All The Math References Frame by Frame From Animation vs. Math

[@ron与数学]

New discoveries as a collective effort from folks in the comment. Updated June 29th 13:00 PM. 1. 14:47 phi is clearly the golden ratio. As many people pointed out that its step size decreases when it approaches. I also noticed that delta shakes while moving, indicate the infinitely small difference it often represents. Zeta jumps with a constant step size, which is a clear reference to the Riemann zeta function. 2. Another small mistake I found, if you pause at 8:34, you will see that the term with 9! is already shot, then at 8:35, the running index still starts at 9. Only after firing the 10! term, the running index becomes 10, which is not what summation index is usually used. 3. I made a mistake at 14:23, e^pi is not the volume of all high dimensional unit spheres, but the volume of all even-dimension high dimensional unit spheres. Zach star has a video on this: kzbin.info/www/bejne/o4nTYomde7yVgcU 4, At 14:36, the running index starts at infinity. The concept of adding volume of spheres from higher of higher infinity is shown in earlier a few seconds but technically at 14:36 the equation no longer holds. In case you want to derive this on your own, be careful. 5. At 9:55, yes TSC has another secret ally that stole the "-" sign at the very left. --- A note on the primary math concepts' discoveries. It is hard to find the exact dates and civilizations of those discoveries. I did my best to do the research. Some people pointed out different opinions. Thank you for sharing, which made the picture more complete. Again, thank you all. It means a LOT for a new channel like this one.

[@MoaiGuyRBLX]

I ain’t readin allat

[@vunderbar9]

⁠@@MoaiGuyRBLXyou don’t have to dude

[@chenweizhi8609]

One of the best, if not the best explanation on this animation. Great work!

[@this_is_naig]

Man I learn these things more than I do in school, great explanation

[@haipingcao2212_.]

☢️ 14:52 ☢️

[@niko5008]

As a pretty amateur programmer I'm liking the idea of making a game like this. Imagine how funny it would be to tell your friend "okay so, stand on top of this number" and then divide it by zero and launch his character to the void out zone and kill him lol

[@monnamonsta]

wait this is brilliantly funny

[@StuffandThings_]

It would quite literally be a "game of numbers"

[@franciscotovar7536]

I would play!

[@galaxi6585]

still can't believe TSC discovered the irrational number thing with sqrt(2) at the start and didn't use it to launch anything into the stratosphere

[@raul-aurelianserban8295]

DO IT

[@stalkerofthenight2022]

the fact that TSC knows how to make a bow, machine gun, and orbital strike in the numbers void after under 15 minutes just shows how smart he actually is

[@tankmonster12345]

Hes creative

[@Icepepot]

Its both​@@tankmonster12345

[@在下一小卒]

And the ability to draw a perfect circle first try simply shown how good of an artist he is

[@TheRedGuyOfficial]

don't forget his brain is fucking invisible tbh

[@RedAce-RTI]

oh boy, cant wait to be able to understand this all this year, the engineering degree calls for it

[@AstraOG]

as another engineering major, saaaame

[@Cyber_N-7660]

Good luck you two o7

[@AndyIsLazy18]

Goodluck to the engineers out there ❤

[@JustSomeGuyWithAMug]

It's a joy to finally understand this videos yet it's a pain to get a 2/10 in the test

[@floss-tg]

as someone who spent way too long pouring over math for my engineering degree, i wish you well, good luck, and godspeed

[@Hornswroggle]

I love that Aleph has no real physical form either. It's so all-encompassing it's just a shimmer in the background. Literally unreachable (no amount of addition, multiplication, potentiation or factorialization of finite numbers will ever reach it). Essentially it is the "stage" upon which all this plays out.

[@Kba197]

Im your second subscriber

[@Spookbina]

is it just me or aleph reminds me of the starting if the arabic alphabet

[@byeolsson]

​ aleph is both the first letter of the Arabic language and Hebrew. That is due to them both being Semitic languages originating from a common proto-language ancestor

[@k_nito7954]

Surprised no project moon brainrot fans have commented about it yet lmao

[@_redniel_]

​@@Spookbina alaf

[@kennyholmes5196]

You may have missed one at the very end. Phi (that circle with a vertical line) is used to represent the Golden Ratio, which is related to Fibbonacci. And if you look, as Phi went further in one direction, the steps it took changed in size accordingly.

