Re: Real world and mathematics

On Sat, 26 Jul 2008 10:16:03 -0700 (PDT), "porky_pig_jr@xxxxxxxxxxx"
<porky_pig_jr@xxxxxxxxxxx> wrote:

On Jul 25, 4:37 pm, Angus Rodgers <twir...@xxxxxxxxxxx> wrote:


V. I. Arnol'd, What is mathematics?, (MCCME, Moscow), 2002, Russian

So, when you wrote of Arnol'd, ``See his book "What is mathematics".'',
just what did you mean? I'm puzzled.

I guess that's what I've meant. ISBN 5-94057-090-9. I'm not sure if
it's translated into English, though. :-)

Damn. (I have enough difficulty just remembering any of the French,
German or Latin I used to know.)

I was browsing through that book, than took a break, checked the
usenet and saw *that* posting.

The book deals with the question whether mathematics is the "bunch of
consequences of some arbitrary axioms or it is a branch of natural
sciences and theoretical physics" (quoting Arnold). IMHO, the axioms
of maths are not as arbitrary as Arnold's straw man - pure
mathematician claims, and yet that does not follow that maths is a
branch of physics. Rather both math and physics (and other natural
sciences) are part of human activities (or human intelligence);
roughly speaking, the humans that produce both maths and natural
sciences are the same humans, with the same limitations and the same
way of reasoning, hence no one should claim that math and natural
sciences are completely insulated from each other. There is always
some interaction going on. Yet it does not necessarily follow that
maths is a branch of physics or natural sciences in general.

I agree that it seems to be a false dichotomy, a bit like "either
everything is meaningless, we're all just a bunch of atoms, and
there is no difference between right and wrong - or else Jesus
Christ died for your sins, God loves you, and homosexuals are all
evil and will burn in hellfire for eternity." :-)

The book, by the way, *is* fun to read, and in fact Arnold gives
substantially complex picture than one can guess by reading just the
first couple of paragraphs from his book.

I get the impression that he has a very interesting perspective on
the field. Also, he's a Wolf prizewinner, and he solved Hilbert's
13th problem at the age of 19 (or was it Hilbert's 19th problem at
the age of 13?) - so I think it's safe to say that he's no slouch,
no outsider crying in the wilderness, and no despiser of rigour
(or indeed abstraction or generality) - just Bourbaki, it seems.

--
Angus Rodgers
(twirlip@ eats spam; reply to angusrod@)
Contains mild peril
.

Relevant Pages

  • Re: Bob Berman: String Theorys trendy, but baseless
    ... But whether it is string theory or something else, I think you should allow mathematical elegance. ... I think the mathematics is the correct theory and the manifestation of the mathematics is what we call physical reality. ... If you allow both physics and maths, ... Ditch physics, stick with maths and you only have one theory to explain and no approximate models. ...
    (sci.physics)
  • Re: Orthography supporting sound changes?
    ... Some disciplines, e.g. maths, attempt to prove non-existence ... justification may be different in maths, physics, and linguistics (if ... they ever attempt to justify their claims) is another matter. ... > concerned the error in classifying mathematics as a science ...
    (sci.lang)
  • Re: A challenge to Tom Roberts re LET,SR and an alternative.
    ... LET does provide an interpretation the modern version ... One is maths + an interpretation which no one likes ... What physics has done it to change the rules such ... had published his mathematics predicting the motion of planets without ...
    (sci.physics.relativity)
  • Re: Real world and mathematics
    ... The book deals with the question whether mathematics is the "bunch of ... sciences and theoretical physics". ... of maths are not as arbitrary as Arnold's straw man - pure ...
    (sci.math)
  • Re: Teaching English?
    ... >>example, the sciences or engineering, will need calculus etc. ... While I'd like to seem more maths taught to all ... > fewer sixth-formers even potentially suitable to go into physics, ...
    (uk.education.maths)