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

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.


The self is directly related to the Dx = "xx" trick, for me.

The Dx=xx trick is about self-replication. Of course entities with a sense
of the self/other distinction needn't replicate (eg certain robots).

Self-replication and self-reference. And many self-transformation (in fact 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 some universal numbers "grossly" different than you, (the most probable physical world), and with self-reference you reproduce yourself mentally, 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

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 by more and more complex infiltration of their filaments. So the closer you zoom, the more complex the set appears, and is, locally. It is most plausibly a compact, bounded, version of a universal dovetailer.

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 life evolution. And both the M set and all creative set, or subcreative, (UD, UMs, LUMs, but also you and me, even without assuming comp) are like that in their extensions. Unbounded complexity.

The M set is not only self-similar, but all its parts are similarly self-similar, making all zoom repeated 2, 4, 8, 16, ... times when you decide 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 the creative sets.

Roughly speaking, a creative set is a machine (a recursively enumerable set of numbers) who complementary is constructively NOT recursively enumerable. It is a machine defining a natural sort of no-machine, capable to refute all attempt done by the machine to make it 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 strong sense) 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_i for ( N minus W_i), N = {0, 1, 2, 3, ...}

W_u is creative iff there is a computable function F producing, from y and 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/


The attempt W_y of making ~W_u into a machine y, has failed, has now we are given a counterexample, the number c, which is in ~W_u, and yet not 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 enumerable set (a non machine), but constructively so, as you can build a transfinite approximation of it, in a communicable way, up to omega_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 true propositions, in (N, +, *) is a typical produce set. Gödel first theorem is constructive: for all theories (recursively enumerbale sets) attempting to get V, the Gödel diagonalization will provide a Godel number of a proposition true but not in the theory (the set of theorems of the theory). N minus Truth is also productive, Truth cannot be isomorphic to the complementary of a creative machine. Creative machine, or universal machine are sigma_1 complete, Truth is sigma_i complete for all i!

Note that I identify here a number or a machine, and its set of behaviors (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!



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