On Wed, Jan 21, 1998 at 10:33:27AM -0800, Hal Finney wrote:
> I'm not sure I follow you here. Are you suggesting that our observations
> of the universe's history might be in error, that we might be instantiated
> for a single instant with all of our memories of the past being illusions?
> We could write down the state of the universe at this instant as a long
> string using a simple mapping, and at some point the counting TM will
> emit this string. At that instant we will all exist with our memories
> of the past, but none of that past will actually have happened. Is this
> right?
Yes, that's what I'm saying.
> The problem then is not so much with the objective question of whether we
> live in the counting universe, which an outside observer could easily
> answer, but rather with the difficulty of us as residents in the universe
> knowing the answer.
>
> A more extreme case occurs if the counting program works in trinary,
> using the 0/1/comma alphabet. Now it outputs not only all numbers, it
> outputs all possible comma-separated sequences of numbers. It eventually
> outputs not only every possible state, but every possible sequence of
> states, including the entire history of our universe. This history would
> be a subset of an enormously larger output string, all created with a very
> short (and therefore a priori probable) input program.
>
> All I can suggest about these problems is that they would imply that the
> universe will shortly cease to behave lawfully. When we don't observe
> this, we can reject this possibility. Otherwise we are forced to say
> that all our perceptions are illusions, that our memories are false,
> that we ourselves may be simply memories of some future self. Logically
> we can't rule this out, but it does not seem reasonable. If we lived in
> the counting universe, there is no reason why the universe should seem
> lawful in the sense we see.
Logically we can't rule this out, but we should be able to rule it out
probabilisticly. My point is that I don't see how to do it under
Schmidhuber's interpretation.
> You solution is somewhat different in nature from Schmidhuber's.
> Your set of possible universes is more structured than his. You have
> a coordinate system, you have regions (which may imply a certain amount
> of continuity in the coordinates). He had binary strings to represent
> the universe state, which would allow for a wider set of possible
> universes.
The coordinate systems and regions are just interpretations to help our
intuition. The procedure that I gave for computing probabilities does not
depend on any structure in the coordinate system. If its not easy to
interpret the input to a TM as coordinates in a universe, then it would be
hard for us to think about that TM as the sort of universe we're familiar
with, but it doesn't matter in the probability computations.
> I'm not sure you can fully avoid the mapping problem with your approach.
> There is still a mapping involved in the choice of coordinates.
> With a sufficiently exotic coordinate system, I suspect we could map
> our universe's state to the output of a trivial program.
Remember that the prior probability of a region is related to the
program length plus the coordinate length. If you have a universe with an
exotic coordinate system, the lengths of the coordinates would be long and
so the regions in that universe would have small priors.
Received on Wed Jan 21 1998 - 15:05:30 PST
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