FOM: Martin Davis on intuition

[Stephen Cook]

I am intruigued by Martin's October 8 message saying

   It seems to me that most mathematical progress has leaned on a small number
   of intuitions derived from real-world experience: counting, space, chance,
   force, motion.

I suspect that at least some of these notions are hard-wired in our brains,
and do not come from experience alone.   For example, we are better
at three-dimensional geometry than four-dimensional geometry not
just because we live in a three-dimensional world, but because we have
an innate ability to visualize in three dimensions.   

I'm not so sure that counting ability is innate.  We must teach children
to count, and in fact we need to use words to count.   We don't teach
children how to visualize.

Steve Cook