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On 29 feb, 18:35, Bruno Marchal <marc...@...> wrote:On 29 Feb 2012, at 15:47, Alberto G.Corona wrote:On 29 feb, 11:20, Bruno Marchal <marc...@...> 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 questionaboutwhat is mathematical and what is not?. The set of real numbers is amathematical structure, but also the set of real numbers plus thepoint (1,1) in the plane is.Sure. Now, with comp, that mathematical structure is more easilyhandled in the "mind" of the universal machine. For the ontology wecan use arithmetic, on which everyone agree. It is absolutelyundecidable that there is more than that (with the comp assumption).So for the math, comp invite to assume only what is called "thesharable part of intuitionist and classical mathematics.I do not thing in computations in terms of "minds of universalmachines" in the abstract sense but in terms of the needs ofcomputability of living beings.I am not sure I understand what you mean by that.What is your goal?The goal by default here is to build, or isolate (by reasoning fromideas that we can share) a theory of everything (a toe).And by toe, most of us means a theory unifying the known forces,without eliminating the person and consciousness.My goal is the same. I start from the same COMP premises, but I do not
not see why the whole model of the universe has to be restricted to
I start from the idea of whathever model of an
universe that can localy evolve computers. A mathematical continuous
structure with infinite small substitution measure , and thus non
computable can evolve computers. well not just computers,
adaptive systems, clearly separated from the environment, that respond
to external environment situations in order to preserve the internal
structures, to reproduce and so on.
The list advocates that 'everything' is simpler than 'something'. Butthis leads to a measure problem.It happens that the comp hypothesis gives crucial constraints on thatmeasure problem.I agree with you. The little numbers are the real stars :)But the fact is that quickly, *some* rather little numbers havebehaviors which we can't explain without referring to big numbers oreven infinities. A diophantine polynomial of degree 4, with 54variables, perhaps less, is already Turing universal. There areprograms which does not halt, but you will need quite elaboratetransfinite mathematics to prove it is the case.that is not a problem as long as diophatine polynomials don´t usurpate
the role of boolean logic in our universe, and the transfinite
mathematics don´t vindicate a role in the second law of Newton. ;)
Kolmogorov complexity might be the key of the measure problem, but fewpeople have succeeded of using it to progress. It might play some rolein the selection of some particular dovetailer, but it can't work, bybeing non computable, and depending on constant. I don't know. I'mafraid that the possible role for Kolmogorov complexity will have tobe derived, not assumed. or you might find an alternative formulationof comp.
As I said above I do not see why a model of the universe as a whole
has to be restricted to the requirement of simulation.
I see (local)
and macroscopic computability as an "antropic" requirement of Life,
but not more.
That is, for example, may be that the boolean logic forexample, is what it is not because it is consistent simpleand it´sbeatiful, but because it is the shortest logic in terms of thelenght of the description of its operations, and this is the reasonbecause we perceive it as simple and beatiful and consistent.It is not the shortest logic. It has the simplest semantics, at thepropositional level. Combinators logic is far simpler conceptually,but have even more complex semantically.I meant the sortest binary logic.Classical logic is not the shorter binary logic. In term of the lengthof its possible formal descriptions.I mean that any structure withcontradictions has longer description than the one without them.,?None logic get contradictions, with the notable exception of theparaconsistant logics.Intuitionist logic is a consistent (free of contradiction) weakeningof classical logic. Quantum logic too.Note also that the term logic is vague. Strictly speaking I don't needlogic at the ..
I can define a set and arbitrary ioperations with contradictions.
can say True ´AND True is False half of the time. and True the other
half.depending on a third stocastic boolean variable that flip
according with some criteria. I can define multiplication of numbers
in weird ways so that i break the symetric an distributive
properties in certain cases . and so on. All of them can be defined
algorithmically or mathematically. In the broader sense, these
structures will be mathematical but with larger kolmogorov complexity
than the good ones.(and useless).
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