But if P(A)=B and P'(B)=C are elegant proofs, it is very unlikely for
P'(P(A))=C to be an elegant proof. This is what the dovetailer is
constructing - it is not possible to know whether the any particular
proof output by the UD is elegant, only that it must contain elegant
proofs since it is comprehensive.

##
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What exactly do you mean by everywhere elegant proof? That each step
of the proof is elegant? But whilst it is necessary for each step of
an elegant proof to be elegant, it is not sufficient
Cheers
Hal Ruhl wrote:
>
>
> 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.
>
> 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
>
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