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.