Re: Epistemology 201: The Science of Science

From: Albert (albertwagner_at_cox.net)
Date: 01/29/05 

Date: Sat, 29 Jan 2005 15:03:31 -0600

Androcles wrote:
> "Albert" <albertwagner@cox.net> wrote in message
> news:uPQKd.1603$7J.1492@okepread04...
>
>>Androcles wrote:
>>
>>>"Albert" <albertwagner@cox.net> wrote in message
>>>news:nTPKd.1600$7J.237@okepread04...
>>>
>>>>robert j. kolker wrote:
>>>>
>>>>>Albert wrote:
>>>>>
>>>>>>Mathematics is nothing but a language for describing relationships
>>>>>>between numbers. Its usefulness to the natural sciences is limited
>>>>>>to what can be counted, even if the counting involves arbitrarily
>>>>>>slicing a continuum into chunks.
>>>>>
>>>>>Nonesense! There are mathematical objects other than numbers.
>>>>
>>>>Objects that don't represent a number?
>>>
>>>Sure.
>>>Consider algebra.
>>>Consider trigonometry.
>>>Consider topology.
>>>Conside group theory.
>>>Mathematics goes WAY beyond arithmetic.
>>
>>I am not talking about arithmetic. I am talking about:
>>algebra, trigonometry, topology, etc. There are no 'objects' in any
>>of these that do not require numbers to represent an instance.
>
> pi is the area of a circle of unit radius.
> You can't give me a numerical value for pi, the best you'll ever do is
> an approximation.

Yet, pi *is* a number. And much in mathematics is an approximation.

> Mathematics is much, much more than the simplistic
> "nothing but a language for describing relationships between numbers."

Nothing simplistic about that statement whatsoever.

> Look at this set:
>
> { e, a, b, c}
>
>
>
> It has an operator, 'o', (similar to the operators +, -, * and / ) such
> that
> a o a = e
> b o b = e
> c o c = e
>
> a o b = c
> a o c = b
> b o c = a
>
> and satisfies
>
> (a o b) o c = a o (b o c) = e.
>
> Such a set with an operator is a called a group.
>
> That is math, and it doesn't have a darned thing to do with numbers.
>
> Look at this:
> http://www.math.nus.edu.sg/~matwyl/Paper/belttrick.pdf

Sorry, I can't read this pdf file.

>
> Don't try to tell a musician what music is, or a mathematician (even a
> poor one like me) what mathematics is, because you simply do not know.

I'm beginning to think that even mathematicians simply do not
know, or have forgotten. It is, however, certain that math has
no utility other than to yield useful numbers. (and of course, to
entertain mathematicians) 

-- 
"Don't you see that the whole aim of Newspeak is to narrow the 
range of thought? In the end we shall make thoughtcrime literally 
impossible, because there will be no words in which to express it."
     -- George Orwell as Syme in "1984"

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