Re: An analogy for Qualia

2012-01-10 Thread John Clark
On Tue, Jan 10, 2012 at 8:54 AM, Craig Weinberg wrote:

> There is more to understanding than logic.
>

If you know the logic behind something then you understand it and if you
understand it you know the logic behind it.

>It says very clearly that the changes are not random - ie, they are
> intentionally edited.
>

It's not even very clear that these changes exist, it's all very tentative,
and as far as your theories go it does not matter if its random or not
because one thing is certain, if the changes are real one of two things is
true, the changes happened for a reason or the changes did not happen for a
reason.

> That's not about analog vs digital,
>

You said it's not digital, I insist it must be.

>it is about crushing the delusion of the machine metaphor in biology.
>

Just like everything else a biological effect has a cause or it does not
have a cause, it's deterministic or it's random, it's a cuckoo clock or a
roulette wheel.

> But I'm not my father or grandfather or great grandfather
>

That's right you are not them and yet you have some of the same genes that
they had, (yeah I know what's coming, genes don't exist either) so the
genes had to make copies of themselves to go into the next generation. If
the copying process had been analog there would be so many errors in your
genes that you'd be dead because the errors are cumulative, but the copying
was digital so you are fine. This Email had to go through a long chain of
copying and retransmitting before you got it but it was all digital so you
can read it, if it had been analog it would be nothing but a big blur.


> Not true. Music companies had a problem with cassettes too.
> http://en.wikipedia.org/wiki/Home_Taping_Is_Killing_Music. Recording
> devices have always been forbidden at popular movies and concerts.
>

You only went down one generation in those examples, from a master tape to
copies, good analog can handle a few generations but not dozens, and with
biology you have many millions of generations so it can't be analog.

> There is nothing particularly digital about the folding problem. It is an
> analog process
>

Bullshit! Every protein ever made starts out in life as a linear sequence
of amino acids like beads on a string, and that linear sequence was
determined by a linear sequence of bases in RNA, and that linear sequence
was determined by the linear sequences of bases in DNA. Its only after the
protein leaves the ribosome does this linear sequence fold up into the
enormously complex shapes of the functional protein. At the temperatures
and pH conditions found in cells any linear protein string with the same
sequence of amino acids ALWAYS folds up into exactly precisely the same
shape. Different sequence different shape, same sequence same shape.

> which occurs through concrete chemical interaction
>

Certainly, but the same linear sequence of amino acids gives you the exact
same super complex shape that those hyper complex concrete chemical
interactions twist those straight linear strings into. And it's true we are
not very good at calculating from first principles what shape any given
sequence of linear amino acids will twist into because it's so
astronomically complex, but we are getting better and we do know for a fact
that the same sequence always gives the same shape.

And its not like any of this is cutting edge news, its been known since
1953; but I guess it takes time for that sort of scientific information to
trickle down so that even philosophers know about it. Oops sorry I forgot,
information does not exist.

>>  There is not a person on this planet who knows what will happen if
>> you program a computer to find the first even number greater than 2 that
>> is not the sum of two prime numbers and then stop.
>>
>
> >That can only mean that you are admitting that the brain is not a
> computer.
>

How on earth do you figure that? A brain can't know what a computer or
other brain will do or even what he himself will do until he does it; and a
computer can't know what another computer or a brain will do or what it
itself will do until it does it.

> It means MWI is born of desperation to preserve the machine metaphor
> of the universe.
>

All interpretations of the way things behave when they become very very
small are desperate because in that realm things  just act weird, your
interpretation is more desperate than most, you just say "nothing is real";
I think you should add "including this theory".


>>  Quantum mechanics predicts it [the magnetic moment of the electron]
>> will Be 1.00115965246 and that agrees well with the experimental value of
>> 1.00115965221. What does your theory predict the value will be?
>>
>
> > My theory predicts that electrons seem one way to electronic
> instruments, another way to human brains, and another way to human minds
> interpreting the exterior behavior of electronic instruments.
>

The difference between a scientific theory of physics and flatulent
philosophical gas is not that 

Re: An analogy for Qualia

2012-01-10 Thread Bruno Marchal


On 10 Jan 2012, at 18:48, meekerdb wrote:


On 1/10/2012 7:48 AM, Bruno Marchal wrote:
In a way, that strong form of CT might already be false with comp,  
only in the 1p sense as you get a free random oracle as well as  
always staying consistent(and 'alive'), but it's not false in the  
3p view...


