The bubble that breaks maths.

The Goldschmid point is at 0.5276973967
The bubble bursts at 0.6627434193

And as you may have noticed, the laser video with Seb is not out yet. I think it's going to trail this one by quite a while.

CORRECTIONS
- None yet: let me know if you spot any mistakes!

Filming and editing by Nico Turner
State-of-the-art computer simulations by Matt Parker
Music by Howard Carter
Design by Simon Wright and Adam Robinson

MATT PARKER: Stand-up Mathematician

[standupmaths]

Hello early people. A bunch of you are saying the video is low res. YouTube is just taking its sweet time to process it. Soon it'll be available in glorious 3840 × 2160.

[RegebroRepairs]

"Something something, energy" is how I will explain all physics from now on.

[jimi]

"Something something energy"

This is how mathematicians do physics.

[weatherseed]

"...something something energy" I see Matt knows his physics.

[stratogott]

Me when I saw it curved inward : "it's cosh!"
Me when I saw the equation : "oh maybe it's harder than I thought"
Matt : "it's cosh!"

Dammit. Never doubt good old cosh.

[harwinkle]

'Mattbook Pro', this is the high comedy I subscribe for

[TomNoddy]

CV Boys, in his lectures given at the Royal Institution, drew a single *closed* bubble apart until it came very close to that state of instability that Matt found (around 21:32). Then he used that instability to read environmental phenomena in the room. Just as Matt was being very careful not to breath so that he wouldn't create a disturbance and cause the structure to divide prematurely, Boys took great care to reach that unstable place and to not disturb it ... until ... he allowed a minute amount of input to see if that could be measured by this delicate tool that he had caused the soap film to be.

At one point, he put electromagnets on either side of the stretched bubble and, from across the room, when he threw the switch that caused the magnets to engage the bubble pulled in two ... only because oxygen is slightly responsive to magnetism. The oxygen inside of the bubble responded to the magnetic charge and that response was instantly read by the soap film which was so unstable that that tiny disturbance caused it to pull into two separate bubbles.

That was during his lectures that began in 1890.

[johnchessant]

"where math stops working is where reality stops working"
That sentence makes me very happy :D

[closerb]

That conclusion at 22:21 is why we need maths, why we need patience, and why we need you. :-) Thanks for the great work Matt!

[Wouter]

Note that b is always x/2. That's because b is just the horizontal translation of the cosh graph. If you plug that in, you only have one variable left to solve. The Newton method would work quite well too.

[jtherrie]

"import math as maths"

I've always wondered how people program in foreign languages =p

[vincentpelletier]

I had a similar situation involving numerical calculations I did during my PhD studies. At some point in my calculations, the more accurate I was trying to be, the less stable the results. Below that point, the calculations made perfect sense. Above that point, the results were inverted from what I expected. After a few weeks of debugging and headaches, my advisor prompted me to work out an analytical solution as an alternative (that is, an exact solution of a slightly simplified problem), and the exact solution showed there was an inversion point where the effect became opposite from what I expected. Then I was able to make sens of the experimental data, which had a high value, then a dip to almost zero, then a high value (I was measuring the square of the calculated value, that is why it was always positive even when it had reversed.

Ok, as I write this, I realize how vague it is. Summary of the actual problem:
I was working on tiny metal line grills to be used them as polarizers for ultraviolet light. With wire line polarizers, one expects that the photons with electrical fields oriented in the direction of the lines will be reflected, the ones with electrical fiels perpendicular will be transmitted. It turns out that as the wavelength becomes really close to the period of the wire grill, the effect reverses, photons with electrical field parallel to the wires actually makes it through, the one perpendicular is reflected.

The calculation I was making involved matrices of infinite size, the numerical calculation was using finite size matrices to approximate the results, the bigger the matrices, the more accurate they were. For some values, say 7 x 7 matrices, I would get a positive value, then at 9x9 I get negative, at 11x11 positive again. That happens at the crossover point, where the answer is actually close to zero.

The reason my experiments measured the square of the polarization is that there are no good UV polarizers, so I was using two of mine at 90 angles and measuring the extinction of light as a function of wavelength. Since I use two identical ones, it does not matter whether the parallel or perpendicular polarization makes it through, it will be blocked by the other polarizer, so extinction will always be higher, except at the crossover point since light is not polarized there.

[Maninawig]

I dunno what is more nerdy in this case:
A man getting excited about playing with bubbles for 25 minutes,
Or me who enjoyed watching a man get excited about playing with bubbles in the nerdiest way possible for 25 minutes.

In either case, this was a blast.

[abrahamx]

In 9:58, "import math as maths" xD, btw it was really nice that moment when your calculations were that close to the actual real value

[gowzahr]

"If people are familiar with my back catalog . . ."

He's talking about the Parker Square, isn't he?

[PapaFlammy]

wouldn't the bubble rather pop maths?

[eglewether]

"something, something energy" .. these sure are math videos :D

[theonetralewolf]

"Let's use maths to calculate this cool shape!" 8 minutes later: "Just kidding, it can't be done."

[wizardo]

All scientific explanations end with "something something energy"

[billysoy]

Ah, the something something energy theorem - one of physic's greatest discoveries...