It's a different pair of trees. A pair of trees inside of a pretty garden, with tons of flowers across a small pond. There's a small group of children walking around, maybe 10 year olds, maybe half of them in school uniforms, with girls and boys both dressed in white skirts and professional looking black sweaters, like those used in British school uniforms. The weather is sunny and warm, but it's a dry heat, so it's just pleasant and not muggy. There's a woman, presumably the class teacher, walking them around the beautiful garden. There's an inviting forest surrounding the garden.

She wants to scream. There are kids so she restrains herself. She pulls out her cell phone and desperately hopes it has signal. It does not. She looks around for a bench to sit down on.

There is one a few feet away from the pond. It's made of some kind of black plastic (presumably) material instead of wood, and it actually feels quite soft and comfortable to sit on.

She will indulge in crying quietly for a couple minutes.

The adult looks at her in confusion, but doesn't say anything. People who need help would know to ask. Instead, she turns to the kids, talking about how the flowers they're seeing today are the results of many hundreds of years to make them as beautiful as possible.

She gets herself more together and listens to the lesson. She's reluctant to interrupt, maybe someone else who isn't busy will come by.

The teacher looks at her for a moment before continuing her talk.

"These flowers have the colors they have due to recessive and dominant alleles. In essence, you can have strong allele that overpowers the weak one, or a weak on that loses to the strong. This white color is strong, and this purple color is weak; one white can beat one purple, so the purple color only shows up if there's no white color overpowering it. In people, there's a very severe illness, that everyone can get on X-chromosomes. But it's a recessive genetic illness. In women, their healthy X-chromosome can "beat it", so they don't get sick, but in men, they only have one X-chromosome, so if they get that illness, there's nothing to fight it back. Actually, one country had a queen with illness allele who gave it to her sons but not daughters, so the country got lots of queens because the kings died of the illness!"

That's an unusual way of framing that information. She's not one to interrupt a fellow educator though, she might ask about it in private but not in front of the kids.

Eventually, the teacher turns to Crystal.

"I haven't seen you before! Are you here to enjoy the pretty flowers and ponds, too? Or even try diving to find some of the sunken treasures?"

"I don't actually know where I am or how I got here and my phone doesn't have service. I'm having a rather alarming day." Through this all she keeps her voice carefully steady.

"What happened? Do you think you have amnesia? Can I see your phone?" The teacher doesn't hide her shock particularly well, but tries to act as reassuring as possible for Crystal.

"I don't think I have amnesia... I was walking through some woods and then suddenly I was here. And these flowers and school uniforms are both unfamiliar. Here's my phone." She takes out her Pixel 6.

The teacher looks at her phone. It doesn't take her many seconds to realize it's not of thomassian make; somehow, a genuine teleporter from another dimension is in front of her. She rapidly dials a number. "Hi, Pandemic Awareness Day came early this year. Tell everyone from Heaviside Arboreal Boarding School that a person has teleported from another dimension, potentially bringing an infectious illness. This is urgent information."

"Excuse me, but what's your name? My name is Clarissa. You must feel so disoriented, but don't worry; we're here for you." She subtly gestures for the children to keep their distance from the woman sitting on the bench.

"Oh. This isn't just another city. This is, oh. I'm Crystal, Crystal Miller. And I'm not getting home soon am I?"

"I wouldn't know that, you shouldn't ask me! But don't worry; we'll be here for you. We'll have a room ready for you by the time we get to the school, trust me."

She motions for Crystal to follow her, as she slowly begins the walk back through the spacious canopy of trees, brightly lit by the sun.

Oh right they mentioned diseases... She will take the N95 mask in her pocket out and put it on. Maybe that will be important. She gets up and follows the teacher.

After 20 or so minutes, they reach a school building that seems to be maybe 8 or 9 stories tall? At least weirdly tall for a school building. Clarissa looks at her phone, before leading Crystal into one of the dorms on the ground floor. It's a reasonably spacious room, with a thick, soft carpet and a small bathroom. It still has 2 upper bunks, above the soft carpet.

