easy to mark

[phil henshaw]

how to mark a map help navigating a territory
 
One of the things that Roger's comments about the discontinuities you
find in tracing organism growth (epigenesis) brings out 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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e-mail: pfh at synapse9.com          
explorations: www.synapse9.com <http://www.synapse9.com/>    
 
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