Re: Maximally constrained

[Tim Gwinn <***>]

> HP: What I call informational or memory constraints are what
> Rosen calls programmable controls. He says they restore degrees
> of freedom. I would say the degrees of freedom were there in the
> configuration space, but not available to the dynamical motion
> without explicit specification. Rosen says, and I agree, that the
> control parameters amount to ?alternative descriptions of the
> constraints themselves.? It is because of these alternative
> descriptions that I call them informational. Memory structures
> themselves are fixed and therefore holonomic, but reading and
> writing require nonholonomic constraints. One cannot function
> without the other.
>
> My argument is that there are no more informational constraints
> than necessary, because they can arise only by costly natural
> selection. It is just the informational constraints (the genetic
> programs) that describe the nonholonomic constraints (the
> rate-controlling enzymes). There are no more enzymes than
> necessary to metabolize and replicate, leaving great plasticity
> in the available dynamics of organisms. That is why I don?t see
> how to interpret Rosen?s maximal nonholonomic constraint
> condition in a consistent way.

Ahhh, ok, "informational constraints" = "control parameters"? Then it seems
to me that to say that a system has a minimum number of such informational
constraints can also be restated as: 'the dimensionality of the parameter
space is as small as possible to effect the desired system behavior', or
perhaps....given the local nature of the nonholonomic constraint
relationships and the time-dependent nature of these parameters (Rosen's Eq.
6):  'the dimensionality of the parameter space at any given time t is as
small as possible'. Does that sound right?

This seems like it would be compatible with Rosen's maximally constrained
system. Indeed, for the control parameters to actually BE control
parameters, there must be non-holonomic constraints for which they can serve
AS control parameters. It strikes me that given a system with N
non-holonomic constraints, where N is the minimum number required to make
all velocities dependent upon configuration, that it would follow that for
that system there would also exist some minimum number M of control
parameters for those N nonholonomic constraints which would be required to
restore degrees-of-freedom (e.g., range of behaviors or "plasticity") to the
system in a controlled manner (that is, without breaking the constraints).
It seems to me that Rosen is focusing on N and you are focusing on M. Both
would be necessary in producing the desired system behavior.

Regards,
Tim