Jack comments on The role of mathematical truths - Less Wrong
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I'm a little confused: did is visual field lose focus such that, instead of seeing the details on objects and their imperfections he actually just saw idealized geometric figures?
One problem with this as evidence of the possibility that geometric forms could exist only in the human mind is that it presumably only applies to a rather narrow class of geometric forms. It would be weird if the geometric forms we have innate access to had a different ontological status from forms that can't be instantiated in the human mind: like a 1000-sided polygon or something in 4+ dimensions.
What I meant was that, if people have simple geometric forms built deep into their minds, then it would be tempting to conclude that math has an objective eternal existence because it feels that way.
In any case, I found the actual quote, and I've very uncertain that it suggests what I thought it did. It seems as though the man was at least as sensitive to simple topology as geometry, However, people don't romanticize topology.
Here's the passage, which I had not remembered as well as I thought:
It's a wonderful extract in any case. It is fascinating to see someone describing the world without anything more than the phenomenology of his surroundings. It is interesting that the concepts he had access to were mathematical and geometric- that these concepts involve a part of the brain separate from the part that involves more complex and obviously learned concepts like shoe, glove, and flower does seem important to keep in mind when evaluating the evidence on this issue. You're right that this fact could lead to us positing a false ontological difference... though of course there are those who will say "gloveness" and "flowerness" are abstract objects as well. The fact that these concepts are processed in different parts of the brain could also be taken as evidence for the distinction in that different evolutionary processes generated these two kinds of concepts. I'm not sure how to interpret this. Good for keeping in mind though.