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.

> >>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...


-- 

----------------------------------------------------------------------------
Prof Russell Standish                  Phone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Professor of Mathematics      hpco...@hpcoders.com.au
University of New South Wales          http://www.hpcoders.com.au
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