"This is where you should probably stay for the quarantine period. We're hoping to convert a nearby room to a medical facility fairly soon; don't worry about a thing."

"Okay. I can do that. Do you know what's going to happen next?"

"Well, we'll send out a swab in case you actually have a virus that's dangerous for us but not you, so we can get a head-start on developing a medicine. And I'll have to stay with you at this point, too. I worry that we'll have to go through the full 10-day quarantine, unfortunately."

"I don't think they could do that in my world. Is it really a good idea for us to be staying together we basically spent half an hour outside together I wouldn't expect you to catch anything from that or vice versa but ten days in close quarters seems like it would effectively guarantee we would get sick if it was going to happen." She pauses. "Unless that's the point."

"Well, yeah... I'm kind of expected to be the one taking one for the team, here. For all we know, I'm sick already. So why risk someone else? Anyway, you sound distressed... I can change into some real PPE and give you a hug, if that makes it better?"

"Uh... you're also risking me and I didn't get asked about that. I don't know why you're being so blase about this but I definitely didn't sign up to get some weird disease that you already have vaccines for."

"Sorry, sorry! I can happily let you quarantine by yourself. It's just... well, I think we'd both probably have to find out, eventually."

She takes a deep breath and steadies herself. "I would really prefer that. I'm okay with being quarantined for longer if that means I get vaccines or whatever else that makes me less likely to die of something that could have been prevented. Assuming, your vaccines are even safe for me to take. I don't know how we're speaking the same language or why we look so similar."

"Well, I guess we can get you vaccines? We just haven't needed them for a while, just because we did such a good job of stamping anything that might need them out. All the vaccines we have are kept in storage, just in case they prove useful. I'm hoping they'd be safe for you, just because we look so similar and even speak the same language. But the separate quarantine thing... yes, I'll 100% walk off and leave you by yourself. To... keep you safe as well."

"Thank you."

Crystal Miller receives a phone. This one does have signal. It's made of some kind of ultra-light plastic, and a few seconds of tapping starts activating the projector, letting her get a big screen view of everything happening the wall opposite the door into the dorm. Thomassia has sappy, slightly cliche romance movies; these are about a couple first meeting and growing ever more intensely in love, before returning to the place they first met and reminiscing on everything that happened.

By the time she's done with the quarantine, the thomassians, adults and children both, are excited and curious to learn from this mysterious human who teleported to their school. The kids were excited to have their first class with her, with her wearing a lightweight and transparent face-mask made from a transparent film that left a faint bluish sheen over her nose and mouth.

Crystal is very glad she has not gotten terribly sick and somewhat worried that might change. The first big thing she wants before teaching a class is to watch one. Ideally without distracting the kids too much.

She also turns her mind to what she should teach. The basics are probably out, math science and vocabulary are all things where it's pretty likely their teachers are pretty out of sync and pre-requisite knowledge is usually pretty important. Well, maybe not necessarily. She could split them into groups and try to have them work on a puzzle of some kind. It's just hard to gauge difficulty level there. Literature could also work she has some short stories on her original phone and maybe reading and discussing one together could be good. The last option is history... history has always been a hard subject to teach finding the balance between being honest about the many mistakes of the past without making it sound like everyone in the past was just an awful person is hard. She usually ends up erring on the side of making things sound better than they were.

She explains all of this to the local teachers and asks for their thoughts.

Clarissa nods at Crystal's suggestion to watch a class before teaching one herself. She finds a recording of a class and projects it onto the wall of Crystal's room, showing another teacher in the middle of a science class. It's a class explaining energy and how it can come in many forms: energy in a battery, moving a car forward, in an exploding a stick of dynamite, and spinning turbines in nuclear reactors.

