DISCLAIMER:This has nothing to do with Neopets or snakes, but it's still my work and still fairly interesting to my target audience for this blog.
DOCTOR: Why do we talk out loud when we know we're alone? (blows out candle) Because we know we're not.
DOCTOR: Mathematics perfects survival skills. There are perfect divisors.
DOCTOR: There are perfect reducers.
DOCTOR: Why is there no such thing as perfect concealment? How would you know? Logically, if mathematics were to perfect a number whose primary skill were to hide from view, how could you know it existed?
DOCTOR: It could be with us every second and we would never know. How would you detect it, even sense it, except in those moments when, for no clear reason you choose to speak aloud? What would such a number want? What would it do? Well? What would you do?
(That last word echoes around the Tardis. The chalk is no longer where he left it. It rolls on the floor to his feet and he picks it up, then sees that what he wrote on the blackboard has been replaced by one word. Listen.)
(Doctor Who and related marks are trademarks of BBC . Copyright © 1963, Present.)
(Math student pushes face down on bedspreads.)
Math student:I really wish I could get some sleep, but I have this huge math test tomorrow and I just can't grasp the concept of an imaginary number! I mean, if I'm only imaging it, is it here?
(Imaginary number appears)
Imaginary number:Depends on whether you think of me as just a figment of your imagination or just simply hiding.
Math student:Wait, who said that?
Imaginary number:I did.
Math student:Well, what are you?
Imaginary number:I am the square root of –1. Or if you prefer, I am i.
Math student:I for imaginary. Makes sense.
Imaginary number:It is i, not I!
Math student:Well, I'm/i'm confused. Is it okay if I call you a capitalized I?
Imaginary number:Yes, I suppose it is.
Math student:Say...if you are an imaginary number, you can help me grasp your concept!
(Imaginary number is not quite sure. Math student seems trustworthy, though.)
Imaginary number:Oh, all right, if you insist. You already know that I'm the square root of –1, correct?
(Math student nods.)
Well, how might such a number be imaginary? What in this mathematical universe could you square to get a negative number? Nothing. If you square –1, you get 1. And how, in the pure mathematical universe, could you square anything to be equal to –1? You can't. But surely there must be a number, perhaps something that's been lying in wait for years, but you never noticed it. Or perhaps you refused to admit it existed, that number whose square is negative one! Surely such a number must not be real. An imaginary thing, perhaps. Do you want to know one of the absolutely wonderful things about mathematics?
Math student:What? If it'll help me ace this test, I'd love to! And are you really a trademark of Apple like all other things that start with a lowercase I, like this iPod?
(Imaginary number hisses. It's probably heard the Apple joke before.)
Imaginary number:The wonderful thing about mathematics is that it can be either discovered or invented! So, if you cannot see me...(Imaginary number disappears), but you imagine me, I appear, but yet I was both discovered and invented. And no, I am not a trademark of Apple.
Math student:Can you please appear again? I think my parents are watching and it seems that right now this place is haunted and I'm talking to a ghost. And if you're a number, where exactly are you on the number line?
(Imaginary number reappears.)
Imaginary number:I am not on the number line, and neither is i. I am not positive, I am not negative, and I am not infinite. At least your horizontal number line cannot measure me. But picture this:a vertical number line between 0 and –1, containing all the numbers such as i, 2i, 3i, 4i, and et cetera et cetera.
Math student:So wait...can I add and subtract imaginary numbers?
Imaginary number:You bet! Guess what 2i+3i equals.
Imaginary number:You are correct! Now guess what 5i-3i is.
Imaginary number:Right again!
Math student:I've heard that weird things happen when you are added with a real number. What kinds of weird things. And why would anybody use you?
(Imaginary number is very enraged. Math student says that he did not mean it but just wanted to know its applications.)
Imaginary number:Yes, some strange things might happen with me and a real number. But together, however reluctant we are to stay together, we have many scientific applications that your pathetic real numbers cannot manage. And did you know that e∏i equals –1?
(Math student shakes head no.)
Well, without me, it would just be e∏ ! And we don't know what that equals, now do we? So there is a purpose for all things, alive, dead, hidden, in sight, real, or imaginary.
Math student:Okay, thank you!
(Math student's mom walks in.)
Math student's mom:It's time to wake up. You have a test today. And why were you muttering things about imaginary numbers in your sleep? You must have studied a lot tonight!
(Math student turns to thank the imaginary number, but it is nowhere to be seen. Maybe it was just a dream...)
DISCLAIMER:No offense intended to actual math students who might be reading this.