Explaining Gojo's Infinity with Calculus

Summary

The video script explores the mathematical concept of limits and infinite series through the lens of 'Jujutsu Kaisen', specifically focusing on Gojo Satoru's Limitless technique. It draws a parallel between Zeno's paradox of Achilles and the Tortoise and Gojo's ability to manipulate space, making it impossible to reach him. The script delves into calculus, explaining limits and infinite sums, and how they relate to Gojo's power. It concludes by connecting the mathematical ideas to the fictional world of anime, where such logic can be manipulated for unique abilities.

Takeaways

• 😀 The script discusses the mathematical concept of infinity and its relation to the anime character Gojo Satoru's technique 'Limitless'.
• 📚 It references Zeno's paradox of Achilles and the Tortoise to illustrate the idea of infinite tasks in finite time, which is a foundational concept in calculus.
• 🧮 The video uses calculus to explain how Gojo's power can be seen as a super task, where he manipulates space to make it impossible to reach him.
• 📈 An analogy is made with a graph to show how limits work in calculus, relating it to Gojo's ability to pinpoint exact percentages of similarity to another character.
• 🤔 The script questions the practicality of these mathematical concepts in the real world, contrasting them with their application in fictional settings.
• 🎯 The concept of a limit is explained as a way to understand the behavior of a function as it approaches a certain value, which is likened to Gojo's technique.
• 🔍 The script delves into the idea of an infinite sum and how taking the limit as a variable approaches infinity can provide a solution, even if that solution is not physically possible.
• 🌐 It discusses how Gojo's 'Infinity' technique can be interpreted as making every half subdivision of space take the same amount of time to traverse, thus never allowing an opponent to reach him.
• 📊 A visual representation using a position versus time graph is used to explain how Gojo's technique could theoretically work, with him existing at the limit of the graph.
• 🎥 The video acknowledges that the mathematics in anime or manga does not have to be perfect and is open to interpretation.

Q & A

What is the main theme of the video script?

The main theme of the video script is the exploration of the mathematical concept of limits and infinity in relation to the fictional character Gojo Satoru's technique 'Limitless' from the anime Jujutsu Kaisen.

Who is the character mentioned in the script that has a technique called 'Limitless'?

The character mentioned in the script with the technique called 'Limitless' is Gojo Satoru from the anime Jujutsu Kaisen.

What is the connection between Zeno's paradoxes and Gojo's technique 'Limitless'?

The connection between Zeno's paradoxes and Gojo's technique 'Limitless' is that both involve the concept of an infinite number of tasks or distances that need to be traversed, which in the case of 'Limitless', makes it impossible for others to reach Gojo.

How does the script explain the concept of a limit in calculus?

The script explains the concept of a limit in calculus by using the example of a function 'bum of X', where the limit as X approaches a certain value is represented by a different value B, illustrating the idea of getting arbitrarily close to a point without actually reaching it.

What is the significance of the 'super task' mentioned in the script?

The 'super task' mentioned in the script refers to the idea of completing an infinite number of tasks in a finite amount of time, which is a paradox that has puzzled mathematicians and is foundational to the understanding of calculus.

How does the script relate the concept of infinity to Gojo's technique?

The script relates the concept of infinity to Gojo's technique by suggesting that 'Limitless' involves an infinite sum or series, where the technique takes a finite space and divides it into an infinite number of parts, slowing down any approach to Gojo to the point where it's impossible within finite time.

What is the practical application of the mathematical concepts discussed in the script?

The practical application of the mathematical concepts discussed in the script is to understand the mechanics of Gojo's 'Limitless' technique, which is based on the idea of infinite subdivision of space and time, making it impossible to reach him in a conventional sense.

How does the script use the analogy of 'Achilles and the Tortoise' to explain Gojo's technique?

The script uses the analogy of 'Achilles and the Tortoise' to explain that just as Achilles can never reach the tortoise if he must travel an infinite number of halves, opponents can never reach Gojo because his technique 'Limitless' involves an infinite subdivision of space.

What is the role of the ASM toote in the explanation of Gojo's technique?

The ASM toote (asymptote) in the explanation of Gojo's technique represents the boundary that approaches but never reaches Gojo, similar to how an asymptote on a graph approaches but never intersects a certain line.

What is the script's stance on the realism of the mathematical concepts in the context of anime and manga?

