Re: request for ideas
From: Craig Feinstein (cafeinst_at_msn.com)
Date: 08/24/04
- Next message: Robert Israel: "Re: multiplicative vs algebraic independence"
- Previous message: Roberto E. Martinez II: "Re: multiplicative vs algebraic independence"
- In reply to: Eray Ozkural exa: "Re: request for ideas"
- Messages sorted by: [ date ] [ thread ]
Date: Tue, 24 Aug 2004 18:30:04 +0000 (UTC)
erayo@bilkent.edu.tr (Eray Ozkural exa) wrote in message news:<cgfjdb$lmp$1@news.ks.uiuc.edu>...
> cafeinst@msn.com (Craig Feinstein) wrote in message news:<cgd62a$no8$1@news.ks.uiuc.edu>...
> > I am planning to write a paper which surveys mathematical results that
> > show that the old "axiom->proof->theorem" way of doing mathematics
> > does not always yield complete information about mathematics. The
> > prime example of this (which started it all) is Godel's Incompleteness
> > Theorem, but there has been a lot of work in this area since then.
> >
> > For instance, Gregory Chaitin has an incompleteness theorem which
> > shows conclusively that a certain number which he calls Omega, which
> > is really the probability that a computer program halts (defined in a
> > way that makes sense), is a random number - which implies that there
> > is no finite axiom system that can yield all of the bits of Omega. He
> > concludes from all of his work that sometimes one has to simply
> > perform experiments in mathematics and form conclusions from the
> > experiments without being absolutely certain that the conclusions are
> > correct.
> >
> > It is these types of very original ideas that I am looking for to put
> > in my paper, that there are some problems out there that are so
> > difficult for us to get a grip on that we might have to approach them
> > like a chemist approaches chemistry, never being 100% sure that his or
> > her theories are always correct.
> >
> > Anyone who knows of results like these or has done work in this area
> > or has original ideas is welcome to respond to me on usenet or if you
> > want, you can email me directly.
>
> Have you looked into Super Omegas? Might be slightly relevant to your inquiry.
>
> http://www.idsia.ch/~juergen/kolmogorov.html
>
> Best Regards,
Thank you very much. That's not only relevant to my inquiry, but it
looks like his whole webpage has lots of neat stuff too.
Any other ideas are welcome.
Craig
- Next message: Robert Israel: "Re: multiplicative vs algebraic independence"
- Previous message: Roberto E. Martinez II: "Re: multiplicative vs algebraic independence"
- In reply to: Eray Ozkural exa: "Re: request for ideas"
- Messages sorted by: [ date ] [ thread ]
Relevant Pages
|
|
