1144. This week, we look at the origin of the letter X as the variable for the unknown in algebra. Then, we look at the phrase "how come," explaining why it's more informal than "why" and how its grammar subtly differs from other question words.
1144. This week, we look at the origin of the letter X as the variable for the unknown in algebra. Then, we look at the phrase "how come," explaining why it's more informal than "why" and how its grammar subtly differs from other question words.
That X segment was written by Peter Schumer, Professor of Mathematics and Natural Philosophy at Middlebury College, and it originally appeared on The Conversation and appears here through a Creative Commons license.
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Grammar Girl here. I’m Mignon Fogarty, your friendly guide to the English language. Today, we're going to look at why the letter X stands for the unknown in algebra (plus some X-related word info), and then we'll look at why we say "how come" for "why."
But first, did you know that right now you can get a free month of the Grammar Girl Patreon and when you do, you also get a free super-list of 100 books that are the best books our podcast guests have ever read. When you're finally relaxing and getting ready to settle in with a good book before the New Year, you'll love this list! The links are in the show notes, which is also called the show description or the episode details on some platforms.
This first segment is by professor of mathematics Peter Schumer.
by Peter Schumer
Even though x is one of the least-used letters in the English alphabet, it appears throughout American culture – from Stan Lee’s X-Men superheroes to “The X-Files” TV series. The letter x often symbolizes something unknown, with an air of mystery that can be appealing – just look at Elon Musk with SpaceX, Tesla’s Model X, and now X as a new name for Twitter.
You might be most familiar with x from math class. Many algebra problems use x as a variable to stand in for an unknown quantity. But why is x the letter chosen for this role? When and where did this convention begin?
Well, there are a few different explanations that math enthusiasts have put forward – some citing translation, others pointing to a more typographic origin. Each theory has some merit, but historians of mathematics, like me, know that it’s difficult to say for sure how x got its role in modern algebra.
Algebra today is a branch of math in which abstract symbols are manipulated, using arithmetic, to solve different kinds of equations. But many ancient societies had well-developed mathematical systems and knowledge without symbolic notation.
All ancient algebra was rhetorical. Mathematical problems and solutions were completely written out in words as part of a little story, much like the word problems you might see in elementary school.
Ancient Egyptian mathematicians, who are perhaps best known for their geometric advances, were skilled in solving simple algebraic problems. In the Rhind papyrus, the scribe Ahmes uses the hieroglyphics referred to as “aha” to denote the unknown quantity in his algebraic problems. For example, problem 24 asks for the value of aha if aha plus one-seventh of aha equals 19. “Aha” means something like “mass” or “heap.”
The ancient Babylonians of Mesopotamia used many different words for unknowns in their algebraic system – typically words meaning length, width, area, or volume, even if the problem itself was not geometric in nature. One ancient problem involved two unknowns termed the “first silver thing” and the “second silver thing.”
Mathematical know-how developed somewhat independently in many lands and in many languages. Limitations in communication prevented any immediate standardization of notation. However, over time some abbreviations crept in.
In a transitional syncopated phase, authors used some symbolic notation, but algebraic ideas were still presented mainly rhetorically. Diophantus of Alexandria used a syncopated algebra in his great work Arithmetica. He called the unknown “arithmos” and used an archaic Greek letter similar to s for the unknown.
Indian mathematicians made additional algebraic discoveries and developed what are essentially the modern symbols for each of the decimal digits. One especially influential Indian mathematician was Brahmagupta, whose algebraic techniques could handle any quadratic equation. Brahmagupta’s name for the unknown variable was yãvattâvat. When additional variables were required, he instead used the initial syllable of color names, like kâ from kâlaka (black), ya from yavat tava (yellow), ni from nilaka (blue), and so on.
Islamic scholars translated and preserved a great deal of both Greek and Indian scholarship that has contributed immensely to the world’s mathematical, scientific, and technical knowledge. The most famous Islamic mathematician was al-Khowarizmi, whose foundational book Al-jabr wa’l muqabalah is at the root of the modern word “algebra.”
One theory of the genesis of x as the unknown in modern algebra points to these Islamic roots. The theory contends that the Arabic word used for the quantity being sought was al-shayun, meaning “something,” which was shortened to the symbol for its first “sh” sound. When Spanish scholars translated the Arabic mathematical treatises, they lacked a letter for the “sh” sound and instead chose the “k” sound. They represented this sound by the Greek letter χ, which later became the Latin x.
It’s not unusual for a mathematical expression to come about through convoluted translations – the trigonometric word “sine” started as a Hindu word for a half-chord but, through a series of translations, ended up coming from the Latin word “sinus,” meaning bay. However, there is some evidence that casts doubt upon the theory that using x as an unknown is an artifact of Spanish translation.
The Spanish alphabet includes the letter x, and early Catalonian involved several pronunciations of it depending on context, including a pronunciation akin to the modern sh sound. Although the sound changed pronunciation over time, there are still vestiges of the sh sound for x in Portuguese, as well as in Mexican Spanish and its use in native place names. By this reasoning, Spanish translators conceivably could have used x without needing to resort first to the Greek χ and then to the Latin x.
Moreover, although the letter x may have been used in mathematics during the Middle Ages sporadically, there is no consistent use of it dating back that far. Western mathematical texts over the next several centuries still used a variety of words, abbreviations, and letters to represent the unknown.
For instance, a typical problem in the algebra book “Sumario Compendioso of Juan Diez,” published in Mexico in 1556, uses the word “cosa” – meaning “stuff” or “thing” – to stand in for the unknown.
