n t r o l w h i c h i n v o l v e s Relative timing  The  t h e way i n w h i c h  i n timing  the proportional  to the  t o preserve t h e speech  m o t o r programming t h e o r i e s  importance  The  when t h e l o w e r l i p  be c l o s e l y i n t e g r a t e d w i t h m o t o r p r o g r a m  the  seem  i n i t s control.  way a m o t o r p r o g r a m must  motor a c t i v i t y  Current  to  i t would  was an a d j u s t m e n t  f e e d b a c k a n d f e e d f o r w a r d mechanisms. skilled  isa  i n b o t h t h e upper and lower l i p s .  of the utterance.  isits  (Abbs e t a l . , 1984) h a s  i n t h e upper l i p served  perturbation  motor b e h a v i o r  such t h a t  components  the r e l a t i v e  as  114 timing  o f t h e r e s p o n s e became i d e n t i c a l  stimulus, varied,  whereas  the o v e r a l l duration  and t e n d e d t o be l o n g e r  The studies  focus  of the present  on i n v a r i a n t r e l a t i v e  to that  o f t h e waveform  than that  given  sufficient  a motor program blind  spots  control  i s learning.  timing  have g i v e n  f o r many o f t h o s e  consideration context,  of learning,  involved  in traditional  Even l e a r n i n g r e s e a r c h e r s  studying of  B u t as Reed  s u c h as  control.  Arguments  reductionistic.  we  have a  (1988) h a s p o i n t e d  little  considers  within  In such a  studies  that  motor  better movement  out, i t i s i n  a better  understanding  a r e i n some  on r e l a t i v e  sense  timing  o f t h e ontogeny o f t h e motor  p r a c t i c e has been g i v e n .  t h e motor program i n l i g h t  20 t r i a l s .  surprising  can g a i n  B e c a u s e most  forced to question in  we  s u c h as G e n t i l e ' s  have a v o i d e d t h e q u e s t i o n program,  of  Gentile  we must move away f r o m  learning i t s e l f  motor  practice i s hardly  u n d e r s t a n d i n g o f t h e "mechanisms u n d e r l y i n g control".  nor  one o f t h e  o f movement o n t o g e n y and 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  of the  to develop  and t h e o r i z i n g h a s b e e n t h e l a c k  (1972) have a r g u e d t h a t learning  Few  extensive  I t seems t h a t  the problem of i n s u f f i c i e n t  surprising.  stimulus.  practice f o r subjects  ( i f one e x i s t s ) .  research  of the  study  enough p r a c t i c e t o a d d r e s s t h e q u e s t i o n have t h e y  of the  But i f one  o f o n t o g e n y , one i s  w h e t h e r a motor p r o g r a m c a n be  With such i n s u f f i c i e n t the invariance  t h e p r o g r a m has n o t b e e n  that  practice,  developed  i t i s not  i s deemed t o e x i s t  found.  Subjects  have n o t  115 been g i v e n  sufficient  time to develop that  A l s o most s t u d i e s on b e e n b a s e d on study) t h a t in  the  important,  and  which f u n c t i o n s its  timing  relationship  to  By  studying  learning.  has that  an  timing  r e v i e w on  of  are  of the  The  continuous  present  forward  of the  This fields  i s an  i s that  most o f t h e  present  research  on  interaction was  of r e l a t i v e it  timing. was  c o n t r i b u t i o n of  focus  on  the  e s s e n t i a l question  question,  humans l e a r n t h e  However, t h e i n the  the  on  study  of psychology  answers t o t h i s  herein,  study,  this relationship  l e a r n i n g , I have p u t  o f a movement.  behind  i s no  understanding  "what i s l e a r n e d " .  been put  i n terms  studies  i n a t r a c k i n g task,  been d i s c u s s e d  is  human-environment  relative  a long h i s t o r y i n the  timing  present  development  One  context  environment  i n v e s t i g a t e the  i n timing control.  behavior.  in a  a motor program  Most o f t h e  environment.  feedback  with  f o r the  i n which there  to gain  question  the  t i m i n g have n e g l e c t e d  possible  In t h i s  operates  Armstrong's  I have a r g u e d above, t h e r e  i n v e s t i g a t e the  during  tasks  to  As  a t r a c k i n g task  between human and designed  timing  of  have  assumption.  relative  chosing  exception  have t h u s p o s t u l a t e d  this  was  timing  i n a p r i m a r i l y open-loop f a s h i o n  In c h o s i n g  invariant  (with the  i n t e r a c t i o n with  control.  problems with  intention  invariant relative  invariant relative  which a continuous  not  by  premise  invariance.  view of paper,  and that  motor has  relative  learning that is different  relative  timing,  than  i n that  116 it  emphasizes  this  view,  organization  as h a s been  rather than representation.  s u g g e s t e d above,  parallels  c a n be  drawn b e t w e e n p r o c e s s e s o f l i v i n g s y s t e m s  ( s u c h as  morphogenesis)  i n that  involve state that  and p r o c e s s e s o f l e a r n i n g ,  the e v o l u t i o n o f t h e organism toward  of organization.  o c c u r s i n l i v i n g systems,  as a " h i g h e r "  function that  of the b i o l o g i c a l same l a w s . the  human  entities. this  This  w o r l d , and t h e r e f o r e assumption  complex  a process considered  removed f r o m t h e r e s t n o t g o v e r n e d by t h e  i s b a s e d on a d u a l i s t i c  view o f  i n w h i c h m i n d a n d body a r e s e e n as s e p a r a t e In c o n t r a s t ,  r e v i e w has been  process  i t has o f t e n been  i s somehow  both  a more  Though l e a r n i n g i s i t s e l f  In  rooted  t h e view  one i n w h i c h  i n biology,  o f l e a r n i n g put forward i n l e a r n i n g i s s e e n as a  r a t h e r t h a n one removed f r o m i t .  117 APPENDIX B PILOT STUDY  INTRODUCTION  I n d e e d , i f t h e n e r v o u s s y s t e m does n o t o p e r a t e - and cannot operate - w i t h a r e p r e s e n t a t i o n of the s u r r o u n d i n g w o r l d , what b r i n g s about t h e 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 o f man and a n i m a l and t h e i r enormous c a p a c i t y t o l e a r n and m a n i p u l a t e t h e w o r l d ? Maturana &  Varella A  (1987, p.133) .  simple but  understand has  essential  learning  been c e n t r a l  i n the  answer t h a t  has  the  i s "What i s l e a r n e d ? " .  