August 2011
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Blind geometry

Would you believe there are blind mathematicians - great ones and specializing in geometry? I am fascinated. Here are a few:

Leonhard Euler (1707-1783) was one of the most prolific mathematicians of all time, having produced around 850 works, half after he became blind. Nicholas Saunderson (1682-1739), blinded in his first year, was Lucasian Professor of Mathematics at Cambridge University. Lev Semenovich Pontryagin (1908-1988), was a renowned Russian topologist. And Louis Antoine (1888-1971) is another. But the list goes on.

A paper mentioned in MindHacks (here) and cited below is mainly about Bernard Morin, famous for showing how to turn a sphere inside out. There are some very interesting observations on blind thought from a few blind mathematicians.

Morin believes there are two kinds of mathematical imagination. One kind, which he calls “time-like”, deals with information by proceeding through a series of steps. This is the kind of imagination that allows one to carry out long computations. “I was never good at computing,” Morin remarked, and his blindness deepened this deficit. What he excels at is the other kind of imagination, which he calls “space-like” and which allows one to comprehend information all at once.

Thus long strings of calculations are hard to keep track of … By contrast, “in geometry, the information is very concentrated, it’s something you can keep in mind,” Giroux said. What he keeps in mind is rather mysterious; it is not necessarily pictures, which he said provide a way of representing mathematical objects but not a way of thinking about them.

Alexei Sossinski points out that it is not so surprising that many blind mathematicians work in geometry. The spatial ability of a sighted person is based on the brain analyzing a two-dimensional image, projected onto the retina, of the three-dimensional world, while the spatial ability of a blind person is based on the brain analyzing information obtained through the senses of touch and hearing.

In a private communication, Sossinski also noted that sighted people sometimes have misconceptions about three-dimensional space because of the inadequate and misleading two-dimensional projection of space onto the retina. “The blind person (via his other senses) has an undeformed, directly 3-dimensional intuition of space,” he said.

Diderot, who involved blind people in his research, concluded that people can gain a good sense of three-dimensional objects through touch alone. He also found that changes in scale presented few problems for the blind, who “can enlarge or shrink shapes mentally. This spatial imagination often consisted of recalling and recombining tactile sensations.”

It seems there are many ways to think about space, especially if you want to play with spheres in 7 dimensions.

Citation: The World of Blind. Mathematicians. 1246. NOTICES OF THE AMS. VOLUME 49, NUMBER 10. (Author was not identified.)

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