Explaining Gojo's Infinity with Calculus

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CHECK THE PINNED COMMENT. I made a pretty serious mistake in this video, but then I also think Gege made this mistake. So I think the video is still alright and I'll leave it up.

So yeah, a bit of a sillier video this time. I had with the idea to try to explain the Epsilon-Delta definition of a limit using Gojo's infinity, and this is what I came up with. If you have any questions or suggestions, leave them in the comments!

Music
“Impact Prelude” - Kevin Macleod
“Late Night Radio” - Kevin Macleod

Credits
Gege gets schooled
Gojo vs Hanami and Jogo Shibuya
Gojo vs Jogo First Time
JJK Wiki
Achilles SVG Flaticon
Tortoise PNG

Phanimations

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Комментарии

I think you have confused Zeno’s arrow paradox with the Achilles and the tortoise.

The arrow paradox require the arrow to go an infinite amount of half ways before moving thus unable to move since needed to do infinite things.

The tortoise and Achilles is where every time Achilles run and gets to the position the turtle was at the turtle has gone forward and is thus still ahead. This means for all time the turtle will always be ahead of Achilles even if he is faster if we require Achilles to get to the position of the tortoise.

While infinity ability works better understanding the arrow paradox Gege cites the tortoise and the hare

Edit: What I called the arrow paradox should actually be the dichotomy paradox. Mistakes on the naming as well

ChucklinHSR

The moment the graph of megumi showed up I was praying for a bum reference. I was not disappointed.

tiringking

Potential man catching stray is crazy 💀

IlI

And here I scoffed at my teachers telling me id use calculus. Dont I look silly now.

degen

I actually had this same realization a while ago, and it also kind of works for his extension techniques too. While blue seems to hinge more on the fact that it’s introducing a negative number into reality, I see it as a point approaching negative infinity which causes it to constantly draw in the space around it. Then red would be causing whatever’s in front of it to “approach positive infinity” by being blasted away, and purple makes a point that approaches positive infinity from one side and negative infinity from the other, so the limit (and thus everything in the purple) does not exist.

chlorine-

Broo no way. Youtube blessed me with this piece of art.

HENRIQUEKOUTAROSAGAHARA

This man did not fail to call Megumi a bum any opportunity he got.

udiomoudochi

In JoJo part 6 there’s a really similar concept which makes much more sense to how Gege explains infinity. Every time someone reaches halfway to Dio’s kid, they shrink to half their size, making the distance to travel to the next halfway point the same every time.

GokuEnjoyer

Bro mahoraga so smart it mastered calculus and mathematics in a matter of 10 spins 🤯🤯

gunther

I had divergence, convergence and the definition of infinity in my first semester studying electrical engineering, while I watched JJK season 1. It was litterally in the same week our professor first used these words when Gojo explained his powers. It still feels surreal.

Fotoschiki

I'm learning math and having fun WHAT!?

blakerenimu

We can prove using basic Diff Eq that an object approaching Gojo can never reach him if it slows down proportionally to the remaining distance left as a fraction of some initial distance from Gojo. The problem could be expressed as a simple ordinary differential equation of the form y’ = v*(p-y)/p, where y(t) is the position (distance traveled to Gojo), p is the initial distance from Gojo, v is the initial velocity, and y’(t) is obviously the current velocity. By separation of variables, this becomes (1/(y-p))dy = (-v/p)dt -> ln|y-p| = -tv/p + C -> y = p + Ce^(-tv/p). At time 0, y = 0, so C = -p. So, y(t) = p(1-e^(-tv/p)). Finally, we try to find the amount of time it takes for the right hand side to equal p (when all the distance is covered). This occurs when e^(-tv/p) = 0. But this never occurs for any value of t, even though the value of the expression exponentially decays towards zero as t goes to infinity. Thus, at no time will the object reach Gojo. Probably an unnecessary amount of work, but still kinda fun to show with a basic ODE lol

The interesting thing is that in the anime, the technique seems to be visually depicted more like a barrier than can actually exert force to push you away from Gojo (without using red), as shown when he crushes Hanami against the wall, or when the knives suspended in mid-air move away from him as he walks forward.

sungod

Maybe what Gojo meant is that he doesn't shower and his stench is literally frying the air molecules around him so much, that they expand infinitely

RixesPuffs

"Gege Akutami kinda sucks at math"

Duh, he's a sadis- I mean a mangaka, he ain't no mathematician 😂😂

arjun_kre

man, this really just reminds me of the two all nighters spent on the math IA -- you expressed it so concisely and in much simpler terms compared to my calc knowledge at the time.

daegukreb

I always interpreted this technique as Gojo believing in the paradox of Achilles and the tortoise so hard that the reality bends over it. The reason why I think that is because (I think it was a Gojo quote) in jjk your ego and your selfishness makes you the better sorcerer, so I always interpreted that as your curse technique being a cheat code that breaks reality in some way, and the more you and the others believe it the stronger the techniques are. Like, our space has motion and Achilles does indeed catch up to the turtoise, "limits" exist for it and in it, but Gojo' "Limitless" technique (aka his schysophrenia and ego) just goes "nah you don't", and so it doesn't.

iamdivan