Extreme math nerd
Epsilon looks quizzically at the pot. "So what's the idea with the arrangement? What would happen if I nudged- oh!" She snaps her fingers, suddenly excited. "Here's something I'm qualified to ask! Is the process of arrangement continuous?"
"What I don‘t like about measure theory is that you have to say 'almost everywhere' almost everywhere." - Attributed to Kurt Friedrichs
Albedo
"No. They're done in batches. Anywhere from a handful to 50 or so, depending on how much of anything you add."
“You carry the aura of the stars, interesting...”
Extreme math nerd
"No, I mean, continuous as in the mathematical sense of, you move one ingredient over by some small degree and erm..." Epsilon pauses to ponder.
f: R->R is continuous at x0 if ∀ε>0 ∃δ>0: |f(x)-f(x0)|<δ => |x-x0|<ε
That's hard to express in words, especially for the situation at hand.
"Well, there isn't like, any sort of discontinuous jump where in one state, you have constellation A, which results in potion A, and if you nudge one ingredient over by any nonzero distance epsilon, you get potion B, which differs from potion A by at least some constant no matter how small epsilon is? I don't know if potions are a metric space, but you get the idea, right?"
And the girl's thoughts are trailing off already, wondering if you could express this formally and use it as an alternate definition for continuity.
"What I don‘t like about measure theory is that you have to say 'almost everywhere' almost everywhere." - Attributed to Kurt Friedrichs
Albedo
"Not really. You could probably nudge ingredients a bit, and get the same results. At this level, there's a little bit of room to adjust. Once you get up to the point where precision is necessary, it's more of a matter of getting things to fit together. Think of it like... a jigsaw puzzle. While the pieces only fit together a specific way, you can rotate and flip and move the whole thing anywhere you like, and the image will be the same."
Edited by KitkatKK2 on Mar 25th 2024 at 9:13:25 AM
“You carry the aura of the stars, interesting...”
Extreme math nerd
Epsilon is typing into her phone.
(x0, f(x0)), nudge x0 by epsilon, get something out that's arbitrarily small away. Requires a metric space
"Sorry. So, er, symmetry is involved... Are you trying to give each ingredient as much space as possible or something? What's this specific configuration about?" She points at the pot.
"What I don‘t like about measure theory is that you have to say 'almost everywhere' almost everywhere." - Attributed to Kurt Friedrichs
Albedo
He paused for a moment. "Hmm... Yes, giving ingredients space is important. For people just getting into the topic, we sometimes ask them to imagine a grid that you're putting ingredients on." He moved his hand over the pot in a straight line to illustrate.
“You carry the aura of the stars, interesting...”
Extreme math nerd
"I see, so like..."
mov(coordgrid ∩ cuboid((-0.1, -0.5, -0.5), (0.1, 0.5, 0.5)))
"This? No, that's way too big..."
A single cross, along with a small sphere where its two lines meet, appears in the air. No part of it would indicate that these two lines are part of a bigger grid that's been cut off.
"Er, hang on."
Epsilon examines the plates on her jacket and picks up one in particular.
coordgrid := ({x∈R3 | (x1∈Z; x2, x3∈R/Z) ∨ (x2∈Z; x1, x3∈R/Z) ∨ (x3∈Z; x1, x2∈R/Z)} ∪ sphere((0, 0, 0), 0.1)) ∩ cuboid((-5, -5, -5), (5, 5, 5))
Right, can probably scale that by a constant
mov(coordgrid*0.1 ∩ cuboid((-0.1, -0.5, -0.5), (0.1, 0.5, 0.5)))
Now the gridlines are finally visible, appearing every 10 centimeters - though as a side effect, the grid now has three vertical layers. Epsilon sighs, and positions the grid over the pot. "Not gonna bother to fix the extra layers right now. Does this still fit, roughly?"
"What I don‘t like about measure theory is that you have to say 'almost everywhere' almost everywhere." - Attributed to Kurt Friedrichs
Albedo
He nods. "Just about." Albedo moved the ingredients to line up with the grid. "Now you try. Line some of the ingredients up with that... well, we usually say "imaginary grid", but you've quite helpfully changed that."
“You carry the aura of the stars, interesting...”
Extreme math nerd
"Er, together with the ingredients that are already in the pot? Maybe we should let that finish cooking first."
