SUO: Re: Manifolds Of Sensuous Impressions (MOSI's)
John F. Sowa wrote:
>
> Jon,
>
> Your excerpt illustrates two points: (1) that the theories
> of manifolds and categories are very powerful and general,
> and (2) that they are terrifying to nonmathematicians.
>
> I agree with you about point (1), but I was trying to make
> some points that are quite different from (2):
>
> 1. Mathematicians are generally lazy, and
> they want to avoid as much tedious writing
> and computation as possible.
>
> 2. Their powerful formalisms actually enable axioms
> to be written in a form that make them easier to
> understand and actually much closer to what many
> people would call "common sense".
>
> 3. Unfortunately, when mathematicians talk to other
> mathematicians, they feel no obligation to make
> their points "obvious" to anyone who doesn't
> immediately see that what they are saying
> is "obvious".
>
> 4. What I was trying to say is that this high-powered
> stuff can make the axioms very much simpler, very
> much more general, and very much easier to explain
> to the "average man in the street" -- provided that
> you don't use typical mathamtical jargon to explain
> your formalism.
>
> Bottom line: Category theory and differentiable manifolds
> are very powerful, they can make life a lot easier for
> everybody, but some work is needed on the human factors.
>
> John Sowa
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
John,
I agree with all that you say here.
I believe that, with the necessary
and sufficient amount of patience
on all sides, most of this stuff
can be rendered very "intuitive",
in the pragmatically humble sense,
and as much as to say "visual" in
the level of its overall clarity.
And if there is anything that I have found demonstrated
in the nigh unto a year that I have been with this crew,
it is the abundance of humane patience that can prevail.
You should know that T.C. Mits is an old friend o' mine --
there but for the grease on a 'Sliding Door' would go I --
I did not spend thirty plus years on propositional calk
in the basement of logic from any lack of sympathy with
the demiurge thereof.
So, we'll work on what you say,
Jon Awbrey
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