Episode 40 — Starting from Zero.
Imagine the nightmare of trying to perform multi-digit multiplication or division using a cumbersome system where values don’t change based on their position—like Roman numerals.
Every time you need to calculate something, you have to bring out a complex counting board, and even an expert has to spend several minutes sweating over it… That kind of inefficiency is the "common sense" of this world.
So, what happens if I inject a potent catalyst called "positional notation" into this society?
Knowledge at a middle-school level would be enough to expose fraud in ledgers, and the precision of architectural design and medicinal compounding would skyrocket. Logistics, taxation—everything would be bound by the chains of "accuracy."
(…To be honest, it feels like I’m forcing the gears of history to turn a bit too fast. But hey, apparently the ancient Babylonians used a similar concept, so it should be fine.)
As I was pondering this, Gustav appeared with a woman in tow.
“Mr. Zect. This is Marta, the representative of the citizens' union.”
“It is an honor to meet you, Mr. Zect. …Or perhaps I should call you the Reformer of this city?”
Marta was a woman in her mid-fifties. she possessed the sharp gaze of someone who had survived harsh medical front lines, tempered by an intellectual composure.
“Just Zect is fine. …I assume you’ve heard the plan from Gustav? A triple-shift school and clinic—think you can handle it?”
“I have no objection to the system itself. However…”
Marta stared intently at the memo pad sitting in front of me.
“The concept of ‘Zero’ that I heard from Lord Gustav… I simply cannot wrap my head around it. What could possibly be the point of counting ‘nothingness’?”
I figured we’d end up there.
I lined up two fresh sheets of paper and picked up my pen.
On the left sheet, I wrote "102" using the local numeral system—a method similar to Roman numerals where the symbols change for large units. On the right sheet, I wrote "102" in Arabic numerals.
“Marta. With the way you write in this world, distinguishing between one hundred and two (102) and twelve (12) requires either a special symbol or a wide, deliberate gap. What if the writer’s hand slips and the gap becomes narrow? Or what if they forget to write a symbol entirely?”
“…It would lead to the number being misread as something else. In medicine, such a mistake can result in a lethal error in compounding.”
“Exactly. But if you place this ‘0’ (Zero) as a ‘placeholder,’ the weight of a digit is determined solely by its ‘position.’ The ones place, the tens place, the hundreds place… No matter how large the number, it can be described using a combination of only ten symbols in a way that is impossible to misread. This is called ‘positional notation.’”
I went further and scribbled out some long multiplication on the paper.
A complex calculation between two three-digit numbers. In this world’s way, this would be a task for a master arithmetician using an abacus, taking several minutes.
“Thanks to the Zero, the numbers align perfectly in vertical columns. By keeping the places aligned and mechanically following the steps, anyone can reach the same answer. With this, calculation stops being a secret art for a few geniuses and becomes a simple task. Even a child will be able to calculate accurately.”
The color drained from Marta’s face visibly.
She was a doctor. She understood the importance of accurate measurement, accurate recording, and above all, "reproducibility" better than anyone.
“…Calculation will no longer be a privilege. Fraud in the ledgers will be exposed at a glance, and medicinal formulas can be shared across the land without a single drop of error. Mr. Zect, you are… by driving in a wedge named ‘Nothingness,’ you are trying to lock the very order of this world into place.”
She took the pen from my hand, wrote a large ‘0’ on the paper, and stood in thought for a moment.
“I understand. I shall teach the children in the morning, save lives in the infirmary in the afternoon, and enlighten the adults of their ignorance in the evening. …However, I shall insist on preparing the evening school’s soup in an extra-large pot. Winning over the stomachs of those who attend is a rational strategy, is it not?”
To grasp the concept of ‘Zero’ in a matter of minutes—Marta was going to be an even better principal than I expected.
“I appreciate you being so quick on the uptake. Bill Gustav for the expenses.”
After seeing the two of them off, I sank into the sofa.
…Phew. Now every resident of Felsen has become a potential recruit to handle my administrative work for me in the future.
“Mew.”
Tama, on my lap, started kneading my stomach with her paws.
I know, Tama. I’m very seriously rewriting the world just for the sake of my own peaceful slumber.
But, well…
Remembering the look in Marta’s eyes as she trembled at the concept of Zero, and seeing Gustav’s face burning with hope, I feel like I might want to watch this scene a little longer—watching a new city being built from this state of absolute "Nothingness." From Zero.