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In a previous post we discussed coordinate changes in linear algebra. In this post, we want to expand upon this by discussing descriptions of linear transformations in coordinates. Using the notation from the previous article, if and are spaces of objects, is a bijective descriptive framework for objects in , and is a bijective descriptive…

Ancient Greek philosophers used to study mathematics, because mathematical thinking provided an ideal model of philosophical thought, free of the complications of hairier subjects in philosophy like ethics. Plato’s dialogue Meno, for example, uses a mathematical demonstration to probe the nature of knowledge. Although at times mathematics can seem like it has no connection to…

The majority of jobs in the US require the use of computers. This is only expected to increase over time. According to the Washington Post, only four states allow inmates access to the internet. Not only is this denying inmates the ability to communicate with their friends and relatives, which might ease their transition back…

N.B. For clarity, text that represents an argument put forward by an ideological opponent (not representing my own views) will be colored purple rather than black. Arguments from a sense of paternalism and from humankind’s supremacy over other animals are pretty common tactics used to defend against the claim that we should give farmed animals…

According to folklore, the physicist Richard Feynman, who boasted about his mathematical intuition, was once asked by some trickster mathematicians whether it is possible to break the unit ball into finitely many disjoint pieces, and re-arrange them by rigid motions to form two unit balls. Such a procedure is known as a “paradoxical decomposition”. Feynman…

While many of the superstitious mathematical beliefs of the Pythagoreans seem silly today, like ascribing philosophical/religious meaning to certain numbers, they were in some ways ahead of their time. Check out their stance on animal rights and women in philosophy: The Pythagoreans advanced the argument that unless an animal posed a threat to a human,…

We can represent a single-player game as a tree, where each node corresponds to a state of the game, and each branch leaving a node corresponds to one of the possible moves you can make. Note that we could also represent two-player games in this way: player 1 makes a move at even levels of…