[@paragonzpluh]

100th liker

[@chopper7867]

This is an actual golden ratio

[@mcokiner_]

​@@chopper7867L + ratio

[@dagurtheone3969]

@@mcokiner_that, however, is not

[@8CanadianBacon9]

How did you notice that?!

[@LeBeaBae]

IS NO ONE GOING TO APPRECIATE THE SOUND DESIGN?! The music feels EXACTLY like how i felt when discovering these concepts while tinkering with math!

[@lukasdeen6226]

the team does, look up the original description

[@LeBeaBae]

@@lukasdeen6226 I mean no shit lmao, but is there a single comment about it?

[@iota-09]

The sound design is top notch, absolutely perfect stuff, every single action and frame is worthy of being one of those "satisfying clip moments" you see on Instagram tiktok etc, not a single misstep, kudos to the sound design team.

[@geniuz4093]

well obviously because its related with "technical/mechanical" activities. which are in turn related with "complex". and math for you is related with "complex". not that mind blowing. i can tell you think 2x + 1 = 6 is hard and complex as well.

[@LeBeaBae]

​​@@geniuz4093 A) I'm an engineer and a software developer, I've made fully functioning AI robots from scratch. B) I played with imaginary numbers and summation and derivatives and intervals when I was 10, figuring them out within 2 weeks (That was the "tinkering" I was talking about, C) I'm going into 10th grade and I've completed 2 honors sciences out of 4 (one of which is almost impossible for freshmen to take) and am starting an AP science class, plus I'm going into pre-calc honors. So yeah, x = 2.5 isn't complex to me. Try again, "geniuz".

[@gallium-gonzollium]

hi, this is way better than the analysis I or anyone else has ever done on it. dates, context, everything! this should be way more appreciated and I want you to know that you have smashed it when it comes to analysis. Ty \o/

[@ron与数学]

Thank you! Really appreciate it!

[@e7diablo]

I watched both commentary/analysis videos and actually thought I enjoyed yours (ever so slightly) more. Both are great though.

[@liaaaaaaaaaaaaaaaaaaaaaaav]

I agree

[@snoopdogg9490]

Your analysis is very good but your video was too fast and required frequent pausing

[@Tecnox735]

​@@ron与数学Really did a good job not gonna lie👏

[@kalashsarode]

One thing that you missed, which is vital to understand why the 3d space works in the first place on a 2d representation, is because @7:20, when the stickman splits Pi into cos and sin, it's actually "cos(t)" and "sin(t)". He essentially creates the time axis. From 7:26, you can see that as the axis progresses, it has a "t" written on the front the the axis which is basically a time axis. So everytime the stickman bangs the circle with the sin(t) and cos(t) onto the f(●), he basically fires off railgun ammo @11:45 onwards. This is just fucking brilliant. Alan Becker and his team are mind blowing.

[@Pete-xw4ig]

Why is it basically railgun ammo when hit with sin and cos?

[@PlutoDarknight]

​@@Pete-xw4ig If we remember back to the discovery of sin(t) and cos(t), Orange turned sin(t) into isin(t), turning it by 90° and aligning it with cos(t) into a double helix. When he grabbed the infinity symbol and slotted it into his f(•) tangent function, it fired infinite tangents that turned the "little monsters" into 0s. And at the end of the fight, he applied the f(•) function to the circle. Since the function's infinite power does very little in limitless realspace, it was instead struck with the cos(t) and isin(t) to transfer the infinite power into the double helix with every strike. And since both of those wave functions are time-based, we now have fast accelerating infinity death spirals, similar to the magnetic acceleration of a projectile fired from a railgun.

[@FreeOrange]

wtf

[@GrubbHubbClips]

​@@PlutoDarknightpretty similar to electromagnetic propogation of alternating waves at right angles. Only infinite lol. What a genius

[@cesarluis6335]

Can you do a video explaning what you undertand from this? I cant with the words here. It's so hard. How the horizontal axis it's a representing time but the numbers are angles hahaha wtf

[@C_Corpze]

The animation is absolutely genius. I wonder how much research and math they had to do to make it accurate.

[@yeetgamer1765]

One of Alan's animators is good with math so it didn't take very much research.

[@octhevossavelios]

@@yeetgamer1765 how'd y know?

