On 17 Dec 2013, at 02:03, meekerdb 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.

Absolutely not. The "physical" shape of the Turing machine was only there for pedagogical purpose. the discovery of universal machine is a purely mathematical, even arithmetical, discovery. "physical implementation" came later (if you except Babbage, but even Babbage will discover the mathematical machine (and be close to Church thesis), when he realized that his functional description language (intended at first as a tool for describing his machine) was a bigger discovery than his machine.

The discovery of the universal machine is the bigger even discovery made by nature. It is even bigger than the big bang. And nature exploit it all the time, and with comp we understand completely why.

That discovery is a theorem of elementary arithmetic, and has nothing to do with the physical, except that with comp, we get the explanation of the physical as a consequence of that theorem in arithmetic.




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.

This beg the question, of both the existence of math, and of a primitive physical reality (and of the link between).

Bruno




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. http://www.amazon.com/The-Evolution-Reason-Cambridge-Philosophy/dp/0521540259

Brent
"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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