On 6/20/2012 3:39 AM, Bruno Marchal wrote:


On 19 Jun 2012, at 19:41, John Clark wrote:

On Tue, Jun 19, 2012 at 6:01 AM, Bruno Marchal <marc...@ulb.ac.be <mailto:marc...@ulb.ac.be>> wrote:

    >> Unlike the proton and neutron nobody has found any
    experimental evidence that the electron has a inner structure,
    that it is made of parts.
    > The primitive matter I talk about is the idea of primary matter
    in the Aristotle sense


Aristotle was a great logician but a dreadful physicist.

    > If I say that electron is not primitive, I don't mean it is
    made of part, almost the contrary, that it is a mathematical
    reality, or that it is reducible to a non physical mathematical
    or theological reality, an invariant in our sharable computations.


I don't know what that means. What experiment would I need to perform, what would a electron need to do to prove it was "primitive".

The electron cannot do that, but my pet amoeba cannot prove they are unicellular, despite they are. It is just that if matter is primitive (not explainable from non material relation) then we have to make it infinite to singularize consciousness.

Dear Bruno,

I am parsing your comments here as I want to fully and clearly understand them.

Do you stand by that implication, that "matter is primitive" = "not explainable from non material relation"? This implies that: "matter is not primitive" = "explainable from non material relation". No? I would like to better understand how the notion of ontological primitives is defined in your dictionary.


With comp, we just abandon the idea of singularize consciousness in bodies, and then the bodies have to be explained in term of number relation.

Why would we have to "singularize consciousness in bodies" at all? What premise or postulate is it that consciousness is "singularized" in a body? I am assuming that "singularize" means "to make singular" in the sense of either a singularity or a singleton. I am not sure which of the latter you are assuming.

It is more easy to understand that reversal at the epistemological level. Physical concepts are not primitive means that we can reduce them to non physical concepts, like those coming from theoretical (mathematical) computer science. It means that physics is not the fundamental science. Exactly like we can reduce biology to physics, we can reduce physics to the study of machine dreams.


At the epistemological level we are assuming that there already exist conscious entities, therefore a reversal cannot be run in a consistent manner if the reversal implies the non-existence of conscious entities. You are now equating "reducible" to "explainable". Is an explanation a "constructive" process in your thinking?



        >> To calculate the first 100 digits of Chaitin's constant
        you'd need to feed all programs that can be expressed in 100
        bits or less into a Turing Machine and see how many of them
        stop and how many of then do not. Some of them will never
        stop but the only way to know how many is to wait a infinite
        number of years and then see how many programs are still
        running. So you'd need to be infinitely patient, in other
        words you'd need to be dead.


    > Only to be sure of the decimals obtained.


Well yeah, it's easy to calculate Chaitin's constant if you don't mind getting it wrong.

After BB(100) computation steps, the decimals will be correct. I will not know it, but they are correct.

Is this correctness that occurs after the BB(100) steps capable of being "forced" to hold for the infinite case, as discussed in this paper http://arxiv.org/abs/math/0509616? I would like to better understand how you leap the gap between the finite case and the infinite case.





    > If I relax that constraints, then I need only to be *very
    patient*. The non computable, but well defined Buzzy Beaver
    function (BB) bounds the time needed to wait. Of course it grows
    *very* fast. But I don't need an *infinite* time to get the 100
    first digits correct. Any time bigger than BB(100) will do.


If we wait a googoplex to the googoplex power years some 100 bit programs will still be running, some of them could be Busy Beaver programs but others could just be very long finite programs. And in the same 1962 paper where Rado introduced the idea of the beaver he proved that a general algorithm to tell if a program is a Busy Beaver or not does not exist.

That is true for all programs. There is no algorithmic way to see if a program compute the factorial function. Again, this does not change anything in the argument.

    What if a factorial is involved in the explanation of consciousness?



It's true that if you knew the numerical value of Chaitin's Constant then you would know that if a 100 bit program had not stopped after a Turing Machine had run n number of finite operations then it never will; but the trouble is you don't know Chaitin's Constant and never can, so you can never know how big n is. So even though they have been running for a googoplex to the googoplex power years one of those programs could stop 5 seconds from now.