[@whonoonenobodynothing3467]

@@octhevossavelios the lead animator was the math guy, it says that in the pinned comment of the video so it took long but not ages

[@Akiora777]

​@@octhevossaveliosits the pinned comment in the original vid

[@ptrkmr]

Yeah like the other guys said a lot of this stuff is “common knowledge” after getting a STEM degree for the more math heavy areas. I’ve never seen all of it down to the basics so eloquently summarized tho, this is amazing. The research likely took the least amount of time. It’s trying to figure out how to connect it all that’s the impressive (and likely most challenging aside from the animation) part

[@korben600]

Wanted to chip in with some stuff I noticed. - This is mentioned in another video, but TSC and little monster are both real numbers. That’s why they can interact with the world, why TSC can multiply his speed and change location, same with LM. But more importantly, they’re both real numbers *on the x axis.* They’re not just stick figures, they’re technically the coordinates with the locations (TSC, 0) and (LM, 0), because those are the only types of coordinates that are real in a complex plane. That’s also why when they want to go upwards, they add multiples of i to themselves, but don’t go into a different plane until they multiply themselves by i. Since as real numbers they can add i values and remain in the complex plane, IE change their coordinates to (TSC, 5i) and (LM, i). - When they’re moving, their coordinates (TSC, 0) and (LM,0) are changing, with LM and TSC increasing at a certain rate, the speed they travel (since this is physically what speed is, the rate at which a coordinate changes). So when TSC wants to increase his speed he multiplies himself, making the rate at which he changes faster (or making the initial value being multiplied higher, tho I suspect it’s the former because of the negative trick I, about to get into). - Speaking of, the negative number trick is actually consistent despite being used in two ways. In the chase scene, since LM’s coordinate is changing at a specific rate (its speed)TSC uses a negative to change LM’s velocity. Changing a velocity of a given point to a negative turns the point in the opposite direction (something that shows up again later). However, at another point in the vid, TSC uses a negative to get to the other side of a circle. Inconsistent, right? Wrong. The reason the second negative teleports TSC is because he’s both not moving, and on a *coordinate plane.* His defining characteristic on a static coordinate plane is his position, *not* his velocity. So rather than making his velocity negative, he made his *position* negative. So rather than reverse speed, he teleports to the other side of the circle, since that’s what making a position negative does. To simplify, first time he turned the equation LMm = x into LM(-m) = x, but the second he turned the position (TSC, 0) into (-TSC, 0). - And for my main point: The “blackworld” they were in was *consistently* a complex dimension (minus maybe the parametric bits), that’s why every time he wanted to move upwards, both LM and TSC had to use a multiple of i. Since that changed their positions from, say (TSC, 0) to something like (TSC, 5i), which was represented physically by height in blackworld. But the blackworld is only imaginary on *one* axis, the y axis. But the “other” dimension had *two* imaginary axes, with the x also being imaginary. Now, TSC and LM, as established earlier, are real numbers, but getting into the “other” dimension requires changing the x axis of a point to *also* be a multiple of i, which is why little monster and TSC had to *multiply* themselves by i to get there, otherwise they’re still just real numbers. - The other dimension had square roots of negative numbers throughout it because it’s the *imaginary plane.* Thus numbers that are only represented by i in the blackworld are represented as their “actual” values in the other dimension, IE as square roots of negative numbers. Also the *reason* square roots were spilling out of the cracks because TSC’s cannon was “cracking” the x axis of the imaginary plane…which was as mentioned earlier made up of imaginary numbers (ie square roots of negative numbers). - Also, TSC wanted to get into the imaginary plane because it was another dimension, and he wanted to return to his home dimension. LM had to clarify that multiplying himself by i multiple times would just send TSC back to blackworld, since TSC = real number, i x TSC = imaginary, and i x i x TSC = -TSC = a real number. Hence why he needed a more complicated equation to actually access other dimensions. - Note also, when LM is demonstrating why just multiplying by i won’t access higher dimensions, he, changes positions. Specifically, he’s flipping around the Y axis. Why? Because i x i x LM = -1 x LM. Since LM’s actual value, e^(i(pi)) = -1, is -1, and he’s flipping his value from (LM, 0) to (-LM, 0), he’s going from position (-1, 0) to (1, 0). He’s doing what TSC did earlier with the negative, only in this case he takes a detour to the other dimension first before teleporting to his new position.

[@1Life4Passion]

How'd you know are you a math major?

