The Art of Learning
December 10, 2016 7:42 PM Subscribe
That's a very nice video! I'd like to just watch a bunch of his animations about various complex functions...I've forgotten everything I ever knew about conformal maps.
posted by leahwrenn at 8:46 PM on December 10, 2016
posted by leahwrenn at 8:46 PM on December 10, 2016
This is fantastic. Such a good demonstration of the intuition and beauty behind math.
posted by esprit de l'escalier at 8:46 PM on December 10, 2016
posted by esprit de l'escalier at 8:46 PM on December 10, 2016
Had Youtube existed in 1996, I would have done much better in my Complex Analysis class.
NB: I ended up dropping that class, as it wasn't required for my major.
posted by tclark at 9:09 PM on December 10, 2016 [1 favorite]
NB: I ended up dropping that class, as it wasn't required for my major.
posted by tclark at 9:09 PM on December 10, 2016 [1 favorite]
I haven't done any real thinking about stuff like that for so long and I kind of miss it, it's just so beautiful - not to mention the pleasure of having all the pieces clunk together in your brain.
posted by Dr Dracator at 3:03 AM on December 11, 2016 [2 favorites]
posted by Dr Dracator at 3:03 AM on December 11, 2016 [2 favorites]
So ... Analytic continuation is elegant, to be sure, but why is it expected?
posted by ZenMasterThis at 5:48 AM on December 11, 2016 [1 favorite]
posted by ZenMasterThis at 5:48 AM on December 11, 2016 [1 favorite]
His videos were good a couple years back, and they've only gotten better. His other recent one about the Towers of Hanoi, recursion, n-ary representation and the Sierpinski triangle is also excellent.
As to expected, I think he's saying - look, the picture of the zeta function has a sort of visual symmetry that looks like it could extend left of where it's actually defined and still be analytic. Like, the factorial looks like it should have a natural equivalent for real numbers that's smooth in-between whole numbers, and it does- the Gamma function (though it's not unique, unlike the analytic continuation).
posted by BungaDunga at 8:47 AM on December 11, 2016
As to expected, I think he's saying - look, the picture of the zeta function has a sort of visual symmetry that looks like it could extend left of where it's actually defined and still be analytic. Like, the factorial looks like it should have a natural equivalent for real numbers that's smooth in-between whole numbers, and it does- the Gamma function (though it's not unique, unlike the analytic continuation).
posted by BungaDunga at 8:47 AM on December 11, 2016
So ... Analytic continuation is elegant, to be sure, but why is it expected?
Well, one nice feature of 1 + 2 + 3 + 4 + ... = -1/12 is that when you encounter apparently infinite sums of this form in physics (which is quite often), substituting those infinite sums with anything other than -1/12 gives you a result that disagrees with experiment. The most famous case is the "Casimir effect," where two plates with neutral charge appear, against all intuition, to attract one another if brought very close together. An apparently infinite sum shows up in calculations regarding the harmonics of the situation, and (1) only a negative number would result in attraction, rather than repulsion, and (2) the strength of the attraction scales as a function of 1/12 the distance, exactly as expected from zeta(-1) = -1/12.
posted by belarius at 9:28 AM on December 11, 2016 [12 favorites]
Well, one nice feature of 1 + 2 + 3 + 4 + ... = -1/12 is that when you encounter apparently infinite sums of this form in physics (which is quite often), substituting those infinite sums with anything other than -1/12 gives you a result that disagrees with experiment. The most famous case is the "Casimir effect," where two plates with neutral charge appear, against all intuition, to attract one another if brought very close together. An apparently infinite sum shows up in calculations regarding the harmonics of the situation, and (1) only a negative number would result in attraction, rather than repulsion, and (2) the strength of the attraction scales as a function of 1/12 the distance, exactly as expected from zeta(-1) = -1/12.
posted by belarius at 9:28 AM on December 11, 2016 [12 favorites]
Whoa.
posted by ZenMasterThis at 11:13 AM on December 11, 2016 [1 favorite]
posted by ZenMasterThis at 11:13 AM on December 11, 2016 [1 favorite]
great video!
posted by Vitamaster at 12:06 PM on December 11, 2016
posted by Vitamaster at 12:06 PM on December 11, 2016
« Older MAN IS SURE WAS EASY TO POST THIS WITH MY... | Blimey, if it don't look like mutton again... Newer »
This thread has been archived and is closed to new comments
posted by sammyo at 7:56 PM on December 10, 2016 [1 favorite]