Animation VS Math gets COMPLICATED!! [Reaction]

Animation vs. Math Reaction
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[breadsticks]

(this is following the timestamps in the original video btw)
0:07 Numbers
0:11 Equations
0:20 Simple Addition
1:24 Simple Subtraction
1:34 Negative Numbers
1:40 e^i(x)pi = -1, Euler's Identity
2:16 Two Negatives Cancellation
2:24 Multiplication
2:29 The Commutative Property
2:29 Equivalent Multiplications
2:35 Division
2:37 Second Division Symbol
2:49 Division by Zero is Indeterminate
3:05 Indices/Powers
3:39 One of the laws of Indices. Radicals introduced.
3:43 Irrational Numbers
3:50 Imaginary numbers
3:59 i^2 = -1
4:01 1^3 = -i = i (x) -1 = ie^-i(x)pi
4:02 One of Euler's formulas. It equals -1.
5:18 Introduction to the Complex Plane (This sucked to learn)
5:36 Every point with a distance of one from the origin on the complex plane.
5:40 Radians, a unit of measurement for angles in the complex plane.
6:39 Circumference/Diameter = PI
6:49 Sine Wave
6:56 Cosine Wave
7:02 sin^2(θ) + cos^2(θ) = 1
7:19 Euler's Formula
7:35 Another Euler Identity
8:25 Simplifies to 1 + 1/i
8:32 sin (θ) / cos (θ) = tan (θ)
9:29 Infinity.
9:59 Limit as x goes to infinity
10:00 Reduced to an integral
11:27 "The imaginary World" Theorem
13:04 Gamma(x) = (x-1)!
13:36 Zeta, Delta and Phi
13:46 Aleph

[phoenixxz]

Here’s my explanation of the math stuff throughout the video:

0:22 - equals sign. It means both sides are the same

0:28 - the + means addition

1:32 - the - means subtraction

1:48 e^i*pi is known as Euler’s identity, and it does equal -1. This is because if you bring anything to e^ix, it creates a unit circle on the complex plane (explained later), and the x is the angle on the unit circle in radians (also explained later). for Euler’s number, x is pi, which means you create a 180° angle on the unit circle (because pi radians is equal to 180°) which lands at the point -1. Therefore, e^i*pi is -1

1:57 - when the e guy multiplied himself by i, I guess it sent him to the “imaginary world”, which is a pretty cool concept in this story

2:32 - this a cool representation of multiplication

2:45 - cool representation of division

2:57 - this is a good visual to why you can’t divide by zero, because you’ll never be able to subtract anything from 6

4:01 - exponents is to multiplication in the way that multiplication is to addition, in that you multiply the big number for the amount of times the small number says

4:27 - negative exponents give a fraction because subtracting the exponent by 1 basically divides the number by 4. 4^0 is 1 because that’s 4/4, and 4^-1 is 1/4 because you divide 1 by 4

4:47 - this is the introduction to imaginary numbers. The letter i is equal to the square root of -1 because you can’t normally square root negative numbers. To counteract this, mathematicians created i as a way to represent the square root of -1 to not end up in a dead end while doing math

4:58 - as I previously said, i is equal to the square root of -1. This means i x i = -1 = e ^ i x pi

5:09 - the e guy didn’t travel through the door because the i he pulled out multiplied with the one the Second Coming threw to make -1, which is a real number, causing the e guy to stay in the real world

5:13 - this expansion is known as Euler’s formula. It’s created because of the unit circle e ^ i*pi creates in the complex plane, and it uses the sine and cosine functions to separate the real and imaginary values of the number in the unit circle

5:16 - the Second Coming was multiplied by the negative sign, causing him to flip aroundirm that

5:20 this goes with the unit circle thing. the e guy changed his exponent to 0, which is the same as 0i. because it changed from i*pi to 0i, he went from pi radians (180°) to 0 radians (0°) on the complex plane unit circle, causing a 180° arc to the right

5:34 similar to what happened earlier with the Second Coming

5:53 the e guy put the 4 into his exponent, causing him to move to pi/4 radians (45°) on the unit circle

6:04 - when he multiplied himself by i here, he rotated 90° on the unit circle because when you multiply a number by i on the complex plane, the number is rotated 90° on the plane

6:15 - here, the Second Coming learns about the complex plane. It’s like a number line with a horizontal axis containing the real numbers, but it has a vertical axis too that contains the imaginary numbers, forming the two dimensional complex plane

6:33 - the Second Coming creates the complex plane unit circle that that e^i*pi is based from

