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Assume you have a pair of dice. If you were to roll them on a desk, few would be able to predict what the result will be.

Take the number that came up from that throw as one example of an outcome. Now, what will happen when the dice are thrown again?

Of course, it usually isn't possible to know for certain what will happen, but let's assume some certain conditions. These conditions are the ones that match the previous conditions of the dice - in other words, the initial states of position, angle, and force.

What happens then? The dice will dance in the air, rotating as they did the first time, striking the desk at the same place, at the same angle, at the same time, and bounce identically. Matching the same exact conditions may be something a youkai could do, but it is much more difficult for human hands. In that case, you could make a device that could do such a thing. In doing so, the dice should once again fall upon the same exact result.

The meaning hidden behind this reality is that everything in this world, no matter when or where it happens, will reach a condition identical to one in the past, and from then on, history will repeat itself. This point in time marks a predictable future. Furthermore, it is safe to assume that the conditions at the end of that repetition must return to the point it is at currently. Perhaps this world has already gone through some untold number of loops?

*Ring-a-ling.*

I was in the middle of my work when the door made a noise that indicated my usual visitors. It is work to confirm whether or not daily life forms a loop.

That task would be writing in my journal. I had begun writing two or three years ago, and already I had filled several books. I was recording my viewpoint of the structure of Gensokyo, and I frankly believe that one day it will become a history book.

Youkai live longer than humans to an overwhelming degree, so there are few sources on Gensokyo's history. Because of this huge advantage over the humans, the youkai likely twist what little history remains to whatever will benefit them. Humans can learn much from history, but the youkai have intentionally stolen this away from them.

The youkai who live near the village are solely concerned with enjoying daily life, the youkai who live in the mountains only record history for the sake of the other residents there, but humans don't have much of an opportunity to make any. It's practically as if the history of Gensokyo has yet to begin.

I am writing a journal for both humans and youkai. I expect it to become an unabridged history book of Gensokyo. It will be a breath of fresh air into the ordinary lives of both humans and youkai who live in Gensokyo.

"But man, that sure was a big'un, wasn't it? I don't think we'll see somethin' like that ever again."

"You're exaggerating - it's like that around this time every year."

Both Marisa and Reimu entered the store, brushing fallen leaves from their shoulders and hats.

A few years ago, the ghosts began increasing in numbers at the turn of the season. Since then, Reimu and Marisa's ghost-herding had become a yearly occurrence. I could faintly remember this infestation happening every year. I suppose history is repeating in this world after all.

"How did the ghost extermination go? Have their numbers decreased a little?"

"We had our hands full of them, the same as always. I wonder if I should come up with a countermeasure...there's more of them every year."

"Would leaving them alone create that much of a loss? But anyway, ghosts are cheerful beings, so maybe throwing a party or festival would gather them in one place."

"If we did that, there would be a loss."

"What would that be?"

"We can't eat the ghosts."

I believe it was over 60 years ago...there was a time where ghosts had increased in number, just like they are now. Gensokyo had resigned to the changes at the time, and resumed their peaceful life in spite of that.

Stable and resistant to change, Gensokyo today exists in a similar "peace" to those days from 60 years ago. History is repeated over 60-year cycles. In other words, everything in the future 60 years may be rather nostalgic.

"Don't you have any ghost traps in this shop? Something you can just leave somewhere that will catch ghosts, or...?"

"Hmm...it's difficult to catch something that has nothing to catch on to. And they'd just slip through boxes and things like that."

"But I have to do something about them. If more keep showing up, this world might become the next Netherworld."

"It'll be fine. The ghosts will settle down after a while. The future is predetermined like that."

Reimu gave me a dubious expression. "The vampires and youkai said the same thing you just did."

Ghosts will appear in public places, but they don't show up at my store often. To begin with, ghosts tend to gather easily wherever there is a lot of commotion. This is because of a ghost's transient nature, where they may vanish at any moment, so they gather at a lively place where it is easier for others to notice their existence. It is likely just as when they were human, preferring to be in crowds of people.

