Re: The Game of Life

From: Christopher Maloney <>
Date: Tue, 07 Dec 1999 21:38:23 -0500

Jerry Clark wrote:
> I meant that the fact that their own world was a Life simulation would
> perhaps not be *directly* deducible (i.e. by 'boiling down' their seeming laws of
> physics until they got to '23/3', the Life rules), or at least much less likely than
> discovering Life first and building up a larger and larger library of larger and
> larger Life objects (as we are currently doing) until a correspondence is noted
> between the larger members of this library and the smaller members of their
> physicists' library of fundamental 'particles'. At this point I'd say that the Life
> rules had been discovered but perhaps not deduced.

I guess that such a thing might be possible. But then, if the life game
can emulate a TM in any portion of it, mightn't it be possible that any
computable laws of physics are emulable by it, if you allow larger and
larger members to be built up? Later in this post you distinguish
between those members that are the result of a TM inside a life field,
and those that "you get 'for free' by running Life sim on a large
enough random field." But perhaps its not so simple to draw the line.

Anyway, though I say that, I suspect that to the simplist, and most
probable (if those are the same set) of SAS's that develop "for free"
on a random field, the rules of life would be discernable. Some
general characteristics of their universe probably would be -- that
they are in two dimensions, for example.

> > > > So if we further assume that our universe is *not* a game of life,
> > > > and if the AUH is true, then by the SSA I would conclude that the
> > > > probability of any SAS finding itself to be in a game of life is
> > > > probably zero. That is, the set of SAS's inside a game of life is
> > > > of measure zero relative to the set of SAS's inside universes like
> > > > ours.
> > >
> How do you deduce that the prob of being in a game of Life is 0? I under-
> stand all the stuff about measure (I'm a mathematician) but where do
> you get the Life-like universes vanishing?

I said probably zero - I didn't claim to deduce anything. I'm just
speculating. See below.

> > And here I make a desperate, arm-waving leap, from the idea that
> > I am a random sample, to the conclusion that SAS's "like me" are
> > the most numerous. Whatever "like me" might mean, I think it's
> > fair to guess that it wouldn't include SAS's inside a game of life,
> > unless you're talking about the ones generated within the UD.
> >
> No I mean the one's you get 'for free' by running Life sim on a large
> enough random field. (Take digits of pi if you don't like 'random').
> I agree: your leap is a desparate, arm-waving leap. My SAS within a
> Life simulation could be justified in making the same leap, surely. Even
> though he/she/it would be by your argument totally wrong.

Well, that's a very interesting point, and I believe it shows that
we can only, each of us, deduce things from the SSA from a first
person perspective. We can't take anyone's word for what they've
deduced from the SSA. So we shouldn't, for example, take the word
of a scientist who's just performed the QS experiment and survived
despite thousand-to-one odds, that QS really works. *He* would have
a strong reason for believing it, but I would have no additional
incentive to believe it.

So, I think, yes, if my argument is correct, it doesn't matter
that a life-SAS would deduce the same thing. I would be correct
and (s)he would be wrong. That is, I still do believe that
different sorts of SAS's have different measure. Taking Hal's
approach and doing away with infinite sets, spoze that there are
a total of one billion SAS's in all the universes everywhere, and
that ten of them are green, but the rest are blue. Any one of
them would be justified in assuming that most SAS's are of the
same color, but the green ones who made that assumption would be

So if the set of life-SAS's is not isomorphic to the set of (3+1
dim. pseudo-Riemannian manifold quantum field)-SAS's, then we'd
have no a priori reason to assume that the measures of these sets
are the same. If the measures are different, then one is larger
than the other. My money will be on our set having the larger
measure. If the measures
are transfinite but of different orders, then I conclude that the
probability of finding oneself to be a life-SAS is zero.

Chris Maloney
"Donuts are so sweet and tasty."
-- Homer Simpson
Received on Tue Dec 07 1999 - 18:48:22 PST

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