[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.18,0:00:01.68,Default,,0000,0000,0000,,So you're me and you're in math class
Dialogue: 0,0:00:01.68,0:00:02.90,Default,,0000,0000,0000,,and you're learning about graph theory,
Dialogue: 0,0:00:02.90,0:00:04.35,Default,,0000,0000,0000,,a subject too interesting to be included
Dialogue: 0,0:00:04.35,0:00:05.66,Default,,0000,0000,0000,,in most grade school curricula.
Dialogue: 0,0:00:05.66,0:00:06.88,Default,,0000,0000,0000,,So maybe you're in some special program
Dialogue: 0,0:00:06.88,0:00:07.85,Default,,0000,0000,0000,,or maybe you're in college
Dialogue: 0,0:00:07.85,0:00:09.70,Default,,0000,0000,0000,,and were somehow not scarred for life
Dialogue: 0,0:00:09.70,0:00:10.50,Default,,0000,0000,0000,,by your grade school math teachers.
Dialogue: 0,0:00:10.50,0:00:11.72,Default,,0000,0000,0000,,I'm not sure why you're not paying attention
Dialogue: 0,0:00:11.72,0:00:12.99,Default,,0000,0000,0000,,but maybe you have an incompetent teacher
Dialogue: 0,0:00:12.99,0:00:14.25,Default,,0000,0000,0000,,and it's too heart-breaking to watch him
Dialogue: 0,0:00:14.25,0:00:15.65,Default,,0000,0000,0000,,butcher what could be a fun subject,
Dialogue: 0,0:00:15.65,0:00:16.74,Default,,0000,0000,0000,,full of snakes and balloons.
Dialogue: 0,0:00:16.74,0:00:19.11,Default,,0000,0000,0000,,Snakes aren't really all that relevant to the mathematics here.
Dialogue: 0,0:00:19.11,0:00:20.66,Default,,0000,0000,0000,,But being able to draw them will be useful later,
Dialogue: 0,0:00:20.66,0:00:22.38,Default,,0000,0000,0000,,so you should probably start practicing now.
Dialogue: 0,0:00:22.38,0:00:24.94,Default,,0000,0000,0000,,I've got a family of 3 related doodle games to show you,
Dialogue: 0,0:00:24.94,0:00:27.10,Default,,0000,0000,0000,,all stemming from drawing squiggles all over the page.
Dialogue: 0,0:00:27.10,0:00:28.60,Default,,0000,0000,0000,,The first one goes like this:
Dialogue: 0,0:00:28.60,0:00:31.02,Default,,0000,0000,0000,,draw a squiggle- a closed curve that ends where it begins.
Dialogue: 0,0:00:31.02,0:00:32.53,Default,,0000,0000,0000,,The only real rule here is to make sure
Dialogue: 0,0:00:32.53,0:00:34.05,Default,,0000,0000,0000,,that all the crossings are distinct.
Dialogue: 0,0:00:34.05,0:00:35.96,Default,,0000,0000,0000,,Next, make it start weaving-
Dialogue: 0,0:00:35.96,0:00:36.97,Default,,0000,0000,0000,,follow the curve around and
Dialogue: 0,0:00:36.97,0:00:38.59,Default,,0000,0000,0000,,that each crossing alternate going under and over
Dialogue: 0,0:00:38.59,0:00:40.47,Default,,0000,0000,0000,,until you've assigned all the crossings.
Dialogue: 0,0:00:40.47,0:00:42.15,Default,,0000,0000,0000,,Then put on the finishing touches, and voila!
Dialogue: 0,0:00:42.15,0:00:44.82,Default,,0000,0000,0000,,You try it again, adding a little artistic flair to the lines.
Dialogue: 0,0:00:44.82,0:00:47.16,Default,,0000,0000,0000,,The cool part is that the weaving always works out perfectly,
Dialogue: 0,0:00:47.16,0:00:49.23,Default,,0000,0000,0000,,when you're going around alternating over and under
Dialogue: 0,0:00:49.23,0:00:50.79,Default,,0000,0000,0000,,and get to a crossing you've already assigned,
Dialogue: 0,0:00:50.79,0:00:52.46,Default,,0000,0000,0000,,it will always be the right one.
Dialogue: 0,0:00:52.46,0:00:55.04,Default,,0000,0000,0000,,This is very interesting, and we'll get back to it later.
Dialogue: 0,0:00:55.04,0:00:57.75,Default,,0000,0000,0000,,But first I'd like to point out 2 things: one is that
Dialogue: 0,0:00:57.75,0:01:00.65,Default,,0000,0000,0000,,this works for any number of closed curves on the plane.
