On 29 feb, 11:20, Bruno Marchal <marc...@ulb.ac.be> wrote: > On 29 Feb 2012, at 02:20, Alberto G.Corona wrote (to Stephen): > > > A thing that I often ask myself concerning MMH is the question about > > what is mathematical and what is not?. The set of real numbers is a > > mathematical structure, but also the set of real numbers plus the > > point (1,1) in the plane is. > > Sure. Now, with comp, that mathematical structure is more easily > handled in the "mind" of the universal machine. For the ontology we > can use arithmetic, on which everyone agree. It is absolutely > undecidable that there is more than that (with the comp assumption). > So for the math, comp invite to assume only what is called "the > sharable part of intuitionist and classical mathematics. > I do not thing in computations in terms of "minds of universal machines" in the abstract sense but in terms of the needs of computability of living beings.

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> > The set of randomly chosen numbers { 1,4 > > 3,4,.34, 3} is because it can be described with the same descriptive > > language of math. But the first of these structures have properties > > and the others do not. The first can be infinite but can be described > > with a single equation while the last must be described > > extensively. . At least some random universes (the finite ones) can be > > described extensively, with the tools of mathematics but they don´t > > count in the intuitive sense as mathematical. > > Why? If they can be finitely described, then I don't see why they > would be non mathematical. > It is not mathematical in the intuitive sense that the list of the ponits of ramdomly folded paper is not. That intuitive sense , more restrictive is what I use here. > > > > What is usually considered genuinely mathematical is any structure, > > that can be described briefly. > > Not at all. In classical math any particular real number is > mathematically real, even if it cannot be described briefly. Chaitin's > Omega cannot be described briefly, even if we can defined it briefly. > a real number in the sense I said above is not mathematical. in the sense I said above. In fact there is no mathematical theory about paticular real numbers. the set of all the real numbers , in the contrary, is. > > Also it must have good properties , > > operations, symmetries or isomorphisms with other structures so the > > structure can be navigated and related with other structures and the > > knowledge can be reused. These structures have a low kolmogorov > > complexity, so they can be "navigated" with low computing resources. > > But they are a tiny part of bigger mathematical structures. That's why > we use big mathematical universe, like the model of ZF, or Category > theory. If maths is all that can be described finitelly, then of course you are right. but I´m intuitively sure that the ones that are interesting can be defined briefly, using an evolutuionary sense of what is interesting. > > > > > So the demand of computation in each living being forces to admit > > that universes too random or too simple, wiith no lineal or > > discontinuous macroscopic laws have no complex spatio-temporal > > volutes (that may be the aspect of life as looked from outside of our > > four-dimensional universe). The macroscopic laws are the macroscopic > > effects of the underlying mathematical structures with which our > > universe is isomorphic (or identical). > > We need both, if only to make precise that very reasoning. Even in > comp, despite such kind of math is better seen as epistemological than > ontological. > There is a hole in the transition from certain mathematical properties in macroscopic laws to simple mathematical theories of everything . The fact that strange, but relatively simple mathematical structure (M theory) include islands of macroscopic laws that are warm for life. I do not know the necessity of this greed for reduction. The macroscopic laws can reigh in a hubble sphere, sustained by a gigant at the top of a turtle swimming in an ocean. > > > > And our very notion of what is intuitively considered mathematical: > > "something general simple and powerful enough" has the hallmark of > > scarcity of computation resources. (And absence of contradictions fits > > in the notion of simplicity, because exception to rules have to be > > memorized and dealt with extensively, one by one) > > > Perhaps not only is that way but even may be that the absence of > > contradictions ( the main rule of simplicity) or -in computationa > > terms- the rule of low kolmogorov complexity _creates_ itself the > > mathematics. > > Precisely not. Kolmogorov complexity is to shallow, and lacks the > needed redundancy, depth, etc. to allow reasonable solution to the > comp measure problem. > I can not gasp from your terse definitions what the comp measure problem is . What i know is that, kolmogorov complexity is critical for life. if living beings compute inputs to create appropriate outputs for survival. And they do it. > > That is, for example, may be that the boolean logic for > > example, is what it is not because it is consistent simpleand it´s > > beatiful, but because it is the shortest logic in terms of the > > lenght of the description of its operations, and this is the reason > > because we perceive it as simple and beatiful and consistent. > > It is not the shortest logic. It has the simplest semantics, at the > propositional level. Combinators logic is far simpler conceptually, > but have even more complex semantically. > I meant the sortest binary logic. I mean that any structure with contradictions has longer description than the one without them.,so the first is harder to discover and harder to deal with.,. > But the main problem of the MHH is that nobody can define what it is, > and it is a priori too big to have a notion of first person > indeterminacy. Comp put *much* order into this, and needs no more math > than arithmetic, or elementary mathematical computer science at the > ontological level. tegmark seems unaware of the whole foundation-of- > math progress made by the logicians. > > Bruno > > > > > > > > > > > . > >> Dear Albert, > > >> One brief comment. In your Google paper you wrote, among other > >> interesting things, "But life and natural selection demands a > >> mathematical universe > >> <https://docs.google.com/Doc?docid=0AW-x2MmiuA32ZGQ1cm03cXFfMTk4YzR4cn... > >> >somehow". > >> Could it be that this is just another implication of the MMH idea? If > >> the physical implementation of computation acts as a selective > >> pressure > >> on the multiverse, then it makes sense that we would find ourselves > >> in a > >> universe that is representable in terms of Boolean algebras with > >> their > >> nice and well behaved laws of bivalence (a or not-A), etc. > > >> Very interesting ideas. > > >> Onward! > > >> Stephen > > > -- > > You received this message because you are subscribed to the Google > > Groups "Everything List" group. > > To post to this group, send email to everything-list@googlegroups.com. > > To unsubscribe from this group, send email to > > everything-list+unsubscr...@googlegroups.com > > . > > For more options, visit this group > > athttp://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 everything-list@googlegroups.com. 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