“To justify its existence, criticism must be partial, passionate, and political, that is to say, written from an exclusive view that opens the widest horizons.”
In reference to an article about economics education, Steve Keen said :
... they use the word "complex" while clearly not understanding its modern meaning
The word "complex" does not have a specific modern meaning. Saying an economist misunderstands the modern meaning complexity is about as meaningful as writing an art review stating an artist misunderstands the modern meaning of complexity, which is to say: not.
In reference to Tony Yates saying Keen was policing heterodox semantics in the use of "complex", Keen goes on to say:
... And it's maths semantics by the way, not economics. Look it up.
I have no idea what Keen means here, because while there are different definitions of "complex" used in mathematics they are either nonsensical in this context or undermine Keen's own work ...
Complex numbers? Obviously not.
Group complexity? Ha ha. No.
Computational complexity? Pretty sure Keen doesn't mean the economy is NP-hard.
Complex dynamics? Does he mean this? Because this is the mathematics definition. What Keen does is actually just dynamical systems (which includes Lorenz attractors) as opposed to complex dynamical systems. Basically, if this is what he means, Keen should leave off the "complex" adjective. However that makes his comment about "complex" self-refuting, and its inclusion a meaningless affectation. Yes, I include complexity. How? By calling them complex dynamical systems instead of just dynamical systems.
Kolmogorov complexity? The definition here is the length of the shortest computer program that reproduces the output. In the context of economics this means that a Kolmogorov complex economy would essentially require simulating the entire economy down to every agent, every firm. In contrast, Keen's approach that says a system of dozens of nonlinear differential equations that can be written down on a few pages can capture the main behaviors of an economy unequivocally demonstrates that by this definition economies are not complex. [As an aside, this is what I mean when I say economic agents are complex.]
Complex adaptive systems? This is not really mathematics, but rather a general collection of ideas. One of those ideas is this:
Complex systems consist of a large number of elements. When the number is relatively small, the behaviour of the elements can often be given a formal description in conventional terms. However, when the number becomes sufficiently large, conventional means (e.g. a system of differential equations) not only become impractical, they also cease to assist in any understanding of the system.
Emphasis in the original. This is a quote from leading complexity theorist Paul Cilliers' Complexity and Postmodernism: Understanding Complex Systems [pdf], and it basically refutes Keen's approach to economics with his Minksy software which consists of differential equations.
* * *
Maybe by the modern definition of complex, Keen just means something like the Facebook setting for relationship status "It's Complicated" (which I used as a title for my piece on exactly this problem, and see also here). Similarly, Keen also appears in the documentary Boom Bust Boom for a few seconds, mentioning money and debt. However, later on the film had someone else say that economics shouldn't be approached like a branch of theoretical physics. If I had to pick an economist who used the most inappropriate physics models, it would be Keen who treats the economy like it's a nonlinear electronic circuit with his Minksy software. It's a very odd juxtaposition. Additionally, like asserting complexity, decrying economics as too physics-like  is another buzzphrase in economics similar to juxtaposition in art (at least in the 90s and 00s).
However with the last complexity definition, you may have noticed the rather jarring appearance of the word "postmodernism" ‒ or at least it might have been more jarring if I hadn't sprinkled this post with references to art criticism, Baudelaire, and juxtaposition.
In reading recent economic criticism, it seems like more and more art criticism ‒ art criticism of a movement falling out of fashion. Noah Smith writes that even the art criticism is becoming predictable:
At this point, blanket critiques of the economics discipline have been standardized to the point where it’s pretty easy to predict how they’ll proceed. Economists will be castigated for their failure to foresee the Great Recession. Some unrealistic assumptions in mainstream macroeconomic models will be mentioned. Economists will be cast as priests of free-market ideology, whose shortcomings will be vigorously asserted. We will be told that economics moves in cycles of fad and fashion. Readers will be reminded that economics deals with humans instead of atoms, making scientific certainty impossible. The piece will end with a call for humility on the part of economists, a more serious consideration of unconventional ideas and reduced prestige for the economics profession.
I had fun reconstructing a loose facsimile of this generic critique out of Baudelaire quotes about art and other things:
In order for the artist to have a world to express he must first be situated in this world ... In art, there is one thing which does not receive sufficient attention. The element which is left to the human will is not nearly so large as people think. ... The priest is an immense being because he makes the crowd believe astonishing things. ... That which is not slightly distorted lacks sensible appeal; from which it follows that irregularity – that is to say, the unexpected, surprise and astonishment, are a essential part and characteristic of beauty. ... An artist is only an artist on condition that he neglects no aspect of his dual nature. ... What is art? Prostitution.
You really only have to read "human will" as "rational agents" and "astonishing" with a negative connotation to pretty much capture it. But the real point here is that these critiques are not scientific ones based on technical arguments and empirical testing. They are critiques of "realism" or the "use of math". Realism is subjective -- it depends on scope and scale of the theory. Math is a tool. The critiques of mathematics in economics play out like critiques of a photographer's use of light, or an artist's use of mixed media. There's something wrong with it in an aesthetic sense, not a technical one (see more here and here).
The terms used in economics critiques take on lives of their own much like how the terms in art criticism take on lives of their own. "Complexity" means something different in economic criticism than it does in science (or even in economic theory). Phrases like "physics envy" and calling for "pluralism" just mean "wrong using math" and "listen to me".
And like many art critics, economics critics don't produce a lot of successful results themselves.
 Each of these quotes can be obtained from Twitter at this link.
 Ironically, the foremost research institute for complex adaptive systems (Santa Fe) was founded by (and is staffed by) several physicists so the the complaint that economics is too physics-like yet doesn't properly understand complexity is ... an odd juxtaposition.