Order Reduction Algorithms and the Second Salon

Li Mo used a piece of stiff paper to gather up the scattered Star Silver Powder bit by bit.

The good news was that quite a lot of the Star Silver Powder had been saved!

The bad news was that the Star-Track Resonance Time Calibration Instrument seemed to have been blown to pieces...

Professor Bryce was exhausted. He rested in his chair for a long while before saying dryly, "Li Mo, was that your way of stopping the ritual?... The explosion method?"

Li Mo scratched his head awkwardly. "Professor, just tell me, did it stop or not?"

Professor Bryce sighed. "Don't be so reckless next time. If the explosion had been any stronger, we'd both be going to meet the Goddess of the Moon."

He got up and walked over to the instrument. "There's no one in Mondel Town who can fix this thing. When you go to the royal capital in a little while, take it to the Moonfall Artifact Workshop for me. They can send it back once they've repaired it."

"Sure, no problem."

After agreeing, Li Mo walked back to his workbench.

There was still a lot of ash on it.

He didn't mind. He opened his notebook to a clean page and began rapidly working through his calculations.

First, he wanted to review what had happened. Second, he wanted to simplify the calculation process.

The Star-Track Resonance Time Calibration Instrument was not a particularly high-order Mystical Artifact.

Nor were there very many threads.

So he could still calculate it using the computing power he had in a state of focus.

But what if he encountered a higher-order Mystical Artifact in the future?

Imagine hundreds or thousands of silver threads, hundreds of coupling nodes, and harmonic orders multiplying.

Then... he definitely wouldn't be able to calculate it.

So he had to prepare in advance.

Li Mo knew that the changing components were the zenith angle displacement caused by planetary rotation and the Doppler frequency-shift correction term.

So he could use Jacobi rotation and perturbation expansion to calculate the fixed high-order harmonic bases in advance and compile them into a standardized Red Moon Harmonic Order Reduction Quick Reference Table.

That would make future calculations much easier.

Li Mo wrote faster and faster.

He didn't know why, but a premonition arose in his heart:

Simplifying this reverse-engineering algorithm is extremely important. It even has to take priority over the math salon.

Professor Bryce was at a loss. When he heard the door open, he glanced back.

The female assistant Lydia's eyes went wide, and she hurriedly apologized:

"I'm sorry, Professor! I went to the break room to make some black tea and wasn't standing guard outside... What happened here?"

Professor Bryce waved a hand. "It's fine, just a little accident. Go get a broom and a rag, and let's clean up together."

Lydia didn't dare ask another question. She hurriedly lowered her head and replied, "All right! Coming!"

Class One's classroom, in Puxiu Academy's main teaching building.

The history teacher was explaining the provincial system of the early kingdom.

Estelle lowered her eyes and looked through her little notebook.

Hmm... From top to bottom, the list implicated nearly half the departments in Mondel Town.

Caroline would probably have her hands full tonight.

She put her notebook away and turned her head slightly toward the classroom's front door. No one knew what she was thinking.

When class finally ended,

Wayne said, "I have to go set up the salon venue. Miss Estelle, shall we go together?"

Estelle nodded. "All right."

"Miss Estelle, please." Wayne left with Anna and Estelle.

As they walked, Wayne began to open up.

He noticed that Estelle seemed particularly interested in Li Mo, so he took the opportunity to tell her about Li Mo's exploits at the academy.

"Estelle, do you know the story of how Li Mo cracked a math problem and Matthew made a miserable exit..."

"Estelle, do you know the story of how Li Mo won the assistant position and Matthew wept bitterly..."

"Estelle, do you know the story of how Li Mo recognized 1729 and Matthew gnashed his teeth..."

It was clear that Wayne really hated Matthew.

As he talked, Estelle listened silently, nodding from time to time.

Wayne felt that he and his new classmate got along especially well, and before he knew it, he began talking about other things:

"Li Mo is incredibly smart. Estelle, do you know about the kidnapping case? We caught the culprit under Li Mo's leadership, and he came up with a lot of new techniques at the time..."

Before he could finish, Anna suddenly interrupted with a smile. "Hey, Wayne, I heard your father's watch shop just brought in a batch of movements from the royal capital last week. Why don't you tell Estelle about watches?"

Wayne brightened. "Right, right, right! Miss Estelle, there's a lot to know about watches. Let me tell you all about them..."

Estelle gave Anna a meaningful look.

Anna seemed to have no desire to confide in her at all. She merely said gently, "Come on, the salon is about to start."

Estelle gave Anna another look and nodded lightly. "All right."

Even more people attended the salon today than yesterday.

Mr. Harrison had specifically invited all his friends from outside the academy.

The crowd gathered in groups of three or five, eagerly discussing yesterday's lecture. The atmosphere was lively.

"Clang-clang-"

The great clock struck on time.

Everyone waited a while before realizing that Li Mo was actually late.

People murmured among themselves.

A moment later,

Li Mo came jogging in.

He had been doing research in a state of focus and had lost track of time.

Only when the professor shook him awake did he come to his senses, and he jogged all the way here.

In such a hurry, he naturally hadn't had time to clean himself up.

Li Mo still looked a mess, and the blood on his cheek had dried.

The people present reacted in different ways when they saw Li Mo like that.

Mr. Harrison looked a little worried, Wayne unconsciously tightened his grip on his cane, and Estelle, seated beside him, also studied the wound on Li Mo's cheek.

Anna reacted most strongly.

She immediately rushed forward and asked anxiously, "What happened?"

Li Mo blinked. "It's nothing."

Anna pressed her lips together.

She knew it wasn't a good time to press him in front of so many people, but she quickly pulled out a handkerchief and wiped his face.

She would spare Li Mo embarrassment in public, but once they got home tonight, she was going to get to the bottom of this!

He's already so grown up! Why does he still make me worry so much!

Li Mo smiled at Anna and walked up to the lectern.

He glanced around at the audience and saw many familiar faces.

He began softly:

"Good afternoon, everyone. I'm very sorry. Something held me up just now, and I'm sorry for the wait."

"Without further ado, let's begin."

"Yesterday we talked about calculus. For today's second salon, I'll be discussing the continuity of functions, the intermediate value theorem, and convergence criteria."

This body of theory came from the nineteenth-century French mathematician Augustin-Louis Cauchy and the Czech mathematician Bolzano, both from Earth.

For over a century, mathematicians had relied entirely on diagrams, observation, and intuition to determine whether a curve was continuous or whether an infinite series could be summed.

Bolzano and Cauchy had successively provided an arithmetic definition of continuity and rigorous proofs of the intermediate value theorem.

These achievements had helped enormously in ending the second crisis in mathematics. The logic of conditional convergence for improper integrals that he had explained to Anna last night also originated from them.

Li Mo saw that there were quite a lot of people in the audience today.

It felt pretty good.

Clearly, the salon's influence was gradually growing.

And Estelle was here too...

From the platform, Li Mo met her gaze and saw that her eyes were as calm as ever, her face expressionless.

A flicker of interest suddenly arose in his heart.

I'd really like to see this mysterious girl look utterly astonished.