Extracts of Allen Farrington’s “Guage Theory Does Not Fix This – Or, why do intellectuals oppose Bitcoin?”

ILR Note : *Eric Weinstein is the Managing Director of Peter Thiel’s Thiel Capital*

I should start off by saying that I have nothing against Eric Weinstein. Readers need not worry that this is another Talebenning. It’s a little suspicious that Weinstein claims Taleb is “*incredibly subtle*”, but we all have our foibles. I liked Taleb once, too, after all.

Unlike Taleb, who is a bullying, cowardly, bullshitting charlatan, Weinstein seems like a perfectly nice and well-intentioned guy. He is certainly extraordinarily intelligent, which might seem like it makes this whole episode all the more bizarre, but I think it points to a deeper truth.

Being smart doesn’t really matter. In fact, it could well be a handicap. I am remound of Robert Nozick’s essay, *Why Do Intellectuals Oppose Capitalism?*I won’t repeat the entire argument here; readers can bookmark the link above and digest in their own time (it’s not long). But the gist of it is that people whose profession or primary intellectual pursuits consist of “*wordsmithery*”, as Nozick calls it — competitively putting forward essentially verbal arguments in the hope of enacting influence—seem inclined to find unfair and unjust a dynamic in which this gets you nowhere. They are used to “*central planning in the classroom*” in which rewards are dished out on the basis of perceived merit — i.e. “politics” — and there is no “*anarchy and chaos of the marketplace.*”

So far, this probably doesn’t sound like Weinstein at all. He certainly doesn’t “*oppose capitalism*”, nor is he a “*wordsmith*”. Quite the contrary, he is a “*numbersmith*” of the variety Nozick goes out his way to exclude, and as Managing Director of Thiel Capital, he could hardly be *more *capitalist. If Peter Thiel is Dr Evil, then Weinstein is Dr Evil’s evil cat.

But there is a subtler undercurrent to Nozick which I feel has some heft here: intellectuals tend to have grand and all-encompassing theories that it is entirely within their power to shape and perfect, and which are constructed such that they are essentially unfalsifiable. In the appropriate intellectual domain, this isn’t even a bad thing, necessarily. But of course, *economics in real life *is a highly inappropriate domain for such tomfoolery, and the intellectuals get very upset that nobody seems to be in charge, shaping and perfecting reality to an unfalsifiable theory that could have been their own with a little more politicking.

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### On Weinstein’s ‘Guage Theory’, As Explained recently on the Joe Rogan podcast

*See Weinstein’s appearance here:*

*I included all the ellipses above so readers might be tricked into watching that video in its entirety before they saw the text that followed. If you fell for this, I sincerely apologize for having wasted so much of your time, but I also feel this experience is an important one to fully grasp what we are dealing with here.*

*Notice, by the way, that Rogan is a journalistic genius. He doesn’t tell Weinstein he hasn’t explained shit; he sets Weinstein so much at ease by playing dumb that Weinstein makes it totally clear on his own that he hasn’t explained shit. Anyway …*

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I want to try to paint Weinstein’s ideas in as generous a light as I can, at least to start with.

In all seriousness, and without meaning to be snarky towards Weinstein, I couldn’t find an explication of his theory *by him *that I am actually happy to endorse. This talk is not bad, but wanders absolutely all over the place and drowns the audience in superfluous formalisms that don’t help much in understanding the core contention.

The best explication I found came from the theoretical physicist Lee Smolin, with whom Weinstein has collaborated, from his paper, *Time And Symmetry In Models Of Economic Markets**. *I quote the relevant section at length as it really does frame the issue nicely:

“The proposal of Malaney and Weinstein is that to construct models of economies that have real dynamics and time dependence in them- so that for example, preferences of households can change in time-it is necessary to hypothesize that the dynamics is con- strained by much larger groups of gauge invariances.

As we have seen in the discussion above, the need for gauge invariance stems from a fundamental fact about prices, which is that they appear to be at least in part arbitrary. It seems that each agent in an economic system is free to put any value they like on any object or commodity subject to trade. How do we describe dynamics of a market given all this freedom? To get started we recall that in the Arrow-Debreu description of economic equilibrium, there is a gauge symmetry corresponding to scaling all prices. This may suffice for equilibrium, but it is insufficient for describing the dynamics out of equilibrium, because away from equilibrium there may be no agreement as to what the prices are. There is then not one price, but many views as to what prices should be. Each agent should then be free to value and measure currency and goods in any units they like- and this should still not change the dynamics of the market. It should not even matter if two agents trading with each other use different units. Thus we require an extension of the gauge symmetry in which the freedom is given to each agent, so they may each scale their units of prices as they wish, independently of the others.

