Chapter 2

Fin and Zei got off the autobus and walked down Kin Min street.

Kin Min street was one of the more lively commercial and industrial streets in Pafogai Du. On both sides of the street, they could see signs with colored blinking lights advertising all kinds of electronics: hand devices, watches, compute boxes, lighting, batteries, sensors and more. Among the stores were miniature factories, building various sophisticated devices and in a few places even computer chips. The buildings were all one or two storeys tall, and many signs were on top of stairways leading underground.

On the left, there were two adjacent stores. One was selling sensors of all kinds - cameras, microphones, biological and chemical sensors, air quality monitors, and of course, sensors designed to detect sensors. The other was selling anti-transmission foil - a common material used by default in many kinds of rooms, to block wireless signals. Privacy and transparency, monitoring and anti-monitoring - the duality of keeping the Dzegojan safe.

Between the two stores, a sign read in large letters:

ZUI FIA KUN ZUN

"Underground safe place".

"gie fe pia kai ci bin hu", Zei thought to himself. "Grow roots, no head". The strategy that Dzego had been employing for half a century to grow and keep itself safe.

Fin and Zei both kept walking, enjoying the shade under the trees between the road and the sidewalk.

"How was the Minpentai game last night?", Fin asked.

"I got third place! Finally figured out a wall structure that reflected their gliders right back at them, completely wreaked havoc on their territory."

"How about you?"

"Studying for the geography exam."

"Boring as usual, I take it?"

"Yeah, we're covering the United Cities, and they're just making us memorize all the co-governance percentages. Freetown gets ten percent votes in Redshire, Redshire gets fifteen percent votes in Devanvil, Devanvil gets..."

"Do you have any new opinions on how effective that whole system is?"

"Oh no, critical governance studies only becomes a topic in university."

"The same way that chemistry is a topic in high school?"

Fin laughed. "So are they also gonna cover an entire year of critical governance studies in two weeks in DU now?"

DU - that reminded Zei. They needed to make sure they got there on time. Zei checked his watch.

"Time just hit sixty nine thousand. The exact location of the classroom should be getting decrypted and broadcasted any moment now."

The watch buzzed. Zei got a notification.

Zei stopped, and showed the watch.

"Huh, yellow checkmark. Looks like they've upgraded to a new cryptographic proof system, gotta make sure we sync our codes when we get to the lesson today."

"Again?"

"Guess so. I hear the Arctic Empire is getting more aggressive, so we're stepping up security."

"Okay, anyway, it says Mun Gui 1842. We... just passed Kin Min 1990. So it's behind us."

"Let's just turn left here on 20th, and then left again on Mun Gui?"

Zei checked over the math in his mind. Named streets were spaced three hundred meters apart. K to M was two streets. House numbers were just meters. So to get from 2000 to 1842 they had to walk one hundred fifty eight meters. Six hundred and one hundred fifty eight together is ... seven hundred fifty eight meters to walk. The lesson starts at seventy thousand, so they had a little under a thousand ticks, or more colloquially, ten minutes. A slow walking pace is one meter per tick, and Fin and Zei were fast. So they were fine.

"Sounds good!"

A few minutes later, they arrived.

---

"Oh Fin, there you are!", a young woman shouted.

Fin and Zei were led down two flights of stairs.

When they got to the bottom, another man was waiting, and stopped them.

"Change of plans, it's on the opposite room on floor -1 now."

Zei sighed.

The four of them walked back up a flight of stairs, entered a large room, and sat down beside each other on one of the rows of chairs.

The walls were covered with a thick hastily-organized layer of anti-transmission foil. Coated on top of the foil was one of the classic aesthetics of Dzego: pictures of cute cartoon animals playing with electronic gadgets and chemistry lab equipment, with a backdrop of green trees and blue skies. At the front of the room, there was an inflated cartoon-style pig on the left and a hamster on the right. The pig, in its left hand, was holding a calculator. The hamster, in its right hand, was holding a vial of some green liquid. With their other two hands, the two together held up a poster with a stylized depiction of DU's Dzegoban name, "dzu fu sun du", and right below that DU's motto:

   PA JAN LI SUN ZO
ZAI GAU FE PA JAN

   GO LI SUN ZO
BAI GAU FE GO

"One man learning will set one man free. A nation learning will make the nation great."

