Re: Simple Question and the philosophy of infinity

On Fri, 29 Sep 2006 14:57:52 +0200, "Leo Meyer"
<leomeyer_NO_SPAM_FOR_ME@xxxxxx> wrote:

"Jonathan Kirwan" <jkirwan@xxxxxxxxxxxxxx> schrieb im Newsbeitrag
news:na7oh2pmlghk395ksdlrpbtrcgpf7rdp1l@xxxxxxxxxx
Of course there IS such a thing as "infinite."

Really? Show me a thing that is denoted by an adjective ;-)

"Infinite sum."

You're not following the grammatical intricacies.

Oh, I followed the grammatical intricacy just fine. You wanted an
adjective and I gave you one.

Maybe I should have written: "Show me an 'infinite'".

I probably am too burrowed into the narrow meanings I carry and cannot
connect them with an imprecise question, except imprecisely. So I'm
still not sure what you want, here.

This gives me a chance to put right and left next to each other in a
sentence:

A point is a "dimensionless geometric object" and is, if I have it
right, left as undefinied in math.

Let me put it into the correct order: "If undefined a dimensionless
geometric object you left, right you are!"
(a bit Yoda-like ;-)

hehe. Anyway, a point is undefined. It must be, in fact. Just as
the situation of 0/0 is also undefined. To define it would be to
define it in terms of yet something else, which would need to be
defined... in terms of something else... which would itself need to be
defined, again in terms of yet something else. Somewhere, this has to
end. In the case of formal mathematics, it ends at the point and at
0/0. To define them would be to make math circular or to go find
something else that is left undefined, instead. As it is, this is
where it is undefined.

How can you be sure that they aren't more than infinite in number?

By failing to find a way to prove it, I suppose.

If my teachers had accepted that as an answer, my math classes would have
been much easier!

hehe. You can never say what the future may yet bring in physics. But
in math, I suppose it is possible to prove things. But not all true
statements within a coherent, non-trivial system can be proven within
that system -- Goedel.

My real point is that unless you define what you mean by "more than"
when discussing infinities, you are in trouble. So you need to be
precise when asking a question like that. And you weren't. So rather
than belabor that, I was flip about it.

I'm not disputing whether your mathematical concept of "infinity" or of
points or lines is correct or not. They are mathematical tools that work
fine for those who know how to deal with them. But in reality you are not
likely to ever encounter "infinity", so you can't have an immediate, sensual
experience of it.

Mathematics just _happens_ to sometimes overlap natural reality as we
experience it. But there is no reason to imagine that all real
concepts in mathematics correspond to sensual experiences. In fact,
I'm pretty sure it's the case that they rarely do. It's just that
some aspects of math are practical, much to the chagrin of
mathematicians. (John Conway once worked on a bizarre 26-dimensional
system with the belief that no one would _ever_ be able to find a
practical use for it -- he hoped, anyway. Sadly, he was wrong about
that.)

It does turn out that nature does behave (on a macro scale) that can
usually be treated as though infinitesimals are real. Whether or not
they are, is another issue. Einstein's general theory of relativity
treats things this way, without quantums, and it corresponds pretty
well. At the micro scale (subatomic) things are different. But
that's not usually at the experiential level we more directly 'know.'

I like the post you quoted. You nicely described the way mathematical ideas
evolved out of the pure mind.

Thanks.

In my previous post, that from which this discussion originated, I wrote:
'On the other hand, this is a play on our inability to conceive "infinite".
There is no such thing, so our experience is absolutely worthless.'

For higher levels of math, organic experience isn't much of a guide,
at all. There is no necessary relationship of natural experience with
mathematics. Mathematics is its own universe, so to speak. Where it
touches upon reality is a matter of fortunate circumstance, not
necessity. It's quite possible that nature would operate in no way
similar to mathematics. We are fortunate that is not the case. (Some
argue that this is because math is the deeper reality, but I'm not
taken with that idea yet.)

Maybe you are not unable to conceive 'infinite'. Maybe you know exactly what
you are talking about. That's fine.

I have almost no problem with the concepts, as they are narrowly used
in mathematics. What problems I do have are usually because of vague
meanderings about such things by those who really don't follow the
usage well and imagine questions where there are none.

Probably a better way to say the above is this: Sometimes people
imagine that there is an end point of some linear spectrum spanning
from, say, complete ignorance to perfect knowledge. Or, let's make
this less religious and more mundane -- that there may be a spectrum
from "perfectly cold" to "perfectly hot." So people may ignorantly
seek answers to questions based upon this primitive conjecture. But
it's just not even the right starting point. What is even meant by
these ideas? Getting answers is more a matter of understanding the
questions better.

What is meant by the question, "What happens when the unstoppable
object meets the unmovable object?" What does 'object' mean? What is
the behavior of 'objects," in some rigorous meaning? What does
'unstoppable' mean? What does 'unmovable' mean? We are in no
position to even ask such questions.

We do not have the perspective. Plain and simple.

However, we can ask more modest questions with some hope. And in the
case of infinities and infinitesimals, they have a great deal of
meaning because the meaning they do have is limited and prosaic.

Your questions smack of making too much out of them. Though I may be
mistaken about that.

Anyway, I'm glad I was wrong about the 0 ohms. Imagine the universe was
infinite! We'd have short-circuits everywhere! ;-)

hehe. You _do_ see!

Jon
.

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