Re: Roger Ebert comes out of the closet!!

On 2009-09-06, Walter Bushell <proto@xxxxxxxxx> wrote:
In article <QNnom.284960$E61.140928@xxxxxxxxxxxx>,
Garamond Lethe <cartographical@xxxxxxxxxxxxxx> wrote:

<q>
I'm not qualified to say whether or not God exists. I kind of doubt
He does. Nevertheless, I'm always saying that the SF [Supreme
Fascist, Erdos's title for God] has this transfinite Book that
contains the best proofs of all mathematical theorems, proofs that
are elegant and perfect... You don't have to believe in God, but you
should believe in the Book.
</q>

Paul Erdos

But one of the things that support the real existence of mathematical
objects is that the axiomatic method has been shown to be a failure. No
matter how many axioms we have there remain things that cannot be proven
or disproved by the axiom for the natural numbers.

I'd also consider the underwhelming success of automated theorem proving
as an indictment of the axiomatic approach.

Some of my professors
were quite adamant[1] about the independent reality of some mathematical
objects.

Poking snex aside, I would really prefer to believe that the natural numbers
are an entirely human construct, that several other rich and viable systems
could exist and we just happened to luck into the one we're familiar with.

But of the many people I know who do math for a living, not one of them
believes this. One in particular trained as a physicist and is now a
theoretical biologist, and she emphatically considers herself a neoplatonist.

I do have to admit, though, that I don't know any coders or computer
scientists who this this way. Programs (and algorithms) are still
thought to be created, not discovered. That may be due to the field
still being in its infancy, or maybe it's because our thinking is
still largely guided by the limitations of the machines. Or maybe
CS folks are much more comfortable with arbitrary manipulation of
meaningless symbols....

Time to reread "The Unreasonable Effectiveness of Mathematics", I think.


[1] Not the first ant as the word seems to shape.


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