Satoru Gojo (五条 悟 ごじょう さとる) is the strongest Jujutsu sorcerer in the big hit anime, Jujutsu Kaisen, and what makes him the strongest is definitely his Jujutsu technique, Limitless (無下限呪術 むかげんじゅじゅつ). The author Gege Akutami (芥見 下々 あくたみ げげ) sensei used the idea of an infinite series in mathematics to create the technique and he explained it in the comics. But sadly…I couldn’t get it at all because I have no clue what an infinite series is about (I was really bad at math…). So, in case you are having the same problem with me, I studied mathematic just a tiny little bit and am going to make an easy-to-understand (I hope) explanation of Satoru’s strongest technique today!
Zeno’s paradox of Achilles and the tortoise and an Infinite series
In the comic, Akutami sensei told us to google “Achilles and the tortoise” and “an Infinite series” to understand the Limitless. So, I did, and this is what I’ve got.
Achilles and the tortoise
Achilles and the tortoise is one the ancient Greek Philosopher Zeno’s paradoxes. The quickest runner Achilles and a tortoise run in a race. Since the tortoise is slow, it starts 100m ahead from Achilles. Of course, Achilles will reach the tortoise…..not.
According to the procedure proposed by Zeno, the quickest runner will never reach the slow animal. Why?
- Achilles starts 100m behind the tortoise.
- By the time Achilles reaches the point A1, the tortoise will move forward to the point A2.
- By the time Achilles reaches the point A2, the tortoise will move a little bit forward again to the point A3.
- By the time Achilles reaches the point A3, the tortoise will move a little bit forward again and again to the next point.
- Again and again and…
- And, by the time Achilles reaches the point A100, the tortoise will still move forward…
So, we can keep doing this infinitely and Achilles will never reach the tortoise. Well, we know this is not true, at some point, Achilles does reach the tortoise, but it seems he can’t, by the procedure and this is the paradox part. But, to understand Satoru’s Jujutsu technique, solving the paradox isn’t important.
An Infinite series
Let’s say Achilles runs 1m per second and the tortoise 0.1m/sec and Achilles will reach the tortoise in 2 seconds. How do we calculate it using the procedure above?
- 1.9 seconds after the start, Achilles will be at the point of 1.9m, and the tortoise at the point A1(1.99m).
- 1.99 seconds after the start, Achilles will be at the point of A1 (1.99m), and the tortoise at the point A2(1.999m).
- 1.999 seconds after the start, Achilles will be at the point of A2(1.999m), and the tortoise at the point A3 (1.9999m)….
So, to reach the tortoise, it seems we need to add up the seconds infinitely and this “adding up infinitely” is an Infinite series. It seems it never reached to 2 seconds. However, it just seems so because this is not the right way to calculate the time Achilles reaches the tortoise. But how will infinite (adding up infinitely) reach finite (2 seconds)? This is the paradox. But again, we ignore the paradox part today. We should focus on this part of the calculation below.
Satoru’s technique brings this part in reality. So, as an object gets close to Satoru, it gets slower and slower as if it even stops and can’t touch him.
And more, according to Akutami sensei, he added “zero” and “negative natural numbers” to the infinite series. The image is like this. This is why the technique is called “Limitless”. Satoru’s Jujutsu technique is 無下限呪術. If you translate directly, 無(no) 下限(lower limit) 呪術(curse technique).
How the Limitless works: Red, Blue and Purple
The Limitless generates the space with the energy which attracts targets. And the technique that strengthen the energy is the Cursed Technique Lapse: Blue. The technique which reverses the energy is the Cursed Technique Reversal: Red. And the technique which combined there 2 techniques is the Hollow: Purple.
The Domain Expansion: Infinite Void (無量空処 むりょうくうしょ)
You might already know what the domain expansion is, but just in case..
Domain Expansion The pinnacle of Jujutsu battles. You use cursed energy to construct an innate domain imbued with a cursed technique in your surroundings.
About the Infinite Void, the special-grade cursed spirit Jogo (漏湖 じょうご) said,
You can see and feel everything! but the information is never complete so that you can’t do anything.
何もかも見える！ 全て感じる！！いつまでも情報が完結しない！！ 故に何もできん！！
Nanimo kamo mieru! Subete kanjiru!! Itumademo jouhou ga kanketsu shinai!! Yue ni nani mo dekin!!
source: Author Gege Akutami 『Jujutsu Kaisen』2 published by SHUEISHA Inc. in 2018, p162 / Anime season 1 episode 7
Also, Satoru himself explained about his domain,
This is the inner world of Limitless. Perception, Communication Every action involved in living is forcibly carried out an infinite number of times. When granted everything, you can’t do anything but just die peacefully,
ここは無下限の内側。”知覚” ”伝達” 生きるという行為に無下限の作業を強制する。皮肉だよね、全てを与えられると何もできず、緩やかに死ぬなんて。
Koko wa Mukagen no uchigawa. "chikaku" "dentatsu" ikiru to iu koui ni mukagen no sagyou wo kyousei suru. hiniku dayone. subete wo atae rareru to nani mo dekizu, yuruyaka ni shinu nante.
source: Author Gege Akutami 『Jujutsu Kaisen』2 published by SHUEISHA Inc. in 2018, p163 / Anime season 1 episode 7
It’s like this. If you press “play” button on your player to listen to “Under the Sea”, it starts from “Ariel, listen to me.” and plays the whole song to the end. But if you hit the button repeatedly and infinitely (if it’s possible), it would go like “Ari,Ari,Ari,Ari,Ari…” and never complete the song, and the player dies peacefully…
Well, I don’t know if it would be peaceful, but this is the Jujutsu technique Limitless which makes Satoru Gojo the strongest Jujutsu Sorcerer. Oh, there is one more factor that makes him the strongest, his eyes “Rikugan (六眼 りくがん). The combination of his special eyes and the Limitless make him the strongest! If you want more information about Rikugan and Satoru himself, read my article →Satoru Gojo’s attraction and strength hidden under his eye mask Jujutsu Kaisen 【Analysis and Quotes】
References: Zeno's paradoxes - Wikipedia
Atarimae! (Japanese)