Dialogue: 0,0:01:00.65,0:01:01.81,Default,,0000,0000,0000,,So go ahead and link stuff up
Dialogue: 0,0:01:01.81,0:01:03.94,Default,,0000,0000,0000,,or make a weaving out of 2 colors of yarn.
Dialogue: 0,0:01:03.94,0:01:04.88,Default,,0000,0000,0000,,The other is that
Dialogue: 0,0:01:04.88,0:01:07.28,Default,,0000,0000,0000,,this doodle also works out for snakes on a plane
Dialogue: 0,0:01:07.28,0:01:09.27,Default,,0000,0000,0000,,as long as you keep the head and tail on the outside
Dialogue: 0,0:01:09.27,0:01:10.44,Default,,0000,0000,0000,,or on the same inside face.
Dialogue: 0,0:01:10.44,0:01:12.72,Default,,0000,0000,0000,,because mathematically it's the same as if they linked up
Dialogue: 0,0:01:12.72,0:01:15.35,Default,,0000,0000,0000,,or just actually link up the head and tail into an Ouroboros.
Dialogue: 0,0:01:15.35,0:01:18.26,Default,,0000,0000,0000,,For example, here's 3 Ourobori in a configuration
Dialogue: 0,0:01:18.26,0:01:19.75,Default,,0000,0000,0000,,known as the Borromean Rings
Dialogue: 0,0:01:19.75,0:01:21.48,Default,,0000,0000,0000,,which has the neat property that
Dialogue: 0,0:01:21.48,0:01:23.86,Default,,0000,0000,0000,,no 2 snakes are actually linked with each other.
Dialogue: 0,0:01:23.86,0:01:25.45,Default,,0000,0000,0000,,Also because I like naming things,
Dialogue: 0,0:01:25.45,0:01:27.56,Default,,0000,0000,0000,,this design shall henceforth be known as
Dialogue: 0,0:01:27.56,0:01:29.24,Default,,0000,0000,0000,,the "OuroBorromean Rings".
Dialogue: 0,0:01:29.24,0:01:30.46,Default,,0000,0000,0000,,But you are me, after all,
Dialogue: 0,0:01:30.46,0:01:31.80,Default,,0000,0000,0000,,so you're finding a lot to think about
Dialogue: 0,0:01:31.80,0:01:34.08,Default,,0000,0000,0000,,even with just drawing one line that isn't a snake.
Dialogue: 0,0:01:34.08,0:01:35.81,Default,,0000,0000,0000,,Such as, "What kinds of knots are you drawing?"
Dialogue: 0,0:01:35.81,0:01:37.22,Default,,0000,0000,0000,,"And can you classify them?"
Dialogue: 0,0:01:37.22,0:01:39.39,Default,,0000,0000,0000,,For example, these 3 knots all have 5 crossings
Dialogue: 0,0:01:39.39,0:01:42.37,Default,,0000,0000,0000,,but 2 are essentially the same knot and one is different.
Dialogue: 0,0:01:42.37,0:01:45.26,Default,,0000,0000,0000,,Knot theory questions are actually really difficult and interesting
Dialogue: 0,0:01:45.26,0:01:47.06,Default,,0000,0000,0000,,but you're going to have to look that one up yourself.
Dialogue: 0,0:01:47.06,0:01:48.85,Default,,0000,0000,0000,,Oh, and you should also learn how to draw rope
Dialogue: 0,0:01:48.85,0:01:50.83,Default,,0000,0000,0000,,because it's an integral part of knot theory.
Dialogue: 0,0:01:50.83,0:01:51.69,Default,,0000,0000,0000,,So integral, in fact, that
Dialogue: 0,0:01:51.69,0:01:53.77,Default,,0000,0000,0000,,if you draw a bunch of integral signs in a row,
Dialogue: 0,0:01:53.77,0:01:56.23,Default,,0000,0000,0000,,a sight which is often quite daunting to a mathematician,
Dialogue: 0,0:01:56.23,0:01:58.53,Default,,0000,0000,0000,,you can just shade it in, and TA-DA.
Dialogue: 0,0:01:58.53,0:02:01.49,Default,,0000,0000,0000,,But, being able to draw snakes is also super useful
Dialogue: 0,0:02:01.49,0:02:03.35,Default,,0000,0000,0000,,especially as this doodle game is excellent for
Dialogue: 0,0:02:03.35,0:02:05.16,Default,,0000,0000,0000,,producing Dark Mark tattoo designs.
Dialogue: 0,0:02:05.16,0:02:06.86,Default,,0000,0000,0000,,Also, this doodle game can be combined
Dialogue: 0,0:02:06.86,0:02:08.02,Default,,0000,0000,0000,,with the stars doodle game.
