On 20 Mar 2012, at 17:56, Richard Ruquist wrote:

On Tue, Mar 20, 2012 at 12:15 PM, Bruno Marchal <marc...@ulb.ac.be> wrote:

On 20 Mar 2012, at 03:42, Stephen P. King wrote:

How is the notion of space coded in numbers? People argue that we can recover a notion of time from the well order of integers, but what about spaces? How do we get those?

Stephen, here I suspect you are confusing comp with digital physics. There are no reason that space (nor God, nor souls, ...) can be encoded in numbers. On the contrary, arithmetic as seen by inside, and taking the 1-indeterminacy into account ('course) is full of things which will exists (from the machine's viewpoint) and which are not encodable with numbers. This comes from standard mathematical logical results. The 1-I is typical with that respect. defining it by "Bp & p" leads to a knowledge logic which can be proved to be not arithmetically definable, nor is truth, nor is sensible matter and most qualia, nor is consciousness itself, and very plausibly, nor are physical spaces and times. The self-referential logics makes possible to "meta-formalize" them, though, notably by those many typical things that the machine cannot formalize, yet can know about.




If you are familiar with the philosophy of Leibniz as stated in his Monadology
I wish you to comment on its relationship to COMP if any.

My guess is that COMP is equivalent to the infinity of possible universes in the ideas of god. But rather than all ideas being realized, god selects only the best universe, e.g.:

53. Now as there are an infinity of possible universes in the ideas of God, and but one of them can exist, there must be a sufficient reason' for the choice of God which determines him to select one rather than another.

Assuming comp elementary arithmetic realizes or implements, all possible subjective experiences, for example the phi_k(j)^n in the UD, with k the Heinsenberg matrix of the state of the Milky Way at 5h pm yesterday (to give a trivial example which in the UD* generates your thought of today, including the reading of this mail).

But, "we", by the computationalist global first person indeterminacy (do you know what it is?) are indeterminate on all such histories, as far as they implement us at the right digital substitution levels (which means already an infinity). So matter and consciousness result from the "statistical competition" of infinities of universal machines, and empirically we have already a first person plural reality (QM) and a very deep "common" history.

Is there an ultimate winners capable of making coherent a unique physical reality? With comp and QM without collapse, we might hope for a common multiverse. With comp the background can be better described as a multidream, but the inside views define something very vast, and almost everything must be rethought on. To sum up: open problem.

Leibniz is interesting, but get different views all his life (like a genuine researcher). It is very demanding in time to figure out what he thought. I have followed some course on him, just to see how far he has been close to comp, and it is striking that he has been very close to all the good (comp) idea, but without CT, and without the universal machine concept, he was stuck, I think. But he got the idea of universal machine and language, but in a philosophical sense, not in the computer theoretical (arithmetical) sense. He got the possible worlds, but miss the importance of the accessibility relations between worlds. Yes Leibniz was quite close.



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