Yes. Comp makes physics a first person plural reality, and a priori  
we might be able to exploit the first plural indeterminacy to  
compute more function, like we know already that we have more  
"processes", like that free random oracle. The empirical fact that  
quantum computer does not violate CT can make us doubt about this.


I don't think that is so clear.  Nielsen has written some papers on  
computations in QM that are not Turing emulable, essentially relying  
on the fact that QM uses real numbers.  He suggests that QM should  
be restricted to avoid this kind of hypercomputation by dropping the  
assumption that all unitary operators are allowed.


Yes. e^i * OMEGA *t is a solution of the SWE. With OMEGA = Chaitin's  
incompressible real number. But are the real numbers "physically  
real"? Open problem in comp, and in our "observable universe". Nielsen  
is aware that, would we met such a quantum wave, we would be unable to  
recognize it or to distinguish it from quantum noise. Which follows  
from comp indeed.


More interestingly e^i * POST *t, with POST = Post "creative number",  
which decimal codes the stopping problem, would be a quantum universal  
dovetailer.  Here the wave will have the computations redundancy  
needed to give sense to the measure problem. With the incompressible  
OMEGA you get a shallow description of all there is by doing a highly  
non constructive reduction of the measure. OMEGA evacuates the  
redundancy of POST. POST is deep (in Bennett sense).


But I am not sure that the decimals in the wave plays any relevant  
computational role. Unless some very low level number conspiracy?


The UD is dumb enough to dovetail all program executions with their  
"products" with *all* approximations of all real numbers, so, so some  
exploitation of the continuum is what to be expected for the most  
stable realities configuration, and it is hard to avoid, logically,  
that some infinite non computable constant might play a role, but why  
would we postulate something like that?


Bruno

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



--
You received this message because you are subscribed to the Google Groups 
"Everything List" group.
To post to this group, send email to everything-list@googlegroups.com.
To unsubscribe from this group, send email to 
everything-list+unsubscr...@googlegroups.com.
For more options, visit this group at 
http://groups.google.com/group/everything-list?hl=en.



Re: An analogy for Qualia

2012-01-10 Thread Stephen P. King

On 1/10/2012 12:48 PM, meekerdb wrote:

On 1/10/2012 7:48 AM, Bruno Marchal wrote:
In a way, that strong form of CT might already be false with comp, 
only in the 1p sense as you get a free random oracle as well as 
always staying consistent(and 'alive'), but it's not false in the 3p 
view...


Yes. Comp makes physics a first person plural reality, and a priori 
we might be able to exploit the first plural indeterminacy to compute 
more function, like we know already that we have more "processes", 
like that free random oracle. The empirical fact that quantum 
computer does not violate CT can make us doubt about this. 


I don't think that is so clear.  Nielsen has written some papers on 
computations in QM that are not Turing emulable, essentially relying 
on the fact that QM uses real numbers.  He suggests that QM should be 
restricted to avoid this kind of hypercomputation by dropping the 
assumption that all unitary operators are allowed.


Brent


Hi Brent,

Could we achieve the same thing by restricting the vector (Hilbert) 
space of linear functionals to a finite (but very large) field? Another 
possibility is that there is a local preference of basis for a given set 
of homomorphisms between the Hilbert spaces of a given pair of 
interacting quantum systems. Here is a nice video lecture on the math of 
this: http://www.youtube.com/watch?v=zkU1UdS4Dps&feature=related


Onward!

Stephen

--
You received this message because you are subscribed to the Google Groups 
"Everything List" group.
To post to this group, send email to everything-list@googlegroups.com.
To unsubscribe from this group, send email to 
everything-list+unsubscr...@googlegroups.com.
For more options, visit this group at 
http://groups.google.com/group/everything-list?hl=en.



Re: An analogy for Qualia

2012-01-10 Thread meekerdb

On 1/10/2012 7:48 AM, Bruno Marchal wrote:
In a way, that strong form of CT might already be false with comp, only in the 1p sense 
as you get a free random oracle as well as always staying consistent(and 'alive'), but 
it's not false in the 3p view...


Yes. Comp makes physics a first person plural reality, and a priori we might be able to 
exploit the first plural indeterminacy to compute more function, like we know already 
that we have more "processes", like that free random oracle. The empirical fact that 
quantum computer does not violate CT can make us doubt about this. 


