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From: Wei Dai <weidai.domain.name.hidden>

Date: Fri, 23 Jan 1998 00:43:24 -0800

On Thu, Jan 22, 1998 at 10:31:50AM -0800, Hal Finney wrote:

*> > Remember that the prior probability of a region is related to the
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*> > program length plus the coordinate length. If you have a universe with an
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*> > exotic coordinate system, the lengths of the coordinates would be long and
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*> > so the regions in that universe would have small priors.
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*>
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*> I'm not so sure. Consider a 1 dimensional universe which is the output
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*> of a cellular automata program, possibly a very complex and long one.
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*> Let's suppose though that the output has about 50% 1's and 50% 0's.
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*>
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*> Consider a typical state:
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*>
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*> 0110001010100101000011110101010110101011010101110
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*>
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*> The natural coordinate system is:
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*>
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*> 111111111122222222223333333333444444444
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*> 0123456789012345678901234567890123456789012345678
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*>
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*> If I understand your model, a TM which took one of these X coordinates
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*> (and perhaps a time coordinate T) and output the corresponding bit of
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*> the state above would in some sense "be" that universe.
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*>
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*> But I could write a trivial program which produced as output the LSbit
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*> of the X coordinate being input. Then I could use a different set of
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*> coordinates to get the output I needed:
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*>
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*> 1 1111112221112 ...
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*> 013246587092416380245791 ...
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*>
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*> These coordinates will not be much larger than the natural ones, but
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*> the trivial TM can now produce the output of an arbitrarily complicated
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*> CA program. (The X coordinate system will have to change with each time
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*> step T, but that is just a complex X,T coordinate system.)
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I don't see how this is a counter-example. In order to specify a region

in this coordinate system, you'd have to give the coordinates of every

point inside the region, so the length of a region that contains

non-trivial content would be much greater in this TM than in a TM with a

simple coordinate system, where you only have to give the coordinates of

the boundaries.

Received on Fri Jan 23 1998 - 00:45:52 PST

Date: Fri, 23 Jan 1998 00:43:24 -0800

On Thu, Jan 22, 1998 at 10:31:50AM -0800, Hal Finney wrote:

I don't see how this is a counter-example. In order to specify a region

in this coordinate system, you'd have to give the coordinates of every

point inside the region, so the length of a region that contains

non-trivial content would be much greater in this TM than in a TM with a

simple coordinate system, where you only have to give the coordinates of

the boundaries.

Received on Fri Jan 23 1998 - 00:45:52 PST

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