Be Smart | How Did X Become the Unknown (and so much else)? | Season 11 | Episode 17

- Hey, smart people.

Joe here.

The letter X is everywhere.

We sign letters with it.

We rate movies with it.

We name generations after it.

And apps too, I guess.

We have a weird obsession with X.

But how did X get so popular?

It's the fourth least common letter in the English language.

It shows up in words 38 times less often than E. And no offense to X, but every soundless letter can make, we can make with other letters.

We don't even need it.

(melodramatic music) Yet, as uncommon as it is in the English language, X is everywhere.

And that's probably all thanks to math.

Weirdly, X seems to have just popped into math out of the blue.

Around 400 years ago, it started showing up in math books as a placeholder for the unknown, and the theories as to why are truly bizarre.

But no matter how it got there, once the unknown entered math, our relationship to the world was never the same.

It helped reveal the universal patterns and rules of math that governed the world.

And it offers a clue as to why we're so obsessed with X today.

(whimsical music) X has been a letter for over 2,000 years.

For centuries, it did more or less the same job.

It made sounds in various words.

Ancient Greeks adopted X from the Phoenicians and called it chi like in the ancient Greek words Kristos or Chimera.

Then it made the leap to Latin and eventually found its way to English in words like exit or xenon.

But X's role completely changed when humans encountered a new idea in math, the unknown.

Before about 5,000 years ago, math was all about known quantities.

How many sheep do I have?

How many days after the winter solstice should I plant my crops?

The only unknown was the answer.

Then ancient Babylonians started doing things like this.

These are 247 math problems carved into a clay slab.

They include problems like say the areas of two square plots of land add up to 25 units and the side of one plot is 2/3 the length of the first plus five units.

How long are the sides of each plot?

The question itself is built around unknown quantities.

In other words, the unknown value isn't the result.

The unknown is in the question.

This was a big deal, a huge leap in the history of mathematics.

That question about the plots of land can be written as one of the first equations with unknowns you probably ever heard of, the quadratic equation.

The Babylonians weren't the only ones doing this kind of math.

The Ancient Greeks, Egyptians, Chinese, and Indian people also had ways of solving math problems with unknowns.

But they didn't use X for the unknown.

For starters, X wasn't even a letter a few thousand years ago, let alone a mathematical symbol.

Ancient mathematicians wrote out their problems in full sentences.

Like in India, the mathematician Brahmagupta, he referred to the unknown as yavattavat, meaning something.

It would take centuries before the symbol X and the concept of the unknown even crossed paths.

But in the Middle East, the world of math was about to change in a big way.

This big step forward came from a Persian scholar named al-Khwarizmi who was working in the ninth century.

Like many people who came before him, al-Khwarizmi worked out solutions to different algebraic problems and he spelled out algorithms, sets of steps that could be used to solve each one.

The English word algorithm even comes from the Latin version of his name.

He also gave us the word algebra.

In Arabic, al-Jabr means something like the restoration of broken parts.

It was originally used in surgical settings to describe the process of putting broken bones back in the right place.

Almost as painful as some of these math problems.

Am I right?

But al-Khwarizmi used al-Jabr or algebra to describe the process of adding equal values to both sides of an equation to solve for or restore the unknown, the broken parts, often the first step in algebra.

Eventually, the whole process became known by this name and now we teach it to teenagers.

But inventing words isn't what made al-Khwarizmi's work so important.

It's that his algorithms, his recipes for finding unknowns, applied to many problems that people came across.

And this is the real magic of algebra.

It's not just for solving a specific limited number of problems.

It gives us a way of understanding the relationship between known and unknown quantities that lets you solve an infinite number of problems.

So where does X come in?

Like the people before him, al-Khwarizmi wrote out his problems in words, but mathematicians gradually started replacing words with symbols.

We can see this gradual shift from words to symbols in the 1500s when the French mathematician Francois Viete wrote equations as a kind of mix of symbols and words.

He decided to use vowels for unknown values, like in this equation, which we'd simply write like this today.

This move to symbols wasn't about saving ink.

Symbols were a way of making the relationships and patterns inside algebra easier to see.

Problem was by the end of the 1700s, people in different places were using different symbols and nobody could read anybody else's math.