I don't think that is so clear.  Nielsen has written some papers on computations in QM 
that are not Turing emulable, essentially relying on the fact that QM uses real numbers.  
He suggests that QM should be restricted to avoid this kind of hypercomputation by 
dropping the assumption that all unitary operators are allowed.


Brent

--
You received this message because you are subscribed to the Google Groups 
"Everything List" group.
To post to this group, send email to everything-list@googlegroups.com.
To unsubscribe from this group, send email to 
everything-list+unsubscr...@googlegroups.com.
For more options, visit this group at 
http://groups.google.com/group/everything-list?hl=en.



Re: An analogy for Qualia

2012-01-10 Thread Bruno Marchal


On 10 Jan 2012, at 12:58, acw wrote:


On 1/10/2012 12:03, Bruno Marchal wrote:


On 09 Jan 2012, at 19:36, acw wrote:




To put it more simply: if Church Turing Thesis(CTT) is correct,
mathematics is the same for any system or being you can imagine.


I am not sure why. "Sigma_1 arithmetic" would be the same; but higher
mathematics (set theory, analysis) might still be different.




If it's wrong, maybe stuff like concrete infinities,  
hypercomputation

and infinite minds could exist and that would falsify COMP, however
there is zero evidence for any of that being possible.


Not sure, if CT is wrong, there would be finite machines, working in
finite time, with well defined instructions, which would be NOT  
Turing
emulable. Hypercomputation and infinite (human) minds would  
contradict
comp, not CT. On the contrary, they need CT to claim that they  
compute
more than any programmable machines. CT is part of comp, but comp  
is not

part of CT.
Beyond this, I agree with your reply to Craig.



In that response I was using CT in the more unrestricted form: all  
effectively computable functions are Turing-computable.


I understand, but that is confusing. David Deutsch and many physicists  
are a bit responsible of that confusion, by attempting to have a  
notion of "effectivity" relying on physics.  The original statement of  
Church, Turing, Markov, Post, ... concerns only the intuitively human  
computable functions, or the functions computable by finitary means.  
It asserts that the class of such intuitively computable functions is  
the same as the class of functions computable by some Turing machine  
(or by the unique universal Turing machine). Such a notion is a priori  
completely independent of the notion of computable by physical means.







It might be a bit stronger than the usual equivalency proofs between  
a very wide range of models of computation (Turing machines, Abacus/ 
PA machines, (primitive) recursive functions (+minimization), all  
kinds of more "current" models of computation, languages and so on).


Yes. I even suspect that CT makes the class of functions computable by  
physics greater than the class of Church.




If hypercomputation was actually possible that would mean that  
strong variant of CT would be false, because there would be  
something effectively computable that wasn't computable by a Turing  
machine.


OK.



In a way, that strong form of CT might already be false with comp,  
only in the 1p sense as you get a free random oracle as well as  
always staying consistent(and 'alive'), but it's not false in the 3p  
view...


Yes. Comp makes physics a first person plural reality, and a priori we  
might be able to exploit the first plural indeterminacy to compute  
more function, like we know already that we have more "processes",  
like that free random oracle. The empirical fact that quantum computer  
does not violate CT can make us doubt about this.




Also, I do wonder if the same universality that is present in the  
current CT would be present in hypercomputation (if one were to  
assume it would be possible)


Yes, at least for many type of hypercomputation, notably of the form  
of computability with some oracle.




- would it even retain CT's current "immunity" from diagonalization?


Yes. Actually the immunity of the class of computable functions  
entails the immunity of the class of computable functions with oracle.  
So the consistency of CT entails the consistency of some super-CT for  
larger class. But I doubt that there is a super-CT for the class of  
functions computable by physical means. I am a bit agnostic on that.






As for the mathematical truth part, I mostly meant that from the  
perspective of a computable machine talking about axiomatic systems  
- as it is computable, the same machine (theorem prover) would  
always yield the same results in all possible worlds(or shared  
dreams).


I see here why you have some problem with AUDA (and logic). CT = the  
notion of computability is absolute. But provability is not absolute  
at all. Even with CT, different machine talking or using different  
axiomatic system will obtain different theorems.
In fact this is even an easy (one diagonalization) consequence of CT,  
although Gödel's original proof does not use CT. provability, nor  
definability is not immune for diagonalization. Different machines  
proves different theorems.




