Constraints: Without and Within

A very useful way of characterizing the behavior of a system is in terms of its constraints. This yields an entire spectrum of “looseness” or “tightness” a system can display without falling into overly-coarse categories like totally “determined” or completely “free”.

When we perform an information theoretic analysis on some system, this is where we start: we ask, “which behaviors seem possible in principle, but are not observed as actualities in practice?”

For instance, say we have two lightbulbs. Each bulb can be ON or OFF at any time. If we consider our “system” to be composed of these two bulbs, we could extrapolate the space of all possible system states. There are four: (1) ON/ON, (2) ON/OFF, (3) OFF/ON, and (4) OFF/OFF.

Now suppose we observe this lightbulbs system behaving however it does, and we notice that despite there being four states in principle, we only ever observe two of them, say, ON/ON and OFF/OFF. The discrepancy between the set of (what appear to be) four possible states and the set of two actualized states reveals the constraint. In this case we could say there is a constraint that prevents the two lightbulbs from being in different states from one another: the are either both on or both off.

In this view a constraint is something that is merely descriptive. We observe in the example above that effectively the whole system has two states, not four, but from this alone we can’t say anything about why that is.

In colloquial language we often think of constraints as something imposed from the outside. The prisoner is constrained by the cell. In principle a person could be anywhere, but when constrained by a prison cell, their actual locations form a much smaller set.

There is a very different and crucially important form of constraint that is not imposed from the outside: self-constraint.

¹

The living world is manifest in a dance between order and disorder, and order demands constraint. For a harmonious world, it has to be the right kind of order. Order per se is not good, and it can be quite bad. The order of slavery, is not good. The order of large-scale conflict, is not good. The order of industrial agriculture, is not good. The order of society as machine, is not good.

In all of these pathological orders, we find a commonality: externally imposed constraint. These are not instances of self-constraint, but rather instances of the organic freedom inherent in the agents of a system being overridden by force.

Order can form otherwise: by the mutual coming together of agents in a voluntary way such that they constrain themselves to form living patterns. This does not guarantee goodness, but it is necessary for it.

In Christian theology, evil enters this world through the free will of man. For reasons I will not claim to comprehend, God determined that this is a necessary cost for the possibility of Good. If we were compelled to “good”, it would not really be Good. It must be chosen, it must be achieved through self-constraint.

And, in a nearly-miraculous way, when we self-constrain the possible, such that we manifest a set of particular actuals, we awaken new possibilities that were hitherto unseen and inaccessible.

We find more by choosing less.

1. I think it is no coincidence that when we study complexity we repeatedly encounter the notion of self: e.g. self-organization, auto-poiesis, self-control, and here I propose self-constraint.