Talking fast and making cool videos does not mean learning is happening
February 22, 2011 7:35 PM   Subscribe

So you're me and you're in math class and you're learning about graph theory, a subject too interesting to be included in most grade school's curricula so maybe you're in some special program or maybe you're in college and were somehow not scarred for life by your grade school math teachers.

I'm not sure why you're not paying attention, but maybe you have an incompetent teacher and it's too heartbreaking to watch him butcher what could have been such a fun subject full of snakes and balloons.

Snakes aren't really all that relevant to the mathematics here but being able to draw them will be useful later so you should probably start practicing now.

I've got a family of three related doodle games to show you all stemming from drawing squiggles all over the page. The first one goes like this: Draw a squiggle, a closed curve that ends where it begins.

The only real rule here is to make sure that all the crossings are distinct.

Next make it start weaving.

Follow the curve around and at each crossing alternate going under and over until you've assigned all the crossings.

Then put on the finishing touches, and voila!

You try it again adding a little artistic flair to the lines.

The cool part is that the weaving always works out perfectly. When you're going around alternating over and under and get to a crossing you've already assigned it will always be the right one. This is very interesting, and we'll get back to it later, but first I'd like to point out two things. One, is that this works for any number of closed curves on the plane, so go ahead and link stuff up or make a weaving out of two colors of yarn. The other is that this doodle also works for snakes on a plane as long as you keep the head and tail on the outside or on the same inside face because mathematically it's the same as if they've linked up.

Or just actually link up the head and tail into a Ouroboros. For example here's three ouroborii in a configuration known as the borromean rings which has the neat property that no two snakes are actually linked with each other. Also because I like naming things this design shall henceforth be known as the Ouroborromean Rings.

But you are me, after all, so you're finding a lot to think about even with just drawing one line that isn't a snake, such as what kind of knots are you drawing? And, can you classify them? For example, these knots all have five crossings but two are essentially the same knot and one is different. Knot theory questions are actually really difficult and interesting but you're going to have to look that one up yourself.

Oh, and you should actually learn how to draw a rope, because it's an integral part of knot theory. So integral, in fact, that if you draw a bunch of integral signs in a row, a sight which is often quite daunting to a mathematician, you can just shade it in, and ta-da. But, being able to draw snakes is also super useful, especially as this doodle game is excellent for producing dark mark tattoo designs.

Also this doodle game can be combined with the stars doodle game. For example, if this pentagram gets knighted, it will henceforth be known as SerPentagram. Also notice that this snake is a five twist mobius strip so you can also call it a mobiaboros but we'll get back to one-sidedness later.

Or, if you want to draw something super complicated like the eighth square star, combining snakes and stars is a great technique for that, too. Here's a boa that ate eight eighth-gons.

The creativity that your mind is forced into during these boring classes is both a gift and a burden.

But, here's a few authentic doodles using these techniques that I did when I was in college just to show you I'm not making all this up. These are from a freshman music history class because I happened to be able to find this notebook, but this is a doodle I actually did most often during my ninth grade Italian class, language being another subject usually taught by unfathomably stupid methods.

For example these snakes are having trouble communicating because one speaks in Parseltounge and the other speaks in Python and their language classes, much like math classes focused too much on memorization and not enough on immersion.

But just pretend you're in math class learning about graph theory so I can draw the parallels.

Because here's the second doodle game which is very much mathematically related: Draw a squiggle all over the page and make sure it closes up. Pick an outside section and color it in. Now you want to alternate coloring so that no two faces of the same color touch.

Curiously enough, much like the weaving game this game also always mathematically works out. It also works really well if you make the lines spiky instead of a smooth curve. And once again it works with multiple lines, too.

It probably has something to do with the two-color-ability of graphs of even degree, which might even be what your teacher is trying to teach you about at this very moment, for all your paying attention.

But maybe you can chat with him after class about snakes and he'll explain it to you, because I'd rather move on to the next doodle game. This is a combination of the last two. Step one: draw a smooth closed curve. Step two: assign overs and unders. Step three: shade in every other face. After that, it takes a little artistic finesse to get the shading right, but you end up with some sort of really neat surface.

For example this one only has one edge and only one side. But if you're interested in this you should really be talking to your resident topology professor and not me.

But here's the thing: If someone asked you five minutes ago what tangled up snakes, demented checker boards and crazy twisty surfaces have in common, what would you have answered?

This is why I love mathematics.

The moment when you realize that something seemingly arbitrary and confusing is actually part of something.

It's better than the cleverest possible ending to any crime show or mystery novel because that's only the beginning.

