On 17 Dec 2013, at 19:55, meekerdb wrote:

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> wrote:In a sense, one can be more certain about arithmetical realitythan the physical reality. An evil demon could be responsiblefor our belief in atoms, and stars, and photons, etc., but it ismay be impossible for that same demon to give us the experienceof factoring 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 controlof them.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"made up" with no idea that it mighe turn out to have physicalapplications.)I'm not sure your premise is true. Calculus was certainlyinvented to apply to physics. Turing's machine was invented withthe physical process of computation in mind.Absolutely not. The "physical" shape of the Turing machine was onlythere for pedagogical purpose.Are you denying that Turing wanted to reason about realizablecomputation??

`Yes. When working on the foundation of math (not when working on`

`Enigma).`

Of course his reasoning itself was abstract and led to amathematical theorem. But Liz was asking about the unreasonableeffectiveness of mathematics. I don't think you can say thatTuring, or Babbage or Post or Church just became interested insequences of symbol manipulation because they dreamed about it.

`They were trying to find solutions to paradox arising arousing around`

`Cantor set theory.`

They were concerned with real instances of inference andcalculation, from which they abstracted recursive functions andTuring machines.

`It is the contrary. Like Gödel discovered the primituve recursive`

`functions, and miss Church thesis, just when working on Hilbert's`

`problem (to find an elementary consistent proof of a set theory). Same`

`for Post, Church, Turing, and the others.`

`In fact I got problem when saying to a mathematician that the work of`

`Gödel, Church, and Turing was relevant to computer science. Such work`

`were classified as pure mathematics, with no applications possible`

`(sic).`

the discovery of universal machine is a purely mathematical, evenarithmetical, discovery. "physical implementation" came later (ifyou except Babbage, but even Babbage will discover the mathematicalmachine (and be close to Church thesis), when he realized that hisfunctional description language (intended at first as a tool fordescribing his machine) was a bigger discovery than his machine.The discovery of the universal machine is the bigger even discoverymade by nature. It is even bigger than the big bang. And natureexploit it all the time, and with comp we understand completely why.I agree with the first sentence. I don't understand the second.

`Don't mind too much. We can come back to this later. I see most events`

`in the physical universe as apparition of universal systems, including`

`the big bang. But then that is how arithmetic has to look like from`

`inside, when we assume comp.`

That discovery is a theorem of elementary arithmetic, and hasnothing to do with the physical, except that with comp, we get theexplanation of the physical as a consequence of that theorem inarithmetic.Non-euclidean geometry of curved spaces was invented beforeEinstein needed it, but it was motivated by consideringcoordinates on curved surfaces like the Earth. Fourier inventedhis transforms to solve heat transfer problems. Hilbert space wasan extension of vector space in countably infinite dimensions. Sothe 'unreasonable effectiveness' may be an illusion based on aselection effect.This beg the question, of both the existence of math, and of aprimitive physical reality (and of the link between).So what's your answer to Wigner?

`Math works because the fundamental reality is mathematical. The`

`physical reality emerge as a persistent first person sharable sort of`

`arithmetical video game.`

Is it just an accident that the math the universe instantiates,

`You assume some primitive universe. But there is no evidence at all,`

`and on the contrary, the simplest explanation (number's dream) does`

`not allow it to exist in any reasonable sense.`

out of all mathematical universes Tegmark contemplates, happens touse the same math we discovered?

`Tegmark forgets to sum on all first person experience/computation-`

`viewed from inside. The physical reality is made conceptually very`

`solid in the comp theory. It is lawful and stable. But that physical`

`reality is only the border of a much vaster reality, that a machine`

`cannot distinguish from arithmetic seen from inside.`

Bruno

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