Although with my incomplete understanding of the AUDA, and I may be  
wrong about this, it appeared to me that it might be possible for a  
machine to get more and more of the truth given the consistency  
constraint.


That's right both PA + con(PA) and PA + ~con(PA) proves more true  
arithmetical theorems than PA.
And PA + con(PA + con(PA + con (PA + con PA)) will proves even more  
theorems. The same with the negation of those consistency.
Note that the theory PA* = PA* + con(PA*), which can be defined  
finitely by the use of the Kleene recursion fi

Re: An analogy for Qualia

2012-01-10 Thread Craig Weinberg
On Jan 10, 12:40 am, John Clark  wrote:
> Craig Weinberg  wrote:
> >No free will = no hunger. No need for it. No mechanism for it. No logic to
> > it.
>
> Cannot comment, don't know what ASCII sequence "free will" means.

The old 'stick your fingers in your ears and say lalalalalala' trick.
Impressive, but deciding to do such a thing would require FREE WILL.

>
> > That was my point. Knowing how to eat does not require logic or induction.
>
> But your question was "Is it induction that provides our understanding of
> how to swallow?", you asked about understanding; for prediction induction
> alone is enough but for understanding you need logic, and for some things
> neither is required. A rock can stay on the ground even though it's not
> very good at induction and nobody has a deep understanding of gravity yet.

There is more to understanding than logic. You need a subject who is
motivated to make sense out of something. They can employ logic,
intuition, induction, insight, memory, etc. Lots of modes of sense
making.

>
> >>  The genetic code in DNA could not be more digital, and it was good
> >> enough to build your brain and every other part of you out of simple
> >> amino acid molecules; if you look at the details of the assembly process
> >> biology uses to make complex things, like your brain, you find its
> >> amazingly computer-like.
>
> > That may not be true even for DNA:
> >http://www.nature.com/news/2011/110525/full/473432a.html
> >http://www.sciencemag.org/content/333/6038/53
>
> DNA translates its information into RNA

It's true that the RNA bases are informed by the DNA bases (just
because RNA is motivated to mirror each base of the DNA) , just as a
baseball game is informed by the score in each inning, but there is no
actual 'information'.

> and RNA tells the ribosomes what
> linear sequence of amino acid molecules to make, after the ribosomes are
> finished the linear sequence folds up into very complex shapes forming
> proteins, and that makes you including your brain. This controversial
> experiment (as I said no experiment is finished until it is repeated) says
> that there is a unknown mechanism that sometimes makes minor changes in the
> DNA to RNA part of that chain. In no place in that paper is it suggested
> that the unknown mechanism (assuming it even exists) is analog and for a
> very good reason, indeed it is very clear that there is no way it could be
> analog.

It says very clearly that the changes are not random - ie, they are
intentionally edited. That's not about analog vs digital, it is about
crushing the delusion of the machine metaphor in biology.

>
> Think of your father and grandfather and great grandfather and all the
> millions of individuals in the past that led up to you; every one of those
> individuals got old and died but their genetic legacy remains as vital as
> is was the day they were born thousand or millions of years ago, and there
> is absolutely no way that could happen if the information was encoded in a
> analog manner.

But I'm not my father or grandfather or great grandfather, nor am I a
combination of my mother and father. The digital aspects are
complemented - always - by analog processes.

> Do you
> remember the old analog cassette tapes, if you made a copy of a copy of a
> copy of a copy of a music tape pretty soon the resulting tape had so many
> errors in it that it could no longer be called music and was unlistenable;
> that was because with analog copying the errors are cumulative, but that is
> not the case with digital copying.

It doesn't matter though because eventually the music has to be output
to an analog audio device to make sense to your analog inner ear. You
are just talking about encoding and recording, not the qualities that
the production of musicality (or life, or consciousness) entails.


>If the internet was based on analog
> technology the big music companies would have had no problem with bootleg
> copies of their product, but it uses
> digital methods so they had a very big problem indeed.

Not true. Music companies had a problem with cassettes too.
http://en.wikipedia.org/wiki/Home_Taping_Is_Killing_Music. Recording
devices have always been forbidden at popular movies and concerts.

