I can't remember whether you read my paper "On Complexity and
Emergence" in Complexity International a couple of years
ago. Basically, I think you are well on the mark, except I disagree
with you on the issue that once a mechanism is known, the process is
no longer emergent. I think it still is emergent, and explain why in
that paper. 

As to mathematics predicting emergent phenomena, I believe that the
answer is categorically no. Emergent phenomena is a result of a
modelling process - eg what a brain does, not an analytic
process. Mathematics can be used to describe the emergent phenomenon
after it is discovered, but I don't think the discovery process can
really be called mathematics.


> The correspondent with that mystical name touched an interesting problem
> (earlier appearing in Hale's and Tim's posts): emergence.
> Colin Hales:
> > Our main gripe is the issue of emergent behaviour and the >mathematical
> treatment thereof? Yes?<
> (Tim's post see below).
> I have an indecent opinion of this concept: it is "human ignorance".
> Let me explain.
> As long as we cannot qualify the steps in a 'process' leading to the
> "emerged" new, we call it emergence, later we call it process.
> Just look back into the cultural past, how many emergence-mystiques
> (miracles included) changed into regular quotidien processes, simply by
> developing "more" information about them.
> I did not say: "the" information.  Some.
> The world as we know about it, consists of models which the mind
> (who's-ever or what's-ever) was capable to construct at a given level of the
> development.
> The natural systems are unconscionably broader and the undisclosed
> (undetected, or just not included) effects play roles in the processes.
> Reductionism closes her limiting/ed eye on such unwanted and
> ununderstandable side-shows and their mathematical treatment as well, since
> the latter is slanted towards the same level of development as is the
> construction of the models considered.
> Why can we not deduce an emergence from our known preriquisites?
> There are  two sides to the reasons:
> Principally:
> Becuase the happenings in nature (I use the word in its broadest sense, like
> existence, or multiverse) are inductive and by deductive thinking we cannot
> reach an induction.
> Practically:
> By churning reasults from the cut-off parts we included into our model we
> cannot reach 'conclusions' including the "rest of it".
> So we call it emergence with awe.
> In Tim's example the watch is a mechanism, made from just that many parts
> for a designed function included in its manufacturing purpose.
> The cell? similarly a mechanism, but under the influence of more than we can
> calculate. Biology cuts its interest to a domain so far studied and
> discovered. From time to time new information occurs and the image changes.
> Who can predict such "emergences" of the coming centuries in the human
> epistemic enrichment?
> Evolution follows the environmental influences (called pressures) of a wider
> involvement than what our 'present' cognitive inventory can cover . (Any
> 'present' of course).
> All kinds of variations occur instead of repetitions and selectively
> survive.
> So do societal changes in organizations, human and other (biosphere,
> body/health, cosmic history, etc. etc.).
> I wonder if mathematics can 'predict' the outcome of such 'emergences' which
> are subject to unlimited variables unknown and their interchanging
> influential efficiency upon a substrate, the total extent of which is also
> unknown, way beyond (the known limitations of) the model we talk about.
> Of course, a TOE may calculate this, but only a "real" one which includes
> and handles all these (limitless) unknown I/O factors in its organized
> mathematical performance.
> John Mikes
> ----- Original Message -----
> Sent: Sunday, November 24, 2002 4:25 PM
> Subject: emergence
> >
> > hi all. in a recent msg I talked about emergence as
> > a theme for the algorithmic revolution & CH zooms in & comments on that,
> > spurring some more of my thoughts.
> > this is a very tricky idea that I feel I definitely have not wrapped
> > my own brain around, nor has anyone else. but, imho, its a genuinely
> > new idea. "emergence" as a buzzword does seem to
> > be a key element of a new TOE & the algorithmic revolution.
> >
> >
> > flash: "emergence" is the opposite of reductionism. just as
> > the 20th century and most of all prior science is about
> > reductionism, we can now study emergence. perhaps that
> > will be a key theme of 21st century science, physics, etc.
> > the algorithm/computer is the breakthrough new tool that allows
> > us to study emergence.
> >
> > emergence <=> reductionism are not mutually exclusive.
> > its a feedback loop, a dichotomy, a bohrian complementarity.
> > the forest versus the trees.
> > mathematics underlies both, but in a different sense. the approaches
> > & techniques are different. emergence tends to be a more qualitative
> > than quantitative picture, rules or equations that one can write down
> > but not so easily derive from the basic principles of the
> > system.
> >
> > also, the clockwork universe theme seems to encourage reductionism.
> > whereas maybe the algorithmical metaphor encourages "emergencism".
> >
> > what is emergence? its a very loaded word. we all pretty much
> > feel we understand "reductionism" probably, but emergence
> > is a new concept. I would argue its being defined as we speak
> > & that science is coming to grips with an accurate definition.
> > perhaps people here will contribute to that definition.
> >
> >
> > my favorite examples of emergence that Ive noticed recently
> > & can expand on if there is interest.
> >
> > - I have a web site that catalogs over 4000 known gliders for
> > the game of life. **breathtaking**. can you predict these given
> > the life rules? or how about, find a theory that predicts
> > the gliders from a given set of rules?? this ties in with
> > a brilliant proof that rule 110 is a universal TM, mentioned
> > in wolframs book, which is very much oriented around glider
> > physics of the rule.
> >
> > - oscillons. emergent behavior from many particles. a picture
> > is worth a thousand words. check em out. still under the radar
> > of just about everyone, but a quite exquisitely beautiful
> > example. I believe it will be shown to predict all particle
> > dynamics in the not-too-distant future.
> >
> > - fractals. another good metaphor for emergence. who would
> > predict the equation z <- z^2 + c could lead to such incredible
> > artwork & tapestries. cosmic.
> >
> > - robotics. imagine the aibo software, and then how that
> > software animates the bot. and imagine putting aibos together.
> > the behavior is emergent, unpredictable, intelligent, dynamic.
> >
> > - the cyberspace web. thriving, pulsing, growing, changing,
> > constantly. all built out of basic building blocks like HTML,
> > HTTP, apache servers, microsoft, whatever.
> >
> > - biology. ecosystems. parasites <=> hosts. predator <=> prey
> > etcetera. biologists are just now starting to get an idea
> > of how the whole fabric is woven together. a zillion interactions.
> > unexpected findings.
> >
> > - graph theory is now starting to study "small world graphs" which
> > have many extraordinary properties entailing emergence ("six degrees
> > of separation"). several new books on the subject.
> > a buzzword in the making.
> >
> >
> > and so on!! so I am out of ideas at the moment
> > until someone else says something else..
> >

A/Prof Russell Standish                  Director
High Performance Computing Support Unit, Phone 9385 6967, 8308 3119 (mobile)
UNSW SYDNEY 2052                         Fax   9385 6965, 0425 253119 (")
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