Question about Mathematics from Zamiatin.

Mon Dec 9 07:57:06 UTC 2013

Up to a point.  It should be remembered that "reckoning" is the primary meaning of "ratio" in Latin, and that the use of the word to mean the capacity for reckoning, or cognitive faculty, is secondary.  Similarly, ἄλογος does mean "unreckoned" or "incalculable" in Greek, as well as "unreasoning", so there is no question of a mistranslation of Euclid into Latin.  What is more - though it comes as something of a shock to those of us brought up in the Christian tradition - it appears that the meaning of λόγος in Greek may well have undergone a similar evolution: after all, λέγω in Homer may mean "count", but not "speak", which is a later meaning.  All this, of course, without prejudice to whatever the Pythagoreans may have made of it.

It should also be remembered that irrational numbers are not unreasonable: it is precisely human reason that allows us to identify π as a number and use it in calculation, even if we cannot quantify it exactly.  And any number, real or imaginary, rational or irrational, is an abstraction.

----- Pôvodná správa -----
Od: "David Powelstock" <pstock at BRANDEIS.EDU>
Komu: SEELANGS at LISTSERV.UA.EDU
Odoslané: nedeľa, 8. december 2013 22:04:48
Predmet: Re: [SEELANGS] Question about Mathematics from Zamiatin.

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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