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From: Jacques Mallah <jackmallah.domain.name.hidden>

Date: Sun, 21 May 2000 16:10:29 -0700 (PDT)

--- 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

Date: Sun, 21 May 2000 16:10:29 -0700 (PDT)

--- Fred Chen <flipsu5.domain.name.hidden> wrote:

[later I said R = sum_r sqrt(p(r) p0(r))]

I think p(r,b) (meaning the probability of the

continuation r given string b) is p0(r+b)/p0(b).

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.

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?

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/

__________________________________________________

Do You Yahoo!?

Send instant messages & get email alerts with Yahoo! Messenger.

http://im.yahoo.com/

Received on Sun May 21 2000 - 16:12:14 PDT

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