A long, long time ago. When “Roswell” was merely a small nameless town next to the Pecos River.

Note:

Roswell is a city in New Mexico, USA. On July 4, 1947, it is said that a UFO crash occurred here.

Conspiracy theorists believe that the U.S. government at the time covered up the truth of the incident; they believe that it involved the crash of a flying saucer, not a research balloon as officially reported.

When “Bikini” was merely the name of an atoll.

Note:

Bikini Atoll is a group of coral reef islands in the Marshall Islands. Since 1946, more than 20 nuclear weapon tests have been conducted there.

“Bikini” has connotations of nuclear explosive power — When a particular, epoch-defining swimsuit design was launched by the fashion industry, it was only natural that they would borrow this toponym.

When I was merely half my current age. 1946. Zürich, Switzerland. … Lieserl, a nice Uncle is coming to have a chat with you today. He's nothing like those ignorant, incompetent psychiatrists from before, ― please try to get along with him. … Don't worry, he said he won't urge you to go back to school and take those boring classes. He's a very famous expert, different from the others. … Hmm … let me clarify with a quick supplement. This person is my mother. She's an auditor. She's usually very busy at work, and could only be at home on Sundays or Christmas. A very boring job, don't you think? This person is my father. He's a designer. To be precise, he designs hands for clocks and watches. An even more boring job, am I right? So, you can imagine: as the only person in this family who is obsessed with musing over metaphysics, how painful it must have been. So, you can imagine: after I voluntarily dropped out of school, they found five “psychologists” to see me over the course of three months. Ah … yes, metaphysics. Since we're talking about a story from back then, I should also describe things from my perspective back then. Hi! I'm Carl … Carl Gustav. You can call me “Carl” or “Gustav”, I don't mind either. … Both “Carl” and “Gustav” … are you supposed to be a King of Sweden? Ahaha … people always tease me about that. … By the way, I heard you were doing some interesting private research lately. Do you mind filling me in? … … Hm. “How could this shrivelled old fart ever understand anything?” ― ― Is that what you're thinking? … … I think you can try and test me first. One should explore all their options before coming to a conclusion. Don't you agree? … I'm not one to brag ― But when I was at university, my grades in science were pretty good. … I swear, it's true. I had the highest mark in “Geometry” class, taught by Hilbert himself! … So. … Do you know, what is the maximum number of straight lines that can be orthogonal to each other in space? If your answer is wrong, please leave, okay? When I thought about it afterwards … I realised this man wasn't an ordinary person. I thought I could use this problem, whose answer I could readily change on the fly, to brush him aside effortlessly — ― But I never expected, that by the time I opened my mouth and posed the problem to him, he would have already won. At the very least, he was already miles ahead of those four so-called “professionals” from before. Orthogonal straight lines … ? Isn't that just: however many lines you want? … ! The dimensions of space can be considered limitless. Just their coordinate axes alone can already be considered to be two infinite, perpendicular straight lines. ― In short: the so-called “space”, these so-called “straight lines”, are all nothing more than man-made, artificial constructs. … Um … W-What's wrong? … D-Don't stare at me with a silly grin like that … a-am I at some verbal exam, flaunting my meagre intellect before some expert?! No … That's not it … I, I, … Uwaaaaaaaaaaaaaaaah ― Yes, at that point, I became a miserable bawling mess. A little girl, who felt like she had just “reunited with an old friend in a foreign land”. If my present self were to see me in that state, I wouldn't be able to keep myself from lampooning the whole situation. But … everyone goes through such a phase of unrestrained emotion, right? It's not an ugly thing … On the contrary, it's very beautiful. It's the kind of beauty that is engraved on the personal clock of your life, one that cannot be actively sought after, but instead comes to you fleetingly and serendipitously. For some, this moment of beauty comes at the age of 18, for others at 80 … In my case, at age 8. That's all. From such a perspective: this man, who could keep up with all my craziness … he was a truly exceptional person. “Given any two polyhedra of equal volume, is it always possible to cut the first into finitely many polyhedral pieces that can be reassembled to yield the second?”. I feel that, even if we stare at it for another hour, we won't be making any progress. Do you have any special ideas? … Silence. I'm still thinking. Hmm … then that means we both can't figure it out. Let's see the answer! Huh!? There's nothing wrong, right? We're here to explore the unknown, not taking part in some quiz show. But … Don't be so disgruntled. Every person's imagination has its limits. Only by learning and borrowing from the imagination of others, will you be able to see more amazing vistas. … Let me see … In this case, an invariant can be defined according to the edge length and dihedral angle of the polyhedron … … What? Let me see it now! S-slow down please! D-don't grab it so suddenly! You're going to tear the book! To tell you the truth, of all the times I spent solving problems with that man, this is the only one I could remember. It wasn't only because the answer was impressive. I'd have you know, not long after, when I raised this question with Planck ― “Wha-?! He used Hilbert's third problem to test you? Is he insane!?”

Note:

The German mathematician David Hilbert gave a speech at the Second International Congress of Mathematicians in Paris in 1900, presenting the “23 Most Important Mathematical Problems of Our Time”.

Of the 23 problems, the third one was: “Given any two polyhedra of equal volume, is it always possible to cut the first into finitely many polyhedral pieces that can be reassembled to yield the second?”.

