George Levy
wrote:
>Everytime a "measurement" is made, the set of
worlds spanned >by this consciousness is defined more narrowly, but the
>number in the set remains infinite. In addition, each >simulation
in the set need not belong to the same "level."
>We're faced with the strange possibility that the >consciousness spans an infinite number of simulations >distributed over widely different levels. I agree that we are
simultaneously in many simulations, and I would agree that there are uncountably
many possible 'histories' or situations consistent with our consiousness and
known history. But I think only a countable number of the 'classical universes'
(and certainly only a small fraction) we might be in are simulations. If we
look at the 'total knowledge' of any living being, including the things not
consciously known but constrained to be decided by the classical history they
evolved from (so, for instance, 'what killed the dinosaurs' is probably a
question with a definite answer, for us, but the trajectory of a certain
electron is not; the former would form part of my 'total knowledge' because if I
worked out the answer by looking at enough historical evidence, I would get the
same answer each time), it is always finite.
As you
suggest, any arrangement of matter consistent with this 'total knowledge' is a
possibility for the universe we will find ourselves in on making further
measurements, and if we live forever, and keep making new measurements, then
there will be a countable number of possible universes we will encounter. But at
any finite time, we will only know a finite amount, and therefore only impose a
finite number of constraints on the possible universe we will find ourselves in
(see my note below on living forever versus having lived forever for more on
this). the relevance of this to the current issue is that the superbeings who
would emulate us obey the same rules: The 'whole world' of any living being
at any given time in their history, being determined only by their thoughts, and
the classical histories likely to give rise to those thoughts, can be described
by a finite amount of information. Therefore the total number of situations in
which a conscious being is simulating our universe is countable. Also, the total
number of finite chains of one being simulating another simulating a third etc.
is countable (being a set of finite subsets of a countable
set).
We are left with the infinite
chains of simulation. Here there are two possibilities: either the chain forms a
'loop', in whih case it has actually already been counted in the finite chains
(so there are countably many of these [you may also reject them as
'unphysical']) or there is a new 'being' at every step up the chain.
But I do not see how these constructions could 'really' be said to tend to
any limit (which would be uncountable) as there is, unlike with real
numbers, no way to say when two chains are 'getting close together': The next
stage could always make them totally different, by any measure (but given the
axiom of choice, these universes will be 'real', mathematically at least. But
they won't be 'dense' as I'll get on to now..).
Whether or not you accept that
these limits exist, it is nevertheless the case that we are more likely, on
making measurements, and reducing the number of universes we might be in to find
more assortments of nonliving matter than aliens, including those aliens who
might 'turn out' to be controlling us. Any series of new measurements we make
can be seen as adding to our 'total knowledge' as described above, a
new stream of data, whih you could translate into a string of 0s and 1s (The
fact that the data is genuinely new to us means that it is necessarily a
discrete uniform distribution of 0s and 1s, apart from correlations you may have
itroduced into the data by 'translating it' from whatever form you found it
in). Then for a sufficiently long 'string' there would be a very small
probability that this information would correspond to the existence of some
living being, but it would be much more likely to correspond to a bunch of
'dead' particles (physically, I would see a typical measurement process as
'collecting thermal radiation from a black hole' or 'going over the cosmic
horizon to see what you find' or 'absorbing a photon' [these examples are
roughly in decreasing order of probability of finding 'life', but even with the
last eample it is in principle possible: you could fire a superenergy gamma ray
at a gold sheet and a virus might come out the other side]).For any finite
'chain' of information there is a small but finite chance of finding 'life', and
even finding'life simulating us' but as you make the chain infinite (as we
would have to to 'discover' an infinite chain of universes all simulating in a
chain) the probability of finding forever higher and higher levels of life tends
to zero. This is because at eah stage, the higher level life would need to be
more complex (to simulate the extra information) so you'd likely find more
'cosmic junk' which the proposed higher level being would have to simulate as
well, so he/she'd have to be even more complex. So it seems highly likely that
we'd never find even one level of simulation: The stuff we'd find looking for
the simulator would make the simulator ever more and more complex and hence
harder to find.
These rather lengthy
arguments are not needed to disprove the specific world of the Matrix, though: A
much more obvious inconsistency is 'why don't the robots eat what they're
feeding us?' I know in scifi stories there's usually stuff that's not explained
but you can imagine there might be some explanation for, but anyone who knows
what a Carnot engine is will know that there's no possible reason to use a human
as a furnace..
Finally, my note about living forever and having
lived forever: Anyone could live forever; you just have to eat well and be made
of metal, but noone could have lived forever: Say if they try to recall their
earliest memory (In the generalised 'total knowledge' sense given above)..Then
the memory they recall will only ever have a finite age. At any time in the
future, there will only be a certain amount of their past that is affecting
them. So there will be different pasts consistent ith where they are now, and
'almost all' of them will involve a less ordered state earlier on (as there are
more such states) from which their current ordered state evolves. Physically,
this corresponds to the evolution of their species and situation, and the
totally random state(s) found sufficiently early on correspond to the 'big
bang', which I conjecture is a 'totally indeterminate' state found at the
beginning of every 'universe.'

 are we in a simulation? John Collins
 Re: are we in a simulation? David Kwinter
 Re: are we in a simulation? George Levy
 Re: are we in a simulation? John Collins
 Re: are we in a simulation? George Levy
 Re: are we in a simulation? Hal Finney
 Re: Are we in a simulation Eric Hawthorne
 Re: are we in a simulation? George Levy
 Re: are we in a simulation? Stephen Paul King
 Re: are we in a simulation? George Levy
 Re: are we in a simulation? Stephen Paul King
 Re: are we in a simulation? George Levy
 Re: are we in a simulation... Stephen Paul King
 Re: are we in a simulation... Eric Hawthorne