Re: Did prime numbers evolve?

Guy A Hoelzer wrote:
dkomo,

I disagree because I think that discrete entities, including systems that
act as agents of causation, emerged in the universe. This is, I think, the
same as saying that continua gave rise to integers (countable entities).
Once discrete entities emerged, the quantitative features of the prime
numbers were also manifested. The evolution of the human mind and culture
eventually led to a mathematical appreciation of prime number qualities, but
those qualities existed whether or not they were appreciated.


This sounds like Herbert Spencer's idea that "all structures in the
universe develop from a simple, undifferentiated, homogeneity to a
complex, differentiated, heterogeneity, while being accompanied by a
process of greater integration of the differentiated parts."

http://en.wikipedia.org/wiki/Herbert_Spencer

Also, you sound like a mathematical realist, defined like this:

"Mathematical realism, like realism in general, holds that mathematical
entities exist independently of the human mind. Thus humans do not
invent mathematics, but rather discover it, and any other intelligent
beings in the universe would presumably do the same. In this point of
view, there is really one sort of mathematics that can be discovered:
Triangles, for example, are real entities, not the creations of the
human mind."

http://en.wikipedia.org/wiki/Mathematical_realism#Mathematical_realism

The Wiki article describes a number of different schools of mathematical
philosophy. I jokingly replied to another post that I'm a
constructivist on weekdays, a mathematical realist on Saturdays, and a
Platonist on Sundays, especially when I'm inside a cathedral. That
way I've got all the bases covered.

I think one's opinion whether mathematical entities have an independent
existence outside of human minds is similar to having a political
opinion. One can be either a conservative or liberal and make a good
argument either way. It is the dynamic opposition between mathematical
realism and constructivism that is important, not whether one position
is correct and the other isn't.

I chose to focus on whether prime numbers evolved because the numbers
are in a borderline area between having an independent existence in the
natural world and being pure mental ideas. I expected to get some good
arguments either way, and got them, both here and on talk.origins.

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?


--dkomo@xxxxxxxx





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