Registered: Oct 2003
The Elusive Edge
While I do do bursts of detailed experiments from time to time, my overwhelming interest is in big picture questions. From that perspective, it was obvious by the late 1980s that the edge of chaos-border of order was where anything interesting happens, thanks in a large part to Stephen Wolfram's identification of Class 4 cellular automata.
Then over a decade, the prevailing wisdom in the complex systems community drifted to the point of regarding that edge/border as at best elusive and at worst unimportant. This retreat has always seemed wrong to me, to the point where I put an essay about it, Beating the Retreat on my Memes site. (Link updated following site reorganisation.)
I don't want to revisit much of that essay here, save for drawing attention to one point which I now see as possibly the heart of the issue:
While Class 1 through 4 processes are readily recognised, there are no Class 4 outcomes. Class 1/2 have regular/cyclic/nested outcomes. Class 3 has random outcomes. Class 4 can exhibit either kind of outcome, so the fact that a process is Class 4 cannot be determined from an outcome in isolation.
Now that the specific experiments I did with "Life in a Tube" are several months behind me, I see that the main thing that kept my attention through a sizable survey were the occasional instances where it did not become clear for many thousands of generations as to whether the outcome would be cyclic/nested or random. (For those who need to know, these experiments were done using Andrew Trevorrow's excellent LifeLab for Macintosh which allows you to run Conway's Life (and other 1D/2D CAs) on an arbitrary grid. Setting Options->Join Edges and using Edit->Tile With Selection makes it easy to "roll out" a few copies of a narrow cylindrical Life world of arbitrary (small) circumference. Seeding a Tube with a single row (circumference) of live cells (superstring) plus some arbitrary thing else produces a vast range of outcomes.)
Those instances whose outcome was not determined for many thousands of generations built up complex structures which finished up supporting very long cycles or what I came to call "metabolic" cycles where a network of "reactions" included at least one apparently random interaction (at the active boundary) and consequently produced an outcome with a random component. The long cycles could arise at any stage provided a certain "phase change" had not previously occurred at the active edge, without which an "ice breaker" configuration could arise at any time at the edge and thereafter propagate at C leaving an outcome with period 2**n for n often reasonably large (> 10). (There will be pictures and a lot more explanation when I finally get around to putting up a Life in a Tube page.)
For now my concern is just to emphasise that, having had more than a year to digest NKS from an extreme generalist perspective, that there is a lot more to be gained by going back to the edge of chaos/border of order (Class 4) and looking harder armed with ever improving tools and understanding.
I became particularly concerned about this after wading through a self published manuscript of a well intentioned and credentialed friend of a (deceased) friend who called on the Principle of Computational Equivalence to support his claim that the "internal" world of a human is equivalent (in complexity) to the universe. The trouble is I do understand all too well where he is coming from and even see that there is a kind of correspondence between mind and world, but run into problems where he extends that into a claim that the social is inherently less than the individual. Such a view collides head on with my own view that we should grant our social structures ethical status as representatives of the (possible) future.
Beyond returning focus and adding legitimacy to the field, I now see that the most useful idea to come out of NKS is the likely role of Class 3 randomness in underpinning the resilience that is such a pervasive feature of the world we find ourselves is (but not of our simple models of that world). While it was not the way that Wolfram did most of his research, the focus on PCE and universality is likely to just serve to invite more effort to be invested on the kind of unproductive couplings of simple mechanisms with highly engineered data which have too often dominated the field (just check any collection of Life patterns). If our ultimate goal is to improve our understanding of the natural universe (physical, biological and social) we should make sure we are looking for both mechanisms and data which have a prospect of a believable (pre-)history. The evidence I see points to Class 4 as the place to look for this.
Last edited by Tony Smith on 11-04-2004 at 09:33 AM
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