There is a further difficulty with price which is that even after issues of measurement units are accounted for different agents will value different currencies or goods differently. Different agents have different views of the economy or market they are in, they have diverse experiences, strategies and goals, and consequently have different views of the values of currencies, goods and financial instruments. Consequently, in a given economy or market it is often possible to participate in a cycle of trading of currencies, goods or instruments and make a profit or a loss, without anything actually having been produced or manufactured. This is called arbitrage.

In equilibrium, all the inconsistencies in pricing are hypothesized to vanish. This is what is called the

no arbitrageassumption. But out of equilibrium there will exist generically inconsistencies in pricing. In fact, we are very interested in the dynamics of these inconsistencies because we want to understand how market forces act out of equilibrium on inconsistencies and differences in prices to force them to vanish. This is essential to answer the questions the static notion of equilibrium in the Arrow-Debreu model does not address.However, in analyzing the dynamics that results from the inconsistencies, we need to be careful to untangle meaningful differences and inconsistencies in prices from the freedom each agent has to rescale the units and currencies in which those prices are expressed. This is precisely what the technology of gauge theories does for economics.

How does gauge theory accomplish this? As in applications of gauge theory to particle physics and gravitation, the key is to ask what quantities are meaningful and observable, once the freedom to rescale and redefine units of measure are taken into account. The answer is that out of equilibrium the meaningful observables are not defined at a single event, trade or agent. Because of the freedom each agent has to rescale units and choose different currencies, the ratios of pairs of numerical prices held by two agents in a single trade are not directly meaningful.

To define a meaningful observable for an economic system one must compare ratios of prices of several goods of one agent, or consider the return, relative to doing nothing, to an agent of participating in a cycle of trading. This might be a cycle of trades that starts in one currency, goes through several currencies or goods and ends up back in the initial currency. Because the starting and ending currencies are the same, their ratio is meaningful and invariant under rescalings of the currency’s value. This is true whether one agent or several are involved in the cycle of trades. We say that these kinds of quantities are

gauge invariant.Such quantities, defined by cycles of trades such that they end up taking the ratio of two prices held by the same agent in the same currency have a name: they are called curvatures. The ratios of prices given to a good by different agents also have a name: they are called connections. The latter do depend on units and hence are gauge dependent, the former are invariant under arbitrary scalings of units by each agent and are gauge invariant or gauge covariant (this means they transform in simple fashion under the gauge transformations.)

It is interesting that the quantities that are invariant under the gauge transformations include arbitrages, which should vanish in equilibrium. This does not mean that they are irrelevant, indeed, they may be precisely the quantities one needs to understand how the non-equilibrium dynamics drives the system to equilibrium. That is, it is natural to frame the non-equilibrium dynamics in terms of quantities that vanish in equilibrium. These are the quantities that the law of supply and demand acts on, in order to diminish them.

There is a precise analogy to how gauge invariance works in physics. In gauge theories in physics, local observables are not defined because of the freedom to redefine units of measure from place to place and time to time. Instead, observables are defined by carrying some object around a closed path and comparing it with a copy of its configuration left at the starting point. These observables are called curvatures. The result of carrying something on a segment of open path is called a connection and is dependent on local units of measure. But when one closes the path, one makes comparison to the starting point possible, so one gets a meaningful observable, which is a curvature.

In general relativity exactly the same thing is true. Here curvature corresponds to inconsistencies in measurements, for example, you can carry a ruler around a closed path and it comes back pointing in a different direction from its start. The dynamics is then given by the Einstein equations, which are expressed as equations in the curvature. But in the ground state-which is roughly analogous to equilibrium in an economic model-the curvature vanishes. The state with no curvature, called flat spacetime, is the geometry of spacetime in the absence of matter or gravitational forces. It is the state where all observers agree on measurements, such as which rulers are parallel to which.

But while the curvatures vanish in the ground state, the physics of that state is best understood in terms of the curvatures. For example, suppose one perturbs flat spacetime a little bit. The result are small ripples of curvature that propagate at the speed of light. These are gravitational waves. The stability of flat spacetime is explained by the fact that these ripples in curvature require energy.

Similarly, it may be that the stability of economic equilibrium can be studied by modeling the dynamics of small departures from equilibrium. These are states where prices are inconsistent, ie where arbitrage or curvature is possible. By postulating that the dynamics is governed by a law that says that inconsistencies evolve, one gets a completely different understanding of the underlying dynamics than in a theory that simply says that inconsistencies or curvatures vanish.

