Wei Dai, <[EMAIL PROTECTED]>, 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:
The natural coordinate system is:
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 ...
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.)