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TG: Holonomic constraints ('rigidity' is a typical holonomic constraints)
is clearly present in structural organization, such as the skeletal components.
In terms of an organism's functional organization that I was concerned with, I
am imagining that the constraints are largely, or all, non-holonomic, such that
the functional organization could be maximally constrained so that it remains
invariant, even when all dynamics are removed (i.e., the cell frozen).
Even rigidity, as in skeletel structure, is context dependent. It
varies according to the context of time, as in where in life-cycle the
organism happens to be. In human childhood, for example, as bones are rapidly
growing, they are much softer and more flexible than in adulthood. In old age,
they are often brittle. (Perhaps this means that rigidity is also dependent on
the context of health.) In pregnancy, female adults structural rigidity alters
radically near the end of term, due to hormonal action. (This allows the bones
of the pelvic girdle to expand as the baby passes through during delivery. I can
tell you from personal experience, it's very strange to feel all your joints
getting loose during the third trimester!)
It is also not true that all dynamics are removed when cells are
frozen. They are simply slowed down. But frozen cells have a "shelf life", even
when the temperature is maintained.
TG: The interesting thing to me is that the (M,R)-system is a model of an
invariant functional organization, and therefore I further conjecture whether
realizing an (M,R)-system involves realizing a maximally constrained functional
organization?
How do you mean that organisms are "invariant functional
organizations"? Specifically, it's the word "invariant" I want to
understand your meaning of.
(I must also reiterate the need to include the words
"non-holonomically" with "constrained" if context changes the constraint
values. Otherwise the meaning is radically different. A "maximally
constrained system" would have to be a very limited subsystem within a
complex system or else a simple system-- like a
toaster.)
TG: I agree that functional organization cannot be equated, and probably
not even mapped, to structure. That is the "structure-function complementarity"
that he mentions in the paper and which I base my conjecture on. This is why I
say it "would be very difficult to describe in strictly structural terms". (It
may well be impossible, but I don't want to exclude a priori such a
possibility.)
Quite right. However, the structure of living organisms is infinite
in variety, but the organization is the same: It is how we recognize them as
"living organisms". When you kill an organism, its structure can remain
completely intact, but you have destroyed the complex organization.
Similarly, functions in a living organism are not entirely the product of a
relation between structural aspects and other structural aspects. The
functions of blood, for example, are fulfilled in many different ways which
utilize many different means, depending on the evolutionary context of each
species of organism.
It seems to me that the notion of "function" could be viewed as an
exploitation of the degrees of freedom created by the action of non-holonomic
constraints on the system-- either from inside or from outside the organization
(or both, perhaps in various modes of interaction...). It also seems
to me that what would be defined as a non-holonomic constraint on one aspect of
system organization could also simultaneously be playing many other roles within
that organization. Some of the roles may be functions, which are themselves
"non-holonomically constrained"-- perhaps even by the the first function's
activity-- in a closed entailment loop. In other words, one function's
activity creates or impacts the context that determines various
non-holonomic constraint values. Those constraints may or may not serve some
functional value, in turn.
An example would be maintainance of body temperature in a
warm-blooded organism. There are constraints on the range of temperature that
will support continued organization (i.e., keep the organism alive), but those
constraints are different depending on on context... A bear in
hibernation would have different "normals", different ranges, than when it is
not hibernating... Illness or injury changes the context again, which impacts
the temperature constraints. Each of these contextual changes has effects on the
constraint values and, in turn, those effects may have
critical functional properties in the organization of the system. (Fever
and immune system function, perhaps.) Yet, temperature is not a
structural component.
It is worth noting that warm blooded animals have certain survival
benefits and options which are conferred upon them by the ability to maintain a
"constant" internal temperature. At the same time, the need to maintain
that temperature, at whatever ranges and levels the context dictates, can also
be regarded as a non-holonomic constraint on the system.
Judith
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