Dialogue: 0,0:02:08.02,0:02:10.50,Default,,0000,0000,0000,,For example, if this pentagram gets knighted,
Dialogue: 0,0:02:10.50,0:02:13.33,Default,,0000,0000,0000,,it will henceforth be known as "Serpentagram"
Dialogue: 0,0:02:13.33,0:02:16.32,Default,,0000,0000,0000,,Also notice that this snake is a 5 twist Mobius strip
Dialogue: 0,0:02:16.32,0:02:17.95,Default,,0000,0000,0000,,so you could also call it a "Mobiaboros"
Dialogue: 0,0:02:17.95,0:02:19.78,Default,,0000,0000,0000,,but we'll get back to one-sidedness later.
Dialogue: 0,0:02:19.78,0:02:21.92,Default,,0000,0000,0000,,Or, if you want to draw something super complicated
Dialogue: 0,0:02:21.92,0:02:23.44,Default,,0000,0000,0000,,like the 8th square star,
Dialogue: 0,0:02:23.44,0:02:26.95,Default,,0000,0000,0000,,combining snakes and stars is a great technique for that too.
Dialogue: 0,0:02:26.95,0:02:29.33,Default,,0000,0000,0000,,Here's a boa that ate 8 8gons.
Dialogue: 0,0:02:29.33,0:02:31.81,Default,,0000,0000,0000,,The creativity that your mind is forced into
Dialogue: 0,0:02:31.81,0:02:34.74,Default,,0000,0000,0000,,during these boring classes, is both a gift and a burden.
Dialogue: 0,0:02:34.74,0:02:37.02,Default,,0000,0000,0000,,But here's a few authentic doodles using these techniques
Dialogue: 0,0:02:37.02,0:02:38.46,Default,,0000,0000,0000,,that I did when I was in college.
Dialogue: 0,0:02:38.46,0:02:40.08,Default,,0000,0000,0000,,Just to show you I'm not making all this up.
Dialogue: 0,0:02:40.08,0:02:41.90,Default,,0000,0000,0000,,These are from a freshmen music history class,
Dialogue: 0,0:02:41.90,0:02:43.96,Default,,0000,0000,0000,,because I happen to be able to find this notebook.
Dialogue: 0,0:02:43.96,0:02:45.81,Default,,0000,0000,0000,,But this is a doodle I actually did most often
Dialogue: 0,0:02:45.81,0:02:47.34,Default,,0000,0000,0000,,during my 9th grade Italian class.
Dialogue: 0,0:02:47.34,0:02:48.52,Default,,0000,0000,0000,,Language being another subject
Dialogue: 0,0:02:48.52,0:02:51.16,Default,,0000,0000,0000,,usually taught by unfathomably stupid methods.
Dialogue: 0,0:02:51.16,0:02:53.95,Default,,0000,0000,0000,,For example, these snakes are having trouble communicating
Dialogue: 0,0:02:53.95,0:02:55.37,Default,,0000,0000,0000,,because one speaks in Parseltongue
Dialogue: 0,0:02:55.37,0:02:56.80,Default,,0000,0000,0000,,and the other speaks in Python.
Dialogue: 0,0:02:56.80,0:02:59.02,Default,,0000,0000,0000,,And their language classes, much like math classes,
Dialogue: 0,0:02:59.02,0:03:02.19,Default,,0000,0000,0000,,focus too much on memorization and not enough on immersion
Dialogue: 0,0:03:02.19,0:03:03.38,Default,,0000,0000,0000,,But just pretend you're in math class,
Dialogue: 0,0:03:03.38,0:03:05.52,Default,,0000,0000,0000,,learning about graph theory so that I can draw the parallels
Dialogue: 0,0:03:05.52,0:03:07.23,Default,,0000,0000,0000,,because here's the 2nd doodle game
Dialogue: 0,0:03:07.23,0:03:08.99,Default,,0000,0000,0000,,which is very much mathematically related.
Dialogue: 0,0:03:08.99,0:03:10.98,Default,,0000,0000,0000,,Draw a squiggle all over the page
Dialogue: 0,0:03:10.98,0:03:12.68,Default,,0000,0000,0000,,and make sure it closes up.
Dialogue: 0,0:03:12.68,0:03:14.39,Default,,0000,0000,0000,,Pick an outside section and color it in.
Dialogue: 0,0:03:14.39,0:03:15.73,Default,,0000,0000,0000,,Now you want to alternate coloring
Dialogue: 0,0:03:15.73,0:03:18.43,Default,,0000,0000,0000,,so that no 2 faces of the same color touch.
Dialogue: 0,0:03:18.43,0:03:19.42,Default,,0000,0000,0000,,Curiously enough,
Dialogue: 0,0:03:19.42,0:03:20.92,Default,,0000,0000,0000,,much like the weaving game,
Dialogue: 0,0:03:20.92,0:03:23.32,Default,,0000,0000,0000,,this game always mathemagically works out.
