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From: Jesse Mazer <lasermazer.domain.name.hidden>

Date: Wed, 14 Mar 2001 02:29:29 -0500

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

_________________________________________________________________

Get your FREE download of MSN Explorer at http://explorer.msn.com

Received on Tue Mar 13 2001 - 23:31:49 PST

Date: Wed, 14 Mar 2001 02:29:29 -0500

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

_________________________________________________________________

Get your FREE download of MSN Explorer at http://explorer.msn.com

Received on Tue Mar 13 2001 - 23:31:49 PST

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