If economics follows the model from physics, then the next step, after one has an- swered the question of what are the observables, is to ask what are the forms of the laws that govern the dynamics of those observables. Given what we have said, the choice of possible laws is governed by a simple principle:

since only gauge invariant quantities are meaningful, the dynamics must be constructed in terms of them alone.”

Here is my attempted translation of all this: if a market is not at perfect equilibrium over a prolonged stretch of time (ignore for now that this is meaningless anyway — we are supposing it isn’t true), there is a serious problem of measurement in comparing the dynamics of the market at any two times because of a lack of an invariant measure.

The paragraph beginning “*there is a further difficulty …*” is particularly astute in identifying essentially radical subjectivism and resultant uncertainty meaning no individual’s perspective can be meaningfully privileged. This is true not only because their preferences can change, but because even their preferred *scale *of preferences is somewhat arbitrary and psychological.

This is the “gauge symmetry” Maldacena alluded to above and that is similar to experiences with redenominations of currency: it means the same if we value one chicken at $1 and 10 chickens at $10 (if that’s even true — it might not be), or ten chickens at one cow and one hundred chickens at ten cows, but none of these denominations make any more sense than any others.

However, Weinstein would argue, this idea of symmetry in the measurement opens an important conceptual door: an arbitrage cycle. The existence of an arbitrage cycle in an out-of-equilibrium market is an economic observable that is *gauge invariant*, and, Weinstein would therefore posit, *fundamentally meaningful in terms of the dynamics of the entire system.*

This notion of invariant measures across agents and across time may sound vaguely familiar to those who have listened to Weinstein’s thoughts on this before, as they are usually put forward more straightforwardly in his criticisms of official inflation statistics.

And here he absolutely has a point — one with which Bitcoiners I’m sure are intimately familiar. Relative to what exactly is *2.3%*, or whatever, supposed to be meaningful? If it’s the “average basket” then who is the average person? If your personal costs are increasing at a rate more like 30% per annum, how much better is this supposed to make you feel?

Michael Saylor has recently popularized the notion that “*inflation is a vector*”, that every good or service has its own rate of inflation, that is hence experienced differently by every individual depending on their purchasing habits, and that reducing the concept as a whole to a single number is a “*metaphysical abstraction*”.

I would take this even further and argue that even the vector is a metaphysical abstraction — it’s just a more useful one for conceptualizing the workings of the economy than the single number. In reality, none of the entries in the vector *really exist*. It’s a conceptual aid, not an *observable*. Every price of every sale is meaningful only at that point in spacetime, and the capital structure facilitating the exchange is reflexively affected by its having happened.

This is where Weinstein’s approach starts to creak at the joints. Having correctly identified the relevance of radical subjectivism in general, one of its many consequences of ill-defined inflation, and the genuinely interesting realization that arbitrage cycles are phenomena worthy of study, he seems to make the entirely uncalled-for leap to something like: *neoclassical economics is a naturally occurring gauge theory.*

**Economics As Literally Anything At All Besides A Gauge Theory**

Pretty much all you need to grasp the essential error in all this is available in a single paragraph on Weinstein’s website under the heading, *Neo-Classical Economics And Gauge Theory*:

“Economic theory is based around the hidden assumption that consumer tastes are absolutely ‘stable’ over time despite the fact that a world with static tastes cannot even be considered a plausible simplification of the world in which we live. Many rationalizations have been given for this fiction which are at times both ingenious and embarrassing. The key problem for economic theory is that the field simply failed to develop mathematical methods for analyzing changes in dynamic preferences.”

This final sentence should be ringing some serious alarm bells. Allow me to translate:

The mathematical apparatus of mainstream neoclassical economics does not cleanly solve every theoretical economic problem. The solution is that we need more and more complicated math.

Um, no.

This is not to say that *some mathematics *is not useful in economics. But a decent caricature of Weinstein’s position is that until *everything has been mathematized*, economics remains unscientific. Which is true, but has exactly the opposite significance to what Weinstein is after: economics is not a science. There are no possibilities for controlled experiments and the fundamental building blocks do not behave in ways that can be coherently mathematically described.

Weinstein seems to think he has found a key component that might bridge the gap: an invariant for measurement. But unfortunately, he is simply so wedded to mathematical formalisms and their hoped-for application in economics that he lacks the proper context in which to place this insight.

Arbitrage *is* a fundamental concept. With enough conceptual leeway, we could interestingly argue that all profit-seeking capital formation and deployment is some or other form of loosely-defined arbitrage. But then, rather than claiming that this profundity can be used to root economics in a sweeping mathematical formalism, I would instead encourage the reader to go read Israel Kirzner’s *Competition and Entrepreneurship**, *in which more or less what I just said is explained totally straightforwardly and with zero equations, as far as I recall.

