On 13 Jul 2006 17:10:08 -0700, firstname.lastname@example.org wrote:
>email@example.com wrote: >> Stephen Montgomery-Smith wrote: >> >> <snip> >> >> > The view that mathematics should try to constrain itself to physical >> > reality is, in my opinion, not a crackpot position. >> >> It does seem to me that - as stated - this is precisely a crackpot >> position. The problem is none of the words "physical", "reality", or >> "constrain", the problem is the word "should". In practice mathematics, >> as referred to by the overwhelming population of mathematicians, means >> the abstract study of formal patterns, and that's all. The mystery of >> it all is the way in which the patterns investigated by abstract >> mathematicians turn out to apply so directly to aspects of the real >> world. But it's going to be hard to develop these abstract theories if >> you have to be consulting one of these "real world characters" [do I >> have to call them other than "cranks"?] to see if _they_ happen to >> think what you're doing is OK. > >And furthermore, such claims of "should" seem to be moving targets. > >For instance: the claim that "there is no such thing as a physical >infinity" is a relatively recent "physical truth". As late as the >1960's, a cosmology consisting of an infinite, steady state universe >was still being debated. > >That isn't to say that I do or don't find the steady state type >theories compelling. What I find is that those who claim that the >concept of mathematical infinity is suspect because "there can be no >such physical thing as infinity" tend to be myopic regarding the >history of what has been accepted as reasonable physical models of our >universe; and close-minded regarding the possibility that further data >may change scientific opinion once again.
It occurs to me that physical arguments related to mathematical infinities are the rather ugly stepchildren of a finite universe and empirical utilitarian justifications for science and mathematics.