Gauge Theory Does Not Fix This

or, why do intellectuals oppose Bitcoin?

the single most important thing in the universe. allegedly.

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.

Now we are getting somewhere. Bitcoin is a microcosm of “capitalism” and the intellectual response to Bitcoin a microcosm of Nozick’s argument. It is falsifying grand and all-encompassing theories of economics, finance, and politics left, right, and center. Weinstein has one such theory, and I’m sorry to have to be the one to say that it is not going to survive contact. Interesting as it may be, Bitcoin does not have to bend to fit it. It has to bend to fit Bitcoin. If it breaks, nobody will care.

In other words, Gauge Theory does not fix this.

Gauge Theory: What Is It Good For?

So what is this Gauge Theory all the cool kids are talking about? Here’s Weinstein explaining it:

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 …

A glance at Wikipedia makes clearer the gravity of the issue:

Okay, so what’s a field theory? What’s a Lagrangian? What is invariance? What is a local transformation? What’s a Lie Group? This doesn’t bode well for something purporting to “explain” … well, anything, really.

So what actually is it? By far the best resource I can recommend if readers really want to explore this is a paper by Juan Maldacena, The Symmetry And Simplicity Of The Laws Of Physics And The Higgs Boson.

There are two interesting things about this paper. First, whereas Weinstein is clearly very smart but is really more of an entertainer than an academic, Maldacena is actually a genius, with next to no public profile beyond his discipline.

But beyond these biographical details, the reader can get an even clearer sense of this by comparing the paper just cited to Weinstein’s performance on Rogan: Maldacena actually explains the intuition, meaning, and relevance of gauge symmetries in English, something Weinstein seems unable to do.

The second interesting thing is that Maldacena finds an economic analogy to be the most accessible introduction to the layman before moving on to particle physics. I really do recommend just reading the paper itself, but I will extract and condense the relevant discussion:

Back to the Wikipedia crib, then: “field theory” just means that it helps to understand the system in question in mathematical terms as consisting of a little arrow at every point that means something helpfully numerical; “Lie groups” can be read as a special class of the more easily intuited “symmetry” — rotating or flipping while preserving size and relative position; “local transformations” means we only enact these flips and rotations on the little arrows at certain well-defined locations within the system as a whole while leaving everything else untouched; “Lagrangian” is a technical specification of the dynamics of the entire system arrived at by a calculation on all the little arrows, and that the Lagrangian is “invariant” under the “local transformations” means that flipping and rotating the arrows only locally doesn’t change the outcome of the calculation, hence also doesn’t change this way of specifying the system as a whole.

Got it? Good. You are ready to go on Rogan.

In the course of introducing this analogy, Maldacena cautions us to,

It’s almost as if he doesn’t have an unfalsifiable grand and all-encompassing theory of everything. What a wuss. Economics is totally a Gauge Theory! LFG!!!

Economics As A Gauge Theory

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:

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 only 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, 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 dynamic economic exchange 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 and the acting humans building that structure are 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

photo by Renate Vanaga, via Unsplash

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:

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

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 return-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 they could be. 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,

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.”


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.


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.

Whatever To Do About Bitcoin?

graphical representation of how Bitcoin works. notice Gauge Theory is not involved.

It’s important to understand the key difference between Weinstein and Maldacena. Weinstein is not really an academic, he is an academically-oriented performer, and there is a large part of this entire debacle that is purely performative. It sure has driven a lot of engagement. I mean, jeez, look at what you are reading right now!

That might be fine if he were just wowing podcast hosts with his musings on interdisciplinary linkages between particle physics and economics, but it is problematic with Bitcoin because Bitcoin is not a theory. It’s a fact. It works, miraculously without having been embedded in a Gauge Theory, and without there even being such a BIP on the horizon, at least as far as I am aware.

It’s even more unfortunate in this case because, although my initial reaction to Weinstein’s thoughts on the matter was that they were little more than complexity-laundering bullshit, I have since been convinced by more patient and tolerant peers that they contain a nugget of insight. When Weinstein says we need to embed Bitcoin in a Gauge Theory, this is what I think he means:

for an aspirationally universal monetary tool, the inevitable transactional information leak beyond assurance of validity would be preferable if curtailed at local consensus rather than global consensus.

But notice how I said that without referencing particle physics? And notice how it can be discussed without proposing radical-to-the-extent-they-are-not-meaningless protocol overhauls by learning about Lightning, taproot, cross-input signature aggregation, and so on?

The critique of local versus global state is answered by Lightning. You might even go as far as to say, if you are being exceptionally cheeky, that Bitcoin is the Gauge Field that makes possible in the first place the kind of local transformations Weinstein is interested in. If Bitcoin’s Lagrangian turns out to be invariant under these transformations, all the better. If not, who cares?

Which brings us full circle: Gauge Theory does not fix this. Taking the time to understand it, and doing real work on it, might fix it just a teeny, tiny bit. But spouting off grand and all-encompassing theories without having understood it, and without offering anything workable as an alternative, will make you no friends and will influence nobody.

We would love to have you, Eric. Really, we would. From what I can tell, you’d be an excellent advocate. The story of your interactions with the Boskin Commission and the inadvertent discovery of the disingenuous political bent of mainstream economics will find in us a near-perfect audience. But you are going to have to knuckle down and listen, learn, and stop pretending Bitcoin is a subset of your theory of everything.

Your theory of everything is a subset of Bitcoin.

It’s nothing personal, but we don’t trust. We verify. Do let us know when our verification ought to begin.

follow me on Twitter @allenf32

thanks to Gigi for edits and contributions



I’m an investor. I think about things. I write some of it down.

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