Hi Eugin,

> I see, we're at the "prove that the Moon is not made from green cheese
> when
> nobody is looking" stage.
> 
> I thought this list wasn't about ghosties'n'goblins.
> Allright, I seem to have been mistaken about that.

You seem to be getting a little hot under the collar!

Here is a justification of why I think arithmetical realism is at least
very plausible...

Let's suppose that a computer simulation can (in principle) exhibit
awareness.  I don't know whether you dispute this hypothesis, but let's
assume it and see where it leads.

Let's suppose in fact that you Eugin,  were able to watch a computer
simulation run, and on the screen you could see "people" laughing,
talking - perhaps even discussing ideas like whether *their* physical
existence needs to be postulated, or else they are merely part of a
platonic multiverse.  A simulated person may stamp his fist on a
simulated coffee table and say "Surely this coffee table is real - how
could it possibly be numbers - I've never heard of anything so
ludicrous!".

Now Eugin, you may argue that the existence of this universe depends on
the fact that it was simulated by a computer in our universe.  I find
this a little hard to fathom - because computer simulations are
deterministic and they give the same results whether they are run once
or a thousand times.  I find it hard to imagine that they "leap into
existence" when they are run the first time.   I'm particularly
motivated by the universal dove-tailing program - which eventually
generates the trace of all possible programs.

Do you say that most of the integers don't exist because nobody has
written them down?

I can see your point when you say that 2+2=4 is meaningless without the
"physical objects" to which it relates.  However this is irrelevant
because you are thinking of too simplistic a mathematical system!  The
only mathematical systems that are relevant to the everything-list are
those that have conscious inhabitants within them.  Within this "self
contained" mathematical world we *do* have the context for numbers.
It's a bit like the chicken and egg problem.  (egg = number theory,
chicken = objects and observers).   Both come together and can't be
pulled apart.