The script acknowledges that the mathematical concepts, while theoretically sound, may not be entirely realistic or airtight when applied to the fictional context of anime and manga, where the logic can be bent for the sake of storytelling.

Outlines

00:00

🧮 Mathematics and Limitless Gojo's Technique

This paragraph delves into the mathematical concept of limits as it relates to the anime character Gojo Satoru's power, Limitless. It humorously starts by questioning the author's mathematical abilities, then transitions into explaining Gojo's power, which is likened to a super mathematical ability. The concept of Zeno's paradox of Achilles and the Tortoise is introduced to illustrate the idea of an infinite series of tasks that paradoxically seem to prevent motion. The video script then connects this paradox to the foundation of calculus, explaining how Gojo's power can be seen as a practical application of calculus in the fictional world of anime. The script uses the analogy of a graph to explain limits and how they relate to Gojo's ability to manipulate space, making it impossible for others to reach him due to the infinite subdivision of space.

05:02

🔍 Analyzing Infinity in Jutsu Kaisen

The second paragraph continues the exploration of mathematical concepts within the context of the anime series 'Jutsu Kaisen'. It discusses the idea of an infinite series and how it applies to Gojo's technique, 'Infinity'. The script explains that in the real world, the concept of reaching a destination after traveling an infinite number of halves of a distance is a workaround to deal with the theoretical impossibility of infinity. It then relates this concept back to the anime, suggesting that Gojo's power can be visualized as a graph where time and position are plotted, and as time approaches infinity, the position never reaches Gojo, who exists at the limit of this graph. The script concludes by acknowledging the fictional nature of the anime and the flexibility it allows in bending real-world mathematical logic.

Keywords

💡Limitless

Limitless is a technique used by the character Satoru Gojo in the anime 'Jujutsu Kaisen'. It allows him to distort and manipulate space, making it nearly impossible for opponents to reach him. The concept is central to the video as it ties into the mathematical concept of limits and infinite series. The video explains how Gojo's technique can be seen as a practical application of calculus, particularly in the manipulation of space to create an infinite series of subdivisions that an opponent must traverse, which is theoretically impossible within a finite time.

💡Achilles and the Tortoise

This is one of Zeno's paradoxes, used in the video to illustrate the concept of infinite series and the idea that motion could be impossible if one must travel an infinite number of halves to reach a destination. The video uses this paradox to introduce the theme of infinite tasks and the limitations of motion, which is then connected to Gojo's Limitless technique and its mathematical interpretation.

💡Super Task

A super task refers to the concept of completing an infinite number of tasks in a finite amount of time. In the video, this is used to discuss the paradoxical nature of Zeno's arguments and to lead into the discussion of how calculus deals with infinite series. The video suggests that Gojo's Limitless technique can be seen as a super task where space is divided into an infinite number of parts, which an opponent must traverse to reach him.

💡Calculus

Calculus is a branch of mathematics that deals with limits, functions, derivatives, integrals, and infinite series. The video uses calculus as a framework to explain Gojo's Limitless technique, particularly in terms of limits and infinite series. It suggests that Gojo's ability to manipulate space can be understood as a mathematical function where the limit of an infinite series is never reached within a finite time.

💡Limit

In mathematics, a limit is the value that a function or sequence 'approaches' as the input or index approaches some value. The video explains how the concept of a limit is crucial to understanding Gojo's technique, as it relates to the idea that an opponent can approach but never reach him due to the infinite subdivision of space.

💡Epsilon and Delta

Epsilon (ε) and Delta (δ) are terms used in mathematical definitions of limits. Epsilon represents an arbitrary small positive number, and delta represents a corresponding small positive number for the input. The video uses these terms to explain how Gojo's technique can create a situation where no matter how close an opponent gets (within delta), they can never reach Gojo because the space between them is infinitely divisible (epsilon).

💡Infinite Series

An infinite series is a sum of an infinite number of terms. The video discusses how Gojo's Limitless technique can be seen as creating an infinite series of subdivisions in space, which an opponent must traverse. It uses the example of the sum of 1/2, 1/4, 1/8, etc., to illustrate how an infinite series can be approached as a limit.

💡ASM (Asymptote)

An asymptote is a line that a curve approaches but never touches. In the video, the concept of an asymptote is used to describe Gojo's position in space relative to an opponent. As time approaches infinity, the opponent's position approaches Gojo's (the asymptote) but never reaches it, illustrating the infinite nature of the task.