Behind them, the instructor walked in, a tall man wearing a Veridian privacy robe, but not putting on the hood - instead, his head was covered with a more distinctive and fashionable hat. He closed the door. Zei checked his watch. 70,001.

---

"Welcome to physics class", the instructor said.

"Today, I'm going to try to introduce an important topic that I think almost everyone gets confused about: thermodynamics."

The more attentive students put away their hand devices, stopped talking, and got ready to listen. The others kept talking at first, but then quickly quieted down.

"Who here has heard of the word 'entropy', in the context of information theory or cryptography?"

About three quarters of the students raised their hands.

"And who here has heard of the word 'entropy', in the context of the second law of thermodynamics - that it always goes up, and one way that happens is that heat always flows from hot to cold, never the reverse?"

Almost every student raised their hands. Entropy was a favorite topic of science fiction.

"Now who here thinks they can explain the connection between the two?"

No one raised their hand.

"Alright. Let's begin."

The instructor pressed a button on his watch, and a slide showed up on the front wall:

"Imagine that we have two jars of gas. Each jar has a million molecules. But in the jar on the left, the molecules are moving much faster. Suppose, in the jar on the left, you can represent the velocities with six-digit numbers, from zero to 999,999. And in the jar on the right, the molecules are moving slowly, so you can represent the velocities with six-digit numbers, from zero to 99."

"Can someone tell me, how many digits do you need to fully represent everything going on in the jar on the left? Assume that they already know it's gas and there's a million molecules, the only free variable is the velocities."

"Six million!", about ten students shouted in unison.

"Good. Now, what about the jar on the right?"

"Two million!"

"So let's recap. From your point of view, as the observer, you know that these are both jars of gas, you know what kind of gas, and that there are a million molecules. But you don't know the velocities of each individual molecule. So for the jar on the left, the amount of information that you do not know is...?"

"Six million digits!"

"And for the right?"

"Two million digits!"

"So eight million digits in total, information that you do not know. Now, what happens if we put the two jars together and let the gas mix? What will we know about the velocities there?"

Zei raised his hand.

"Yes, you there?"

"The molecules will bounce against each other a lot randomly. When things settle down, because of conservation of energy, we can expect the new velocities to all be somewhere in the middle, between zero and five hundred thousand."

"Yes, excellent! Now technically, energy is proportional to velocity squared, and we can argue about how these velocities are represented, also in reality the distributions are Gaussian and not uniform and bounded, and by the way we're also completely ignoring positions, but let's just keep it simple and say zero to five hundred thousand."

The instructor tapped his watch again. Next slide.

"Now, how many digits do we need to represent the information we don't know about this new system?"

Another student raised his hand.

"Go ahead."

"From zero to five hundred thousand is more than five digits but not quite six digits, if we go by logarithm, it should be about five point seven for each molecule."

"So what's the total?"

"Eleven point four million digits."

"Very good! So the conclusion is: by mixing the two jars, we have lost knowledge. We know less about the gas than we did before. And we can quantify how much knowledge we lost: it's three point four million digits."

"This is what we mean, when we say that entropy goes up, when heat flows from hot to cold. For each tiny increment of heat, heating up a cold thing adds more unknown digits than cooling down a hot thing by that same increment takes away, and so the total unknown goes up. Every possible action that you can do to these bottles will, on average, make the total unknown either stay the same or go up - and if you're doing anything useful or making any mistakes, it will go up. This is the second law of thermodynamics."

"Now, how do we prove this? Let's prove by contradiction. Suppose we did have a magic procedure that could go in reverse: start with the merged jars with eleven point four million digits of unknown, and bring us to the separate jars with eight million digits of unknown."

Zei raised his hand once again.

"Can I try this?"

"Go ahead."

"I remember the laws of physics of our universe are fully time-reversible, right? So if you can do something in one direction, you can always run that process in reverse."

"Exactly. Now why does that time reversibility, at that level of atom-by-atom physics, imply that temperature equalization is something you cannot reverse? Isn't that a paradox?"

"Well if we could separate medium temperature into hot and cold, then we would be able to do unlimited data compression."

"Like, imagine you had a file with eleven point four million digits of data. You would make a really perfect double-jar, and have a gun that shoots out the gas molecules with exactly the right velocities. Then, you would use your process to un-mix the gas, then split the jar, and measure the velocities at the end. You would get eight million digits out."