- David



> -----Original Message-----
> From: Eugen Leitl [mailto:[EMAIL PROTECTED]
> Sent: Wednesday, 14 January 2004 1:32 AM
> To: [EMAIL PROTECTED]
> Subject: Re: Is the universe computable?
> 
> On Tue, Jan 13, 2004 at 03:03:38PM +0100, Bruno Marchal wrote:
> >
> > What is the point? Do we have experimental procedure to validate
> > the opposite of the fanciful scenario? Giving that we were talking
about
> 
> I see, we're at the "prove that the Moon is not made from green cheese
> when
> nobody is looking" stage.
> 
> I thought this list wasn't about ghosties'n'goblins.
> Allright, I seem to have been mistaken about that.
> 
> > first person scenario, in any case it is senseless to ask for
> > experimental procedure. (experience = first person view; experiment
=
> > third person view).
> 
> So the multiverse is not a falsifyable theory?
> 
> > Don't tell me you were believing I was arguing.
> 
> You were asserting a lot of stuff. That's commonly considered arguing,
> except
> you weren't providing any evidence so far. So, maybe you weren't.
> 
> > About logic, it is a branch of mathematics. Like topology, algebra,
> analysis
> > it can be *applied* to some problem, which, through some hypothesis,
> > can bear on some problem. With the comp hyp mathematical logic makes
> > it possible to derive what consistent and platonist machine can
prove
> about
> > themselves and their consistent extension.
> 
> Except that machine doesn't exist in absence of implementations, be it
> people, machines, or aliens.
> 
> > >My point is that formal systems are a very powerful tool with very
> small
> > >reach,
> > >unfortunately.
> >
> > But I never use formal system. I "modelise" a particular sort of
machine
> by
> > formal system, so I prove things *about* machines, by using works
> > *about* formal system. I don't use formal systems. I prove things in
> > informal
> > ways like all mathematicians.
> 
> Above passage is 100% content-free.
> 
> > >Because we know that QM is not a TOE. You haven't heard?
> >
> > How could be *know* QM is not a TOE?  (I ask this independently of
> > the fact that I find plausible QM is not a *primitive* TOE).
> 
> Because general relativity and quantum theory are mutually
incompatible.
> So
> both TOE aren't. We have several TOE candidates, and an increased
number
> of
> blips heralding new physics, but no heir apparent yet.
> 
> > You believe that the theorem "there is an infinity of primes" is a
human
> > invention?  (as opposed to "a human discovery").
> 
> Of course. Not necessarily human; there might be other production
systems
> which invented them. Then, maybe there aren't.
> 
> Infinity is something unphysical, btw. You can't represent arbitrary
> values
> within a finite physical system -- all infoprocessing systems are
that.
> You'll also notice that imperfect theories are riddled with
infinities;
> they
> tend to go away with the next design iteration. So infinities is
something
> even more primatish than enumerable natural numbers.
> 
> > >I do not see how arithmetic realism (a special case of Platonic
> realism, is
> > >that correct?) is an axiom. I agree with the rest of
> > >your list.
> >
> > Perhaps I have been unclear. By Arithmetic Realism I mean that
> Arithmetical
> > Truth is independent of me, you, and the rest of humanity. There
exist
> 
> Oh, I disagree with that allright. Nonliving systems don't have an
> evolutionary pressure to develop enumerable quantities representation.
> 
> > weaker form of that axiom and stronger form. Tegmark for instance
> > defends a much larger mathematical realism (so large that I am not
sure
> > what it could mean). As I said some ultrafinitist defends strictly
> > weaker form of mathematical realism.
> > The more quoted argument in favour of arithmetical realism is the
one
> based
> > on Godel's theorem, and presented by him too) which is that any
formal
> > systems (and so any ideally consistent machines) can prove, even in
> > principle,
> > that is with infinite time and space, all the true proposition of
> > arithmetic.
> 
> Sure. Notice that infinite time and space is unphysical, and of course
a
> machine which doesn't exist doesn't produce anything.
> 
> I was hoping for a falsifyable argument, showing that this spacetime
is an
> operation artifact of some finite production system.
> 
> > But look also to the site of Watkins
> > http://www.maths.ex.ac.uk/~mwatkins/zeta/index.htm
> 
> Oh, basically you're arguing that the unreasonable applicability of
> mathematics in physics is anything but unreasonable, and that a TOE
arisen
> from a formal system is in fact the universe itself?
> 
> > for a lot of evidence for it (evidence which are a priori not
related to
> > my more theoretical computer science approach).
> > Now my goal (here) is not really to defend AR as true, but as
> sufficiently
> > plausible
> > that it is interesting to look at the consequences. You can read
some
> 
> I do not deny that a TOE can be immensely useful (but not necessarily
so,
> higher levels of theory tend to require increasing amounts of crunch
to
> predict anything useful), but that TOE has anything to do with the
> metalayer,
> or that in fact that distinction is meaningful.
> 
> You don't seem to disagree, so we're not actually arguing.
> 
> > main post I send to this list where I present the argument according
to
> > which if we take comp seriously (comp = AR + TC + "yes doctor") then
> > physics is eventually a branch of machine's psychology (itself a
branch
> > of computer science" itself a branch of number theory.
> 
> Ah, some severe leap of faith required here.
> 
> > If you find an error, or an imprecision, please show them.
> 
> I'm experiencing a severe cognitive dissonance, trying to understand
why
> you
> think formal systems do exist in absence of their production systems.
> 
> > Or, if there is a point you don't understand, it will be a pleasure
for
> me
> > to provide more explanations.
> > Also, I thought you were postulating an universe, aren't you? (I
just
> try
> 
> Sure, we're having a conversation (albeit a bit surreal one), so we
seem
> to exist.
> 
> > to figure out your philosophical basic hypothesis).
> >
> > Regards,
> >
> > Bruno
> >
> -- Eugen* Leitl <a href="http://leitl.org";>leitl</a>
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