[@korben600]

@@1Life4Passion I'm a math minor actually! But for all of these things I pointed out, that was more just paying very close attention to the video. Additionally, a lot of the conclusions I bring up is logical progressions of some of the other things I and everyone else have brought up. IE if they're already on a complex plane, why are they transported to another plane when they touch an i? Well, it's because *they* weren't complex numbers until they touched an i. Not exactly simple conclusions, (and maybe not interesting enough to get pinned), but they definitely didn't require my math minor to do!

[@HappyFunJay]

@korben600 Underrated comment.

[@livelittle411]

Thats like the best and funniest way of explaining imaginary numbers !!!! Hats off

[@damri_notfound]

incredible work on this comment, but i don't get the part where tsc is a real number. is it an infinity number, or is it an imaginary number, or something?

[@RlOltRe]

"Is it possible to learn that much information in only 15 minutes?" Python: *yes.*

[@mfirdanhb]

learn? yes, solving it? the angels can only pray for that

[@ChickenMcKicken]

as a 7th grader, i really stopped understanding everything after the first circle appeared

[@FreeOrange]

@@ChickenMcKicken💀

[@stxllr4687]

@@ChickenMcKicken how did you manage to learn complex numbers before trig??

[@Shifty_fl]

BRO I AM A 7TH GRADE AND SAME HAPPENED TO ME@@ChickenMcKicken

[@pichooooo]

The fact that you can find every possible mathematical reference in the animation is amazing

[@ron与数学]

Thank you!

[@joda7697]

12:48 i think that's the branch cuts actually. Sqrt(-5) for example has multiple solutions, and just as those are called branch cuts, there is a rift in the world, cracking it apart.

[@ron与数学]

This is a good point. I thought about this possibility. When I paused at 12:55, I felt like Alan Becker is going for the aesthetic side of this visualization. Can't imagine branch cuts that looks like that, hence my "guess". Thanks for the point!

[@SeriouslySamuelyearsago]

I thought it was more like the ‘complex world’ was breaking due to TSC’s laser. When the other ones fired, even for a split second, it left a scar on the ground. Maybe the extended blast was enough to affect the ‘complex world’.

[@joda7697]

@@SeriouslySamuelyearsago that's a possibility as well

[@JwalinBhatt]

Yes that was my first thought as well, definitely branch cuts.

[@gaturno4377]

i think its by the fact that they are in the imaginary numbers world and TSC is real so where he goes it breaks, and when he comes back it fixes

[@Kxre_]

I’m honestly glad this got recommended. I already admired Alan’s style of animation and to understand the meaning behind every sequence as well is probably the best thing I could’ve asked for in recent times. Thank you!

[@GlacierTheCat]

"Banish little monster to negative infinity" at 9:13 Is just so stupidly funny without the proper context

[@indigohued]

I love how expressive Alan animates. For a stick man with no face and a letter, it's pretty easy to tell how they're feeling

[@critixil]

I cant stop rewatching this video cause i wouldnt stop until i found an explanation for everything and you have done that. Btw the dimension part near the end is a reference to the imaginary dimension i think Edit: TSC is a real number because the imaginary dimension collapses if you add a real number to any imaginary equation and the imaginary dimension is a dimension of equations made of imaginary numbers Edit 2: TSC is confused when dividing by zero as somehow 6/0 doesnt equal to 6/0 with the other division sign

[@OKKirby]

yep at 12:53 i can see many negative square roots

[@DavidLopez-gs1fb]

What is TSC?

[@critixil]

TSC is the second coming, aka the orange guy

[@JayronWhitehaus]

@@critixil I still don't understand! Jesus? Trump? The little stick man in this video? I feel dumb I'm so sorry.

[@KipBlade]

​@JayronWhitehaus the little man in the video he's part of a series animation vs animator and there was like 2 other stick figures before him

[@reluarrelude]

"math is a gift from above?" nah, math is a curse from hell

[@SunnyKimDev]

13:52 eipi is demonstrating that his "doors" would not help TSC escape, as going through it 4 times would result in the original position (i^4=1)

[@brrrrrr]

Isn't eipi supposed to be Euler's number?

[@brrrkic]

​@@brrrrrreipi

[@iexplainjokesforaliving.5415]

@@brrrrrr eipi

[@CharlesUrban]

​@@brrrrrrNot really an expert, but if I remember my math classes from when I was in school (the Bronze Age), Euler's Number is just e. e^iπ is Euler's Identity.

