[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

*To*: address@hidden*Subject*: fielders, fly balls, and formal loop specs*From*: Dave Long <address@hidden>*Date*: Mon, 24 Nov 2003 08:31:18 -0800*Sender*: address@hidden

There is a brief communication in this week's _Nature_* which claims fielders repeatedly satisfy a simple constraint problem when intercepting fly balls. Their observation, tested in simulation and against traces of real fielders, is that fielders keep track of the rate of change of the two angles relating their position to the ball's. The horizontal change in angle is held constant, while the vertical change is decreased. As psychophysicists, they put it in the following terms: the vertical decrease means that the fielder's possible spots are located on shrinking circles around the ball, while the horizontal constant ensures that the fielder will run in a straight line towards the interception point. If the fielder obeyed the first constraint alone, he might arrive at an impractical solution requiring either a discontinuous motion or a motion faster than he could run. As computer scientists, we would put it in changed terms: the vertical decrease as loop variant, the horizontal constant as loop invariant. The variant ensures that the fielder intercepts the ball in (pace Zeno) a finite time; the invariant ensures that the fielder doesn't arrive at an impractical solution requiring an invalid access: either well outside of, or not following the natural structure of, his datatypes. -Dave :: :: :: * McLeod, Reed, Dienes, "How fielders arrive in time to catch the ball", _Nature_ v426 20 Nov 2003

- Prev by Date:
**Re: dynamic vs. static typing** - Next by Date:
**Re: dynamic vs. static typing** - Previous by thread:
**RE: The Accessibility of Type Theory Research** - Next by thread:
**type inference in imperative langauges** - Index(es):