A change in perspective is worth 80 IQ points

February 4, 2019 8:12 AM

Three weeks ago, ace math visualizer 3Blue1Brown posted an extremely weird and surprising method of deriving the value of pi. Why does this work? Well, it has to do with a velocity phase diagram. Wait, it's a semicircular fan of mirror universes.

The original paper.
An interactive model of the thought experiment.

posted by theodolite (10 comments total)

This is really freakin' cool, a nice accessible explanation with visuals to help. I sent it to my personal mathematician.
posted by entropone at 8:35 AM on February 4, 2019 [1 favorite]

Wow, that was beautiful.
posted by Ipsifendus at 8:37 AM on February 4, 2019 [2 favorites]

I love 3Blue1Brown.

After years of bouncing off of calculus, their intro series layed it out like I've never seen anywhere. Just really opened up the idea that calculus is more about thinking than about calculating. Got me over that first big hurdle.

And their visualization of the Fourier transform is gorgeous and helped cement the intuition I was building up by reading the books.

Also, they have a good intro series on linear algebra, if that's your kink.
posted by Horkus at 9:11 AM on February 4, 2019 [5 favorites]

After years of bouncing off of calculus, their intro series layed it out like I've never seen anywhere.

I recently watched their video on Taylor Series and it totally galaxy-brained me....in school these sequences seemed so mysterious and arbitrary
posted by thelonius at 9:24 AM on February 4, 2019 [1 favorite]

After years of bouncing off of calculus

You just need a frictionless surface and someone 100,000 times as massive as you to bounce against and you'll be calculating pi in no time.
posted by a snickering nuthatch at 9:26 AM on February 4, 2019 [4 favorites]

Fantastic post, thank you very much.

I was pleasantly surprised that the third video shows why the audio of the clicks sounds like it does, though it's not addressed directly. (Spoiler: the straight line through the mirror world hits a theta boundary more often as it reaches its closest distance from the center of the circle.)

I *think* I hear a real world approximation of this sound when two large rigid glass/ceramic/ball bearings get pushed together, just before they come to rest touching each other. Though upon reflection (no pun intended) it's probably just “similar sounding”, not actually mathematically the same.
posted by lothar at 9:41 AM on February 4, 2019

This channel's visualizations are so amazing. This is a good topic for their vis instead of trying to make me cry visualizing the complex plane doing shenanigans. I'd seen the first two of these but not the mirror solution one.

I think there's a mistake in counting the mirror bounces though? I think the answer should be ceil(pi/theta)-1, not floor(pi/theta). In the video at 12:38 he goes wrong by counting the first slice (where no bounces have happened) and discarding the last slice (which the light beam does enter).
posted by fleacircus at 10:50 AM on February 4, 2019

I *think* I hear a real world approximation of this sound when two large rigid glass/ceramic/ball bearings get pushed together, just before they come to rest touching each other.

I hear the sounds my Dad's first metal detector would make when it was near a quarter.
posted by 922257033c4a0f3cecdbd819a46d626999d1af4a at 4:58 PM on February 4, 2019

There have been a couple of 3 Blue 1 Brown episodes about the surprising places circles, and thus π, show up like this one about the Basel problem, but this one made me say out loud, "What? Noooooo…. Huh."
posted by ob1quixote at 8:00 AM on February 5, 2019

I seriously have to stop myself from posting every new 3blue1brown video here. They're all just so neat.
posted by zengargoyle at 1:13 PM on February 5, 2019 [2 favorites]