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Oh, my - why pi??
Posted: January 20th, 2019, 12:19 pm
by sasha
This animation is an idealized representation of the energy and momentum conservation laws, with an amazing, unexpected, mind-blowingly non-intuitive result. The basic physics is actually quite simple - I can almost do the math in my head - and now I want to write a program to do this. It won't be as slick as the presentation here, but it seems like a fun way to spend a few dangerously cold days holed up inside!
https://www.youtube.com/watch?v=HEfHFsfGXjs
Re: Oh, my - why pi??
Posted: January 26th, 2019, 3:18 am
by mnaz
Pi is just such a weird ratio, thing, whatever it is. Almost like humans discovered math and suddenly everything was completely calculable and figured out, and the universe said "uh uh, not so fast"...
Re: Oh, my - why pi??
Posted: January 26th, 2019, 1:54 pm
by sasha
The motions of the planets, nuclear decay, gravitational attraction - it crops up everywhere, peeking around the most unexpected of corners. It even shows up in the statistics describing random processes, in tandem with another mysterious universal constant, e, approx. 2.71828... the distribution of heights of 1st-graders... the weights of apples... the length of bolts off an assembly line... Deep Magick.
Here's another one that blew my mind. The Fibonacci numbers form a sequence in which each member is the sum of the previous two, starting with zero and one: 0,1,1,2,3,5,8,13,21,... etc. The ratio of any two consecutive members of the series approaches a constant, around 1.618034... Interesting enough, but what blew my mind was that it doesn't matter which two numbers you use to start the series. You can start with 12 and -374 - and you'll eventually get the ratio between two consecutive elements converging to 1.618034... You can check this yourself easily enough in Excel.
I've dug a little deeper and now I understand why this is so - but it's still pretty remarkable on the surface.
Deep Magick.
Re: Oh, my - why pi??
Posted: February 3rd, 2019, 10:36 pm
by gypsyjoker
"a change of perspective is worth 80 IQ points"
I liked this comment on the third video:
Minstorm
7 hours ago
I'm continually impressed on how this channel can make me feel completely lost in the first 5 minutes but completely enlightened in the last 5
Re: Oh, my - why pi??
Posted: February 4th, 2019, 11:40 am
by sasha
gypsyjoker wrote: ↑February 3rd, 2019, 10:36 pm
"a change of perspective is worth 80 IQ points"
I liked this comment on the third video:
Minstorm
7 hours ago
I'm continually impressed on how this channel can make me feel completely lost in the first 5 minutes but completely enlightened in the last 5
That was how I felt watching his video on Fourier transforms. "What the hell is he
doing??" Then it all suddenly fell into place... an "oh, wow" moment...
Re: Oh, my - why pi??
Posted: February 5th, 2019, 9:10 am
by mnaz
Fibonacci? Yeah, consecutives eventually converging on 1.618 is a mind blower, but at least it wasn't 1.5708! (Half of pi...) That would've been downright scary...
Re: Oh, my - why pi??
Posted: February 5th, 2019, 2:04 pm
by sasha
Don't let your guard down just yet! The total area under the bell curve is... (drum roll please) ... the square root of pi! (1.7724539 etc etc)
This was important to us for designing laser marking systems because energy within an ideal laser beam is normally distributed around the beam axis, following a statistical bell curve. I wrote a shitload of Fortran code exploiting that equivalence.