to psychology  behaviorism  some k i n d  q u e s t i o n f o r t h o s e who  1930's  been put  of memorial  since the  (Gibson, forward  this  b e e n d e s c r i b e d i n many d i f f e r e n t many d i f f e r e n t Schmidt,  labels  1975),  motor program historical  such  as:  development  This question  inception Weimer,  central  plays i n this  underestimated.  ways and has schema  Schmidt,  (Pribram, 1988).  (MacKenzie & Dugas, believe  & Marteniuk,  1987; that  Proteau,  what is  1985;  and  has  Marteniuk,  learned  his  Proteau,  of  Within  1932;  1971),  and  Although  the  been  l e a r n i n g p r o c e s s cannot Marteniuk  One  been g i v e n  (Bartlett,  of these concepts  Indeed,  1977).  r e p r e s e n t a t i o n has  most o f t e n w i t h open l o o p c o n t r o l p r o c e s s e s , t h e feedback  of  representation.  image o f a c h i e v e m e n t ( K e e l e , 1975;  to  invokes the development  (or c e n t r a l )  a r e a o f motor l e a r n i n g ,  1969;  seek  associated role  that  be  co-workers  Marteniuk,  & Levesque,  Girouard,  1988)  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 t h e a c t i o n  and  the  information that  is  118 p r o d u c e d as a c o n s e q u e n c e o f s u c h a c t i o n s . intent  I t i s not the  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 question learned  v i a the concept  marry b o t h start  The  that  organization  term t o use than  notion  of representation,  as i t i s g e n e r a l l y  authority'  ( C a r e l l o , Turvey, Kugler, Reed,  1988).  t o the problem o f & Shaw,  Maturana & V a r e l l a  proposed a s o l u t i o n t o the problem o f Though l e a r n i n g may n o t i n v o l v e it  does i n v o l v e  skillful as  Instead  representations,  internal that  they  organization,  that  Meijer,  (1987)  have  representationalism.  representation  of conceiving  c a n be t h o u g h t  which t r a n s f o r m  are d i f f e r e n t .  we t h i n k  of these  o f movement, a b o u t more  of these  experiment  of t h i s  idea.  o f as s t a t e s o f with  learning,  Sperry  surgically  After  will  the surgery,  f r o g stuck  stick  and t h e  and m o t o r p r o c e s s e s . (1945) as an  A f r o g when p r e s e n t e d  field,  such  changes i n terms o f i n t e r n a l  c o n d u c t e d by S p e r r y  visual  changes  M a t u r a n a and V a r e l l a s u g g e s t  internal  c o r r e l a t i o n s between s e n s o r y  the  1984;  t h e i n t e r a c t i o n s between t h e p e r s o n / o r g a n i s m  environment  an  'higher  changes i n t h e b r a i n , which b r i n g  movement.  l e t us  i s representation.  i n e v i t a b l y leads  and  But, f i r s t  i s p e r h a p s a more  conceived,  1988;  i n s u c h a way as t o  f e e d b a c k and r e p r e s e n t a t i o n .  by a r g u i n g  appropriate  of organization,  o f what is  with  Consider  illustration  a f l y in his  h i s t o n g u e o u t and c a t c h  the f l y .  r o t a t e d t h e e y e s o f a f r o g by 90 d e g r e e s . when he p r e s e n t e d  the frog with  i t s tongue i n a d i r e c t i o n e x a c t l y  a fly,  90 d e g r e e s  119 away f r o m where t h e f l y a c t u a l l y was.  Thus t h e  nervous  system  seems t o have c o r r e l a t e d s e n s o r y  events,  rather  t h a n t o have r e p r e s e n t e d  environment  i n i t s brain.  encompasses  a highly  correlations,  Skilled  the  and m o t o r  external  human movement  complex and i n t e g r a t e d  facilitating  frog's  a highly  array  efficient  o f such  interaction  with the environment. An a l t e r n a t i v e t o t h e n o t i o n is  organization  loop  (which c o u l d  control processes).  consists  of s h i f t s  of representation,  i n v o l v e b o t h open a n d  Thought o f i n t h i s  i n internal  states  There i s evidence t o i n d i c a t e t h a t learning  and p r o c e s s e s  toward a higher differentiates  order  of l i f e  involve  organizational  Schrodinger  f r o m t h e non l i v i n g  and e n t r o p y .  order  o u t o f t h e e n v i r o n m e n t " and i n so d o i n g ,  living  levels  of organization.  and  there  higher  Fuchs  level  learning  (1962)  "drink  defy  (1976)  i s also the basis  subjects  and he b a s e d h i s  have  that  i n motor  developed  a  while  progression-  subjects  change  over the course of l e a r n i n g . evidence  order  of learning,  motor o r g a n i z a t i o n ,  h y p o t h e s i s on t h e f a c t  d i d provide  entropy.  f o r such a p r o c e s s  found t h a t  of perceptual  strategy  experiment  & Nacson  evidence  a t r a c k i n g task  regression control  organization  i s behavioral  learning.  i n terms o f  they progress t o higher  Gentile  shifts  (1944)  " L i v i n g o r g a n i s m s " he w r i t e s  organisms evolve  suggested that  learning  organization.  order  As  closed  both processes of  organization.  the l i v i n g  of  way,  then,  for a progression  This in  their  120 learning  toward  progression kind  of A  representation similar  structure as  "a  that  unit".  The  the  formally of  coordinative  body p a r t s ,  such that  refined the  and  these  during  Morphogensis  differentiation forms in  of  the  and  development  of  body  moves i n a  often  instance,  f r e e d o m by hand has define  are  the  an  joints  and  integrated  illustration  of  and  whole.  more  this  consider  the  coordinative  of  morphogenesis.  ongoing  and  complementary processes  A  similar  stages and  batter body  task  of  lead  to  p r o c e s s may  coordinative  be  will  freeze An  during  expert  the  fashion.  the on  constraints  degrees the  of  other  that  (Tuller,  i n l e a r n i n g the  later  order  a motor task,  out  of  occurring  undifferentiated  appropriate  rigid,  higher  structure  learning  rigidly.  Whereas e a r l y  e i t h e r random or  of  feedback  r e l a t i o n s h i p s become  of  (1980,  functional  various  as  a l .  a number  single  r e l a t i o n s h i p s amongst body p a r t s  1982).  et.  incorporates  development  rigid  the  coordinative  process  early  holding  the  The  Kugler  a  any  the  the  a novice  learned  the  Fitch,  the  as  to  a  and  organization.  In  &  an  in  spanning  i n t e g r a t i o n which  learning.  For  As  learning  by  function  feedback  involves  act  such  learning.  occurring  amongst t h e  comparison between the  structure  often  to  these  organized.  explain  structure.  