[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.70,0:00:02.76,Default,,0000,0000,0000,,Okay, let's say you're me and you're in math class
Dialogue: 0,0:00:02.76,0:00:04.37,Default,,0000,0000,0000,,and you're supposed to be learning about
Dialogue: 0,0:00:04.37,0:00:05.69,Default,,0000,0000,0000,,exponential functions, but you're having
Dialogue: 0,0:00:05.69,0:00:07.67,Default,,0000,0000,0000,,trouble caring about exponential functions
Dialogue: 0,0:00:07.67,0:00:10.08,Default,,0000,0000,0000,,because unfortunately your math class
Dialogue: 0,0:00:10.08,0:00:11.74,Default,,0000,0000,0000,,is probably not terribly engaging.
Dialogue: 0,0:00:11.74,0:00:14.72,Default,,0000,0000,0000,,You're supposed to be drawing and labeling some axes
Dialogue: 0,0:00:14.72,0:00:16.90,Default,,0000,0000,0000,,so that you can graph this y equals 2 to the x thing
Dialogue: 0,0:00:16.90,0:00:18.27,Default,,0000,0000,0000,,and your teacher seems to think
Dialogue: 0,0:00:18.27,0:00:19.88,Default,,0000,0000,0000,,that drawing and labeling axes
Dialogue: 0,0:00:19.88,0:00:21.95,Default,,0000,0000,0000,,is the very essence of mathematics
Dialogue: 0,0:00:21.95,0:00:24.54,Default,,0000,0000,0000,,but you're bored and you can't help but wonder...
Dialogue: 0,0:00:24.54,0:00:25.80,Default,,0000,0000,0000,,Why?
Dialogue: 0,0:00:25.80,0:00:28.40,Default,,0000,0000,0000,,So you do what any conscientious student would do
Dialogue: 0,0:00:28.40,0:00:29.70,Default,,0000,0000,0000,,in this situation and start doodling
Dialogue: 0,0:00:29.70,0:00:31.21,Default,,0000,0000,0000,,and because you're me
Dialogue: 0,0:00:31.21,0:00:33.32,Default,,0000,0000,0000,,you like to play games with yourself when you doodle.
Dialogue: 0,0:00:33.32,0:00:34.50,Default,,0000,0000,0000,,Here's one game.
Dialogue: 0,0:00:34.50,0:00:35.99,Default,,0000,0000,0000,,You're drawing a line, but when it crosses
Dialogue: 0,0:00:35.99,0:00:37.94,Default,,0000,0000,0000,,one of the blue lines on your little piece of paper
Dialogue: 0,0:00:37.94,0:00:39.43,Default,,0000,0000,0000,,it splits into two lines.
Dialogue: 0,0:00:39.43,0:00:42.19,Default,,0000,0000,0000,,Maybe this line is like the neck of the mythical hydra
Dialogue: 0,0:00:42.19,0:00:44.26,Default,,0000,0000,0000,,where every time one of its heads gets chopped off
Dialogue: 0,0:00:44.26,0:00:47.60,Default,,0000,0000,0000,,by a blue line, it grows two more in its place.
Dialogue: 0,0:00:47.60,0:00:49.16,Default,,0000,0000,0000,,You want to see if you can get all the way
Dialogue: 0,0:00:49.16,0:00:50.83,Default,,0000,0000,0000,,to the bottom of the page following this rule
Dialogue: 0,0:00:50.83,0:00:52.86,Default,,0000,0000,0000,,because if you do, you can draw
Dialogue: 0,0:00:52.86,0:00:54.99,Default,,0000,0000,0000,,all of the little hydra heads at the end.
Dialogue: 0,0:00:54.99,0:00:56.98,Default,,0000,0000,0000,,But you don't get very far on your first try.
Dialogue: 0,0:00:56.98,0:00:58.79,Default,,0000,0000,0000,,You decide to try again, this time
Dialogue: 0,0:00:58.79,0:01:00.88,Default,,0000,0000,0000,,spacing things out a little more at the beginning.
Dialogue: 0,0:01:00.88,0:01:02.37,Default,,0000,0000,0000,,Unfortunately, things are filling up fast,
Dialogue: 0,0:01:02.37,0:01:03.83,Default,,0000,0000,0000,,though you got farther than last time.
Dialogue: 0,0:01:03.83,0:01:04.90,Default,,0000,0000,0000,,Maybe if you had more room.
Dialogue: 0,0:01:04.90,0:01:06.75,Default,,0000,0000,0000,,Or maybe if you sharpened your pencil more,
Dialogue: 0,0:01:06.75,0:01:08.24,Default,,0000,0000,0000,,you could get to the bottom of the page.
Dialogue: 0,0:01:08.24,0:01:10.33,Default,,0000,0000,0000,,Oh, and don't forget to draw and label your axes.
