ABSTRACT
Ruud van der Weel Developmental Neuroscience Laboratory, Department of Psychology,
Norwegian University of Science and Technology (NTNU), Trondheim, Norway
Cathy Craig School of Psychology, Queens University Belfast, Belfast, NI
Audrey van der Meer Developmental Neuroscience Laboratory, Department of Psychology,
Norwegian University of Science and Technology (NTNU), Trondheim, Norway
Over the past three decades or so, the concept of tau (W) (Lee, 1976, 1980, 2005) has undergone a series of rapid changes, with each change emphasizing a greater
generalizability of the concept. Initially, the value of the tau-margin specified
instantaneous time to contact with a surface or target in critical timing situations,
such as diving gannets folding their wings (Lee & Reddish, 1981) and human
participants leaping up and punching balls that were dropped from varying
heights above them (Lee, Young, Reddish, Lough, & Clayton, 1983). However,
when timing an action, identifying the variable(s) that control its initiation is not
always sufficient. Given a large enough time-window, actions are often timed by
controlling optical variables in a continuous fashion. The concept of continuous
visual control was then introduced in the form of the tau-function (W(x) = x/ x ). Somersaulters (Lee, Young, & Rewt, 1992), humming birds (Lee, Reddish, &
Rand, 1991), bats (Lee, Van der Weel, Matejowsky, Holmes, & Pettigrew, 1992;
Lee, Simmons, Saillant, & Bouffard, 1995) and pigeons (Lee, Davies, Green, &
Van der Weel, 1993) all appear to rely on the derivative of tau (W ) to control
their deceleration when landing. Thus, “braking” in these actions was achieved
by keeping the rate of change of W constant with respect to time. But what about the continuous visual control of acceleration of movement? To be able to
account for an entire movement, including both acceleration and deceleration,
the W concept was in need of revision. In more recent developments, the notion of tau-g, or, more general, tau-G, has been introduced. This notion provides us
with the interesting possibility of controlling an entire movement by keeping the
(changing) tau of a motion-gap in constant ratio with an intrinsically generated
(changing) tau value. The hypothesis here is that the intrinsic tau equals in value
the tau of a gap to a goal that is generated by motion from rest at constant
acceleration. Putting food into the mouth (Lee, Craig, & Grealy, 1999), directing
gaze when looking at a target (Grealy, Craig, & Lee, 1999), controlling a golf
swing (Craig, Delay, Grealy, & Lee, 2000), and infants sucking milk from a
bottle (Craig & Lee, 1999), are all examples of self-paced actions where the
timing of the movement is prescribed by the way an intrinsic tau-guide evolves
over time.
