Prime

Today being the 11th of December, let me point out that 11 is what mathematicians call a número primo/prime number. The primes are one of three categories into which the positive whole numbers are divided. Most common are the composites, each member of which can be represented by a rectangular array of dots with the same number of dots in each row. For instance, we can represent the composite number 12 as three rows of four dots each:

•    •    •    •
•    •    •    •
•    •    •    •

In contrast, a prime number cannot be represented as a rectangular array. We may try with the prime number 11, but we have one dot too few to fill up a second row

•    •    •    •    •    •
•    •    •    •    •

or we have a surplus dot that spills over into a third row

•    •    •    •    •
•    •    •    •    •

(That last dot can also serve as the period at the end of the previous sentence.) No, the only possible arrangement for 11 is

•    •    •    •    •    •    •    •    •    •    •

In other words, all the dots end up in the first—and only—row. That’s one way of explaining why such a number is called primo/prime, from the Latin word for ‘first,’ primus. Historically, the ancient Greeks had the notion that the primes are first in importance, the fundamental type of whole number. The composites were secondary because they can always be expressed as products of primes (which amounts to saying that we can make rectangular arrays of dots to represent them).

Ironically, as fortunate readers may remember having been taught during their years en la primaria/in primary school, the Greeks placed the very first positive whole number, 1, which was of prime importance to them, in a category of its own. The ancients accorded the number 1 that distinction for being the first [positive whole] number, the generator (by addition) of every other number.

All of this tempts me to proclaim the primacía/primacy of mathematics over everything else, but I would never do such a thing in a column about etymology, where words are our prime consideration.

————

For more about the English word eleven and its not-at-all-obvious connection to something in Spanish, see last year’s post “The hidden one in once and eleven.”

© 2015 Steven Schwartzman

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In my prime

The previous article was the 181st in this series, and you’ll forgive the eternal math teacher for saying that that post certainly makes me feel like I’m in my prime—not only because 181 is a lot of articles for a little over half a year, but also because 181 is what mathematicians call a número primo/prime number. The primes are one of three categories into which the positive whole numbers are divided. Most common are the composites, each member of which can be represented by a rectangular array of dots with the same number of dots in each row. For example, we can represent the composite number 12 as three rows of four dots each:

•    •    •    •
•    •    •    •
•    •    •    •

In contrast, a prime number cannot be represented as a rectangular array. We may try with the prime number 7, for example, but we have one dot too few to fill up a second row

•    •    •    •
•    •    •

or we have a surplus dot that spills over into a third row

•    •    •
•    •    •

The only possible arrangement for 7 is

•    •    •    •    •    •    •

In other words, all the dots end up in the first—and only—row. That’s one way of explaining why such numbers are called prime, from the Latin word for ‘first,’ primus (which we discussed in the recent entry for primavera). Historically, the ancient Greeks had the notion that the primes are first in importance, the fundamental type of whole number; the composites are secondary because they can always be expressed as products of primes (which amounts to saying that we can make rectangular arrays of dots to represent them).

Ironically, as fortunate readers may remember having been taught during their years en la primaria/in primary school, the Greeks placed the very first positive whole number, 1, which was of prime importance to them, in a category of its own. The ancients accorded the number 1 that distinction for being the first [positive whole] number, the generator of all others.

All of this tempts me to proclaim the primacía/primacy of mathematics over everything else, but I would never do such a thing in a column about etymology, where words are our prime consideration.

© 2011 Steven Schwartzman

Spanish numbers come to American football

In 2008, Chad Johnson, a wide receiver for the Cincinnati Bengals football team, legally changed his last name to Ochocinco to reflect the fact that his uniform has the number 85 on it. According to Wikipedia, Hispanic Heritage Month in 2006 provided the impetus for the name change.

Aficionados of football may not have noticed that 8 and 5 are Fibonacci numbers, but the MathWorld article on the subject includes a comic strip that manages to connect the Fibonacci numbers to football (though not to Chad Johnson).

And speaking of fútbol, a word that Spanish borrowed from English to designate ‘soccer,’ the Mexican soccer team América has a portero ‘goalkeeper’ named Guillermo Ochoa, though there have been no reports, nor are there likely to be, that his uniform has a large 8A (Ocho A) on it.

(For an earlier posting that included ocho, see the article on octubre.)

© 2011 Steven Schwartzman

Save 0¢

As I wandered the aisles of my local Whole Foods one afternoon not long ago I, noticed a bright yellow sign attached to the glass door of a showcase containing packages of frozen vegetables. At the top of the sign was the word SALE, but when I looked at the other information on the sign I saw that the “sale” price was $1.49, which also happened to be the regular price of one of those bags of frozen vegetables. Truth-teller that the sign was, its “You save ___” section read “You save 0¢.” Now, I don’t think I’d ever seen a sign making a big to-do of the fact that customers would save nothing by buying an item, so I called over the first person I could find who worked in the store and pointed out the sign to him. He was baffled by it too, so he ended up giving me a bag of vegetables for a price equal to the advertised amount of the “savings,” which is to say that I ended up paying zero for my bag of frozen vegetables.

