Earlier analyses of the generation and spread of innovation led me to look into the generator and scatterer, man. 



Applying the same analytic techniques as are used for examining societal structures, I found that man is highly ordered and regulated. His output therefore can be simply described and, to an extent, predicted. This generalizes the principle that the biological paradigm can be extended to social behavior

Marchetti, C.

International Institute for Applied Systems Analysis (IIASA)

Action Curves and Clockwork GeniusesMarchetti, C.IIASA Working PaperWP-85-074October 1985 Marchetti, C. (1985) Action Curves and Clockwork Geniuses. IIASA Working Paper. WP-85-074 Copyright © 1985 by the author(s). http://pure.iiasa.ac.at/2627/ Working Papers on work of the International Institute for Applied Systems Analysis receive only limited review. Views or opinions expressed herein do not necessarily represent those of the Institute, its National Member Organizations, or other organizations supporting the work. All rights reserved. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage. All copies must bear this notice and the full citation on the first page. For other purposes, to republish, to post on servers or to redistribute to lists, permission must be sought by contacting repository@iiasa.ac.at W O R K I N G  P A P E R  l n t e r n a t ~ o n a l  l n s t ~ t u l e  for Appl~ed Systems Analys~s NOT FOR QUOTATION WITHOUT PERMISSION OF THE AUTHOR ACTION CURVES AND CLOCK- WORK GENIUSES C. Marchetti October 1 9 8 5  PTP-85-74 Working Papers are interim reports on work of the International Institute for Applied Systems Analysis and have received only limited review. Views or opinions expressed herein do not necessarily repre- sent those of the Institute or of its National Member Organizations. INTERNATIONAL INSTITUTE FOR APPLIED SYSTEMS ANALYSIS A-2361 Laxenburg, Austria RESUME E a r l i e r  ana lyses  of t h e  genera t ion  and spread of innovat ion l e d  me t o  look i n t o  t h e  gene ra to r  and s c a t t e r e r ,  man. Applying t h e  same a n a l y t i c  techniques a s  a r e  used f o r  examining s o c i e t a l  s t r u c t u r e s ,  I found t h a t  man i s  highly  ordered  and r egu la t ed .  H i s  output  t h e r e f o r e  can be simply descr ibed  and, t o  an e x t e n t ,  predic.ced. This g e n e r a l i z e s  t h e  p r i n c i p l e  t h a t  t h e  b i o l o g i c a l  paradigm can be extended t o  s o c i a l  behavior.  ACTION CURVES AND CLOCKWORK GENIUSES Tu ne quaesieris, sc i re  nefas, Q m n m i h i q u e m t i b i  Finem dii dederint, Leuconoe, nec Babylorn rls Temptaxis numros. Horace Odes, Book I, Ode x i  F a t e  and d e s t i n y  a r e  c r o s s c u l t u r a l  e l e m e n t s  i n  p h i l o s o p h y ,  r e l i g i o n ,  and a r t ,  p e r h a p s  r e a c h i n g  t h e  h i g h e s t  emot iona l  and i n t e l l e c t u a l  i n t e n s i t y  i n  Greek t r a g e d y  and t h e i r  most s u b t l e  e x p r e s s i o n  i n  C a l v i n i s t  theo logy .  Man p e r c e i v e s  e x t e r n a l  f o r c e s ,  endowed w i t h  an  i n t e r n a l  l o g i c ,  t h a t  frame h i s  a c t i o n s ,  f e e l i n g s ,  and t h o u g h t s  i n  an u n b r e a k a b l e ,  i f  n o t  v i s i b l e ,  cage .  S u r e l y  it would be  s t r a n g e  i f  such a  g e n e r a l  p e r c e p t i o n  d i d  n o t  co r respond  t o  some o b j e c t i v e  f a c t .  Tha t  t h e  s o c i e t y  around us  frames o u r  a c t i o n s  i s  a  t r i v i a l  o b s e r v a t i o n .  However, from my socioeconomic a n a l y s e s  ( e . 9 .  