Chapter 220: A Mage’s Aspiration |
Morale Support: Scherzo
Patreon: https://patreon.com/ScherzoTranslations
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“This…”
Roger, having advanced to the intermediate level, naturally understood Reiner’s meaning.
If imaginary numbers were used to replace the vertical coordinate axis, then numbers could simply be written in the form of X + Xi [1]. Additionally, points expressed in this form can directly use conventional arithmetic operations without needing complex coordinate calculations.
As everyone knows, the Cartesian Coordinate system is closely related to spell models. Coordinate and vector calculations are required courses for every mage. If the imaginary number system is introduced, the efficiency of constructing spell models will be greatly enhanced.
More importantly, the introduction of imaginary numbers directly expands the dimensions available. It’s like comparing a single number line on the blackboard to the entire blackboard itself: there’s no doubt which one is broader.
“But this is just a number game. Even without imaginary numbers, coordinate calculations can still proceed, and using imaginary numbers to explain motion equations is just too strange.”
While using imaginary numbers does make constructing spell models more convenient, magic should avoid introducing unnecessary elements. Imaginary numbers, in this context, were redundant.
“Everyone, I believe you all know the Newington-Holland equations, correct?”
Reiner didn’t respond to Hannah’s question directly but asked another instead.
“Of course. These are the four equations describing electromagnetic fields, with which the two gentlemen proved that light is an electromagnetic wave.”
Roger answered, curious why Reiner brought this up.
“What are you trying to say by mentioning this?”
“If we introduce the concept of imaginary numbers into these four equations, what conclusions would we reach?”
Reiner began writing formulas on the blackboard, skillfully transforming them into a form involving imaginary numbers.
Without a doubt, the Newington-Holland equations with imaginary numbers were more concise and easier to understand.
“I believe you have all seen the formula in the thesis. If we introduce this formula into the equations and perform calculations, we can discover that the sine wave electromagnetic field changing over time can directly be converted into exponential form. Simultaneously, the exponential form can also be expanded into trigonometric functions.”
Reiner’s explanation led the review committee members into deep contemplation, as his words seemed to hint at some astonishing truth.
“…Wait, you mean…?”
Igor, a member of Storm Council who often participated in discussions about the nature of light, was a staunch supporter of the wave theory. Reiner’s words made his mind race, and he thought of many things.
“The Sirius Transformation and Sirius Series [1] mean that any exponential function can be converted into the sum of countless trigonometric functions…in other words, endless countless waves…if this is reflected in the real world, it means…”
Mumbling to himself, Igor widened his eyes, finding it hard to believe these words came from his mouth.
“Everything can be expanded into Series and turned into countless overlapping waves. This world is made up of countless overlapping waves!?”
“How is that possible…”
Roger was astonished, his mouth agape. He hadn’t expected pure mathematical deduction to touch upon the truth of the world in some sense.
Of course, Igor’s conclusions were speculative. He had no way to prove them theoretically or experimentally, so he couldn’t obtain feedback from the world.
But this was an incredibly innovative idea, providing mages dedicated to exploring the world’s truth with a new direction.
“This indeed is a possibility. Perhaps only the lords of High Council can explore it further.”
Reiner shrugged, then continued.
“However, I believe this thesis’s value has been adequately demonstrated here.”
Hearing Reiner’s words, even Roger remained silent.
Imaginary numbers, a purely mathematical concept difficult to understand, unexpectedly allowed a glimpse of the world’s truth. This was unimaginable.
Yet, all of this was presented before everyone, making it irrefutable.
Seeing the opposition gradually quieting down, Reiner then said.
“Actually, this thesis was completed ten years ago. At that time, the Newington-Holland equations had not been proposed, and this thesis was judged to be worthless. Its author already died of illness and I only received this from the author’s mother, an old woman who couldn’t even read.”
His words surprised everyone. Ten years ago, the Newington-Holland equations hadn’t been proposed, and the application field of imaginary numbers was non-existant.
“At that time, everyone who read this thesis for the first time had the same reaction as you, believing it to be worthless because it didn’t contribute anything to the real world. If you don’t believe me, you can ask Lord Percival, who witnessed this thesis back then.”
Reiner spoke solemnly, glancing at Percival. The mage’s face was gloomy, and he remained silent.
“Indeed, as a mage, focusing on enhancing one’s magical power is not wrong. Efficiency and pragmatism are the principles mages adhere to. Spending time on seemingly meaningless mathematics is indeed foolish.”
In the vast conference room, where a pin’s drop could be heard, only Reiner’s voice echoed.
“New spell achievements are like flowers blooming on the hillside, beautiful and enticing. But we must not forget that beneath these blooming flowers, in the soil, lies the roots.”
He announced, his voice gradually growing louder and louder.
“If elementalism, alchemy, laws and the other magic departments are flowers, then mathematics is the foundation of everything. We cannot expect every theory to bloom beautifully because some things are fundamentally the roots! Judging things simply by their utility and contribution to magic development is too short-sighted.”
Reiner’s words widened Roger and others’ eyes, but at the other end of the long table, one person clenched his fists quietly.
It was Savros.
He had spent ten years compiling a dictionary that might never be useful. Wasn’t this also considered “meaningless” work by some?
A strong resonance surged in Savros’ chest, making his nose tingle and his eyes slightly moist.
“Everyone, we are mages. Lord Braggs defined mages not as wielders of power but as seekers of truth. Many may have changed their initial reasons for learning magic. They pursue greater power, higher status, or a perfect life through magic. I don’t blame these people because these are also human pursuits.”
Reiner warned.
“But don’t forget, there are still people who learn magic only to answer their doubts and to open the door to truth. These people should be respected. Yet, in reality, many who gained power and status through magic often mock these ‘fools’ dedicated to research and judge their achievements, considering those theories meaningless.”
He walked from the blackboard to the long table, approaching Percival.
“To those who recklessly ridicule others’ research, I have only one word to say.”
Reiner paused, then articulated.
“Unworthy.”
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T/N:
[1] Imaginary numbers standard form is a+bi, but the author uses a representation where x represents any number.
[2] I believe this is inspired from Fourier series and transformations.
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