REPLY Getting a Good Problem Statement (SD6573)

[SDMAIL Ken Lloyd]

Posted by  "Ken Lloyd" <kalloyd at wattsys.com>

Jack,

What if the problem in the problem statement is an ill-posed problem?  Here,
I use ill-posed in the mathematical sense, meaning that at the time the
problem statement is created, it is not "known" whether a, or any, solution
to the problem exists; whether the solution is unique; or whether the
solution model continuously relates to data measurements.

This is the curse and error of determinism to the solution of dynamic
problems, which says: If we are smart, and work hard, we will find the ONE
TRUE RIGHT answer to our problem. It doesn't work that way.

This is my concern with many academics and esp. mathematicians.  They have
taught their students how to arrive at answers to which they already know an
answer exists, and may even know that answer.  Thus, the problem statement
is at equilibrium - there is no "Arrow of Time" (AOT) and the problem is
reversible, meaning that if you played the solution functor backward (in
time), you would arrive at the problem statement. It has to be this way,
because the problem statement was created before the time the exam was
taken.  But this doesn't often happen in real dynamical systems.  The
problems are NOT at equilibrium, either internally, or with their temporal,
environmental contexts, and the solutions are ensembles not trajectories.
AOT means the path back is not the path you took, and probably does not
exist at all any more. For example, one cannot un-bomb a building and
un-kill 3 people.

Then what of the offered heuristics? Wasn't it Jack Ring that once offered
"Experience is a bad teacher, because it gives the exam first and the lesson
later?"

I also believe that to state Forrester champions only descriptive modeling
as incomplete.  However, I also believe that control theory, while very
illuminating is also incomplete because of directionality (from both AOT and
ensembles [or vector fields & bundles]) and that SD is more complex than
merely circular feedback with bias. This is the reason I champion
formalizing non-equilibrium dynamics as the paradigm for understanding
system dynamics. It is conceptually reachable and now computationally
feasible to couple modeling with probabilistically superposed simulation in
an evolutionary context, with emergence.

My apologies to William of Occam.  I tried, but it didn't work.  

=============================
Kenneth A. Lloyd
CEO and Director of Systems Science
Watt Systems Technologies Inc.
Albuquerque, NM USA
Posted by  "Ken Lloyd" <kalloyd at wattsys.com>
posting date  Tue, 4 Sep 2007 16:53:20 -0600