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?
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This first segment is by Professor of Mathematics 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 Rhine papyrus, the scribe Amis 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 wasn't 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 an 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 Yavadava.
When additional variables were required, he instead used the initial syllable of color names, like ka from kalaka for black and Ya from Yatava for yellow, Ni from Nilak for blue, and so on.
Islamic scholars translated and preserved a great deal of both Greek and Indian scholarship that had contributed immensely to the world's mathematical, scientific and technical knowledge.
The most famous Islamic mathematician was al-Khwarizmi, whose foundational book Al-Jabr Wa'al Maqbala is 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-shayyoun, 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 chi, 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 chi 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 Sumerio Combendicio of Juan Díaz, 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 Xs 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 chi.
The Greek word for Christ is Christos, meaning anointed.
The X 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 Röntgen 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.
It appears here through a Creative Commons license.
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 it 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 versus writing issue?
Formal versus informal?
Or what?"
Thanks, Barbara.
That is a great question.
The oldest reference for how come in the Oxford English Dictionary 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, quote, doubtless an English phrase brought over by the original settlers, unquote.
Well, 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's 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's 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.
Well, one theory is that how come is short, for how did it come about that?
How is it that?
Or how comes it that?
For example, here's a line from the British poet Edmund Spencer's Sonnet 30, first published in 1595, that uses the older, longer phrase.
How comes it then that this her cold so great is not dissolved through my so hot desire?
And here's an even older one from an English translation of Machiavelli's The Prince, which was written around 1513.
How comes it that the church has attained such greatness in temporal power?
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're first born.
How come they to run so naturally to their dams without any director?
We do love to shorten things.
Pantaloons became pants and omnibus became bus, 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?
Erica Okrant pointed 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 then 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 almost nine-year-old daughter.
So when she was little, we were in the car and she had asked me what the handles in the car that are above the windows were.
And I said they were called the O 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 handle.
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're like your private language, and people have friendilects with their friends, too.
If you want to share the story of your familect or friendilect, leave a message on the voicemail line at 83-321-4GIRL or record a message on SpeakPipe.
You'll find both of those in the show notes.
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