💡Function

In mathematics, a function is a relation between a set of inputs and a set of possible outputs. The video uses the concept of a function to describe the relationship between similarity to a character (input) and a corresponding 'bum' value (output). This is used as an analogy to explain how Gojo's technique can be seen as a function where the input (an opponent's position) approaches a certain output (Gojo's position) but never reaches it.

💡Graph

A graph is a visual representation of data, typically with axes representing different variables. The video uses graphs to illustrate the concepts of limits, infinite series, and asymptotes in the context of Gojo's technique. It shows how a graph can represent the relationship between time and position, and how an opponent's position can approach but never reach Gojo's position.

Highlights

Gojo Satoru's Limitless technique is super mathematical, allowing him to distort and manipulate space.

The technique makes it impossible to reach Gojo by creating an infinite number of subdivisions in space.

The concept is explained using Zeno's paradox of Achilles and the Tortoise, which questions the possibility of motion.

The paradox suggests that Achilles can never catch the tortoise because he must cover an infinite number of half distances.

The idea of an infinite number of tasks in a finite amount of time is a supertask, which is foundational to calculus.

Gojo's power is likened to calculus, where limits are used to understand the behavior of functions as they approach certain values.

The concept of limits in calculus is used to explain how Gojo's technique can make him unreachable in a finite time.

An example using a graph illustrates how limits work in calculus to pinpoint values with arbitrary accuracy.

The idea of infinity in Gojo's technique is compared to an infinite sum, which can be understood through limits in calculus.

The sum of an infinite series can be evaluated by taking the limit as the number of terms approaches infinity.

The concept of motion in the real world is contrasted with the fictional world where Gojo's technique can defy logic.

Gojo's Infinity is described as the convergence of an immeasurable series, slowing down any approach to never reach him.

The technique is visualized as a graph where position versus time approaches a vertical asymptote, representing Gojo.

The video concludes by relating Gojo's mathematically-based technique to the concept of an asymptote in calculus.

The video also mentions the existence of a Patreon for those who wish to support the content.

The video invites viewers to explore more anime-related math videos and supports the channel through Patreon.