6:38 - these are radians. A radian is the angle at which its arc length is equal to the radius, which ends up being 180/pi degrees. The little gap shoes that in a full circle, there are 2pi, or about 6.283 radians

6:58 - I’m not sure why these appear to be multiplied, but the r means the radius and the weird 0 with a line is theta, which is the angle (typically in radians)

7:35 - because theta (the angle) is pi radians and the radius is 1, theta/the radius is pi

7:47 - this shows how sine and cosine can be used to separate the horizontal and vertical aspects of a circle

8:07 - here, he multiplied sine by i, which caused the sine wave to rotate 90 degrees

8:15 - he added them together to create Euler’s formula, which as previously stated is equal to e^i*x, and x is pi because the trig functions contain pi. Therefore. Combining them created the e guy


8:26 - more of the unit circle stuff

8:32 - the e guy expanded into his Taylor expansion form. Thee giant E thing is sigma notation, and it basically adds the part after it, replacing it with integers consecutively going up. You can see this with the the bullets it fires

8:46 - volume of a cylinder

9:02 - he pulled the negative trick again

9:22 - the e guy used the formula for himself and the formula for the trig functions to split himself up a lot

9:29 - here, he made a function, which is basically a placeholder for an expression. Unfortunately, I don’t understand the arrow above it is

9:59 - he changed the angle to pi radians (180°)

10:26 - I’m guessing here, but I think when the Second Coming replaced the dot with the infinity symbol, it caused the function to expand to every point on a graph, which also created the tangent lines (since the Second Coming put the tangent function into that function)

10:55 - the blast became an integral symbol with a limit, because the tangent graph was kind of infinitely long, so the limit allowed the tangent graph to converge I guess. The integral symbol means nothing, it just looks like a cool staff

11:14 - he added an imaginary number, which causes things to move vertically in the complex plane

12:23 - now you see the imaginary world

14:01 - I didn’t entirely understand what this is, but looking at other comments, it seems like the e guy expanded into an equation that can find the volume of spheres beyond the third dimension, but i can’t confirm that, though

14:29 - these symbols are zeta, phi, delta, and aleph

[victorgarland]

This really shows how smart the second coming is he went from learning basic math to calculous in a matter of minutes

[SuprAJ]

During the episode it should be noted that The Second Coming is also considered a number by the rules of the dimension, it can be speculated that his number is his "Frames Per Second" which is how fast his animation runs (e.g being around 20 frames a second). This number is probably the only reason any of the mathematical things had any impact on him (such as being effected by the multiplication and subtraction symbols)
I don't understand much of the maths stuff itself though so for anyone who wants to learn more about the intricate details, i'd recommend watching "A Complete Over-Analysis of Animation vs Math" made by someone a lot smarter than I am.

[vettyyt]

its funny seeing how different the reactions from mathematicians to normal reaction youtubers are

[Radioactive-Braincell]

honesty, imagination and animation can make anything look interesting

[dollyaigacha]

I have a theory. There is a possibility that this is where every stickman that's created ends up before being converted to a symbol as seen in AvA 1, 2 and 3. TSC woke up literally in pitch black. A void of nothingness. A world of nothing but symbols, letters, and numbers. When you code/make something digitally, you would use symbols, letters, and numbers. And since the stick figure is still in the making, it would make sense for there to be just a void of black.

If this is where every stick figure has been before being converted to a symbol, then the evil stick figures such as TCO, (TCO isnt evil anymore though) TDL and Victim most likely caused terror. This explains why Euler's identity (e^ipi) is afraid of TSC when they encounter one another. And it also explains why all the other symbols that appear at the end come out of nowhere. They were probably hiding. They were aware that some of these figures were dangerous, moreso the ones with empty circle heads. It all adds up.

Here's something that can also be connected to this: TSC came alive during his process of creation. He was not converted into a symbol yet, TSC found a way out of the void, which was not supposed to happen. This could lead to why TSC cannot control his power the same way TCO and TDL can, he is not working properly due to the fact he was not finished/converted properly.

[brynsutherland]

This video is mostly about "Euler's Identity", which is an incredibly elegant formula that unites 5 of the most fundamental numbers in all of mathematics. e^iπ + 1 = 0
where e = Euler's number (2.7812...)
i = The square root of negative one (this is referred to as an 'imaginary' number).
π = Pi (3.1415...)
1 (one)
and
0 (zero).
Many mathematicians think this formula contains some incredibly fundamental truths about the universe. It's supposed to be the most beautiful equation in all of mathematics. Both e and π are referred to as 'transcendental' numbers, but my math knowledge isn't good enough to explain why. This video probably does though.