"There's no way ya can predict the future. Some people are only able to get by on luck, y'know," Marisa said, looking at Reimu.

"Well, if by 'luck' you mean 'intuition', there is actually a foundation for intuition."

Marisa's expression said that she didn't believe her.

"Whenever we play Chinchirorin at parties, you've seen horrible odds win out anyway. How can ya say there's a foundation for that?"

Chinchirorin? Oh, the 'Simple Game Played with Dice'. It goes hand-in-hand with the Underworld.

"Marisa, I believe the reason why Reimu can guess the outcome of dice rolls must be because she can forecast using the predetermined future."

I told them my idea, about the mechanism by which the outcome of dice was set. Perhaps Reimu can determine the initial state and result of the dice by her intuition? There are those in this world with such "luck."

"That's not it at all, Rinnosuke; I can't forecast anything no matter how long I look at the dice. People who do that only think of probabilities. Besides, for all their calculations, they can still be wrong."

"Why do you think so? While I suppose you don't do that, wouldn't that still let you tell the future if you could?"

Reimu looked shocked. "I happen to have a very deep understanding of fortune, so today, I'll be doing the lecturing on the mechanism of fortune - and something you won't be able to forecast afterward."

Reimu brewed tea for the three of us and gladly served it.

We looked forward to hearing the reason behind the quality of Reimu's intuition. I brought the tea to my lips, forgetting it had gone cold.

"...Ah. So what you're saying is that even if the initial conditions of the dice are the same, it's still possible to get different results?"

"Of course I am. Those are the only things deciding the outcome."

Reimu's tale was a complex one, but there was a shocking truth contained therein.

She says that the world is made up of three layers:

First is the physical layer that moves in accordance with the laws of physics, including all living things, objects, etcetera. It is on this layer that an object falls toward the ground, and that the water of the river flows.

The second layer is one that moves with the spirit, which includes things such as magic and sorcery - the mental layer. One's mood turning sour when meeting an unpleasant person, and releasing all your stress and cares during a party lie here. Since most youkai can control the world through both the physical and mental layers, they say that history repeats itself and the future is predetermined as a prank.

But according to Reimu, there is a third layer that rejects loops: this third layer is the memory layer, which is the recollection of events that lies within all things. Since it is only possible to add to the memory layer, it's impossible to completely recreate the past; if something were to happen that already occurred in the past, then there would be a contradiction because that would imply that that memory was lost, which is impossible. The memory layer always continues to build up.

The physical layer follows the laws of physics, the mental layer explains the outcomes, and the memory layer alters probability, mutually creating the future. Reimu said that excepting the cases when something has already happened in the past, it is absolutely impossible to predict the future with certainty.

So, take the dice roll as an example. If you were to somehow throw them with the same initial conditions as before, unless they don't recall being thrown in that way, the probability of the same outcome isn't as high as you might assume.

I followed her explanation up to that point, but then Marisa asked, "So how are ya able to tell how the dice will fall?"

While I was entranced by Reimu's new illustration of the world, Marisa was unfazed. I didn't think she wanted to know just to beat Reimu at Chinchirorin, but to use that idea to become as lucky as Reimu.

"I'm not really 'telling' anything; the way I can guess how the dice will fall is by feeling the dice."

The naturally-lucky Reimu, simply by using the memory of the dice, could make the outcome favor herself. The results just seemed to side with Reimu.

"Whaaat? Howzzat gonna help anyone but Lady Luck over here?" Marisa sulked.

I doubted the existence of things such as fortune in this world, deeming it too unreliable. This was largely in part of my thinking that the future was predictable. I saw good luck charms as nothing more than lumps of fallacy.

