Hi Bruno Marchal 

Yes, but those numbers are not extended in space, so 
they have no physical size.


[Roger Clough], [rclo...@verizon.net]
12/31/2012 
"Forever is a long time, especially near the end." - Woody Allen
----- Receiving the following content ----- 
From: Bruno Marchal 
Receiver: everything-list 
Time: 2012-12-31, 08:20:44
Subject: Re: Ten top-of-my-head arguments against multiverses


On 31 Dec 2012, at 14:05, Roger Clough wrote:

> Hi Bruno Marchal and Brian,
>
> "Bigness" can only limit physical entities (those extended in space),
> but is irrelevant with regard to nonphysical or mental entities,
> as these are not extended in space.

?

Is is not natural to say that 10^100 is bigger than 0? And 2^Aleph_0 
bigger than Aleph_0?

Bruno



>
>
>
> [Roger Clough], [rclo...@verizon.net]
> 12/31/2012
> "Forever is a long time, especially near the end." - Woody Allen
> ----- Receiving the following content -----
> From: Bruno Marchal
> Receiver: everything-list
> Time: 2012-12-30, 08:57:29
> Subject: Re: Ten top-of-my-head arguments against multiverses
>
>
>
>
> On 29 Dec 2012, at 20:51, Brian Tenneson wrote:
>
>
>
>
>
>
>
> Why not take the categories of all categories (besides that Lawyere 
> tried that without to much success, except rediscovering 
> Grothendieck topoi).
>
>
> I'm more interested in the smallest mathematical object in which all 
> mathematical structures are embedded but the category of all 
> categories will do.
>
>
>
> Except that it is too big, and eventually lawvere extract the topi 
> from this, which model well, not the mathematical reality, but the 
> mathematician itself.
>
>
> Also, we have already discuss this, but the embedding notion does 
> not seem the right think to study, compared to emulation, at least 
> with the comp hypothesis.
>
>
>
>
>
>
>
>
>
> But if you assume comp, elementary arithmetic is enough, and it is 
> better to keep the infinities and categories into the universal 
> machine's mind tools.
>
>
> Enough for what, in what sense?
>
>
>
> Enough for a basic ontology (and notion of existence) to explain all 
> the different sort of existence, notably of persons, consciousness, 
> matter appearances, etc. See my papers, as I pretend that with comp 
> we have no choice in those matter, except for pedagogical variants 
> and practice.
>
>
>
>
>
>
>
>
>
>
>
>
>
>
> To have a single mathematical object that all mathematical 
> structures can be embedded would give us an object that, in a sense, 
> contains all structures. If one follows Tegmark's idea that ME=PE, 
> then a definition for universe just might be a mathematical object 
> (which by ME=PE is a physical object) that contains, in a sense, all 
> mathematical objects (i.e., all physical objects).
>
>
> I think that this is deeply flawed. We cannot identify the physical 
> and the mathematical. We might try theory on the physical, or on the 
> mental, or on the mathematical, which might suggest relation between 
> those thing, but I doubt any non trivial theory would identify them, 
> unless enlarging the sense of the words like mental, physical.
>
>
>
> Isn't it simpler to assume there is only one type of existence?
>
>
> It seems to me part of the data that this is not the case. My pain 
> in a leg has a type of existence different from a quark. The game of 
> bridge as a different type of existence than the moon material 
> constitution.
> Then for machine, once we distinguish their different points of view 
> (intuoitively like in UDA) or formally like in AUDA, we get many 
> different sort of existence.
> The ontic one is the simpler ExP(x), but we have also []ExP(x), 
> []Ex[]P(x), []<>P(x), []<>Ex[]<>P(x), etc. All this in 8 different 
> modal logics extracted from self-reference.
>
>
>
>
>
>
> What are the actual flaws of a mathematical universe?
>
>
> Too big. It is a metaphor.
>
>
>
>
>
>
> A physical system can be mathematically encoded by its corresponding 
> set of world lines. This encoding is an isomorphism. A very simple 
> example of what I mean is the nearly parabolic path taken by a 
> projectile. The set of world lines would be some subset of R^4 or 
> R^n if it turns out that n != 4. I am aware that indeterminacy due 
> to Heisenberg's uncertainty principle kicks in here so we may never 
> "know" which subset of R^n a physical system is isomorphic to but by 
> a pigeonhole principle, the physical system must be isomorphic to 
> some subset of R^n, several in fact.
>
>
>
> May be. But I am driven by the mind-body problem, and what you show 
> above is mathematical physics. With comp, by UDA, we have to extract 
> the belief in such physical idea by ultimately explaining them in 
> term probabilities on computations (that the result I invite you to 
> study and criticize).
>
>
>
>
>
>
>
>
>
> With computationalism, the coupling consciousness/physical is a 
> phenomenon, person perceptible through numbers relations when they 
> (the persons) bet on their relative self-consistency. This explains 
> the appearance of the physical, without going out of the 
> arithmetical. It works thanks to Church thesis and the closure of 
> the comp everything (UD*, sigma_1 completeness).
>
>
>
>
> How are you defining consciousness here?
>
>
>
> I can't define it. I just hope you know what I mean. Basically 
> something true but non provable about yourself, and, by comp, 
> invariant for some local digital substitution.
>
>
>
>
>
>
>
>
>
>
>
>
> It's not super clear to me that the cocompletion of the category of 
> all structures C exists though since C is not a small category and 
> thus Yoneda's lemma doesn't apply. I would have to fine-tune the 
> argument to work in the case of the category C I have in mind.
>
>
>
> The n-categories might be interesting, but we don't need so rich 
> ontology. If we are machine, the cardinality of the basic TOE is 
> absolutely undecidable from inside. Omega is enough.
>
>
> Do you have an argument that proves that our minds can't transcend 
> "inside"?
>
>
>
> The mind can do that. Math, by diagonalization, does that, actually, 
> even in a 3p way.
> But the fact that "number's mind" can do that invite us to not reify 
> the transcendental. This is what lead to superstition and non 
> necessarily complex ontologies.
>
>
>
>
>
>
>
>
>
>
>
> If the cocompletion of C is the One, that which all mathematical 
> structures can be embedded, then the parallel universe question 
> would be a matter of logic and category theory; it would depend on 
> how you defined "the visible universe" and "parallel" universe.
>
>
>
> You will have to define an observer, its points of view, and to take 
> into account its many distributions in that super-mathematical 
> structure, but you can't do that, as you will need an even bigger 
> structure to define and study the indeterminacy. So you will have to 
> limit your notion of observer and use some "comp" hypothesis (an 
> infinite variant if you want).
>
>
> With comp, it is easier: you cannot really take more than 
> arithmetic. God created the Natural Numbers, all the rest belong to 
> the (singular and collective) number's imagination. If nature 
> refutes this, it will still remain time to add the infinities 
> needed. I think.
>
>
>
>
> How is the arithmetical structure going to give rise to a 
> description of reality that takes into account observer, its points 
> of view, and its many distributions without the need to study the 
> indeterminacy?
>
>
>
> You might take a look on my paper(s)(?), or my posts here, as this 
> is what I keep trying to explain here. I am not sure how you can 
> study the relation between the first person and its possible 
> realities without using the first person indeterminacy, which is the 
> building block of the physical realities.
> The observer are the (Turing) universal numbers. Physics is given by 
> the measure on the computations going through their state. This 
> extends Everett on arithmetic. It leads to a many-dream view of 
> arithmetic, and can be shown to be developed by almost all universal 
> numbers.
>
>
> Bruno
>
>
> (?) http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html
>
>
>
>
>
>
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