P.S. The more famous of the 23 questions include:

1. The Continuum hypothesis

2. Consistency of arithmetic axioms

8. The Riemann hypothesis, Goldbach's conjecture, and the twin prime conjecture

18. Densest arrangement of spheres

― Well, such a horrifying event, of course I would remember it for a lifetime. Ah. You want to know how I knew Planck back then? About that … Everyone, let me introduce you to someone. This is Miss Emma Planck … the youngest physics professor ever to teach at Princeton University. Hi! I'm Emma! Carl's cousin! ― I don't know whether he does it on purpose or not, but every time he introduces me he always forgets to mention this. But, it's not that I really care, right? Ahaha … … Ahem. Err … back to the topic at hand. Previously, we had initially discussed the possibility of allowing your child to advance to university directly. As soon as we all agreed, I contacted Emma at the first available opportunity. From the perspective of educating your child, her gender and age should be a strong asset. And that's not all! I'm also very interested in her too! Please, you must let her accompany me in chasing down the mysteries of this universe! … Hahaha … Sorry, Emma can get a little overexcited on occasion. No, isn't that a good thing? … I think our daughter will definitely get along with her. … … On this point, I also have no objections. If Carl was the one who introduced me to a new world, Emma was the ultimate navigator. … Although, at some point later in life, I started calling her “Professor Planck” for fun. Emma back then … how should I put it, didn't show any signs of the “midlife crisis” she has now. A consummate scholar, a consummate beauty. A woman who would always illuminate you with her own sunshine ― She'd take you to play the piano, to sing songs, to watch the stars at night together. She was more of a mother, than my blood-related one. … Of course, I don't mean to imply there was anything wrong with Carl. This was purely a “gender advantage”. Carl, are you going back to Germany tomorrow? Yes … This weekend is the last day of my holiday. I have to report back to Headquarters. Headquarters? The Allied Kommandatura, Berlin City Defence headquarters, Psychological Counselling Office. Mm … so you really are a genuine “expert”? Haha … only now do you believe me, you must've had a really a bad first impression of me. Well, it certainly wasn't as good as you thought it was. But … Working at the headquarters … Are you responsible for treating post-war trauma? Pretty close … it's a tough job if you're not a professional. After all, many people are not fond of hearing the grievances of others ― before long they'll start feeling the same pain. How is a professional any different? How are they special? A professional treats the other person as a subject of analysis. We analyse their pain, treat their pain, but never let ourselves experience their pain. As soon as any personal relationship develops, the patient must be passed on to someone else for therapy. … So is Carl handing me over to Emma? … No no no, that's not the case at all. Firstly; you're not a patient; secondly, I'm not treating you. Emma's also not a clinician. Hehe, seeing Carl's flustered face is so funny! … Huh? Are you teasing me? You little brat, I'm gonna mop you up! Ah! Uncle Carl is gonna hit someone! D-don't cry wolf on me! Stay still! Phew … You've tired me out … Carl clearly considers himself a young man, yet I didn't expect him to have the stamina of an old man. W-watch your tongue … I blame it on Switzerland, life is too comfortable here … Darn it, I really don't want to return to Berlin! … … In the future, will we meet again? … Yeah, if we can get a vacation. It would be nice if Carl were a few years younger. Huh? If only Carl were … 10 years younger? I could match-make you with Sister Emma! Yeesh! You imp, your evil bag of tricks is growing! Hehe … Indeed, Emma once told me ― “Men often call others evil, but in reality they secretly look forward to being even more diabolical!”. Hey! What is she teaching you!? Hehe … you think I would tell you? If you can, try and become 20 years younger so we can be Emma's students together! Oh, that sounds nice! Do your best, Carl! E-Emma!? When did you ― Hehe, “if only Carl were 10 years younger … ”. Even if you weren't 10 years younger, I wouldn't mind!? Aaaah w-w-where are you going with that!!!! At the time, although I was still young, I already had a certain premonition. “It would probably be very difficult for us to meet again in the future”. It's just that, at the time, nobody could anticipate … That the last day of that summer, was also the last day that our life trajectories overlapped. Carl was a very busy man, and he never really enjoyed a genuine holiday. As for me, learning and conducting research under Planck, I cannot say that I had much free time either. Everyone was probably thinking, “Anyway, there'll always be time in the future”. Until 3 years ago. That's right, January 1, 1952. The day the Honkai incident levelled an entire city. He was in Berlin at the time. That's right, Berlin. City centre. Carl … next holiday, you'll have to go help children in other places, isn't that right? Yeah … that's about right. The little brat has already found her own path in life, hasn't she? And in this world, there are even more people who have yet to find their path, and they need me to help them find it. Haha … that is so you. … Well, Emma. I'm leaving now. … No, please wait a moment for me. Huh? No, it's no big deal. It just that I remember … when you were at school, you used to participate in choir, right? Mmm, I've borrowed our instruments without a hitch. I've decided on the song myself, without your permission ― but I'm sure you know the lyrics anyway. What are you spacing out for? Go hurry up and grab that little brat! That foolish girl even tried to give us some “time alone”! Oh, Danny Boy, the pipes, the pipes are calling From glen to glen, and down the mountain side, The summer's gone, and all the roses falling, It's you, it's you must go and I must bide. But come ye back when summer's in the meadow, Or when the valley's hushed and white with snow, It's I'll be here in sunshine or in shadow, Oh, Danny Boy, oh Danny Boy, I love you so! But when ye come, and all the flowers are dying, And I am dead, as dead I well may be, Ye'll come and find the place where I am lying, And kneel and say an "Avé" there for me; And I shall hear, though soft you tread above me, And all my grave will warmer, sweeter be, For you will bend and tell me that you love me, and I shall sleep in peace until you come to me …