firstname.lastname@example.org wrote: > 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.
Yes. I wish I knew what this "angels on a pinhead" argument was really about. I know that us moderns like to laugh at the old theologians for discussing this, but I wonder if I am only getting half the story, and in fact there are some very real issues at stake here.