Question about Mathematics from Zamiatin.

[David Powelstock]

I don't think this etymology is false, although it is, perhaps, incomplete.
If I'm not mistaken, the Pythagoreans referred to irrational numbers as
*alogos*--'inexpressible,' but also 'irrational,' insofar as the inability
to express something in terms of whole numbers offended the Pythagoreans'
sense of the rational order of the cosmos (*logos*, in its other sense).
Presumably, the earliest Latin translators of Euclid chose the wrong aspect
of*logos *to emphasize in translating it as *ratio *('reasoning,'
'calculation'). Only because of this translation--or mistranslation--did
*ratio *acquire the meaning in Latin of 'proportion,' which was then
propagated into English and other modern languages. Even if we see this it
as a mistranslation (at the very least it is a misleading one!), it is
nevertheless the etymological source of 'ir/rational number.' For
historically contingent reasons, the term retains a piquant trace of
Pythagorean cosmology. At least this is as near as I can figure it.

Cheers,
David P.

 * * * * * * * * * *
​David Powelstock
Brandeis University
​

On Sun, Dec 8, 2013 at 3:38 PM, R. M. Cleminson <rmcleminson at post.sk> wrote:

> The Russian textbook, as so often, is wrong: "ratio" in this context does
> not mean "reason", but "ratio", and (as someone in this discussion has
> already stated) a rational number is one that can be expressed as a
> fraction (i.e. the ratio between two whole numbers), whereas an irrational
> number cannot.  (This all goes back to ancient Greek mathematics.)
>  Nevertheless, a false etymology is also a cultural datum...
>
> ----- Pôvodná správa -----
> Od: "Alexandra Smith" <Alexandra.Smith at ED.AC.UK>
> Komu: SEELANGS at LISTSERV.UA.EDU
> Odoslané: nedeľa, 8. december 2013 12:23:19
> Predmet: Re: [SEELANGS] Question about Mathematics from Zamiatin.
>
> Dear Terry,
>
> A similar explanation in Russian is given here, so you could check the
> terminology used in Russian textbooks on mathematics:
> http://numbers.kalan.cc/irrational.php
>
> And here: http://school.xvatit.com/index.php?title=Иррациональные_числа
> The latter explains why the word "irrational" is being used to signify
> smth. that is opposite of something that is rational: "Прежде всего
> заметим, что в математике не принято говорить «нерациональное число»,
> обычно используют термин иррациональное число. Термины «рациональное
> число», «иррациональное число» происходят от латинского слова ratio —
> «разум» (буквальный перевод: «рациональное число — разумное число»,
> «иррациональное число — неразумное число»; впрочем, так говорят и в
> реальной жизни: «он поступил рационально» — это значит, что он
> поступил разумно; «так действовать нерационально» — это значит, что
> так действовать неразумно)."
>
> All best,
> Alexandra
>

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