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 realitythan the physical reality. An evil demon could be responsible forour belief in atoms, and stars, and photons, etc., but it is maybe impossible for that same demon to give us the experience offactoring 7 in to two integers besides 1 and 7.But that's because we made up 1 and 7 and the defintion offactoring. They're our language and that's why we have control ofthem.If it's just something we made up, where does the "unreasonableeffectiveness" come from? (Bearing in mind that most of the non-elementary maths that has been found to apply to physics was "madeup" with no idea that it mighe turn out to have physicalapplications.)I'm not sure your premise is true. Calculus was certainly inventedto apply to physics. Turing's machine was invented with thephysical 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 Einsteinneeded it, but it was motivated by considering coordinates on curvedsurfaces like the Earth. Fourier invented his transforms to solveheat transfer problems. Hilbert space was an extension of vectorspace in countably infinite dimensions. So the 'unreasonableeffectiveness' 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 maththat has no reasonable effectiveness.Another answer is that we're physical beings who evolved in aphysical world and that's why we think the way we do. That not onlyexplains why we have developed logic and mathematics to deal withthe world, but also why quantum mechanics seems so weird compared toNewtonian 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 andeven projects it into the future. http://www.amazon.com/The-Evolution-Reason-Cambridge-Philosophy/dp/0521540259Brent "The duty of abstract mathematics, as I see it, is precisely to expand our capacity for hypothesizing possible ontologies." --- Norm Levitt --You received this message because you are subscribed to the GoogleGroups "Everything List" group.To unsubscribe from this group and stop receiving emails from it,send an email to everything-list+unsubscr...@googlegroups.com.To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.

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