Math not necessary sometimes

It seems hard to believe that any educated person thinks that plants can do math, despite the almost endless crop of headlines such as Plants ‘do math’ to control overnight food supplies from the BBC and

Plants do ‘sophisticated’ math to ration food at night from UPI. These are just news release and headline writers trying to get attention. But the idea that all the problems that we would potentially see as math problems are actually solved with symbolic, rule based, serial operations rather than some other method seems fairly general. It takes something like plants using math to make us insist on some other answer. Cognition does not have to always involve semantic, mathematical or logical manipulations of symbols.

There was an old argument, largely settled, about how a fly ball (a ball that is batted high in baseball) is caught. The ball flies, the fielder runs, and he ends up at the same place at the same time as the ball – puts out his gloved hand and the balls falls into it. The math is complicated but the skill is not. The fielder runs so that the ball has a constant bearing. If the fielder can manage to keep the ball in exactly the same place in his visual field he will be able to catch it. The rule is used on the high seas – if one captain see the another ship stay at the same bearing, he must take evasive action. If he doesn’t the two ships will hit (in fact, hit at that bearing angle). How does an airplane pilot know the direction that his plane is moving? It is moving towards the only stationary spot in his vision. And, for the car driver, the reason that a blind spot in his vision is dangerous, is that anything that stays hidden in the blind spot (keeps the same bearing behind the obstruction) will inevitably hit him. Most people know this unconsciously, some learn it consciously, but few do the math it takes to understand exactly why this is a ‘fact’ about moving in a changing world. We use embodied cognition via a perception-action loop more or less automatically.

Now we have some indication of where in the sensory-motor feedback system this skill resides. We follow the bearing of an perceived object in space, as opposed to a spot in the visual field. The object is perceived and placed in space prior to tracking its bearing. We have this indication because we can catch using the sound of an object without being able to see the object.

The experiments are in a paper by Shaffer, Dolgov, Mcmanama, Swank, Maynor, Kelly, and Neuhoff, Blind(fold)ed by science: A constant target-heading angle is used in visual and nonvisual pursuit, published in Psychonomic Bulletin & Review. (ScienceDaily review)

Here is the abstract:

Previous work investigating the strategies that observers use to intercept moving targets has shown that observers maintain a constant target-heading angle (CTHA) to achieve interception. Most of this work has concluded or indirectly assumed that vision is necessary to do this. We investigated whether blindfolded pursuers chasing a ball carrier holding a beeping football would utilize the same strategy that sighted observers use to chase a ball carrier. Results confirm that both blindfolded and sighted pursuers use a CTHA strategy in order to intercept targets, whether jogging or walking and irrespective of football experience and path and speed deviations of the ball carrier during the course of the pursuit. This work shows that the mechanisms involved in intercepting moving targets may be designed to use different sensory mechanisms in order to drive behavior that leads to the same end result. This has potential implications for the supramodal representation of motion perception in the human brain.

2 thoughts on “Math not necessary sometimes”

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