structure  communications  learning,  to  With  make r e c o u r s e  defined  muscles  i s constrained  to  be  coordinative  been  group  may  feedforward  With  organization.  i n order  progression  of  has  joints  order  i t seems u n n e c e s s a r y  development  p.17)  a higher  Turvey  relationships  i n learning they  become  121 more d e f i n e d and coordinative an  organized.  s t r u c t u r e i s not  ongoing process  manifests its  Thought  of i n t h i s  a fixed  development  the  s t r u c t u r e , but  of d i f f e r e n t i a t i o n  i n c e r t a i n ways a t c e r t a i n  way,  and  i n t e g r a t i o n which  stages  involves a progression  rather  of l e a r n i n g ;  toward a h i g h e r  order  organization. Such a s y s t e m a t i c learning (Franks  a motor s k i l l & Wilberg,  systematic of  that by  (Marteniuk  appears to manifest of higher  Over the  practice  & Wilberg  course  (1982),  itself  order  component  or response  developed  of l e a r n i n g , the resolution.  frequencies i n the  information  by V o s s i u s ,  only  fundamental an  periods of  the  that  the  frequencies movements  In t h e  study  extensive  and  frequency  approximation  of the  of p r a c t i c e d i d the w h o l e waveform and  were i n h e r e n t  i n the  r e q u i r e d to  a b s e n c e o f any  visual blanking  Early in learning, general  features  T h e i r response contained  of the  stimulus,  original.  Only  subjects gain  begin  then  (a method o f i n p u t  1965).  complex movement p a t t e r n .  major  through  component  s u b j e c t s were a b l e t o r e p r o d u c e o n l y t h e this  and  & Romanow, 1983) .  s u b j e c t s were g i v e n  r e p r o d u c e t h e waveform p a t t e r n  first  1988),  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 o f t h r e e  stimulus  i n tracking studies  J a g a c i n s k i & Hah,  are produced r e v e a l a f i n e r  Franks  of organization i n  been e v i d e n t  tasks  acquisition  a movement.  has  1982;  movement r e p r o d u c t i o n This progression  progression  an  and  after  T h i s was  the  was  long  overall  c o n s t r u c t i n g the  stimulus.  thus  of  mastery  details  achieved  by  122 the  addition  waveform,  of h i g h e r order harmonics t o the  suggesting that people  movement i n t e r m s o f component The  h y p o t h e s i s put  can produce a response movement and  learn  forward  was  the  maps t h e reliance  control processes.  Few  n e e d t o be  undertaken  accurate.  However, n o v i c e p e r f o r m e r s  l i m i t e d but invoke  the  frequently Although data,  Fourier  h y p o t h e s i s was  analysis and  task  of the  a  need  to  more  movement. given  were o n l y s u b m i t t e d  input b l a n k i n g stage  the  actions  and  criterion  processes  taken  system  corrective  considered plausible  was  o f feedback  of the  to of  the  a the  subject's  t r a c k i n g phase  s t i m u l u s and  control  d u r i n g the p u r s u i t  were a t b e s t  present  response  of  cursors  study  was  t h a t the process  upon  the  t r a c k i n g phase of  undertaken,  That  learned  of l e a r n i n g  involves a nested process  superimposed c o n t r o l .  processes  the  the  only speculative.  g e n e r a l q u e s t i o n o f what is  hypothesis  of the  Certain conclusions therefore, regarding  response  experiment  criterion  t h a t produce only  during the p u r s u i t  when b o t h  superimposition  the  account  composition  were v i s i b l e .  The  during the no  the experiment,  produced  feedforward  s u b j e c t s ' responses  experiment, response  and  performers  i s detailed  of the  i n dealing with d e t a i l s  this  the  response  general approximation feedback  organize  that s k i l l e d  that closely  i f the  and  frequencies.  t h e r e f o r e reduces  upon i t s f e e d b a c k  may  response  therefore, to and  the  specific  a pursuit  of response  i s , i n order to  address  tracking  generation fulfill  with  the  123 requirements  of the task  stimulus  and  response  generate  a movement.  stimulus  and  feedback  control  this  Several study.  with The  zero lag) the observed  generated system  specific  Firstly,  (maintain alignment  i t was  felt  that  further  learn  the higher frequency  complex w a v e f o r m d u r i n g t h e  t h e way  Secondly,  f r e q u e n c i e s over the  feedback)  which the and  both  visual  s t i m u l u s and  display.  subjects. of  response  s u b j e c t s do  the  produce  produce  retention.  by  components t o t h e i r  the  response  after  and  of the  the  given to  the  stability  their  ability  If subjects learn  response,  withdrawn  the  a retention period  adding  are they  same h i g h e r h a r m o n i c s a f t e r  s u b j e c t s were t r a n s f e r r e d  was from  was  systematically  F o u r t h l y , at the time  of  T h e s e were c o n d i t i o n s i n  ability,  l e a r n e d waveform.  these  of  three  involved a manipulation  a retention test  tracking  complex r e s p o n s e s  frequency  fact  skill  of learning,  t h r e e months i n o r d e r t o i n v e s t i g a t e  reproduce  in  was  components o f a  were w i t h d r a w n  S u b j e c t s were r e t e s t e d  of t h e i r  to  withdrawn,  Thirdly,  longevity  in this  evidence  stages of  course  were i n t r o d u c e d .  s t i m u l u s was  error.  i n f l u e n c e s the expression of  i n p u t b l a n k i n g c o n d i t i o n s (which visual  a  i n o r d e r t o g a i n an u n d e r s t a n d i n g  i n which feedback  component  later  the  w i t h by  q u e s t i o n s were a d d r e s s e d  the hypothesis that  acquisition.  i s dealt  o p e r a t e s upon t h i s  needed t o v e r i f y to produce  s u b j e c t must  e r r o r between  response  that  between  and to  to higher  also  able  a p e r i o d of  retention  test,  t o f o u r waveforms w h i c h v a r i e d  in  124 base  frequency,  angles  a n d two waveforms w h i c h v a r i e d t h e p h a s e  o f t h e component  c o n d i t i o n was g i v e n  frequencies.  i n order  to test  a movement i n t e r m s o f t h e r e l a t i v e  The f i r s t  transfer  whether s u b j e c t s timing  learn  of the response  e l e m e n t s o f t h e movement, o r i n t e r m s o f t h e o v e r a l l duration given in  o f t h e movement.  i n order  t o determine whether s u b j e c t s  t e r m s o f component  features.  