Tag Archives: posets

the Begats

The word < is normally defined to mean less than in some quantifiable sense. For example, considering the set {3,6,1441}, one could say that 3<6<1441. But in the abstract language of partially ordered sets, < is reinterpreted many ways — … Continue reading

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It’s not always possible to say A ≻ B or A ≺ B. Sometimes neither A nor B is smaller.        A≹B neither A nor B is more successful.   A≹B neither A nor B is prettier.   … Continue reading

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What’s Wrong with OKCupid’s Matching Algorithm

OKCupid is using the wrong mathematics to match potential dates together. But before I critique them, let me compliment them on what they’re doing right: “Our” mutual score is the geometric average of your score of me, and my score … Continue reading

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Paul Finsler believed that sets could be viewed as generalised numbers. Generalised numbers, like numbers, have finitely many predecessors. Numbers having the same predecessors are identical. We can obtain a directed graph for each generalised number by taking the generalised … Continue reading

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Ethnic Food as a Poset

I like Indonesian food better than Japanese food i ⪰ j, and I like Japanese food better than English food j ⪰ e. I also like French food better than English food f ⪰ e, but I see French food as so different … Continue reading

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Popularity

At my secondary school, the high-scoring wide receiver was more popular than the fat lineman. And the fat lineman was more popular than the team statistician. But you couldn’t really compare the wide receiver’s popularity to that of the actor … Continue reading

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Blood Types

Blood types form a topological space (and a complete distributive lattice). There are three generators: A, B, and Rh+. Above the “zero element” is the universal donor O− and the “unit element” is the universal receiver AB+. A topological space contains … Continue reading

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