1, 2,3) I conc lude  t h a t  t h i s  frame i s  q u a n t i t a t i v e .  The u n d e r l y i n g  l o g i c  i s  hard .  Although e x p r e s s e d  a t  t h e  c o l l e c t i v e  l e v e l ,  it may y e t  be a b l e  t o  accormpdate t h e  i n d i v i d u a l .  A s  Greek t r a g e d y  and C a l v i n i s t  t h e o l o g y  f o c u s  on t h e  i n d i v i d u a l ,  I t h e r e f o r e  c o n f i n e d  my a n a l y s i s  t o  t h e  i n d i v i d u a l ,  t o  de te rmine  whether  t h e r e  is  a  str ict  l o g i c  o p e r a t i n g  t h e r e .  C e r t a i n l y  l o g i c a b o u n d s  a s  long  a s  w e  remain w i t h i n  t h e  biological realm. The more we know about genetics, the more we can observe its pervasive and steely control. It might even clock the day of our death. The evidence is indeed mounting ( 4 ) .  Intellectual activity is a good example. Although patterns have been sought and found ( 5 ) ,  basically they have not gone beyond the level of qualitative descriptions. Youngsters are naive and oldsters are tired, so that activities such as sports and writing books must go up and down with age. I sought to harden the analysis. As usual, I started with facts, hard and proven. And, as usual, I searched exclusively for patterns, avoiding as much as possible the fly paper of explanations. For appropriate documentation, I concentrated on persons whose actions have been appreciated, studied, and classified: artists and scientists provided a good start. I assumed that a piece of art or science is the final expression of a p u l s e  5' action, which started in some obscure part of the brain and worked its way through all the intermediate steps. This led me to study the time patterns of these pulses. In my heuristic mental image actions are transcodifications of information structures. This relationship is true at the biological level, where information is processed in the DNA, as well as at the personal or social level, where the coding has a different suLstrate but the same basic processing rules apply ( 6 ) .  One of the consequences of this mental image is the as- semblage of pulses of action into growth processes. Integrating these over time, I found that the growth function is in fact the temporal organizer of these processes. The curves pre- suppose a final target (a "niche") and a rate, which in biology is directly proportional to the product of the level reached (i.e. the current size of a population) and the part yet to be bridged (i.e. the unfilled niche) to meet the target. As competition, for example, can keep one from reaching this final target, I chose to call this target a virtual or, better yet, a perceived target. This is a constant in the growth equation and remains so throughout the entire growth period. I have applied these concepts to analyses of a disparate array of socioeconomic structures, classifying the growth of populations such as railway networks (with the inauguration of the first line taken as the birth date) ( 2 1 ,  automobiles ( 3 ) ,  and clusters of innovations ( 1 ) ,  Application to individuals comes automatically, provided that one takes the backward step of assuming that information is processed essentially at the individual level, as in society as a whole. Anyway, the reason- ing is heuristic. The results will tell whether we are on the right path. The analytic results for a selection of outstanding person- alities from science, music, and the visual arts are given in Figures 1 to 13. In each case, I took as the population the "brain-children" of these people, plottingitsgrowth and then fitting the data to a logistic curve. I call the resulting chart the action curve, analogous to the growth curve of an individual, and refer to the saturation level as the perceived potential. These l o g i s t i c s  have on ly  t h r e e  parameters .  