The connection I drew is of people who have a strong ideological worldview that simple mechanisms would solve things, if only everyone agreed; two examples are the "free market will solve everything" right and the "going back to nature will solve everything" left.

If you think proponents of the "free market" think it's simple, you don't understand them. Or it. It's precisely because it's so complex that managing it is prone to error.

I don't actually understand why the same people (in general) will assert ecologies are extremely complex and we shouldn't meddle without being very careful to understand the effects, and at the same time think that the market is manageable from the top down without unintended consequences on the same order as the intended ones.

That's a view I can certainly buy, that intervention must be careful and is error-prone--- perhaps even so error-prone that it's rarely worth doing. In libertarian circles at least, though, I often encounter a much stronger claim. I don't hear people say things like: maybe it'd be great if we could intervene in an ideal world, but alas such interventions are error-prone so we'd better not. Instead, a much stronger claim that no intervention is necessary because the unfettered free market is already at least reasonably close to ideal. This is particularly strong in Rand-influenced areas of the libertarian universe. The explanations are usually some extremely simple version of classical economics, invisible-hand, etc., leading to assertions that the free market efficiently allocates resources, rewards merit, etc.

That's the part that reminds me most of the ecologists: a belief that we're fortunate enough to live in a universe perfectly constructed such that these complex dynamical systems (economies, ecologies), if only we'd stop mucking with them, would live on in magical harmony, aligning with normative notions like "merit" and "balance" and whatnot. I tend to view them both, instead, as difficult to analyze, hugely complex systems filled with all sorts of weird attractors and unstable states, which won't necessarily result in particularly great outcomes whether left alone or not.

In short, I agree that most of the people who claim to know what will happen if you intervene in a market are naive (i.e. unintended consequences are likely), but I also think most of the people who claim to know what will happen in a free market (e.g. that it will reward merit) are also naive. And most libertarians I've met fall into the latter category.

In a comment he mentions that government needs to manage externalities, but this is still a somewhat tenuous connection in my mind. What is the relationship between complexity of civilization and the complexity of the resulting externalities? One might guess that more of one creates more of the other, but I have no evidence.

Moving complexity around isn't eliminating it.

Social Security is vastly simpler than the various schemes proposed to privatize it, for example.

Incorrect solutions are nearly always less complex than their counterparts.

Incorrect according to whom?

If you're going to say "look I just want it that way because that's my ideological bias", that's fine. But don't pretend there's some objective measure involved here.

Social security is unsustainable. It is a solution which will not work unless every attribute but its name is replaced. How is that not an objective enough measure for anyone?

However, social security also has enrollment forced under thread of punishment. Social security has a clear negative impact on free enterprise. Social security embroils the government in private matters for which government's involvement simply limits liberty with no other benefit to social welfare. Social security is less effective than other solutions such as defined contribution retirement packages, IRA, individual savings when coupled with strong community support and a basic welfare program.