A Complete Over-Analysis of Alan Becker’s Animation Vs. Math

**Read here first**
I know this video is from the channel Alan Becker. The animations his team make are phenomenal and I am simply doing an analysis (more generally a criticism and review) on it.
Please watch their original video first before commenting that I didn’t make this :)
Original Video: • Animation vs. Math

[@voidtv8401]

It makes infinitely more sense when you stop thinking of TSC as a stick figure, and start thinking of him as the numerical value that he is: *frames per second.* He is innately math meeting visuals. That’s why, for example, the multiplication sign speeds him up: it increased his play rate.

[@Izzythemaker127]

I never thought about it like that, but yeah they are canonically an animation, and that makes sense.

[@yigitpasa7743]

Yeah! That makes alot of sense😮

[@FireyDeath4]

What is he being multiplied by? Two? There wasn't a 2 there and the multiplicative identity is 1 (1x=x), so without any multiplication factor it seems like it essentially should've just done nothing...

[@verbugterherrderdunkelheit6086]

​@@FireyDeath4 I know that's a far reach, but if he's f.ex. 24 frames/second he could do 2×4, making it 8 frames/second. This would lead to this effect from old movies, where everyone is moving slightly faster than in reality, because you need to speed it up to get a flowing image.

[@notsocuteslime2297]

Genius

[@Janfon1]

I'm always so shocked to see the attention to the tiniest of rules and details in their videos. Most of the tricks we saw in the Minecraft series could be done in-game, which is insanely cool as the videos serve an "educational" role too in that regard. Same with this video, just nothing but tremendous praise

[@sethstuffanimates8419]

These guys really know their attention to detail!

[@godlyvex5543]

I don't think the animations really serve as educational, they're just really cool. The only reason I learned anything from the video was because it made me want to learn what it meant, not because it taught me itself.

[@satanhoainterlocucaodoaman7412]

​@@godlyvex5543for me that really counts as educational

[@henriquemedranosilva7142]

@@godlyvex5543 The basic concepts and the circumference basics I think could be used to exemplify a teacher's point honestly

[@Glacorite]

This level of attention to detail reminds me of that Oscar-nominated Tom and Jerry Piano Animated Short

[@ElioSch1423]

You see that a youtuber makes a really masterpiece when even the university teachers are talking about it.

[@weirdskunk]

Wow, ok, I was not expecting that but at least I know my whole middle school is talking about that video but I was not expecting it to leak to the univerity teachers at all

[@Iochris]

​@@weirdskunkI'd wish people from my school watched Alan Becker.

[@xuanyizhao4952]

Well to be fair, Alan Becker is an absolute master of not just animation but also visual storytelling, script writing and all the other things that a master movie director would do, and he is really way beyond just a KZbinr in terms of talent and skills. I think he chose to still only make projects that have a scale appropriate to KZbin and only posting his videos on KZbin instead of making one of those cash grabs called Hollywood movies in 2023 and charge insane amount of money, because he is humble and has integrity, NOT because he doesn't have the capacity to lol

[@ayuballena8217]

@@xuanyizhao4952well that scaled quickly get it? scaled? as in *matrixes*

[@AarPlays]

There's a lot of people who are going to finally understand concepts by seeing them in visual form. This is incredibly well done

[@32bit27]

I don't have maths as majors nor did I ever tried to understand these concepts , but it still looks baffling from what i can make out. So epic , it's an endless universe.

[@Flacto-vs6np]

lol this vid was what i used yo explain to some of my friends the of complex numbers

[@mrspiffy8587]

10:04 something interesting about the integral is that it leaves behind a trail because the integral is the area under a curve

[@gallium-gonzollium]

I didn’t even notice that. Yeah that’s so much cooler.

[@CatCat99998]

Good point, another thing I hadn't realized but makes sense in hindsight.

[@davidarvingumazon5024]

@@gallium-gonzollium 3 equal equal equal equal D

[@pixelgamer6199]

@@davidarvingumazon50248 year old trying to look cool in front of a genuine mathematician

[@epikitee2186]

@@pixelgamer6199 ...not quite.

[@da3577]

I think the reason symbols work on TSC is because he's using the number on his attributes, such as speed and position, the two attributes he edits in the animation. He isn't a number, but he's composed of them, like atoms.

[@uncolored2060]

Makes sense, he's a computer code

[@a17waysJackinn]

imagine making vector graphic version of TSC *exact details i mean exact is his outline orange sprite same thickness as Alan when drew him in Alan his painting editor if you look closely in desmos somthing..

[@WatercraftGames]

@@a17waysJackinn Flash animations use vectors, TSC is already that.

[@onetwo9500]

Which makes sense why "exit" is a higher dimension for euler... Cuz TSC is literally a higher dimension being, made up of numbers

[@TierdDoktor6391]

​@@a17waysJackinn Flash animations are vector based So he is already a vector shape

[@mrmadhusudhan3142]

