Mathematics as a Common Language (Wonkish)
My interview with physicist and fund manager, Eric Weinstein, ranged from George Soros’s Theory of Reflexivity to the Wu Tang Clan.
Yes, that Wu Tang Clan.
It was my first time attending a conference hosted by the Institute for New Economic Thinking. During the cocktail hour, I bounced between conversations until my eyes landed on a familiar face. I had never actually met him, but weeks of endless preparation made Eric Weinstein instantly recognizable. By education Dr. Weinstein was a mathematical physicist, but by reputation, he was a serial contrarian. He was also the person I came to meet.
Last year, Weinstein stirred controversy in his native field by proposing a 14-dimension ‘observerse’ theory to unify general relativity and quantum physics — the holy grail of scientific discoveries. It was met with scorn despite its critics’ grudging admission that Weinstein employed some truly elegant mathematics. In economics, he imported sophisticated techniques from Gauge Theory to better track inflation. Development of the metric was commissioned by the Senate Subcommittee on Social Security, but it was eventually discarded in favor of a more politically palatable option. Time and again, Dr. Weinstein arrived at unpopular conclusions for which he was shunned. And yet, as I saw him drifting through the crowd with an amiable, but slightly bemused expression on his face, I got the distinct feeling that this was a man who felt comfortably out of place. Studying the language of the cosmos, which is what math is, probably gives you a long view of things. So to him, maybe ruffling a few feathers was just a minor sacrifice on the path to profound truths.
Interview
Gaurav S. Iyer: You didn’t come to the world of economics and finance via the traditional route. You earned your doctorate in mathematical physics at Harvard and now you are an asset manager. How does that inform your investing style?
Eric Weinstein: Well, I think I ended up with an interest in finance somewhat by accident. I was given a technical problem in the pricing of illiquid assets and what I found was that finance, as a relatively young discipline, has room for slightly non-standard toolkits to make an impact.
Iyer: And it is not a new concept. Take Louis Bachelier, who was a mathematician working on the Paris stock exchange during towards the end of the 19th century. He predated Einstein’s work on Brownian motion, but his work on the random walk principle was derived from stock prices, rather than an analysis of nature.
EW: Yes, one thing you’re touching on is that not everything will come from the physical sciences towards economics. It can be the case that economics could provide fundamentally deep mathematical insight. There is no reason to think that an idea cannot first occur in economic thinking and then move into the sciences. For instance, take Malthus and the effect of his work on Darwinian thinking.
(Malthus was an early pioneer of economics who argued that unrestrained population growth would rapidly outpace the food supply. His writings on the subject crystallized Darwin’s theory of natural selection.)
The real issue is who can glean value from what. If you are a market agent with a particular specialty, it is possible that you may detect a real pattern in the market through technical analysis. But on the other hand, somebody who has a very keen ear for narrative and the ability to piece together language at a linguistic or prose level, might gain an advantage there. What markets give us is the ability for people with different specialties to trade with each other.
Iyer: You often speak about building a toolkit, an interoperable toolkit of mathematical techniques that could be pieced together like Lego in order to decipher what is happening in the world. It sounds like you want mathematics to be the common language.
EW: Well, it’s so interesting that you’d say that. Sometimes when we study different fields…let me just take a few: screenwriting, journalism, and professional wrestling. All of those are narrative fields, and in each case, the idea of the storyline is broken into pieces. In opinion writing there is the ‘to be sure’ paragraph, where you spike out the concerns raised by your detractors. In screenwriting there is a unit called ‘the beat’, where there are approximately 40 ‘beats’ in a film. The idea is that the narrative arc traces through them with an uptick or a downtick in the emotional quantities, surely understood by the people who write the screenplays, but is never put in front of the audience. And lastly you have professional wrestling, where the bookers who write the storylines have vocabulary for different layers of deception. In all these cases, what is presumed to be a free form art is, in fact, a highly technical analytic toolkit. So what we find is that the narrative arts already have more of this kind of structure than the heteredox approach to economics, which seems to be sprawling and incredibly non-unified.
Iyer: But wouldn’t those tools be more descriptive than predictive?
EW: It depends. You see the big problem in economics is the inability to break out particular quantities with enough regularity that you can clearly divide the model into the descriptive part and the part that has yet to yield to our toolkit. A model which is ignorant on the details of how the market is put together can still be capable of producing insight, but it is anyone’s guess if economics will yield to the same partitioning, into fast variables and slow variables, that has been so successful in the other sciences.
Iyer: I think many people are skeptical of that argument because it still sounds like an equation will manifest to explain all the economic phenomena we observe in the world. But it sounds like what you’re saying is there will be various tools to be used given specific circumstances, and we still require intelligent professionals to use the right tools. Forecasting won’t suddenly get easier.
EW: If I were to knock over this glass onto the floor, neither you, nor I, would worry about the conservation of energy or momentum being violated. But it would be very difficult to predict whether a shard of glass will scatter into that corner. The idea that you have some knowledge of a system does not mean that you have a detailed understanding of what happens when that system operates in the wild. And I think people are confused about what we can hope for, and what is almost certainly beyond our grasp.
Iyer: Not to delve too far into one analogy, but take the example of knocking over the glass. You or I would not be able to calculate where the shard goes, well, maybe you might…But if we brought in a CSI team and gave them a week to compute it, would they be able to predict where the shard goes?
EW: Well this is exactly what happened with the roulette wheel in Monte Carlo.
(In 1913, several gamblers in Monte Carlo lost millions of francs when the ball fell on black 26 consecutive times.)
