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: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-mXp1VgFWbKc.html 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.
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
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.
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.
@@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".
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
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 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!
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?
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.
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!
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’.
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
@@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.
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.
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 !
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 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
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.
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!
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!!"
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 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.
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
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.
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.
"Wow! You got Outlook working on my computer again! You're a genius!" "...thanks, but watch this video and rethink what you called me..." Seriously, my brain melts after a certain level of mathematics so I'm glad you can describe it in a way where I can see exactly where my knowledgebase runs out and I can no longer comprehend it. It feels better to know that everything in the video "adds up" and that I don't have to fully understand how.
probably my favorite reference of all, at the end we see aleph as a dark grid meaning there isn’t anything there (null) which is a reference to aleph-0 which is a super popular song made by LeaF
Where TSC’s body is at the beggining is what I believe to be the origin point of that whole world. The reason the one comes down at that specific area is because it marks the unit above it. Go to when he discovers this plane, and you’ll see when the y axis tick marks are shown, it’s at the same spot the one was.
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.
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.
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.
philosophically speaking, the mathematical moral of the story is: When you define your values and know where you are coming from, you can go wherever you want, and the possibilities are infinite.
Goddamn I thought this was just gonna be like "And this is what this symbol means in math and how it's utilized here" not the goddamn HISTORY AND THEORY OF MATH. Bravo man, bravo.
Thanks! You may enjoy the following up video as well :) And The Volume of A 0-Dimensional Ball ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-GR1eBuzycjg.html
9:30 The machine gun is actually a derivative gun. Remember f'(x)=y=tan. Recall at 5:55 the dot represents the y axis. When he (TGC) shoots a e^ipi he takes the derivative of constant -1, reducing it to zero. At 10:41 he reloads with infinity converting the derivative gun to the integral. The integral of a constant is zero but since it is an integral it is the summation of all the individual e^ipi derivatives so he can blast an infinite number of them. They run in fear. TCS blasts the transformer with an integral but the transform absorbs it converting it to its own integral via the summation sign.
This is the best interpretation of the "Animation vs Math" video! Learned few information regarding Math's history. Very nice indeed. Thank you. Btw, I love the original video background music. It's a thrilling one but encouraging.
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.
You forgot to mention what “!” means. “!” Is a factorial, which is the number times the number before times the number before times the number before all the way down to 1. Example: 3! = 6 (3x2x1 = 6).
[notice at 0.25x] ---- at 10:00 when TSC shoots tangents relatively left side, they are represented by -ve tan graphs, ....but at 10:01 when it shoots right side, they are represented by +ve tan graphs. Genius !!💡
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
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
animation vs math just goes to show that math really does get complicated fast, one second im watching as 1+1 = 2, the next second im looking at a damn circle and a bunch of alien looking letters
9:52 if you look closely there are actually 3 are helping him if you look carefully 3 of them are walking in the other direction. You may not see it at 1st, but the 3rd one is hidden on the left side
Though I had plans to watch John Wick tonight, I just couldn't take my eyes off this masterpiece, which has both more action and depth to it. Amazing work !
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...)
4:42 Actually, in Euler's formula, e^(iπ) is exactly equal to "cos(π)+isin(π)". No other equations for this. It's just the "-" sign that the two i's emerged to become "i²" and attached to e^(iπ), making it look like it was apart of it.
I'm actually going for an undergrad in maths and cs in oct, and this thing looks absolutely fabulous 😂 I am truly amazed!! I look forward to watching the next video !!
