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

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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

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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

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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

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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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