Updated on 20 Out. 2008

 

 

 

 

Keynote abstracts

"Natural solutions to complex problems"
David Lee

  
About twenty years ago the BBC broadcast a brilliant documentary film “Animal Olympians”, which has continued to inspire me. It shows a wide range of species, including humans, performing natural skilled acts, and reveals how similar we animals are in how we move. It is evident that there must be some simple universal principles of movement. My quest to discover those principles led to developing General Theory. My talk will be about the principles underpinning natural purposive movements and about how those principles, encapsulated in the equations of General Theory, operate in athletic, musical and other learned skills. I will start by outlining the elements of the theory.
General Purposive action is goal-directed and requires prospective control, control with an eye to the future. This requires setting up in the nervous system action-formulae to prescribe essential elements of the trajectory of the action (Bernstein 1967), to ensure that the prescribed trajectory does not exceed the animal's physical power. For instance, when running toward a cliff edge, an animal needs to regulate its deceleration adequately ahead of reaching the edge to avoid running out of braking power and so falling. Purposive action also requires prospective perceptual monitoring. Moving the body, or part of it, requires interacting with external forces, such as gravity, wind, currents and friction, which are not wholly predictable. Therefore, to keep the action on its prescribed trajectory, an animal needs to pick up, through its perceptual systems, prospective information about where the action is actually heading and adjust the power to its muscles to keep it on course (Gibson 1966; Bernstein 1967). A bird landing on a twig in gusty weather is a wonderful demonstration of precise prospective control of purposive action.
When performing an action, the information in the action-formula guiding the action has to be speedily coupled with the information from the perceptual systems monitoring the action. It would be efficient, therefore, if the two types of information were in the same 'currency', i.e., expressed in common informational variable. General theory of action guidance (Lee 1998) indicates what the common informational variable is. Given that all purposeful action entails controlling the closure of action-gaps between the current states an animal is in and the goal states to be achieved, the theory shows that an informational variable that is both necessary and sufficient for regulating the closure of an action-gap is the function of the gap. This equals the time-to-closure of the action-gap at the current closure-rate, or the current size of the gap divided by its current rate of change. Thus, is a prospective informational variable with the dimension time - no matter what the dimension of the action-gap itself is (distance, angle, force etc). Furthermore, of an action-gap, A, is, in principle, directly specified in all known sensory fields, by virtue of being proportional to the value of the of a gap, S, in the sensory field (e.g., the optic flow field). That is
(1)where is a constant. In contrast, other measures on an action-gap, such as its size, velocity and acceleration, are not directly perceptible, but are only perceptible at ‘second-hand’ through sensing the of another action-gap that relates to a body or action dimension. Direct perception of has been demonstrated experimentally (Lee 1998		   Thus, theory and experiment indicate that is a primary sensory variable for controlling closure of action-gaps. Theory and experiment also indicate that  is a primary action-formula variable for controlling action-gaps. General theory shows that the principle of -coupling (keeping two s in constant ratio) can be used to formula-guide the closure of an action-gap. The idea is that the of a changing action-gap is constantly sensed and the muscular forces controlling the closure of the gap are constantly adjusted to try to keep the of the action-gap in constant ratio with a changing formula-gap generated in the nervous system. (There is recent evidence for a formula-gap in the electrical activity in the brain; Lee et al. 2008.) Analyses of skilled actions have revealed two such formula-gaps (Lee 2005). They comprise a bisymmetric pair, D and G, that close with constant deceleration and constant acceleration, respectively - like the gaps between a bouncing perfectly elastic ball and its zenith and the ground, repectively. Keeping the of an action-gap, A, in constant ratio with the of D, i.e., keeping
(2)
where is a constant, directs the deceleration-to-closure of a gap, and is equivalent to keeping constant the time derivative, , of of the action-gap. Keeping the of an action-gap, A, in constant ratio with the of G, i.e., keeping
(3)
where is a constant, directs the acceleration-then-deceleration movement when an action-gap closes from rest to rest, as when reaching or stepping. Evidence for -guidance and -guidance of movement has been found in a range of species, including humans (Lee 2005).

In the final part of my talk I will show how the principles of General Theory, encapsulated particularly in the above three -coupling equations, can be applied to understanding skilled performance. Examples will be drawn from sports skills such as sprinting, jumping, somersaulting, hitting and catching; from musical performance skills such as singing, bass playing and dancing; and from the use of music in aiding skilled performance.

References
Bernstein NA (1967) The co-ordination and regulation of movements. Oxford: Pergamon
Gibson, J. J. (1966). The senses considered as perceptual systems. Boston: Houghton Mifflin.
Lee, D. N. (1998). Guiding movement by coupling taus. Ecological Psychology, 10, 221-250.
Lee, D N (2005) Tau in action in development. In Rieser JJ, Lockman JJ, Nelson CA (eds) Action as an organizer of learning and development. (pp 3-49). Hillsdale NJ: Erlbaum.
Lee, D. N., Georgopoulos, A. P., Lee, T. M. & Pepping, G-J (2008). A neural formula (tauG) that guides movement. (submitted)

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