On 17 Oct 2012, at 23:57, Russell Standish wrote:
On Wed, Oct 17, 2012 at 07:19:09PM +0200, 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:
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).
Yes - but self-organisation is not really about
self-reference either. Classic self-organised systems are things
like Per
Bak's sandpile, and Benard cells.
OK, that's different, but probably related, although a proof of this
might be difficult.
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.
OK - in that sense, the Mandlebrot set is as creative.
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.
Thanks - I'll dig into this topic later. It sounds
interesting. Unfortunately, I don't time today :(.
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, ...}
No I don't. Could you please refresh my memory? This is probably why I
found the Wikipedia page confusing, it introduced a set W_i as an
arbitrary subset of N, but if it is some special set instead, then
maybe it might make more sense.
What follows seems straight out of the Wikipedia page. But we'd better
get the W_i confusion sorted first...
The W_i are the domain of the phi_i. phi_i is the partial computable
function from N to N described by the ith code of such a function
written in a fixed universal system once and for all (say Fortran, or
Lisp, or Arithmetic, or Game Of Life, etc.).
Then it can be show that all the W_i are also the range of total
computable functions, which makes them into the recursively enumerable
subsets of N. So W_i are NOT arbitrary subset of N, but the one we
can generate mechanically. I will probably prove this on FOAR, soon,
or probably later. I am also rather busy, and now my server does not
send the mails ...
Note that if both W_i and ~W_i are recursively enumerable then W_i is
recursive, decidable.
Best,
Bruno
http://iridia.ulb.ac.be/~marchal/
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