The bead game is underdevelopment, however part of the function of the game comes from clicking the forward and back links above and from game players sending in Remarks.

Viable Systems

I would like for us to think about Peter's note in the context that he and I developed, in part, many years ago. I liken and contrast his case to one of my favorite pragmatic cases: the sustainability of many patients with chronic, developing diseases by successful medical practice at a hospital (e.g., an aids treatment clinic).

Play production exemplifies working cooperatively to create something new and viable as an entertaining and dynamical art form. Aids clinic work exemplifies efforts to prevent the creeping annihilation of a viable system that has become unable to sustain itself.

In examining these two cases, we want to bring our attention to bear on the necessary role nested contexts creation-annihilation operators which transact business, not only at the same level, but across levels as well. I believe the future of nonlinear complex system studies will ultimately hinge on our ability to appreciate and understand the principles of viability and sustainability of the nested boundary conditions where the context of the system, internal or external, is undergoing nonlinear development or deterioration.

To be successful, the required dynamical treatment practices (e.g., play production or medical practice) must find a way to sustain the viability of the intentional system when the context-conditioned variability is constantly threatening to destroy its supporting boundary conditions which are nested over several levels.

The dynamics of treatment aimed at supporting the requisite nonholonomic boundary conditions is in strict complementarity with the dynamical holonomy of "laws" of treatment applied directly to the system. The former are the cascading constraints of "open, cross-scale" transactions which force changes of the nested system's "control" laws governing its "closed, same scale" interactions. I call this source of context-conditioned variability "situational dynamics" in order to force our focus on the system's context rather than the system's intentional dynamics alone.

Let me elaborate: The context of ordinary dynamics is parameter dynamics, and the context of parameter dynamics is geometrodynamics, and the latter's context is, of course, topological. The requisite boundary conditions for a viable system at each level are sustained by the dynamics at the deeper level.

One might ask what underlies topological dynamics? The only answer possible is a dynamical logic of creation-annihilation operators whose effects leach upward across scales, from bottom to the top, infecting the same scale dynamics at each level with an undeniable, nonholonomic (nonintegrable) situational dynamics. Each level of higher boundary conditions are altered by the "leaching" of effects from below so that at the top, the space-time dynamics of the manifest system either suffer or benefit.

(NOTE: By "system" here we mean ALL of the people involved in producing the play--production and design team, actors and audience, etc.; or ALL the people in aids treatment--patients, doctors, nurses, lab technicians, family, friends, etc.)

The viability of the system, or lack thereof, depends on these nonlinear cross-scale interactions that both modify and are modified by the interactions at each given level. Crudely, imagine an elevator ascending a building where at each floor designated experts get on and off so that at the top floor a viable team (a coalition of functions) has been assembled to do a given job. Miss a floor or pick up the wrong people (which displaces the room for the right people), and the effective treatment afforded at the top floor (the coalition) needed to sustain viability will be infirmed due to lack of integrity.

Of course, the experts across floors are the sources of constraint at each level of nested boundary conditions, and the elevator a simplistic reference to the dynamical transaction of business across levels. Getting on and off refer to creation and annihilation operations that alter the constraints. Conservation of integrity is afforded by the right action at each floor--that is, the proper management of the available degrees of freedom.

The mathematical model for this multilevel approach is gauge field theory, where the gauge freedom of the gauge transformation must keep invariant the integrity of the resultant treatment team that dynamically accrues over levels. Hence "integrity of treatment" over the dynamical transactions is the required conservation of a generalized action, termed "sustainability.

"This simplistic and only partially described scheme expresses only the nonlinearity leaching up as a cascade of constraint from one level to another.

It does not incorporate the true differences of each level (i.e., of being logical, topological, geometrical, kinematical, dynamical). It is fashioned crudely from a model of the cerebellum that Endre Kadar and I have published a note on, and therefore expresses only one of many factors that are sources of constraint and complexity in freedom to create, annihilate, and dynamically interact in the ways mentioned.

Peter and I tried to say something like this in our chapter in Haken's synergetics of cognition book some time ago. There, as I recall, Peter contributed the notion of same-scale versus cross-scale interaction/transactions while I contribute the notion of the coalitional interpretation of Newton's "action-reaction" law generalized from same-scale to cross-scale actions.