Re: OT: In the 'ignorance on parade' file

On Monday, August 13, 2001, at 07:09 AM, Thomas R. Wier wrote:

[snippage of interesting stuff I will go back and read after my projects
are due...]

> Mr. Miner's comments are indeed well thought out, but I must
> differ with him on at least this one point:
>
> "Something would still be a human language if it did not change,
> as long as it had all the other familiar features of a human language."
[snip]

> This is not to say that languages like mathematics or predicate calculus
> must change; but then, they are not human languages, are they?
>
I'm a poor excuse for a mathematician, and apologize if I offend...

But mathematics *as a human realm of endeavor* most certainly changes; or
to put it another way, the human conception of mathematics changes.
Whether you believe there exists "out there" a "pure" and discoverable but
not-invented realm of mathematics (platonism) or that it's all an
artificial game played to artificial rules (formalism) or even that, since
it's all human-devised, nothing beyond the bounds of (finite) human
devision as some conceive it should be included, like infinities
(constructivism)--if nothing else, the way we play the game does change.
When they teach high school calculus they sure don't use Newton's fluxions.
   :-)  Or geometry: you could certainly argue that non-Euclidean
geometries were "out there" all along

Not to mention, the "language" or expression of math changes, and is
subject to human vagaries and frustrations.  The definition of "continuous"
  has evolved through time.  "Function" took a while to be formalized in
its present, er, form.  I'm sure others can think of far more interesting
examples.  Again, put another way: mathematics is a quasihuman
quasisublanguage insofar in that humans do use it to communicate, though I
grant you that most humans' brains would turn off if I started "talking
math."  8-)

Even math-as-perceived/used/conceived adapts to the changing needs of the
humans who use it (applied) or devise it (theoretical--if you'll excuse
the simplistic division as an approximation).

(I must admit, I lean toward the platonists, though frustratingly, I know
of no convincing way to *prove* it...merely tantalizing hints and glimpses.
)

Sorry to nitpick...I just spent most of this quarter trying to hash out,
for Literacies class, what "literacy" might mean vis-a-vis mathematics.