THE MATH LORE 0:07 The simplest way to start -- 1 is given axiomatically as the first natural number (though in some Analysis texts, they state first that 0 is a natural number) 0:13 Equality -- First relationship between two objects you learn in a math class. 0:19 Addition -- First of the four fundamental arithmetic operations. 0:27 Repeated addition of 1s, which is how we define the rest of the naturals in set theory; also a foreshadowing for multiplication. 0:49 Addition with numbers other than 1, which can be defined using what we know with adding 1s. (proof omitted) 1:23 Subtraction -- Second of the four arithmetic operations. 1:34 Our first negative number! Which can also be expressed as e^(i*pi), a result of extending the domain of the Taylor series for e^x (\sum x^n/n!) to the complex numbers. 1:49 e^(i*pi) multiplying itself by i, which opens a door to the... imaginary realm? Also alludes to the fact that Orange is actually in the real realm. How can TSC get to the quantity again now? 2:12 Repeated subtraction of 1s, similar to what was done with the naturals. 2:16 Negative times a negative gives positive. 2:24 Multiplication, and an interpretation of it by repeated addition or any operation. 2:27 Commutative property of multiplication, and the factors of 12. 2:35 Division, the final arithmetic operation; also very nice to show that - and / are as related to each other as + and x! 2:37 Division as counting the number of repeated subtractions to zero. 2:49 Division by zero and why it doesn't make sense. Surprised that TSC didn't create a black hole out of that. 3:04 Exponentiation as repeated multiplication. 3:15 How higher exponents corresponds to geometric dimension. 3:29 Anything non-zero to the zeroth power is 1. 3:31 Negative exponents! And how it relates to fractions and division. 3:37 Fractional exponents and square roots! We're getting closer now.. 3:43 Decimal expansion of irrational numbers (like sqrt(2) is irregular. (l avoid saying "infinite" since technically every real number has an infinite decimal expansion...) 3:49 sqrt(-1) gives the imaginary number i, which is first defined by the property i^2 = -1. 3:57 Adding and multiplying complex numbers works according to what we know. 4:00 i^3 is -i, which of course gives us i*e^(i*pi)! 4:14 Refer to 3:49 4:16 Euler's formula withx= pi! The formula can be shown by rearranging the Taylor series for e^x. 4:20 Small detail: Getting hit by the negative sign changes TSC's direction, another allusion to the complex plane! 4:22 e^(i*pi) to e^0 corresponds to the motion along the unit circle on the complex plane. 4:44 The +1/-1 "saber" hit each other to give out "0" sparks. 4:49 -4 saber hits +1 saber to change to -3, etc. 4:53 2+2 crossbow fires out 4 arrows. 4:55 4 arrow hits the division sign, aligning with pi to give e^(i*pi/4), propelling it pi/4 radians round the unit circle. 5:06 TSC propelling himself by multiplying i, rotating pi radians around the unit circle. 5:18 TSC's discovery of the complex plane (finally!) 5:21 The imaginary axis; 5:28 the real axis. 5:33 The unit circle in its barest form. 5:38 2*pi radians in a circle. 5:46 How the radian is defined -- the angle in a unit circle spanning an arc of length 1. 5:58 r*theta -- the formula for the length of an arc with angle theta in a circle with radius r. 6:34 Fora unit circle, theta /r is simply the angle. 6:38 Halfway around the circle is exactly pi radians. 6:49 How the sine and cosine functions relate to the anticlockwise rotation around the unit circle -- sin(x) equals the y-coordinate, cos(x) equals to the K-coordinate. 7:09 Rotation of sin(x) allows for visualization of the displacement between sin(x) and cos(x). 7:18 Refer to 4:16 7:28 Changing the exponent by multiples of pi to propel itself in various directions. 7:34 A new form!? The Taylor series of e^x with x=i*pi. Now it's got infinite ammo!? Also like that the ammo leaves the decimal expansion of each of the terms as its ballistic markings. 7:49 The volume of a cylinder with area pi r^2 and height 8. 7:53 An exercise for the reader (haha) 8:03 Refer to 4:20 8:25 cos(x) and sin(x) in terms of e^(ix) 8:33 This part +de net tnderstand, nfertunately... TSC creating a "function" gun f(x) =9tan(pi*x), so that shooting at e^(i*pi) results in f(e^(i*pi))= f(-1) = 0. (Thanks to @anerdwithaswitch9686 for the explanation - it was the only interpretation that made sense to me; still cannot explain the arrow though, but this is probably sufficient enough for this haha) 9:03 Refer to 5:06 9:38 The "function" gun, now 'evaluating" at infinity, expands the real space (which is a vector space) by increasing one dimension each time, i.e. the span of the real space expands to R^2, R^3, etc. 9:48 logl(1-i)/(1+i)) = -i*pi/2, and multiplying by 2i^2 = -2 gives i*pi again. 9:58 Blocking the "infinity" beam by shortening the intervals and taking the limit, not quite the exact definition of the Riemann integral but close enough fo this lol 10:17 Translating the circle by 9i, moving it up the imaginary axis 10:36 The "displacement" beam strikes again! Refer to 7:09 11:26 Now you're in the imaginary realm. 12:16 "How do I get out of here?" 12:28 Den't quite get this-One... Says "exit" with t being just a half-hidden pi (thanks @user-or5yo4gz9r for that) 13:03 n! in the denominator expands to the gamma function, a common extension of the factorial function to non-integers. 13:05 Substitution of the iterator from n to 2n, changing the expression of the summands. The summand is the formula for the volume of the n-dimensional hypersphere with radius 1. (Thanks @brycethurston3569 for the heads-up; you were close in your description!) 13:32 Zeta (most known as part of the Zeta function in Analysis) joins in, along with Phi (the golden ratio) and Delta (commonly used to represent a small quantity in Analysis) 13:46 Love it - Aleph (most known as part of Aleph-null, representing the smallest infinity) looming in the background. Welp that's it! In my eyes anyway. Anything I missed? The nth Edit: Thanks to the comment section for your support! It definitely helps being a math major to be able to write this out of passion. Do keep the suggestions coming as I refine the descriptions! Comment credit goes to @cykwan8534

[@ahmed_abdelaal_official]

😮

[@starsyt3164]

🤓

[@NySx_lol]

@@starsyt3164 “you call me a nerd, therefore I am smarter then you” 🤓

[@starsyt3164]

@@NySx_lol bro realize its a joke reply that your serious onto

[@NySx_lol]

@@starsyt3164 that reply was a joke too…

[@MrBern-ex3wq]

This reminded me of why I started to like math in school, before college ruined it. Feels nostalgic.

