• These two videos are part of a larger series summarizing and explaining Marx's arguments from the volumes of Capital, but they stand on their own and I think exemplify my strengths as an educator and theorist. In it, I build off of Morishima's suggested completion of Marx's unfinished argument from volume II. Unlike Morhishima, who is clearly only interested in talking to fellow academics, my presentation intends to be accessible to a general audience. All of the math is simple and should be understandable to any high school student.

• In Volume II Marx attempts to analyze the foundational contradictions and vulnerabilities of a capitalist system of commodity circulation. He goes about this by breaking the economy down into two conceptual departments - a capital goods department, and a wage goods department. He then analyzes the three macro circulations implicit to that framing: circulation within the two departments, and circulation between the departments.

• His analysis of the intra-departmental circulations is fruitful. In the circulation within the capital goods department, Marx identifies the potential for supply chain crises. In the circulation within the wage goods department, he identifies the potential for crises of overproduction. He stumbles, however, in his analysis of the inter-departmental circulation. Nonetheless, he starts off on the right track. He asks the right questions, but lacks the mathematical tools required to properly answer them.

• That question is: what does steady state equilibrium growth in a capitalist economy actually look like? He initially attempts to model a situation in which capitalists on the whole reinvest a fixed proportion of their surplus, but then seemingly backtracks to look at a simpler and less realistic equilibrium condition - one in which the capitalists one department are purely reactive, adjusting their reinvestment to provide whatever is required by the reinvestment desires of the other department.

• By completing the argument that I believe Marx wanted to give, one obtains a startling set of new conclusions. Capitalists determined to reinvest at the same rate as their competitors will be forced to shift their capital to and from different industries, giving way to periodic disproportionality crises. During these crises workers are routinely laid off en masse, while essential goods go underproduced. Moreover, when capital shifts away from the more labor intensive industries, an inevitability in the majority of cases, those workers who were laid off won't find jobs in the newly favored industries. We therefore also obtain an argument for a growing reserve army which is supplementary to the one Marx gave in volume I.

• More generally, I believe that this model demonstrates the fundamental flaws of any economy trying to accumulate a single aggregate quantity such as value or money. Any economy which is incentivized to accumulate just one thing will inevitably produce disproportionalities anywhere and everywhere else. This is consequential to anyone attempting to develop a planned economy - it shows that the planning must be done in real terms. That is, in terms of the actual number of things one wants and needs: number of cars, number of workers, number of houses, and so forth.

• I developed a Desmos app in order to demonstrate these conclusions visually, which can be found by clicking here. A write up on how to use the app can also be found here, although it has errors which are corrected in the video. I recommend watching part II over reading the write up until I have time to rewrite it.

What originally started as a series of talks that I gave in the graduate logic group seminar balooned into an online class building up from the definition of a Turing machine all the way to a full proof of Gödel's incompleteness theorems. A particular videos is embedded here on the left, but the entire playlist can be found by clicking the link underneath.

What I like about these videos is that despite the material being discussed, the material is accessible to any audience regardless of what they know. You don't need to have a master's degree in mathematics to understand Gödel's theorems, and my videos prove that. They don't have many views, but if I'd found them back when I was an undergraduate CS major, I would have been all over them.