Manifolds are called 多様体 (tayōtai) in Japanese, which very roughly means "many-kind-objects" and I think that's beautiful; not as confusing as "where are all the folds though"-manifolds in English.
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Replying to @BiCapitalize
It's misleading to translate 様 (yō) as "kind." Its meaning is closer to "manner," or "style," or "fashion." It describes how a person or thing habitually behaves, as a means to its unique specification (as in "Le style, c'est l'homme-même.") You're thinking of 類 (rui.)
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Replying to @MathPrinceps
No, I'm not thinking of 類 or 種 or anything like that. You misinterpreted the meaning of "kind" I used; you could make a point I should have chosen a different word in English, but I'm honestly not sure which.
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Replying to @BiCapitalize
Then please explain the meaning of "kind" you intended. I assure you that there was nothing willful or uncharitable about my failure to interpret it as you wished. I still maintain that the most common use of the word "kind" is clearly different from the most common use of 様.
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Replying to @MathPrinceps
Basically exactly what you said. "Kind" is synonymous to "manner", or "style" in certain use cases, and this is one of them (or at least I intended it to be). It seems that most people understood what was intended; at the very least, nobody apart from you complained.
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Replying to @BiCapitalize
Perhaps the most common use of 様 (yō) in Japanese is in the phrase "~の様に" (~ no yō ni), which means "in the manner of ~." It does not mean "of the same kind as ~." Words may flow in the manner of a river, but words and rivers are not things of the same kind.
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This is not a complaint. It is an observation about Japanese usage that aims at the preservation of distinctions on which the Japanese have found it useful to insist. The precise articulation of meaning is just as important to the Japanese as it is to mathematicians.
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