Talking about mathematics with Gregory has gotten me wondering confusedly about the ultimate stimuli of mathematics, so I thought I’d spend a little time in this entry trying to get a start on that. I think it begins with a brain’s awareness of “one” and “more than one.” My guess right now is that this depends on a fairly sophisticated mechanism or set of mechanisms in the brain that notify the brain’s owner (in a manner of speaking) of a repeated stimulus–a dot in the environment, say. As the eye scans what’s out there, it sees dotX1 when the eye is looking in direction A, so records the sighting as dotX1/A in the pre-visual awareness, and in the repetition-center, but only as dotX1 in the latter. If the eye then sees dotX1 (i.e., not really dotX1 but a twin of it) when the eye is looking in direction B, a record of dotX1/B will go into the pre-visual awareness. Meanwhile, the nervous system will try to record dotX1 again in the repetition-center, but fail, because the m-cells activated by the dot’s twin are still active. Sensory-cells sensitive to such a failed attempt to activate will reflexively cause a tag meaning “two dotX1s” to be added to the person’s record of the moment. Or some such operation will be carried out.
Result: the person experiences the visual perception of dotX1 at A and at B, and a numerical feeling of twoness related to dotX1, or a feeling of 2 times dotX1. This, I should think, would come about fairly early in the evolution of animals, probably long before mammals evolved. And it could easily be auditory, too–except the same sound in two close-together moments rather than in the same visual space.
With the coming of speech, true elementary numeracy would have begun, with the splitting off of twoness from particular dots or the like, abetted by language in ways I’ve shown using my theory of knowlecular psychology (I hope) for similar epistemologic events.
Obviously, a sense of threeness and higher numericalnesses would evolved the same was the sense of twoness did–but not get two high due to the law of diminishing returns. Once there were words for twoness (and oneness) and higher quantities (hey, I’m talking about quantification here, I just now realize), arithmetic and high mathematics would have developed.
I think I can give just-so stories for most of them, but not today.
My conclusion, I think, is that “asensual” numbers exist “out there.” We can sense quantities without feeling their material.
I would add that numerals and words for numbers like “seven” are all part of our verbal language.
Odd thought I had: the sounds representing for numbers and colors I just realized all stay the same as adjectives. “Cold,” too. There are others. It makes intuitive sense to me that all the colors and numbers would do this, but I can’t make rational sense of it yet.