37: Mesmer Jr. told me the story of Neptune.
37: Using the elegant formula of gravitational theory, people discovered Uranus. But they found that Uranus didn't follow its calculated trajectory.
37: They began to wonder: Was the theory wrong? Did they fail to account for something?
37: Some people chose to deny it, others to avoid it, but some decided to face the challenge head-on.
37: They wanted to prove that what they believed in was correct, so they made a hypothesis: what if gravitational theory wasn't wrong?
37: What if the deviation in Uranus's trajectory was caused by another, as yet undiscovered, eighth planet?
37: Proving this wasn't too difficult. Astronomers only needed to point their telescopes in the right direction, following the calculations precisely.
37: And then they discovered it, Neptune.
A Reply from Across the Waves: I really liked that story. I think now I understand what people mean by "fantasy."
A Reply from Across the Waves: People often make decisions that are difficult to understand—decisions based on sentimental likes and dislikes. But behind those seemingly irrational decisions, there may actually be logic.
A Reply from Across the Waves: Mesmer said that people have things they love and things they believe in, so when they find something in the phenomenal world that aligns with these things, they feel happy.
A Reply from Across the Waves: I think one way of understanding it is: people make their own hypotheses. When those hypotheses are proven, when they find results that fit the rules, people give them special meaning.
A Reply from Across the Waves: That meaning is invisible, intangible. In the same way, numbers exist in everything—untouchable but real.
A Reply from Across the Waves: They all connect to the transcendent world we long for.
A Reply from Across the Waves: We make our own hypotheses, too. Sometimes we can prove them and discover a new theorem; sometimes reality tells us, "No, you're wrong."
A Reply from Across the Waves: I'm glad that my ice cream didn't say "no" to me.
A Reply from Across the Waves: This project opened my eyes to something.
A Reply from Across the Waves: I took my problem from a logarithmic axis to the addition axis, and turned my numbers into corresponding addends, so now ...
A Reply from Across the Waves: I should take my sum back to the original axis.
A Reply from Across the Waves: It's such a simple answer. If only I would have thought of it sooner.
A Reply from Across the Waves: Still, I think I'm starting to see the outline of my next square.
37: After that, whenever my research progress stalled, I would go to the museum to relax. It's not as ideal as the beach, but it's nice in its own way.
37: The ice cream shopkeeper is still very grateful to us. Every time I go, she tries to treat us to free ice cream.
37: But I've done a lot of jobs for the researchers at the computing center, and I've earned enough points to pay for myself and treat everyone else now.
37: The shopkeeper stopped making the "Star of Wonder" flavor after the special exhibition ended, but I don't mind. My favorite flavor is chocolate anyway.
37: Her ice cream is really wonderful. Its beautiful geometric shape helps me organize my thoughts.
37: So every time I go to the museum, I choose to eat just the right amount of ice cream.
Shopkeeper: Don't be shy. Eat as much as you like! There's plenty more where that came from!
Medicine Pocket: Don't you worry about that. I never pass up a freebie.
X: And what does this prove? That good things happen to good people.
Mesmer Jr.: Really, you two? You don't feel any shame over accepting 37's ice cream benefits on her behalf?
Medicine Pocket: I know I don't.
Mesmer Jr.: Of course, you don't.
X: But more seriously. It's not recommended to consume ice cream in large quantities. Be careful not to get a stomachache, 37. If I'm not mistaken, you've had more than one cone already.
37: Don't worry, this is only my third cone today.
37: 1 and 2 make 3, representing the virtues of moderation and prudence. 3 ice creams couldn't possibly be too much.
37: Though perhaps 4 is a better number. It's the smallest composite number among positive integers, the "greatest miracle," the "most perfect number"! Clearly, 4 is a better final answer.
Mesmer Jr.: You mean you want another one? I don't recommend it.
37: Why not? 4 is obviously better than 3.
Medicine Pocket: I think 10 is better, myself. It's the smallest two-digit number in the decimal system, and when you write it in the ten's column, it only counts as a 1! How cool is that?!
Medicine Pocket: But just a friendly reminder: this refreshments area doesn't have a restroom.
37: I often see my friends, Mesmer Jr., X, Medicine Pocket, and Ezra there. They're all fascinating people in their own rights.
37: Being with them often reminds me of the times we spent with Sophia, and even with 210.
37: Sometimes we see Spathodea and Desert Flannel. They're Ezra's friends from far away.
37: Spathodea is a positive integer and always full of energy, while Desert Flannel is a bit like Mesmer Jr.—a fraction who can be strict with herself at times. They're fascinating too.
37: But then one day, we received bad news. Terrible, heartbreaking news.
37: All things in the phenomenal world are uncertain and unstable. I have known this truth for a long time, but it still came as a surprise.
Shopkeeper: Hey, sorry to interrupt you.
Shopkeeper: I just wanted to let you know, the ice cream shop's closing ... again.
Medicine Pocket: Huh?
Medicine Pocket: What nonsense is this now? Look at this long line. Are you really telling me you can't even manage with this much success?
Shopkeeper: No, it's not that I need to close. But ... I did some math, just like 37 taught me.
