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According to the Fields medal winner Cédric Villani, in the Japanese language the word 'analysis' is (I quote) "the same word" as the word for 'fine cuisine'.

Such can be seen in a video of a recorded lecture of him entitled "The Extraordinary Theorems of John Nash" at the Royal Institution, published on 2 November 2016, about 22 minutes and 12 seconds through the footage.

I assume that Villani has more knowledge of mathematics than of Japanese, and we have to bear in mind this was not the focus of the speech but one of many trivialities to (quite successfully in my opinion) spice up the comprehensibility and inspiration of a math lecture.

Of further interest: is the Japanese word for 'analysis' at least part of the Japanese term for 'mathematical analysis', or requires the second specific mathematical meaning an exclusive expression instead?

Who can elaborate on, clarify, validate or debunk this please? In particular, it is not clear what is insinuated by the usage of the expression "the same word". Which word is being concerned here please?

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No. Japanese "haute cuisine" is called 懐石(料理). Mathematical analysis is 解析(学). What is true is that 懐石 and 解析 are homophones, both pronounced かいせき and, in context, both may be referred to as かいせき. However, they are not the same word.

By the way, there are more homophones for かいせき, so he could have also said that "analysis" is the "same word" as bizarre stones (怪石) or dissection (as in dissected/heavily eroded plateau) (開析) or even meeting place or party table (会席).

  • is the pitch accent the same in these homophones? – James K Dec 14 '16 at 22:04
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    @JamesK Yes, maybe I should have said. The pitch accent is the same in all of these homophones (flat low pitch). – Earthliŋ Dec 14 '16 at 22:17
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While the pronunciation is the same, the words' etymologies are unrelated.

Mathematical analysis is 解析(kaiseki かいせき) while (Japanese) fine cuisine is 懐石(kaiseki かいせき).

Both 解 and 析 roughly stands for "understanding", "taking apart". For example, 解説(kaisetu) means "To orally explain", 分析(bunseki) means "To analyze". On the other hand, 懐(kai) refers to the pocket-like space that is created above the belt, around the belly button and 石(seki) means stone. It originally refers to a technique used by Buddhists, where they would pack a warm stone in that pocket to suppress hunger.

I.e. they are not at all the same word, but they do share the pronunciation.

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