NP Alabama Pi

[jporter]

Josh:

> 
> Even believing that physics and pure math don't intersect (which I
> think pretty much no one believes anyway), you're not forced into
> metaphysical explanations. At least, not immediately - how much
> the various solutions to this problem result in metaphysical
> hooha is a matter of debate.

If you believe in that intersection then the next question is: what is the
product of that intersection?

> 
> Wittgenstein's solution (that statements of mathematics are "rules of
> syntax"), for one, appears to avoid metaphysical quandaries without
> even caring whether or not there is a "pure" mathematics separate
> from physics.
> 

Syntax are rules. It's the same wolf, naked. At some point there is no form
independent of content.

> 
> The definition of pi that you're familiar with is only a definition
> insofar as you also use the definitions of circle, diameter, etc.
> that are part of Euclidean geometry. Of _course_ "pi" would vary
> in some other geometry where "circle" and "diameter" didn't mean the
> same things as in Euclidean geometry. But those numbers are no longer
> pi. Context matters.

Here, here!
 
> There are definitions which don't rely on geometry.
> 

Whichever method you prefer for generating pi, and then decide is a "new"
definition, especially as that process becomes more and more abstract and
removed from the original conception of the ratio of the circumference to
the diameter of an ideal circle, it only tends to make the point clearer
that pi is an invention of human beings, not a discovery of a absolute
perfect ideal, independent of human evolution and history.

All the numerical techniques for generating more and more digits, are
inconceivable without the original geometrical conception. You can
hypothesize the possibility of a mathematics which invented a specific
transcendental number out to 210 billion decimal places- for non-geometric
reasons of its own- but that is speculation, and not the sequence of events
which actually occurred. Such is not how the concept of pi entered into the
culture.

> Again, precision helps:

Precision is nice, but I prefer reality.

jody