On 10/24/2012 10:15 AM, Bruno Marchal wrote:


On 24 Oct 2012, at 06:03, Stephen P. King wrote:

What difference does what they refer to matter? Eventually there has to be some physical process or we would be incapable of even thinking about them! The resources to perform the computation are either available or they are not. Seriously, why are you over complicating the idea?


Let us be clear. For humans to be able to think, not only you need a physical process, but you need a solar system, a planet, ... many things, including much resources.

Dear Bruno,

Sure, but that only is about explanations of the physical systems involved. But let me ask you, given that there is a 1p for each and every observer, does it not follow that there should be a bundle of computations for each and one? There would be a great deal of overlap between them (as that would be equivalent to the commonality of the experienciable content of the observers). The point is that the computation is not of a single object in a world. We have to consider computational simulations of entire universes!


But, ...

... for the couple [thinking humans===== Earth, solar-system-physical process-resource] you need only arithmetic.

A bit like in Everett the couple [physician's sad consciousness in front of a collapsed wave===== a dead Schroedinger cat] you need only the universal quantum wave.

Just that once we assume comp "enough consciously", if I can say, the universal wave itself, if correct for observation, has to be retrieved from a larger statistics, on all computations, going through our local computational states.

Literally, the laws of physics are invariant from the choice of the physical basic laws, as long as they are at least Turing universal (synonym important for AUDA: Sigma_1 complete).

I am not sure what this means: "laws of physics are invariant from the choice of the physical basic laws". Could you explain this more?


Literally: very elementary arithmetic is a good TOE:

x + 0 = x
x + s(y) = s(x + y)

 x *0 = 0
 x*s(y) = x*y + x

It is in *that* theory, that we have now to define the notion of observers, believers, knowers, experiencers, experimentalists, and formulate a part of the "measure problem". Mathematically, we can test the first person limiting observation by the person "incarnated by the genuine computation" in arithmetic.

Another TOE:

((K, x), y) = x
(((S, x), y), z) = ((x, z), (y, z))

It operates on the combinators, and the combinators are K or S, or (x, y) with x and y combinators. So (K, K), (K, (K, S)), ((K, K) K), etc are combinators.

What they do? They obeys the laws above.

Those defines Turing universal realities, and they will emulate/define other universal realities, in the same relative proportions, which will be the observers-universe, a coupled universal machine (it is another way to view Löbianity (although technically it is a bit weaker)).

Any universal machine contains in itself a sort of war between *all* universal machines until they recognize themselves.

Obviously some universal machines get more famous than other, apparently, like ... well arithmetic, combinators, but also, in relation with the observable reality, quantum computers.

It makes comp testable, or at least the definition of observer, believer, knower used in the derivation of physics, and here I provide only the propositional physical theory (and even some choice as different quantum logics appears in S4Grz1, Z1*, X1*, the logic of the material hypostases, in Plotinus terms).


All of that is a theoretical explanation, that supposes that since arithmetic is all that is needed to encode all of the information and representations, but this is just an explanation, nothing more. Until we can derive phenomenology that can be tested, we have only a hypothesis or conjecture. My proposal is that, following Pratt's suggestion, we consider the arithmetic to be equivalent to a Boolean algebra and its evolution is "the computation" of the UD. That way we do not have a body problem, since the dual of the Boolean algebra, the topological space, is the body whose evolution is physics.

With comp, trying to singularize consciousness with a particular universal machine (a physical reality), is like a move to select a branch in a wave of realities, and can be seen as a form of cosmical solipsism negating consciousness for vast span of arithmetical truth, just because those realities are only indirectly accessible, by looking below ours substitution level.

But solipsism is not the absence of consciousness, it is the inability of one 1p to bet on the existence of the possible content of other 1p.


I have translated a part of the "philosophical" mind-body problem in mathematics (and partially solve it).

Sure, but your claims of an immaterial monism worry me. It is as if you have resurected Berkeley's Idealism in a formal mathematical model and dismissed the attack by Mr. Johnson (who famously rebounded his foot from a rock and yelled 'I refute it thus.') as "an arithmetic body problem".


I made a mistake as the mathematicians don't know about the mind body problem, and the philosophers don't know the math (here: computer science/mathematical logic).

Sure, I cannot write it, but I do understand it. I can barely write English! It is hard to explain the effects of dyslexia.


The physicists, at least those who don't believe in the collapse are closer to get the picture coherent with what can be like a physics from the persons supported by the combinators reduction (or by the numbers addition and multiplication), as it has to be the case if we assume comp.

When I will have more time I will continue to explain the math needed for this.

Bruno


http://iridia.ulb.ac.be/~marchal/ <http://iridia.ulb.ac.be/%7Emarchal/>



--
Onward!

Stephen

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