On episode #116 of the InFi podcast, I had a two-hour-plus conversation with Eric Weinstein, who has a math PhD from Harvard but also is a regular guest on the Joe Rogan Show and coined the term “Intellectual Dark Web.” In the wake of that discussion, I received a lot of feedback—both positive and negative—on Eric’s ideas for reforming economics. On the forthcoming episode #119 of the podcast, I do a solo “post-game show” analysis, explaining Eric’s main points and responding to the critics. Here on the infineo blog, I am providing a three-part written series to flesh out these themes.
To give an outline of the series: In this Part 1, I will explain the big picture, using plain English, of what Eric claims to be doing in applying “gauge theory” to economics. In Part 2, I will go through an example of using different price indices to measure the increase in the cost of living between 1950 and 2025, and illustrate why Eric (and Pia Malaney) end up favoring the Divisia index and why “path dependency” is a feature, not a bug. Finally, in Part 3 I will show why two ostensible refutations of Eric’s claims—namely, two important “impossibility results” in the economics literature—don’t actually apply to Eric’s framework.
What Is Gauge Theory?
Unfortunately, even the Wikipedia entry for “gauge theory” is chock-full of jargon that would be incomprehensible to the lay reader. Suffice it to say, it is an area of mathematics that studies the conditions under which a dynamic system will remain constant. It proved very useful in the hands of Yang and Mills in the 1950s to unify the modeling of several different phenomena in physics. (Eric Weinstein’s doctoral dissertation at Harvard involved a generalization of the Yang-Mills results to higher dimensions.)
While discussing economics in the 1990s with Pai Malaney (who was getting a PhD in economics from Harvard, and whom Eric would later marry), Eric had an epiphany and saw that the mathematical economic models in use were quite unsophisticated. By applying gauge theory to this realm, Eric thought certain age-old puzzles in economics could be easily resolved, and more important that this new approach would open up new opportunities that economists literally hadn’t even considered with their crude tools.
An Intuitive Example of Using a New “Derivative”
In standard mathematical economics, it is typical for households and firms to engage in “optimizing behavior,” where there is some function that the agent wants to maximize, subject to a constraint. For households, the goal is to maximize utility subject to the budget constraint (i.e. how to spend the available income to maximize happiness, given the market prices of all the possible goods and services). For firms, the goal is to maximize profit subject to the technological constraint (i.e. how to spend money hiring workers and other inputs to maximize profit, given the prices of inputs and prices of outputs, as well as the “production function” that transforms inputs into outputs).
Because economists wanted to use calculus to solve these types of problems, they made the necessary assumptions and used the simple derivative operator that students learn in an introductory course. Utility or profit is maximized when you take the first derivative of the function with respect to the choice variable and set it equal to zero—that’s a “local maximum” (so long as you check some other conditions).
What Eric is claiming is that economists should use a broader concept of “the derivative” (or “differential operator”), that can handle a more sophisticated meaning of “the function doesn’t increase if we move away from this spot.”
When I asked him about this in the interview, Eric gave an intuitive example to illustrate: Suppose there is a labor contract that says the employer must pay the worker “the same wage” over time. Using a standard approach, we could take a function that specifies the wage paid at any particular time, and take the first derivative with respect to t. If that first derivative (using high school calculus) equaled zero for some time period that we were interested in, it would seem to indicate that yes, the employer wasn’t changing how much it paid the worker—and hence, was paying a “constant wage.”
But Eric went on to explain that in economics, this isn’t usually what we mean. It is standard in union contracts for example to include clauses for a “cost of living” adjustment. In this case, we want a derivative that doesn’t spit out “zero” when the absolute dollar amount of the wage stays constant. No, we want a derivative that spits out “zero” whenever the wage being paid perfectly tracks some index of the cost of living. So for example, if the cost of living for the worker (which we will talk about more in Part 2 of this series) goes up by 4.3% from one year to the next, then the dollars paid in wages also must go up by 4.3%, in order for the properly calibrated derivative to spit out “zero” in this time period.
Does Weinstein Pass the Smell Test?
In this introductory post, let me give indirect evidence that Eric’s proposal isn’t mere crankery (as some of his harshest critics allege). If you first watch my interview with Eric, talking about mathematical economics, and then compare it to his 2-hour-plus discussion with Nobel laureate Roger Penrose, you’ll find that Eric uses much of the same terminology. In other words, it is clear that when applying gauge theory to physics, Eric is holding his own in a conversation with a physics master. This isn’t surprising, since—as I said above—Eric has a PhD in math from Harvard, where his dissertation generalized prior results of using gauge theory very successfully in physics.
At the same time, I’m here to confirm that when he’s talking about the cutting-edge mathematical models in economics, Eric was speaking quite knowledgeably. I knew exactly what he meant, and (as I will explain in Part 3 of this written series) I agreed with him in our interview that he had successfully defended his approach from an initial critique from a Nobel laureate in economics (Kenneth Arrow).
Conclusion
Eric Weinstein undeniably has an incredibly intelligent mind and is conversant with the history of results in several diverse fields. When it comes to economics, he has already changed the way I view the problem of price indices (as I will explain in Part 2). Maybe applying gauge theory to economics will, in the long run, prove to be too little bang for the buck, but he isn’t speaking gibberish. I hope other economists will follow my lead and give some more attention to Eric’s claims on how we can improve our field, at least for those who are inclined to mathematical models.
Dr. Robert P. Murphy is the Chief Economist at infineo, bridging together the dependability of Whole Life insurance policies with the benefits of blockchain-based finance.
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