"Where are the real books?"

[Dreamstalker]

So that's why my school's attempt kept failing*...even It didn't want to tackle the insanity that was already there.

* Of course, nobody could find an entire script, and the sets are a technical impossibility...

[Geek King]

Everyone knows the fake books can be found from 001i-999i

[Chromatix]

No, that's 001j-999j. </nitpick engineer>

[Geek King]

No, that's 001j-999j. </nitpick engineer>

Hey, you stick to your imaginary numbers, and I'll stick to mine!

[MannersMakethMan]

Hey, you stick to your imaginary numbers, and I'll stick to mine!

No, that's 001j-999j. </nitpick engineer>

Imaginary book fight!

Being a mathematician, I call the i's. Have at you!

[Lingering Grin]

Imaginary book fight!

Being a mathematician, I call the i's. Have at you!

Yep, I gotta vote for the I's... just because I like for-loops




...yeah yeah, for-loops can use any letter, but 99% of coders start with i

(Though, I sometimes use to start with Q, just to confuse people.)

[depechemodefan]

Everyone knows the fake books can be found from 001i-999i

I don't get the joke.

though I suppose then 2 of the only real books would be The consultant's calling : bringing who you are to what you do, call # 001 B445 and The Mars mystery : the secret connection between earth and the red planet call # 999.23 H234

[Chromatix]

Okay, a short explanation for the uninitiated:

Numbers, as you and I know them, lie along a line between minus-infinity and positive-infinity, passing through zero on the way. For reasons that will shortly become clear, we call these real numbers.

But mathematicians are typically not satisfied with real, concrete things. They like to deal with abstract concepts. One of the simpler such concepts is the complex number plane.

A complex number has two components - a real part, and an imaginary part. Together, they form a vector, but they are usually written as (R + Ii), where i represents the unit vector on the imaginary axis. Because i is orthogonal to the real number line, the sum doesn't cancel.

Numbers lying on the imaginary axis are called imaginary numbers, and have no real part. Numbers lying on the real axis are still called real numbers, and have no imaginary part. Numbers lying away from both axes are complex numbers.

So books filed at 001i to 999i have imaginary filing locations, and therefore do not really exist.

Let's approach this from a different direction, just to spice things up. The i vector is usually defined as the square root of -1. (In fact, that results in ±i.) But this means that i^2 is -1. And you can extrapolate that i^3 is -i, while i^4 is +1. Generalising, you can see that multiplying by i is equivalent to rotating by 90° in the complex plane.

Much less obvious is that raising a real number to the power of i also results in a rotation. Engineers find this very useful when talking about periodic wave phenomena, which happens a lot, especially in electronics.

But there's a problem. In electronics, the letter i stands for instananeous current. Which is why engineers use j as the imaginary unit vector instead of i.

[Lingering Grin]

Let's approach this from a different direction, just to spice things up. The i vector is usually defined as the square root of -1. (In fact, that results in ±i.) But this means that i^2 is -1. And you can extrapolate that i^3 is -i, while i^4 is +1. Generalising, you can see that multiplying by i is equivalent to rotating by 90° in the complex plane.

Much less obvious is that raising a real number to the power of i also results in a rotation. Engineers find this very useful when talking about periodic wave phenomena, which happens a lot, especially in electronics.

Sounds like a unit circle. Man did that thing make trigonometry and calculus SO much simpler.

It all becomes turns on a wheel rather than all those damn numbers

[depechemodefan]

The i vector is usually defined as the square root of -1. (In fact, that results in ±i.) But this means that i^2 is -1. And you can extrapolate that i^3 is -i, while i^4 is +1.

I dont' get that. Why is i^2 is -1, but i^4 is +1?

I would go read a book, but their are customers out there, and they are bound to stop me to make my life a living hell.

[Chromatix]

Algebraicly, i^4 = i^2 * i^2 = -1 * -1 = +1. Similarly, i^3 = i * i^2 = -1 * i.

Graphically, start with one, which points (conventionally) to the right, along the real axis. Multiply by i, now you're pointing (conventionally) up, along the imaginary axis. Multiply by i again, you have i^2 which is -1, pointing *left* on the real axis. Now keep going in that vein.

[Lady Legira]

My brain hurts...

But my hubby understands it! But then he's done electrical engineering.