The teacher in the recording repeatedly underlines how the phenomena are connected, and fundamentally commensurable, by explaining how each of these examples of some amount of energy, can be measured by comparing it to another example. How an EV battery has as much energy as you spend on 400 miles of driving, how many miles of driving needs as much energy as is found in one stick of dynamite, how many sticks of dynamite are needed to release as much energy as a nuclear power plant makes in a day, and how a nuclear power running for a day can fully charge all these EV batteries.

The heart of the idea is seeing connections, unity, and context: seeing how energy can come in many different forms, and be measured in many different ways, but ultimately only be one concept.

Alright, have the kids in question been taught about the scientific method and about how to test out ideas?

The kids have in fact gone beyond that. They not only learn about the scientific method, but they even learn about the design of experiments and how information theory and multi-armed bandits can be used during assignment in adaptive trials, so you don't need as much time or resources to perform the experiment and learn whatever you wanted to learn!

Oh... she hasn't ever heard of multi-armed bantits. So Petals Around the Rose would be too basic for a lesson then? Where are they with math do they know algebra and exponents?

They know both algebra and exponents (and also logarithms), extremely well! The Heaviside school is mostly an opportunity for kids who aren't too strong academically to enjoy nature; it has a kind of poor academic reputation.

Petals Around the Rose seems like a really fascinating thing to have a lesson about. It'd be cool to show off how inductive reasoning and exploring hypotheses really is universal; it can even work for something that nobody has seen before.

Oh good, she can definitely do that.

Clarissa prepares a classroom for Crystal; there are 25 kids, with a statistics/probability book on their desks. They have their phones out, ready to take notes on what Crystal's saying. Clarissa has brought her phone and placed it on a stand, filming the dice tray from above. The dice are black, with gold pips; they're the ones Clarissa uses for her tabletop games.

"Everyone, this is Crystal! She comes from a different dimension. She wants to teach us by using an inductive reasoning and inference puzzle that's popular in her home dimension. It's going to be so cool to see how induction really is universal, even letting you understand total aliens! Now, Crystal, roll some dice. And see how induction and hypotheses work to help us understand absolutely everything!"

Crystal obligingly rolls six dice there's a 1, 3, 5, 6 another 1 and a 4. 

"The name of the puzzle is 'Petals Around The Rose' whenever I roll the dice I can give you a number which matches to that dice roll. In this case the number is 6.

"Does anyone have any questions before I roll again?"

The students quietly tap their phones a few times, but don't ask any questions. They focus intently on what Crystal's doing. After a few seconds, one of them speaks up.

"I think it's quite obvious that one dice roll isn't enough? You know, underdetermination of hypothesis by data? So I think we should just do the next roll already."

"Not every question needs to be a guess of what the rule is." She still rolls again. This time the dice come out in two neatish rows: 1, 3, 4 and 5, 3, 6. "Eight this time."

The students keep their eyes on Crystal. A few of them nod; they smile, thinking that they had just gotten quite lucky.

When she rolls the dice next time one of them lands where the camera can't see. She picks this one up but doesn't put it back down the other dice are 5, 5, 3, 6, 3. "Twelve."

One of the kids looks up at Crystal, with a face indicating that he's had a revelation. "I actually have a pretty good idea, already. Can you roll another 6 dice, but not tell us the number? It really helps when sifting through hypotheses, to kind of have a question in front of us."

"Of course. If you have a guess first you can tell me the number you think it is. If you get three in a row then you can send me a message with your guess. That way everyone has a chance to figure it out themselves." This time the dice form an arc: 5, 5, 1, 5, 1, 3.

The same student who asked for one more roll then closes his eye. "Everyone, I have an answer! No peeking!" Eventually, all the students close their eyes, and the excited student holds up two hands. He lifts one finger on one of them, and 4 fingers on the other. Clarissa nods quietly. "Yup, I think you'd know if your answer was correct. I'm sending you feedback now." Then the class opens their eyes again, looking stunned at the student who said he had an answer.

Crystal is also impressed. "Okay, does anyone else want to make a guess before I roll again?"

