On Wed, Jan 14, 2004 at 10:38:51AM +0800, David Barrett-Lennard wrote:

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

Nope, just a bit polemic. I was getting tired of glib assertions, and needed
to poke a stick, to find out what's underneath.
 
> Here is a justification of why I think arithmetical realism is at least
> very plausible...

I'm all ears.
 
> 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.

With you so far. We already have simulated critters with behaviour, and
awareness of their environment. Computational neuroscience even attempts to
do it with a high degree of biological realism.
 
> 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

That wouldn't be abstract "numbers". You'd have a system with a state, evolving
along a trajectory. In your case, that system state is being rendered (in
realtime, I presume) for external observers.

You'd be a bit pressed to enumerate all possible system trajectories, though.
You'd run out of time and space even for very, very small assemblies.

> 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

Exactly. No implementation, no state, no trajectory. Information doesn't
exist without systems encoding it. (This applies to this universe being the
metalayer for a simulated system; I don't make any assumptions about our own
metalayer, which is pretty meaningless, since unknowable unless).

> 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

Absolutely. Provided, they're run. (In practice, you'll see system running
floats are not as deterministic as you think). 

> 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.

I don't deny that this universe exists. I do deny that the metalayers is
knowable in principle, provided that metalayers is not operated by
cooperating beings (which is a very purple requirement).

What I *am* interested in is a simple TOE, or a set of simple equivalent
TOEs, which has enough predictive power to be usable with some finite amount
of computation.
 
> Do you say that most of the integers don't exist because nobody has
> written them down?

Yeah. I'm saying that, say,
0xf2f75022aa10b5ef6c69f2f59f34b03e26cb5bdb467eec82780c2ccdf0c8e100d38f20d9f3064aea3fba00e723a5c7392fba0ac0c538a2c43706fdb7f7e58259
didn't exist in this universe (with a very high probability, it being a 512
bit number, generated from physical system noise) before I've generated it.
Now it exists (currently, as a hex string (not necessarily ASCII) on many systems 
around the world, rendered in diverse fonts), as soon as I remove all 
its encodings it's gone again. P00f!

Ditto applies to generator systems -- they're a bit more widespread within a
lightday from here (though most of them are concentrated within a fraction of
a lightsecond), but you take them out -- all of them -- numbers cease to exist. 
They're gone, until something else comes along, and reinvents them.
 
> 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

No, they're meaningful without observers with world models. The physical objects 
(unless
they're infoprocessing systems) can't observe themselves.

> 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

I don't know what "conscious" means, but machine vision systems and animals can sure
count. No need to use vis vitalis for that.

> 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.

You're anthopomorphising awfully. It sure nice to be a conscious observers,
but most parts of this universe have been doing fine without, and given
that multiverse exists, most of those seem to do without as well.

-- Eugen* Leitl <a href="http://leitl.org";>leitl</a>
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