>
> > The primary sequence of DNA is just part of the story though. Secondary
> > and tertiary epigenetic factors are can determine which genes are used
> > and which are not, and they are not digital.
>
> Of course they're digital!! Cytosine and guanine are 2 of the 4 bases in
> DNA and it is the variation in the sequence of these 4 bases that carry the
> genetic code. The epigenetic factors you're talking about happens because
> sometimes at the point where cytosine and guanine meet a molecule called a
> "methyl group" is sometimes attached. A methyl group is a very small
> molecule consisting of just one carbon atom connected to three hydrogen
> atoms, and the existence of a methyl group changes the way the sequence of
> bases in DNA is 

Re: An analogy for Qualia

2012-01-10 Thread acw

On 1/10/2012 12:03, Bruno Marchal wrote:


On 09 Jan 2012, at 19:36, acw wrote:


On 1/9/2012 19:54, Craig Weinberg wrote:

On Jan 9, 12:00 pm, Bruno Marchal wrote:

On 09 Jan 2012, at 14:50, Craig Weinberg wrote:


On Jan 9, 6:06 am, Bruno Marchal wrote:



I agree with your general reply to Craig, but I disagree that
computations are physical. That's the revisionist conception of
computation, defended by Deustch, Landauer, etc. Computations have
been discovered by mathematicians when trying to expalin some
foundational difficulties in pure mathematics.



Mathematicians aren't physical? Computations are discovered through a
living nervous system, one that has been highly developed and
conditioned specifically for that purpose.


Computation and mechanism have been discovered by many people since
humans are there. It is related to the understanding of the difference
between "finite" and "infinite". The modern notion has been discovered
independently by many mathematicians, notably Emil Post, Alan Turing,
Alonzo Church, Andrzei Markov, etc.
With the comp. hyp., this is easily explainable, given that we are
somehow "made of" (in some not completely Aristotelian sense to be
sure) computations.



They are making those discoveries by using their physical brain
though.


Sure, but that requires one to better understand what a physical brain
is. In the case of COMP(given some basic assumptions), matter is
explained as appearing from simpler abstract mathematical relations,
in which case, a brain would be an inevitable consequence of such
relations.





We can implement
computation in the physical worlds, but that means only that the
physical reality is (at least) Turing universal. Theoretical computer
science is a branch of pure mathematics, even completely embeddable
in
arithmetical truth.



And pure mathematics is a branch of anthropology.


I thought you already agreed that the arithmetical truth are
independent of the existence of humans, from old posts you write.

Explain me, please, how the truth or falsity of the Riemann
hypothesis, or of Goldbach conjecture depend(s) on anthropology.
Please, explain me how the convergence or divergence of phi_(j)
depends on the existence of humans (with phi_i = the ith computable
function in an enumeration based on some universal system).


The whole idea of truth or falsity in the first place depends on
humans capacities to interpret experiences in those terms. We can read
this quality of truth or falsity into many aspects of our direct and
indirect experience, but that doesn't mean that the quality itself is
external to us. If you look at a starfish, you can see it has five
arms, but the starfish doesn't necessarily know it had five arms.



Yet that the fact the starfish has 5 arms is a fact, regardless of the
starfish's awareness of it. It will have many consequences with
regards of how the starfish interacts with the rest of the world or
how any other system perceives it.

If you see something colored red, you will know that you saw red and
that is 'true', and that it will be false that you didn't see 'red',
assuming you recognize 'red' the same as everyone else and that your
nervous system isn't wired too strangely or if your sensory systems
aren't defective or function differently than average.

Consequences of mathematical truths will be everywhere, regardless if
you understand them or not. A circle's length will depend on its
radius regardless if you understand the relation or not.

Any system, be they human, computer or alien, regardless of the laws
of physics in play should also be able to compute (Church-Turing
Thesis shows that computation comes very cheap and all it takes is
ability of some simple abstract finite rules being followed and always
yielding the same result, although specific proofs for showing
Turing-universality would depend on each system - some may be too
simple to have such a property, but then, it's questionable if they
would be powerful enough to support intelligence or even more trivial
behavior such as life/replicators or evolution), and if they can, they
will always get the same results if they asked the same computational
or mathematical question (in this case, mathematical truths, or even
yet unknown truths such as Riemann hypothesis, Goldbach conjecture,
and so on). Most physics should support computation, and I conjecture
that any physics that isn't strong enough to at least support
computation isn't strong enough to support intelligence or
consciousness (and computation comes very cheap!). Support computation
and you get any mathematical truth that humans can reach/talk about.
Don't support it, and you probably won't have any intelligence in it.

To put it more simply: if Church Turing Thesis(CTT) is correct,
mathematics is the same for any system or being you can imagine.