[@macandcheese2262]

Grade's 1-3: You Said It's Ez Grade's 4-6: It's Getting Harder Now Like My Vitamin D💀 Junior High: There Are Gonna Be More Canon Events Senior High: You Better Read And Study Or Else... Before College: SUMMER BRAKE B****ES!!! During College: See You In The Next 4 Years P.S. Study Hard, No Phone, No Sleep Etc. After College: Time To Find A Job... Interview: We Don't Talk Abt That... The Job: It Depends But You Gonna Work Your Back, Eyes, Hands, Legs, Feet, Etc. For 20 Years 💀 Retirement: You Can Now Rest But For How Long?...

[@Kanamo4781]

5:04 in this case, TSC Is considered as X, since he is not a number, the "math dimension" has to do something with him if he include himself in an equation of sort, so TSC is X, making X rotate 90° on the axis, so watever his position was (if x was a point on the axis), it is rotated by i

[@gallium-gonzollium]

Yeah, that makes sense.

[@AstarasCreator]

Oh yeah that makes sense. My theory was since he was a drawing made in Adobe Flash/Animate, which is a vector based drawing program, that he was a collection of bezier points that have numerical values that can be manipulated with the math in this dimension. Yours make just as much sense and is easier to understand though.

[@Whydoiexisthere-]

@@AstarasCreatorI was thinking something similar, they are eventually tied to the code in some way or another, in fact, when TSC first appeared he was in the files, which my amateur brain can only assume boils down to a form of code.

[@Aftonny]

12:25 Well, the fact that TSC was able to get X from his pocket to spell out "exit"..

[@freerobux49]

@@Aftonny i think that was a multiplication sign actually

[@CobaltXMusic]

While I don't like maths all that much, I used to and this brings a smile to my face. This is amazing.

[@NO_ir777]

they do it very often, animators, storyboard artists, etc are overworked by such a high demanding industry

[@CobaltXMusic]

@@NO_ir777 if you mean the Alan Becker channel, I agree with you, their animations are always top-notch!

[@vampyreo2861]

@@NO_ir777overworked

[@roserina4416]

Ok syg tq cikgunanti tolong bagi tahufaris zafran saya datang

[@jusacommentor3973]

I think we don't like how it is teached, or how it effects on world in real-time. Video games does that that's why people prefer that then plain maths

[@trainerlsw]

It’s insane that this animation about math is not only flashy, but also makes sense! Props to Alan Becker’s team for making this animation, and to you for giving an in-depth analysis!

[@pakistan_aviation]

0:08 Everything starts with 1 0:15 a=a 0:18 Addition discovered 0:28 You can add as many numbers as you want 0:33 2-digit numbers discovered 0:45 2 = (1+1) 0:48 You can add any number 0:58 3-digit numbers discovered 1:24 Subtraction discovered 1:35 Negative numbers discovered 1:39 -1 = e^i(pi) 2:05 Negative numbers are unique too 2:23 Multiplication discovered 2:35 Division discovered 2:48 a ÷ 0 = undefined 3:03 Square numbers discovered 3:17 a³ = area of cube with side length a 3:29 a⁰ = 1 3:30 a^-1 = 1/a 3:37 a^(1÷2) = sqrt(a) 3:43 sqrt(2) is irrational 3:50 sqrt(-1) = i 3:57 i + i = 2i 3:59 -1 = i × i 4:46 -1 + 1 = 0 (Look at the swords) 4:53 2 × 2 = 4 part 2 at 5 likes Midway edit: Whoa 11 likes?! Ok ok KZbin didn’t even tell me I hit 11 likes I will do part 2 today

[@ItzRokyLol]

Imagine this is like a game, where you discover maths and the dialogue explain to you endlessly

[@PSIChris]

This is real. Math is real.

[@vAR1ety_taken]

​@@PSIChrisMath is not real. It's just paints on paper

[@PSIChris]

@@vAR1ety_taken is language real?

[@vAR1ety_taken]

@@PSIChris As math, language exists for communication

[@josepedrogaleanogomez4870]

​@@vAR1ety_taken Is logic real? Do you think that logic exists? Math is essentially logic. If you think logic exists, then it is real; then math is real. Math isn't something tangible, it exists as an abstract concept. It exists anyway, so it is real.

[@mr.looper7935]

You have managed to condense trigonometry, algebra, introduction to calculus, and all the fundamentals required for those subjects within a single animated video with an entertaining plot of 14 minutes. Outstanding work. Definitely will be sharing this as a reference for anyone I end up teaching some math to.

[@gallium-gonzollium]

To be crystal clear, I made a criticism and review on Alan Becker’s latest video. You can find the video in the desc. Reason why I am saying this is that I don’t want to take credit for an animation I didn’t make, it was simply an analysis I added over the top.

[@mr.looper7935]

@@gallium-gonzollium yeah in hindsight i realize that it was one of Alan's animations so I feel sheepish over that. Still, its noteworthy that you managed to find the mathematical principles to back it up which still falls in line with what i said before minus the video animation.

