Re: basic questions

From: Hal Finney <hal.domain.name.hidden>
Date: Thu, 22 Jan 1998 10:31:50 -0800

Wei Dai, <weidai.domain.name.hidden>, writes:
> On Wed, Jan 21, 1998 at 10:33:27AM -0800, Hal Finney wrote:
> > 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.

I'm not so sure. Consider a 1 dimensional universe which is the output
of a cellular automata program, possibly a very complex and long one.
Let's suppose though that the output has about 50% 1's and 50% 0's.

Consider a typical state:

        0110001010100101000011110101010110101011010101110

The natural coordinate system is:

                  111111111122222222223333333333444444444
        0123456789012345678901234567890123456789012345678

If I understand your model, a TM which took one of these X coordinates
(and perhaps a time coordinate T) and output the corresponding bit of
the state above would in some sense "be" that universe.

But I could write a trivial program which produced as output the LSbit
of the X coordinate being input. Then I could use a different set of
coordinates to get the output I needed:

                 1 1111112221112 ...
        013246587092416380245791 ...

These coordinates will not be much larger than the natural ones, but
the trivial TM can now produce the output of an arbitrarily complicated
CA program. (The X coordinate system will have to change with each time
step T, but that is just a complex X,T coordinate system.)

Hal
Received on Thu Jan 22 1998 - 10:48:27 PST