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> 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. 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.

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.

>> 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.

> 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.

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.

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.

> 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.

> 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.

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.

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.



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