On Getting Through the Long Night by Explaining Advanced Math
Li Mo's first thought was: This woman's crazy!
Immediately afterward came his second thought: I have to turn around and hug her right now!
Who isn't a little crazy?
If you're going crazy, I'll go crazy with you.
Li Mo steeled himself and was just about to turn around.
Then he felt pressure on his shoulder.
Anna pushed him back down.
Then, with a hint of pleading, she said:
"Don't turn around."
Li Mo: "..."
He could barely keep it together.
Wait, Teacher Anna, what's this supposed to be?
Who stops halfway through seducing someone? Are you going to let me sleep or not?
After a long while, Li Mo couldn't take it anymore. He sighed and said:
"Anna, I can't sleep like this."
"Just close your eyes and you'll fall asleep."
"Closing my eyes doesn't help. My head's full of all sorts of things... Look, I can't even change positions."
"Then don't move. Count moons."
"One moon, two moons... Wait, what nonsense are you talking about?"
"Oh, then count stars..."
"Counting stars won't work. I'm sixteen already. I could count ten thousand and still be wide awake."
"Then what do you want? Either way, you're not allowed to turn around..."
Li Mo was at a loss.
If this went on, neither of them would get a wink of sleep tonight.
He compromised:
"Then let me explain some problems to you. It'll take my mind off things."
"Sure, that works! Actually, I got halfway through the first one just now, but I have no idea how to do the second."
"For the first problem, the integrand oscillates over an infinite interval. When you worked on it, did you go straight for absolute convergence?"
"Mm... I tried putting it in absolute value signs to get an upper bound, but the resulting integral diverged, so I couldn't prove anything beyond that."
"That's the problem. Divergence of the absolute-value integral doesn't mean the original integral diverges. When you have a trigonometric function alternating between positive and negative multiplied by a monotonically decreasing function, first use integration by parts to extract the oscillating term. Put the sine term inside the differential and turn it into a cosine, and the original expression splits into a bounded term and a new integral with a squared denominator."
"Once the denominator is squared, the second term converges absolutely as the independent variable approaches infinity?"
"Right. That's called conditional convergence. At tomorrow afternoon's salon, I'll cover the convergence tests used specifically for oscillatory integrals like this."
"What about the second problem?"
"The second problem tests your analysis of singularities. As the independent variable approaches zero, the denominator also approaches zero, making the function unbounded. So you have to split the integral at one, into two parts: zero to one, and one to positive infinity. The whole expression only converges if both parts converge..."
Math problems really were a powerful sleep aid.
As he went on explaining, the two of them gradually grew accustomed to sleeping in that position.
In the end, Li Mo didn't know how he fell asleep.
All he knew was that he had some more rather indecent dreams that night.
Early the next morning.
Li Mo woke up stark naked again.
After getting dressed in utter embarrassment, he went downstairs for breakfast.
Anna brought over a ham and fried egg sandwich and set it in front of Li Mo, seemingly using a little extra force.
It landed with a bang.
How scary!
Li Mo obediently ate his sandwich without saying a word.
Anna turned and went to the kitchen to get some hot milk.
Li En asked curiously:
"Did you two have a fight?"
"Uh," Li Mo said, "I don't think so? I don't know either..."
"Make it up to her. Anna's a good girl. Don't make her sad."
"I know, I know." Li Mo nodded repeatedly and changed the subject. "By the way, Dad, I ran into Mrs. Turner while I was having tea at the Egret Tea Room yesterday afternoon."
"Mrs. Turner, the tax officer's wife?"
"Yes, that's her. She said she hadn't seen you in a long time and asked me to pass on a message. The ladies in town all miss you, and if you run into any trouble, you should just tell them."
After hearing this, Li En rubbed his chin and said, "Even if she hadn't said so, I was planning on doing just that."
Li Mo asked, "What do you mean?"
"That old bastard Oliver didn't buy up all the raw cotton in stock in town at once using only his own money. I had someone make inquiries at the Mondel Joint Venture Bank. He borrowed quite a lot from the bank last month, and that's how he scraped together enough cash to monopolize the market."
"So?"
"So there's no need for me to hold back with him either... Since the ladies in town are so enthusiastic, I'll use my charms a little, have afternoon tea with them, and chat."
Li Mo blinked. "What good will that do?"
"Haha, Mrs. Turner's husband is in charge of business and tax inspections in the western district, and Mrs. Crawford, who's always at her side, happens to be married to the joint venture bank's credit manager. Once I go to the salon and tell them my troubles, I'll have the ladies whisper a few words in their husbands' ears. The tax office can investigate Oliver, and the bank can suspend his access to further bill discounting on the grounds that the war has tightened credit... That'll be enough to give him a nasty headache and let him know I, Li En, am not someone to be trifled with!"
Li Mo listened with newfound respect and gave him a thumbs-up. "666. That's my dad for you."
Li En was puzzled. "Six what? What does that mean?"
"Nothing. I'm saying you're still going strong and as charming as ever. Dad, Anna and I are heading to school."
Li En waved. "Go on. Remember what I just told you."
Anna took off her apron and hung it up, picked up her schoolbag, and quietly followed Li Mo out of the house.
The morning air was slightly cool.
Their neighbor Green was already waiting at the door with Helen.
As soon as he saw Li Mo, he said in surprise:
"Oh, it's Mr. Li Mo! What a coincidence, you're just heading out too!"
Mr. Green gave Helen a gentle nudge and urged her on. "Helen, what are you standing there for? Come on, hurry up and go to school with Mr. Li Mo!"
Helen's cheeks flushed crimson. She was so embarrassed she was about to faint.
Mr. Green also produced a breakfast box and held it out.
"Mr. Li Mo, you see, Helen slept especially soundly last night, and she's truly grateful to you. So she got up on her own before dawn today and spent ages working in the kitchen, making you some breakfast herself. She wanted to bring it over especially for you!"
Helen, standing beside him: "!!!"
This was a development she had never anticipated.
What does he mean, I got up before dawn and made breakfast myself?!
Dad made it himself today! He never said a word to me about it beforehand!
And most importantly-
I just stayed over at Li Mo's house and ate a sandwich Anna made!
After seeing Anna's cooking, who would dare come and make food for Li Mo? Wouldn't that be embarrassing?
He's crazy! He's really crazy!
Helen was so anxious that her eyes were nearly red, but while she wanted to explain, she didn't dare expose her father.
She stood rooted to the spot, her toes curling with embarrassment, wishing she could just faint on the spot.
Li Mo, however, smiled naturally, reached out to take the breakfast box, and said gently:
"Thank you, Helen. I tend to get hungry between classes in the morning, so I'll save it for a snack. It's getting late. Let's go."
Green waved. "All right, all right, take care on your way!"
Carrying the breakfast box, Li Mo walked on with Anna and Helen.
Green stayed where he was, smiling as he watched the three young people walk away side by side. The more he looked, the more pleased he was.
Look at that. Send him a homemade breakfast, and going to school together follows naturally!
My assist this time was flawless, absolutely perfect!
As an old saying in Mendel Port went: a fisherman who cast his net diligently would never come home with an empty hold.
Mr. Green nodded with great satisfaction, then turned and headed home with his hands behind his back, humming a tune.