A new post up on my blog! Last time we talked about the algebraic numbers, and how just wanting to solve simple equations can create a ton of different numbers. But they don’t get us everything.
So this time we start off with the idea of measurement, and wind up inventing the real numbers. The real numbers are weird. Real weird. But they show up when we start asking questions about size or measurement. And in part 3, we’ll see they’re exactly the right way to do calculus.
Based on context clues I've put a green dot where I kinda think Tom's house might be. They come out of the forest, which can be seen from Tom's west window, and they saw the downs to the east of his house. And then there's this bit:
By his advice they decided to make nearly due North from his house, over the western and lower slopes of the Downs: they might hope in that way to strike the East Road in a day's journey, and avoid the Barrows.
The yellow arrow is the journey they're hoping to make today :]
Rey left the Falcon behind, walking up the steps on the Ahch-To island, and she fought the urge to run.
It had taken all this struggle to get here. All this time. The map BB-8 had carried… so many who’d been lost on the way… and now she was here.
She was going to ask Luke Skywalker for help. The legendary Jedi Master, the one who had defeated the Emperor.
As she climbed, though, a niggling little feeling began to gnaw at her.
Where was he, anyway?
She’d been assuming he was somewhere high up, and the Force wasn’t pointing her anywhere else. But she couldn’t see him, and as she reached the very top of the stairs… there was no sign of him.
“Master Skywalker?” she asked, looking around. “Master Luke?”
“Jee-dhai?” one of the locals asked, in a curious voice.
“Huh?” Rey replied, turning. “I… well, I don’t think… I want to be, but I’m not one yet… do you know where Master Skywalker is?”
The hooded alien shrugged, and pointed to one of the rock huts.
Curious, Rey entered.
It was immediately obvious Master Skywalker wasn’t in the hut. There wasn’t room. There was barely room for Rey… but, after a moment, she spotted something odd.
A folded piece of flimsiplast, with a metal-rimmed piece of crystal on it.
Taking the crystal, Rey was surprised to find that it felt… warm, and tingly. It fizzed with an unidentifiable but oddly familiar energy, and she turned it over before opening the flimsiplast.
It held only one sentence.
Use the Force on the crystal.
“...is this going to be a riddle?” Rey asked. “Or a trial of some sort?”
Silence answered her, and she took a deep breath before closing her eyes and focusing.
It was still… difficult, to call on the Force at will, but she could do it.
As she did, the crystal glowed, then filaments of light streamed out of it to form a face.
Master Skywalker’s face. She was sure of it.
“To whoever has found this,” he began. “Firstly, if this is Ben… well done for coming back to the light. And if not… I’m glad there are others besides myself who can use the Force without being tainted by the Dark Side. This crystal has been constructed using the techniques of the ancient Holocrons, which would shatter if they were forced open by the Dark Side.
He paused. “The Caretakers have a few of them, in case they need to replace one. Anyway… if you came here, then either the Force guided you here to Ahch-To or you came following the map. And if you came following the map, you came looking for me.”
Master Skywalker’s expression turned rueful. “So I’m sorry to disappoint you. I’m not here. I left. I grew up on a desert planet, and this place just… unsettles me. It gives me the creeps to see all that water. Hurricanes should be illegal, and this planet has some really nasty ones… anyway, I’ve moved somewhere where I don’t need to worry about that. You’ll find me in the Bespin system, on Cloud City…
Rey’s eye twitched, as the blue illusion of Master Skywalker’s face listed off an address.
The crystal fizzed slightly, and she dropped it before she could break it somehow, then crouched down and picked it up again – not accessing it with the Force, this time.
“Right,” she said, her voice tight, and turned to go right back down the slope again.
“You’re back early,” Chewbacca said, concern in his voice.
“Luke’s not here,” Rey replied, hitting the switch to raise the Falcon’s ramp. “Do you know where Bespin is?”
Chewie blinked.
“What?” he asked. “Yes, I know where Bespin is… you’re saying he’s on Bespin?”
“Apparently,” Rey replied. “Though I suppose the map is a map to where he went, not where he is. It’s not like he was updating it…”
Cloud City was an amazing sight, though it had begun to pall slightly for Rey when it took them half an hour to get a landing permit.
Eventually Chewbacca called in a favour from someone called Lobot, and ten minutes after that Rey rang the door chime on the address Luke had given her.
Then she stood outside, waiting.
It was strange to be in a completely built environment. Even the ground under her feet ultimately had nothing beneath it but air… and yet all this was kept in the air by technology.
If Rey hadn’t known quite so much about how solidly built repulsorlift units were, she might have been unsettled.
The door hissed open, and a woman looked out. “Yes?”
“I’m looking for Luke Skywalker?” Rey asked, awkwardly.