[@epikoof]

this one is amazing, explains things quickly and is still entertaining

[@omeiga]

tof agree

[@markoprskalo6127]

Math wars

[@TheAdvertisement]

7:35 Would like to note that splitting pi in half also made the halves resemble "t" with sine and cosine on top, equating to sine/cosine over time, and thus creating a graph.

[@specktrumm0]

this video made me realize anything can be beautiful as long as you understand whats behind it, how it works down to the core, the meaning of it. what you do with it next stems from passion. thank you a lot for this, i saw the original once but didnt give it a second thought. beautiful.

[@Blackholing]

As a math and physics student, I was so impressed and excited. I've always loved interpreting math concepts in a creative way, the idea of ​​merging math and "art" is smart, it helps to better visualize concepts (and understand their usefulness) Shout out to the 2x2 bow, the design is so cool !

[@vincanlas8796]

2×2?

[@Blackholing]

@@vincanlas8796 yeah the bow in the video, it's made of 2×2 and it shoots "4" arrows

[@irrelevant_noob]

@@vincanlas8796 5:23 ... and it appears later at 8:15 too.

[@Baburun-Sama]

...And the =f(•) Gun?

[@Blackholing]

@@Baburun-Sama it's cool too ! but my fav one is definitely the 2×2 bow !

[@Airifying]

This genuinely deserves alot of attention, You focused on every single bit of detail here and gave a very well splendid explanation, Sure im dumb af, But watching this was very entertaining and made me learn a few things. My hats off to you brother.

[@proxxylord6]

This came out just in time I have been helping some relatives with summer tutoring in math and the kid is brilliant but unmotivated, I showed him this video and his response was absolutely golden: "WHY DID NOBODY TELL ME THAT MATH COULD BE THAT COOL!!"

[@Sh1penfire]

3:12 Since the / sign is more commonly used in programming I'mthink that bit's a reference to how division by zero won't compile into usable code and for TSC doesn't have an output, not that there is no answer ;) Amazing video, love watching this type of breakdown!

[@niko5008]

I dunno some of them throw an integer limit, others "infinity" and others just hang the program

[@jukit3906]

@@niko5008 No, most of the languages have /0 as NaN /0 itself is undefined Only lim x->0+ (1/x) is positive infinity

[@eduardonavarro4172]

Exactly, not many non math people know that the value of the limit and /0 are different.

[@SuperGamersgames]

I'm not an entirely big math nerd, but as I'm glad someone was able to explain some of the bits I wasn't able to get (which I was strangely able to grasp a lot of the concepts). :)

[@amanvijayjindal5742]

This is one of the greatest videos ever produced by humanity. PhD level knowledge of mathematics storyboarding,the music the animation the concept and execution is mind blowing

[@tobysda1297]

9:52 There's actually a third, on the left you an see a Little Monster facing the other way holding a negative sign. If you look back you can also see it moving away from TSC

[@mrtoast244]

I can't believe that these characters, who don't speak, have better character development and a more satisfying arc in 10 minutes than some some characters from big budget studios are able to have in entire seasons (looking at you "Rings of Power"). What's brilliant about this video is how it's sort of a pseudo history of math, but done in the most creative way possible. Alan Becker is an actual mad man for making millions of people in love with characters who are literal numbers and letters, it's like Alphabet lore all over again.

[@the_mariocrafter]

but without the cringe kids

[@lawbreakerlawrence]

you cannot compare this to fucking alphabet lore bud 💀

[@mrtoast244]

@@lawbreakerlawrence letters are canon to the math verse

[@G_N_8]

I'm surprised this only has 1.2k views right now, beautiful art, this is something I always wanted, a sort of show which displays math so I could avoid learning it and kinda take it all in as a form of a show

[@astronomist29]

it's not this guys video, the original video is under alan beckers channel

[@Sammy_Scratch]

Check the original

[@G_N_8]

@@astronomist29 yea my bad i forgot to delete this comment after I went to the original in the desc, beautifully made and ig this guy showed the history behind it and stuff, nevertheless good

[@Cyan_Scug]

YOU DON'T SAY ITS 300K+

[@mofi_lki]

@@Cyan_Scug now 1m

[@pedrokrause7553]

I believe the imaginary world cracking is simply due to the energy being released by the huge circle. At 13:04 you can clearly see that the black/cracked region follows the energy ray with pretty much the same angle/inclination, as if it were an extension of it. At 13:18 you can see the cracks on the floor caused by the energy, and at 14:02 they "heal" when e^(iπ) stops the circle and brings it back.

