Groucho Marxism
Questions and answers on socialism, Marxism, and related topics
Category: Mathematics
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Most people assume that numbers are the basic building blocks of mathematics. But mathematicians take sets to be the basic building blocks and construct numbers from them. In this blog post I will explain how this is done. First we need to construct the natural numbers: 0, 1, 2, 3, and so on. There are…
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When children first start learning about numbers, a question they often ask is: what is the biggest number? At which point we adults usually explain that there is no biggest number as whatever number you can think of, you can always add 1 to make an even bigger number. But what if that wasn’t actually…
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It is now generally accepted by most (although not all) people that promoting and delivering Equality, Diversity, and Inclusion (ED&I) is a good idea. But what exactly do we mean by ED&I? The usual definition given is something along the lines of: ‘equality’ means ensuring everyone has the same rights and opportunities, regardless of their…
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Quantum computers are advanced computing systems that harness quantum mechanics—specifically superposition and entanglement—to solve complex problems beyond the reach of classical computers. Unlike classical computers that use binary bits (0 or 1), quantum computers use quantum bits (qubits), allowing them to process vast amounts of data simultaneously. Qubits can exist in multiple states at once,…
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In 1937 the Hungarian mathematician and physicist Jon von Neumann published a paper entitled A Model of General Economic Equilibrium, in which he set out an abstract mathematical model of an economy. Von Neumann’s model is still used widely today, particularly by Marxist economists. In this blog post I will provide a brief summary. The…
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The socialist calculation debate was a discourse held in the 1930s and 1940s that centred on how a socialist economy would perform economic calculation in the absence of private ownership of the means of production. The debate was primarily between the ‘Austrian School’, represented by economists Ludwig von Mises and Friedrich Hayek, who argued against…
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Happy new year first of all, to anyone who happens to be reading this. One of my new years’ resolutions is to make an effort to finally understand some concepts that I’ve always struggled to get my head around. I am going to start with the concept of ‘dialectics’. The term ‘dialectic’ comes from the…
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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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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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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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