- define "complexity" as something like the total number of parts of a system and the total number of connections between such parts;
- stipulate that the purported increase in complexity over time applies only to entire ecosystems (i.e., is an assertion concerning the increase in average complexity of systems within an ecosystem);
- further stipulate that the change is a stochastic process, meaning that ecosystem complexity fluctuates in the short term and only generally increases, usually, and in an uneven manner, over the long term.
On the basis of that, then, a useful approach to making the case for directed change is the temporal cross-section, whereby we consider an entire ecology at long intervals of time and try to assess the complexity level of organisms or systems within that ecology. And it seems reasonably clear, at least in a quick examination of the history of both biological and cultural systems, that such cross-sections do in fact display increasing complexity. (We could also note that the universe itself appears to display a certain directedness to its evolution, not simply in an entropic, “running down” sense, though that certainly is happening, but also in a steady increase in heavier, more complex elements over time.)
Without going any further into the dispute at this point, then, I'd like to just make the hypothesis that the phenomenon of directed evolution is real, and ask what could account for it. Gould is at least right to assert that Darwinian natural selection as such does not explain it. It could only do so if complexity in itself somehow conferred greater adaptational advantage upon a system. But while that might be so in particular instance, there are also lots of both reasons and evidence to show that, other things being equal, simplicity wins out over complexity in a straightforward competition. If the phenomenon of a long-term, or “teleological” trend toward complexity is nonetheless real, then other explanations are needed.
One such might be something like a "complexity ratchet". Random fluctuations within an ecology (biological or cultural) will produce systems of varying levels of complexity from moment to moment. But suppose that occasionally one of the more complex systems takes on a form that’s more stable than others – this would raise the average complexity of the ecosystem as a whole, then, at least as long as the system persisted. And if, very occasionally, that system was in a form that was self-reproducible, then the increased stability would generate an enduring increase in ecological complexity. Which, interestingly, seems very much like what those particular chemical systems known as “life” represent.
Of course, if such a ratchet were to violate the Second Law of Thermodynamics, then it’s not going to work – it would be as illusory as perpetual motion. The usual "out" here is to say that the Second Law really only pertains to closed ecosystems, not necessarily to particular systems or subsystems within those environments. But the real question is simply whether it's possible at all, in a stochastic environment, and within the constraints of the Second Law, for a more "complex" system (as defined above) to be more stable, even to a slight degree, than a less complex one -- if the answer is "yes" (which again I'll assume, for the sake of the hypothesis), then the complexity ratchet becomes a possibility.
(An aside: is "disorder", in the entropic sense, necessarily the opposite of "complexity", in the above sense? Could a closed environment simultaneously become more disordered and more complex? Like a kind of crystallization process? If so, maybe it's not that God created the universe, but that the universe is in the process of creating God, hmm? Or, maybe I should just cut down on the caffeine.)
So assuming that they're possible at all, then we'd expect complexity ratchets to come in all sizes at all times – they would be "fractal", in a sense. But at long intervals – depending on their relative improbability – there would appear major ratchets that provide a floor for a fairly sudden expansion in possible system complexity after that point. A major example of that, of course, as we've seen, would just be the molecular systems we call "life" itself. But now look at the history of life on earth: billions years of simple unicelled packets, and then, fairly suddenly, maybe half a billion years ago, the appearance of a significant increase in complexity – nucleated cells. And after that, the advent of multi-celled forms. It was as though, in stumbling across this invention of an inner, protected wall for the growth of the coding molecule, a new complexity ratchet was attained, which allowed for the proliferation of the enormously more complex machinery underlying developmental biology. This seems to say that eukaryotes were an even larger – even more improbable – step forward in complexity than the relatively simple chemical packets of prokaryotes.
If we describe “life” as the phenomenon of molecularly coded and transmitted complexity, then "culture" could be described as the phenomenon of aurally coded and transmitted social structures -- "language", in other words, could be viewed as a complexity ratchet for animal behavior. Let’s say that such cultural social formations first make their appearance some half million years ago or earlier – then, again, for a relatively long stretch, very little changes. Until, only some 7 to 10 thousand years ago, farming first appeared, and so did writing. Whichever constituted the ratchet -- and another possibility might have been the purely cultural invention of new, surplus-generating religious forms -- it does seem clear that a major advance in social complexity took place in isolated pockets around that time, giving rise to the first urban cultures. And then these persist, in varying forms, spreading slowly and intermittently, but at roughly similar levels of complexity for thousands of years themselves, until about 500 years ago – when we see the first hints of an industrial culture. Was the invention of “science” the ratchet in this case? The emergence of the "bourgeois" class of merchant producers? The appearance of the modern notion of the "individual"? Whatever it was, here again we see a form of social organization at least an order of magnitude more complex then its predecessors, simply in terms, again, of the number of parts and the number of connections between them (communication, transport, velocity).
And what, we might ask, about now? Would the advent of the digital computer, digital information, global networking, etc. be another major complexity ratchet? Perhaps we'll need to include, as parts of the systems under consideration, entities other than those carbon-based ones we've usually focused on....