[lightningterry]

5:29 I only got through third year of college calculus so bear with me. TSC is playing around with Euler formula aka the “e” which is like one of the most important numbers in math cause it’s the base for ALL natural logarithms which in short meats it kinda shows up everywhere. Hence why it’s so powerful here. Plus a cool thing about the “i” is that it represents imaginary numbers. a general rule is i x i = -1 and e^(ipi) is also equal to -1 it’s just another way of writing it. What’s cool about e^(x) is that it’s the only number that’s the derivative of itself so when you find the derivative of e^(8x) for example you get 8e^(8x). i and e together have this power that when it’s multiplied to stuff it kinda “switch dimensions” so when TSC threw an i at ie^(i pi) it was forced back here as iei^(ipi) or -e^(ipi) pretty cool way to show that imo. Also while sin(a) = y coordinate and cos(b) = x coordinate. The two waves when forces next to each other due to i “switching dimensions” don’t exactly line up. The fact that they can look like a helix when applied in a 3d scope surprised even me. I love how Alan’s team displayed that! And they essentially turned it into a rail gun.😂

[just-apt]

TSC is like a little kid who is fantasised by Math until he discovers harder sums 😂

[Radioactive-Braincell]

It's interesting how bland and forced education is in school to the point where you don't even want to remember it but I think you just need some amazing visuals and it all comes back like a boomerang that hasn't come back for years.

[Nikifuj]

Math teacher here. I’d like to explain what i and e^(iπ) mean, but first I need to lay some background.

When math gets more complicated, that’s because you *want to do more things.* For example, suppose you’ve been doing subtraction on whole numbers. You know that 2 − 1 = 1 and 7 − 3 = 4. But then you want to calculate 3 − 7. Well, to solve this problem, you must invent negative numbers. Now you can *do more* (you can subtract anything from anything), but you have introduced more numbers – thereby *adding complexity.*

You can see The Second Coming grapple with this repeatedly in the video as he encounters negative numbers, irrationals, fractions, and exponents.

*The letter i stands for the square root of negative 1.* Multiples of i are called *imaginary numbers, * and numbers of the form x + iy such as 3+2i or 7−12i are called *complex numbers.* Just like negative numbers, i was invented to *do more things.* It turns out that when you introduce a square root of -1, every polynomial equation has a solution. Thus, i is like the ultimate cheat code for a mathematician who wants to *do more things.*

Complex numbers can be graphed, as well. The number x + iy corresponds to the point (x, y). So 7−12i corresponds to the point (7, −12).

To explain e^(iπ), I need to talk about Euler’s formula. Suppose you have an angle, θ (“theta”). Euler’s formula says that e^(iθ) = cos(θ) + i sin(θ). In English, this means both e^(iθ) and cos(θ) + i sin(θ) are ways of writing *the point on the unit circle with angle θ.* This is why you see so much action with circles in this video.

One more thing: θ must be in _radians._ Radians are another way of writing angles. You can even see TSC discover radians at 6:31 in the video!

Let’s try putting π in for θ. Well, π radians means 180° – a half-turn around the circle. Conventionally, 0° on the unit circle means (1, 0), so 180° must mean (−1, 0). And remember, we can turn a point into a complex number, so (−1, 0) ↦ -1 + 0i, which is just a fancy way of writing -1.

Thus, e^(iπ) = -1. This is called *Euler’s identity.* Sometimes it is written as e^(iπ) + 1 = 0, and it is often praised as one of the most beautiful equations in all of mathematics.

I believe that, when e^(iπ) sticks an i on itself in the video, it is multiplying itself by i to enter the imaginary realm. That’s why you see a door open when it does that. You can also see it turn itself into cos(π) + i sin(π) to punch TSC at times 🤭

[TheOfficialHannah]

When you don’t know your math, Alen Becker can help😎

[pixelatedluisyt]

I love this animation so much.
Also nice reaction!

[wafflegames]

Honestly watching you nerd out was so adorable

[Packguardian_gacha]

The mechanics here would make an awesome and educational puzzle game.

[adventurevlogs]

This is so good even tho ive saw it like 5 times already BUT I LOVE IT

[yaboyjay]

Fun fact!In 5:39, SC hold the "+" sign like the cross, It is mentioned in AvG reacts

[ivanguajardomunoz]

I remember seeing a lot of math in class but i honnestly gave up trying to understand it all
felt like that would be something i'd never understand and leave it to those who actually did.

[Sillybird]

I have waited for this and I am amazed that your watching stickmam you are a legendary