--- Fred Chen <flipsu5.domain.name.hidden> wrote:
> Jacques Mallah wrote:
> > If b was random, the continutation r will
> > probably also be random, but now we lose the
> > specific information about the exact specification
> > of b. If b was simple, the continuation will
> > probably also be simple.
> > In both cases, consider R = sum_r p(r) p0(r)
[later I said R = sum_r sqrt(p(r) p0(r))]
> > where p0(r) is the probability distribution of
> > continuations for an empty string, ie is the
> > universal distribution.
>
> So, wouldn't p(r,b)=p0(r+b)?
I think p(r,b) (meaning the probability of the
continuation r given string b) is p0(r+b)/p0(b).
> So p(r,b) is large(r) for r, b both random or r,b
> both simple.
Not quite (if I understand you correctly). If b
is random, r is probably also random, but for any
fixed b and fixed r the p(r,b) when they look random
will be very small. However, the sum over all
random-looking r's of p(r,b) will be large.
> If b is simple, but r is random, that is probably
> your wabbit. The remaining case (b random, r
> simple) - order out of chaos, also seems unlikely.
I don't think it's that simple. The wabbits, I
think, are present when b is not too simple or too
complex but still contains a lot more "interesting"
information than would be expected based on the
anthropic significance of b in a
universal-distribution-like-ensemble.
Foiled again by that wascally wabbit!
Another possibility is to somehow define wabbits
based on exactly the above idea. Who knows exactly
how?
> There is no trivial representation of p0(b) in terms
> of its possible truncated segments, is there? You
> would have to capture all possible relationships
> between the segments, etc., right?
Right.
=====
- - - - - - -
Jacques Mallah (jackmallah.domain.name.hidden)
Physicist / Many Worlder / Devil's Advocate
"I know what no one else knows" - 'Runaway Train', Soul Asylum
My URL:
http://hammer.prohosting.com/~mathmind/
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Received on Sun May 21 2000 - 16:12:14 PDT