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From: Hal Ruhl <hjr.domain.name.hidden>

Date: Thu, 19 Apr 2001 19:58:36 -0700

Let me correct one little issue which I think helps to clarify what I am

saying. I add a comment on the universal dove-tailer.

1) Yesterday I said that the cascade 1+1=2, 2+1=3, 3+1=4, etc. was not

everywhere elegant. But I went outside my identification process for

"determinism" = "everywhere elegant proof" to do so. The error was to slip

into full number theory and think: "84" one of the strings this cascade

will eventually reach for example has more than one proof. That is true

because number theory is richer than just "data + 1 =".

But here the working definition of "deterministic" I use is that all of the

selected set of rules of a cascade act at each step on all the data. You

should not have within the idea of "deterministic" some of the rules active

today and some others active tomorrow, some of the data regions exempt from

some rules today and other data regions partially exempt tomorrow unless

that was itself in Rj.

Deterministic as I understand it = all the rules of physics always apply to

the entire state of the universe.

So for the above cascade we have selected "data + 1 =" as the exclusive

expression - the entire rule set of the operative FAS - for which we are

seeking the cascade of values given some start data [effectively the axiom

of that cascade] in this case "1".

The fact that this rule may also belong to a different and richer FAS is

not germane to the cascade viewed as an attempted deterministic sequence.

The operative FAS contains just this one rule as its Rj and applies it to

all the data at each step. That makes this cascade everywhere elegant

because there is no other proof of any of the output strings available in

the operative FAS. Thus hits the complexity wall established by the

complexity of the operative FAS.

2) A universal dove-tailer generating all strings using a fixed algorithm

every part of which applies to all the current data in the same way at each

step seems an odd thing.

A dove-tailer is not directly generating the "whole" ensemble. What it is

doing is selecting by fixed rules a particular string out of the ensemble

and adding some quantity of bits, putting that back in and selecting

another and adding some quantity of bits to it etc., etc. That is a very

selective and complex process on a step by step basis. You wind up

constructing this incredibly complex everywhere elegant proof of what must

then be an incredibly complex object that is nevertheless considered to be

a very low complexity object.

If I have the ideas of a UD, elegant proof, and AIT complexity correct the

UD appears to be a contradiction.

The contradiction again is that we have a FAS that constructs a proof it

knows is elegant that is nevertheless far more complex than any proof it

can know is elegant.

Hal

Received on Thu Apr 19 2001 - 17:10:28 PDT

Date: Thu, 19 Apr 2001 19:58:36 -0700

Let me correct one little issue which I think helps to clarify what I am

saying. I add a comment on the universal dove-tailer.

1) Yesterday I said that the cascade 1+1=2, 2+1=3, 3+1=4, etc. was not

everywhere elegant. But I went outside my identification process for

"determinism" = "everywhere elegant proof" to do so. The error was to slip

into full number theory and think: "84" one of the strings this cascade

will eventually reach for example has more than one proof. That is true

because number theory is richer than just "data + 1 =".

But here the working definition of "deterministic" I use is that all of the

selected set of rules of a cascade act at each step on all the data. You

should not have within the idea of "deterministic" some of the rules active

today and some others active tomorrow, some of the data regions exempt from

some rules today and other data regions partially exempt tomorrow unless

that was itself in Rj.

Deterministic as I understand it = all the rules of physics always apply to

the entire state of the universe.

So for the above cascade we have selected "data + 1 =" as the exclusive

expression - the entire rule set of the operative FAS - for which we are

seeking the cascade of values given some start data [effectively the axiom

of that cascade] in this case "1".

The fact that this rule may also belong to a different and richer FAS is

not germane to the cascade viewed as an attempted deterministic sequence.

The operative FAS contains just this one rule as its Rj and applies it to

all the data at each step. That makes this cascade everywhere elegant

because there is no other proof of any of the output strings available in

the operative FAS. Thus hits the complexity wall established by the

complexity of the operative FAS.

2) A universal dove-tailer generating all strings using a fixed algorithm

every part of which applies to all the current data in the same way at each

step seems an odd thing.

A dove-tailer is not directly generating the "whole" ensemble. What it is

doing is selecting by fixed rules a particular string out of the ensemble

and adding some quantity of bits, putting that back in and selecting

another and adding some quantity of bits to it etc., etc. That is a very

selective and complex process on a step by step basis. You wind up

constructing this incredibly complex everywhere elegant proof of what must

then be an incredibly complex object that is nevertheless considered to be

a very low complexity object.

If I have the ideas of a UD, elegant proof, and AIT complexity correct the

UD appears to be a contradiction.

The contradiction again is that we have a FAS that constructs a proof it

knows is elegant that is nevertheless far more complex than any proof it

can know is elegant.

Hal

Received on Thu Apr 19 2001 - 17:10:28 PDT

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