However, upon listening to Reimu's world, I have reaffirmed the existence of fortune. The blessed man and the cursed man both exist, certainly. There is a man who succeeds in shouldering his trials. There is a man who is a failure, captive to jinxes, as well. It might certainly be reckless to just think of each one starting in the same initial conditions.

If we assume that probability is determined by the power of memory, it may be natural that such a power can be manipulated by good luck charms. The more complicated and unusual the origins are, the more knowledge a charm will have, thereby raising its effectiveness.

Reimu added to this, "In this world, both physical and mental probabilities are determined by how fortunate they are in the memories they hold."

I remember hearing that phrase before. "In the material world, that all things exist without probabilities is already common knowledge;" something along those lines was written in a science textbook from the outside world.

With only a vague understanding of its meaning, I wondered, "So that means someone already determined these probabilities?"

But Reimu had come up with the same idea, and even worked in her idea of the memories changing the probabilities! It was surprising.

"Memoriy determines probability...in other words, it works like karma. That's pretty amazing. It may very well be true. By the way, how did you come across this knowledge?" Your lifestyle appears so idle, I was about to add, but to preserve the current subject I changed my mind.

"I heard it from a really, really smart human."

"If ya say it like that, it makes ya sound even dumber..." Marisa muttered.

I wondered if there was any human in Gensokyo who knew the roots of the world like that.

"The reason why it feels like history repeats itself to youkai is purely because they aren't human. A human's memory is only as short as its lifespan, but in a youkai's lifetime, they will see the same things over and over again. Just like you, Rinnosuke," Reimu said smugly. The situation is usually reversed, so I was slightly annoyed. "And this really, really smart human has the memories of all the books stored by her ancestors for generations. She knows things that not even youkai who have lived for a long time know, much less any other human."

That was a rather lengthy conversation. The color of the window has already changed to match the color of the evening. The autumnal tint of the leaves outside had begun to permeate the room.

"Even though the sun is beginning to set, did you have any business for coming here today?"

"Ah, that's right. We were here because we had nothing else to do."

"Chase out some ghosts, then go have a party at the shrine. We came here ta invite ya. Whaddaya say, Kourin?"

I see. It took quite a while for it to come to this. They hadn't announced why they were here, and we thoughtlessly ended up talking for longer than expected.

"I appreciate the offer, but I still have an important job to do. And besides, if we played Chinchirorin, I doubt I would be any match for Reimu."

"Job? Ya mean writin' your book?" Marisa said while pointing at my journal.

"That's true, but I also have to tend to my store, as well."

"So you're still writin' that thing, huh? Thought ya gave up on it by now."

"Sooner or later, this journal will become a history book; I cannot stop so easily. This will be a history book that enriches human knowledge, a product of Kourindou."

A number of years ago, I started writing this journal since paper had become an easily-obtainable commodity, and I now have a considerable amount stored up. I plan on making a book to pass down these records. If the book becomes the history book of Gensokyo, the academia of Gensokyo will begin to move rapidly. This will bring Gensokyo closer to the outside world, and it will become a secure place in the future. (At the same time, if it sells well, the shop will also be secure.)

And today I learned about the mechanism of how reality can be determined from randomness, why there is a difference in the amount of fortune between people, and how there are people who can know the coming reality - surprisingly from Reimu. I should note the "not records, but memory determines the future" concept in my book. And then, if whomever reads my book learns of this person who already has the mechanism of fortune, then they will probably be unable to guess the future. Humans living moving forward in a future unprecedented by youkai. And since the youkai will also be unable to know what will happen tomorrow, they will be fortunate enough to get a taste of the future we humans will enjoy.

It had become completely dark outside. I wonder if Reimu and Marisa are holding a party at the shrine by now? Their behavior, as always, drinking sake, as always, with Reimu winning the bets, as always, and drinking too much, as always...

However, this world has never repeated itself.

Because Reimu, Marisa, the youkai, and myself, the half-human, half-youkai, remember these things.

Because these memories make every day more enjoyable, little by little.

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