Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math

Topic: Mathematics and the Roots of Postmodern Thought
Replies: 101   Last Post: Apr 7, 2013 10:38 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
fom

Posts: 1,968
Registered: 12/4/12
Re: Mathematics and the Roots of Postmodern Thought
Posted: Apr 1, 2013 10:40 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On 4/1/2013 9:03 AM, Dan wrote:
> On Apr 1, 3:40 pm, Frederick Williams <freddywilli...@btinternet.com>
> wrote:

>> Dan wrote:
>>> Real mathematicians do their own thing ... no physicist thought
>>> Hilbert spaces or Riemannian geometry would have any real application
>>> when they first appeared .

>>
>> That's a big claim to make. It seems likely that when they (Hilbert
>> spaces and Riemannian geometry) first appeared, not every physicist
>> voiced an opinion that has come down to us.
>>
>> If it was von Neumann[1] who invented Hilbert space, then it seems it
>> was invented in order to give quantum mechanics a rigorous underpinning.
>>
>> [1] von Neumman, _Mathematical foundations of quantum mechanics_,
>> Princeton UP.
>>
>> --
>> When a true genius appears in the world, you may know him by
>> this sign, that the dunces are all in confederacy against him.
>> Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting

>
> https://en.wikipedia.org/wiki/Hilbert_space#History the concept of
> Hilbert Space was developed prior to the realization of its utility
> within quantum mechanics, although Von Neumann was the first to give a
> completed axiomatic formulation, specifically for this purpose . My
> point was that ,while I do believe set theory to be excessive, this is
> not so for anything up to second order arithmetic . Furthermore , as
> mathematicians , we should not let ourselves be constraint by the
> narrow vision of what empiricists believe as legitimate. Leibniz ,
> Euler , and Russell used infinitesimals in developing their results .
> The same empiricist stigma was once manifest against the 'fictions
> quantities' we now refer to as imaginary numbers . Imagine doing
> modern physics without imaginary numbers. While 'empirical exploration
> of numbers' may sometimes give us hints (and sometimes false ones
> http://en.wikipedia.org/wiki/Graham%27s_number , as the
> counterexamples are too far of to be determined empirically ) ,
> mathematics isn't about empiricism, it's about rational proof . If we
> proved Fermat's theorem true , we need not check every number for
> counterexamples . Furthermore , doing so would be a futile endeavor .
> No one has ever "seen the numbers" , or "performed an experiment on
> the numbers" , unless it was fundamentally a 'thought experiment' .The
> essential difference between 'thought experiment' and 'empirical
> experiment' should be the theme of this discussion .


One can find a critic for everything:

"A thought experiment is no substitute for a real experiment, he
claimed, and should be forbidden in science, including science
education." (A paraphrase of Duhem)

The next sentence, quite naturally being the statement:

"However, in view of the important role of actual thought experiments in
the history of physics ? from Galileo's falling bodies, to Newton's
bucket, to Einstein's elevator ? it is unlikely that anyone will feel or
should feel much sympathy for Duhem's strictures."

http://plato.stanford.edu/entries/thought-experiment/#DebOveThoExp

> I also recall
> someone mentioning "The Unreasonable Effectiveness of Mathematics in
> the Natural Sciences" .
>


Perhaps it is the unreasonable effectiveness of thought experiments.