[@sunburst3476]

I think it also could possibly represent TSC not belonging in the imaginary world as he is "made" of non-imaginary numbers (animation is technically math as he is constituted of points on a plane, we could even stretch this to vectors, frames per second (why he sped up when he "multiplied" his legs), and other stuff as well). He basically broke the imaginary universe by being in it

[@pedrokrause7553]

@@sunburst3476 I feel that this and some other interpretations, while possible, weren't the intention of the author. But who knows!

[@PixalonGC]

this kind of analysis is great because i learn a lot more about the history of math and some concepts like the complex plane

[@quellavenix1262]

This is bonkers brilliant. I have always believed mathematics should be taught in a more playful and engaging manner. We all know the intricacies behind mathematics and not everyone can handle the deep abyss of the field. But what I am saying is that I want more people to think mathematics as something else other than stressed moments in their life filled with souless homework and tests. Alan Becker did an amazing job, and you Python with Prosper did an astounding job on taking the time to go through all the details in the video along with bits of history that just makes the video more flavourful. Thank you for putting in the effort for this video. I wish you success. Also Imagine if Brian Cox for narration, that would be insane.

[@SilicosisNotBeta]

honestly i was never really interested in math due to how boring the classes were and i just didnt find the fun in learning math and then this shit drops and im like "WHAT"

[@monnamonsta]

we wish math classes have these :(

[@iota-09]

Honestly if an assignment was "discover as many mathematical laws in this video and then reapply said laws to create new problems and solutions" I would bet you that a ton of people would suddenly find a renewed interest in math. But lol as if any school in the world that isn't homeschool or an extracurricular project is gonna do that.

[@Miguelmax50]

I'm a fifth grader, when I grow up, I'm going to study math at college, and then I'll watch this video again, and I think I'll understand almost everything.

[@paradox9551]

Good luck bud! Don't give up when you encounter hard mathematics like calculus and linear algebra.

[@Miguelmax50]

@@paradox9551 ok tysm

[@_Longwinded]

It’ll still be tough to understand but I wish you luck champ

[@nicolasoyarce9734]

You can understand it now, why wait

[@TheDutchFoxx]

As someone who really struggled with math this video is just as great as the original with explanation of how things work in a basic sense. Also infinity is scary AF, constantly reappearing

[@AbsoluteDark]

This is actually one of the best KZbin videos ever made, every time somebody makes a video on it I'm learning (and forgetting I cannot memorize this all) so much and the way its portrayed not only in literal equations but in the small plotline the characters have is genuinely insane. The video takes advanced mathematics and combines it with writing as well.

[@shinnmei3614]

There's an easter egg mentioned by another from Bilibili at 2:11, we know the formula's answer is -1, which means TSC is "-1" as well when he stands behind the equal mark.

[@ron与数学]

That would be really interesting! A little bit stretchy but could be true.

[@KarelSeeuwen]

Thank you Alan and team and thank you too Ron. The "r and theta" helping out, I did not notice, and the replacement of the factorial with the gamma function went beyond my old brain's capacity to comprehend.

[@yoshi_chuck05]

I love how Alan was able to make an entertaining video while also teaching us math! He’s a legend!

[@phonicalnotion248]

I have learned more about the foundational uses of mathematics here than I EVER DID in school. I have been studying this second by second since I first saw it, and my understanding of math has only gotten stronger from this. Thanks for making this video. I already loved mathematics as a whole, but this just gave me an even greater appreciation of it.

[@hyperpsych6483]

11:05 The summation absorbing the power of the limit to become a deadly integral was legendary

[@welovfree]

When I reached the animation character adding ones and you mentioned induction I knew that this video is going to be the most accurate analysis I will watch. I thought it was an obvious reference but others missed it.

[@ron与数学]

Great catch. It depends on people's knowledge background :)

[@xanderplayz3446]

13:45 Makes sense, because iiii = 1 and 1 * e^ipi = e^ipi

[@qhelios]

Honestly, dude, you did a very good job explaining this. Props to Alan Becker and his team for making this masterpiece. I'm currently looking forward to becoming a programmer. Best of luck on everyone's dream. o7

[@ron与数学]

Thanks! My channel is actually a programming channel. This video is a side project. Hope I can create something useful for you in the future.

