Question about Mathematics from Zamiatin.

Sun Dec 8 22:04:48 UTC 2013

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
Assoc. Prof. of Russian and Comparative Literature
Director, Master of Arts in Comparative Humanities
Brandeis University
Waltham, MA 02453

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
>
>
> Quoting Terry Moran <t.moran at NEW.OXON.ORG> on Sun, 8 Dec 2013 10:48:04
> +0100:
>
> > A note on imaginary / complex and irrational / transcendental numbers.
> >
> > If we place real numbers on the horizontal axis (1, 2 etc. going right,
> -1,
> > -2 etc. going left), then the vertical axis (intersecting with it at zero
> > on both axes) represents *imaginary numbers:* i, 2i etc. going up, -i,
> -2i
> > etc. going down. i is the symbol arbitrarily assigned to the square root
> of
> > minus 1, obviously imaginary because no real number gives minus 1 when
> > multiplied by itself. Any point located on the plane formed by these two
> > axes but not actually on either of them is called a *complex *number: i +
> > 4, -7 - 3i for example, in the north-east and south-west quadrants
> > respectively.
> >
> > Irrational numbers have numerical expansions that never end and never
> > repeat. Examples are pi (3.14159...), e (2.71828...) and the square root
> of
> > 2 (1.41421...), but these aren't all the same: some irrational numbers
> are
> > also *transcendental*, which means they're not the root of a polynomial
> > equation. The square root of
> > 2<http://en.wikipedia.org/wiki/Square_root_of_2> is
> > irrational but not transcendental, since it's a solution of the
> polynomial
> > equation x2 - 2 = 0. There are no polynomial equations to which the
> > solution is pi or e, so they're transcendental as well. There are lots of
> > others.
> >
> > Russian uses the same terms: мнимые / комплексные and иррациональные /
> > трансцендентные числа. I assumed the Russian for *real numbers* would
> > be реальные числа, but on checking I find it's вещественные числа.
> >
> > I'm open to correction on both the maths and the language!
> >
> > Terry Moran
> >
> >
> > On 7 December 2013 18:46, Anthony Anemone <AnemoneA at newschool.edu>
> wrote:
> >
> >> Dear colleagues,
> >>
> >> I'm puzzled about Zamaitin's usage of иррациональный when referring to
> the
> >> square root of -1.  As far as I understand math terminology in English
> (not
> >> that far!), wouldn't that be an imaginary number?  Perhaps terminology
> in
> >> Russian is different?
> >>
> >> Thanks!
> >>
> >> Tony
> >> --
> >> Tony Anemone
> >> Associate Professor
> >> The New School
> >> 72 Fifth Ave, 702
> >> New York, NY 10011
> >>
> >>
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