The s e c o n d t r a n s f e r c o n d i t i o n was  In t h i s  frequencies  t r a i n i n g waveform.  frequencies  as t h a t  In v a r y i n g t h e phase angles  frequencies  topological  o r i n terms o f t o p o l o g i c a l  c o n d i t i o n , t h e t r a n s f e r waveforms a r e  composed o f t h e same component  component  l e a r n movement  one c r e a t e s  of the  o f these  a waveform w i t h  different  features  METHOD Subjects Four u n i v e r s i t y students and  no m o t o r o r v i s i o n  their participation had  previous  deficits  in this  tracking  with  hand  preference  r e c e i v e d course  credit for  study.  a right  None o f t h e s e  subjects  experience.  Task Subjects controlled  a response cursor  oscilloscope stimulus  were r e q u i r e d t o move a j o y s t i c k  screen.  cursor  (point l i g h t  The s u b j e c t ' s  (point l i g h t  task  which  display)  on an  was t o f o l l o w a  d i s p l a y ) which  appeared  125 directly in  above t h e  a series  Subjects  The  c u r s o r on t h e  sat at a t a b l e with t h e i r The  oscilloscope  o f them a t a v i s u a l l y  subjects h e l d the  thumb.  s c r e e n and  o f h o r i z o n t a l movements a c r o s s t h e  supported. front  response  The  wrist  plane while the  right  s c r e e n was subtended  and  j o y s t i c k was  comfortably  p l a c e d 50  j o y s t i c k between t h e  pronated  screen.  forearm  angle  moved  cm  in  o f 11.4 index  supinated i n the  degrees.  finger  and  coronal  b e i n g moved.  Apparatus An  industry standard p l o t t i n g  Company CONOGRAPHIC - 12 model control, its  was  adapted  internal  filtered  electronics.  30 v o l t  split  analog to d i g i t a l daughter digital ranged  f o r use  board  resident  10 v o l t s ) ,  +32767  (+10  j o y s t i c k was  The  t h e X a x i s had  ordinate  i n an  IBM  spring  was  into  10,000 Ohms, and  was  linear  to  The  Labmaster values  joystick  (zero v o l t s  The  being  dead Y  potentiometer  one  had  (-  was  therefore only X  signal,  (within  an  whose  centered along the  recorded.  an e l e c t r i c a l  a  Microcomputer.  B o u r n s number 3852A-282-103A), w h i c h t r a n s f o r m e d displacement  bypassing  f e d by  t o -32768 d i g i t a l  free displacement,  displacement  by  converter of the  t o -5 v o l t s  Aircraft  order  connected  w h i l e the v o l t a g e range of the  center).  zero  (Techmar L a b m a s t e r ) ,  volts)  + 5 volts  (Hughes  i n the experiment  t h e A/D  approximately  and  with  power s u p p l y and  v a l u e s g i v e n by from  6110)  T h i s j o y s t i c k was  converter  was  joystick  axis co(a  joystick  a resistance  percent)  of  throughout  126 the  full  range o f j o y s t i c k  A computer g e n e r a t e d oscilloscope digital  used t o maintain and  s t i m u l u s was  using a d i g i t a l  input of the  stimulus  movement.  output  joystick.  1 cm  response  A  of v e r t i c a l  p r e s e n t e d on  equivalent to  second analog displacement  the  signal  was  between  the  c u r s o r s on t h e o s c i l l o s c o p e .  v a l u e s were s a m p l e d e v e r y  the  Response  four milliseconds.  Waveform The = A/2 of  one  s t i m u l u s waveform was  + C c o s cot + C/2 cycle  of the  cos  g i v e n by  2cot + C/4  s t i m u l u s was  2048  equation  cos ms.  4cot.  (1):  The  f(t)  period  127  Procedure I. T r a i n i n g This  phase  consecutive 200  Phase o f t h e experiment took place  days.  Each  experimental  over  five  session consisted of  cycles of practice i n pursuit tracking the stimulus  waveform. practice  This  w a s f o l l o w e d b y 10 t e s t  c y c l e s were broken  down i n t o  trials.  The 200  four blocks  o f 50  cycles. The  first  1) p u r s u i t cursors 2)  five  tracking  remained  partial  input  test  trials  (PT) i n w h i c h b o t h  total  nor  input  blanking  of  blanking  t h e response were Each  I  (PIB1)  i n which  c u r s o r were  and response  only the  shown on t h e s c r e e n ;  (TIB) i n w h i c h  neither the stimulus  shown on t h e s c r e e n .  of these f i r s t  five  trials  c o n s i s t e d o f 15 c y c l e s  PT, f o l l o w e d b y 7 c y c l e s o f P I B 1 ,  TIB.  D a t a was s a m p l e d  these  three The  stimulus  phases:  on t h e s c r e e n ;  movements o f t h e s t i m u l u s 3)  consisted of three  f o l l o w e d by 8 c y c l e s o f  from t h e middle 2 c y c l e s o f each o f  phases.  second f i v e  1) p u r s u i t  tracking  2) p a r t i a l  input  test  trials  (PT) a s  blanking  c o n s i s t e d o f two phases:  above;  II  (PIB2)  i n which  only the  r e s p o n s e was shown on t h e s c r e e n . Each  o f these second  five  trials  o f P T , f o l l o w e d b y 15 c y c l e s o f P I B 2 . the  m i d d l e two c y c l e s o f b o t h  phases.  c o n s i s t e d o f 15 c y c l e s Data  was s a m p l e d  from  128  II.  Retention The  same f o u r  phase o f the period  of  3 months.  that  The original tested  returned task  waveform  in this  c y c l e s o f PIB1,  by  10  cycles of Subjects  following ten  200  of each of  f o l l o w e d by  training  laboratory after  i n the  first  phase  waveforms were  equation  10 10  10  1)  waveforms  a  the  used.  c y c l e s o f p r a c t i c e on  1 and  c o n s i s t e d of  i n the  phase o f  stimulus  (see F i g u r e  trials  to the  to t h a t used  s u b j e c t s were g i v e n  Each t r i a l  the  t h a t were u s e d  several different  10  1)  The  identical  f o r two  below.  subjects  experiment  e x p e r i m e n t was except  Phase  and  the  then  described  c y c l e s o f PT,  by  followed  c y c l e s o f PIB2,  followed  TIB.  were t e s t e d on  their  ability  to track  the  waveforms:  original  experiment  waveform  at  from the  i t s original  training  phase o f  the  base  frequency  of  0.4 9  Hz.;  2)  the  original  waveform a t a b a s e  frequency  of  0.31  Hz.;  3)  the  original  waveform a t a b a s e  frequency  of  0.41  Hz.;  4)  the  original  waveform a t  a base  frequency  of  0.61  Hz.;  5)  the  original  waveform a t a b a s e  frequency  of  0.69  Hz.;  6)  transformation  waveform w i t h  the  component and C  60  cos  of the  frequencies  d e g r e e s and  original shifted  given  (cot + T C / 2 ) + C/2  by  cos  out  o f p h a s e by  equation  (2):  90,  30,  f ( t ) = A/2  (2cot + 7T./6) + C/4  cos  +  (4cot  + 71/3) . 