Explaining Gojo's Infinity with Calculus
Summary
TLDRThe 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
- ๐ The script discusses the mathematical concept of infinity and its relation to the anime character Gojo Satoru's technique 'Limitless'.
- ๐ 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.
- ๐งฎ 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.
- ๐ 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.
- ๐ค The script questions the practicality of these mathematical concepts in the real world, contrasting them with their application in fictional settings.
- ๐ฏ 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.
- ๐ 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.
- ๐ 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.
- ๐ 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.
- ๐ฅ 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
๐งฎ 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.
๐ 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.
Mindmap
Keywords
๐กLimitless
๐กAchilles and the Tortoise
๐กSuper Task
๐กCalculus
๐กLimit
๐กEpsilon and Delta
๐กInfinite Series
๐กASM (Asymptote)
๐กFunction
๐กGraph
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
Browse More Related Video
The ENTIRE Jujutsu Kaisen Power System Explained (Cursed Energy, Vows...)
What is a Singularity? | Eternally Curious #11
Lecture 36: System of Linear Equations
JUJUTSU KAISEN SHOCKED EVERYONE: SUKUNA LOSES, GOJO WAS TOO STRONG! BUT YUTA DIES IN GOJO'S BODY? ๐ญ
Proving God exists using Math
how to get the Fourier series coefficients (fourier series engineering mathematics)
5.0 / 5 (0 votes)