Why do we solve for X?


Those of us who love algebra (and even those who don’t) are familiar with problems that end up with the command to ‘solve for X’. But why, of all the letters in the alphabet, has X been chosen for this singular honor of representing the unknown, a practice that has extended well beyond algebra? To the extent that any of us thought of this at all, we may have put it down to sheer accident. Someone back in time picked that letter for who knows what reason and it stuck as others followed the practice.

But it turns out that there is actually a reason for this and on the NPR show Ted Radio Hour, host Guy Raz talked with Terry Moore about it. Moore says that the explanation lies in the roots of modern mathematics that can be traced back to the first couple of centuries in the Common Era.

About six years ago, I decided that I would learn Arabic, which turns out to be a supremely logical language. To write a word or a phrase or a sentence in Arabic is like crafting an equation because every part is extremely precise and carries a lot of information. That’s one of the reasons so much of what we’ve come to think of as Western science and mathematics and engineering was really worked out in the first few centuries of the Common Era by the Persians and the Arabs and the Turks.

Moore says that in the original Arabic, the word for the unknown was ‘sheiun’ which meant ‘something’ or ‘some undefined thing’ and that this word was represented by the Arabic letter for the sound ‘sh’. As the importance of these mathematical techniques became more widely realized, these early Arabic texts made their way to Europe via Spain in the 11th and 12th centuries and needed to be translated and this is when the first Spanish translators encountered a problem.

The problem for the medieval Spanish scholars who were tasked with translating this material is that the word sheiun can’t be rendered into Spanish because Spanish doesn’t have that S-H – that sh sound. So by convention, they created a rule in which they borrowed the C-K sound – the cuh sound – from the classical Greek in the form of the letter Chi [Χ]. Later, when this material was translated into a common European language – which is to say Latin – they simply replaced the Greek Chi with the Latin X. And once that happened, once this material was in Latin, it formed the basis for mathematics textbooks for almost 600 years. But now we have the answer to our question. Why is it that X is the unknown? X is the unknown because you can’t say sh in Spanish.

Fascinating.

You can watch Moore’s Ted talk.

You can also listen to Moore’s interview with Raz.

Comments

  1. robert79 says

    Argh, I wish I had known about this a few months earlier! I *just* finished teaching a course on the history of mathematics and would have loved to share this with my students. I’ll try and share it anyways, but I doubt many will bother to click a link when they already have handed in their papers (and now I have to grade them all…. ugh…)

  2. psweet says

    I suppose, then, that this also explains why the Spanish chose X to represent the “sh” sound in Mayan?

  3. flex says

    @ robert79,

    If you just finished teaching a course in the history of mathematics, you probably already know this, but it was only a few months ago that I found the thing Fibonacci should be famous for is not his famous sequence (which was known before him, but used by him to describe population growth), but because the evidence suggests that it was Fibonacci who broadly introduced the concept of zero, and representational notation, into Europe.

    I mean the Fibonacci sequence is fascinating, and certainly deserving of fame. But, come on, we talk about how the introduction of Arabic numerals into Europe changed European history. I’ve been taught that lesson since I was a tyke. But that we actually know who introduced them is amazing, and that it turns out it was Fibonacci! I mean, wow!

  4. Pierce R. Butler says

    psweet @ # 3: … the Spanish chose X to represent the “sh” sound in Mayan…

    Uh, does this mean that country’s name was originally not pronounced “me-hee-ko”?

  5. Pierce R. Butler says

    … the word sheiun can’t be rendered into Spanish because Spanish doesn’t have that S-H – that sh sound. … they borrowed the C-K sound – the cuh sound – from the classical Greek in the form of the letter Chi [Χ].

    But why substitute a “K” phoneme for a “SH” sound, instead of an “S” or a “CH” or something phonetically closer?

  6. Mano Singham says

    Pierce,

    If you listen to his talk, he says that the actual sounds in Arabic are hard to reproduce without a lot of practice and so the sounds he tries to say and write phonetically are approximations. This is not peculiar to Arabic but is why people who grow up in one linguistic environment find it almost impossible to accurately reproduce sounds in another. There are certain words in English, for example, that I seem to be never able to pronounce as an native American speaker would, however hard I try.

  7. Numenaster says

    The difficulty with pronunciation goes both ways. Even after 3 years of classes in Mandarin and a year living in mainland China, my rendering of the X in Mandarin doesn’t sound the same as a native speaker’s. And this is without taking into account the greater difference between English and all the Chinese dialects, which is that English uses tone to indicate punctuation while Chinese dialects (among other languages) use it to create a larger population of different vowels.

  8. Kilian Hekhuis says

    “About six years ago, I decided that I would learn Arabic, which turns out to be a supremely logical language.” – A load of bullocks, also said about Latin, and probably some other languages (I’ve at least heard someone say this about Russian). It’s a shame that people perpetrate myths about languages like this.

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