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.
I had stopped at a florist on my way to his apartment and bought myself an extravagant red rose for my buttonhole. Now I removed this and handed it to him. He took it like a botanist or morphologist given a specimen, not like person given a flower.
“About six inches in length,’ he commented. ‘A convoluted red form with a linear green attachment.’
‘Yes,’ I said encouragingly, ‘and what do you think it is, Dr P.?’
‘Not easy to say.’ He seemed perplexed. ‘It lacks the simple symmetry of the Platonic solids, although it may have a higher symmetry of its own… I think this could be an inflorescence or flower.’
‘Could be?’ I queried.
‘Could be,’ he confirmed.
‘Smell it,’ I suggested, and he again looked somewhat puzzled, as if I had asked him to smell a higher symmetry. But he complied courteously, and took it to his nose. Now, suddenly, he came to life.
‘Beautiful!’ he exclaimed. ‘An early rose. What a heavenly smell!’ He started to hum ‘Die Rose, die Lillie…’ Reality, it seemed, might by conveyed by smell, not by sight.
I tried one final test. It was still a cold day, in early spring, and I had thrown my coat and gloves on the sofa.
‘What is this?’ I asked, holding up a glove.
‘May I examine it?’ he asked, and, taking it from me, he proceeded to examine it as he had examined the geometrical shapes.
‘A continuous surface,’ he announced at last, ‘infolded on itself. It appears to have’ – he hesitated – ‘five outpouchings, if this is the word.’
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.
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.