[@royhyde8842]

@@gallium-gonzollium I always love someone with integrity👏.. Great work in the explanations by the way.

[@davidarvingumazon5024]

@@gallium-gonzollium 3 equal equal equal equal D

[@theyeetfamily2668]

It is not even his video

[@emimimix]

as someone who hated doing math but loved learning the concepts and what math can do, this video is amazing; visuals are so important for learning and being able to see it in form helped me learn what I couldn’t in class. Your analysis really helps!!

[@ryanrester]

Thank you!!!!! I’ve been waiting for someone to do this! ❤ I loved the Aleph at the end. I have dyscalculia but love the concepts of math. So frustrating! It was so nice to see all this laid out like it was and I was just hoping someone would label all the different functions and formulas!

[@TheProGamerMC20]

0:27 I think you should’ve added the fact that the “motion blur/blending/in-between” frames actually have an equals sign! I find that really neat and fascinating, because they took the 1 = 1 concept and smudged it in with animation!

[@myla2495]

Oh i never noticed that- I thought its just like playing with clay, things stretch like this before separating TwT

[@user-xw4mu6nz4t]

Yeah I noticed that, there's so many hidden cool things in this man, like this is actually amazing. It's already blowing up, but I can't wait to see this blow up even more

[@user-xw4mu6nz4t]

Only 350k views! This deserves 10 million at least...

[@demetrisbarnwell2798]

@@user-xw4mu6nz4tGAINED 5K IN 5 MINS

[@XxpolakxX.]

This is stolen. This animation make Alan Becker

[@infernianthedragoon6210]

Of all the analysis videos I've seen on this animation so far, this one is definitely the best

[@mapelli547]

the video does not belong to him, he simply stole it from the original artist to gain views

[@infernianthedragoon6210]

@@mapelli547 Care to tell me who the original is then?

[@mapelli547]

@@infernianthedragoon6210 Alan Becker, but i Just misunderstood things and it's not Just a resposted video, sorry ;w;

[@mapelli547]

@@Nubbdz.v2 yeah, sorry about that this is the result of not paying attention to things😅

[@DrSalluDMallu]

As a physician who loves physics and maths, I absolutely love this gem of a masterpiece ❤️

[@Sciman0231]

Thank you for this! I loved the original video but knowing more of the context behind it is great

[@Ben_R4mZ]

I knew that there was a lot of math in this video that was going directly over my head, but I trusted the animator to have done their research. I'm glad to see that I was correct. I'll have to send this to some of my engineer friends and see what they think.

[@user-38rufhoerh3id]

Actually, according to the comment he pinned on the original video, Alan Becker's lead animator was the math nerd behind that, so yeah he was able to do all of this.

[@ryukokanami7645]

@@user-38rufhoerh3id His name is Terkoiz and it's revealed in the description below.

[@user-38rufhoerh3id]

@@ryukokanami7645 Oh thanks. Didn't know that before you told me

[@chilldo5982]

That's a really good video! It explained everything in a good way, and was the first one that came in the recommendations that actually says something smart about the math. As a big math fan, I learned today some new stuff. The Tailor series, the small integral references etc. were all incredibly helpful. Thanks for the video!

[@Tecnox735]

This explanation was so incredibly made, I'm just here for when it blows up

[@LavaCreeperPeople]

A Complete Over-Analysis of Animation Vs. Math

[@lucascomerci6728]

Es de Alan becker el vídeo

[@moadot720]

*Taylor. I would know, it's my first name. No offense, of course, and I know that the “Taylor” of the Taylor series is a last name, but still.

[@RyuDieDragonGD]

yreeeees

[@winterforest8132]

Python with Prosper also covered this animation frame by frame and with some historical explanation. The effort being put into the animation and analysis is insane.

[@rslashontario]

I have watched many analyses on this subject, but none of them noticed the exponential relationship with dimensional shapes like you did. Impressive stuff.

[@jerryhu9005]

10:32 had me stumped for a while, but I think the interpretation is that he's feeding every point along the circumference of the circle (sinx + cosx) into the tan function simultaneously, so every point along the circumference of the circle is emitting the tan death ray at once

[@aguyontheinternet8436]

then it wouldn't be confined to a circle, it would spread to half the screen, like the tan function did

[@aguyontheinternet8436]

then it wouldn't be confined to a circle, it would spread to half the screen, like the tan function did

[@Elementus21]

I think if you remember earlier I the video, when the circle was smaller, the "amplitude" of the resulting wave graph was equal to the diameter of the circle it was mapped from, and bigger amplitude = more power.

[@hie3800]

⁠@@aguyontheinternet8436the circle acts like a border, e^i 𝝿 used the circle to bring tsc near it, and while tsc was using the tan function + infinity the wave wasn’t crossing the circle, it collided with it, creating the span thingy, basically, the circle restricts the wave in some form, and that’s why it didn’t fill up half of the screen, also, by the animation’s logic, that would have completely broken e^i 𝝿’s realm, which didn’t and wouldn’t have happened

[@hie3800]

also when tsc brought out the tan function, it didn’t even have the infinity, which is the part which makes it fill up half of the screen

[@TrickyTalon23]

Everything Alan Becker touches is given full respect of the concept

[@user-xw4mu6nz4t]

I watched this and was like "Well, here's clearly copying Alan Becker, can't wait to see the comments of people complaining" Kept watching and was like "Aight, you get a pass."