If that sign was strange, so is the word cero/zero. If you’re wondering why I say cero/zero is peculiar, ask yourself whether zero is singular or plural. The number one is certainly a singular, and any attached noun shows that: un centavo, one cent. Two, three, four, and every higher number are plurals, and any modified noun takes a plural form: dos centavos, two cents. Now for the strangeness: zero isn’t even as big as one, zero is in fact nothing, but when zero comes before a count noun (a noun that can be pluralized because it refers to things that are countable), that count noun appears in the plural. For example, a review of the children’s book How Many Elephants included the sentence “We open the flap that is the closet door to find zero elephants in the closet.” Spanish treats cero the same way, and I even found an example with the same noun; a Spanish-language Wikipedia article on cero has this question and answer: “¿Cuánto tiempo tardaremos en llenar la caja [con elefantes]? Jamás la llenaremos si tenemos cero elefantes.” And if you let me use the word singular with its meaning ‘out of the ordinary, unusual, strange,’ then I can put the striking conclusion this way:

The singular number cero/zero behaves like a plural.

This strange behavior of the number 0 most likely comes from the fact that for most of human history, whenever people started to count things, they began with 1, and that’s still almost always true today. Indo-European reflected human history: it had a set of endings for the singular, and another set for the dual, which was used for things that come in natural pairs, like eyes. Beyond that, all other whole numbers were put into the plural category, for which there was a third set of endings. After thousands (probably tens of thousands) of years of human development, some very smart people—notably among the ancient Hindus and Mayans—conceived the idea of zero. Psychologically, we seem to think of the number 0 as just another late addition to our number system, and we lump it in with all the large numbers that we are free to add to the right end, which is the plural end, of the infinite chain of numbers.

But wait, you object: this is a language blog, not a blog devoted to grocery stores or mathematics, and you’ve told us zero about the origins of the word cero/zero itself. All right, let’s zero in on that bit of etymology. Spanish and English borrowed their words from Italian zero, which was simplified from Medieval Latin zephirum. That had come from the Arabic sifr that meant ’empty, nothing,’ which is a good description of zero. In a different line of development, Medieval Latin turned the Arabic word into cifra, which passed unchanged into Spanish; it also became Old French cifre and then English cipher, which originally meant the same as its doublet zero. A cifra/cipher came to be ‘a character in general, whether a letter or a digit.’ Then, because people have long used numbers and letters to encode messages that they wanted to keep hidden, cifra/cipher added the meaning ‘a secret system of writing.’ Corresponding to that sense of the word we have the verb descifrar/decipher, with its extended meaning ‘to figure out’ (and notice how English figure can be a synonym of cipher).

© 2011 Steven Schwartzman

Note: For another take on zero and cipher, see a recent post at The virtual linguist.

octubre

Yesterday a friend passed along a message noting that October 1, 2010, which is today’s date, can be written as 011010. We understand the pleasantry of that faux binary notation, which more straightforwardly represents the first day of the tenth month of the year [20]10. Ah yes, octubre/October, the tenth month of the year. But wait, doesn’t octo- mean ‘eight,’ and didn’t Latin octo evolve to ocho, the Spanish word for ‘eight’? And isn’t eight, with its gh that used to be pronounced, the native English cognate of Latin octo? There’s no escaping all that eightness. So why is October the tenth month of the year? The answer is that the Roman calendar originally began with the month of March, and October was the eighth month of that year. The later addition of January and February bumped everything two months further down the line, leaving septiembre/September, octubre/October, noviembre/November, and diciembre/December etymologically untrue to their numerical names.

©2010 Steven Schwartzman

y e i

Yesterday’s column mentioned that the Russian cognate of Spanish y is И, which has the same pronunciation and meaning. Much closer to the Spanish-speaking world is Catalan i, which also means ‘and.’ Spanish has taken its share of words from Catalan, including a couple of picturesque phrases with i in them. One is Catalan canta i plora, which translates as canta y llora ‘it sings and it cries.’ Spanish has converted that to cantimplora, a noun that means ‘a siphon, water bottle, canteen, flask.’ The phrase originated as a clever description—we might say an imaginative and poetic one—of the sounds that people imagine they hear when a liquid gurgles its way through any of those containers. The other Catalan phrase that has flowed into Spanish is cap-i-cua, which corresponds to cabeza y cola ‘head and tail.’ Spanish has rewritten that as capicúa ‘a numeral that reads the same from “head” to “tail,” i.e from left to right, as it does from “tail” to “head,” i.e. from right to left.’ In other words, a capicúa is ‘a palindromic numeral’ like 14641. The arithmetically adept will recognize 14641 as the square of the likewise palindromic 121, which is itself the square of the palindromic 11. An impressed English speaker can reply in kind, which is to say palindromically, with “Wow!” or “Yay!” or “Aha!” Any Spanish speaker who would like to add an appropriate response in that language is welcome to post it as a comment.

©2010 Steven Schwartzman

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©2011–2016 Steven Schwartzman
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