A process that is thought to be perfectly random may actually have a tiny bias. At some level, you cannot tell whether the floor has a tiny bias towards or away from the corner. This is effectively what we reward speculators for doing in the market, for removing the sources of bias as they push the system towards randomness. Someone could speculate on whether or not the floor has a tiny bias towards the corner, but we should hope that the profits from such activities are subject to diminishing marginal returns.
Iyer: A few years ago you launched an enterprise called The New Manhattan Project. Can you tell us a little about it?
EW: One of my biggest problems with economic theory is that it behaves differently from any other subject with that level of mathematical and scientific content. If you get a neurobiologist, an evolutionary theorist, a particle theorist, and a differential geometer into a room, they may not understand each other, but very few will have trouble understanding the expertise of the others. If you add an economist to that mix, very quickly the mathematicians will say, well, what you’re doing is technically accurate, but why would you do it in such a fashion. The physicists would say you’re violating various rules we know about good scientific practice. The behavioral theorists will say we know human beings do not behave in the capacity you’re talking about, so why aren’t you incorporating the best information we have? The New Manhattan Project is a collegial outreach from the sister sciences to economics to ask how we can help. What is it that we can contribute? And how can we get to the point where economics is fully integrated and interoperble with the sorority of sister fields? There needs to be some check on the system so that it does not become fully self-referential and, in particular, disconnected from reality.
Iyer: And part of that project is to expand the Wu-Yang Dictionary. I doubt too many people are familiar with Wu-Yang, so could you briefly describe it for our audience?
EW: Do they know the Wu Tang Clan? We can start from there.
(We both laughed for a bit. It’s not every day I meet a physicist who casually drops Wu Tang references.)
The Wu-Yang dictionary was an incredible piece of mathematics and geometry which is largely forgotten. The great geometer Jim Simons, now hedge fund manager extraordinaire, and C. N. Yang, arguably the greatest living theoretical physicist, figured out that two fields had come up with more or less the same quantities, just with different names. And by putting together a two-way dictionary, they created a Rosetta Stone by which elements of particle theory could be ported into differential geometry and vice versa. So, both groups were dealing with the same objects, but they gleaned different insights. And it became the basis for what is, in my lifetime at least, the perfect example of a sudden and spontaneous scientific renaissance.
Iyer: One of the first expansions of that dictionary into economics was your work on Gauge Theory applications, which I thought was path-breaking. Can you elaborate on it a little?
EW: Thank you very much. Sure. We know that modern economic is built largely on the ‘marginal revolution’, which is the invasion of differential calculus into economic thinking. And if you think about calculus as the rise over run of a function, Gauge Theory dares ask the question: above what level should the rise be calculated? The level, or the derivative as it were, is made endogenous to the model. Specifically, our work shows that substitution effects and indifference effects form a natural system of Gauge potential, so the fit is perfect, and it is almost a too good to be true situation.
Iyer: So why are DSGE models (Dynamic Stochastic General Equilibrium) still so common? What needs to happen in order for this type of sophisticated calculus to make its way into economic and financial policy?
EW: Well, you seem adventurous, so let’s be adventurous in speculating. Let’s imagine that what needs to happen is a renegade movement where some people understand what the problem is and start publishing models with data-typing that is more in line with reality. I think that this is possible if biologists, physicists, and differential geometers take a greater interest in economic structures. An interesting parallel is what physicists did for biology when they invaded a sister science and gave it all sorts of academic rigor that the biologists who were previously resident were structurally incapable of doing. Likewise, economics has a structural problem.
Iyer: Would it include mathematizing previous insights? Hyman Minksy was a largely undervalued economist for most of his career, but since 2008 his theory on the inherent instability of capitalism has gained prominence. Would a project include getting together a few biologists, physicists, and economists to read Minsky and craft his framework using these new tools?
EW: What a terrific idea. I mean once economics becomes interoperable or at least recognizable as a scientific discipline, there is great scope to give analytic meaning to what has previously existed as narrative. I’m thinking in particular of George Soros and his Theory of Re—
Iyer: —flexivity. Yes.
EW: Should we riff on that?
Iyer: Absolutely.
EW: Well, George reminds us that there is a cognitive function and a participating function, where our participating function uses our beliefs and preferences to move markets, but somehow the movement of those markets changes our beliefs and preferences. What was it that John Wheeler said about Einstein’s field equations for general relativity? It was very beautiful. He rendered equations as prose by saying “Space tells matter how to move, but matter tells space how to curve.” Now isn’t this effectively the description of how Soros’s cognitive and participating functions interact? What if we began with this linguistic statement only to find that the same types of curvature equations are as relevant in economics as they are in physics?
Iyer: As a financial journalist I bore witness to those kinds of feedback loops all the time. Whether it is the self-fulfilling pessimism of a bank run or seeing the market rise on news of austerity and plunge later on news of weak demand, these chicken and egg conundrums are certainly a fixture in the market.
EW: When George was telling me this, I told him it sounded like a curvature equation. He didn't quite know what curvature meant in that context so I took out four sugar packets and stacked them like an Escher staircase.
He immediately resonated with it and said it was the exact image he had formed in his head. So, this gives me hope. If you reflect that Darwin was unaware of DNA nucleotides, yet he managed to hypothesize the mechanism for speciation through natural and sexual selection, it becomes clear that the impressionistic perspective often precedes the analytic perspective. I think it is important that we scientists not denigrate that, so we can hear the music as we try to write it down in a way that’s more durable.
This interview was lightly edited for clarity and brevity.
