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: 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