Not if I waited, by chance or whatever, a time bigger than BB(100). If a decimal change after that, then we got a computable function growing more quickly than BB.

You do realize that this dependence upon a number of steps in a computational process is not equivalent to the notion of time in a strict way simply because time is not just the number of steps, it is also the transitional flow from one step to another.


And a Busy Beaver program grows faster than any computable function but to my knowledge it has not been proven that all non-computable functions grow as fast as the Busy Beaver.

That would be false. There are many non computable predicate, with non growing values.

What would be the ration of computable to non-computable predicates? Are you considering an ensemble or a space of predicates?



    > Lawrence Krauss in his book "A Universe From Nothing" says
    that someday something close to that might actually be possible.

    > You mean? Deriving addition and multiplication from physics?


No, Krauss talks about deriving physics from addition and multiplication, or at least from logic; he talks about proving that in the multiverse only certain fundamental laws of physics are logically self consistent. He even talks about the distant dream of showing that "something" is consistent but "nothing" is not.

OK. Nice.

Is not the proof (showing) that "something" is consistent and "nothing" is not consistent a triviality because "nothing" cannot be exactly defined such that a proof can be constructed.




    > That is impossible.


I think both Krauss and I would give the same response to that, maybe.

    > Why do you use "gibberish" to condemn free will, and not to
    condemn event without cause?


Because the meaning of "a event without a cause" is clear and no circularity is involved.

Cause is a fuzzy notion, and so "non causal" is even more fuzzy.

I agree! This is why the entire discussion of free will is incoherent if it involves notions of cause and effect given an ambiguous notion of cause.


Even the meaning of the question "what caused a event without a cause?" is clear, although it is a stupid question because the answer is so obvious. But the meaning of "free will" is anything but clear and circularity abounds.

In computer science, circularity is not a problem. We can eliminate it with the second recursion theorem of Kleene. Free-will seems to me rather clear, except that some philosopher defend a contradictory notion of free-will. I gave my definition of c-free-will, and I don't see why we should reject it.

I would like to better understand how this elimination occurs. Could you point us to a good discussion of Kleene's second recursion theorem? Would you recommend this article http://www.math.ucla.edu/~ynm/lectures/2009csl.pdf <http://www.math.ucla.edu/%7Eynm/lectures/2009csl.pdf> ?

The wiki article <http://en.wikipedia.org/wiki/Kleene%27s_recursion_theorem> defined the 2nd theorem as: "*The second recursion theorem*. If/F/is a totalcomputable function <http://en.wikipedia.org/wiki/Computable_function>then there is an index/e/such that\varphi_e \simeq \varphi_{F(e)}.

Here\varphi_e \simeq \varphi_{F(e)}means that, for each/n/, either both\varphi_e(n)and\varphi_{F(e)}(n)are defined, and their values are equal, or else both are undefined."


The point here is that either a fixed point obtains or the functions cannot be defined (aka are non-constructable). What is instructive to me is that fixed points have certain requirements to exist when we are thinking of them in the case of physics. For example, in the Brouwer fixed point theorem, we see that closure and convexity of a set of points is required. Exactly what would play the role of these in the computable function case?


And "why do we have free will?" is not a stupid question, its not smart and its not stupid and even though it contains a question mark it's not even a question, it's just a sequence of ASCII characters.

We agree that nc-free-will does not make sense, but you have not succeeded in convincing me that all notion of free-will is non sensical.


I would really like to understand why it is that John Clark insists on this elimination attitude toward the referent of that "sequence of ASCII characters". It seems that he does not understand the ramifications of such a postulate! IMHO, it makes anything that claims to be produced by his mind to be a meaningless "sequence of ASCII characters" as it clearly cannot be the result of an act of "his" will. He can have no will and thus there is not really a "his" associated with the supposed entity that is denoted by the sequence of ASCII characters : "John Clark". There is no such thing as a possessive modifier <http://people.umass.edu/partee/docs/partee-puzzles.pdf> for universes accessible by "John Clark" if we are to be consistent with claims.

--
Onward!

Stephen

"Nature, to be commanded, must be obeyed."
~ Francis Bacon

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