Le 15-nov.-05, à 00:28, Russell Standish a écrit :

Equivalence in the sense of category theory's notion of duality. In
Venn diagrams, for instance, the empty set is the dual of the
universal set.

Most set theories does not have a universal set. Version of Quine's New Foundations (NF) does but are known only by specialist of NF.

More particularly to the "bitstring ensemble" ASKA "Schmidhuber
ensemble"* or UD*, the empty observer moment can be identified with Nothing,
and the empty observer moment is the whole plenitude.

I don't see relation between the bitstring ensemble and UD*. Actually I don't see UD* as a set (of course you can code it as a set and then it will be a non trivial subset of the bitstring ensemble). It is really the whole of computer science which makes the Universal Dovetailer (UD) and its complete platonist execution UD* (on which depend the first person experiences, cf UDA) a highly non trivial universal structure.

Of course the flip side to "can be" is "can't be" - but in that case,
I'm afraid, Nothing does not seem to be a well defined concept (I
stand to be corrected of course!).

It is the problem with the notion of "nothing", it is relative to the basic theory we chose. It can be implemented in a notion of empty set, but then in which set theory? (and then in which model of that set theory, and this question would lead to the critics I made in this list (some years ago) to the way Tegmark proceeds when he tries to describe a general notion of math reality).

* I'm being cautious with my terminology here, as this bitstring
  ensemble is not the same as the one generated with speed prior, what
  I sometimes call Schmidhuber II. It is the same as the output of a
  UD, what you call UD* I beleive.

I have read in Schmidhuber and in comments on Schmidhuber the expression that the universe is a computable object (Schmidhuber form of comp) and that this would mean that the universe is the output of a program. This should be enough to realize that the UD has nothing to do with Schmidhuber's notion of great programmer. Indeed the UD has no outputs at all. The program UD never stops. That is why, in order to make UDA easy, I introduce the "extravagant hypothesis" according to which we are in a concrete steady sort of "physical" universe capable of running forever the UD, before using the "more subtle" movie graph for eliminating that hypothesis and eventually any hypothesis that there is primitive "physical" universe. It is really because the first person cannot be aware of any delays in the dovetailing computation of the UD that the relative measure on the observer-moments will depend on the whole trace or execution of UD*.

PS - Maybe this section of my book needs a little more work...

Sure it needs imo. Let me give an exercise for everybody (interested). Why does the Universal Dovetailer have to dovetail? This is not obvious at all. A simpler exercise: where do I have already answer this question on the list?



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