7)  transformation component  of the  frequencies  original shifted  0.5 out  Hz  waveform w i t h  o f p h a s e by  30,  the 60,  129 45  and  C cos +  8)  10)  and  + 7C/6)  g i v e n by  + C/2  cos  (3):  equation  (2cot + JC/3)  f ( t ) = A/2  + C/4  +  (4cot  cos  .  entirely  A/2 9)  (cot  71/4)  an  degrees  + 170  new  waveform g i v e n by  c o s cot  + 65  cos  equation  2cot + 45  waveform v a r y i n g i n  b e t w e e n 0.391  1.904  and  a waveform w i t h t h e as t h e  with those  associated with d i f f e r e n t (5) :  f (t)  = A/2  + C/4  frequency  Hz.  same a m p l i t u d e  o r i g i n a l , but  f(t) =  4cot  cos  a randomly generated Hz  (6):  and  frequency  amplitude  values  f r e q u e n c i e s g i v e n by  c o s cot  + C cos  values  2 cot  equation  + C/2  cos  4  cot.  Data A n a l y s i s  Root mean squared the pursuit accuracy. root  is  Poulton  of the  interval,  tracking  sum  data (1974)  of the  d i v i d e d by  g i v e n by  the  stimulus value  response  value  RMS  at time  e r r o r has  p.38).  indicates  d e f i n e s RMS  squares  interval  response  [ L  calculated  as t h e  error  at each  t , and  i s sampled  "overall  s u b j e c t has  2  sampling  p  I/,  It  where  1 2  t, r i s the  p i s t h e number  of  over. Poulton  adequacy  i n the value  square  intervals.  (s-r) /  on  response  error  interval  b e e n recommended by  A decrease  t h a t the  of the  RMSE =  at time  measure f o r e v a l u a t i n g t h e (1974,  was  i n order to determine  equation:  that the  (RMS Error)  t h e number o f s a m p l i n g  s i s the  intervals  error  o f RMS  as t h e  of  best  tracking"  error  become more a c c u r a t e  scores and  130  precise  i n tracking,  and t h u s i s i n d i c a t i v e  of learning  ( 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 , Variability within  o f each  s u b j e c t ' s r e s p o n s e was  each b l o c k o f f i v e  phase based (1982). sampled curves  trials  on a p r o c e d u r e  Two  cycles  (for a total  1974).  f o r the pursuit  tracking  from F r a n k s , W i l b e r g ,  from each o f t h e f i v e of ten cycles).  The  another  i n order to calculate  score.  At each  o f t h e 512  a within  sampling  (sd) o f t h e t e n r e s p o n s e  & Fishburne  trials  were  displacement-time  f r o m t h e s e t e n c y c l e s were s u p e r i m p o s e d  deviation  calculated  upon  subject  intervals  one  variability a standard  displacements  was  calculated  using the following equation:  S.D.  - r )  j  at a given  2  / 10  interval  2  ,  where  subject  a profile  variability  f o r each  indicating  differential  subject  used  set of five  intra-subject  r  time  at which r i s as t h e i n d e x  f o r a given t r i a l .  on e a c h  (Mean  It also t o be trials,  variability  thus  throughout  waveform. Lead-lag  i n d e x was  used t o determine  which the s u b j e c t ' s response during pursuit was  s d ' s was  [ £  o f w i t h i n waveform v a r i a b i l i t y  calculated  the  r i s the response  The mean o f t h e s e 512  within  allowed  /  and p i s t h e number o f i n t e r v a l s  sampled. of  1  =  tracking.  the extent to  l e d or lagged the stimulus  A cross-correlation  coefficient  c a l c u l a t e d u s i n g t h e s t i m u l u s and t h e r e s p o n s e  ( e a c h composed constant intervals  o f 512 p o i n t s ) ,  and t h e r e s p o n s e  with the stimulus being  s i g n a l b e i n g advanced  of ten milliseconds.  waveforms  F o r each  i n time  held by  advancement o f t h e  131 response s i g n a l coefficient The  a P e a r s o n product-moment  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  time a t which  was u s e d t o d e t e r m i n e  the response with respect The  lead-lag  indicant  t h e average  location  i n t h e waveform a t w h i c h  Harmonic  i t only  or l a g , rather than the s p e c i f i c the subject  was l e a d i n g  or  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  component  yielded the following frequencies  & Wilberg,  1974).  analysis  waveforms i n t o  as an  u s e d by  measure i s t h a t  reflects  (Poulton,  strategies  (Franks, 1 9 8 2 ; Franks  of this  lead  or l a g  to the stimulus.  o f the changing response  The l i m i t a t i o n  lagging  the lead  index has p r e v i o u s l y been used  subjects during tracking 1982).  calculated.  t h e c o r r e l a t i o n between s t i m u l u s and  r e s p o n s e was g r e a t e s t of  correlation  frequencies.  information:  o f the response;  The H a r m o n i c  analysis  i ) t h e component  i i ) the amplitude values o f angle values o f  t h e s e component  frequencies;  i i i ) t h e phase  t h e s e component  frequencies;  and i v ) t h e p e r i o d  of the  waveform; Bernstein analysis 1900's,  (1967)  was among t h e f i r s t  i n t h e s t u d y o f human movement. he p e r f o r m e d  experiments  filmed performing various filing link  o r hammering.  i n which  this  RT d a t a , b y F r a n k s  In t h e e a r l y subjects  were  e v e r y d a y movement t a s k s s u c h as  The movement k i n e m a t i c s o f t h e v a r i o u s  segments were t h e n a n a l y z e d i n t o  More r e c e n t l y  t o use harmonic  component  frequencies.  a n a l y s i s h a s b e e n u s e d by G r e e n & Wilberg  (1982)  i n tracking,  by  (1971)  on  132 Marteniuk by  & Romanow  Richardson  performance. used  (1983) on arm movement t r a j e c t o r i e s ,  & Pew  (1968) i n m e a s u r i n g s t a b i l o m e t e r  In t h e p r e s e n t  i n order t o determine  response,  The  the composition  i n Lowry and Hayden  of the subject's  i n a l l four  i n t o p equal  units  xO, x l , x2, ...  integration  xp, w i t h t h e i r  corresponding  yp.  The  determined  a n d e a c h o f t h e s e p o i n t s were  divided labelled  ordinate  The t r a p e z o i d a l  rule of  was a p p l i e d o v e r t h e p e r i o d y i e l d i n g t h e  equations:  1) a  D  = 2/p % y  2)  a  n  = 2/p  7t  y  r  cos n x  r  3)  b  n  = 2/p  7C  y  r  sinnx  r  r  2 gave t h e harmonic c o e f f i c i e n t s  component  on a method  T h i s waveform was t h e n  v a l u e s b e i n g yO, y l , y2, ...  Equation  feedback  (1951 pp 324 - 3 2 8 ) .  ( p e r i o d = 2 7t) was  o f t h e waveform  an a u t o c o r r e l a t i o n .  