[@muh.suudcandra5231]

​@@user-xw4mu6nz4tcopying how? He's breaking dow the video

[@Artist_of_Imagination]

@@muh.suudcandra5231 the guy was high

[@fascher_]

Please make more of these, I know you didn't animate this but it adds so much to the video, really cool

[@Railnof]

I was thinking the video was going to explain more the maths, but its very cool like this !

[@shadeowsline]

Now when it's explained like this, i would love to have a game that makes us use maths like they did in the animation. Learning maths like that would have been way more fun!

[@ThaCataBoi]

The video really is just “what if Math could also be a military grade weapon?”

[@paolarei4418]

​@@ThaCataBoiLMAO

[@Luna_LU6546]

@@ThaCataBoi E=mc²

[@stellanovaluna]

@thacataboithefurret4038 It already is. N U K E

[@friskthefallenchildd]

If u were to make it vr and then use it in an actual school math lesson, it would be everybody's favourite lesson

[@hanchen267]

3:16 power is repeated multiplication (which itself is repeated addition) 5:05 the bow that TSC uses is actually just '2x2=' oriented differently (idk how to explain it), which is why the projectile is '4' (answer)

[@gallium-gonzollium]

It is orientated like a crossbow, from 2 2’s and a multiply sign.

[@hanchen267]

@@gallium-gonzollium if it were to be a crossbow, then it would be shaped 'horizontally' more also, you can in theory calculate TSC's 'number' by using pixel measurements you look at what the length of 'i' is, then you compare that to TSC's normal pose, (i think TSC's length is 2i), now that you have TSC's length, you can use it as a glorified ruler to calculate how much i's TSC has gone upwards, then just divide the 'height' by i and you get TSC's 'number'

[@DatBoi_TheGudBIAS]

​@@hanchen267it's a bow, not a crossbow

[@master_yugen7278]

@@DatBoi_TheGudBIAS it's technically a "cross"bow

[@Syuvinya]

@@master_yugen7278 ba dum tss

[@Overh3ven]

You are the best explaining everything in this video and helping me understand this!

[@NintendoGamer789]

Best explanation on the video so far, a lot of others I found missed more intricate details and the ending concepts

[@angelofhell3701]

4:34 I believe this is mostly a velocity thing where instead of TSC’s speed Accelerating by let’s say 1.2units(or Meters)/second, by adding a Multiplication Symbol to their legs, TSC’s Acceleration is now x1.2ups instead of +1.2ups. 7:26 This is fun because the Number just normally clashes with the Arclength/Radii, unlike the Number Sword Clashing Earlier. The Radius Length is a defined term, and therefore cannot be “deducted” or other similar variables would also have to adjust to this truth. However, the Arclength(of r=1), is as strong as a 1 +/- sword, and will be deflected by a 2 or higher.

[@dacomplex1Yuhanhan.hanna-Xia]

note at 8:52 "what a traitor"

[@angelofhell3701]

@@dacomplex1Yuhanhan.hanna-Xia those damn e^i(pi)’s….

[@dweebteambuilderjones7627]

100th like! :D

[@cheeeeesepete]

so glad this is here! i'm really happy with how much i was able to recognize the first time (aleph, complex plane, ∞-dimensional ball) but the slightly more in depth explanations of the sum figure and the integral staff helped a lot!

[@Joyscp999]

that will tecnically mean that the ''real world''or the computer at least,it is a infinite dimensional structure,or even beyond the cardinalities(at least the aleph)

[@mayoral90s38]

Im sure the original video gona become an Internet timeless classic.

[@bdletoast09]

There is still a lot of stuff with which I struggle in here (everything that involves the radian gives me a headache) but there are some stuff that I finally begin to grasp when given visual form. Alan truly outdid himself with this one and your explainations are very welcome.

[@aramdominsect895]

My question is how TSC learnt math so fast, enough to use things people who have been studied for years cant remember

[@monsieurtoutlemonde1549]

TSC is the smartest animation drawn by Alan Becker, change my mind

[@Zliarx]

For a stick figure with it's own consciousness made by it's creator, it definitely learns fast. Maybe it's an effect of "things" gaining it's own consciousness and able to learn fast. Kinda like how in stick figure vs minecraft, it was able to adapt real quick.

[@Delta-es1lg]

TSC is crazy smart.

[@BetterCallBigShotAutos]

​@@ZliarxTSC has the power of very fast machine learning

[@Filename99]

I think it's because he watched math as a weaponry, not some boring test paper. And we know TSC is a fighter.

[@Pixelcraftian]

Was completely expecting text to show up at 1:00 saying "Math sends you to the void" or something lol

[@Bananappleboy]

Where the heck did you come from, and why are you receiving little attention???

[@cr1stel12]

haha yea!

[@Jr-jx4yv]

Dude that was boss. Loved it. I was happy to have already learned 99% of that stuff otherwise it would have be way harder to follow along. Still had to slow down the speed to .5 to really grasp what was happening though. made me so happy watching this.

[@evanlim9098]

Honestly, There is SERIOUS work done in alns video, the insane attention to detail, its almost like itts full of MATH REFERENCES? Wasn't expecting this from the channel with stick figures on a windows desktop

[@theblackvoid]

You sir, are a hero, spreading our word of math to the world. Goddamn, now everyone can appreciate the beauty of math :)

[@theyeetfamily2668]

This is Allen Baker's video

[@theblackvoid]

@@theyeetfamily2668 No, I know it's Alan's video (and I love his AvA and AvM series), but a lot of the math details that are in the Animation vs Math video can happen in 1 second - there's been a few times where I had to rewind just to see a tiny detail in the weapons that either e^(i*π) or TSC uses (that includes the pi bombs, the sigma sum machine gun etc). And lots of people sadly wouldn't understand why a lot of the attacks and movesets in Alan's video are the way they are, which is why this video is great, because it explains nearly all of them.