[@qhelios]

@@ron与数学 What a coincidence! I sure am looking forward to learn from you. Oops, edit here: I'm doing JavaScript lol, but it's fine. I'll probably learn a little or 2 from you still. I might even change to Python.

[@DynestiGTI]

1:44 casually jumping 2,000yrs of mathematical discovery

[@philosophicsblog]

At 5:49, TSC finds a zero-dimension dot he uses to create 1D space (the Y, imaginary axis and then the X, real, axis), foreshadowing 2D planar space but opting instead for the complex 2D plane. Euler's number, e, is the natural log constant (2.718). Euler's identity is e^(iπ) + 1 = 0. (obvs, pi = 3.1415...)

[@G0of_Ball]

11:14 “WAAAAAH” Edit: Alan Becker did the animation but not just thank him, than one of the people working for him who is a complete math wiz B)

[@_redniel_]

"WAAAHHHH!!! 😭😭😭😭" e^iπ

[@solidturtle6910]

Alan paid someone to voice that

[@DrGiggleTouch67]

The amount of references in this is insane.

[@ron与数学]

Thank you!

[@randomstickman16]

This deserves a million views, dude! This is amazing! Alan Becker should see this!

[@egwuchikatochukwu6900]

I like the way you used the word "discovery" rather than "invention". Eg: discovery of negative numbers

[@memebruh2024]

This is really more detailed than other explanations out there Nice job man

[@syroshiro7234]

One more thing I would like to point out is at 12:51, the cracks actually look like roots which is kinda funny because the square roots of negative. numbers are shown.

[@s-ata-n]

1:11 bro overanalyzed so much he even went on to beginning of philosophy💀

[@pakdosen9325]

I love this version of explanation because you point out all of the history references.

[@ianfarquharson2933]

A true masterpiece by Alan This video taught me so much about the lore of math, some math breaking stuff, and other cool stuff All of this is amazing

[@ankitmallik6264]

both the idea and making of animation took an immense effort and time

[@asthalis]

This video is pure gold for math addicts !

[@sabikikasuko6636]

One thing I think goes severely unappreciated is the abdolute GENIUS of the sound design. I don't know how he did it, but that's exactly how I always envisioned math to sound, as advanced, almost futuristic little machines doing things and giving results.

[@IAmTheCheddarMan]

11:43 *"It's over Anakin... I have the high ground."* *death ray*

[@robertmcpherson138]

The 2nd analyses of this video I've seen... both have given me deeper and deeper appreciation for the video as a math smooth brain.

[@rubenvanderark4960]

3:43 Also a reference to how x^0 = 1 for x≠0

[@daniellaizekemoe1967]

Very in-depth explanations, educational, and humorous! Massively underrated.

[@gierickgabriel]

NICE Its probably better than the other one I watched

[@nokiaairtel5311]

You are the one who caught the minute details(like using x to gain speed, the bow made of 2x2 shooting 4), that every other channels missed. Thank you for that.

[@michael88704]

I think at 14:50 phi is Euler's Constant (0.57721). It would make sense that they're friends! :)

[@ManioqV]

Phi propably is the golden ratio, 1.618..., ½+√(1+¼)

[@catinjar9460]

thank you for deciphering this masterpiece! I feel like I learned more than I ever had.

[@rai_rye.]

Finally, math becomes fun for once, now i can learn even better

[@jojoginni]

My maths nerd friend recommended I watch this - my maths knowledge is pretty basic, just good enough to graduate high school xD But thanks to your video, I think I actually understood what's going on in the video and learned some maths along the way. Thank you

[@hongkonger885]

9:40 damn, the allies are so cute

[@FishSticker]

Glad you actually analysed the story, I didn’t catch the concept of e escaping by going complex, and I didn’t realise that it wouldn’t work after they reached the complex dimension (at the end)

[@UgurTas46]

This video started to make me love math. I mean what Alan did and that's it. :)

[@stardreamix786]

So amazing, love that math bow of 2x2, shooting number 4 arrows!!!!

[@turtturtle]

as a middle schooler. I don't feel so bad only being able to barely comprehend the information up to around 6:00

[@iota-09]

Definitely don't; back when i went to middle school(mid 2000s/early 2010s italy) square roots and exponential was the main mathematical thing, going far past that in middle school means you're already better at math than half the Italians your age* *Dunno if this applies to other countries tho, of course besides the fact that standards may have changed since then.