Thus t h e  time d i s t r i b u t i o n  of t h e  work of a  g r e a t  man can be condensed i n t o  t h r e e  numbers: one d e f i n e s  t h e  perceived p o t e n t i a l ;  t h e  second f i x e s  a  r a t e  c o n s t a n t  ( o r ,  more i n t u i t i v e l y ,  a  t ime c o n s t a n t )  t h a t  measures t h e  sp read  over  t ime;  and t h e  t h i r d  i s  a  time c u r s o r  t h a t  l o c a t e s  t h e  s t r u c t u r e  w i th in  t h e  l i f e s p a n  of t h e  person. These parameters  can be e x t r a c t e d  from a  segment of t h e  d a t a ,  making t h e  r e s t  of t h e  d a t a  de te rmina te .  I t  must b e  obvious  t h a t  I d i d  n o t  t a k e  aim a t  t h e  holy cow of  c r e a t i v i t y ,  on ly  a t  i t s  mooing. For t h i s  reason  I c a l l  such c h a r t s  a c t i o n  curves .  Because I t h i n k  t h i s  r e l a t i o n s h i p  i s  of g e n e r a l  c h a r a c t e r ,  I con t inue  t o  s ea rch  f o r  a p p r o p r i a t e  ind ica-  t o r s  and s t a t i s t i c s  t o  prove t h a t  it a p p l i e s  a l s o  t o  l e s s e r  a c t i v i t i e s .  These t h r e e  numbers c r e a t e  p o s s i b i l i t i e s  f o r  p ry ing  i n t o  t h e  l i f e  of gen iuses ,  c a t e g o r i z i n g  and c l a s s i f y i n g  them. To i l l u s t r a t e  f u r t h e r  what I mean by t h e  perce ived  p o t e n t i a l ,  con- s i d e r  t h e  amount of beans a  man c a r r i e s  i n  h i s  bag and t h e  amount l e f t  when he  f i n a l l y  d i e s .  Looking a t  t h e  c a s e s  men- t i o n e d  h e r e  and t h e  o t h e r s  excluded t o  keep t h e  paper r e l a t i v e l y  b r i e f ,  I f i n d  t h a t  the l e f t o v e r  beans a r e  u s u a l l y  f i v e  t o  t e n  p e r c e n t  of  t h e  t o t a l .  Apparently when Mozart d i e d  a t  35 y e a r s  of age ,  he had a l r e a d y  s a i d  what he had t o  say .  My choice  of cases may be  b iased .  That i s  p o s s i b l e ,  a s  it w a s  determined by t h e  a v a i l a b i l i t y  of s e r i o u s  d a t a  s t r i n g s .  For example, my pe r sona l  i n t e r e s t  i n  t h e  v i s u a l  a r t s  and t h e  abundance of c r i t i c a l  in format ion  i n  my persona l  l i b r a r y  has b i a sed  m e  towards p a i n t e r s .  A s  my i n v e s t i g a t i o n s  a r e  a t  t h e  beginning,  t h e r e  a r e  many open q u e s t i o n s  -- e . g . , ,  how l a r g e  i s  t h e  a r e a  of a p p l i c a t i o n .  My guess  i s  t h a t  t h e  observed p a t t e r n  i s ,  indeed,  a  gene ra l  one which can be used t o  d e s c r i b e  human a c t i o n s .  I n  F igure  1 4  I show t h e  r e s u l t s  of ana lyz ing  ch i ldbea r ing ,  a s  a  c o u n t e r p a r t  t o  t h e  look a t  b ra in-ch i ld ren .  The c h a r t s  r e v e a l  some i n t e r -  e s t i n g  p e c u l i a r i t i e s  i n  t h e  s o c i a l  and c u l t u r a l  modulation of f e r t i l i t y .  On o t h e r  occas ions  I have examined t h e  gene ra t ion  and sp read  of  innova t ions  i n  Western s o c i e t i e s .  A f t e r  a l l ,  man is  the prime mover and f i n a l  r e c i p i e n t  of innova t ion .  COMMENTS TO THE CHARTS The c h a r t s  f i t  t h e  cumulative number of t h i n g s  produced, independent  of t h e i r  s i z e  and t h e  importance a t t r i b u t e d  t o  them. The f i t t i n g  equa t ion  i s  a  t h r e e  parameter  l o g i s t i c  of t h e  t y p e  - N N ( t )  = 1 + exp - (a t+b)  where N i s  t h e  cumulative number of o b j e c t s  a t  t ime t and N i s  t h e  asymptote o r  s a t u r a t i o n  l e v e l .  