"flipper" wrote in message
...
On Tue, 14 Mar 2006 20:57:30 GMT, "Rich Wilson"

If you'd like to study on the philosophy of mathematics this might be
a place to start.

http://en.wikipedia.org/wiki/Philosophy_of_mathematics

Wow, I hadn't realised there was so much religion in mathematics. Platonic
heavens full of numbers?! I thought mathematicians were meant to be
*logical* people!


Your parochial definition of 'exist' seems intuitive on the surface
but, to turn a phrase, "an idea can change the world."

Not without people to think it.

And according to Schroedinger the cat is neither physically alive nor
dead till observation fixes the quantum state..

http://www.lassp.cornell.edu/ardloui...e/Schrcat.html

But to your 'complaint' with an idea changing the world, the mechanism
of implementation doesn't alter the fact that the world does change
and we have a 'classic', or for you - mystical, cause-effect
situation: the 'real world' being altered by what you claim doesn't
exist.

Would you mind not telling me what I think...? ;-)

I think you need to take a step back - maybe a few hundred of them - forget
all the philiosopy you've learnt and look at what's actually happening. I
guess this is one of those things that's really obvious until you start
thinking about it, and then you've got to do an awful lot more thinking to
make it obvious again.

This is what's obvious to me:. numbers are abstract ideas. They are concepts
we use to help us think about the world, and they're nothing more than that.
The fact that they're useful doesn't imply that we "discovered" them from
somewhere. The human brain is quite capable of coming up with useful
abstract ideas and generalisations on its own; in fact, that's exactly why
it's so useful.

Your cause-and-effect argument makes no sense to me. You could trace the
chain of effects from a real-world phenomenon, through the abstract idea
stage via a chain of electrical and chemical processes in the brain, and
back to the real world as movement caused by the person's nerve impules.
Where's the problem?


Or, put another way, we accept the reality of things we can, by some
means, verify even if we can't 'see' them, like electrons and protons.

Stand in front of a source of beta radiation for long enough and you'd
be
able verify the existence of electrons.

Well, at least the observed results will, hopefully, be consistent
with present day theory.

I'm mean they'd have a direct effect on your body that you could
experience
with your senses.

Yes, I knew what you meant. But concluding that 'effect' is due to
beta radiation, as opposed to the gods being angry with you or some
other belief, is a matter of present day scientific theory.

You could say that about pretty much anything.

The only reason you accept the 'existence' of the electrons is because
the 'results' are consistent with a theory that's useful in what is,
apparently, the only kind of 'existence' you accept. But, similarly,
numbers exist because that (mathematical) theory is also useful, even
in the same 'reality' you insist is the only one. It isn't the same
kind of 'existence' you insist on but the usefulness is observable.

Why is it so hard to accept that a useful idea may still be just an idea?


One the other hand, '5' is consistent with present day mathematical
theory too.

We can devise tests that 'confirm' their existence and, similarly, we
can confirm the 'existence' of 5 by it's adherence to mathematical
principles and useful, even necessary, applicability to the 'real
world'.

Go ahead, prove it. I think all you're going to show is that it's a
useful
idea.

Which I contend exists, in the broader view.

Meaning what exactly? How do you differentiate between an idea that exists
and one that doesn't?

The same way one differentiates between 'beliefs' of what is 'real'
and, back to our electrons, it wasn't but a few hundred years ago
people would have told you they were nothing but your imagination.

Questions about the existence of sub-atomic particles have typically been
answered when someone's managed to isolate one of them. OK, you can question
their measuring equipment but that can be proved beyond reasonable doubt to
be working as expected.
I'd like to see you do the same for a number.


You would, of course, say they're 'real' whether man knew of them or
not

No I wouldn't.

but Schroedinger and Heisenberg will explain that, well, not
really.

Yes, taken to extremes, reality becomes "everything I am observing right
now". I think you'll find that my argument still holds, as numbers are not
observable.

At least not in your Newtonian view of it as they're a wave
function and don't 'exist' at any particular 'place and time'. To make
matters worse, beyond not ever being either 'here or there', they
also, apparently, regularly oscillate in and out of 'existence'
because they go places not possible in 'this reality' (loose use of
the term). One version is called "tunneling" and is the basis of a
'real world' device: the tunnel diode.

It's odd how people get so wedded to a model (like electrons being little
solid balls) that when the model is proved wrong they have to start
labelling things as "impossible". At the end of the day an electron is just
an electron and it can do whatever electrons do.


As far as I can tell, some people have a notion of some kind of "ether" of
mathematical laws and rules that had to exist before any matter could
exist
in the universe. That's what I'm trying to argue against.

Well, I don't know who those 'some people' are or what they said,

Try reading your own Wikipedia reference!

precisely, and I certainly didn't say it nor am I sure what the point
is.

Do you think the laws of physics exist?

No. Again, they're abstract generalisations and as such "existence" has no
meaning for them. Do you think they exist?

You seem to think electrons
exist but 'electron' is just a word. If I have a capacitor with 5
electron volts on it do the electrons exist? Does the electromagnetic
field exist? Does the magnitude 5 exist? They're all just words and
'concepts', you know. But don't they all 'relate' to the 'real world'?

Some are concepts to which the verb "to exist" can apply, some aren't.
Have you ever done any object-oriented computer programming? It forces you
into a way of thinking that makes problems like this very easy. "Electrons"
would be a subset of "Real Concepts", which would in turn be a subset of
"Concepts". "Numbers" would, again, be a subset of "Concepts". The property
of "Existence" would be a true-or-false value within "Real Concepts", and so
"Electrons" would inherit the property of "Existence" whereas "Numbers"
wouldn't. That'd probably be easier to understand on a diagram. Why can't
you draw stuff on Usenet?!


You may invoke the Shakespearian "a rose is still a rose by any other
name," fair enough (and my point) but the mathematical relationship
between field strength and the number of electrons is also the same
regardless of the symbols used. And they 'add' the same whether one
uses those words or not. Mathematics 'exists' because it relates to,
and describes, the 'real world' just as the word 'electron' represents
a thing you consider 'real'. One is what you think of as the
'physical' where the other speaks to properties and behavior of those
'physical' things, and I contend that their properties and behavior
are just as 'real' and that, indeed, you don't have 'reality' without
them.

And maybe that will help explain why I don't understand the 'which
came first' point you say you're arguing against.

It's not "which came first"!! It's "did one of them come at all"!

It's like asking
which came first, the electron or it's negative charge? huh?