Irreducibility: Weak and Strong
Conversation, life, and the global order
Irreducibility is arguably the main theme of complexity science. Like so many of the terms invoked in this context, it is cast in the negative: something is irreducible if it can not be reduced.1 2
So what does it mean that something can be reduced? Simply, that you can study all the parts separately, without seeing how they relate or interact with one another, and you in principle will know everything you need to to understand the behavior of the total system. The behaviors of the parts SUM. They’re just “added together”, without any structure.3 You won’t lose any information when you break it apart.
So when we say something is irreducible we mean that if we take it apart and try to study the parts separately, we will lose something. Not necessarily everything, but something. The parts don’t just SUM. There is structure, there are relations, organization.
Irreducibility is in general the case for systems we encounter in the “real world”. They are highly organized and structured. Irreducibility is everywhere. When we dismember, we destroy.
Reductionist science has assumed that reducibility is the general case, with some irreducible special cases here and there4. This assumption has taken on the mantle of “self-evident”. But it is not self-evident, it is in fact wrong.
To take complexity seriously really amounts to taking irreducibility seriously — as a general feature of the world — and recognize that only special circumstances grant any degree of reducibility. Somewhat disappointingly perhaps, irreducibility is not something exotic. It only seems exotic because we have become so accustomed to seeing wrongly.
Part of the tendency to see irreducibility as something special comes from the fact that there are many ways to be irreducible, and so the things that are irreducible look quite particular, not necessarily alike one another in their structure and organization. Whereas there is only one way to be reducible, and that is to lack any internal structure.
With that, I want to draw a distinction between two different kinds of irreducibility which I will call weak and strong irreducibility.
With weak irreducibility it is not so much a system that is irreducible, but rather some behavior(s) of a system is. Take for example a conversation between two people. When they are together talking back-and-forth, there is a behavior that is a property of the dyad proper. If they walked away from one another, and each continued carrying on a half of a conversation we would rightly say they are crazy.5
A whole conversation does not come from two half-conversations. There is no such thing as a half-conversation!6 I repeat: the behaviors do not SUM. The conversation emerges as a whole out of two people interacting with one another directly. It is an irreducible behavior.7
The thing I’d like you to note is this: when the two people walk away from the conversation, the behavior (“the conversation”) is destroyed, but the people are intact.
Because they are no longer interacting, the behavior we call “conversation” ceases to be; but the parts that made up the system do not cease to be. They persist beyond this irreducible conversation. They can disconnect, and perhaps will reconnect at a later time, generating more conversation. The two-person conversation system is weakly irreducible.
When we observe strong irreducibility it is not just a behavior or a property that is irreducible, but rather the system itself.
Unlike the two people in conversation, this kind of a system can’t come apart and then go back together again. It is the proverbial Humpty Dumpty system. Humpty broke apart, and there was nothing that could be done to put him back toegther.
A strongly irreducible system can’t ever go back together because when the parts are separate they don’t just do something different like the people do who walk away form a conversation — instead they rapidly decay and then cease to exist.
Organisms are such strongly irreducible systems. The parts of your body don’t merely depend on one another in the sense that they would behave differently if they were separated — they would not exist if they were separated! The mark of life.
[[[ Note for especially interested readers. Can be skipped:
There are difficulties in constructing models of strongly irreducible systems. Standard modeling paradigms don’t deal well with the passage out of existence of entities. Physical models invoke a state space which directly implies what exists in the universe of the model: the things that exist are the things whose states are represented in the state space. These things can change states, get rearranged and shuffled around, but nothing really goes away.
There are of course attempts at building such models. Some have made computational models of autopoietic organization for instance, but even in these models the notion of “existence” is something that is ultimately an interpretation of the observer of the model — the only thing that really happens in the model itself amounts to state changes among pre-indexed entities which are asserted by the model-maker.
What to be
While strong irreducibility is more fascinating to ponder, I don’t want to give the impression that it is necessarily a better thing. The failure mode of a strongly irreducible system is system-wide disintegration. It’s nice to be able to walk away from a conversation (relatively) intact.
Consider what kind of a global society we are making. A weakly irreducible globe would be one where we could interact, trade, prosper more fruitfully together, but in which we could walk away if we needed to. Disconnect for a bit, and remain intact. Reconnect later and
Of course, the global order we are seeing is not weakly irreducible, but strongly. We are increasingly having not just our behaviors, but our existence depending on the integrity of all other parts of the system. We can’t disconnect, we can’t walk away.
We used to be able to. We should remember how — for everyone’s sake.
More commonly we hear about “emergence” and “emergent properties”, but I think irreducibility focuses our attention more clearly; anyway, this is “mere semantics”. The fact that “emergence” is used as both a verb and a noun does not help matters.
A few other terms closely related with the study of complexity that are cast in the negative: Nonlinear, Nonergodic, Nondeterministic, Nonstationary, Irreversible, Noncommutative, Nonisolated, Asymmetric. Generically, there are man more ways to be NOT something, than to be something.
“Summing” amounts to a structureless aggregation. It’s like throwing things in a bag together, with no order or particular relationship between them.
They often qualify further: “Maybe. Likely just an illusion, an epiphenomenon”.
Talking to oneself is an activity distinct form conversation. Nice try! Maybe you’re just nuts.
Of course there is the phenomenon of someone “talking at you” — but this is absolutely not even CLOSE to half a conversation. It is an anti-conversation.
There is a heuristic for spotting irreducible behaviors: do the parts act differently when they are in contact versus when they are not? We often speak of the behavior of the “whole” having irreducible/emergent properties, but it follows that the behavior of the “parts” must also be modulated depending on whether they are in isolation or in contact with other agents.ge