"And because our universe's physics is time-reversible, you would be able to do the same thing in reverse: take those eight million digits, put them into the gun to shoot out gas molecules at the right velocities, apply the exact same un-mixing procedure backwards, measure it, and you would get out whatever your original eleven point four million digits were. The output of the time-reversed process has to equal the input of the original process. And so we get a fully general-purpose way to represent any eleven point four million digits inside of eight million digits. And we could apply that again and again, and represent the whole planet in eight million digits, or even make it smaller and do it in eight digits. And that's impossible!"

"Exactly. Or in other words, you can't go from not knowing more things to not knowing fewer things in a universe with time-reversible physics. In a universe with time-irreversible physics, you could, because you can just destroy all the things you don't know."

"Just like the Arctic Emperor!", Zei wanted to shout. But he kept quiet. It's bad form to openly explain a joke that is so obvious, that half the students probably already have it on their minds. The instructor and the students briefly paused to appreciate the joke and smirk and enjoy a few moments of mental communion. The instructor then moved on.

"But in a universe with time-reversible physics, there's always things you don't know, and that lack of knowledge can only be shuffled around, and inevitably increased. The best we can do, is go from not knowing things we care about, to not knowing things we don't care about. Like going from not understanding thermodynamics, to not knowing the velocities of the molecules that are coming out of the projector showing these slides as waste heat."

"Amazing job, kid. What was your name?"

"Zei."

"Well, Zei, you got it per-"

A loud noise erupted from a nearby room. The whole room shook.

A fraction of a second later, part of the wall and the floor came crashing down.

The next thing Zei knew, a fragment of stone hit him in the arm.

---

Zei found himself on the ground, his knocked-over chair beside him.

His mind flashed back to the man who had redirected them last minute to a different room, one floor above where they had been supposed to go.

He understood immediately. All of the extra precautions that DU had been taking - the cryptography, the sudden changes in location, the anti-transmission foil - they were not just a game. And the Arctic Empire was not just a unit in geography class. This stuff was real.

"Is everyone okay? Anyone injured?", the instructor yelled.

Zei thought for a second, tried to figure out if his arm was injured enough to be worth complaining. He tried raising and lowering it, and made a few random gestures with his fingers. He decided that he was fine.

The next thing he felt was two arms grabbing on to his arm, and pulling him up off the ground. Zei turned around. It was Fin - to Zei's relief, completely uninjured.

Smoke filled the room. Every student's watch, among its many features including an air quality monitor, started beeping loudly. The students tapped their watches, and soon the beeping died down. Slowly, the students helped each other get back up, as the instructor walked around to check if there was anyone who seriously needed help.

For about a minute, the room was almost silent. Once all the air quality alarms shut off, the only thing interrupting the silence was the instructor asking "are you okay?" and a student responding "I'm fine".

The air filters activated to full power, and soon the smoke cleared. Fin and Zei looked at each other. For a few moments, the students and the instructor held an awkward silence.

"I think we know much less about this wall than we knew two minutes ago", Zei joked.

Half the class laughed. He had judged the audience's mood well.

"No one hurt, are you all sure?"

"I'm fine", about ten people replied.

"Alright, I think we've had enough entropy for one day. Let's go home."

---

Fin and Zei stayed in the classroom longer than the others, grabbed a broom, and pushed all the debris to one side. Soon, only they and the instructor were left.

"Wow, the Arctics are getting aggressive. They didn't use to go after physics education."

"Whoever moved our room last-minute was a genius. Just saved our lives there."

"Unfortunately I expect it will only get worse from here."

Fin and Zei looked at the instructor in shock.

"Remember, their game is to permanently keep down our level of heavy industry and technology. Let us live, but only at the level of civilization where we can never be a threat."

"And our counter-game is 'gie fe pia kai ci bin hu': grow roots, no head. Use distributed manufacturing to build all our tools. Let the official government keep going and be stupid and corrupt just like it was when we lost the war a hundred years ago, but use cryptography to coordinate the decisions that matter anonymously, without needing any exposed individual leaders at the helm. All of DU already runs this way, soon big parts of our power generation, agriculture and medicine will."

"And it's been effective. After the last few years, we're finally almost at the level where we can stand up for ourselves without needing any heavy industry at all. The problem is, it looks like they're catching on."

"Dze go ba fau gie", Fin and Zei said in unison, calmly but defiantly.

"Dzego will rise again."