Chapter 130 - 129: The Formula is Missing an Interference Constant

Chapter 130: Chapter 129: The Formula is Missing an Interference Constant

"Huh? It doesn’t seem as complicated as the rumors make it out to be. Isn’t it just simple formula calculations in the end?

"The complexity of these formulas is high school level at best... and the notation is far from concise."

This was the first thought that popped into Gaode’s mind after finishing the notes on the Six Major Rune Rules.

"So, to ensure the Magic Array holds up as much as possible, one should minimize the Actual Robustness Value or maximize the Theoretical Robustness Value.

"Minimizing the Actual Robustness Value means reducing the occurrence of two identical Runes connecting to decrease the number of interference pairs, and using as many lower-Energy secondary basic Runes as possible to increase the total number of Runes.

"Maximizing the Theoretical Robustness Value means increasing the number of Runes and Rune pairs, or selecting Magic-guiding Materials with low Magic Resistance.

"However, while increasing the number of Rune pairs, the number of interference pairs will also increase..."

This was the second thought that flashed through his mind.

He subconsciously began to comprehend and derive the formula. After going over the Six Major Rune Rules one more time, Gaode firmly committed them to memory, synthesizing them with his own understanding. Only then did he feel confident enough to continue reading.

The next thing to catch his eye was a very simple illustration.

The main body of the diagram was a large hexagon, cleverly divided into six equal regions by its six sides. Each region contained a pattern: four were identical hexagons, and two were squares. The patterns within these six equal regions all shared one side with the central hexagon. Furthermore, the center of each pattern was marked with either a "0" or a "1".

Below the illustration was an explanatory text:

"Assume a simple Magic Array can be formed by a single Composite Rune, which consists of seven basic Runes: five zero-level basic Runes and two first-level basic Runes.

"According to the Six Major Rune Rules, calculate whether this Magic Array can be successfully constructed on a Mithril material with a Magic Resistance of one percent, and on a brass material with a Magic Resistance of forty-five percent, respectively."

"There are even after-class exercises?" Gaode mused inwardly. Grabbing a blank sheet of drafting paper and a quill from the workbench, he began scribbling rapidly. SCRATCH, SCRATCH, SCRATCH.

"In this Magic Array, the maximum number of same-level Runes connected to each Rune is 4 q = 41.12, according to Rule One, the Magic Array can be successfully constructed.

"When the Magic-guiding Material is brass, R = 0.45. According to Rule Six, Q = m*N*(1-R) = 7*11*(1-0.45) = 42.35.

"q = E*n = 20.56*2 = 41.12.

"Since Q = 42.35 > q = 41.12, the Magic Array can still be successfully constructed on the brass Magic-guiding Material."

Gaode calculated the results in less than two minutes.

It was indeed a rather basic and simple computation problem. As long as one understood the Six Major Rune Rules, even an elementary school student could quickly find the solution. Calculating the answer wasn’t praiseworthy; what truly deserved praise was the person who had summarized these six rules. It was precisely because of these Six Major Rune Rules that a complex problem could be solved through a simple formula calculation.

Gaode was mildly delighted to realize he still had the chance to solve math problems in this world. The familiar muscle memory was awakened. Solving problems was inherently an immensely enjoyable activity.

"Why do I feel like something is missing?"

Looking at the formulas he had laid out on the paper, Gaode unconsciously stroked his chin, his eyes revealing an indescribable sense of confusion and unease.

His gaze swept over the formulas derived from the basic Rune rules; every step strictly adhered to the theorems. Yet, the sense of emptiness in his heart lingered from the moment it appeared. That feeling of "missing something" stubbornly persisted.

If he had to describe this feeling, it was like solving a math problem where all the conditions provided in the prompt had been used, yet some hidden critical clue had been overlooked, leading the entire problem-solving process astray.

"It must be an illusion..." Gaode thought. After double-checking a few more times and confirming there were no omissions in his calculations, he finally put down the answer sheet, stopped dwelling on it, and continued reading.

"According to the formula calculations based on the Six Major Rune Rules, this simple Magic Array can be successfully constructed on both Mithril and brass materials.

"In actual practice, however, the construction of this Magic Array on the brass material failed... Why did it fail?"

These were the only two sentences at the end of the notes.

Below the question of why it failed was a line of annotations written in a smaller font:

"Rules One through Five have been verified as correct through multiple methods on numerous occasions. The cause of failure must lie in an error in the formula for Rule Six.

"The formula for Rule Six already encompasses all the variables that appear in Rune combinations, and its calculation method has been derived multiple times. It is the calculation method that best aligns with the laws of Rune arrangement and has the lowest error rate. The error rates of other calculation methods are staggeringly high and clearly unreasonable.

"Where is the problem?"

Looking at the final question mark, Gaode frowned, his thoughts involuntarily mobilizing.

Why did it fail?

The Theoretical Robustness Value on the brass material was clearly greater than the Actual Robustness Value of the Magic Array. According to the rules, this should have been sufficient to support the construction and operation of the Magic Array. But the facts proved otherwise.

That meant the annotation was right: the formula was flawed.

But where was the error in the formula?

Gaode glanced again at the formula listed under Rule Six:

Q = m*N*(1-R) > q = E*n.

That peculiar feeling of "missing something" surfaced in his heart once more, like an invisible hand gently plucking his heartstrings. As his eyes repeatedly roamed over the formula, Gaode became increasingly certain that something was indeed missing.

"It’s likely a structural defect in the formula itself, missing some crucial correction term..." Driven almost by instinct, Gaode arrived at an explanation.

People who study math and excel at it develop a certain ability through long-term problem-solving training, accumulating experience, and seeing enough formulas. This ability is commonly known as mathematical intuition.

Mathematical intuition can help them "perceive," to some extent, the potential structure and form of a formula. It allows them to make a preliminary guess about a problem’s solution or a formula’s morphology based on their past experience and understanding of formulas in general. This process can include pattern recognition, symmetry perception, and function behavior prediction.

Of course, while mathematical intuition is an important tool—extremely useful in the exploration and hypothesis stages to guide mathematicians in proposing assumptions and conjectures—it cannot replace actual proof. Genuine formulas and conclusions must still be verified through rigorous logical reasoning and proofs.

Immersed in the formula, Gaode instinctively followed his intuition and unconsciously added a "C" to the end of the Actual Robustness Value "q = E*n".

q = E*n*C.

Then, he nodded in satisfaction.

Looking at it this way was much more comfortable.

Gaode shifted his gaze back to the final question in the notes. He thought for a moment before finally providing his own answer below it.

"The formula is missing an interference constant C."

A constant refers to a number with a fixed, unchanging value in mathematics. It does not change with variations in other variables; it is a fixed number that can appear in any formula. Constants provide stability and fixed reference points for formulas, enabling them to describe and predict various phenomena and processes more accurately.

Anyone who has received a high school education would notice that many formulas, whether in physics or mathematics, often contain a fixed, unchanging constant value in addition to variables. Many laws of Nature are also described through formulas involving constants. These constant terms reflect fundamental attributes or physical characteristics within the laws of Nature. For instance, the speed of light c, the gravitational constant G, and so on.

Take the famous mass-energy equivalence formula E = mc2. If you strip away the constant c, all that remains is "E = m". No matter how you look at it, it becomes a glaringly incorrect formula, yet it seemingly still contains all the variables involved in a nuclear reaction...

It was exactly the same issue with the final Rune formula.

Thinking it over again, Gaode added the word "might" to his answer.

"The formula might be missing an interference constant C."

That was much more rigorous.