[@LawrenceHermes]

Just to think somebody could illustrate such complex math in a simple youtube video makes me appreciate being alive

[@CrazedKen]

Learns math, breaks it in 14 minutes, leaves.

[@lukatolstov5598]

2:55 How to divide: 1. Add as many as you want 2nd digit, until it equals to 1st digit. Next count how many 2nd numbers you need to make 1st number. Or like in video subtract as many as you want 2nd digits from 1st digit, until it becomes a zero. Next count how many 2nd numbers you need to make 1st number to a zero.

[@victorquach5712]

0:09 “God created the natural numbers; all the rest is the work of man.” - Leopold Kronecker

[@Wolan-_-1]

Seeing math is pretty cool

[@Zicrus]

12:36 Notice the 90 degree rotation

[@ron与数学]

Great eyes! I didn't figure out why it rotated so I thought it is a pure visual choice.

[@thechosenone7400]

Wick Rotation and Imaginary Time reference detected?👀

[@rionmotley2514]

Aleph! You're literally the only one who mentioned the big guy in the background!

[@andiasfanmacaroba8591]

15:00 what does "Big guy" mean on "Aleph, used to represent cardinality of infinite sets Big guy"?

[@Helloworld-xu2ui]

because infinity is a huge concept and there are different infinities larger than others

[@Crazycam425]

@@Helloworld-xu2uivsos

[@eliminativegaming6189]

i want this to get viral on internet

[@thebubblybubblybub]

9:28 Why is it perfect

[@ron与数学]

Because it 1, covers the whole plane 2, can propagate to infinity ( periodic function )

[@thebubblybubblybub]

Thanks!@@ron与数学

[@Sapphire-qo2ij]

This single 15 minute video made me learn more math then 9 years of boring 40 minute lectures about it. Thank you!

[@floppy8568]

3:18 he really forgot implied multiplication

[@d1kgaws12]

Glad this video broke the algorithm.

[@dorianc.4372]

Math class after you skip one lesson

[@dachosens1]

Wow! This was amazing! I got a lot of it while watching but this showed so many things i still missed! This is probably the best break down video I've seen and it is SO GOOD and the references are ON POINT! Great Work!

[@carlfilipmadsen3537]

Do you want to mention that (sometime during or after 6:42) that the letter r here is the variable for the radius of a circle? r = 5 when The Second Coming first looks at the variable's value, but then he adds 2 to increase the radius to 7, and then subtracts 5 by 2 (by flipping the expression) to make it equal to 3.

[@carlfilipmadsen3537]

P.S. θ (theta) is also a variable; it is used for the position of a point on a circle relative to the point with the coordinates (r , 0) where r is usually 1 for simplicity. For example: in a circle where r = 1, θ = pi is at the coordinates (-1 , 0), and θ = pi/2 is at (0 , 1), which is also where θ = 5*pi/2 is.

[@eiraishiki]

I had to do multiplication and division in assembly language. This Multi and Div trick helped me a lot. Thanks Alan.

[@betabravo3300]

I believe you should be tanking Terkoiz as well. He's the one with the idea for this and the lead animator for this I think.

[@justarandomguy9133]

12th grade student here just started calculus and integration, but the logic behind this animation is amazing!

[@jeffreyzhang1796]

i was like 'i understand this' :) and then at 11:00 I just lost it bro wtf is happening anymore

[@Wilfoe]

Thanks for the run down! I was able to pick up on more stuff from the video thanks to this!

[@amansings]

0:43 my guy 0 didn't appear casually in mesopotamia. 0 was invented by Hindu/Indian mathematician Aryabhata. Have some respect to those that we have today so advanced in maths

[@DiabolicalOrganisation]

Bro commented something that was wrong, like could you not be bothered to just google it but now you're wrong on the internet something you don't want to do 💀💀 aryabhata invented the digit btw

[@DiabolicalOrganisation]

Also what does have some respect to those that we have today so advanced in maths

[@amansings]

@@DiabolicalOrganisation stop living in propaganda kido

[@ayakashusband]

Yup

[@suukushisakura9333]

Wow, really great video; both the original and your explanations. I did the German finals this year and had to do math orally. What confused me was that the questions weren't this typical "here is a formula and here some numbers now deal with it" but rather seeing if you can grasp the complexity of the topic and the logical connections. An guess what- that was so much easier for me! So yeah, math can be fun and interesting 😄

[@馬嘉朗]

12:28 Speed multiplied 82794 times😅