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.
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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