## Odevity or parity

[This is a guest post by Jeffrey Shallit]

A Chinese student here at Waterloo used the term "odevity" for what English-speaking computer scientists typically call "parity" — the property of an integer being odd or even.

I had never heard this term before, so I used Google Scholar to look at where it is being used.  It is used almost exclusively by Chinese engineers, mathematicians, and computer scientists.  The first usage I was able to find with Google Book Search was in 1972, obtained with this search.

I asked my student where he had learned the term, and this is what he replied:

The word "odevity" is the translation of jī​'ǒu​xìng 奇偶性 that was found in an online Chinese-English dictionary. The conception behind this word is widely introduced in mathematic course of primary schools in China. I believe this is the reason that leads us to the same choice of word.

Bing search for "odevity" [VHM:  yielded nothing on my computer; this Google search returned 3,160 results]

Anyway, I found it interesting that Chinese researchers have coined their own English word  for this concept, which only they use.

=========================

When I look up ​jī​'ǒu​xìng 奇偶性 online (for which I receive 555,000 ghits), I find that it is usually translated as "parity (odd or even)".  The three characters individually mean "odd even nature".  This term is also written as jī'ǒushù 奇偶数 (which returns 282,000 ghits).  The three characters of this variant expression of the concept individually mean "odd even number".

N.B. 奇 has two pronunciations:  ​jī​ ("odd [number]") and qí ("strange; odd; weird; wonderful; surprisingly; unusually").

A final note

So far as I can tell, the term "odevity" has never appeared on Language Log.  In contrast, "parity" is not a stranger to our posts and comments, but it usually is in reference to human equivalence in automatic machine translation or equivalent levels of purchasing power, etc.

1. ### Jonathan Smith said,

May 15, 2019 @ 3:24 pm

Apparently beyond "translation" this a fairly awesome calque mash of 奇偶性 (od+ev+ity). I suppose one should also pronounce it thusly…

2. ### Jonathan Smith said,

May 15, 2019 @ 3:39 pm

*is.
Certain biases could be removed by coining all "degree"nouns in this manner a la Chinese, thus length = loshity, height = tashity, etc.

3. ### Anthony said,

May 15, 2019 @ 3:40 pm

My favorite palindrome: "never odd or even"

4. ### Jeffrey Shallit said,

May 15, 2019 @ 3:44 pm

For me, the bing search returns this.

5. ### David Morris said,

May 15, 2019 @ 3:48 pm

Surely the property of being odd or even is 'oddivity'!

6. ### Jerry Friedman said,

May 15, 2019 @ 5:49 pm

Is it odd that the English word and the Chinese character for "odd (parity)" both also mean "strange"?

7. ### Jim Breen said,

May 15, 2019 @ 6:16 pm

Is there a Chinese equivalent for the Japanese 和製英語 (wasei eigo – Japanese-made English)? Surely "odevity" would be a candidate.

Actually it would be a handy word in Scrabble, having both a "v" and a "y", but I doubt it would get past my wife.

8. ### Kenny said,

May 15, 2019 @ 7:21 pm

Somehow a site called "WikiDiff" has learned enough about this word to create a page about "the difference between parity and odevity", but not enough to understand that "odevity" is in some sense a word. And somehow this page comes up above the current Language Log post when I search for "odevity". The lower things are mainly Chinese translation dictionaries.

https://wikidiff.com/odevity/parity

9. ### Ken said,

May 15, 2019 @ 7:39 pm

Computer science also has the odious and evil numbers, terms coined by John Conway for numbers having an odd (even) number of bits in their binary representation.

10. ### Jonathan D said,

May 15, 2019 @ 7:43 pm

It's worth noting that the results in Jeffrey Shallit's search, and also many of the top search results for 奇偶性, are talking about odd and even functions, rather than odd and even integers.