Dialogue: 0,0:01:10.33,0:01:12.83,Default,,0000,0000,0000,,If each broad swing of Hercules' sword chops off
Dialogue: 0,0:01:12.83,0:01:14.61,Default,,0000,0000,0000,,all the heads thus doubling your number, well,
Dialogue: 0,0:01:14.61,0:01:16.28,Default,,0000,0000,0000,,you can see where I'm going.
Dialogue: 0,0:01:16.28,0:01:17.77,Default,,0000,0000,0000,,I'm not going to try and teach you math,
Dialogue: 0,0:01:17.77,0:01:19.62,Default,,0000,0000,0000,,just how to wield it for doodling purposes.
Dialogue: 0,0:01:19.62,0:01:21.70,Default,,0000,0000,0000,,In this case, that's going to be a lot of heads.
Dialogue: 0,0:01:21.70,0:01:23.62,Default,,0000,0000,0000,,Good luck Hercules.
Dialogue: 0,0:01:23.62,0:01:26.45,Default,,0000,0000,0000,,But maybe drawing binary trees all straight like that
Dialogue: 0,0:01:26.45,0:01:28.84,Default,,0000,0000,0000,,is not an interesting game to hold your attention for long
Dialogue: 0,0:01:28.84,0:01:30.85,Default,,0000,0000,0000,,so you start drawing them in arbitrary shapes.
Dialogue: 0,0:01:30.85,0:01:32.91,Default,,0000,0000,0000,,Or less arbitrary shapes.
Dialogue: 0,0:01:32.91,0:01:35.00,Default,,0000,0000,0000,,Maybe you start drawing a binary tree
Dialogue: 0,0:01:35.00,0:01:36.24,Default,,0000,0000,0000,,that looks like a tree.
Dialogue: 0,0:01:36.24,0:01:38.17,Default,,0000,0000,0000,,And maybe you can't see this tree in very high quality
Dialogue: 0,0:01:38.17,0:01:40.21,Default,,0000,0000,0000,,because your camera, very much like your math class
Dialogue: 0,0:01:40.21,0:01:43.54,Default,,0000,0000,0000,,is fuzzy, unfocused, and all together not very good.
Dialogue: 0,0:01:43.54,0:01:45.38,Default,,0000,0000,0000,,Maybe you changed the rules slightly and
Dialogue: 0,0:01:45.38,0:01:47.60,Default,,0000,0000,0000,,make a ternary bush where each branch sprouts
Dialogue: 0,0:01:47.60,0:01:48.96,Default,,0000,0000,0000,,three more branches.
Dialogue: 0,0:01:48.96,0:01:51.84,Default,,0000,0000,0000,,Unfortunately, your math class is 45 minutes long
Dialogue: 0,0:01:51.84,0:01:54.21,Default,,0000,0000,0000,,and soon you need a more interesting doodle game.
Dialogue: 0,0:01:54.21,0:01:56.24,Default,,0000,0000,0000,,Say you go back to the game
Dialogue: 0,0:01:56.24,0:01:57.64,Default,,0000,0000,0000,,where your line splits at every level.
Dialogue: 0,0:01:57.64,0:02:00.12,Default,,0000,0000,0000,,Only this time, instead of trying to squish all the lines in,
Dialogue: 0,0:02:00.12,0:02:02.48,Default,,0000,0000,0000,,you let them hit each other.
Dialogue: 0,0:02:02.48,0:02:04.60,Default,,0000,0000,0000,,And when they crash, there's a firey explosion
Dialogue: 0,0:02:04.60,0:02:07.81,Default,,0000,0000,0000,,and the crashing lines end there.
Dialogue: 0,0:02:07.81,0:02:09.26,Default,,0000,0000,0000,,Maybe you turn your notebook sideways
Dialogue: 0,0:02:09.26,0:02:10.37,Default,,0000,0000,0000,,so that you can make sure
Dialogue: 0,0:02:10.37,0:02:12.48,Default,,0000,0000,0000,,you're getting the horizontal spacing right.
Dialogue: 0,0:02:12.48,0:02:14.22,Default,,0000,0000,0000,,Maybe, to go back to mythology,
Dialogue: 0,0:02:14.22,0:02:16.21,Default,,0000,0000,0000,,Hercules has a method where, instead of cauterizing
Dialogue: 0,0:02:16.21,0:02:19.19,Default,,0000,0000,0000,,the necks of the Hydra to keep them from growing back
Dialogue: 0,0:02:19.21,0:02:21.98,Default,,0000,0000,0000,,he's found that the necks stick together if they get too close
Dialogue: 0,0:02:21.98,0:02:23.92,Default,,0000,0000,0000,,And instead of growing new heads,
Dialogue: 0,0:02:23.92,0:02:26.22,Default,,0000,0000,0000,,they just fill up with blood.
