|
|
Re: Humanistic mathematics (Cantor's Theory)
Posted:
Jun 14, 2005 5:57 AM
|
|
Han de Bruijn a écrit :
> Nathan wrote:
>
>> david petry wrote:
>
>
>>> So occasionally the anti-Cantorians end up in sci.math and
>>> sci.logic, thinking they have some insight that should be
>>> of interest to mathematicians. And what happens? They get
>>> called ignorant cranks by the Cantorians.
>>
>>
>> It's not just an insult; it's an accurate description. They
>> are ignorant because they don't understand that which they
>> criticize. I'm not saying the problem is that they don't
>> accept it; it's that they don't understand it. The same
>> kind of ignorant cranks pop up in many fields.
>
>
> Well, being a theoretical physicist by education, I would call myself an
> anti-Cantorian. But I can assure you that I understand Cantor's theory
> good enough. The point is that there are people here who should be taken
> serious. And other people who are in kind of a learning process. Some of
> of us are both. But calling everybody just a crank is too easy.
>
>> I googled but couldn't find the quotation from Isaac Asimov's
>> "The Stars in Their Courses" where he says, IIRC, "Know that
>> which you would supplant". He talks about the anti-Einstein
>> physics cranks who come up with all kinds of revolutionary
>> criticisms of relativity, but at the heart of their arguments
>> they just plain don't understand relativity. He explains that
>> those who make genuine advances are already well-versed in
>> the systems they replace.
>
>
> Relativity, especially in combination with Quantum Mechanics, still *is*
> something to think about. If you force me to choose, my choice would be
> in favour of QM and against SR. Read the book "Relativity Reexamined" by
> Leon Brillouin (: a great physicist BTW) and you will understand why.
The fact that you are a complete crank (ie a math/physic/etc. one) comes
as no surprise, but you illustrate it quite well.
>
>> Hypocrisy. The scientists and engineers who become
>> anti-Cantorian cranks wouldn't tolerate equivalent behavior
>> in their own fields--and quite rightly.
>
>
> That is certainly not true. Don't forget that scientists have to employ
> mathematics. But the reverse is not true: mathematicians don't have to
> employ any other discipline than just mathematics. What if we find that
> the math tools supplied to us are not good enough for our purposes?
It hppens often. Good physicsts create then new tools (distributions, or
renormalisation). Cranks just make speeches
>
>> It might be fun to see an extensive foundation of mathematics
>> that allowed only computable entities to exist. I'm not sure
>> if it's really been tried; it hardly seems worth the effort.
>> I think intuitionism and constructivism have tendencies in
>> this direction, but I don't know much about them.
>
>
> Yes, it has been tried. And yes, intuitionism and constructivism have
> tendencies in this direction. But there is also Turing with his Turing
> machines. And Church with his lambda calculus. And so many others, who
> have been working in the gray area between modern Computer Science and
> Mathematics. Why not learn more about these people and their work?
Yes, *you* should. For instance, you would discover that constructivists
*all* accept infinite sets and Cantor arguments...
>
>> In order to add your "common sense criteria" to the
>> mathematical system you would create, you would have to
>> change almost every axiom and definition. Again, this is a
>> great deal of effort, just to create a system of mathematics
>> less powerful than the existing one.
>
>
> You are right: a mathematics that allows only computable entities to
> exist would cease to be powerful. But that is not the point. The point
> is not that mathematics should be Applied. The point is that mathematics
> sould be Applicable. Quite a subtle difference ...
>
> Han de Bruijn
>
|
|
