This will be more of a maths and history thing than it is a post heavily on Jujutsu Kaisen so feel free to skip it if you like~
I had no intentions to write something like this. I don’t even have a category for such posts. When I was reading the manga and saw that Gojou’s infinity technique was called convergence, I just laughed because it didn’t make any sense and moved on. Yesterday morning I was searching for something else on Twitter when I came across the infographic below on his techniques, which seemed like it was making rounds. So I said…. why don’t I bore my dear readers out of their minds and explain why this analogy wouldn’t work!
I love you all, I promise.
Now, this is just meant to be fun. I’m not at all “angry” or “peeved” about this or think it’s a plot hole or anything. It’s almost every day where we see science-related analogies brought into anime, be it correctly or not. If we have been blogging buddies for a while, it should be given now that I love writing on this topic. And Saturday felt a nice day to talk a bit about the history of zero, how our religious beliefs have shaped science, and why Gojou’s technique is not convergent.
Let me talk about what is correct in the infographic above first. That pizza slice analogy is a very useful description to make sense out of the idea of summing up infinitely many pieces to get a whole. The OP refers to the Zeno paradox with Achilles and the tortoise, which again, is an example of convergent series. If we were to take a trip down the memory lane and remember what it was about; Zeno of Elea claims that if a tortoise and Achilles were to race where he starts the race with some handicap, he could never catch up to the tortoise because first, he’d have to run the half of that handicap. Then half of the remaining half, and it would continue for a very long time, but he could never catch the tortoise. Wikipedia has a cute illustration for this:
How can we express this series in mathematical terms? Achilles first covers a distance, let’s say, 1 meter. Then, covers half of the rest, which is 1/2. Then, half of that, which is 1/4. The denominator progresses as powers of 2. The most general expression for this series, for any n>1:
Put n=2 and we’ll see the sum is equal to 2. What this says about the series is, going back to my original point, that you can get something finite by adding things that are infinite. This is also the reason why Achilles can outrun the tortoise because all the infinitely small pieces do not increase the distance. They add up to a finite distance, not to some range that you can’t ever cover. Hence, when Gojou manipulates the space and adds ‘infinitely small pieces of space’ what it does is to add up a certain distance and all we have to do is to cover that gap, hold his hand and go on a picnic or something. Sorry, Gojou.
As for “Amplifying the limitless…” part. The image on the left is just the graph of 1/x. This function has a limit, doesn’t matter if the function itself doesn’t intersect the y-axis and actually take the value x=0. I see no relation to what is said next to it. What was the point in adding this, I didn’t understand but … good job trying, I guess?
Some Historical Bits on Zero
The reason why Zeno was preoccupied with thoughts similar to this is that he wanted to prove that movement was an illusion. Along with Parmenides, the prevalent school of thought in Miletos dictated that whatever we saw were illusions and we could only trust our minds. And Zeno states that if his proposition made sense but we still saw Achilles outrunning the poor tortoise who just wants to go home, then it just means we are under an illusion.
Although Zeno seems like a cheeky guy who’d come up with these paradoxes just for the heck of it (Gojou, is that you??), this discussion led to other important discussions that contributed to our understanding of atoms. To mathematically express and answer this paradox, we require two concepts: zero and infinity. However, Aristotle strictly rejected the idea of ‘void’, ‘absolute infinity’, atomism, and considered all substance to be continuous. Our universe was contained and it had a finite shape.
Indian religions and Islamic beliefs, on the contrary, had a different view of the world and were comfortable with the existence of the infinite and the void. It didn’t take too long for Islamic countries to take Greek geometry and the Indian numeral system to come up with the Arabic decimals we use today, zero included. Algebra, integration, and algorithms we know today all originated from the same period. It makes sense when we say language, science and art are all born out of necessity one way or another, but actually reading on the details and how the fields we think are not that related with our post-modern thinking are more correlated than we assume is quite fun. I added the books I’ve previously read on these topics, considering the tiny chance you might be interested in further reading. It’s not easy to find proper popular science books.
But wait…. there’s more??
When I wrapped up the post last night and was on my way to read manga in the comfort of my bed, I wanted to add the link to the infographic before I turn off my laptop and to my surprise, there was an updated version! With additional particle physics this time!! Oh boy….
Mass is a really complicated concept in physics, let alone making sense of negative mass or negative probabilities. Closest concept that has a physical reality is the negative pressure densitiy created by the Casimir effect. With our everyday intuition that is governed by classical, non-relativistic physics laws, it’s straightforward to think that if something has a mass, then it occupies a certain volume in space. Even with that logic, negative mass do not equate to void because void means no mass. But the particles of lights, photons, do not have mass either. They do have fields where they can interact with other particles though, and those fields have importance. I’ll probably just stop here before it turns into Particle Physics 101 and wish you a nice weekend. I certainly didn’t need to know physics to enjoy yesterday’s episode of Jujutsu Kaisen, it was a masterpiece!!