Dialogue: 0,0:02:26.22,0:02:28.04,Default,,0000,0000,0000,,It might seem a little morbid for math class,
Dialogue: 0,0:02:28.04,0:02:31.26,Default,,0000,0000,0000,,but maybe, if the curriculum wasn't so appalling
Dialogue: 0,0:02:31.26,0:02:33.45,Default,,0000,0000,0000,,and the teaching methods wern't so atrocious,
Dialogue: 0,0:02:33.45,0:02:35.23,Default,,0000,0000,0000,,you wouldn't have to entertain yourself
Dialogue: 0,0:02:35.23,0:02:37.15,Default,,0000,0000,0000,,with these stories and games.
Dialogue: 0,0:02:37.15,0:02:38.63,Default,,0000,0000,0000,,Speaking of this doodle game,
Dialogue: 0,0:02:38.63,0:02:40.49,Default,,0000,0000,0000,,something very interesting is happening.
Dialogue: 0,0:02:40.49,0:02:42.57,Default,,0000,0000,0000,,Looks like your simple rules about splitting
Dialogue: 0,0:02:42.57,0:02:45.63,Default,,0000,0000,0000,,and crashing are creating Sierpinski's triangle.
Dialogue: 0,0:02:45.63,0:02:47.11,Default,,0000,0000,0000,,Which is a pretty awesome fractal.
Dialogue: 0,0:02:47.11,0:02:48.51,Default,,0000,0000,0000,,But the point is not to learn about fractals
Dialogue: 0,0:02:48.51,0:02:50.77,Default,,0000,0000,0000,,or cellular automata or Sierpinski,
Dialogue: 0,0:02:50.77,0:02:52.37,Default,,0000,0000,0000,,but to show that simple doodle games
Dialogue: 0,0:02:52.37,0:02:53.67,Default,,0000,0000,0000,,can lead to mathematical results
Dialogue: 0,0:02:53.67,0:02:56.81,Default,,0000,0000,0000,,so cool and beautiful that they're famous.
Dialogue: 0,0:02:56.81,0:02:59.30,Default,,0000,0000,0000,,At least, famous to people like me.
Dialogue: 0,0:02:59.30,0:03:00.65,Default,,0000,0000,0000,,And if you're good at inventing doodle games,
Dialogue: 0,0:03:00.65,0:03:01.79,Default,,0000,0000,0000,,you might even end up
Dialogue: 0,0:03:01.79,0:03:05.76,Default,,0000,0000,0000,,doing some real mathematics during your math class.
Dialogue: 0,0:03:05.76,0:03:08.71,Default,,0000,0000,0000,,Anyway, maybe you don't care about accuracy.
Dialogue: 0,0:03:08.71,0:03:09.58,Default,,0000,0000,0000,,Maybe you try the game again,
Dialogue: 0,0:03:09.58,0:03:11.51,Default,,0000,0000,0000,,only you don't keep track of spacing,
Dialogue: 0,0:03:11.51,0:03:12.12,Default,,0000,0000,0000,,and when you make a mistake and
Dialogue: 0,0:03:12.12,0:03:14.02,Default,,0000,0000,0000,,accidentally grow heads where you shouldn't
Dialogue: 0,0:03:14.02,0:03:15.78,Default,,0000,0000,0000,,you just roll with it.
Dialogue: 0,0:03:15.78,0:03:18.04,Default,,0000,0000,0000,,Now you've introduced an element of random error
Dialogue: 0,0:03:18.04,0:03:19.31,Default,,0000,0000,0000,,and you want to know
Dialogue: 0,0:03:19.31,0:03:20.98,Default,,0000,0000,0000,,how this will affect the final picture.
Dialogue: 0,0:03:20.98,0:03:22.97,Default,,0000,0000,0000,,It still looks like a pretty awesome doodle,
Dialogue: 0,0:03:22.97,0:03:24.45,Default,,0000,0000,0000,,and has many of the same elements,
Dialogue: 0,0:03:24.45,0:03:25.81,Default,,0000,0000,0000,,though it lacks the structure.
Dialogue: 0,0:03:25.81,0:03:27.00,Default,,0000,0000,0000,,Speaking of the structure,
Dialogue: 0,0:03:27.00,0:03:28.92,Default,,0000,0000,0000,,maybe because you're really super bored
Dialogue: 0,0:03:28.92,0:03:31.70,Default,,0000,0000,0000,,and your class is seemingly never going to end,
Dialogue: 0,0:03:31.70,0:03:34.61,Default,,0000,0000,0000,,you start looking at the number of necks at each level
Dialogue: 0,0:03:34.61,0:03:37.20,Default,,0000,0000,0000,,and trying to figure out the pattern.
Dialogue: 0,0:03:37.20,0:03:40.06,Default,,0000,0000,0000,,Maybe you haven't forgotten about powers of two.
Dialogue: 0,0:03:40.06,0:03:41.45,Default,,0000,0000,0000,,Anyway, I hope I've provided you with
Dialogue: 0,0:03:41.45,0:03:44.58,Default,,0000,0000,0000,,something entertaining to do next time you're bored.
Dialogue: 0,0:03:44.58,0:03:48.00,Default,,0000,0000,0000,,Good luck with your math class.