following  was  (PT, P I B 1 , PIB2, a n d T I B ) .  periodicity  o f t h e waveform, w h i l e  harmonic c o e f f i c i e n t s The  Harmonic a n a l y s i s  h a r m o n i c a n a l y s i s was c a l c u l a t e d b a s e d  described  using  study,  d u r i n g movement p r o d u c t i o n ,  conditions  and  equation  of the cosine • 3 gave t h e  o f t h e s i n e component  o f t h e waveform.  e n t i r e waveform 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 / 2 Q  + K A  n  c o s ncot + B  This  e q u a t i o n was e x p r e s s e d  f(t)  = A /2 0  + 7t C  n  n  s i n ncot  i n terms o f a c o s i n e  c o s (nu)t-(j) ) n  where Cn = A  2 n  function: +  B  2 n  (j) 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  necessary  timing relationship  components.  among v a r i o u s  harmonic  T h e s e p h a s e a n g l e v a l u e s were d e t e r m i n e d  using  133 the  following equation: In o r d e r  the  stimulus  to test  t a n <|> = B / A n  the accuracy  waveform i t s e l f  frequencies.  n  These d a t a  n  o f t h e harmonic a n a l y s i s ,  was a n a l y z e d  i n t o component  were t h e n r e s y n t h e s i z e d  w a v e f o r m w h i c h was compared t o t h e o r i g i n a l  into a  w a v e f o r m by  c a l c u l a t i n g t h e RMS e r r o r between t h e two w a v e f o r m s . p r o d u c e d an RMS e r r o r o f 1.8  This  mm.  RESULTS and DISCUSSION  Pursuit  Tracking  As  expected,  performance errorful  i n the pursuit tracking condition  improved w i t h  practice.  a s m e a s u r e d b y RMS e r r o r  became more c o n s i s t e n t i n t h e i r within block  variability  score  Subjects  the  stimulus  and l a g g i n g  not  use a wait  Rather  continuously  3) .  that  also  a s m e a s u r e d by a  approached zero but block  as l e a r n i n g  s u b j e c t s were b o t h  i t , suggesting  a n d move s t r a t e g y  i ti s likely  They  (see F i g u r e 2 ) .  became more c o n s i s t e n t w i t h i n e a c h t r i a l From t h e b e g i n n i n g ,  less  r e s p o n s e a s m e a s u r e d by a  function not only  progressed.  1).  (see F i g u r e  In a d d i t i o n , t h e l e a d l a g i n d e x crosscorrelation  became  that  leading  subjects d i d  i n pursuit tracking.  f e e d b a c k was b e i n g  t o modify the s u b j e c t ' s  used  response  (see F i g u r e  134  Figure R o o t Mean' S q u a r e d E r r o r training  1.  as a f u n c t i o n  and r e t e n t i o n  of practice  days.  for  RMS ERROR 60  R m s E r r  3 50  4  M  0 n t h s  o  30  o r  o  phase new  X  .69  £  .49 .31 .61 .4 1  m  20  1  2  4  '3  Training D a y s x  * R M S Error  A  .49 Hz wave  +  .31 H z w a v e  .69 Hz wave  0  phase shifted  Retention * A  .41 H z w a v e  •  .61 H z w a v e  new  6 4 0 u n i t s = 10.0 c m CO Cn  136  Figure Mean o f 512  standard deviation  time p r o f i l e s  o f 10  cycles and  2. v a l u e s from t h e  of pursuit  retention  tracking  days.  displacement for raining  Variability v  a r  3 M  i  I  a b  o  0  phase  n  A  new  X  .69  •  .6 1  •  .49 .4 1 .31  t  h s  *  +  t y  1  2  3  Training x  * Variability  4  Days  Retention  .49 Hz  wave  +  .31 H z  .69 Hz  wave  0  phase shifted  6 4 0 u n i t s = 10.0 c m  wave  * A  .41 H z  wave  D  .61 H z  wave  new  £  138  Figure 3 . The  standard deviation  subjects'  responses  of the  lead-lag  r e l a t i v e to the training  days.  index  of  the  stimulus over the  five  Variability of Lead-Lag  Days  * a v e r a g e d over the four  subjects  140 When s u b j e c t s further  days o f t e s t i n g  subjects  and  variability In o r d e r  timing,  and  the  original  the  exception  RMS  and  on  In o r d e r  scores  scores  an  to those  (see F i g u r e s  subjects  or  waveforms was  new  waveform w h i c h  t o p o l o g i c a l p r o p e r t i e s than the  learn  variability  waveforms was scores,  a movement i n t e r m s o f  seem r a t h e r t o features  A l l three  1 and  that  i t s component  2).  the the  compared  with  contained had  original.  l e a r n a movement i n t e r m s o f  (see F i g u r e s  of  two  waveforms  equivalent  indicating  higher  2).  than  these  frequencies.  with  i n terms of i t s  phase angles  different  and  both  on  l e a r n a movement  frequencies  component  RMS  achieved  were t r a n s f e r r e d t o  component  entirely  these  RMS  maintained  waveform,  1 and  different  P e r f o r m a n c e on  that  relative  They  waveform w h i c h had  waveform a t d i f f e r e n t  p e r f o r m a n c e on  learn  waveform.  frequencies  P e r f o r m a n c e on  to  2).  t o determine whether s u b j e c t s  waveforms c o n t a i n i n g t h e  that  as m e a s u r e d by  1 and  equivalent  fastest  features,  found  r e t e n t i o n d a y s , were t r a n s f e r r e d  original  t e r m s o f i t s component  original.  one)  (see F i g u r e s  these  of the  for 2  of performance e q u i v a l e n t  waveform f o r a l l s p e e d s o f t h e  variability  original  i t was  t o determine whether s u b j e c t s  variability  topological  a 3 month p e r i o d  (experiment  speeds o f the  RMS  in  scores  subjects,  to various  four  after  ( r e t e n t i o n days),  retained a level  of days t h r e e and  returned  as m e a s u r e d  subjects  do  frequencies  by  not but  i t s topological  141  T r a c k i n g under V a r i o u s Feedback The  response waveforms  Conditions  from each o f t h e four  conditions  were  analysis.  With p r a c t i c e at the t r a c k i n g task,  learned phase, that had  compared and analyzed  t o produce a response frequency  4 -  (see Figures  studies  by Franks  more c l o s e l y  than those 6).  This  of their  i s i n line  (1982)  & Wilberg  an Harmonic subjects  ( i n a l l conditions)  and amplitude  of the stimulus,  using  feedback  whose  approximated  earlier with  responses  evidence  and Marteniuk  from  & Romanow  (1983) . In  comparing the harmonic p r o f i l e s  responses with considered: contained  o n e , how t h o s e  not contained  response)  different  Subjects  With p r a c t i c e  the stimulus,  conditions  i n with  i n the pursuit tracking feedback  t h e amplitude  contained  conditions) i n values  i n the stimulus  ( i . e . by day f i v e )  and t h i s  (see Figures  4 -  the amplitude  was m a i n t a i n e d  those 4 -  values  to  those  over t h e three  For the stimulus 6), such  of  (Figures  components became c l o s e r i n v a l u e  month r e t e n t i o n i n t e r v a l . however  (but expressed  of practice.  