Consider a victimist alternative physicist who has literally made a career out of his nonsensical proposed alternatives to key theories in physics - such as quantum mechanics, relativity, or string theory.
Important sciences such as theoretical physics are critical enough so that they can apparently afford to feed a few 100% horseleeches.
But back to the ADM theory.
In this neoclassical setup, prices are assigned not only to particular products but to particular products at arbitrary locations and different moments in the future. The price space is highly multi-dimensional.
Lee Smolin begins with some universal promotion of alternative theories in general that he essentially copies from his victimist physics papers. A discussion of the ADM theory follows; it makes less sense than the text on Wikipedia. Very soon, he offers you absurd claims, e.g. that neoclassical economics knows no mechanisms that drive the system towards the equilibrium (Smolin, middle of page 4/41).
Well, the classical mechanism doing this particular thing is very simple. If the current price is lower than the (future) equilibrium price, demand exceeds the supply and the prices go up. As they go up, the demand is decreasing and the production is increasing, helping to reach the equilibrium point.
Later in the paper, on page 8, Smolin seems to be aware of this mechanism. On that page, he repeats these well-known things with some colorful words (like "making people happier"), suggesting that he was perhaps the father of classical economics.
Landscape in economics
Smolin tries to import two physics buzzwords, "landscape" and "gauge invariance", to economics. In doing so, he reveals that he completely misunderstands these basic notions in physics, too.
Concerning the "landscape problem", he claims that much like string theory, economics has a lot of "equilibrium points". That's simply a wrong analogy. What we have in economics is a lot of possible configurations. But none of them is static.
These configurations of prices are analogous to points in the configuration space or phase space in physics (depending on the degrees of freedom you include). But the landscape in string theory is composed out of vacua which are perfectly stationary states.
In any useful enough application of economics, one always works in some vicinity of an equilibrium. That would be analogous to knowing the right compactification of string theory. There may exist "very different equilibria" but they're "very far on the configuration space" which also implies that they can't become relevant for the dynamics in a near future. So the degeneracy of the equilibrium points - certainly the large degeneracy - is irrelevant for any realistic enough homework problem in economics. After all, configurations in economics can be viewed as special examples of those in physics, and we know that there is no "additional" exponentially degeneracy of the vacua coming from non-fundamental laws of physics.
What Smolin misunderstands even more is that we almost always have to work with effective field theories that only concentrate on some dynamical degrees of freedom, corresponding to an interval of time scales.
In this approximation, all faster degrees of freedom (than this interval) are assumed to take on the equilibrium values instantly (like the relative electron-proton wave functions in a Born-Oppenheimer approximation: they sit into the ground state "instantly"). And all slower degrees of freedom (than this interval) play the role of external parameters (that influence the internal dynamics of the system but are unaffected by it, and can be either constant or otherwise functionally given).
Whenever a proper truncation to an effective theory is made in this way, the markets will have a small number of equilibrium points (for each configuration of the external parameters). If the space of possible out-of-equilibrium metastable states grows arbitrarily, it is always possible to demonstrate this diversity as a consequence of effects at ever slower time scales.
If we tried to incorporate arbitrarily long time scales into economics, e.g. billions of years, we would need to know all processes that are faster than this time scale and economics would become geology. It's very clear that geological degrees of freedom must be treated as external parameters in a sensible model of economics.
Whenever we avoid this trap, it may be seen that a sensible and useful model of economics will only have a small number of equilibrium points. Smolin's exponentially large "landscape" is an artifact of his sloppy treatment of time scales.
Smolin's misunderstanding of gauge invariance is comparable to his misunderstanding of effective theories and the landscape. On page 16, he claims that the neoclassical Arrow-Debreu model has the following "gauge invariances":
- prices get rescaled by a constant, Lambda
- utility functions are rescaled by different constants, lambda_a, that can be chosen to differ for different households because their evaluations of utility are independent