One person might write X to stand for the unknown, but another might use letter Q or N or a circle with a dot in it.

Back then, if you were a mathematician trying to keep up with current work, you'd need to know at least 25 different sets of symbols.

And this kind of defeated the purpose.

If you had to constantly translate different algebra codes in your head, this goal of finding universal rules and patterns in math wasn't gonna work.

Then a few a hundred years ago, a French fella started using one unknown that got picked up by mathematicians everywhere.

But the story of exactly how and why that happened is a bit of an unknown itself.

There are a few different theories that attempt to explain how X became the universal symbol of the unknown.

One theory blames the Spanish translation of al-Khwarizmi's work.

When al-Khwarizmi wrote out problems, he often used the Arabic word shay to represent unknown quantities.

Shay means thing, and in Arabic, it starts with the letter shin which makes a shh sound.

This theory proposes that when his works were translated into Spanish, Spaniards who had no letter for sh borrowed the Greek symbol chi instead, then chi turned into X when the works were translated into Latin, which maybe happened, but it's not really clear that Spaniards would've really cared about preserving the sound at the beginning of the word shay, and there doesn't seem to be any actual documentation directly showing this evolution from shay to X.

So this one's a maybe at best.

A couple other theories trace our use of X back to that French fella I mentioned earlier, Rene Descartes.

Descartes was a big deal.

While his predecessors were mainly focused on solving specific problems, Descartes realized something.

Once you had an equation, you could plot the solutions to an algebraic formula on a graph.

Instead of getting one single solution, you got a shape on a graph representing all possible solutions to an equation of this form.

This revealed the relationship between two variables without even solving an equation for specific values.

This discovery ushered algebra into a new era and Descartes collected these game-changing methods in a very popular book.

And in that book, he used letters from the beginning of the alphabet to represent known values and letters from the end of the alphabet to represent unknowns.

By the end of his book, he was using X to stand in for the unknown more than any other letter.

One theory has it that Descartes just kinda randomly chose X as a symbol, and it just caught on as other mathematicians built on his work.

But at least one math historian has suggested that Descartes' choice might not have been that arbitrary after all.

In Descartes' native French, X is much less common than Y or Z.

And when he went to get his book printed, well, back then in the era of movable type and people placing letters by hand one by one, the guy running the printing press just might've had more spare X's lying around than any other letter.

So maybe we all use X for the unknown because Descartes' printer was lazy.

Bottom line, we don't know where the choice of X first came from, if it was just a whim or if there was some logic behind it.

But either way, since Descartes' time, it's been the unknown that mathematicians love the most.

No matter where X came from, writing the unknown into math changed math forever and it changed the way we perceive and explore the universe.

It gave us insights into the patterns that make up the world.

Because now when we see pieces of those patterns, we can fill in the blanks and explore the world more deeply.

Like we can calculate the unknown mass of a galaxy based on how fast the stars are whizzing around it.

We can predict the unknown path of a planet using known properties like its position and mass.

Scientists even discovered Neptune on paper using algebra before they ever saw it through a telescope.

Yeah, your teacher wasn't lying to you when they said you'd actually use this algebra stuff in the real world.

Algebra and unknowns are behind our GPS systems, our WiFi, our decisions about which block of cheese is a better deal.

Whether it's us or computers, our world wouldn't run without solving for X.

It's become such a thing.

X also represents the unknown in lots of places outside math too.

Malcolm X adopted the letter to represent the unknown African name taken from his family during slavery.

X-rays got their name because the physicists who discovered them didn't know what they were.

Even the X chromosome might've been named that way because it was a mysterious unknown chromosome that didn't act quite like the rest.

The unknown planet X, X marks the spot of unknown treasure, and now nerds' love of X has grown beyond the unknown.

I mean, Steve Jobs called Apple's operating system macOS 10 or X, and they kept that 10 name for more than a dozen new versions.

And of course, every other thing that Elon Musk creates like SpaceX, the Model X Tesla, and now just plain X.

So why are we so obsessed with X?

Maybe because its history in math gives X a sense of mystery and intrigue.

It implies trailblazing into unknown territory or because it gives us a way to name what we don't know so that we can explore it.

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