And that’s basically the end of that. You don’t need particle physics or algebraic geometry. You just need Kirzner’s realization that entrepreneurship is, by its nature, non-exclusionary. It is a price discrepancy between the costs of available factors of production and the revenues to be gained by employing them in a particular way — or, profit. In other words, it is perfectly competitive. It does not rely on any privileged position with respect to access to assets; The assets are presumed to be available on the market. They are just not yet employed in that way, but could be, with capital that is presumably homogeneous. Anybody could do so — they just need the incentive of profit and guts.

In other words, markets are *always out of equilibrium*. The arbitrage cycles Weinstein identifies as a meaningful invariant *are the motivating force of all economic activity. *They are everything. Ironically, his insight may be so profound that its true significance has gone over his head. He has narrowed down his search for the economic holy grail all the way to … entrepreneurship.

Weinstein basically doesn’t fully grasp that *subjective value* cannot be mathematized. Nor can the intuition, motivation, taste, and creativity that drives entrepreneurship and competition and from which literally all economic activity follows, *some of which *can admittedly be helpfully mathematically characterized, albeit with a pinch of salt.

If you want to know why academic economics is such a mess, go read *Principles of Economics *by Menger, *A General Mathematical Theory of Political Economy *by Jevons, and *Pure Elements of Political Economy *by Walras, and decide which you like the most and which makes the most sense. Then go check which had the most academic influence. Then be sad.

Here, Weinstein describes the flourishing that followed these works, nowadays called *The Marginal Revolution*, as, “*the introduction of the differential calculus formally into economic theory,*” which is about the most ridiculous description of it I have ever come across. In case the reader is unfamiliar, The Marginal Revolution solidified the centrality of subjectivism over cost- and labor-theories of value and spurred a variety of methodologies as to *how to deal with it*. Some methodologies involve differential calculus and other methodologies are good.

In the same interview, Weinstein tellingly later says that, “*I think that George Soros’s theory of reflexivity has not been taken seriously because we haven’t had the mathematics to incorporate it within the standard canon.*” I’m honestly not sure Weinstein has ever really read or thought about Soros’ line of thinking here in any depth because the *entire point *of *The Alchemy of Finance*is that the principle of reflexivity renders finance irresolvably *unscientific. *Amongst many wonderfully quotable extracts, Soros writes,

“The attempt to transpose the methods and criteria of natural science to the social sphere is unsustainable. It gives rise to inflated expectations that cannot be fulfilled. These expectations go far beyond the immediate issue of scientific knowledge and color our entire way of thinking.”

Weinstein says shortly thereafter, “*there is no question that agents move markets. But what [Soros] is saying is that markets move the minds of agents. And you have to ask yourself the question: what is the mathematics of moving a mind?”*

No, you really don’t need to ask yourself that. If you find yourself asking yourself that, stop and read Kirzner immediately.

Weinstein’s intellectual lineage (and associated inflated expectations) on this topic can of course be traced *not *from Menger, but from Walras and Jevons through Pareto and Marshall to Paul Samuelson, whom Weinstein consistently praises, and whose only flaw Weinstein deems to have been not being quite mathematical enough, despite being probably the single worst and most insidious influence on academic economics in the twentieth century.

The reader may not be familiar with Samuelson, although he was world-famous in his heyday, and while I don’t want too much of a digression, two biographical details seem pertinent.

First, he wrote the once-standard English language textbook on economics, rather obnoxiously called *Economics*, believed to be the best-selling economics textbook in history, which, from its first edition in 1948 up until its 12th edition in 1985 predicted in its introduction that the Soviet economy would overtake that of the US before too long. Naturally, this date was pushed back every time, and although the embarrassment was finally removed in 1985, *in 1989*, Samuelson claimed that, *“contrary to what many skeptics had earlier believed, the Soviet economy is proof that … a socialist, command economy can function and even thrive.”*

Mhmm.

Second, as will be mostly meaningful and possibly infuriating to long-time readers of mine, Samuelson claimed that, “*the ergodicity assumption is essential to advance economics from the realm of history to the realm of science.*” In other words, we must assume something we absolutely know to be false in order to pretend economics is scientific, which we absolutely know it is not.

Mhmm.

This is the thread Weinstein is picking up, and the results are every bit as silly as you might imagine.

In fact, it’s all a shame because, as I argued above, and as Maldacena demonstrated without even really meaning to, there are areas of economics in which gauge symmetries are a useful abstraction. But they aren’t a scientific analysis. The absolute most you could sensibly say would be something like: *if you already understand gauge symmetries, that’s a useful shortcut to grasping the mechanics of xyz, but if not, don’t worry about it.*

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