Cambridge Mathematician Reacts to 'Animation vs Math'

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The reason that zeroes were appearing in the first swordfight between Euler and Stickman was because Euler had a -1 and Stickman had a +1. -1+1=0, so every time their "swords" clashed, it made a zero.

17:14 "This is a very aggressive stick person" The most succinct explanation of Alan Becker's channel. Well done.

27:42 it was aleph, the smallest cardinal infinity, that's why it was so big

26:09 Here the stickman was looking for an exit, quite hard to spot after an overload of mathematics ahhah.

the ending: the stickman was looking for a way out. e, ×, i and then the first half of π, altogether look like the word "exit"

There was a lot missed here. 2:20 The first appearance of Euler's. At this point, we only have addition and subtraction, so Stickman doesn't have the tools to understand, let alone contest e^i(pi) 10:46 Previously, e^i(pi) multiplied by i to go imaginary. i x i x i forces Euler's back to reality 13:45 Stickman has +1. Euler's has -1. +1-1 = 0 After that, Euler's goes to 4, and this breaks Stickman's weapon three times. Stickman then draws a second sword, and +1+1-1 = 1, which knocks back Euler's. That then combines into 2x2=4 giving Stickman a bow. 17:25 A lot happens quickly here. Multiplying sin by i rotates sin 90 degrees. Now having isin(t) and cos(t), this becomes Euler's again. Fencing is as before, with Euler's manipulating its power to do complex moves. 18:45 Stickman multiplies a radian by 4 to make a circle, then the circle by pi to get a disc as a shield. Multiplying the disk by 8 gives a cylinder 19:20 Sin(t) of the circle going left creates 0 > sint(t) > -inf, which blows Euler's out of the circle. Euler then multiplies itself while Stickman makes 9 tan (t) as a vector function. 9 tan (Euler's) = 0 21:42 Pi radians onto the angle swings stickman 180 degrees. 22:56 Integrals can handle infinities thanks to limits, so the function gun to infinity no longer works. 23:36 Adding the function gun to theta. Then i sin(t) and cos(t) applied to the function makes the wave that was shown earlier, and the tangent function obliterates everything. 24:08 A single integral cannot handle a multivariable. 25:00 It was once believed that imaginary numbers broke math, and the function beam, thanks to its now very high amplitude, is adding a lot of pressure. 26:08 This spells Exit 26:30 e^(i(pi)/2) rotates Euler's 90 degrees, bringing him back to the gun, which has been in an always-on state thanks to pi jamming the trigger. 26:50 The gamma function can be used to deal with a non-integer, such as Stickman. Euler's then places an i, turning e^(pi) to e^i(pi), which simplifies to -1 and banishes Stickman. 27:50 The big grey thing is aleph. aleph(0) is the smallest infinity, which is why it is so big.

A lot of reactors don't really pick this up, but when they were adding 1 to the power at 7:43, the animation is illustrating it by changing its dimensional visualization. So when they go up to 5th dimension, all the 1s are making giant 1s that add together in a 5th dimensional array.

So the game you were talking about is called 2048 and yes it was huge a few years back! You unlocked a core memory for me lol

At the end, Stickman was asking Euler to help him find a way out of mathspace - he was looking for an EXIT (e x i, and half of pi is visible). I think Euler then created the formula for the volume of an n-dimensional hypersphere to use as a portal to send Stickman back to his own reality. At the very end, the difficult-to-see giant in the background was Aleph-null. :)

Me, a 32 year old, sitting here and watching a 28min fun video about maths with a smile on my face while knowing full well all context of what I learned in school has been almost completely wiped out of my brain 🥲

Big thing moving in the background at the end: Aleph Null "Stickman" was looking for an exit to go back to his world

oh boy, it’s fun to see a proper mathematician recognizing everything (well, most of) in real time. you should also check out becker’s sequel to this, “animation vs physics”. spoiler without spoiling: the hollow orange stickman is about as reckless as he is aggressive

It's mildly upsetting to me that only now, in my middle years, that I find maths this fascinating. Whereas, as a youth, maths was such a huge disappointment and I was turned off it. Maths was the only subject at school that I actually struggled with. Top sets for everything EXCEPT maths. And yep, it still galls me! 😂

My take on the sudden appearance of Eulers identity is that it’s kind of inherent in what’s so strange about negative numbers to begin with. When people first started accepting negative numbers, there’s this whole quality of mystery which already takes you off the map of things that you can count in real life

I love how she knows all these complex math equations that my mind can't even comprehend and didn't get that he was asking for the Exit

As someone who is NOT a mathematician, hearing the phrase "Oh are we moving into another dimension? Oh four? The fourth dimension? So surely time's gonna play a big part in this" broke my brain a bit.

Euler's number runs away and is 'growling' because it's an irrational number

Nice reaction lmao, this animation has inspired me in so many ways and I was NOT expecting a channel about silly Minecraft and Stickman animations to make such a cool animation for the maths community on YT to enjoy. Some stuff I wanted to quickly mention: -19:55 Nah the dot operator is just referring to "nothing" here, basically the arrow was just above the animation was just tryna show he simplified it heavily into by saying 'tan is just a function (at the end of the day)' -26:09 Euler's identity was spelling out "exit" here -The stickman's name is "The second coming" and is an important character from Alan Becker's other animations and he's just trying to go home (which is Alan's - the maker of these animations - desktop loool)

13:50 Their hilts. "e" has - and "The Second Coming" (yes, that's his name) has +. That's why when they both have 1 blades they result in 0. 22:56 "The Second Coming" shoots with infinity and e catches it with integral. 27:40 That symbol is Aleph. It's so big because it's the smallest infinity.