There’s a interesting interview in Scientific American about the possible intersection in advanced mathematics of physics and economics (http://blogs.scientificamerican.com/cross-check/2013/05/01/author-of-the-physics-of-wall-street-ponders-strings-black-swans-and-a-final-theory-of-finance/).

While I’m all for any kind of cross-fertilization of ideas across different disciplines (A great quote I once heard is that Universities shouldn’t teach Psychology, History, Literature or other liberal arts disciplines but just one thing, “Human Studies”. And Math), I feel there’s an elephant in the room in this discussion that isn’t mentioned, and that’s the fact that economics/finance differs from Physics in their fundamental inputs.

Both of the disciplines use math to attempt to explain, and thus accurately predict, reality. However, economics is attempting to describe reality while looking through the rear-view mirror, as it were, while physics by definition describes reality in a more all-encompassing sense. Physics is independent of what’s gone before, so predictive behavior is just that: a mathematical physics model will accurately say what we can expect in future. To choose just one example, the idea of a red shift, of an expanding universe, was understood to be correct even if we couldn’t see it with the tools at our disposal when first posited. With more advanced telescopes, the theory was shown to be demonstrably true. One can attempt an economics experiment which ignores basic human behavior, but the predictive qualities are, to be kind, lacking (Soviet Union, anyone?).

The study of economics and finance also has a completely different rewards system than that of physics. While a finance mathematician is looking to, in a very real sense, maximize profits, a physicist is looking only to validate theory. Rewards come only if the theory is true, not if it proves a temporary benefit relative to other researchers. This is important because we don’t have any notion of objectivity in finance equivalent to the objectivity found in physics (Demonstrable and replicable testing to prove validation). Instead, finance and/or economics is a rolling road of constant experimentation where the inputs are not fully understood, and the experiment cannot be easily replicated, if at all. In addition, there is a financial incentive to misdirect others in order to maximize gain (On the most basic level, something like insider trading of classified information, on a macro level, lobbying for financial policies which are detrimental to the economy at large but serve a narrow,parochial, temporary interest). Math is that circumstance is just a tool, to be used for “good” (accurate, predictive, explanation of behavior) or “ill” (temporary profits at the cost of understanding).

The ideal in both cases is to explain the world we live in. Attempting to understand the world in an all-encompassing way through math is not a recent human endeavor. Descartes, for example, used the clockwork analogy of the universe to explain reality: the universe is predictable, like a clock, working with predictable mechanisms. Our lack of understanding the future is dependent on the fact that we simply don’t know what all the pieces are, what they do, or how they interact. If one could have a massive consciousness (He used this to argue for the existence of God, since such an understanding was obviously beyond our limited human brain capacity), one could see the future, because we could see how the interaction of everything, from the proverbial beating of a butterfly’s wings in Brazil to the marching of an army, interacts and affects reality.

Math in the service of science, whether economics or physics, has the same primary purpose: to predict what will happen next. But economics in general, and finance in particular, does not start from a truly scientific base. Simply put, there is no objective reality when it comes to money. Our economic system “works” in the sense that people can have jobs, earn money, procure goods and services, and hopefully enjoy a rising physical standard of living, but there is little that is objectively demonstrable or replicable in this field of human behavior. To take it to the most fundamental level, the dollar bills in my wallet are nothing but pieces of paper, of no inherent value, without the collective notion of the world in which I live, that they do, indeed, have a value commensurate with the numbers printed on them. The digital flow of ones and zeros that make up “money” in the modern financial world is even more arbitrarily connected to any physical value.

This is a far cry from classical physics. A hydrogen atom does not gain electrons or protons because of changes in politics, tax or fiscal policy or the movements of markets. The element table we all learned (In my case, sort of learned) in High School doesn’t change due to social change. But the value of a dollar, or of any currency, does in fact change, rather arbitrarily at times. It changes because although there are hard, physical factors which make up part of the input data base of economics (A factory turned out x number of widgets this month. An oil well produced so and so many barrels last year), there are also factors which, though influential, are incredibly hard to predict because they are disconnected from that type of real, physical thing or process (For example, political instability in a country causing a run on banks).

In this case, the seeming certainty of mathematical models can have a detrimental effect on economic studies because the mathematical model will only be as reliable as the information on which it is based. To be truly accurate, mathematical economic models must be able to incorporate all the incredibly diverse sources of information, from crop yields in Argentina to the housing market in Singapore, which might possibly have an impact on any economy in our interconnected world. Not only that, but the model must incorporate this information in correct proportion to its effect. Not only that, but it must also incorporate those “non-economic” factors, mainly but not solely political, which affect economies, again in proper proportion to likely effect. Not only that, but the data itself has to be valid and trustworthy, and ideally, immutable.

This is an extremely tall order.

Now, this essay is a bit of a red herring, in the sense that these quasi-philosophical musings are not, strictly speaking, what the article cited above is about. The two individuals in the discussion are talking about math in the service of financial models such as what hedge funds use to maximize their returns, and whether the math models of physics might have some useful influence. But those financial models remain divorced from the sort of real, verifiable data from which physics benefits. It is for this reason that, despite some of the best mathematical minds residing and working in Wall Street, we have “unexplained” financial catastrophes that no one supposedly sees coming. As the saying goes, it’s hard to build a castle on sand, and the economic data which goes into the models Wall Street uses are really just that.

This is not to argue that finance or economics doesn’t benefit from advanced mathematics. But as useful as economic models are, whether derived from physics and applied to finance, or created in situ, they can only serve with the constant understanding that just because they are numbers, and therefore seemingly certain and distinct, they remain at best estimates based on a sea of informational uncertainty.