Hi Bruno Marchal
I have to confess that I have been of two minds
on the subject of creation of structure and life:
a) creation of structure by an intelligent (meaning living) body or self
(which requires subjectivity)
b) the act of structure creation without a self (and hence is objective)
or life which would apply to comp and it looks like Peirce's categories
and also self-organizing systems. This would be sumulated life.
Roger Clough, [email protected]
10/18/2012
"Forever is a long time, especially near the end." -Woody Allen
----- Receiving the following content -----
From: Bruno Marchal
Receiver: everything-list
Time: 2012-10-17, 13:19:09
Subject: Re: Computational Autopoetics 1
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 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.
>
>>
>>
>>
>>>
>>> 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 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.
>
> 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.
>
> 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.
john Myhill will prove that such set are equivalent (in some strong
sense) to the universal Turing set (machine).
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.
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.
~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).
Truth, Arithmetical Truth, the set V of the G?el numbers of the true
propositions, in (N, +, *) is a typical produce set. G?el first
theorem is constructive: for all theories (recursively enumerbale
sets) attempting to get V, the G?el 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.
More on this on FOAR asap :)
Bruno
http://iridia.ulb.ac.be/~marchal/
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