On 01 Mar 2012, at 01:59, Alberto G.Corona wrote:



On 29 feb, 18:35, Bruno Marchal <marc...@ulb.ac.be> wrote:
On 29 Feb 2012, at 15:47, Alberto G.Corona wrote:




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.

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 from
ideas 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
being computable.

Indeed. The COMP premises makes this impossible. If "I am a machine" then

1) the appearance of the universe existence and structure is derivable entirely from comp/arithmetic, in a precise way. 2) we can already deduce many things about the physical universe, notably that it is NOT computable.

Don't confuse comp "I can survive with a digital brain in the physical reality" with digital physics (the physical universe is Turing emulable). The second implies the first, but the first implies the negation of the second, so digital physics is completely contradictory by itself. With or without comp, digital physics leads to a contradiction, and so is false.




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,

It has to be like that with comp. It is part of the consequences of comp.



but problem
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.

No problem.


The list advocates that 'everything' is simpler than 'something'. But
this leads to a measure problem.

It happens that the comp hypothesis gives crucial constraints on that
measure problem.




I agree with you. The little numbers are the real stars :)

But the fact is that quickly, *some* rather little numbers have
behaviors which we can't explain without referring to big numbers or
even infinities. A diophantine polynomial of degree 4, with 54
variables, perhaps less, is already Turing universal. There are
programs which does not halt, but you will need quite elaborate
transfinite 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. ;)

There is no primitive physical universe, with comp. The physical universe is what numbers can observe from inside arithmetic. You might read the proof (UDA). It is not entirely obvious.









Kolmogorov complexity might be the key of the measure problem, but few people have succeeded of using it to progress. It might play some role
in the selection of some particular dovetailer, but it can't work, by
being non computable, and depending on constant. I don't know. I'm
afraid that the possible role for Kolmogorov complexity will have to
be derived, not assumed. or you might find an alternative formulation
of 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.

But if you accept comp, the physical universe cannot be emulated digitally at all. It is only a projective view from inside. To predict any observable events, you have to make an infinite sum that NO computers can ever do. To understand this you have to understand the first person indeterminacy, and some invariance lemma for first person (conscious) views.



I see  (local)
and macroscopic computability as an "antropic" requirement of Life,
but not more.

The problem is that your consciousness is distributed uniformly on all computations. You need to take that into account. I am afraid that you are using an identity thesis like brain-mind which is incompatible with the comp theory.







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.

Classical logic is not the shorter binary logic. In term of the length
of its possible formal descriptions.

I mean that any structure with
contradictions has longer description than the one without them.,

?
None logic get contradictions, with the notable exception of the
paraconsistant logics.
Intuitionist logic is a consistent (free of contradiction) weakening
of classical logic. Quantum logic too.
Note also that the term logic is vague. Strictly speaking I don't need
logic at the ..

I can define a set and arbitrary ioperations with  contradictions.

I have no idea of what is a set with contradiction. A contradiction is a proposition in a theory. A set is not a theory, but a mathematical object.



 I
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).


But if you assume comp, you can no more impose a simplicity criterium, you have to derived from the measure problem. read the papers or the archive. There is no doubt that simplicity is at play, and you can assume it for a while, but it might contradict comp, for the big numbers and theories does play a role, and it is up tp us to understand why they don't interfere so much. Open problem.

Bruno

http://iridia.ulb.ac.be/~marchal/



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