Hi Bruno Marchal Yes, but those numbers are not extended in space, so they have no physical size.
[Roger Clough], [[email protected]] 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], [[email protected]] > 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 > > > > > > > -- > You received this message because you are subscribed to the Google > Groups "Everything List" group. > To view this discussion on the web visit > https://groups.google.com/d/msg/everything-list/-/XqN5TmRQ1n0J > . > To post to this group, send email to [email protected]. > To unsubscribe from this group, send email to > [email protected] > . > For more options, visit this group at > http://groups.google.com/group/everything-list?hl=en > . > > > > http://iridia.ulb.ac.be/~marchal/ > > -- > You received this message because you are subscribed to the Google > Groups "Everything List" group. > To post to this group, send email to [email protected]. > To unsubscribe from this group, send email to > [email protected] > . > For more options, visit this group at > http://groups.google.com/group/everything-list?hl=en > . > http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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