At 12:17 11/04/04 +0100, Brett Hall (FOR-LIST) wrote:


(I was saying:

<snipped > More shortly: if we are living in a massive computer then we are
> in arithmetic-platonia, and by the church thesis and other
> theoretical constraints, this is testable.)

Actually this is the whole subject of my thesis. Let me try to explain
briefly without technics. Let us suppose there is a physical universe.
Let us suppose "we are living in a massive computer" belonging to
that universe.
This means comp is actually true, that is: there is a level of description
of ourselves such that we could survive any functional substitution
made at that level. I guess you will agree with the following propositions:

1) If the clock of that massive computer slows down, we cannot, from
our first person perspective, be aware of that slowing down. In case
the computer stops for one year, and then proceeds again, we cannot
be aware of that stopping. OK?

2) If a description of the computer is made, at some stage, and then
destroyed by "real inhabitants" of that universe, and then build again
again we will not be aware of that destruction reconstruction. OK?

3) Suppose now that the computer is again "read" and destroyed, and
then build, but now in two different places of the "universe", and in two
slightly different states. I mean the inhabitant of the universe programs
the computers in such a way that in the simulation 1 some event A will
take place, and in the simulation 2 some event B (different from A)
will take place. Then in case the simulated person would be aware of
this (because the inhabitants of the universe would have tell us the truth,
we would know that we are completely ignorant about which events A or
B will take place. This is the first person indeterminacy.

4) This remains true even if the first copy is run quasi-immediately, and
the second copy of the massive computer is run after a long delay,
because the simulated people cannot be aware of any imposed "external
delay" OK?

5) As a particular case, we can consider that the inhabitants just make
a copy of the computer (in which A will be realized), and build from that
copy a version of the computer in which B be realized. Again the
first person probability of A and B remains the same (consider that the
first computer has been destroyed and reconstituted with a null delay, so
that this is a particular case of the preceding step).OK?

6) This shows that if we are in a massive computer running in a
universe,  then (supposing we know it or believe it) to predict the future
of any experiment we decide to carry one (for example testing A or B)
we need to take into account all reconstitutions at any time of the
computer (in the relevant state) in that universe, and actually also
in any other universes (from our first person perspective we could
not be aware of the difference of universes from inside the computer).

7) Here is an admittedly more difficult point: from the first person
point of view the simulated people in the computer cannot make
the difference between a "real universe" or any "fictive universe" which
belongs to Platonia. We can go back to this point later. This has been
discovered by myself and independently Tim Maudlin gave a better
(more informative) proof. See ref in my thesis.

8) So, if we are being simulated by a massive computer somewhere
in a real universe, then to make any first person verifiable prediction
we must take into account all the possible computations going through
our actual state. So "the laws of physics", which we can temporarily
define as the laws of whatever we can predict consistently, should
be given by a measure on those 1-person computational histories.

9) Now, from computer science and logic, startlingly enough perhaps,
we can isolate a measure on the 1-person comp histories, and this
give us the laws of physics (this is too technical to be put here, and
actually I have derived only the logical structure of the probability
one, but I got something non trivial and very close to a quantum logic
(which can be seen as the logic of the quantum probability one, as
von Neumann has shown).

10) Having extracted the necessary (with comp) physical laws, let
us compare it with the laws we can infer from our neighborhood (actually
simulated by your massive computer). If it is the same, then we can
conclude we are NOT simulated by a particular massive computer
embedded in a universe (only apparently so for the inhabitant of the
"universe"). More precisely we are no more simulated by it than by
any of those emulated in Platonia. Or we discover some discrepancies
between the inferred "physical" laws (from our experiences inside the
massive computer) and the laws which comes from the measure on
all comp histories, then, either comp is false and we are then
obviously not executed by a massive computer, or we keep comp,
and then, like in a lucid dream, we can correctly infer we are simulated
by a computer.
Put in another way, *either* the massive computer simulates the exact
laws of physics (exact with comp = the laws extractible from the
measure on all 1-computations) in which case we belong to it but
in that case we belong also to all its "copy" in Platonia, and our
prediction or physics relies on all those copies (so that to say
we belong to the massive computer has no real meaning: if it stops,
nothing can happen to "us" for example); *or* the massive
computer simulates only an approximation of those laws (like a
brain during the night), and then we can in principle make the
comparison, and find the discrepancies, and conclude we inhabit
a fake reality ... OK?

If you want we can discuss the more subtle point 7, but please
let me know if you have followed the nine other steps. You can also
look at my URL and at some of the everything-list explanations for
some precisions, but don't hesitate to ask any question if I have been
unclear (at any steps).


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