The halting problem revisited

[Robert Klemme]

Fortunately the human mind is not limited to the limitations of the
human brain.

Non sequitur. In fact, self-contradicting. The human mind is implemented
on the human brain*. Your statement is analogous to saying that some
computer program you ran on your dual-core x86-64 machine was not
limited to the limitations of your dual-core x86-64 machine [...]

Obvious nonsense.

Not so fast. You are creating an analogy but it is not entirely clear
whether that analogy actually holds. For example, it is not entirely
clear what Lew meant with "human mind". I for example would take it as
a more abstract thing than a computer program, especially can "human
mind" refer to a single mind but also to a multiplicity of minds. And
they can interact in multiple ways which are certainly not limited by a
single human brain.

Even if we go back to one brain and one mind: although it is pretty sure
that activities of the human mind are somehow related to the brain's
activities and we can pinpoint some effects (via tests and effects of
injuries) it is not entirely clear how this relation works. Which means
that we would not be able to infer mind limitations from brain
limitations. In light of that the statement "mind is limited by brain"
is trivial and meaningless at the same time.

Off recoiling my tape. ;-)

Cheers

robert

 

[Stefan Ram]

mind" refer to a single mind but also to a multiplicity of minds. And
they can interact in multiple ways which are certainly not limited by a
single human brain.

An open (interactive) system might be more powerful than a
Turing machine:

http://www.engr.uconn.edu/~dqg/papers/myth.pdf

 

[javax.swing.JSnarker]

An open (interactive) system might be more powerful than a
Turing machine:

http://www.engr.uconn.edu/~dqg/papers/myth.pdf

The same reasoning applies to a computer. It's still limited by the
collective capabilities of the hardware in the network as a whole.

 

[Robert Klemme]

The same reasoning applies to a computer. It's still limited by the
collective capabilities of the hardware in the network as a whole.

Even though. That was not the only argument.

Cheers

robert

 

[javax.swing.JSnarker]

Even though. That was not the only argument.

?

 

[Joshua Cranmer]

An open (interactive) system might be more powerful than a
Turing machine:

http://www.engr.uconn.edu/~dqg/papers/myth.pdf

Not really... If you model those examples of supposedly
not-computable-with-a-Turing-machine problems as control systems (which
indeed, all of the ones they gave are), then you could essentially turn
all of those into Turing-computable functions by including the parameter
that is the description of the universe. If it is possible to simulate
the universe with a Turing machine, then all of those problems are
really solvable with Turing machines. The implicit assumption in the
paper is that the Church-Turing thesis does not hold (that you can't
model the response of an environment by a computable function); by
assuming this fact, they arrive--surprise, surprise--at the result that
the Church-Turing thesis is false.

That, in essence, is the Church-Turing thesis, as I understand it: you
can use a Turing machine to simulate the universe.

 

[Andreas Leitgeb]

That, in essence, is the Church-Turing thesis, as I understand it: you
can use a Turing machine to simulate the universe.

"I thought Laplace's daemon was impaled with aspen stake by Heisenberg's
uncertainty principle."

(This is a literal quote I picked from a random pick of google's result
for laplace's demon and heisenberg. I meant to say the same, but wouldn't
have arrived at that elaborate a wording, myself.)

 

[Joshua Cranmer]

"I thought Laplace's daemon was impaled with aspen stake by Heisenberg's
uncertainty principle."

Heisenberg's uncertainty principle only states that we don't know the
(P)RNG of the world.

 

[Martin Gregorie]

"I thought Laplace's daemon was impaled with aspen stake by Heisenberg's
uncertainty principle."

(This is a literal quote I picked from a random pick of google's result
for laplace's demon and heisenberg. I meant to say the same, but
wouldn't have arrived at that elaborate a wording, myself.)

I like it a lot but a google search doesn't find an attribution. Have you
any idea who said it? Feynman?

 

[Stefan Ram]

Heisenberg's uncertainty principle only states that we don't know the
(P)RNG of the world.

Only since as recent as 2010 we have

»evidence that quantum randomness is indeed
incomputable. That means that it could not
have been be generated by a computer.«

http://www.technologyreview.com/blog/arxiv/25041/

»Ref: arxiv.org/abs/1004.1521:

Experimental Evidence of Quantum Randomness
Incomputability«

http://arxiv.org/abs/1004.1521

 

[Lawrence D'Oliveiro]

Heisenberg's uncertainty principle only states that we don't know the
(P)RNG of the world.

Bell’s inequality states otherwise.