Anyway, have fun with that.

posted by achmorrison (32 comments total) 169 users marked this as a favorite
I was overwhelmed when I hit the "more inside", my wife, who teaches math, will appreciate this much, I'm sure.
posted by tomswift at 7:42 PM on February 22, 2011

Sweet Jesus... Where do I send the ransom??
posted by LordSludge at 7:49 PM on February 22, 2011 [15 favorites]

Randomly clicked the last link first and the whole post is a transcription of that video with links added... I'll be spending some time with this, thanks.
posted by Huck500 at 7:49 PM on February 22, 2011 [3 favorites]

Holy crow! I'm gonna be here all night. Let me get my beer.
posted by bayani at 7:50 PM on February 22, 2011

I honestly don't know whether to wash my hair or kill the ONE teaching educators now.
posted by Sidhedevil at 7:51 PM on February 22, 2011

Well, at least now we know who DFW's reincarnation is.
posted by mannequito at 7:54 PM on February 22, 2011 [1 favorite]

posted by tomswift at 7:58 PM on February 22, 2011

You lost me at "so you're me and you're in math class".... but I shall look through this post anyway.

Thanks Huck500 for the tip on where I might actually want to start.
posted by hippybear at 7:58 PM on February 22, 2011

To understand this post, the following diagram may be helpful:
   math -------> graph theory ------> interesting
     |                  |                   |
     |                  |                   |
    \/                 \/                  \/
   class --------->  doodle -----------> crime
     |                   |                   |
     |                   |                   |
    \/                  \/                  \/
  attention -------> squiggle --------> balloon
posted by twoleftfeet at 7:59 PM on February 22, 2011 [6 favorites]

clever post, well researched... well done! I have to admit, my initial impression was somewhere in a snark/ocd/loose association/crazy as hell place. I'm glad I kept my fingers off the keyboard until it flowed for me.
posted by tomswift at 8:00 PM on February 22, 2011

In case you're lost in the links, this is the first video you should watch.
posted by twoleftfeet at 8:12 PM on February 22, 2011

twoleftfeet: I don't suppose that's a commutative diagram?
posted by oonh at 8:26 PM on February 22, 2011

I would like to anti-favorite the commutative diagram comment, but that's not an option.

posted by madcaptenor at 8:33 PM on February 22, 2011 [1 favorite]

twoleftfeet: I don't suppose that's a commutative diagram?

In the category of nonsense, the 2-category of free objects over morphisms makes sense.
posted by twoleftfeet at 8:33 PM on February 22, 2011 [1 favorite]

Wow - I randomly started by picking the link to the video of Who Wants to Be a Millionaire where the guy can't figure out that 3^2 + 4^2 = 5^2

And then the entire audience couldn't figure it out.

And then the entire internet couldn't figure it out.

But I didn't wake up.
posted by Salvor Hardin at 8:36 PM on February 22, 2011 [3 favorites]

There's a lot of love in this post. Awesome.
posted by LordSludge at 8:55 PM on February 22, 2011

Metafilter: commutative weblog
posted by 7segment at 9:13 PM on February 22, 2011 [1 favorite]

I'm only about 10 links in and this is becoming my most favoritest post evah!
posted by Mister Fabulous at 9:14 PM on February 22, 2011

Hmm... I'm a big fan of math but I kind of feel that this style of post really takes away from the individual links.
posted by delmoi at 9:24 PM on February 22, 2011

Metafilter: commutative weblog

No, as this post illustrates, it's a distributive network
posted by Neiltupper at 9:35 PM on February 22, 2011

There's other videos by the same person, all as awesome. And I'm totally digging the Le Petit Prince allusions.
posted by NMcCoy at 12:35 AM on February 23, 2011

I have a tattoo of Oroboromonean rings. This simply confirms the coolness of said tattoo and thus makes me better than all of you.

(I got into trouble in college for using the word "thus" as the logical connector for most of my arguments in my humanities papers. Writing too many math proofs can do horrible things to your writing style.)
posted by Hactar at 1:16 AM on February 23, 2011

This really is an amazing post. Well done.
posted by mikeweeney at 4:33 AM on February 23, 2011

This post, does it take math to understand?
posted by FreezBoy at 5:24 AM on February 23, 2011

Barbie says math post is hard.
posted by drlith at 6:49 AM on February 23, 2011

Just so you know, Hactar, right now the only Google result for a search on 'Oroboromonean rings' is your post right there. I don't know what that means.
posted by komara at 7:30 AM on February 23, 2011

Borromean rings.


I don't really know what an oroboromonean ring is, but it probably has something to do with those two things.

The Worm Ouroboros is a fun book to read.
posted by jsturgill at 8:28 AM on February 23, 2011 [1 favorite]

posted by Patbon at 9:27 AM on February 23, 2011

I love squiggly sudoku.
posted by mrgrimm at 10:44 AM on February 23, 2011

Wow. I was familiar with the original vid and several of its sequels and thought, on first glance that this was just a repost
Well Done OP!
posted by OHenryPacey at 11:28 AM on February 23, 2011

twoleftfeet: If the rows are exact, then you can form an exact sequence from the kernels and cokernels. Which leads us back to the snakes.

Sorry, I had to.
posted by eruonna at 2:58 PM on February 23, 2011

I love that this post has over a hundred favorites and only thirty or so comments. We're all just in awe.
posted by wallaby at 3:39 AM on February 24, 2011

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