What are people's ideas about the problem of a global measure on
"everything?" It seems to me that a lot of the TOE's I've seen make an
assumption like "one structure, one vote." For example, if one assumes that
"everything" is the set of all computations, then one strategy might be to
look at the behavior of an average large turing machine and see what the
computation might look like "from the inside", treating it as a simulation
of a universe of some kind. But the notion of "average" seems to assume
that each possible turing machine is given equal weight...how do we know
they shouldn't be weighed by kolmogorov complexity or something else?
Similarly, Max Tegmark's TOE involves looking at all possible mathematical
structures, dividing them into equivalence classes, and then seeing what
kind of universe the majority of self-aware observers will find themselves
in. But again, this assumes that if one possible mathematical structure
contains 10 observers and another contains 100, then an observer is ten
times more likely to find himself in the second structure than the
first...but why should this necessarily be the case? Are we assuming that
the land of Platonic forms contains exactly one "copy" of each distinct
structure? Again, isn't it possible that some other measure would make
sense?
The main appeal of TOE's is that they reduce the amount of arbitrariness in
our basic assumptions about reality. If all possible universes are real to
observers inside them (or all possible observer-moments are real, to cut out
the middleman), then we can escape the problem of "why these laws of physics
and not some others?" But I think we do need some kind of global measure on
the set of "everything", since everything obviously includes worlds (or
observer-moments) that seem to be identical to this one up to a certain
point but in which the laws suddenly break down, and we want to be able to
say that this is less probable somehow (I've never been sure what people
were talking about when they referred to 'white rabbits' but I think it's
another version of this problem...isn't white actually a pretty common color
for rabbits though? Is it an Alice in Wonderland reference?) The problem
is that in introducing a global measure we run the risk of bringing back
exactly the same arbitrariness that we had before--"why this global measure
and not some other?" It seems to me that this is really the central problem
in divising a good TOE.
One solution is to say there is no global measure...this is what James Higgo
believes, if I understand him correctly, and possibly Hans Moravec as well.
James Higgo's picture of reality is a pretty honest look at what "no global
measure" implies--basically we can't talk about the probabilities of any
future events at all, and our knowledge is limited to the particular things
we're experiencing in this observer-moment and the statement "all possible
thoughts exist." Another solution is the "one distinct structure, one vote"
idea that Max Tegmark seems to use, and possibly some others as well. A
third solution might be to try to show that given some other more basic
assumptions, there is only one possible measure consistent with the
assumptions--this is the one I'm in favor of, and I have a rough idea about
how a kind of formalized version of anthropic reasoning might provide the
necessary constraints. The last solution I can think of would be to treat
the many-worlds theory as a measure on the set of all computations (assuming
that all computations actually end up being instantiated in some branch or
another) and then work backwards to see what the properties of this measure
are...perhaps it will be elegant enough that we can think of some kind of
philosophical "justification" for it.
A lot of people have a lot of different ideas about TOE's on this list, so
maybe the global measure issue could help clarify where we all stand in
relation to each other...do people have specific proposals about this? I
guess the other relevant question is, what is the set of "everything" that
you're putting the measure on...all computations? All mathematical
structures? All observer-moments?
Let me know what you think...
Jesse
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Received on Tue Mar 13 2001 - 23:31:49 PST