I think that the most plausible explanation is to credit the influential French scholar René Descartes for the modern use of x. In an appendix to his major work “Discourse” in the 17th century, Descartes introduced a version of analytic geometry – in which algebra is used to solve geometric problems. For unspecified constants, he chose the first few letters of the alphabet, and for variables, he chose the last letters in reverse order.
Although scholars may never know for sure, some theorize that Descartes may have chosen the letter x to appear often since the printer had a large cache of x’s because of its scarcity in the French language. Whatever his reasons for choosing x, Descartes greatly influenced the development of mathematics, and his mathematical writings were widely circulated.
Even if the origins of x in algebra are uncertain, there are some instances in which historians do know why x is used. The X in Xmas as an abbreviation for Christmas definitely does come from the Greek letter χ. The Greek word for Christ is Christos, written χριστοσ and meaning “anointed.” The χ monogram was used as a shorthand for Christ in both Roman Catholic and Eastern Orthodox writings dating back as far as the 16th century.
There are also some contexts in which x was chosen specifically to indicate something unknown or extra, such as when the German physicist Wilhelm Roentgen accidentally discovered X-rays in 1895 while experimenting with cathode rays and glass.
But there are other cases in which scholars can only guess about the origins of x’s role, such as the phrase “X marks the spot.” And there are other contexts – such as Elon Musk’s affinity for the letter – that may just be a matter of personal taste.
That segment was written by Peter Schumer, Professor of Mathematics and Natural Philosophy at Middlebury College, and it originally appeared on The Conversation and appears here through a Creative Commons license.
by Mignon Fogarty
A listener named Barbara wrote in wondering about the phrase "how come":
The other day I was formulating a question for a Google search in my mind and started out with the phrase "how come ..." I then quickly realized that I should probably use the word "why" instead. Then I noted to myself that my natural tendency was to say "how come ..." instead of "why ..." and this made me wonder how common that is. Is it a regional kind of thing, where people in certain parts of the world would tend to say one more than the other? Or is it a speaking vs. writing issue? Formal vs. informal? Or what?
Thanks, Barbara. Great question!
The oldest reference for "how come" in the Oxford English Dictionary (OED) is an entry in Bartlett's Dictionary of Americanisms published in 1848. Although the OED says "how come" was invented in the United States, the entry in Bartlett's indicates it originated in England. That entry reads, "Doubtless an English phrase, brought over by the original settlers."
Regardless of whether "how come" truly originated in the United States, a search of the text in books scanned by Google Books shows that at least in those books, it is still more common in American English than British English. So there are regional differences, at least at the country level, but I wouldn't say it is limited regionally.
And yes, “how come” is considered to be more informal than “why.” The OED labels it as colloquial, and you’re more likely to see it on Facebook than in a corporate annual report.
As for speaking versus writing, this is getting a little bit beyond my research skills, but if I control for how big the databases are, it looks like “how come” appears more often in a corpus of spoken English than in a corpus of written English, and that matches what my guess would be. Since it’s informal, I’d expect it to be more common in spoken English than written English.
Barbara also asked where we get the phrase “how come.”
For example, here’s a line from the British poet Edmund Spenser’s “Sonnet 30,” first published in 1595, that uses the older, longer phrase:
And here’s an even older one from an English translation of Machiavelli’s “The Prince,” which was written around 1513:
Even in that type of use, it can be “how come” instead of “how comes.” For example, here’s a line from a British book printed in 1702 talking about how young animals know to function when they are first born:
We do love to shorten things. “Pantaloons” became “pants,” and “omnibus” became “bus,” and so “how comes it that” could have become “how come.”
And Barbara noted that “how come” can be something slightly different from “why.”
And she's right. In her book "Highly Irregular: Why Tough, Through, and Dough Don’t Rhyme," Arika Okrent points out that "how come" acts differently, grammatically, from "why."
You often have to use the words "do" or "does" with all the question words like "why." For example, if I tell Squiggly, "You always try to cover up the confetti incident," and you want to join the conversation with that rephrased as a question, you'd have to ask, "Why DO you always try to cover up the confetti incident?" You need that word "do."
But if you start with "how come" instead, you don't need the word "do." You can just ask, "How come you always try to cover up the confetti incident?" It's a subtle difference, but a real one that highlights the way "how come" isn't an exact substitute for "why."
And Okrent also points out reasons "how come" actually may not come from a shortening of "how comes it that" and similar phrases. For example, there's no direct line of evidence from one to the other, and the first uses of "how come" exactly the way we use it today don't appear until the mid-1800s in vernacular speech attributed to African Americans, Native Americans, and German immigrants.
So as with many informal phrases, there are multiple stories about where it might have come from, but what I can tell you is that it's quite widespread and is usually interchangeable with "why," even though grammatically it's a little different.
Thanks for the question!
Finally, I have a familect story.
"Hi, Mignon. I have a familect story. I will preface this by saying, you may need to bleep out a word. It may not be suitable for children, although it is about my 9-year-old daughter. So when she was little, we were in the car, and she'd asked me what the handles in the car that are above the windows were, and I said they were called the 'oh, shit' handle. And she said, what? And I repeated it, and she kind of just changed the subject, and a few weeks later, she said, 'Look mama, I'm grabbing the water handles, and she thought that I had said, ocean handle, and then she couldn't remember the word. And so, she just knew it had something to do with water and so now, we call those handles 'water handles.' I hope that made you giggle. It makes me laugh. Every time I think about it. Thanks."
Oh, that definitely made me laugh. Thanks!
Familects are words or phrases you use with your family that nobody else does. They are like your private language, and people have friendliects with their friends too. If you want to share the story of your familect or friendliect, leave a message on the voicemail line at 83-321-4-GIRL or record a message on Speakpipe. You'll find both of those in the show notes.
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