Well, here we are. Just one more entry until the launch.
When I first heard that my topic for today was “Minus One”, I knew that there was only one possible interpretation worth considering – imaginary numbers.
My mind wound back like an old VHS machine. The year was 2001 (at the time) and I found myself in a stale smelly lecture theatre listening to a stale smelly academic. Both the theatre and the lecturer were old enough to be unaesthetic but not old enough to be charming. He was babbling on about some facet or other of the Cartesian plane (some early form of aviation, I think) when the two words slipped past his lips – “imaginary numbers”.
The mind boggles, well at least my mind did, at the possibilities for imaginary numbers. A few likely candidates presented themselves in my brain:
- Neight: The smallest number of bananas on a hand that will make you look twice to see if that really is just one hand or if it is two hands on top of each other.
- Vero: The number of Saturday newspapers left at the newsagent at 4pm that still have the free CD of “Mozart’s Least Known Polkas” jammed inside the front cover.
- Bleviteen: The number of times per minute you can clear your throat in a library before the man reading a textbook at the next table shoots you a stern glance.
- Sive: The number of times you say “Hello, hello…” after answering a phone before you can be sure that there is nobody there.
- Blirty-sive: The number of times per minute you can clear your throat in a library before the man reading a textbook at the next table throws the textbook at your head.
But sadly, brilliant though these suggestions are, the real ‘imaginary numbers’ caper is slightly less interesting. Nevertheless, I will try to explain it in such a way that my reading demographic will stay to the end. It will come in handy if ever you are a contestant on Temptation or want to impress slightly less geeky people at parties. For those who read this through, I will include an original limerick at the end. Please show your honesty and only read the limerick if you ploughed through the next paragraph.
Not this one, the next one. This is just filler.
As you are no doubt aware, whenever you square a number (times it by itself), the result will always be positive. For example, four squared (or four times four) is sixteen; and minus two squared (or minus two times minus two) is four. A ‘square root’, you will remember, is the opposite of squaring. So the square root of sixteen means, what two numbers multiplied together gave us sixteen? The answer being four. Some clever chappy then decided to make the rule that since all squares are positive, it is impossible to find the square-root of a negative number. That is, you can’t, for example, find the square-root of minus sixteen, because like I said before all squares are positive (four squared and minus four squared both give (positive) sixteen).
And so it remained till one day this bloke thought that it would be a nice idea if you could find the square-root of a negative number. Well, some other blokes didn’t agree and said that it was stupid. The first guy said it wasn’t stupid, they were stupid. To try and build their case a little, the other blokes put something to the first bloke: if you found the square-root of a negative number, what would the answer be? certainly not a real number. To this the first guy agreed, “Sure, okay” he said “not a real number.” “Ohhhhh” said the others “so… some sort of magical mysterious imaginary number”. At this point the first guy became sick of this constant criticism of what had initially sounded like a decent scheme and he was beginning to wish he hadn’t invited everyone back to his house for a pasta-bake and a play of his Wii. “Yes” he said “the square-root of a negative number is an imaginary number”. And thus imaginary numbers were born. (History doesn’t record whether or not he added “…you boneheads, and wash your hands before you play Wario Moves, you’re getting pasta sauce all over my Wii-motes.”
Now we get to the nub. Yer basic imaginary number is “i“. And i is the square-root of minus one. That is, the square-root of minus-one is i. (And, therefore, i squared equals minus one.) From there it’s easy to make an imaginary number out of the square-root of any negative number. You just need to remember your root laws (I don’t, I had to look them up). Basically, if we wanted to find the square root of minus forty-nine, we would follow this process:
- The square-root of minus forty-nine equals:
- The square root of minus one, multiplied by, the square-root of (positive) forty-nine.
- The square-root of minus one equals i, and the square root of (positive) forty-nine equals seven.
- So the square-root of minus forty-nine equals seven time i, or “7i“.
This is about all the average Joe-on-the-street needs to know about imaginary numbers, perhaps even slightly more.
I propose to promote the use of imaginary numbers in general society by applying to Australia Post to have my house number changed to an imaginary number. Any other suggestions?
And here is the limerick I promised you:
There once was a chap called Bombelli
Who buried himself in red jelly.
He drew up a chart
of the lives of Descartes,
and also Evangelista Torricelli.
“Descartes” is correctly pronounced “day-CART”. Doing so will futher boost your success at geek parties and on Temptation.