On 12/17/2013 1:51 AM, Bruno Marchal wrote:


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 <mailto: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.

Are you denying that Turing wanted to reason about realizable computation?? Of course his reasoning itself was abstract and led to a mathematical theorem. But Liz was asking about the unreasonable effectiveness of mathematics. I don't think you can say that Turing, or Babbage or Post or Church just became interested in sequences of symbol manipulation because they dreamed about it. They were concerned with real instances of inference and calculation, from which they abstracted recursive functions and Turing machines.

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.

I agree with the first sentence.  I don't understand the second.


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).

So what's your answer to Wigner? Is it just an accident that the math the universe instantiates, out of all mathematical universes Tegmark contemplates, happens to use the same math we discovered?

Brent

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