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October 9, 2013 5:59 AM Subscribe

Triforces all the way down!

OK, this is going to take some time to understand, but I am determined to read through it and not just scroll through looking at awesome renderings.

posted by ignignokt at 6:07 AM on October 9, 2013 [2 favorites]

OK, this is going to take some time to understand, but I am determined to read through it and not just scroll through looking at awesome renderings.

posted by ignignokt at 6:07 AM on October 9, 2013 [2 favorites]

Well. great, now I have a nosebleed.

Also:

Heh.

posted by hearthpig at 6:12 AM on October 9, 2013 [2 favorites]

Also:

*From what I can tell, one of the settings used to deal with division by 0 is the so-called Riemann sphere, which is where we take a space shuttle and use it to fly over and drop a cow on top of a biodome, and then have the cow indiscriminately fire laser beams at the grass inside and around the biodome. That's my intuitive understanding of it anyway.*Heh.

posted by hearthpig at 6:12 AM on October 9, 2013 [2 favorites]

Things get pretty ͔Z̴̹A͎̱͉̟Ḷ̴̙̟̜̹̺G̛̪̟͕̰̘̪Ọ̢̳͇!̘̼̕-esque down near the bottom of that page. <shudder>

posted by Rock Steady at 6:18 AM on October 9, 2013 [1 favorite]

posted by Rock Steady at 6:18 AM on October 9, 2013 [1 favorite]

Of course, as soon as I finally give in and buy a Cyclotron 4000, they announce the monstrously more powerful Cycowtron 4800.

posted by mcoo at 6:19 AM on October 9, 2013 [1 favorite]

posted by mcoo at 6:19 AM on October 9, 2013 [1 favorite]

There's showing off and then there's this. Whooo.

posted by BinGregory at 6:27 AM on October 9, 2013 [1 favorite]

posted by BinGregory at 6:27 AM on October 9, 2013 [1 favorite]

Seriously, that would make a bad assed tattoo for a guy from Iowa.

posted by cjorgensen at 6:28 AM on October 9, 2013

posted by cjorgensen at 6:28 AM on October 9, 2013

Warning: Math.

posted by Curious Artificer at 6:28 AM on October 9, 2013 [2 favorites]

posted by Curious Artificer at 6:28 AM on October 9, 2013 [2 favorites]

This is like if that movie Pi was a comedy.

posted by BinGregory at 6:29 AM on October 9, 2013 [6 favorites]

posted by BinGregory at 6:29 AM on October 9, 2013 [6 favorites]

*And just so we're all clear, time isn't "the fourth dimension." That statement is the conceptual version of eating bagels without cream cheese, namely a manifestation of meaninglessness.*

This guy, he's killing me.

posted by BinGregory at 6:35 AM on October 9, 2013 [4 favorites]

I don't get the point.

posted by Samizdata at 6:38 AM on October 9, 2013 [1 favorite]

posted by Samizdata at 6:38 AM on October 9, 2013 [1 favorite]

In High School I got VERY into Fractals, Chaos Theory, and Sierpinski's triangle, his gasket, and Tesseracts(not of Marvel fame).

This was caused by Jurassic Park and Lost World(the books) as they touch heavily on Chaos Theory and fractals.

There are more than a few notebooks of mine from High School that have Sierpinski's Triangles drawn on them.

I can't wait to get home and read this in depth.

posted by Twain Device at 6:47 AM on October 9, 2013 [2 favorites]

This was caused by Jurassic Park and Lost World(the books) as they touch heavily on Chaos Theory and fractals.

There are more than a few notebooks of mine from High School that have Sierpinski's Triangles drawn on them.