frequencies  of  that are  residual  feedback  (as compared t o t h e o t h e r  the response  be  equivalent  i n the stimulus  i n the four  will  components  t w o , how t h o s e  performed best  of  two a s p e c t s  a r e matched by  of accurately producing  component 6).  manifest  amounts  condition  frequency  i n t h e response,  frequencies  terms  of the stimulus,  i n the stimulus  components  the  those  of the subjects'  only  an improvement  condition, with  142  Figure The  amplitudes  of the harmonic  r e s p o n s e waveforms u n d e r  the  components t h a t  four  1.  4.  feedback  comprised  conditions  on  the day  Pursuit Tracking Day 1  1  2  3  <  S  (  component frequencies  Response Only  Day 1  Response Waveform  component frequencies  1  8  144  Figure The  amplitudes  of the harmonic  r e s p o n s e waveforms u n d e r  the  components t h a t  four  5.  5.  feedback  comprised  conditions  on  the day  Pursuit Tracking Day 5  Stimulus Only  component frequencies  component frequencies Input Blanking Day 5  Response Only Day 5  Response Waveform  Response Waveform  1  2  3  4  5  Day 5  (  component frequencies  1  1  component frequencies  146  Figure The  amplitudes  of the harmonic  r e s p o n s e waveforms u n d e r  the  6.  components t h a t  four  retention  feedback day.  comprised  conditions  on  the the  Input Blanking Retention  Response Only Retention  Response Waveform  1  2  3  4  S  (  7  1  2  4  3  5  (  7  6  component frequencies  component frequencies  Stimulus Only  Pursuit Tracking Retention  Retention  Response Waveform  1  component frequencies  2  3  4  5  component frequencies  (  7  1  148 practice  was  not  stimulus  only  In comparing  finds that  the  stimulus  subjects  only  seem t o p r o d u c e  condition.  This  may  be  they  in learning  better which  later  in a situation there  stimulus to  the  Early of  condition  stimulus, about  the  The  component  to  stimulus  the  order  of their  for the  the  break,  stimulus.  performance  are those  information  has  may  information This  blanking  response  t o produce  that  on t h e  suggests that  screen FB  and  about  forms  waveform  t o be  favorably This  was  critical  in  approximation a 3  month  decrement  in  response  Thus i t a p p e a r s  that  between the  t h e movement o f t h e i r  o n e s own  error.  Visual  after  i n which the v i s u a l  the correspondence  the  given  decrements.  accurate  return  attend  are  condition.  appeared an  to  to these three  show t h e g r e a t e s t  been removed.  forget  and  in  the  required  in learning.  When s u b j e c t s  the conditions  subjects  later  own  subjects  In  of the response  input  than  perform  c o n d i t i o n compared more  than the  case b o t h e a r l y and  information  of  only  in  i n learning,  condition)  to.  the response  performance  frequencies  the response  are only  to attend  seems t o c a u s e  during  the  stimulus,  one,  response  i n pursuit tracking they  i n learning attempting  information  day  the  pursuit  they  only  to attend  subjects  whereas  1980),  stimulus  i s less information  only  information  the  early  from  attentional capacity  (Neisser,  (like  i n the  because  have a more l i m i t e d  on  a better  c o n d i t i o n t h a n t h e y do  when s u b j e c t s do  performance  and 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  one  tracking  evident.  response  the visual hand.  i s critical  in  149 order  to  produce  Pribram's sensory  of  (1971)  movement.  contention  that  a l l four  feedback  is in line  residual frequencies  by  the  of  a c c u r a c y was  interval  i n a l l four  tracking  condition  as  compared w i t h  virtually  day  five  were d i m i n i s h e d ,  The  other  was  predicted  condition  would  higher  frequency tracking  fewer high  conditions that  conditions.  And  components than the  were  by  w h a t was  conditions.  I t was  other not  conditions  available.  that  when  respond to seems  i n which t h i s This  feedback e r r o r by  from the  and  error  based  that  pursuit  would  information on  the  rather  in  was  assumption  i s available, subjects  findings that  It  tracking  they  making d i s c r e t e c o r r e c t i o n s .  present  in  the  response than  p r e d i c t i o n was  about  in  about  discrepancy  found  thought  where t h e y were g i v e n  feedback  were  frequency  tracking  stimulus  components  pursuit  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  between  five  expected.  subjects  discrepancy  present  day  than were  more r e s i d u a l h i g h e r  other  pursuit  components  r e s p o n s e s made i n t h e  contain  the  condition.  tracking condition to  This  retention  residual  frequency  i s contrary  a  creating  stimulus.  In  in  amplitudes  thus  3 month  conditions.  pursuit  pursuit  the  residual frequencies  other  the  fact that  the  feedback  fewer  i n the  i n the  c a r r i e d over the  the  none of  were p r e s e n t  found  in  residual noise  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 level  with  movement i s r e p r e s e n t e d  conditions,  response d i s s i p a t e d such that the  This  terms.  For the  accurate  will  However i t  than making  any  150  Figure 7 . Mean c y c l e d u r a t i o n conditions  (period)  during  under  training  the four  and  feedback  retention.  Period of Training Wave p e r r  2200  I 0  d 2100  m s e c  2000  1  2  3  R2  Training D a y s Pursuit  Tracking  R e s p o n s e Only  Retention +  Stimulus  D  Input  Only  Blanking  152 kind  of discrete corrections,  feedback t o modulate t h e i r  subjects  response  used t h e v i s u a l  i n a more  continuous  fashion. As  regards  pursuit cycles  that  In t h e response subjects  frequencies  determining  in  loop  process  learning  that  processes  only  of the subjects  with  the  results  condition,  response  i n determining  stimulus  absolute  nor response  longer  timing.  i s necessary,  in  learning  response  information  i s sufficient.  