Dialogue: 0,0:03:23.32,0:03:26.13,Default,,0000,0000,0000,,It also works really well if you make the lines spiky
Dialogue: 0,0:03:26.13,0:03:27.31,Default,,0000,0000,0000,,instead of a smooth curve
Dialogue: 0,0:03:27.31,0:03:29.19,Default,,0000,0000,0000,,and once again, it works with multiple lines too.
Dialogue: 0,0:03:29.19,0:03:30.36,Default,,0000,0000,0000,,It probably has something to do with
Dialogue: 0,0:03:30.36,0:03:32.33,Default,,0000,0000,0000,,the 2 colorability of graphs of even degree,
Dialogue: 0,0:03:32.33,0:03:33.61,Default,,0000,0000,0000,,which might even be what your teacher is trying to
Dialogue: 0,0:03:33.61,0:03:34.71,Default,,0000,0000,0000,,teach you at this very moment
Dialogue: 0,0:03:34.71,0:03:36.01,Default,,0000,0000,0000,,for all you're paying attention.
Dialogue: 0,0:03:36.01,0:03:37.52,Default,,0000,0000,0000,,But maybe you can chat with him after class about snakes
Dialogue: 0,0:03:37.52,0:03:38.69,Default,,0000,0000,0000,,and he'll explain it to you
Dialogue: 0,0:03:38.69,0:03:40.42,Default,,0000,0000,0000,,because I'd rather move on to the next doodle game.
Dialogue: 0,0:03:40.42,0:03:42.16,Default,,0000,0000,0000,,This is a combination of the last 2
Dialogue: 0,0:03:42.16,0:03:44.52,Default,,0000,0000,0000,,Step 1: draw a smooth closed curve
Dialogue: 0,0:03:44.52,0:03:46.37,Default,,0000,0000,0000,,Step 2: assign overs and unders
Dialogue: 0,0:03:46.37,0:03:48.42,Default,,0000,0000,0000,,Step 3: shade in every other face
Dialogue: 0,0:03:48.42,0:03:51.23,Default,,0000,0000,0000,,After that, it takes a little artistic finesse
Dialogue: 0,0:03:51.23,0:03:52.30,Default,,0000,0000,0000,,to get the shading right,
Dialogue: 0,0:03:52.30,0:03:53.37,Default,,0000,0000,0000,,but you end up with some sort of really neat surface.
Dialogue: 0,0:03:53.37,0:03:56.77,Default,,0000,0000,0000,,For example, this one only has one edge and one side
Dialogue: 0,0:03:56.77,0:03:58.12,Default,,0000,0000,0000,,but if you're interested in this,
Dialogue: 0,0:03:58.12,0:03:59.37,Default,,0000,0000,0000,,you should really be talking to
Dialogue: 0,0:03:59.37,0:04:00.92,Default,,0000,0000,0000,,your resident topology professor and not me.
Dialogue: 0,0:04:00.92,0:04:02.54,Default,,0000,0000,0000,,But here's the thing:
Dialogue: 0,0:04:02.54,0:04:03.84,Default,,0000,0000,0000,,if someone asked you 5 minutes ago
Dialogue: 0,0:04:03.84,0:04:05.70,Default,,0000,0000,0000,,what tangled up snakes, demented checkerboards,
Dialogue: 0,0:04:05.70,0:04:07.65,Default,,0000,0000,0000,,and crazy twisty surfaces have in common?
Dialogue: 0,0:04:07.65,0:04:08.96,Default,,0000,0000,0000,,what would you have answered?
Dialogue: 0,0:04:08.96,0:04:11.30,Default,,0000,0000,0000,,This is why I love mathematics:
Dialogue: 0,0:04:11.30,0:04:12.73,Default,,0000,0000,0000,,the moment when you realize that
Dialogue: 0,0:04:12.73,0:04:14.38,Default,,0000,0000,0000,,something seemingly arbitrary and confusing
Dialogue: 0,0:04:14.38,0:04:16.66,Default,,0000,0000,0000,,is actually part of something.
Dialogue: 0,0:04:16.66,0:04:18.74,Default,,0000,0000,0000,,It's better than the cleverest possible ending
Dialogue: 0,0:04:18.74,0:04:20.19,Default,,0000,0000,0000,,to any crime show or mystery novel,
Dialogue: 0,0:04:20.19,0:04:22.41,Default,,0000,0000,0000,,because that's only the beginning.
Dialogue: 0,0:04:22.41,0:04:24.69,Default,,0000,0000,0000,,Anyway, have fun with that.