 

[Dirk Bruere at NeoPax]

Only since as recent as 2010 we have

»evidence that quantum randomness is indeed
incomputable. That means that it could not
have been be generated by a computer.«

http://www.technologyreview.com/blog/arxiv/25041/

»Ref: arxiv.org/abs/1004.1521:

Experimental Evidence of Quantum Randomness
Incomputability«

http://arxiv.org/abs/1004.1521

Also google hypercomputing eg
http://en.wikipedia.org/wiki/Hypercomputation

 

[Dirk Bruere at NeoPax]

Only since as recent as 2010 we have

»evidence that quantum randomness is indeed
incomputable. That means that it could not
have been be generated by a computer.«

http://www.technologyreview.com/blog/arxiv/25041/

»Ref: arxiv.org/abs/1004.1521:

Experimental Evidence of Quantum Randomness
Incomputability«

http://arxiv.org/abs/1004.1521

I do not see that the paper demonstrates that the process underlying QM
randomness is not algorithmic.

However, I do not believe it is algorithmic.
QM randomness seems to be a result of asking questions for which there
is no physical answer. The return is zero information ie a random string
that cannot be algorithmically compressed.

 

[Dirk Bruere at NeoPax]

Just to be clear, in the time of writing of that book Fermat's last
theorem wasn't yet proven nor Penrose provides the proof. That was done
later of course.
http://en.wikipedia.org/wiki/Wiles'_proof_of_Fermat's_Last_Theorem

In his book, Penrose argues that such problems cannot be solved
algorithmically.

Given that computer programs have produced mathematical proofs that have
eluded Humans it clearly does not apply to all of mathematics.
[I am not talking about computer aided proofs]

 

[Andreas Leitgeb]

I like it a lot but a google search doesn't find an attribution. Have you
any idea who said it? Feynman?

No It was some nicknamed user in a forum. I didn't intend to take
him as an authority, just borrowed his wording (impaled with aspen stake)
for what I had intended to say. With simpler wording (just "killed")
I vaguely remember it from the old school days, but still without any
source other than the physics teacher.

 

[Martin Gregorie]

No It was some nicknamed user in a forum. I didn't intend to take
him as an authority, just borrowed his wording (impaled with aspen
stake) for what I had intended to say. With simpler wording (just
"killed") I vaguely remember it from the old school days, but still
without any source other than the physics teacher.

Thanks for the clarification. I suspected that might be the case but its
just such a nice turn of phrase.

 

[javax.swing.JSnarker]

I do not see that the paper demonstrates that the process underlying QM
randomness is not algorithmic.

However, I do not believe it is algorithmic.
QM randomness seems to be a result of asking questions for which there
is no physical answer.

Actually, QM randomness is a symptom of indexical uncertainty about
which exact universe you're in out of many that look identical up to a
certain point in time and then diverge, more or less.

In fact, copies of you end up experiencing each possible universe that
has you in it, so the uncertainty is really about which *you* you are
out of many that have had thus-far-identical experiences.

Which means the randomness is actually in data from a source external to
any computer inside the universe. But if you simulated the whole
multiverse, by just running Schrödinger's wavefunction for the initial
state forward without collapse, in that simulation would be implicit
emulations of the smaller computer, each receiving a different random
bit-string -- and all embedded in a deterministic whole.

 

[Dirk Bruere at NeoPax]

Actually, QM randomness is a symptom of indexical uncertainty about
which exact universe you're in out of many that look identical up to a
certain point in time and then diverge, more or less.

In fact, copies of you end up experiencing each possible universe that
has you in it, so the uncertainty is really about which *you* you are
out of many that have had thus-far-identical experiences.

Which means the randomness is actually in data from a source external to
any computer inside the universe. But if you simulated the whole
multiverse, by just running Schrödinger's wavefunction for the initial
state forward without collapse, in that simulation would be implicit
emulations of the smaller computer, each receiving a different random
bit-string -- and all embedded in a deterministic whole.

That's what I said (in a different way)!
But I agree with you that it is a plausible mechanism in the MWI context

 

[javax.swing.JSnarker]

That's what I said (in a different way)!
But I agree with you that it is a plausible mechanism in the MWI context

Well, in principle there is a "physical answer" in this case, but in
practice you can't actually get at it.

 

[Lew]

That's what I said (in a different way)!
But I agree with you that it is a plausible mechanism in the MWI context

A full model of how the state space collapses must account for Mind, mind and
consciousness, and must somehow seek to formalize whimsy.

Nothing is determined but that nothing is determined.