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Tag Archives: metric spaces
[T]he point of introducing L^p spaces in the first place is … to exploit … Banach space. For instance, if one has ƒ − g = 0, one would like to conclude that ƒ = g. But because of the … Continue reading
Movie Ratings
Another unmeasurable distance is ★★★ movie ratings. Movie ratings are drawn from the set {★,★★,★★★,★★★★,★★★★★} and related by the total ordering >: ★★★★★ > ★★★★ ★★★★ > ★★★ ★★★ > ★★ ★★ > ★ and the transitivity of > gives … Continue reading
Posted in Uncategorized
Tagged abstract algebra, Amos Tversky, distances, film, isomorphism, math, mathematics, maths, metric spaces, metrics, movies, Netflix, recommendation engines, topology
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The Hotness Scale
One example of a total ordering ≤ is the “hotness” scale from 1–10. Because of the widespread disagreement about the meaning of the numbers, the only thing one can infer based on a man’s rating of a woman is that … Continue reading
Posted in Uncategorized
Tagged attraction, boys, comparable, distance, geometry, girls, hotness, LGBTQ, liking, math, mathematics, maths, measures, metric, metric spaces, metrics, norm, norms, partially ordered set, partially ordered sets, poset, posets, quantification, sex, sex appeal, sexiness, size
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Unmeasurable Distances
I wrote earlier about the many different ways to measure distance. One way I didn’t include is unmeasurable distance. Sometimes A is tastier, sexier, cooler, more interesting, or otherwise better endowed than B … but it’s impossible to quantify by … Continue reading
Posted in Uncategorized
Tagged comparable, distance, economics, education, geometry, imagination, math, mathematics, maths, metric, metric spaces, metrics, norm, norms, philosophy, preference, preorder, rank, ranking, size, total order, unmeasurable distance, utility
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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
Posted in Uncategorized
Tagged angle, circle, education, geometry, Henri Poincaré, imagination, long reads, Lp norm, L_p norm, math, mathematics, maths, metric, metric spaces, metrics, noncommutative, norm, norms, Poincaré disk, size
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