of organization  identical  than  from t h e environment  information  some k i n d  late  the overall  stimulus  evidence  as  such that t h e  i s typically  feedback  early i n  as w e l l  response becomes  When n e i t h e r  Thus  timing.  i s utilized  learning  present  lower  that  in  The  of the  stimulus.  (or immediate)  are available t o the subject  seems t o be i m p o r t a n t  as those  o f response m o d i f i c a t i o n are  i n t h e response  of the stimulus.  movement  i s important i n  tracking condition,  of the subject's  and  o f a movement c y c l e ( s e e  absolute  of the stimulus.  information  that  information  only  blanking  than  o f response m o d i f i c a t i o n  timing  duration  and input  periods)  timing  i n the pursuit  absolute to  stimulus  i n determining  learning  frequency  I t seems f r o m t h e p r e s e n t  closed  This  only  produced  p r o d u c e d movement c y c l e s  the overall  7).  utilized  subjects  ( i . e . longer  Thus i t seems t h a t  the  i n the stimulus  w e r e o f t h e same b a s e  conditions,  Figure  control,  tracking conditions,  stimulus.  base  timing  indicates that  Early  whereas  subjects  late  develop  o f movement i n w h i c h t h e r e  seems  153  to  be,  as  (1932)  Bartlett  interplay  b e t w e e n FB  from t h i s  study  exhibited  certain  that  in recalling own  cultural  on  s u b j e c t s make s y s t e m a t i c when s u b j e c t s  relative  to  America,  they  putting  Lima which  east This  occurring  locations be  of  The  present  west  recall  of North  west  south  of  coast  space.  the  location  America  of the  people  South two  of North  Lima,  locations  of  of  i s , i n the the  A  or  i s also  found  similar  process  reproduction  of  the  continents  America.  Thus  t h i n k of i t  the  i n the may  waveforms  input blanking  r e v e r s a l s and  be in  condition  changes  i n space d u r i n g  of  brain's  this the  speed  seem  to  movement  "memory". that  frequencies  data.  coast the  distortion  hypothesis  component  details  geographical  distortions  asked to  directly  systematically distorted  reproduction  in recalling  relationship  homunculus.  i n the  of  are  east  the  found  Lima.  kind  That  that  i s on  i s i n fact  of  sensori-motor  study.  distort  South America  though Miami being  the  line  the  memory f o r s p a t i a l  locations  illustrates  i s on  is in  context.  1981)  of Miami which  also  memory i n w h i c h he  (Tversky,  example,  This  an  movements  subjects would d i s t o r t  More r e c e n t l y r e s e a r c h  For  The  f r o m memory  distortions.  s t u d i e s on  stories  f o r h i s schema,  schema i t s e l f .  systematic  (1932)  Bartlett's  f i ttheir  the  suggested  t h a t were reproduced  with  to  and  has  Rather  of  subjects  systematically acquire  a m o v e m e n t was  in this  study,  not  supported  subjects  seemed  by to  the the  systematically course  of learning.  acquisition (Franks task large  diminish the residual frequencies  I t i s possible that the progressive  o f component  & Wilberg,  specific  over the  frequencies  1982;  Marteniuk  previously  found  & Romanow, 1983) was  i n t h e sense t h a t both these  s t u d i e s used a  a m p l i t u d e movement w h i c h i n v o l v e d t h e w h o l e arm.  present  study  movement.  on t h e o t h e r  hand used a s m a l l e r  wrist  The  155 APPENDIX C KINEMATIC PROFILES INPUT BLANKING DAY 15  (BEST  Figure 1.  2.  3.  4.  5.  6.  RMS) Page  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 s t i m u l u s and response during input blanking f o r subject on day 15 wl  1  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 s t i m u l u s and response during input blanking f o r subject on day 15 wl  2  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 s t i m u l u s and response during input blanking f o r subject on day 15 wl  3  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 s t i m u l u s and response during input b l a n k i n g f o r subject on day 15 wl  4  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 s t i m u l u s and response during input b l a n k i n g f o r subject on day 15 wl  5  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 s t i m u l u s and response during input b l a n k i n g f o r subject on day 15 wl  6  157  158  159  160  161  162  162 APPENDIX  D  KINEMATIC PROFILES INPUT BLANKING DAY 15 V A R I A B I L I T Y AMOUNGST THE F I V E CYCLES  Figure 1. 2.  3. 4.  5. 6.  Page  V a r i a b i l i t y across five cycles during b l a n k i n g f o r s u b j e c t 3 o n d a y 15 w l  input  V a r i a b i l i t y across five cycles during b l a n k i n g f o r s u b j e c t 3 o n d a y 15 w l  input  V a r i a b i l i t y across five cycles during b l a n k i n g f o r s u b j e c t 3 o n d a y 15 w l  input  V a r i a b i l i t y across five cycles during b l a n k i n g f o r s u b j e c t 4 o n d a y 15 w l  input  V a r i a b i l i t y across five cycles during b l a n k i n g f o r s u b j e c t 5 o n d a y 15 w l  input  V a r i a b i l i t y across five cycles during b l a n k i n g f o r s u b j e c t 6 o n d a y 15 w l  input  164 165  166 167  168 169  169 APPENDIX E HARMONIC PROFILES DAY  15  (Wl -  W7)  Figures 1. 2.  3. 4. 5. 6. 7.  Page  Amplitudes of harmonic w l o n d a y 15  components t h a t  Amplitudes of harmonic w2 o n d a y 15  components t h a t  Amplitudes of harmonic w3 o n d a y 15  components t h a t  Amplitudes o f harmonic w4 o n d a y 15  components t h a t  Amplitudes of harmonic w5 o n d a y 15  components t h a t  Amplitudes of harmonic w6 o n d a y 15  components t h a t  Amplitudes o f harmonic w7 o n d a y 15  components t h a t  comprised 171 comprised 172 comprised 173 comprised 174 comprised 175 comprised 17 6 comprised 177  Day 15  Wave 1  350 300  1  2  3  4  component  5  6  frequencies  7  8  Day 15  Wave 2  350 300  1  2  3 4 component  5 6 7 frequencies  8  Day 15  Wave 3  I  Standard  WW  Stimulus  ZH  Response  Deviation  4 2  4 6 3 component frequencies  7  8  Day 15  Wave 4  350 300  1  2  3 4 component  5 6 7 frequencies  8  Day 15  Wave 5  350 300  component  frequencies  Day 15  2  Wave 6  3 4 component  I  Standard  Hi  Stimulus  ZZI  Response  5 6 frequencies  Deviation  7  8  Day 15  Wave 7  350 300 a  m 250  1  2  3  4  5  6  component frequencies  7  8  177 REFERENCES Abbs,J.H., Gracco,V.L., & C o l e , K . 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