A fair question: how did “i” get the name of “imaginary number”?
It seems harsh. In some sense, all numbers are imaginary. After all, is there really such a thing as negative numbers? You can’t have -2 friends, no matter how alienating your Facebook posts are.
Or what about the irrationals? If you take a 1-meter stick and mark it up into equal segments, then no matter how tiny and minute the divisions, you’ll never get an irrational length. Even if you go down to the atomic level. That’s kind of weird.
Heck, what about the natural numbers, like 7 and 15? Isn’t it a little weird to pretend that these exist? I mean, 7 what? Numbers are made for counting. How can you have a number without anything to enumerate?
So sure, I’ll grant that i is imaginary, but only insofar as every number is!
Of course, back in the day, mathematicians saw something fishy about these numbers. After all, they’re neither bigger than zero, nor smaller than zero, nor equal to zero. THey give negative results when squared. So you can’t blame mathematicians like Euler for using names like these:
“imaginary”
“impossible”
“inconceivable”
“fancied”
Clearly, we ought to envy the inhabitants of the nearby parallel universe where these are called “fancied” numbers. But I, for one, pity those poor souls in the universe where they are called “inconceivable,” which lacks the playful color of “imaginary.”
(The word “imaginary,” by the way, came from Descartes. Like many other great names, it began as a slur.)
It’s fun to try to think of other names for i and its multiples.
“Orthonumbers” or “orthogonal numbers” seems like a popular choice. It was the first that came to my mind, and I’m not alone. After all, they appear not on the number line, but perpendicular (or “orthogonal”) to it.
I also think we could call real numbers “posroots” (since they are the square roots of positive numbers) and imaginary numbers “negroots” (since they are the square roots of negative numbers).
(Bonus for “Guardians of the Galaxy” fans: you get to picture i saying “I am negroot.”)
Do names really matter? Maybe not. Mathematical creatures are whatever they are, no matter what we call them.
(A rose by any other name would have the same fractal dimension.)
Still, it’s hard not to want our names to reflect the symmetry and structure of the mathematical world.
Now, when it comes to imaginary numbers, you may say I’m a dreamer.
But I’m not the only one.
I hope someday, you’ll join us.
And the world will know i is “real” as 1.