“Oh!” the woman said. “You know, he didn’t leave a forwarding address, but he did ask that something be given to anyone who came looking for him… hold on a moment, please.”
The door hissed closed again, and Rey leaned on her staff and groaned.
“I’m guessing we’re leaving?” Chewbacca asked.
“We’re leaving,” Rey confirmed. “For somewhere called the Dagobah system.”
She held up the crystal she’d been given. “If you’ve never heard of it, this should help, at least. It’s got a planetary map, as well… and a long, long complaint about vertigo.”
“He did once fall out the bottom of Cloud City,” Chewbacca volunteered. “That would give anyone vertigo… here, anyway.”
“So after spending a month here, I realized what training with Master Yoda had let me forget until then,” the pseudo-visible Jedi Master explained, as Rey focused – not without some annoyance – on the crystal she’d found in a hut. “Which is that Dagobah is damp. I can’t walk very far without sinking into the swamp, the only food available is moss soup… Master Yoda stayed here for decades, and I can see the argument that a Jedi should be inured to physical discomfort, but I just can’t take it any more. I’m going to Ajan Kloss.”
“Really?” Rey asked. “Really?”
She focused, drawing out her anger, and expelled it with a sigh.
Where on Ajan Kloss was she supposed to be looking, anyway?
The holocron-alike crystal shimmered, showing an Ajan Kloss planetary map, and Rey committed it to memory before closing her hand around the delicate-seeming crystal.
“All right,” she said. “Ajan Kloss, then! And there had better be a Jedi Master there.”
There was not.
“So it’s been the rainy season…” the next crystal declared. “And it’s not as swampy as Dagobah or as rainy as Ahch-To, but it’s a lot warmer and the combination is absolute hell. I thought it was the rainy season when I was here before, but it turns out that it was actually the dry season. This is the rainy season, and it never gets dry. Nothing gets dry. The humidity is absolutely one hundred percent constantly. The floor’s covered with millipedes and our robes are growing fungus on them.”
Rey shuddered involuntarily.
It did sound bad.
They were fortunately in the dry season again, or at least she assumed so since the rain coming down outside was only moderately heavy and the geography hadn’t been entirely covered by cloud.
“What’s worse, the plants here even grow at night,” Luke complained. “So that’s it. I’m done with this place. We’re moving somewhere where there’s no need to worry about plant life at all…”
“Are you sure this is necessary?” Rey asked, two hours later.
“Yes,” Chewbacca replied, giving her another parka, and Rey put it on somewhat awkwardly. “You’re from a desert world. You know how Dagobah was cold and wet?”
“I’m having trouble forgetting,” Rey replied.
“Well, that’s about fifteen degrees,” Chewbacca explained. “Hoth is minus forty. I was cold there.”
Rey stared.
“...do you have any more warm clothes?” she asked.
Eventually, with some difficulty, Rey struggled into the ruins of the Rebellion’s Echo Base.
It was below freezing cold, and intensely annoying, and what was worse was that there wasn’t even a Jedi Master there. Instead, there was another crystal.
It mostly contained Luke complaining about how kriffing freezing it was, and that he’d spent three days here before electing to move to the Forest Moon of Endor.
“What is this?” Rey asked, after extracting herself from the parkas and as the Falcon sped towards the Endor system. “Is it some kind of sick joke?”
“I’ll give this for Endor, it’s warmer than Hoth,” Chewbacca contributed.
The Endor map led to an Ewok village, where they treated Chewbacca like an old friend and sniffed at Rey with great suspicion before Chewbacca managed to make himself understood enough to explain that she was a friend.
Then an Ewok shaman said… something… and Rey found herself involved in some kind of blessing ceremony. It was surprisingly useful, in that it actually involved the Force, but Rey was struggling to concentrate by the second hour… and it wasn’t until the fifth that she actually managed to convey the question she had.
The Ewoks discussed amongst themselves, then finally realized what she meant, and led her to a large treetop hut.
An empty hut, with nothing but some folded flimsiplast on the table, and a crystal on top of it.
Rey wanted to scream, but she didn’t want her hosts to take it the wrong way.
“If you’ve ever met Ewoks, you’ll know they’re brave warriors and good people,” Luke said, as Rey slumped over the Dejarik table on the Falcon.
Both she and Chewbacca were watching Luke’s latest message, and part of Rey hoped that wherever it was going to be was far away enough that she could get some rest.
The rest of her was wondering if they could just give up looking.
“But they’re also… a bit much,” Luke went on. “It took a month or two, but ultimately it got to be too much for us, so we decided to move on. This time we’re going to somewhere where we should be able to be alone, and as a bonus we can be out of the rain as well… it’s a lot like a homecoming, in some ways. We’re going to the Great Temple on Yavin Four.”
Chewbacca muttered something, and went to set the autopilot.