[@BestieKing]

I still can't believe that is literally a lot of math explained just on one video!

[@epicosexio]

Wild, might use this to refresh myself on basic stuff before college classes start this week

[@creativemusicpianofun1821]

extremely amazing the way you expresses all these

[@FerroMancer]

This was exactly the mathematical breakdown I was looking for. Thank you so much for posting it!

[@jackmack4181]

9:59 this my favorite part of you commentary, really nails what happened

[@user-js4xl7pw7l]

"Handle". Literally

[@seanlord7177]

This really helped me understand the math founding this animation. Thank you for your work!!!!

[@cybertar]

I learned new things out or Alan's animation and your explanation, thank you very much!🎉❤

[@highpiner]

5:04 I think he uses i with his arrow to make the translation upward (2x2xi) but since he was running so it makes an arc. That also explains why he can't sustain his elevation like e and falls down right after.

[@WatcherObsi]

I personally thought the reason why the circle increases is because more E^i[pi] enters it, thus 'adding' to the radius. I only noticed with multiple watches, but as more enter the circle, it increases in size. I don't think any of them are actually touching the equation-just that their mere presence is adding into it!

[@mintaroum.9096]

I think so too!

[@FenicxCE]

At 8:37,you could see the radius was lying around. Later on at 8:42 the eulers were taking them. They might've used that to change the radius

[@DimkaTsv]

Then.... Shouldn't it have been reduced as e^iπ=-1?

[@jonathan_herr]

​@@DimkaTsvremember at the end e produced 4 i's and made a 1 out of it? Could use that to add to the radius... Or just two e^iπ 's multiplied to each other...

[@DimkaTsv]

@@jonathan_herr √(-1)^4=1 It showed that you cannot just stack "i" to travel dimensions as each other will cancel first.

[@beefboss5979]

I love how the music gets more complex as the square/cube/hypercube/5-cube increases in dimensions

[@thevalarauka101]

this is literally the best analysis of it I've seen so far

[@yeasarmahmud9071]

I still remember calling math an easy subject when I was 1st, 2nd grade etc. But oh boy! Match is much harder than I thought it would be.

[@CatCat99998]

10:00 One point i think you missed is right after the integral appears, there's some expressions that appear on the left and right of it. The integral is 5 separate integrals, which are in the exponents of the e^...i on the left of the integral, each of the top 3 evaluate to π/2, the fourth goes to 3π/8, and the last to π/3, meaning that each of the five expressions evaluate to e^iπ. Also at 8:30 i didn't realize why the tan function was cancelling out the e^iπ since I didn't see the π that was multiplying in the tan function, good job spotting that. And at 13:04, while i knew the formula for the volume, It just didn't connect for me, so overall great job of explaining it.

[@kentamashi9365]

THank you, i really needed that. I was actually wondering so this js good.

[@Jack_______]

thank you for this analysis,very entertaining,is a very cool additive to the original video

[@blackbird3327]

Seriously somebody better make a game based on this animation as I'm pretty sure it can be a real entertaining way to teach kids of any age Mathematics how i know I'm pretty sure mathematicians and math teachers would agree to the idea

[@ZerickKilgore]

I'm a computer programmer, maybe I can try that sometime.

[@theaprilsonlyfool]

This would be a sick VR game w/o a doubt

[@ZerickKilgore]

But I mostly do front end...

[@johnlourencecarlos9620]

​​@@ZerickKilgoreadd it with a deep story like this: A not ordinary human suddenly wake up in a destroyed laboratory He went outside to see the world real dead, no signs of life, ruins of everything humans have built No more atmosphere This male character doesn't need to breathe He wanders around back to lab, but when he touched the number 1 written on the board, it attached to his hands He tried to remove it but it just got divided into 2, resulting in 0.5 He's wandering what's happening His vision starting to look some sort of not natural, seeing some settings or inventory, but it's actually just a slot of discovered math symbol, equations or formula he have seen Because he seen number 1 and and 0.5 , his artificial vision makes his discovered slot appear on screen(his vision) He start to walk around to calm himself and see a piece of paper When he flipped it, he sees some basic math symbol and numbers: +, -, ÷, × and numbers of 1 to 9 And it automatically collected by his "discovered slot" Now it's up to you what the character will encounter and discover in his journey But I would like the ending to be him floating in space discovering he is a equation, a numbers. He is the math. He suddenly see a dark red light approaching, and consuming dead planets and blackholes while he's floating, his last solution if he can do anything because he is the math Maybe he can restart the universe. So he rush to make the equation of making or restarting the universe. It's for the player to think the equation for restarting the universe. Any equation, symbol or number the player typed will cause 3 outcomes: 1. Equation didn't work. So Game Over 2. Instead of restarting the same universe, it created a different universe. 3. If the equation got right, the universe will restart and will start showing the character's background story. Edited version: A man wakes up in a destroyed lab and finds out the world is completely dead. After wandering around, he goes back to the lab and the telescope catches his attention. He looked at it and saw that some sort of shockwave was approaching to planet millions of light-years away, and it was getting faster than the speed of light. He feels that he is in danger so he hurries up to save himself and suddenly sees a book filled with only half of the entirety of the math. He also discovers that he can manipulate things using math with his hands. The first thing he did is add the same object and created two objects. Fast forward, he now solves half of the math. Finds out he is the math itself, he is an experiment. Now the shockwave is very near the cluster of galaxies where the milky way galaxy is. He hurries ups to get to the point where he can make an equation to restart the universe because he knows he can manipulate anything. He's rushing to make equations until he gets the right formula. Closed his eyes and throw the equations at the approaching shockwave at the speed of light and the universe restarted.

