Stephen Montgomery-Smith <email@example.com> wrote: > guenther vonKnakspot wrote:
>> I agree with you in that it is not a crackpot view that "mathematics >> should try to constrain itself to physical reality". It is however a >> very deplorable one, comparable to an intelligent person intentionally >> constraining himself to the intellectual level of his environment.
> I answered this elsewhere. I think my statement has been > overinterpreted. What I meant was that mathematicians should use > reality as a guide. Otherwise they may fall into the trap of discussing > things that future generations will compare to discussions about how > many angels can fit onto a pinhead.
But opinions of reality change as well. When people were considering the question of how many angels can fit onto a pinhead, angels were considered a reality. The underlying question is, how many infinitely small objects can fit into an infinitely small space. The "reality" of infinitely small objects is unknown. Electrons are currently believed to be point particles, but that may change someday.