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.