Quite easy to mark

post to FRIAM 1/20/07

marking a map to help navigating the sysems territory

One of the things that Roger’s comments bring out about the discontinuities you find in tracing organism growth (epigenesis) is the question of markers. Normal single growth curves are famous for representing huge changes and having almost no markers at all to signify what’s really happening.

There really are only two places on them that are easy to mark, the upward and downward inflection points (¸¸ .·|´ ¯ and ¯`|·. ¸¸ respectively). The origins and endings of the curves seem completely disguised by the smallness of events at their tails.

Elsewhere in the history of their changes the wide distribution of seemingly unconnected but well orchestrated events makes it very hard to single out any particular thing for significance. The inflection points, however, can be made quite mathematically precise, and do approximately correspond to matching major changes in what’s going on.

One of several ways to say why these points are mathematically precise (despite within the margins or error the curve is locally a straight line at that point) is because it marks where the changes before and after switch from being in proportion to an asymptote in the past, to being in proportion an asymptote in the future. Growth systems behave as if their explosive growth is spent looking to where they’re coming from and then switch to looking to where they’re going to, an orientation backward changing to an orientation forward. This bears out in studying the feedbacks.

In most kinds of growth systems there is demonstrably no ‘looking’ going on, but people need images to help them understand things and I don’t think representing what a system is responding to as ‘looking’ is completely inaccurate. It’s also necessary to use simplified terms when trying to discuss the process switches of such a wide range of different kinds of behaviors.

A third reason to be a little general about it is that we actually don’t seem to have any good general models for describing growth system mechanisms. There’s a fundamental mismatch between what is physically happening and how we tend to represent it, with fixed rules of various kinds. Growth systems are physically a process of changing structures. That’s why I prefer to use models to just refer to the physical systems, and try to avoid using models to represent them.

Picking up on one major popular conversation about changing systems, I think a useful general statement of what happens at the inflection point is the switch toward sustainability. The loops of the system switch from increasing instability in their design to increasing stability, changing from explosion toward homeostasis.

When you borrow other people’s words for new meanings there’s usually some trouble, but I think this one does largely coincide with both the technical meaning of the term, ‘possible to be sustained’ and it’s widespread modern usage referring to the transformation of our life support systems to be compatible with both the fact and spirit of living on earth.

Up to the inflection point it’s often quite uncertain from the behavior that there will ever be a turning point. Afterward it’s usually clear whether you have a stable change to a new steady state or just a flash in the pan that quickly decays. For some the trigger for the switch is external, for others it’s internal, an amazing difference that opens another rich new field of study.

Our maps of systems, mine being just a bump on a curve, are very inadequate representations of what’s happening in the physical systems. We can use them as exploration guides though, pointing back to the physical subject when and where there are interesting things to find.


Phil Henshaw ¸¸¸¸.·´ ¯ `·.¸¸¸¸



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