On 10/17/2012 1:19 PM, Bruno Marchal wrote:

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On 17 Oct 2012, at 08:07, Russell Standish wrote:On Tue, Oct 16, 2012 at 03:39:18PM +0200, Bruno Marchal wrote:On 14 Oct 2012, at 23:27, Russell Standish wrote:On Sun, Oct 14, 2012 at 04:44:11PM -0400, Roger Clough wrote:"Computational Autopoetics" is a term I just coined to denote applying basic concepts of autopoetics to the field of comp. You mathematicians are free to do it more justice than I can. I cannot guarantee that the idea hasn't already been exploited, but I have seen no indication of that. The idea is this: that we borrow a basic characteristic of autopoetics, namely that life is essentially not a thing but the act of creation. This means that we define life as the creative act of generating structure from some input data. By this pramatic definition, it is not necessarily the structure that is produced that is alive, but life consists of the act of creating structure from assumedly structureless input data. Life is not a creation, but instead is the act of creation.So any self-organised system should be called alive then? Sand dunes, huricanes, stars, galaxies. Hey, we've just found ET!I am not sure a galaxy, or a sand dune has a "self", unlike a cell, or a person.You are, of course, correct that the self/other distinction is crucial to life (and also of evolution - there has to be a unit of selection - the replicator). I was responding initially to Roger's claim that life is the act of creating structure. Any self-organised system can do that.Yes.The self is directly related to the Dx = "xx" trick, for me.The Dx=xx trick is about self-replication. Of course entities with asenseof the self/other distinction needn't replicate (eg certain robots).Self-replication and self-reference. And many self-transformation (infact self-phi_i, for all i).Self-reference and self-replication, are basically the same processes,except that in replication you reproduce yourself relatively to someuniversal numbers "grossly" different than you, (the most probablephysical world), and with self-reference you reproduce yourselfmentally, that is with respect to the universal number you are.

Dear Bruno,

`We need to have some way of explicitly defining the phrase "you`

`reproduce yourself relatively to some universal numbers "grossly"`

`different than you". I think this can be done locally but not one that`

`can be globally extended.`

Actually, I was just reading an interview with my old mate Charley Lineweaver in New Scientist, and he was saying the same thing :).If life is such a creative act rather than a creation, then it seems to fit what I have been postulating as the basic inseparable ingredients of life: intelligence and free will.I don't believe intelligence is required for creativity. Biological evolution is undeniably creative.Is life more creative than the Mandelbrot set?, or than any "creative set" in the sense of Post (proved equivalent with Turing universality)?I would say yes. The Mandelbrot set is self-similar, isn't it, so the coarse-grained information content must be bounded, no matter how far you zoom in.The M set is not just similar, the little M sets are surrounded bymore and more complex infiltration of their filaments. So the closeryou zoom, the more complex the set appears, and is, locally.It is most plausibly a compact, bounded, version of a universaldovetailer.

`Could you explain a bit on the definition of compactness for our`

`List readers? It is a very important concept that we all need to`

`understand, IMHO! I understand it, but not in a way that I can put into`

`words...`

Life, on the other hand, exhibits unbounded information through evolution, in contrast to all ALife simulations to date.To be fair you must look at some artificial evolution as long as lifeevolution. And both the M set and all creative set, or subcreative,(UD, UMs, LUMs, but also you and me, even without assuming comp) arelike that in their extensions. Unbounded complexity.The M set is not only self-similar, but all its parts are similarlyself-similar, making all zoom repeated 2, 4, 8, 16, ... times when youdecide to focus on a minibrot.

Would you say that this is an example of compactness?

I had a look at the Wikipedia entry on creative sets, and it didn't make much sense, alas.OK. On the FOAR list, I will do soon, or a bit later, Church thesis,the phi_i and the W_i, and that will give the material to get thecreative sets.Roughly speaking, a creative set is a machine (a recursivelyenumerable set of numbers) who complementary is constructively NOTrecursively enumerable. It is a machine defining a natural sort ofno-machine, capable to refute all attempt done by the machine to makeit into a machine.

`Might it be exactly represented by a non-standard model ala`

`Robinson via Tennenbaum?`

john Myhill will prove that such set are equivalent (in some strongsense) to the universal Turing set (machine).

`This "fact" seems to confirm my suspicion that such as set does`

`have a non-standard model!`

If you remember the recursively enumerable set W_i,, and noting ~W_ifor ( N minus W_i), N = {0, 1, 2, 3, ...}W_u is creative iff there is a computable function F producing, from yand u, for all W_y contained in ~W_u, a number c in ~W_u minus W_y.

`Could you elaborate on an example of this in non-math terms? You`

`definition reminds me of "creativity" as defined by Bart Kosko in one of`

`his book /Neural networks and fuzzy systems: a dynamical systems`

`approach to machine intelligence, Volume 1/`

http://books.google.com/books?id=fbJQAAAAMAAJ&q=creative#search_anchor

The attempt W_y of making ~W_u into a machine y, has failed, has nowwe are given a counterexample, the number c, which is in ~W_u, and yetnot capture by W_y.

`Note how the number c is defined after the fact of the attempt!`

`This is close to my thought that "truth" (as a true statement) is an a`

`posteriori and not an a priori.`

~W_u is called a productive set. It is a NON recursively enumerableset (a non machine), but constructively so, as you can build atransfinite approximation of it, in a communicable way, up toomega_1^CK, (Church Kleene first non constructive ordinal), and beyond(but at the machine risk and peril).

`This is getting very close to what I am trying to do with my`

`attempt to weaken Tennenbaum's theorem!!!!! Is the approximation exactly`

`representable by a finite integer?`

Truth, Arithmetical Truth, the set V of the Gödel numbers of the truepropositions, in (N, +, *) is a typical produce set. Gödel firsttheorem is constructive: for all theories (recursively enumerbalesets) attempting to get V, the Gödel diagonalization will provide aGodel number of a proposition true but not in the theory (the set oftheorems of the theory). N minus Truth is also productive, Truthcannot be isomorphic to the complementary of a creative machine.Creative machine, or universal machine are sigma_1 complete, Truth issigma_i complete for all i!Note that I identify here a number or a machine, and its set ofbehaviors (input-output) or beliefs/theorems.

`OK, is this machine something that can be represented by a finite`

`Boolean Algebra?`

More on this on FOAR asap :)

I am eager to read your posts! -- Onward! Stephen -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.