I am not sure why. "Sigma_1 arithmetic" would be the same; but higher
mathematics (set theory, analysis) might still be different.





If it's wrong, may

Re: An analogy for Qualia

2012-01-10 Thread Bruno Marchal


On 09 Jan 2012, at 19:36, acw wrote:


On 1/9/2012 19:54, Craig Weinberg wrote:

On Jan 9, 12:00 pm, Bruno Marchal  wrote:

On 09 Jan 2012, at 14:50, Craig Weinberg wrote:


On Jan 9, 6:06 am, Bruno Marchal  wrote:



I agree with your general reply to Craig, but I disagree that
computations are physical. That's the revisionist conception of
computation, defended by Deustch, Landauer, etc. Computations have
been discovered by mathematicians when trying to expalin some
foundational difficulties in pure mathematics.


Mathematicians aren't physical? Computations are discovered  
through a

living nervous system, one that has been highly developed and
conditioned specifically for that purpose.


Computation and mechanism have been discovered by many people since
humans are there. It is related to the understanding of the  
difference
between "finite" and "infinite". The modern notion has been  
discovered
independently by many mathematicians, notably Emil Post, Alan  
Turing,

Alonzo Church, Andrzei Markov, etc.
With the comp. hyp., this is easily explainable, given that we are
somehow "made of" (in some not completely Aristotelian sense to be
sure) computations.



They are making those discoveries by using their physical brain
though.

Sure, but that requires one to better understand what a physical  
brain is. In the case of COMP(given some basic assumptions), matter  
is explained as appearing from simpler abstract mathematical  
relations, in which case, a brain would be an inevitable consequence  
of such relations.






We can implement
computation in the physical worlds, but that means only that the
physical reality is (at least) Turing universal. Theoretical  
computer
science is a branch of pure mathematics, even completely  
embeddable

in
arithmetical truth.



And pure mathematics is a branch of anthropology.


I thought you already agreed that the arithmetical truth are
independent of the existence of humans, from old posts you write.

Explain me, please, how the truth or falsity of the Riemann
hypothesis, or of Goldbach conjecture depend(s) on anthropology.
Please, explain me how the convergence or divergence of phi_(j)
depends on the existence of humans (with phi_i = the ith computable
function in an enumeration based on some universal system).


The whole idea of truth or falsity in the first place depends on
humans capacities to interpret experiences in those terms. We can  
read

this quality of truth or falsity into many aspects of our direct and
indirect experience, but that doesn't mean that the quality itself is
external to us. If you look at a starfish, you can see it has five
arms, but the starfish doesn't necessarily know it had five arms.



Yet that the fact the starfish has 5 arms is a fact, regardless of  
the starfish's awareness of it. It will have many consequences with  
regards of how the starfish interacts with the rest of the world or  
how any other system perceives it.


If you see something colored red, you will know that you saw red and  
that is 'true', and that it will be false that you didn't see 'red',  
assuming you recognize 'red' the same as everyone else and that your  
nervous system isn't wired too strangely or if your sensory systems  
aren't defective or function differently than average.


Consequences of mathematical truths will be everywhere, regardless  
if you understand them or not. A circle's length will depend on its  
radius regardless if you understand the relation or not.


Any system, be they human, computer or alien, regardless of the laws  
of physics in play should also be able to compute (Church-Turing  
Thesis shows that computation comes very cheap and all it takes is  
ability of some simple abstract finite rules being followed and  
always yielding the same result, although specific proofs for  
showing Turing-universality would depend on each system - some may  
be too simple to have such a property, but then, it's questionable  
if they would be powerful enough to support intelligence or even  
more trivial behavior such as life/replicators or evolution), and if  
they can, they will always get the same results if they asked the  
same computational or mathematical question (in this case,  
mathematical truths, or even yet unknown truths such as Riemann  
hypothesis, Goldbach conjecture, and so on). Most physics should  
support computation, and I conjecture that any physics that isn't  
strong enough to at least support computation isn't strong enough to  
support intelligence or consciousness (and computation comes very  
cheap!). Support computation and you get any mathematical truth that  
humans can reach/talk about. Don't support it, and you probably  
won't have any intelligence in it.


To put it more simply: if Church Turing Thesis(CTT) is correct,  
mathematics is the same for any system or being you can imagine.


I am not sure why. "Sigma_1 arithmetic" would be the same; but higher  
mathematics (set theory, analysis) mi