E, a  and b  have t o  be c a l -  c u l a t e d  by f i t t i n g  t h e  d a t a .  The c h a r t s  show F = N ( t ) / g  i n  a l i n e a r i z e d  form: l og  (F/l-F) = a t  + b. - N i s  given  i n  p a r a n t h e s i s ;  it i s  c a l l e d  t h e  p e r c e i v e d  p o t e n t i a l  i n t h e  t e x t .  A T  g i v e s  t h e  temporal spread  of produc- t i o n :  t h e  t ime t o  go from 10% t o  90% of N; it r e p r e s e n t s  a more i n t u i t i v e  way of exp res s ing  a. The parameter b i s  a time c u r s o r  l o c a t i n g  t h e  p u l s e  i n t o  t h e  l i f e  of t h e  person.  The y e a r  of maximum p r o d u c t i v i t y  i s  u s u a l l y  marked. I t  corresponds t o  t h e  p o i n t  i n  t h e  curve where . 5  N i s  reached.  The f i r s t  d a t a  p o i n t s  a r e  u s u a l l y  below t h e  equa t ion  l i n e ;  t h i s  I i n t e r p r e t  a s  a c a t c h  u p .  The l i n e  may be i n t e r p r e t e d ,  imply- i n g  t h a t  t h e  c r e a t i v e  impulses e x i s t e d  be fo re  they  could be t e c h n i c a l l y  exp res sed ,  a s  i s  t h e  c a s e  wi th  t h e  f e r t i l i t y  of g i r l s  of 1 4  years .  But a s  t h e  dynamic of ca t ch ing  up shows, t h e  impulses a r e  delayed h u t  n o t  suppressed.  ( G i r l s  have a l -  ready met t h e i r  p r e s c r i b e d  quota  by 1 8  yea r s  of  age a s  do a r t i s t s  very  e a r l y  i n  t h e i r  c r e a t i v e  p e r i o d . )  When dea th  i s  approaching (very  o f t e n  around 9 0 %  of E l ,  u s u a l l y  t h e r e  i s  a s l i g h t  i n c r e a s e  i n  o u t p u t  wi th  r e s p e c t  t o  t h e  p r e s c r i p t i o n  of t h e  equa t ion .  See,  t y p i c a l l y ,  Mozart. In  t h e  ca se  of Shakespeare,  t h e  e x t r a  p l ay ,  a s  I l a t e r  d i s cove red ,  was i n  f a c t  w r i t t e n  by somebody else. Other c a s e s  n o t  shown h e r e  a r e  s t i l l  under e l a b o r a t i o n .  They show t h a t  sometimes a double -bar re l  l i f e ,  w i th  two p u l s e s ,  may be p o s s i b l e .  REFERENCES (1) Marchetti, C. (.1980) Society as a Learning System: Dis- covery, Invention, and Innovation Cycles Revisited. T e c h n o l o g i c a l  F o r e c a s t i n g  and S o c i a l  Change 18:267-282. (2) Marchetti, C. (1983) On a  F i f t y  Y e a r s  P u l s a t i o n  i n  Human A f f a i r s :  A n a l y s i s  o f  Some P h y s i c a l  I n d i c a t o r s .  PP-83-5. International Institute for Applied Systems Analysis, Laxenburg, Austria. (3) Marchetti, C. (1983) The Automobile in a System Context: The Past 80 Years and the Next 20 Years. T e c h n o l o g i c a l  F o r e c a s t i n g  and S o c i a l  Change 23:3-23. (4) Winfree, A.T. (1980) The Geometry  o f  B i o l o g i c a l  T i m e .  Springer Verlag, New York. (5) Simonton, D.K. (1984) G e n i u s ,  C r e a t i v i t y  and L e a d e r s h i p .  Harvard University Press, Cambridge, Mass. (6) Marchetti, M. (1983) On the Role of Science in the Post- industrial Society: "Logos - The Empire Builders". T e c h n o l o g i c a l  F o r e c a s t i n g  and S o c i a l  Change 24:197-206. Note These references are basically limited to my connected work. Literature on the application of Volterra-Lotka equations is vast and easily retrievable. 

Action Curves and Clockwork Geniuses

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