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naraburns  nihil supernum  1yr ago (text post)   32994 thread views

Culture War Roundup for the week of February 13, 2023

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People in the distant past managed to build functioning societies without necessarily being able to rotate shapes in their heads or even being able to play all that many word games.

This is a really uncharitable interpretation of what intelligence (IQ tests) actually is.

It's not the shape rotating or word games, it's the ability to do those things. Modern people might deadlift an Olympic bar instead of lifting up a log into a wagon, but the ability to do both those things is identical. Similarly, the ability to internalize the principle of modern civil engineering is the same ability to internalize that the columns in the Pantheon are not only there for the aesthetics, it's the same thing as shape rotating ability.

Do you really think if Homer were alive today he couldn't fill out a crossword? Or Al-Khwarizmi wouldn't be able to do matrix multiplication? The amount of intelligence difference to understand something and invent something is the same difference between an ant and a human. I might know more math than Arcemedes, but I am an ant compared to him. Don't confuse standing on the shoulders of giants with being taller than them.

I think Homer would have trouble with a crossword, considering he was blind.

Don't be so confident! He might have required external help, but I still would expect him to give @f3zinker a run for his money.

In general, blind geniuses may have much less of a problem with spatial reasoning than one naively expects.

Antoine’s Necklace is not a mere curiosity and has very interesting properties. One would suppose that constructing such a structure would require considerable visualization, which is indeed true. However one of the most interesting things about this knot is that it was formulated and studied by Louis Antoine, who was blind. After he lost his eyesight, the famous mathematician Henri Lebesguesuggested to him that he study topology.

I have noticed (it is a common observation) that it is almost a rule that mathematicians who are blind are usually geometers/topologists. Such a correlation can not be mere coincidence.

Before reading Sossinsky’s book which also mentions G. Ya. Zuev as another influential blind topologist, the two best examples that I was aware of were L. S. Pontryagin and the great Leonhard Euler. Pontryagin is perhaps the first blind mathematician that I had heard of who made seminal contributions to numerous areas of mathematics (Algebraic Topology, Control Theory and Optimization to name a few). Some of his contributions are very abstract while some such as those in control theory are also covered in advanced undergrad textbooks (that is how I heard of him).

Pontryagin lost his eyesight at the age of 14 and thus made all of his illustrious contributions (and learnt most of his mathematics) while blind. The case was a little different for Euler. He learnt most of his earlier mathematics while not blind. Born in 1707, he almost lost eyesight in the right eye in 1735. After that his eyesight worsened, losing it completely in 1766 to cataract.

“It is not surprising at all that almost all blind mathematicians are geometers. The spatial intuition that sighted people have is based on the image of the world that is projected on their retinas; thus it is a two (and not three) dimensional image that is analysed in the brain of a sighted person. A blind person’s spatial intuition on the other hand, is primarily the result of tile and operational experience. It is also deeper – in the literal as well as the metaphorical sense. […].

recent biomathematical studies have shown that the deepest mathematical structures, such as topological structures, are innate, whereas finer structures, such as linear structures are acquired. Thus, at first, the blind person who regains his sight does not distinguish a square from a circle: He only sees their topological equivalence. In contrast, he immediately sees that a torus is not a sphere […]”

I imagine, in my mediocrity, that crosswords are in fact much easier solved using a visible 2D grid as the foundation. Who knows if that's true. Maybe «seeing» some modular-alphabetic arithmetic, or word embeddings rotating through each other and locking upon letter matches, would make for a faster solution.

Learn something new everyday indeed.

Learn something new everyday. In that case, any other great author or poet could do the hypothetical crossword.

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