On 01 Nov 2012, at 22:34, Stephen P. King wrote:

On 11/1/2012 11:47 AM, Bruno Marchal wrote:

On 01 Nov 2012, at 01:01, Stephen P. King wrote:

Dear Bruno,

Exactly what do these temporal concepts, such as "explain", "solve", "interacting" and " emulating", mean in an atemporal setting? You are mixing temporal and atemporal ideas. ...

Study a good book in theoretical computer science. You told me that you have the book by Matiyazevich. he does explicitly emulate Turing machine, which have a quite physical look, with a moving head, and obeying instruction is a temporal manner, and yet they can be shown to be emulated by a the existence or non existence of solution of Diophantine equations.

Dear Bruno,

That book, full of wonderful words and equations, is a physical object.

True, but non relevant.

That physical object is, in my thinking, an example of an implementation of the "emulation of a Turing Machine..." just as the image on my TV of Rainbow Dash and her friends is a physical implementation of magical Ponies. You seem to ignore the obvious...

You assume physical objects, but this contradict your own theory (on which you point to, but without ever giving it).

But this is already no more an enigma for many physicists which agree that temporality is just an illusion resulting from projection from higher dimension.

Those physicists are wrong in their belief. This is argued well in this paper http://xxx.lanl.gov/abs/gr-qc/9708055 and in any other places. I recall a long chat that I had with Julian Barbor. In it I tried to ask him about the computational complexity of implementing his 'time capsule' and 'best matching' ideas, he seemed to not understand what the heck I was talking about and yet bemoaned the very problem at length in one of his papers on the idea!

From pg 52 of http://www.platonia.com/barbour_hrp2003.pdf

"About ten years ago, I did some computer calculations to find such
configurations with the Macintosh computer I then possessed. I was able to do exhaustive calculations up to N = 27, which took the computer about three days. Because the number of combinations that must be checked out grows
exponentially with N, even with a modern supercomputer I doubt that
calculations much beyond N = 50 would be feasible."

BTW, it was reading this paper that opened my eyes to the NP-Hard problem of Leibniz' Pre-Established Harmony.

I thought you agree that physics (and thus time) is not primitive.

I agree, physics (and all that it such as particles, forces, matter, energy) impels cannot be ontologically primitive. But it must exist nonetheless. My challenge is showing how. I start with a notion of a property neutral "totality of all that exists"

But what exists has properties, and besides, we don't know what exists (beside our consciousness), so you take for granted much too much, exactly what we have to explain.

and consider how from that ground two aspects emerge simultaneously, the physical and the mental as mutually distinct dual aspects that when added together yield back the neutrality. This idea is very similar to Russell Standish's Theory of Nothing.

I have no clue what you mean.

This means that they can and need to be explain from non temporal notion.

Arithmetic is the bloc mindspace.

   Is it a Singleton?


Can it be exactly represented by a Boolean Algebra?


I see 'mindspace" as one half of the dual aspects.

You pretend to see a flaw. I am not interested in your "theory". You have to work in the theory you are criticizing, to find the flaw in that theory. If not you are like someone pretending that abelian group are ridiculous as you know a non abelian group. Use comp, without adding any other axioms, please.

There is nothing more dynamical than the notion of computations, yet, they have been discovered in statical math structure.

Mathematical objects are the epitome of static objects. I think that this view of math is blinkered. A description of a dynamic process may be static, but the evolutionaly Becoming aspect is still there, just hidden. Just as a photograph acts to freeze a moment in time...

So you assume a primitive time. This contradicts your "theory" (the few I ahve grasped, but which becomes more and more confused, when you try to escape some comp's consequence, for reason which eludes me, as in some post you seem to have agreed with them.

This is made possible as the statical sequence 0, 1, 2, 3, ... reintroduces a lot of quasi-time notion, and it is explained how some of them will play the role of the "observable timing of events" locally, by relative numbers.

This is where you make the mistake. You are assuming that the ordering of numbers *is* the dynamic.


I claim that the ordering of numbers *is a representation* of the dynamic.

It can be. But the confusion is not made in comp, or in my posts.

We should be very careful when we identify the map with the territory! I agree that there are situations when there is an exact isomorphism between map and territory, but that is only in the case of automorphisms and fixed points. We can use sequences of relative numbers, surely, but only when the conditions to define them occur.

This makes no sense. It leads directly to infinite regress, as the condition will usually be much more complex than the definition of the numbers. You are asking to the centipede to understand how its brain and legs function before walking.

We cannot assume that the properties of relative numbers exist in the absence of the means to define the "timing", "locality" and "relations" required.

Then give me your theory of numbers. And make sure it is simpler than the first order usual arithmetical theories. Good luck ...



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