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

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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 "Schmidhuberensemble"* or UD*, the empty observer moment can be identified withNothing,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?`

Bruno http://iridia.ulb.ac.be/~marchal/