Re: Did prime numbers evolve?

Lorentz wrote:
n Apr 14, 1:17 pm, dkomo <dkomo...@xxxxxxxxxxx> wrote:

Guy A Hoelzer wrote:

dkomo,


Had I asked the question "Did Hilbert spaces evolve?" I would have
gotten far fewer people arguing that Hilbert spaces have an independent
existence outside human minds. Hilbert spaces are infinite dimensional
vector spaces where the vectors are functions, but Hilbert spaces are
the underlying mathematical foundation for quantum mechanics, and
quantum mechanics certainly deals with the physical world. Moreover,
there is a continuum of mathematical ideas starting with integers and
prime numbers, and leading to abstractions like Hilbert spaces. I'd say
this progression is part of the general process of evolution. How is it
possible to put a dividing line between prime numbers and Hilbert spaces
and say prime numbers exist in the real world, but Hilbert spaces don't?


How is it possible to present without proof the idea that Hilbert
spaces don't exist, then claim without proof that fewer people claim
Hilbert spaces exist, and then ask how it was possible for most people
to believe Hilbert spaces and not prime numbers exist?
The logical contradictions are yours, not mine.


I wasn't presenting without proof the idea that Hilbert spaces don't
exist. I simply stated my opinion that most people don't think "that
Hilbert spaces have an independent existence outside human minds." Do
you disagree? If they don't have an independent existence, then I
think they evolved -- as *ideas*.

As for asking "how it was possible for most people to believe Hilbert
spaces and not prime numbers exist", I don't know where you got this.
It certainly wasn't a question of mine.

Rather, I asked where is the dividing line between believing in the
*actual* existence of prime numbers and believing that Hilbert spaces
exist only in the mind, since there is a continuous development of
mathematical ideas between them.

If you believe they *both* exist in the real world, that's fine by me,
although I think that's a belief that is weird as hell.


--dkomo@xxxxxxxx


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