“I never thought I’d say this, but I have actually got bored of green,” Rey said, as they flew low over the jungles of Yavin Four. “I didn’t think it was possible to get bored of something that quickly.”
Chewbacca shrugged.
“Are we picking anything up?” he asked.
“Not on the long range,” Rey replied, sitting down and checking the scanners. “Nothing on passive… that’s just because Luke wants to hide, right?”
She detected a note of desperation in her voice. “It’s not because he’s moved on again, right?”
Chewbacca didn’t say anything, but he did raise an eyebrow at her.
Searching the Great Temple took about an hour, and they didn’t find a Jedi Master.
They did, however, find one of the now all-too-familiar crystals, and Rey stared balefully at it before clasping her hands and letting out her anger.
Again.
Then she snatched it up, wanting to know where they were going to have to go this time.
“You know…” Rey said, as they broke orbit. “I actually almost sympathize with that one.”
“You do?” Chewbacca asked.
“Yeah,” Rey agreed. “Knowing that the temples here were literally built by slaves who were members of the original Sith species… it’s a Sith Temple. I imagine any Jedi would be uncomfortable with that.”
She looked down at the crystal. “I really wish he’d put one of these on Ahch-To, though.”
“No argument there,” Chewie mumbled. “At least Naboo is an easy one…”
“I don’t know much about the place,” Rey said. “Only that it was involved with the Clone Wars, somehow. Or maybe something before the Clone Wars.”
The crystal pointed them to a very fine town house in Theed, which did not have Master Luke in it.
Instead, it had a droid, who beeped and whistled at them.
“We’re looking for Master Skywalker,” Rey said. “Please tell me you know where he went.”
The droid beeped again.
“...Master Amidala?” Rey repeated. “But Master Skywalker said to come here…”
“Same person, it’s just his mother’s surname instead of his father’s,” Chewbacca provided. “Show the droid one of the crystals?”
“It can’t hurt,” Rey conceded. “Is this some kind of ancestral home, then?”
She activated one of the crystals, and the droid whistled gleefully before opening an internal compartment and depositing another crystal in her palm.
“Right,” Rey said, rubbing her forehead with her free hand. “It’s a good thing the Falcon is so fast. We must have done a lap of the galaxy by now.”
“We’ve mostly been going through the middle, but yes,” Chewie agreed. “Where now?”
“That’s always the question,” Rey conceded, focusing.
If there was one thing this was good for, it was learning to master her anger.
“I know, I know, I said we’d be here for good,” Luke apologized. “But I ran into a Palpatine on the street yesterday, and it freaked me out.”
He shook his head. “I know, they’re from a different branch of the family, not everyone called Palpatine is evil… but it really unsettled me and I can’t feel comfortable here any more. Not after I heard from Binks about how Palpatine exploited both my parents… and him.”
The Jedi Master let out a long sigh. “But being somewhere I inherited… it helped, really. It reminded me of the other place that I inherited. We’re going back home. Beggar’s Canyon and the Lars homestead. Ben, if you’re the one hearing this… I’m sorry that we couldn’t give you the childhood that my aunt and uncle gave me.”
The force hologram disappeared, and Rey closed her eyes.
“That didn’t even give us a planet,” she said.
“No problem,” Chewbacca replied. “I know where we’re going. I know where Luke grew up.”
He nodded to the droid. “Thanks for your help.”
The droid whistled, waving a probe cheerfully.
Naboo to Tatooine. Mos Eisley to the Jundland Wastes to the Lars homestead, and from there on to Beggar’s Canyon.
Rey could feel the tension building in the air. Like the signs of a sandstorm, but more positive.
Signs of… something. Maybe signs of hope.
“Found something,” Chewbacca said. “Zeroing in on it now.”
The Falcon banked, slowing, and Rey went to the ramp as it opened. Around her, the light transport hovered on repulsorlifts, and she held on to a stanchion as she leaned out into the hot, dry air.
“I can see something!” she reported, through her comlink. “Bring us down another four metres… all right… I’m getting out here, land as near as you can.”
“Got it,” Chewbacca replied, and Rey slipped out of the door.
She landed with a roll, and shaded her eyes to look closely at what she’d spotted.
There was no mistaking it. It was a hangar bay. Built into the side of Beggar’s Canyon, concealed from above except at exactly the right angle, and big enough to service plenty of ships at once.
There were ships there, in fact. Two transport shuttles, a light and utilitarian variety, and a heavier and heavily modified yacht. But there was space for several more, and Rey frowned as she approached.
This didn’t feel empty in the way the other places had been, a difference that only made sense now she’d felt both sides of it.
It felt… lived in.
Then three young adults – a strange four-legged two-armed half-equine, a more familiar Bothan, and a human – came out of a doorway, all looking at her warily.
