Chapter 22: Mathematics
Senju Tobirama wasn't being sarcastic—he was simply stating facts.
Even though he'd used one more clone than Hajime during the Rasengan trials, at this stage of development, stabilizing the technique was far more important than considering its combat practicality. Combat would come later.
The clone responsible for generating the spin released the chakra sphere and stepped aside. Tobirama's main body and another clone carefully supported the Rasengan, moving it toward a nearby tree trunk.
The Rasengan didn't disappoint. It embedded itself effortlessly into the bark.
Tobirama was thoroughly satisfied with the power it displayed. At last, the Rasengan could be considered complete, at least in its initial form.
After dissipating the chakra, the three Tobiramas regrouped. Moments later, another Rasengan appeared in their hands—proof that his earlier success wasn't just dumb luck. He had truly grasped the technique.
Dispersing the chakra again, Tobirama noticed that Hajime looked like he wanted to ask something. He beat him to it.
"I'll explain after I rest. I really need to lie down first."
Without waiting for a reply, Tobirama made his way to the spot where Hajime had been lying earlier, flopped down, and within seconds, the soft sound of snoring filled the air.
He was exhausted.
Despite his natural genius for jutsu development, the result hadn't come without a massive investment of effort and trial-and-error. That said… Hajime couldn't help but feel this kid had a real knack for leaving people in suspense.
——
Tobirama slept for four to five hours. Once he'd eaten and rehydrated, he finally sat down to explain everything.
"Usually, to control the shape of a Rasengan, you need to find a specific balance," he began.
"Most shinobi rely on intuition, their senses, and countless attempts to figure it out. It's not uncommon for someone to spend three to five years just to find the right 'feel' for it."
He wasn't wrong. If Hajime remembered correctly, even the Fourth Hokage had taken about three years to develop the Rasengan.
"But I'm different. I used a dumb method," Tobirama continued, "and turned that abstract feeling into actual numbers."
"Numbers?" Hajime was intrigued. "Go on."
"When using chakra for the Rasengan, it can be divided into two parts: the chakra that causes the rotation, and the chakra that stabilizes the shape. The question is—how much of each should you use?"
"There's a specific answer to that. Say we fix the internal rotating chakra at a base value of 100. The external chakra required to keep that shape would, naturally, need to be greater than 100 at first. Makes sense, right?"
"When the internal spin is at a low speed, you need 57 units of external chakra to maintain the shape."
"At medium speed, the required amount drops to somewhere between 35 and 23."
"At maximum rotation speed, it drops further to 15."
"I figured this out through pure trial-and-error. Nothing to do with talent—it really was just the dumbest method possible."
"…"
Hajime understood that Tobirama wasn't referring to literal units, but rather to ratios or proportions. Still… this was a very grounded approach. He had never thought of developing a jutsu using such a data-driven method.
And he was fairly certain the Fourth Hokage hadn't either.
"Surprisingly effective," Hajime muttered. "But precise chakra control like that isn't exactly common."
It was one thing to be told when to use '57'. It was another to actually deliver that exact amount with chakra.
Tobirama nodded. "Which is why consistent practice is essential. You can produce a Rasengan with rougher numbers, of course. But when developing a jutsu from scratch, it's about precision."
"These numbers—57, 15, and so on—aren't even the final values. I'm planning to fine-tune the internal/external chakra ratio to another decimal place."
"…"
There wasn't much more Hajime could say. "Not surprised. That's so very you."
Tobirama stuck with his "dumb method" and spent another week refining the data. In the end, he successfully increased the precision by another order of magnitude—down to decimals. But at that point, Hajime knew he couldn't keep up.
He was just aiming to use the Rasengan reliably in battle. He didn't need the optimal or maximum version.
According to Tobirama, even if you made a perfectly balanced Rasengan, the damage increase would only be from 100 to maybe 110. The gain was minimal.
Hajime was realistic about his limits. Chakra control wasn't his strongest suit, and he knew what he could and couldn't do.
Of course, even Tobirama hadn't achieved the combat-ready version yet. For him, the standard was to "cast Rasengan instantly with one hand," ideally while using Body Flicker.
Still a long way off.
Regardless, with the preliminary development complete, it was time for Tobirama to leave. His injuries were fully healed now, and truthfully, he'd already stayed too long because of the Rasengan.
When he expressed his intention to leave, Hajime didn't try to stop him. The guy had been "milked" enough—it would be rude to keep squeezing.
"This is it, then. I have a feeling we'll meet again someday," Tobirama said after walking a little ways from camp.
Though their meeting had been brief, and Tobirama had gained much (and maybe lost more), the rogue shinobi hidden deep in the mountains had made a deep impression on him.
He was an exceptionally skilled sensor, and had already memorized Hajime 's chakra signature—subtly but deliberately.
"We'll meet again? Maybe. People like us—rogue ninja—can be wiped out at any moment. The Senju and Uchiha… they'll never understand that kind of fear," Hajime replied.
Tobirama opened his mouth to speak, hesitated, and then said,
"The Senju are strong, yes. But… have you ever heard the phrase 'Swift as lightning, fluid as flowing water'?"
Hajime blinked. What was that supposed to mean? Was there an even stronger clan than the Senju?
Tobirama had ignored the Uchiha entirely—which didn't surprise him.
Tobirama shook his head, not explaining further. "The world's in chaos. No one knows what's coming. Like I said… goodbye, and maybe we'll meet again."
No need to drag it out. He turned and left.
Hajime watched him go, then returned to camp.
Tobirama had made a dramatic exit—if you ignored the fact that he was carrying a scroll full of tea leaves on his back.
——
Though Tobirama was gone, his legacy wasn't.
When Hajime returned to camp, he found something on the makeshift wooden desk where Tobirama had been staying—a lone scroll.
Hajime smiled. Knew it.
He walked over, opened it, and found it contained a Water Release technique: Water Severing Wave.
This wasn't a gift in return for the tea—it was a trade for the Rasengan.
Even though Tobirama had cracked the toughest part of its development, the idea and structure of the Rasengan had originated from Hajime . In invention, that critical 1% of insight outweighs the other 99% of execution.
Tobirama had received the Rasengan. In return, he offered a jutsu of equivalent offensive power.
Hajime carefully stored the scroll. As expected, Tobirama was a man of principle.
People called that version of Tobirama—grizzled, older, and politically ruthless—a cunning manipulator who'd do anything to achieve his goals. But after actually working with him, Hajime was ready to let go of that stereotype.
Tobirama was a decent man: grateful, fair, and true to his word.
Once he finished his book The Art of Communication, Hajime thought, maybe he'd write another one:
The Art of the Deal.