On Aug 19, 2004, at 2:00 PM, Hal Finney wrote:
It's not clear to me that causality and time are inherent properties
of worlds. I include worlds which can be thought of as n-dimensional
cells that satisfy some constraints. Among those constraints could be
ones which induce the effects we identify as causality and time. For
example, a two-dimensional cell where C[i,j] == C[i-1,j] XOR C[i-1,j-1].
This particular definition has the property that C[i,.] depends only on
C[i-1,.], which lets us identify i as time, and introduce a notion of
causality where conditions at time i depend on conditions at time i-1.
But we could just as easily create a cell system where there was no natural definition of time, where C[i,j] depended on i+1, i-1, j+1 and j-1. You could still imaging satisfying this via some constraint satisfaction algorithm.
I'll have to think about the CA implications --- what is a "cell" in such a CA, and what is meant by the various "nearness" relationships of such cells? (I'm still processing Wolfram's book, a couple of years after reading it the first time. ;-)
I'm just adopting a relatively conventional GR point-of-view here, where time is just another direction, albeit one in which travel is (in most circumstances, depending on the local differential geometry and geometrodynamics) directionally constrained. (I'm ignoring the thermodynamic interpretation of time's arrow, though when you throw 2LT into this particular brew things would seem to get rather interesting. ;-)
Now these jinni worlds are ones which mostly have these conditions we identify as time and causality, but which locally, or perhaps rarely, do not satisfy such rules. Seen in this perspective, there is a full range of possibilities, from fully causal worlds, to ones which are 99.999% causal and only .0001% noncausal, to ones which are 50-50, to ones for which no meaningful concept of causality can be defined.
We're begging the question re: causality; it was perhaps unfortunate that I chose to use that word, as it's interpretive rather than descriptive in itself. The argument Boulware's making appears to be inherently probabilistic and geometric rather than ontological. That became less clear in my exposition, my bad.
I'll have to look at this. It doesn't sound quite right. If
probabilities are non-unitary that violates the fundamental rules of QM,
But do they? This is, I think, perhaps a very interesting and pertinent question. It certainly appears to throw both the QM formalism as well as its interpretations into disarray, but I think perhaps the result is less than fatal. One can certainly do statistics (and hence QM) with non-unitary probabilities --- the method involves a kind of normalizing transformation between different probabilistic measures. (In fact this very issue was dealt with by one of Gott's grad students; the citation escapes me at the moment, but he found that you could patch things up by simply supplying a kind of local correction coefficient. I.e., while this appears prohibitive on the surface, in fact "fixing it up" isn't all that difficult. The ontological interpretation of the relationships between these patch coefficients, OTOH, is IMHO pretty surreal.)
I think you're getting awfully speculative here.
This is a criticism, in *this* group in particular? ;-) It's admittedly speculative.
It sounds like you are suggesting that it would be simpler to suppose
that "all universes exist which contain jinn" than "all universes exist".
Not precisely; I'm suggesting that "simple" is difficult to measure when speaking about TOEs. There might be some measures of "simple" for which the above is true; there are others, e.g. the Champernowne machine and so forth, for which it is certainly not. But Occam's Razor isn't much help here by itself.
That doesn't seem at all plausble to me. My heuristic is that any rule
of the form "all universes exist except X" is going to be more complicated
than one of the form "all universes exist".
On the surface, sure. But consider: the statement "all universes exist" presupposes a definition of universe that it omits. What is meant by "universe" requires an exhaustive definition, and the algorithmic hypotheses make varying assumptions about that definition. My intuition would be that the most parsimonious definition would be the preferable one; but we don't have any metrics for "parsimony" on such definitions. It could be that definitions that statically embed such jinn might be more parsimonious by some measure than other ones; the statically-defined jinn might "ground out" the definition and permit a higher-order / more abstract / terser "universe generation algorithm." (Think Python vs. its own bytecode.)
Think of it this way: any formal system has its base axioms. In this context, the "universe generator" is the system in toto; the jinn could form (at least a part of) its axioms. Or, thinking about it in nonlinear dynamical terms, the jinn form the attractors which "condense" permissible universes out of the space of all possible universes. Or, thinking about programming languages: this works the same way that e.g. code generation templates for various programming language compilers (and the associated high-level language primitives and syntax) define the space of permissible programs. This doesn't restrict program behavior at a high order, but does prohibit the direct expression of nonsensical things like 1/0. (Okay, the latter analogy is stretching things pretty far... ;-)
To be clear about all of this, though: I'm not really proposing any hypothesis here, more like musing out loud. :-)