On 12/6/07, Gabriel Dos Reis wrote:
>
> On Thu, 6 Dec 2007, Bill Page wrote:
>
> | If you wish can treat the sequence of symbols:
> |
> | ( x ( x x ( x ( x ) ) x ) )
> |
> | as encoding a kind of "curve" is some abstract differential geometry.
> | Then each '(' and ')' token has some associated unit "curvature" or
> | something like that. But I do not see any advantage to this point of
> | view.
>
> Are the '(' and ')' needed?
??? Yes of course!
> And in case they are needed, why should they be thought of as
> curvature, as opposed to mere boundary markers?
>
Perhaps they can be thought of as boundary markers. I was talking
about a geometric visual analogy for the structuring of program code,
but you apparently want to take a more abstract topological view.
Since topology logically precedes the the usual notion of geometry
perhaps in this case the notion of dimension is not of much
importance. It is not clear what advantage this might have. Could you
explain?
Regards,
Bill Page.
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