Above the mage

The formula in Chapter 130 is missing an interference constant.

Hmm? It doesn't seem as complicated as rumored. In the end, it's just a simple formula calculation, isn't it?

This formula is at most at a high school level in terms of complexity. And the way it's written is far too simplistic.

After reading through the "Six Basic Rules of Runes" recorded in his notes, this was the first thought that popped into Gao De's mind.

"Therefore, to ensure the magic circle functions as effectively as possible, we should minimize the actual robustness value or maximize the theoretical robustness value."

"Reduce the actual robustness value, that is, minimize the occurrence of two identical rune connections to reduce the number of interfering pairs, and use as many low-energy secondary base runes as possible to increase the number of runes."

"Increase the maximum robustness value, that is, increase the number of runes and the number of rune pairs, or choose a conduit material with low magic resistance."

"However, increasing the number of rune pairs also increases the number of interference pairs."

This was the second thought that flashed through Gaode's mind.

He subconsciously began to understand how to derive the formula.

After reviewing the six basic rules of runes again, and combining them with his own understanding, Gao De had firmly memorized them.

Only then did he feel relieved and continue browsing.

The first thing that catches the eye is a very simple illustration:

The main body of the pattern is a large hexagon, which is cleverly divided into six equal areas by its six sides;

Each region contains a pattern, four of which are identical hexagonal patterns and two are square patterns;

Each of the six equally divided regions has one edge that coincides with the hexagon in the center.

In addition, the center of each pattern is marked with the numbers "0" and "1".

Below the image, there is a text description:

"Suppose a simple magic circle can be constructed from a single composite rune, which consists of 7 basic runes, including 5 level 0 basic runes and 2 level 1 basic runes."

"Based on the six fundamental rules of runes, calculate whether it can be successfully constructed on mithril material with a magic resistance of 1% and on brass material with a magic resistance of 45%?"

There are also "homework exercises"?

Gao De thought to himself, while simultaneously grabbing a blank sheet of paper and a quill pen from the worktable and starting to write furiously.

"Each rune in this magic circle can connect to a maximum of 4 runes of the same level, which is less than 8, and can connect to a maximum of 2 identical runes, which is less than or equal to 2, thus conforming to Rule 3."

"Let the number of rune pairs be N, the number of interference pairs be n, the number of runes be m, the total energy of the magic circle be E, the magic resistance rate be R, the theoretical robustness be Q, and the actual robustness be q."

According to rule five, we can deduce from the diagram: N=11, n=2, m=7.

「根据规则二可得E=4.64*2（相同零级符文相邻能量升级）+1*2+4.64*2=20.56。」

「当导魔材料为秘银时：R=0.01，由规则六可得：Q=m*N*(1-R)=7*11*(1-0.01)=76.23。」

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

"Since Q=76.23>q=41.12, according to Rule 1, the magic circle can be successfully constructed."

「当导魔材料为黄铜时：R=0.45，由规则六可得：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 circle can still be successfully constructed on brass magic-conducting material."

The entire process took no more than two minutes, and Gaode Maps calculated the result.

It is indeed a fairly basic and simple calculation problem.

Once you understand the six basic rules of these runes, even an elementary school student could quickly calculate the solution.

It's not commendable to calculate the answer; what deserves praise is the person who summarized these six rules.

It is because of these six basic rules that a complex problem can be calculated using a simple formula.

Unexpectedly, there was still a chance to do the problem in this world. Familiar muscle memory was awakened, and Gao De felt a little happy.

Doing problems is inherently a very enjoyable thing.

"Why do I feel like something's missing?"

Gao De looked at the formulas he had listed on the answer sheet, unconsciously touched his chin, and his eyes revealed an indescribable confusion and unease.

His gaze swept over the formulas listed on the answer sheet according to the basic rules of runes, each step strictly following the theorem.

But the emptiness in his heart was something he could not shake off from birth; the feeling of "something missing" stubbornly persisted.

If I had to describe this feeling, it would be like solving a math problem where you've used all the conditions in the problem statement, but you've overlooked some hidden, crucial clue, causing the entire solution process to go astray.

It must have been his imagination. Gao De checked his answers several more times, and after confirming that he hadn't missed anything, he finally put down the answer sheet, stopped thinking about it, and continued browsing.

"Based on the formula calculations of the six basic rules, this simple magic circle can be successfully constructed on both mithril and brass materials."

"In practice, the construction of the magic circle on the brass material failed. Why did it fail?"

At the end of the notes, there were just these two sentences.

Below the question about why it failed, there was a comment written in a smaller font.

"Rules one through five have been verified to be correct through multiple methods. The reason for the failure is that the formula for rule six is ​​incorrect."

"The formula of Rule Six already includes all the variables that appear in the rune combination, and the calculation method has been derived many times. It is the most consistent with the rune arrangement rules and has the lowest error rate among all the calculation methods. Other calculation methods have alarming error rates, which is obviously unreasonable."

"Where did the problem lie?"

Looking at the final question mark, Gao De frowned, his thoughts already racing.

Why did it fail?

The theoretical robustness value on brass material is clearly greater than the actual robustness value of the magic circle.

According to the rules, this is sufficient to support the construction and operation of the magic circle.

This is not the case.

That means the formula mentioned in the annotation is wrong.

So where is the formula wrong?

Gaode then glanced at the formula listed in Rule Six:

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

That strange feeling of "as if something was missing" resurfaced in his heart once again, like an invisible hand gently plucking at his heartstrings.

As Gaode's gaze lingered on the formula, he became increasingly certain that something was indeed missing from it.

The formula itself may have structural flaws, and the near-instinct of missing a key correction term is one of the explanations that Gaode has come up with.

People who study and excel at mathematics develop a certain ability through long-term problem-solving training and experience accumulation, and after encountering a sufficient number of formulas.

This ability is often referred to as mathematical intuition.

Mathematical intuition can help them to "perceive" the possible structure and form of a formula to some extent.

This allows them to make a preliminary guess about the solution or the form of the formula based on their past experience and understanding of the formula.

This process can include pattern recognition, symmetry perception, and prediction of function behavior.

Of course, while mathematical intuition is an important tool and very useful in the exploration and conjecture stages, guiding mathematicians to make hypotheses and conjectures, it cannot replace proof.

The true formulas and conclusions must be verified through rigorous logical reasoning and proof.

Immersed in the formula, Gaode, following his intuition, subconsciously added a "C" after the actual robustness value "q=E*n".

q = E * n * C.

Then, he nodded in satisfaction.

It looks much better this way.

Gao De's gaze returned to the last question in his notebook.

He thought about it for a while and finally gave his answer later.

"The formula is missing an interference constant C."

A constant is a number in mathematics that has a fixed and unchanging value.

It does not change with the changes of other variables; it is a fixed number and can appear in any formula.

Constants provide stability and fixed reference points for formulas, enabling them to more accurately describe and predict various phenomena and processes.

Anyone who has received a high school education can find that many formulas, whether in physics or mathematics, often contain a fixed constant value in addition to variables.

Many natural laws are also described by formulas that include constants.

These constant terms reflect the fundamental properties or physical characteristics of natural laws.

For example, the speed of light c, the gravitational constant G, etc.

The famous mass-energy equivalence formula E=mc, if we remove the constant c, then we are left with only "E=m".

It's a formula that just doesn't seem right, yet it appears to contain all the variables in a nuclear reaction.

Just like the final question in the rune formula.

After thinking about it again, Gaode added the word "possibly" to his answer.

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

That's much more rigorous.

(End of this chapter)