Shopkeeper: I've been making good money recently, but once this rush is over, my revenue won't be as high. Even with decent daily earnings, it would take over two years for me to break even.
Shopkeeper: So I thought, why not hand the shop over, like someone did to me? If I sell it while it's hot, I can recoup my investment.
37: It sounds like you've changed your thinking and improved your reasoning skills. I guess that's ... a good thing.
37: But if the shop is closing, soon, I'll have no ice cream to eat.
37: I'll never see those beautiful dodecagrams again, which is definitely not a good thing.
37: But that's not the worst part.
Medicine Pocket: So, that's it? After all we went through, I'm still gonna have to live life without these cones? What happened to your dream?!
X: Regardless, I must say, it's a very rational decision. Don't worry, ma'am. I support you fully.
Mesmer Jr.: And if this unreasonable customer tries threatening you, you can contact the curator over there.
Medicine Pocket: Hey, Ezra! Is this allowed? Do something!
Ezra: Transferring ownership of the shop isn't a violation of her contract. I can't abuse my power on this one.
Medicine Pocket: What will I eat when I go for my walks? Those visitors passing by? I bet they'd taste terrible! Anyway, what's the new owner gonna sell here?
Shopkeeper: I heard he's going to sell beans in all kinds of weird flavors. You know, like crab, Scale of Demonic, snail eyeball ...
Medicine Pocket: Who would want to eat snail eyeball-flavored beans?!
37: But we can't eat beans!
Medicine Pocket: Huh?
Medicine Pocket: You don't mean that eating beans is against your religion, do you?
37: Of course, it is! Eating beans is a terrible sin—the worst sin imaginable!
37: If you eat beans, you'll be sentenced to death.
Ezra: That's ... Sorry, no offense, but that sounds a bit harsh.
37: Considering you're not from our school and we're not on the island, you won't get punished.
37: But I can't eat them all the same.
37: What a shame! A shop mutated from selling beautiful ice cream into evil beans.
Medicine Pocket: Hold on, but you're eating chocolate ice cream! Isn't that the same as eating beans?
37: What?
Medicine Pocket: Chocolate ice cream is made from chocolate, and chocolate is made from cocoa beans. Cocoa beans are beans.
Medicine Pocket: Therefore ...
Medicine Pocket: You've been eating beans.
37: ...
37: No.
37: It's impossible.
37: Impossible! If I really ate beans, then ... then I should have been taken by an Abraxas by now!
37: But I haven't been taken by an Abraxas! This result is contradictory, so there's only one possibility: the hypothesis is incorrect! You must be lying to me!
Ezra: 37, your ice cream's melting! I brought a handkerchief. Here, you can wipe it up.
X: Save the poor ice cream! And don't worry. They're not beans.
Medicine Pocket: You really believe that? You're gonna believe this guy? Hah! Maybe your Abraxas is simply on its way.
Mesmer Jr.: Can we all just have some peace and quiet?
Shopkeeper: Hey, the reporter who wants to interview me before the shop transfer goes through is here. Would you like to take a picture together?
Shopkeeper: They're the ones who made this ice cream miracle happen—the young researchers from Laplace.
37: My hypothesis is correct. Medicine Pocket is lying. Chocolate ice cream isn't beans.
37: It's true that cocoa beans have "beans" in their name, but they're from the Malvaceae family, not the Fabaceae family. What's more, cocoa beans are processed into chocolate ice cream.
37: It's like getting a very bad negative infinite non-repeating decimal, like -1.414213562373 ...
37: It can't be written as a ratio of two integers, and the string of digits after the decimal point never ends. It looks awful.
37: However, if we square it—it makes 2! A favorable number!
37: So, there's nothing wrong with chocolate ice cream.
A Reply from Across the Waves: I hope you can try ice cream too. I asked Regulus to bring you some. Along with this letter, I've enclosed further papers, journal clippings, and printed materials I've collected. You can use these to update the island's database.
A Reply from Across the Waves: I've also gathered many new puzzles proposed by mathematicians from the outside. Some are extremely challenging, and I already have ideas for a few solutions.
A Reply from Across the Waves: But to be fair, I'll give you some time to work on them too. That way we can exchange our thoughts in the next letter.
A Reply from Across the Waves: And there's also this "newspaper." Mesmer found a report on me and suggested I send it so you can see how well I'm doing for yourself.
A Reply from Across the Waves: All in all, I'm happy here, and my research is progressing.
A Reply from Across the Waves: This time, I'll find a better answer. It might not be perfect, but I believe it will be good enough.
A Reply from Across the Waves: Then I'll return to the island, and Sophia will come back too. We'll all share the light of Truth, just like before.
A Reply from Across the Waves: You may have noticed that the total word count of this letter is a palindrome. I trust you understand what I mean; just don't try writing me a short reply. That would be cheating.
A Reply from Across the Waves: I look forward to your reply.
As the last stroke falls on the letter, the writer successfully completes her declared goal.
There is no need to count again. The reader confirms this to be the case.
6: Hah.
Upon unfolding the letter, the young man unmistakably expresses his first sign of emotion. Of course, the other party present doesn't miss this significance of the moment.
Regulus: Woah! Did you just smile? I thought that pale, gloomy expression was welded to your face.
Sonetto: Regulus!
