Christopher Maloney wrote:
> 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.
Actually I doubt if they would quickly arrive at that conclusion or even that
they would easily arrive at a concept of dimension (perhaps their most abstract-
minded mathematicians would): *Our* universe is very quickly perceivable as
3 dimensional because of strong geometric properties approximated in our
physics. There is a sorry lack of such geometric symmetry available in the
Life world. In fact, the Life universe *isn't* two dimensional really (being countably
infinite, it is necessarily 0 dimensional).
>
> > > > > 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.
>
But if deductions from the SSA can only be made from a first person perspective
then that makes all deductions from the SSA completely bankrupt because all the
deductions I've seen made from the SSA are very *general* statements (e.g.
your one about Life universes not subjectively existing). You can't say that deductions
are
subjective unless what they are *about* is also subjective. Or do you believe that
there is no fact of the matter about whether the probability of finding oneself in
a Life universe is 0? Is there one probability as far as Chris Maloney is concerned
and another as far as, say, Al Gore is concerned? Hmmm.
> 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
> wrong.
>
But you are not putting forward an argument, just speculating that there
might *be* an argument, as far as I can tell. There may be
an argument for saying that 'one' is less likely to be an SAS in a Life
universe but I don't think that one can simply say that *I* am not in a
Life universe therefore it is unlikely. On the same grounds I could
argue that is extremely unlikely that one is an American citizen.
>
> 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.
>
I don't personally believe that our universe *is* a 3+1 dim. pseudo-Riem.
manifold quantum field, but that's another story.
Where your argument falls down is betting on our set having the larger measure,
based (I'm presuming) on the evidence that *you* are in the latter sort of world.
If you wanted to construct a Bayesian proof of your statement you would end up
showing that you are *minutely* more likely to be in this world.
Once you start talking about transfinite measures I give up. The Bayesian arguments
that underpin all these anthropic arguments are based on *probability* and
therefore on *natural* numbers, counting etc.
jerry
Received on Wed Dec 08 1999 - 03:00:28 PST
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