Amen to that, Brent!
On Mon, Dec 16, 2013 at 8:03 PM, meekerdb <meeke...@verizon.net> wrote:
> On 12/16/2013 4:41 PM, LizR wrote:
> On 17 December 2013 13:07, meekerdb <meeke...@verizon.net> wrote:
>> In a sense, one can be more certain about arithmetical reality than
>> the physical reality. An evil demon could be responsible for our belief in
>> atoms, and stars, and photons, etc., but it is may be impossible for that
>> same demon to give us the experience of factoring 7 in to two integers
>> besides 1 and 7.
>> But that's because we made up 1 and 7 and the defintion of factoring.
>> They're our language and that's why we have control of them.
>> If it's just something we made up, where does the "unreasonable
> effectiveness" come from? (Bearing in mind that most of the non-elementary
> maths that has been found to apply to physics was "made up" with no idea
> that it mighe turn out to have physical applications.)
> I'm not sure your premise is true. Calculus was certainly invented to
> apply to physics. Turing's machine was invented with the physical process
> of computation in mind. Non-euclidean geometry of curved spaces was
> invented before Einstein needed it, but it was motivated by considering
> coordinates on curved surfaces like the Earth. Fourier invented his
> transforms to solve heat transfer problems. Hilbert space was an extension
> of vector space in countably infinite dimensions. So the 'unreasonable
> effectiveness' may be an illusion based on a selection effect. I'm on the
> math-fun mailing list too and I see an awful lot of math that has no
> reasonable effectiveness.
> Another answer is that we're physical beings who evolved in a physical
> world and that's why we think the way we do. That not only explains why we
> have developed logic and mathematics to deal with the world, but also why
> quantum mechanics seems so weird compared to Newtonian mechanics (we didn't
> evolve to deal with electrons). There's a very nice, stimulating and short
> book by William S. Cooper "The Evolution of Reason" which takes this idea
> and develops it and even projects it into the future.
> "The duty of abstract mathematics, as I see it, is precisely to
> expand our capacity for hypothesizing possible ontologies."
> --- Norm Levitt
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Stephen Paul King
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