All the other students seem too unsure to be willing to take a guess. "Please roll again. I'm hoping that getting a super-low number could make a huge difference."

The next roll is 5, 3, 3, 2, 5, 1.

"Well, uhh. Could you also say the number? Just for the newest roll, not the last one."

"This one is twelve."

Almost the entire class raises their hands at basically the same time.

She calls on someone in roughly the middle of the room.

"So I have 3 thoughts just from the first 2 dice rolls: first, the numbers are fairly low. So this means that it's unlikely that there's some kind of system where you have pluses and minuses. Because it's unlikely that they'd cancel each other out to get close to zero?

Second, the first 2 rolls have many of the same numbers in both, but not in the same order. But the values are super-close to each other. So it's unlikely that you have a system where the position matters, because then it's unlikely for the numbers be placed in the new order in a way that cancels each other out so you get close to the last order of essentially the same numbers?

Third, they're also both even. Which is a vague hint that the end result only grows by an even amount?

So now I'm thinking, we probably have a rule where order doesn't matter, and we add an even number of points, and there are only a few different dice results that can add points. 

If we compare the numbers in roll 1 and roll 2, the second one has the same numbers except for one more 3, and it has an associated number 2 more. So 3 increases the answer-number by 2 is a perfectly fine and good hypothesis to get started with.

That means that all the other numbers in the first two sequences put together, the 1, 4, 5 and 6, add 4 to the answer-number, right?

After this, you mentioned one sequence that resulted in 12, and another sequence that resulted in 12. And what I noticed was that both had two 3s and two 5s. So two 5s add 8 to crate 12, or one 5 adds 4 was a hypothesis explaining all outcomes. 2s add 8 also technically speaking make sense for the two sequences resulting in 12, but it's unlikely that the the one die we didn't see was a 2. So I think the rule is: 3s adds two to the number, and 5s add four to the number, because it explains the pattern perfectly, and 2s add eight required the one die we didn't get to see to be a two, making it a shakier hypothesis."

"Very good that's correct. Does anyone want to give a guess as to how the rule relates to the name of the puzzle?"

The kids seem to have no idea.

"Alright, let's start by breaking down the name. Who can tell me what petals are?"

"They're analogous to leaves, placed at the end of a flower's stem, where they help with photosynthesis?"

"That's a very technical answer, petals do help with photosynthesis but they also help attract pollinators and when people, at least where I come from, think about flowers they're often thinking about how the petals of the flower look. A Rose is a type of flower. Does that give anyone any ideas?"

It really doesn't, actually!

"Alright, I'll just explain, the name of the puzzle is meant to be a hint at the arrangement of the dots on the dice. If there's a dot in the center of the face that's the rose and the petals are the dots arranged around it. 2, 4, and 6 don't have a dot in the center so they don't have any petals and 1 has a rose but no petals around it."

The children just seem weirded out. "It's a good mnemonic, I guess?"

"Alright, for the rest of the time you can either do your normal work or form small groups and take turns making up your own rules and seeing if the other people can figure them out."

They spend the time inventing their own rules, or just using their phones to take cloze tests and going over flashcards, very intently. The children display a very intense level of concentration. One of them is very slowly pacing the classroom, trying to understand some particularly tough concept and explain it to themselves.

"Should one of us see if they need help?" she whispers to Clarissa regarding the pacing child.

"They know to ask for help! It's one thing that really gets drilled into them." Eventually, someone walks up to Clarissa. "Could you explain the parts of the entropy formula, again?"

"Well, the first part, the innermost part, is how many 1s and 0s you'll need. Then of course you have to multiply that by the chance that you get that symbol. You do this for all your possible symbols. But of course, the innermost part is always negative, and you want a positive value. So you negate it again.

And you want the biggest number, right? And the way you do that is that you try making a square: basically, you want the 2 inner parts to both be the same, because going from 5*3 to 4*4 is bigger than vice versa, it's a bigger percentage increase for the smaller one of the two."