Date Subject Author
3/25/13
Read Mathematics and the Roots of Postmodern Thought
David Petry
3/25/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
3/25/13
Read Re: Mathematics and the Roots of Postmodern Thought
David Petry
3/25/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
3/25/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
3/25/13
Read Re: Mathematics and the Roots of Postmodern Thought
David Petry
3/25/13
Read Re: Mathematics and the Roots of Postmodern Thought
scattered
3/25/13
Read Re: Mathematics and the Roots of Postmodern Thought
David Petry
3/25/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
3/25/13
Read Re: Mathematics and the Roots of Postmodern Thought
David Petry
3/25/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
3/25/13
Read Re: Mathematics and the Roots of Postmodern Thought
David Petry
3/25/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
3/26/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
3/30/13
Read Re: Mathematics and the Roots of Postmodern Thought
Jesse F. Hughes
3/25/13
Read Re: Mathematics and the Roots of Postmodern Thought
dan.ms.chaos@gmail.com
3/25/13
Read Re: Mathematics and the Roots of Postmodern Thought
David Petry
3/25/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
3/25/13
Read Re: Mathematics and the Roots of Postmodern Thought
David Petry
3/25/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
3/30/13
Read Re: Mathematics and the Roots of Postmodern Thought
Jesse F. Hughes
3/30/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
3/25/13
Read Re: Mathematics and the Roots of Postmodern Thought
dan.ms.chaos@gmail.com
3/25/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
3/25/13
Read Re: Mathematics and the Roots of Postmodern Thought
David Petry
3/26/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
3/26/13
Read Re: Mathematics and the Roots of Postmodern Thought
Virgil
3/26/13
Read Re: Mathematics and the Roots of Postmodern Thought
David Petry
3/26/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
3/26/13
Read Re: Mathematics and the Roots of Postmodern Thought
dan.ms.chaos@gmail.com
3/26/13
Read Re: Mathematics and the Roots of Postmodern Thought
dan.ms.chaos@gmail.com
3/26/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
3/26/13
Read Re: Mathematics and the Roots of Postmodern Thought
dan.ms.chaos@gmail.com
3/26/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
3/26/13
Read Re: Mathematics and the Roots of Postmodern Thought
David Petry
3/26/13
Read Re: Mathematics and the Roots of Postmodern Thought
dan.ms.chaos@gmail.com
3/26/13
Read Re: Mathematics and the Roots of Postmodern Thought
Frederick Williams
4/2/13
Read Re: Mathematics and the Roots of Postmodern Thought
Jesse F. Hughes
3/26/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
3/26/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
3/26/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
3/29/13
Read Re: Mathematics and the Roots of Postmodern Thought
Shmuel (Seymour J.) Metz
3/29/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
3/30/13
Read Re: Mathematics and the Roots of Postmodern Thought
Shmuel (Seymour J.) Metz
3/31/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
3/30/13
Read Re: Mathematics and the Roots of Postmodern Thought
Jesse F. Hughes
3/26/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
3/30/13
Read Re: Mathematics and the Roots of Postmodern Thought
Jesse F. Hughes
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
David Petry
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
dan.ms.chaos@gmail.com
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
Frederick Williams
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
dan.ms.chaos@gmail.com
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
dan.ms.chaos@gmail.com
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
Frederick Williams
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
dan.ms.chaos@gmail.com
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
David Petry
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
David Petry
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
dan.ms.chaos@gmail.com
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
David Petry
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
dan.ms.chaos@gmail.com
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
David Petry
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
dan.ms.chaos@gmail.com
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
David Petry
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
dan.ms.chaos@gmail.com
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
dan.ms.chaos@gmail.com
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
David Petry
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
dan.ms.chaos@gmail.com
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
David Petry
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
dan.ms.chaos@gmail.com
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
David Petry
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
Virgil
4/2/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
Virgil
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
Jesse F. Hughes
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
David Petry
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
Jesse F. Hughes
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
rt servo
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
Jesse F. Hughes
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
Virgil
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
David Petry
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
Jesse F. Hughes
4/6/13
Read Re: Mathematics and the Roots of Postmodern Thought
Rotwang
4/7/13
Read Re: Mathematics and the Roots of Postmodern Thought
David Petry
4/7/13
Read Re: Mathematics and the Roots of Postmodern Thought
Jesse F. Hughes
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
David Petry
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
3/25/13
Read Re: Mathematics and the Roots of Postmodern Thought
bacle
3/29/13
Read Re: Mathematics and the Roots of Postmodern Thought
HOPEINCHRIST

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.