I think a discussion of complexity needs to focus on the difference – which occurs at every level – between the things involved and the relationships that can happen between those things. For example, between atoms and the relationships atoms have with each other, which are the basis for forming molecules.
That is, instead of thinking in terms of simpler things (systems) “aggregating” to form larger things, we could imagine the hierarchy in terms of things having relationships, which allow for the formation of more complex kinds of things, that can have more complex relationships, etc.
“Thing” in this context means a structure that lasts over time and continues to be what it is, though it may also change, over time. Things typically have both constant and variable properties.
A “relationship” is something that happens between things, made of specific interactions taking place at a certain times. A relationship between two things can last over time, but only to the extent there is a repetitive pattern in their interactions. The characteristics of relationships are not properties they possesses in themselves, but have to do with the effect these patterned interactions have on the things involved.
When it comes to consciousness, for example – if we look at the brain as a thing, an organ consisting of an aggregate of cells, its complexity is perhaps comparable to other organs. What makes the brain different is the kind of relationships that happen through synaptic connections between neurons. These relationships support a kind of real-time information processing that’s specific to the neural system, which operates at a much higher level of complexity than anything else in the body, or anything else that we know of.
The new kind of “things” that these neural relationships make possible are animals. Whether or not we think of animals as “conscious” is purely a matter of how we like to use that word. But we are not yet at the level of human consciousness.
The kind of simple unity that we indicate with the words “I” and “You” – that we experience and think about as “subjective awareness” – doesn’t emerge out of any characteristic of the neural system, per se, though our brains have obviously evolved to support it. But it can develop only in a certain kind of relationship that can happen between two animals.
So far as we know, this kind of relationship is highly evolved only between humans, though many other animals have relationships with some of the same characteristics. But to the extent we humans learn to talk to each other and think about each other, we also learn to talk to ourselves and think about ourselves. This kind of "internal self-awareness" is not comparable with whatever internal processing may happen in other animals. We can call both "consciousness" if we want to, but we're talking about two different things.
And of course, it's out of this kind of communicative I-You relationship that there arises a whole new hierarchy of “things” like words and ideas and corporations.
I guess my point is that a word like “complexity” doesn’t capture very well the profound differences that can emerge in the hierarchy of systems. At each level, the types of complexity that pertain to things is quite different from the kinds of complexity that can happen in their relationships.