[@ZerickKilgore]

@@johnlourencecarlos9620 That's a good idea, I'll try to remember that one.

[@autezz]

Finally someone that can explain it easier and straight to the point, great job!

[@punelopepunstop5515]

Thank you for doing an analysis of this.

[@ChristopherLaHaise]

Okay, thank you for breaking this down. Most of it's over my head, but I love how you explained everything.

[@willow5768]

respect for this guy for putting hard work for this so the kids can understand some stuff

[@Goreboxvideossince2023]

ITS stolen

[@Asterism_Desmos]

@@Goreboxvideossince2023It’s got the original link in the description, and everyone already knows about this video. It’s just an explanation of the mathematical properties within the video. This still took effort and research on gallium’s part.

[@Goreboxvideossince2023]

@@Asterism_Desmos ok

[@Asterism_Desmos]

@@Goreboxvideossince2023 I do want to point out that if you suspect a video being stolen, you should mention it. I was just saying that this one specifically isn’t :)

[@builder1013]

This is by far one of my favorite animations of all time, because it combines two things I love: math and epic battles.

[@Goreboxvideossince2023]

ITS stolen

[@thatoneguy9582]

@@Goreboxvideossince2023 aint no way

[@hie3800]

@@Goreboxvideossince2023from who

[@FA...]

​@@thatoneguy9582yes it is

[@FA...]

​​​@@hie3800Alan becker (Original)

[@EchosTackyTiki]

That's like impressively well put together.

[@bagusthoriqul]

A best content always get a explanation that some people dont get it. Thanks man

[@lukeeatschips6324]

I love it that you chose this form of anaylsis with editing in text instead of stopping it every time something comes up, much better

[@lukeeatschips6324]

Also releasing an analysis in less than a day, pretty impressive!

[@ProfessorHeavy1]

Seeing all of this makes me realise just how visually striking this animation is in terms of what it conveys, such as 8:15 and 9:57

[@username-ur6dq]

Good job on going viral! you deserve it

[@TheMorpheuuus]

Fantastic video shown to me by my kid, now he is excited by complex numbers and integrals. What a great way to make Maths lovable and Interesting 👍👏 Big Thank you

[@spirittail4958]

Im glad I found this its the only review/breakdown video I could find that properly covers everything that happens thanks a ton for the explanation of all this it was amazing to learn

[@pokebronyborn]

I'm surprised how much of this I actually totally understood after just a little explanation lol. And THANK YOU, the mystery of Aleph has been itching my brain for days. Couldn't figure out how to even search for it by visuals.

[@SnackFiend002]

8:51 got me dead 😂 " someone touched that radius again"

[@beta_banter3013]

"The smallest cardinal infinity (hence why its so big)" you realize how insane that sounds right /pos AVM has me in a chokehold man. And watching this video explaining the things in it just made me love it even more. Thank you so much!

[@benjaminmenist]

8:25 I think you might have put sin(x) and cos(x) the wrong way round? Still the best explanation of this I’ve seen, with so many easy-to-miss details!

[@gallium-gonzollium]

Yep, I did. Thanks for the correction!

[@matangover]

I think there's also a mistake in the original video: when isin(π) is expanded it has 2i in the denominator, but it should be 2 (the i is eliminated). Technically both identities are correct because the numerator equals zero, but still...

[@Levelgap]

That was amazing. Thanks for the analysis, I learned something from this.

[@phantom9831]

Even tho I knew Alan did research for this video (by understanding most of the math method he used) I'm still amazed at how he made a great animation by keeping such logic in it, truly a masterpiece

[@phantom9831]

@BNe0 yeah right sorry, but still, being able to make such an animation based on maths is incredible

[@VrayCat]

Let’s explore the differences between Parabolas and Hyperbolas in a simple way: 1. **Parabola**: • A Parabola is like a graceful curve ⤴️ that looks like a smile 😃 or a frown 🙁, depending on its orientation. • It’s the shape you get when you graph a quadratic equation, like . • Picture throwing a ball into the air 🏈- its path forms a parabola as it goes up and then comes back down. • Parabolas have a special point called the VERTEX, where the curve changes direction. It’s like the peak of a hill 🏔️ or the bottom of a valley. 2. **Hyperbola**: • A Hyperbola is like two mirrored curves🪞⤴️ that stretch out to infinity ♾️, forming a symmetrical shape. • Imagine two branches of a tree 🌲 that grow apart from each other, but NEVER touch ❌. • Hyperbolas have two SPECIAL LINES called ASYMPTOTES, which the branches get closer and closer to but never actually touch ❌. It’s like chasing after a dream that you can never quite reach. (Differences: • Parabolas have a SINGLE curve ⤴️, while Hyperbolas have TWO distinct branches ↩️↪️. • Parabolas can open upwards, downwards, left, or right, while Hyperbolas stretch out horizontally or vertically. • Parabolas have a Vertex, while Hyperbolas have Asymptotes.) (Similarities: • Both Parabolas and Hyperbolas are types of conic sections, which are shapes formed by SLICING a cone. • They’re both used in mathematics to model various phenomena and in engineering to design structures like satellite dishes and reflectors.) In summary, while both Parabolas ⤴️ and Hyperbolas ↩️↪️ are curved shapes, they have distinct characteristics that set them apart. Parabolas are like graceful smiles or frowns 😃🙁, while Hyperbolas are like mirrored branches stretching out to infinity🪞📏♾️.