“Who are you?” the bothan asked. “Why are you here?”
“I’m looking for Master Luke Skywalker,” Rey explained.
“...oh, well, you just missed him,” the half-equine replied. “He’ll be back-”
“Lusa!” the Bothan protested. “Operational security!”
“Right, right,” the now-identified Lusa said. “Why do you want to speak to him?”
“Because we need him,” Rey said, simply. “To fight the First Order. I… brought his old lightsaber?”
She held it out.
“Whoa,” all three youngsters said, at once.
Then the Falcon came flying back over, still looking for a landing spot, and the human gasped.
“Is that the Millennium Falcon?” he asked. “Did you come here with Han Solo and Chewbacca? Does that mean Ben-”
“No,” Rey replied. “Han’s dead. He… Ben killed him.”
That put a damper on the mood.
“...so, where is Master Luke?” Rey asked, after a few seconds. “Who are you? What are you doing here? I’ve been following his messages for more than a day!”
“Well…” Lusa began. “We’re… trainees?”
“The old word was padawans,” the Bothan supplied. “Master Luke decided that… uh… he said that he remembered what Master Yoda said, and that the only thing that mattered was the spirit. That you had to learn to avoid the Darkness, and that everything else you could learn at your own pace, however fast or slow that was.”
“And all the teachers left about two hours ago in their X-Wings,” the human contributed. “So we’re the ones defending the Academy!”
“I am going to need some time to process this,” Rey said. “...wait, in X-Wings?”
“We had a fleet,” Poe said. “Now we’re down to one ship, and you’ve told us nothing!”
He waved his hands, for emphasis. “Tell us that we have a plan! That there is hope!”
Admiral Holdo stared back.
“There is a plan,” she said. “But I don’t have to tell you what-”
“Admiral!” someone interrupted. “Hyperspace signatures! It looks like… they’re snub fighters, twelve of them!”
Holdo’s shoulders slumped.
“And there it is,” she declared, as the tension left, and she sat back into her seat. “Turn the ship! Prepare for close engagement!”
The radio crackled.
“All wings report in,” came a voice, Luke Skywalker’s voice, and it was so unexpected that Poe staggered back a pace.
“Katarn standing by,” one of the fighters reported.
“Horn, standing by,” another voice added.
The reports came, one by one. Jade, Dracos, Solusar, Durron, Ikrit, Binks, Desann, Korr, Penin. Then they broke for an attack run, and Poe could only stare.
He knew he was a good pilot. One of the best.
But even he had to admit that he couldn’t outdo that squadron.
@paradife-loft recently posted something jokingly commenting about how the fact that Hobbits call the Baranduin the “Brandywine” implies that the words for “brandy” and “wine” in Westron are in fact, “brandy” and “wine.”
I used to wonder about that myself and a while ago I looked it up. The truth is, maybe unfortunately, something different, but really interesting and it involves not one but two layers of puns:
Brandywine is actually a very loose translation of the pun. The Hobbits first named the river Branda-nîn, which means border water, because it is, in fact, a border marker, and it sounds like the Sindarin name, Baranduin. But then later they started calling it the Bralda-hîn, which means “heady ale.”
So from there we have Tolkien “translate” it to Brandywine, to preserve the pun being based on a very Hobbit-like alcoholic drink and the sound similarity to the Baranduin, even if it did miss one of the linguistic layers.
But here’s the best part - the Hobbits named the river the Bralda-hîn because it was the color of ale. And the original Sindarin name, Baranduin? It means golden-brown river. So basically the Hobbits took a Sindarin name whose meaning they probably didn’t know, gave it a similar sounding name in Westron, and then made a pun off that Westron to give the river’s name a meaning similar to its original Sindarin one in the first place.
Happy 2025!
I worked like mad to finish this but here it is – some insanely large number of words about the year that was, through the lens of Billy Joel songs with "night" in the title because they are fascinating as all get out.
Special shoutout to @thebreakfastgenie for helping to infect me with the urge to go even deeper into the old man research.
people trying to insist a fandom is tiny when it /only/ has a few thousand works on ao3 meanwhile my current fandom is a sixteen book series and has several hundred fewer works than goncharov, a movie that, and i cannot stress this enough, doesn’t even exist
blood is not kosher
assuming vampires breathe, and are therefore alive, what do they do
I have a new post up on my blog, continuing the Fictional History of Numbers series. In part 1 we started with the natural numbers and built up the algebraics, which let us solve equations. In part 2 we started asking geometric questions, and constructed the real numbers.
But the real numbers are weird and hard to define. In part 3 we see one way they're extremely strange, and then talk about why we want them anyway. In the end, we shouldn't worry about the definition of the reals; we should worry about what they allow us to do. And it turns out they're exactly what we need to make calculus function as it should.
Interchange station for a variety of parallel lines
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