Re: Cantor's diagonal proof wrong?

From: Curt Welch (curt_at_kcwc.com)
Date: 11/17/04 

Date: 17 Nov 2004 20:00:40 GMT

"Shmuel (Seymour J.) Metz" <spamtrap@library.lspace.org.invalid> wrote:
> In <20041114013915.877$0a@newsreader.com>, on 11/14/2004
> at 06:39 AM, curt@kcwc.com (Curt Welch) said:

For some reason, your posts seems to have shown up two days late here.

Most of what said already been well covered in many other messages, but
there was a point or two I wanted to comment on...

> >They are the result of mechanical computation.
>
> I see that it is not only the Mathematicians who are not
> psychologists. To the best of our knowledge and understanding, mental
> processes are electrochemical, not mechanical.

I am using the word mechanical in a non conventional way above, but not one
that violates the basic meaning of the word. I've simply extended it to
include all interaction of physical matter. Whether it's a collection of
atom formed into a wheel, or individual atoms pushing and pulling each
other in a chemical reaction, or individual electrons pushing and pulling
each other in an electrical circuit, it's all still "mechanical" in the
fact that physical matter is interacting with other physical matter to
produce a behavior unique to that configuration of the matter.

The word "mechanical" is normally used to describe the macro level behavior
of matter and I just extended it in my usage to cover micro level of mater
because when you use separate words to describe the different types of
behavior, we tend to start thinking that there is a fundamentally different
processes at work when there is not.

> >If you "pretend" the job of construction does end
>
> Why are you pretending that there is a "job of construction"?

This is just more of how I choose to look (and talk) about things because
I'm trying to understand something larger than just math. I'm trying to
understand the brain that creates it and how all of our understanding of
the physical world and mental world are related and connected.

Everything must be brought into existence. And I call that act
"construction", because the only way anything can be brought into existence
in this universe requires that physical matter be moved. And that always
happens as a result of matter interacting with other matter.

Math is a language that starts on a foundation well rooted in the physical
world. But then, with the power of language, it creates self referencing
loops and seems to cut the physical world out of the story, and then allows
itself to wander into a fantasy world created by the manipulation of
language.

We all know how this happens when writing fiction, but math is interesting
because it seems to be stronger than fiction. It's not completely
arbitrary. Yet, it does seem to have separated itself from reality at some
point. I'm curious about just what has happened in the language of math in
this regard.

When I talk about construction as a physical act in connection with math
concepts, I'm trying to tie various mathematical ideas back to the physical
foundation they grew out of. I'm trying to see if at some point, we
accepted some fact that seemed valid, but was actually a violation of the
physical world the language started off explaining. 

-- 
Curt Welch                                            http://CurtWelch.Com/
curt@kcwc.com                                        http://NewsReader.Com/