> Hi Marc --
> it's interesting to wonder about "what it would be like" to directly
> perceive mathematics -- but we also have to acknowledge when we ask
> the question, what are the philosophical assumptions we're smuggling
> along. For instance, the human brain is not capable of direct
> perception of tables, either.
> What raises a flag for me in your question is the following apparent
> 1) "The human brain is not capable of direct perception of
> mathematical entities"
> 2) "We could imagine some super-intelligence that possessed this
> ability . . ."
I'd like to suggest a far more interesting prospect: that we _literally are_ a
mathematics. The form of that mathematics, and our role within it as its
metamathematics, the status of abstract symbolic mathematics within that
-metamathematics-R-us universe and its relationship with the
mathematics-as-reality (I have called this 'entropy calculus' elsewhere..for
the sake of having a name)....these things are very interesting and worthy of
some thought... happy new year, all...