[@ommer15]

much appreciation for this. its quite crazy how youve managed to explain everything here so well, and even though im not a big fan of math youve made me stay throughout the whole video. awesome job and thank you!!

[@gallium-gonzollium]

ty :)

[@Deevster]

As someone who took honors math classes throughout high school, the fact that recognize almost all of these mathematical concepts both amuses me and horrifies me.

[@dragonhunter690]

Man how much time you edit this video? This is super amazing because there's always something in this video I don't understand but you explain it very carefully Truly good work man 👌😎👌

[@gallium-gonzollium]

Took me 1h nonstop? I don’t have that much time at my computer (I am constantly away from home) so it took 2 days from start to finish :)

[@Anonymous__S]

I knew id find this video! Thank you so much

[@aimansyahmi6712]

4:41 "By the power of addition, i compels you -e^i(pi) !!"

[@user-or5yo4gz9r]

Noone's talking about this, but in 5:53 TSC multiplies itself with the radian(or seems like it) making another copy of it impling that TSC's value is 2 in the "math dimension". Just theory crafting over here lol

[@yigitpasa7743]

This is why we're calling it The 😊*2nd* Coming

[@fazlaykhan]

i understand it better now. please do more review like this.

[@woodonfire7406]

You and Alan have just made the best math tutorial video in Human history

[@albert4866]

6:22 When a circle is stretched like that, it turns into an ellipse. So, any ellipse with major and minor axis greater than or equal to the radius of a circle and be created by stretching said circle.

[@tiddly5]

was hoping someone would make something like this, love it! it's clear you know your stuff

[@ArkayeCh]

The hypercube explanation just blows my mind because that's probably my first time realizing how people imagined dimensions with numbers. It's not just the sides that are measured. It's the unit space in between.

[@Isaac-lj9on]

This one is one of mind blowing video that I have ever seen

[@lavaavalon]

13:40 right, one infinite can be bigger than the other

[@pixelgamer6199]

I get the feeling that you’re saying this sarcastically, so I’m going to clarify that in math, this is fucking true and I hate the fact that it is.

[@lavaavalon]

@@pixelgamer6199 it's the basis in which our current computing technology is made, apparently, I just watched a video a good while back of someone explaining how a infinite hotel would not be able to handle an infinite number of infinite buses

[@Numbergamer2024]

I didn’t even notice that aleph was there, too!

[@ThDynamicGamer]

9:57 "Integrals can handle infinites". Bro is saying it like he's a marvel supervillain or something

[@MaoMaster69]

more things to note and perhaps clarify, 4:22 graphically, using a negative sign on the x coordinate of a point in space flips it about the y-axis. Here, it flips TSC around. This happens again at 8:03 but relative to the graph's (0,0). 6:01 θ and r are polar coordinates. Where θ is a phase and r is a magnitude. The equation θr equals the arclength the dot travels from a reference direction. 7:04 the highlighted area is equal to the area of the unit circle. This becomes more significant at 10:38, when it projects into an area of effect. 7:30 subtraction of radians when depicted in the complex plane results in a clockwise rotation, which is the direction that the slash arcs travel. 7:45 The formulation for this is a little confusing. 2πr is the equation for circumference, while πr² is the equation for a circle's area. The way TSC forms his shield suggests that his shield has a circumference of 4, and an area of 4π, which isn't possible. A circle with an area of 4π has a radius of 2, and the circumference of a circle with a radius of 2 is 4π, not 4. (But interestingly enough, a circle with a radius of 2 has the same circumference and area.) 8:26 Personally, I would depict e^(-iπ) as cos(π) - i*sin(π) because that negative symbol bears a lot of significance when working with signals. Sine and cosine have this weird relationship with negative symbols. cos(x) = cos(-x), but sin(x) ≠ sin(-x). Instead, sin(x) = -sin(-x).

[@Lunar-Shadows]

Amazing. this is being added to my favorites.

[@svis6888]

This video made me realise how much detail they put in ! Even the having the "bullet" make a tangent wave !

[@TheProGamerMC20]

wait what when was that

[@gallium-gonzollium]

@@TheProGamerMC20 8:30 :)

[@pigeonxd]

I first don't saw something unique, but with your analysis i know that anything got sense.

[@AdrianWoodUK]

12:59 - I'm not sure if it's intentionally, but when e is stood next to the circle and beckoning TSC to enter, the "iπ" part overlaps with the circle and looks like it says "in", which is where it wants TSC to go.

[@TGC442]

A freaking god

[@TopchetoEU]

i was looking forward to such a video

[@BmanpowWang]

Honestly I was scared looking at all this without an explanation, fearing I forgot “how to math” but once I saw this I understood I had an understanding of the math because I recognized it, I’m filled with calm now that I can understand this level of math, thank you?

[@alferrbidelspatch158]

2nd comment: This analysis video is incredibly amazing. It made the animation more impactful knowing what it is happening and what it all means. Most of all the last part explaining what was the big thing is and that gave more impact to the animation. 10/10 analysis video

[@puppygirlman18]

Thanks for making this commentary! Once they started dealing in calculus, the original animation lost me, 😅 but your explanations really help!

[@idkmyname12]

0:14 Reflexive Property!!! My favorite math property in that category.