In my experience, many mathemeticians don't use the English word 'parity' to describe whether a function has odd and/or even status. (For one thing, most functions are neither odd nor even, unlike integers, and parity is often reserved for concepts that split a set into exactly two parts.) So it's not particularly surprising that someone used to the term 奇偶性 invented a new English term that could be used in that context. From there, it's understandable that it might also be used for the parity of integers.

11. ### Jim Breen said,

May 15, 2019 @ 8:30 pm

奇偶性 can be found in Japanese too (きぐうせい kigūsei), but it is far less common than the usual loanword パリティ(ー) (parati). The only places I can find 奇偶性 in Japanese dictionaries are in EJ dictionaries where it is often given as a translation of "parity" in a computing context, along with パリティ(ー).

12. ### B.Ma said,

May 15, 2019 @ 11:58 pm

In primary school we used "oddness".

13. ### Richard Warmington said,

May 16, 2019 @ 12:50 am

Jim Breen: "… is far less common than the usual loanword パリティ(ー) (parati)."
That should be (pariti).
Or, when the final syllable is lengthened, (paritī).

14. ### Victor Mair said,

May 16, 2019 @ 5:52 am

If you're going to use "oddness", might as well use "oddity", except that's already taken for something else.

15. ### jpiitula said,

May 16, 2019 @ 5:55 am

I'm totally calling it oddity. And the oddest prime is two, because it's the only one that's even.

16. ### unekdoud said,

May 16, 2019 @ 7:00 am

I find this interesting because the general concept for numbers is called "divisibility". Are there any languages that prefer "evenness" over "oddness", or "even/odd" over "odd/even"?

17. ### KeithB said,

May 16, 2019 @ 8:42 am

I don't know if computer science is different, but the only usage of parity that I have seen is as a "check bit". It is a simple way to verify that the serial character you sent came through with all bits intact. You can set whether the parity bit is odd or even and it is simply the oddness or evenness of the count of "one" bits in the character.

18. ### cameron said,

May 16, 2019 @ 9:40 am

Yeah, "odevity" is highly weird – it's plainly not something a native speaker would ever have come up with. Oddness or oddity would be unremarkable.

Of course, the word "parity" itself could be glossed in non-Latinate form as "evenness".

19. ### RP said,

May 16, 2019 @ 10:35 am

"Parity" and "oddness" mean slightly different things. "Parity" (like "odevity") means the quality of being odd or even, whereas "oddness" means the quality of being odd. An even number would lack oddness, whereas both odd and even numbers have parity (just a different parity from each other).

Historically, the word "parity" did indeed mean "evenness" (the quality of being even), as Cameron suggests. It's only recently that its meaning has shifted to the quality of being odd or even.

In the OED:
II 4 (a) (two citations, 1620, 1646): " The property of a number of being even and not odd. Obsolete."
(b) (first cited 1879): " Mathematics. The property of an integer by virtue of which it is odd or even. Also: (Computing) the property of using an odd or an even number of digits."

Oddness: "the quality of being odd or uneven; unevenness of number".

By contrast, the OED doesn't have a mathematical definition of "evenness" – so there is possibly no equivalent now to the old/original meaning of "parity".

20. ### cameron said,

May 16, 2019 @ 2:38 pm

Aside from the historical usage of "parity" in English to refer to "evenness" in the mathematical sense, what I was getting at is that if you're familiar with Latin or its modern daughter languages, the word "parity" is obviously and transparently equivalent to "evenness".

21. ### Melissa said,

May 16, 2019 @ 2:49 pm

In German, “odd” of numbers is expressed merely as “uneven” – «gerade», «ungerade». However, for the concept as a whole, the Latin-derived «Parität» is typically used, though «Geradheit» “evenness” would seem like a natural term for it.

22. ### Brett said,

May 16, 2019 @ 10:59 pm

@Jonathan D: I head about the "parity" of even or odd functions all the time.

23. ### eub said,

May 22, 2019 @ 1:02 am

@Brett doesn't that make for a three-valued parity? What is said about a general function, that it has no parity?

What about the 0 function that's both even and odd?