Transcripts

gay akutami kind of sucks at math don't

take my word for it look see he can

barely count he mixed up the numbers 5

and 50 why is it then that the coolest

power in jjk is super mathematical if

you haven't figured it out by now I'm

talking about Limitless Gojo's technique

if you clicked on this video I'm sure

you're familiar with it but on the off

chance you aren't Limitless allows Gojo

saturo to distort and manipulate space

one of the uses of this makes it

literally impossible to reach him but

what does that mean gig explains this

with the story of Achilles and the

Tortoise imagine Achilles racing a

tortoise but the tortoise has a head

start this is one of Zeno's paradoxes

who is an ancient Greek philosopher he

argues that it's impossible for Achilles

to reach the tortoise which sounds

stupid but the reasoning is tricky first

Achilles has to go halfway to the

tortoise then another half of that then

another half Etc in essence he has to

travel halfway between him and the

Tortoise an infinite amount of times so

he'll never reach it but that's kind of

stupid I mean think about it if that

reasoning checked out then nobody

nothing could ever move which to be fair

is what Zeno argued motion would be

impossible since you can technically

subdivide any distance into Infinite

Parts first of all I can move and second

of all that still doesn't really explain

Go's technique yes I'm overanalyzing

this but just stick with me here and

it'll be worth it also I have a patreon

now so if you want to support me click

the link in the description now believe

it or not what we're debating here is

something that stumped mathematicians

for over 2,000 years this idea of doing

an infinite number of tasks in a finite

amount of time like traveling half of a

distance infinite times has a name a

super task actually vau did a video on

these a while back now these are

paradoxes but they're like incredibly

impractical who cares if you tell me

that motion is impossible that's not

going to stop me from punching you in

the face or somewhere else but believe

it or not this whole idea is literally

the foundation of calculus Gojo's power

is literally calculus here let's take a

simple example on the x- axis is how

similar someone is to meami and on the

y- axis the chances of being a bum a

simple linear relationship I'll call it

bum of X now let's say that I'm about

53% similar to Mega again I'm not proud

but just looking at the graph I can

pinpoint How likely I am to be a bum but

there's always going to be some

inaccuracy in where I put this dot now

let's say I know I'm within about 5% of

53% similar to Megami again I'm not

proud but then we can draw boundary

lines on the X and Y axis so we know how

Bumm I am lies somewhere in this

rectangle okay now let's say Gojo looks

at me with his six size and he can

quantify that I'm exactly 53.2 45%

similar to Megami or something like that

that corresponds to some bum value B I'm

leaving it arbitrary for a reason now we

can let the horizontal lines hone in

arbitrarily close to B no matter how

close they get we can always squeeze our

vertical lines to hone in on 53.2 45

in calculus what we can say is that the

limit as X approaches 53.2 45 of bum of

X is B and you can write that in this

compact mathematical notation we say

that this is the limit because for some

arbitrary margin of accuracy on the bum

axis we'll call the error Epsilon I can

always choose some range we'll call it

Delta on the Megami axis such that the

difference between our function value

bum of X and our value B is within the

purple lines now this whole time we've

been assuming my bumpiness is always

directly related to my similarity to

potential man but what if we're wrong

what if that's true for most points but

not our point maybe that percentage

corresponds to a bummin index up here

then it doesn't really matter how far we

zoom in these lines we'll always be

wrong about my bum value the important

thing to note here is that we actually

don't care what value B is what value

bum of 53.2 4 5 is it could be a point

anywhere along this vertical line all I

care about is what value bum of X

approaches as X gets arbitrarily close

to 53.2 45 this is the concept of a

limit so what does this have to do with

Gojo's Infinity well Infinity is kind of

just a limit we can think about Achilles

and the Tortoise as an infinite sum one2

plus 1/4 plus 1/8 plus 116th and so on

this is a bit clunky to write out so we

we have a more compact if a bit scarier

notation we read this as the sum from 1

to n of 1/ 2 to the^ I all we're doing

is plugging in values ranging from one

up to some arbitrary number n for I and

then adding up all those terms you can

see how these two statements are

equivalent but what if we let N be

Infinity well that's impossible in the

real world but we have a workaround now

instead of actually plugging in Infinity

just take the limit as n approaches

Infinity of the

sum this is the same idea as before we

just want to see what value or sum

approaches as n gets larger and larger

and larger and approaches Infinity we're

not actually plugging in Infinity it's

just a clever workaround so we don't

have to deal with it anyways you can try

to work this out for yourself if you do

this just in a calculator and plug in

like a really big number for n you'll

see that the value that it seems to

approach is one which is what we expect

all that means is that after traveling

an infinite halves of a distance you'll

reach the end which in hindsight seems

obvious so everything I've mentioned

seems to support our sense of reality

motion is real but in the world of

fiction and

sorcery such logic can be be toyed with

we have our preconceived notions about

movement and motion but Gojo being able

to distort space messes with this here

let's look at the Jutsu kaisen Wiki The

Infinity is the convergence of an

immeasurable series anything that

approaches the infinity slows down and

never reaches the user this is because

the technique takes the finite amount of

space between the two subjects and

divides it an infinite amount of

times honestly I think that's kind of

word soup as we mentioned before you can

theoretically subdivide any amount of

space into Infinite pieces no Infinity

required but to be fair it is a shown in

anime or Manga I don't expect the math

to be airtight I'll interpret this as

such if you could approach Gojo for

infinite time he would be the limit he

makes it so that every half subdivision

of space takes the same amount of time

to Traverse here I'll try to visualize

this going back to the bum Gra all

replace the axes with time t on the

x-axis and position s on the y-

AIS this graph now shows a plot of

something moving at a constant velocity

through

space now let's say that Gojo exists at

a point in space corresponding to this

white line his technique Infinity has a

certain range to it that Gojo can

control so let's say that the boundary

is at this gray line now the graph will

stay the same before it enters

Infinity's range but once it does the

position versus time graph will become

an ASM totic function with Gojo at its

ASM toote essentially as time goes out

to Infinity the graph will approach his

line but will never reach it

Bingo Gojo is at the limit of this graph

as time approaches Infinity but you can

never reach him in finite time so in the

end Gojo is an ASM toote and you learn

some

math if you enjoyed that I have another

anime slm video you can click on the

left and if if you want to support these

videos I mentioned I have a patreon

Linked In the description and on the

channel profile bye-bye