Groucho Marxism
Questions and answers on socialism, Marxism, and related topics
Category: Mathematics
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In a previous blog post I derived discrete versions of two key equations in quantum mechanics: the canonical commutation relation between position and momentum, and the Schrödinger equation. I did this by considering a particle moving in discrete time and space where time was taken to be imaginary. The eagle-eyed reader would have noticed a…
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Mathematical optimization is the selection of a best element, with regard to some criterion, from some set of available alternatives. The criterion is specified using an objective function on a given domain and the aim is to find the variable that maximizes or minimizes this function within this domain. Mathematical optimization is generally divided into…
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Calculus is the mathematical study of change. It has two major branches: differential calculus and integral calculus. The former concerns rates of change and the slopes of curves, whereas the latter concerns accumulation of quantities and areas under or between curves. Calculus was formulated separately in the late 17th century by Isaac Newton and Gottfried…
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In linguistics, the term ‘phoneme’ refers to any of the perceptually distinct units of sound in a specified language that distinguish one word from another; for example p, b, d, and t in the English words pad, pat, bad, and bat. Languages vary considerably in the number of phonemes they have, from as few as…
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The principle of stationary action is a great unifying principle of physics, and is usually presented in a continuous-time framework. In this blog post I will attempt to present a discrete-time formulation of the principle in accordance with the materialist conception of physics I put forward in a previous blog post. Let x(t) denote the…
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Consider an economy which produces m commodities using n types of labour. For such an economy we can define a commodity vector as a vector with positive elements of length m, and a labour vector as a vector with positive elements of length n. The economy is defined by an activity set, with the interpretation…
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Marxists often claim that workers are exploited under capitalism. In fact this is usually considered a central tenet of Marxism. But what exactly do we mean by ‘exploited’? In this blog post I will attempt to provide a rigorous definition (actually three rigorous definitions). To kick things off, consider an economy which produces m commodities…
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In a previous blog post I suggested that some ideas in physics that seem strange when formulated in a continuous framework based on infinite sets make more sense in a discrete framework based on finite sets. In this blog post I will attempt to flesh this out in more detail. Consider a particle moving in…
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An axiomatic system is a set of formal statements (axioms) used to logically derive other statements. Zermelo-Fraenkel set theory, henceforth ‘ZF’, is an axiomatic system proposed by mathematicians Ernst Zermelo and Abraham Fraenkel in the early twentieth century to formulate a theory of sets. Today, ZF is the standard form of axiomatic set theory and…
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