I can't wait to get home and read this in depth.

posted by Twain Device at 6:47 AM on October 9, 2013 [2 favorites]

*This cow does not cower. Infinity cannot bully this bull, cannot bloviate this bovine. By all appearances this cow is wearing infinity on its mane. Its horns are probably made of ℵℵ⋱ down 4 or 5 levels, an immutability surpassed only by that of the tusks of the Alephant. Our cow isn't staring into infinity. It's looking down at infinity, observing infinity with detached understanding. If our cow were not so enlightined, and also had the facial muscles, it might betray the subtlest of smiles at infinity's infinity face, for infinity's turbid fractal whirlpools and vast lethargic swamps are but swathes of data like any other to this cow.*

Favorite added! [!]

posted by Sebmojo at 6:52 AM on October 9, 2013 [2 favorites]

*I don't get the point.*

It can be a bit difficult, because once you think you've got the point, it shoots off halfway to some other vertex.

posted by a snickering nuthatch at 6:52 AM on October 9, 2013 [5 favorites]

Does someone have a TL;DR version for this?

posted by TheLittlePrince at 6:59 AM on October 9, 2013

posted by TheLittlePrince at 6:59 AM on October 9, 2013

tl;dr infinite triangles

posted by Twain Device at 7:03 AM on October 9, 2013

posted by Twain Device at 7:03 AM on October 9, 2013

tl;dr

tl;dr tl;dr

tl;dr tl;dr tl;dr tl;dr

tl;dr tl;dr tl;dr tl;dr tl;dr tl;dr tl;dr tl;dr

tl;dr tl;dr tl;dr tl;dr tl;dr tl;dr tl;dr tl;dr tl;dr tl;dr tl;dr tl;dr tl;dr tl;dr tl;dr tl;dr

posted by lalochezia at 7:13 AM on October 9, 2013 [35 favorites]

tl;dr tl;dr

tl;dr tl;dr tl;dr tl;dr

tl;dr tl;dr tl;dr tl;dr tl;dr tl;dr tl;dr tl;dr

tl;dr tl;dr tl;dr tl;dr tl;dr tl;dr tl;dr tl;dr tl;dr tl;dr tl;dr tl;dr tl;dr tl;dr tl;dr tl;dr

posted by lalochezia at 7:13 AM on October 9, 2013 [35 favorites]

just because trying to get LaTeX to do something simple has ruined my morning (\fbox = \fuckbox)...

if you call $number/0 = \infinity and decided -\infinity = + \infinity, then infinity becomes just one point which you add to the real number line, which you can get to by going through infinitely many positive numbers or infinitely many negative numbers... that is, adding that point turns the real number line into a circle. You could reverse this by resting a circle on the x-axis, call the "North pole" of that circle infinity, the "South pole" '0' and identifying the circle with the x-axis by associating each point on the circle with the point defined by drawing a line through the north pole through the point and intersecting that line with the x-axis. Every point on the circle gets identified with a point on the x-axis except the north pole, which has a line parallel to the x-axis through it... i.e. that parallel line to the x-axis intersects with it, line train tracks, at infinity.

You can think of "complex numbers" as points in a real two-dimensional plane. Then, you can do the same thing as above by resting a two-dimensional sphere on that plane, calling the south pole '0' and the north pole infinity. The association by straight lines is now called "steroeographic projection. It's the kind of "mapping" which makes Canada, Russia and the Arctic infinitely large. However, stereographic projection preserves angles and circles, so latitude and longitude still make sense.

maybe it makes more sense with cows...

posted by ennui.bz at 7:15 AM on October 9, 2013 [2 favorites]

*From what I can tell, one of the settings used to deal with division by 0 is the so-called Riemann sphere...*if you call $number/0 = \infinity and decided -\infinity = + \infinity, then infinity becomes just one point which you add to the real number line, which you can get to by going through infinitely many positive numbers or infinitely many negative numbers... that is, adding that point turns the real number line into a circle. You could reverse this by resting a circle on the x-axis, call the "North pole" of that circle infinity, the "South pole" '0' and identifying the circle with the x-axis by associating each point on the circle with the point defined by drawing a line through the north pole through the point and intersecting that line with the x-axis. Every point on the circle gets identified with a point on the x-axis except the north pole, which has a line parallel to the x-axis through it... i.e. that parallel line to the x-axis intersects with it, line train tracks, at infinity.

