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".
>> 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
> > 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.
> 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. 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.
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.
> 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.
> 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. 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. 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
John K Clark
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