Tag Archives: angle

In philosophical debates about absolute truth, people cite “the truths of pure mathematics” as beyond reproach—eternal and universal things discovered/invented by us fallible mortals. But the more deeply I look into these issues myself, the more I see evidence that … Continue reading

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Space

The word ‘space’ has acquired several meanings, which is what you would expect of such a sexy, primitive, metaphorically rich, eminently repurposeable concept. Outer space, of course, is where cosmonauts, Hubble telescopes, television satellites, and aliens reside. It’s ℝ³, or … Continue reading

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Angle = Volume

This is trippy, and profound. The determinant — which tells you the change in size after a matrix transformation 𝓜 — is just an Instance of the Alternating Multilinear Map. (Alternating meaning it goes + − + − + − + … Continue reading

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How to multiply matrices

This is for my homies in math class. Mathematical matrices are blocks of numbers, arrayed in 2-D. (Higher-dimensional arrays are called tensors.) Left “times” right equals target. Each entry in the target is the result of a series of +’s … Continue reading

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Circles

A circle is made up of points equidistant from the center. But what does “equidistant” mean? Measuring distance implies a value judgment — for example, that moving to the left is just the same as moving to the right, moving forward … Continue reading

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Vectors

Vectors, concretely, are arrows, with a head and a tail. If two arrows share a tail, then you can measure the angle between them. The length of the arrow represents the magnitude of the vector. The modern abstract view is … Continue reading

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