You can think of "complex numbers" as points in a real two-dimensional plane. Then, you can do the same thing as above by resting a two-dimensional sphere on that plane, calling the south pole '0' and the north pole infinity. The association by straight lines is now called "steroeographic projection. It's the kind of "mapping" which makes Canada, Russia and the Arctic infinitely large. However, stereographic projection preserves angles and circles, so latitude and longitude still make sense.

maybe it makes more sense with cows...

posted by ennui.bz at 7:15 AM on October 9, 2013 [2 favorites]

It's Scary Sierpinski Skull Time!

It's Scary Sierpinski Skull Time!

Ritalin's a helluva drug.

posted by lalochezia at 7:20 AM on October 9, 2013 [3 favorites]

So what you're saying is, triangles?

posted by Kabanos at 7:21 AM on October 9, 2013 [2 favorites]

posted by Kabanos at 7:21 AM on October 9, 2013 [2 favorites]

Latke Manifold

.

Latke-Hamentaschen Debate

posted by lalochezia at 8:15 AM on October 9, 2013 [3 favorites]

Do those Sierpinski triangles freak you out? Don't worry, Benoit Mandelbrot to the rescue!

posted by Pirate-Bartender-Zombie-Monkey at 8:19 AM on October 9, 2013

posted by Pirate-Bartender-Zombie-Monkey at 8:19 AM on October 9, 2013

I am pretty sure this page describes how the Event Horizon's gravity drive worked.

posted by Steely-eyed Missile Man at 9:18 AM on October 9, 2013 [2 favorites]

posted by Steely-eyed Missile Man at 9:18 AM on October 9, 2013 [2 favorites]

“At the chasm of infinity, our cow glances past its precipice, stares down its abyss. You know that machine in the Hitchhiker's Guide that explodes your mind or whatever by showing you how pathetically insignificant you are compared to the universe? Well this is like a Windows 3.1 version of that. Our poor cow friend's soul is being wrung on the very clothesline of endlessness itself. I think this is the first time I'm happy I'm not a cow.”

posted by mr. manager at 9:52 AM on October 9, 2013

posted by mr. manager at 9:52 AM on October 9, 2013

From the homepage, apt:

posted by grog at 9:53 AM on October 9, 2013 [2 favorites]

*So while the sierpinski triangle page to end most sierpinski triangle pages ™ purports to be some kind of exploratory rundown of the Sierpinski triangle, it's also a fractal expression of just how carried away I get, namely very.*posted by grog at 9:53 AM on October 9, 2013 [2 favorites]

Metafilter: a fractal expression of just how carried away I get, namely very.

posted by lalochezia at 10:08 AM on October 9, 2013 [3 favorites]

posted by lalochezia at 10:08 AM on October 9, 2013 [3 favorites]

Ok, no joke, I just went to the top of the page and hit "Page Down" as fast as I could. I swear, it freaked me out a bit and I had to stop.

posted by Pirate-Bartender-Zombie-Monkey at 10:16 AM on October 9, 2013 [2 favorites]

posted by Pirate-Bartender-Zombie-Monkey at 10:16 AM on October 9, 2013 [2 favorites]

Cool. My very first Commodore 64 Assembly language program drew one of these using the "pick a random vertex and move/plot a point halfway toward it" method.

posted by rocket88 at 11:25 AM on October 9, 2013

posted by rocket88 at 11:25 AM on October 9, 2013

*This cow does not cower. Infinity cannot bully this bull, cannot bloviate this bovine. By all appearances this cow is wearing infinity on its mane. Its horns are probably made of ℵℵ⋱ down 4 or 5 levels, an immutability surpassed only by that of the tusks of the Alephant. Our cow isn't staring into infinity. It's looking down at infinity, observing infinity with detached understanding. If our cow were not so enlightined, and also had the facial muscles, it might betray the subtlest of smiles at infinity's infinity face, for infinity's turbid fractal whirlpools and vast lethargic swamps are but swathes of data like any other to this cow.*

Metafilter: Stop by for the unfathomable math, but stay for the funny cow puns

posted by not_on_display at 11:33 AM on October 9, 2013

Need a Menger sponge to wipe the nerd drool up in here.

posted by BrotherCaine at 11:58 AM on October 9, 2013 [3 favorites]

posted by BrotherCaine at 11:58 AM on October 9, 2013 [3 favorites]

Mmmmmm fractal drooling hahllllhallllgallllllllhallllllllllll

Menger Sponge Cake

Sierpinski Cookies

posted by lalochezia at 1:19 PM on October 9, 2013 [2 favorites]

Menger Sponge Cake

Sierpinski Cookies

posted by lalochezia at 1:19 PM on October 9, 2013 [2 favorites]

lalochezia: "

I make hella latkes for a goyim. I used to have a lady friend who had my ingredient list memorized so she could show up with a bag of groceries, plonk it down, and say something to the effect of "Latkes. Now. And no one gets hurt."

Does this mean I am a mathematician now? My family will be SO proud!

posted by Samizdata at 10:56 PM on October 9, 2013

*Latke Manifold*

.

Latke-Hamentaschen Debate".

Latke-Hamentaschen Debate

I make hella latkes for a goyim. I used to have a lady friend who had my ingredient list memorized so she could show up with a bag of groceries, plonk it down, and say something to the effect of "Latkes. Now. And no one gets hurt."

Does this mean I am a mathematician now? My family will be SO proud!

posted by Samizdata at 10:56 PM on October 9, 2013

Does someone have a brief on Mathematica syntax that makes it comprehensible for someone familiar with other coding systems? I have a few infinities to visit but I can't read the alphabet on this map.

posted by 23 at 11:08 PM on October 9, 2013

posted by 23 at 11:08 PM on October 9, 2013

Ah, OK, here are some of the weird parts:

Module[X, Y] means "execute Y with local variables X", kind of like "let X; do Y".

# signifies a positional parameter for anonymous lambdas, which are terminated by &. So you can do this:

/@ is a functional map and other things involving @ are variations on function application. I am not sure that covers all the uses of @.

posted by 23 at 11:21 PM on October 9, 2013

Module[X, Y] means "execute Y with local variables X", kind of like "let X; do Y".

# signifies a positional parameter for anonymous lambdas, which are terminated by &. So you can do this:

f = #1 + #2 &Also the number after the hash isn't needed (or maybe not allowed?) if you have only one parameter.

f[3,4]

// gives 7

/@ is a functional map and other things involving @ are variations on function application. I am not sure that covers all the uses of @.

posted by 23 at 11:21 PM on October 9, 2013

Wow, some of these are incredibly gorgeous. My favorite part was at the bottom, namely the second music example. I would love to learn how to use mathematics to create music like this, but it's probably way out of my league.

posted by gucci mane at 12:14 AM on October 10, 2013

posted by gucci mane at 12:14 AM on October 10, 2013

gucchi mane, creating music from cellular automata is actually relatively simple if your'e already familiar with programming of any kind. Give the Wolfram Tones explanation a look.

posted by 23 at 12:25 AM on October 10, 2013

posted by 23 at 12:25 AM on October 10, 2013

This page made me "buy" Mathematica.

posted by oceanjesse at 8:57 PM on October 10, 2013

posted by oceanjesse at 8:57 PM on October 10, 2013

*"There are bound to be many elementary number-theoretic constructions of the Sierpinski triangle given that it looks like a percolation pattern (as in the cellular automata above). The Wikipedia article mentions that it appears in Pascal's Triangle when differentiating between even and odd numbers. Sure enough: [img]"*

Hot damn. Still reading, but this is the shit I love. Straight up my jam.

posted by Eideteker at 7:50 AM on November 4, 2013

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This equation is in what's called "straight ballin'" formNow that's funny.

posted by joecacti at 6:05 AM on October 9, 2013 [5 favorites]