"What I don‘t like about measure theory is that you have to say 'almost everywhere' almost everywhere." - Attributed to Kurt Friedrichs
Extreme math nerd
Gonna try to save this
"I have a really silly idea… If this works, I’m very sorry in advance."
Epsilon reaches for her pocket, and starts looking up stuff.
genshin strength potion
Potion Event Recipe Guide | Genshin Impact | Game8
Potion event recipes and market news list for Genshin Impact
Alchemy Exam Event Guide | Genshin Impact | Game8
Hey, wait a minute.
How to Pass the Alchemy Exam - Event Guide
She shows her phone‘s screen to Albedo.
"Hey, um… I know this wasn‘t exactly the potion recipe I was looking for, but is this
the practical part of the exam?"
Albedo
Albedo looks at the phone screen for a moment, reading the guide. "It is. Where did you find this?" He scans through it. "These formulas definitely make sense, as solutions."
“You carry the aura of the stars, interesting...”
Extreme math nerd
Epsilon has a look at the guide herself.
"Pretty much anyone can find this in my homeworld if they type in 'Genshin Strength Potion' into a search engine, and..."
She scrolls around some more.
"I'm not sure how many people visit this site, but it seems well maintained, so probably quite a few people visit it."
A concerned smile appears on her face.
"And that's the reason why I'm mildly nervous around here, because at any moment the Keeper of Heavenly Principles could swoop down and screw me over for knowing this stuff, just like she did with Aether and his sister."
That's not quite the only reason - but the other one she isn't ready to say yet.
Edited by StepexNo2 on Mar 30th 2024 at 11:56:35 AM
"What I don‘t like about measure theory is that you have to say 'almost everywhere' almost everywhere." - Attributed to Kurt Friedrichs
Albedo
"Information like that... I wonder how much else you could just find so easily..." He paused, placing a hand on the four-pointed star on his neck as he looked away briefly.
"The Keeper of... sorry, who?" He looked back at Epsilon, confused. "The name certainly sounds impressive, I suppose."
The existence of the Sustainer is not common knowledge
Edited by KitkatKK2 on Mar 30th 2024 at 5:11:30 AM
“You carry the aura of the stars, interesting...”
Extreme math nerd
"The Keeper of Heavenly Principles, I believe she was called... She shows up in the opening cutscene for Genshin Impact and strips Aether and his sister of their powers. If she's real here, Aether himself might know more about her... Anyways!"
Epsilon grabs a nearby ladle and lowers it into the concoction. "This stuff looks ready, should we bottle it?"
"What I don‘t like about measure theory is that you have to say 'almost everywhere' almost everywhere." - Attributed to Kurt Friedrichs
Albedo
Albedo didn't look like he was listening to Epsilon, as if in thought about something else, but when she mentioned the potion, he snapped back to what he was doing, and took a breath, as if to center himself."You're correct, this is ready to bottle." He grabbed a plain glass bottle, and dipped it into the pot, barely flinching at the heat. He poured some out, and set it aside for a bit. "We'll put the cap on in a moment, once it's cooled down a bit."
“You carry the aura of the stars, interesting...”
Extreme math nerd
Epsilon holds a hand over the pot, feeling the heat of its vapor. This definitely isn't a temperature bearable for humans.
"Hey", she wispers into Albedo's ear. "Isn't sticking your hand into the pot a bit suspicious? I mean, we're in public..."
don't mind the avatar, I'm doing a bit
Edited by StepexNo2 on Apr 1st 2024 at 3:16:06 PM
"What I don‘t like about measure theory is that you have to say 'almost everywhere' almost everywhere." - Attributed to Kurt Friedrichs
Albedo
Albedo gave a confused Hm? as he looked at Epsilon. "I don't see why it would be." He shook off his hand. "It's a bit of an unconventional method, but it's certainly much faster."
“You carry the aura of the stars, interesting...”
Extreme math nerd
"I mean, unless you‘re wearing protection gloves, wouldn‘t you burn your hands? I wouldn‘t stick my hands into that pot.“
"What I don‘t like about measure theory is that you have to say 'almost everywhere' almost everywhere." - Attributed to Kurt Friedrichs
Albedo
”I am wearing protective gloves, so that’s something of a moot point.” He took off the glove that wasn’t covered in potion and gave it to Epsilon.
“You carry the aura of the stars, interesting...”
Extreme math nerd
"Oh, thanks, you can keep that!" Epsilon hands the glove right back, and grabs an empty bottle and a metal plate from her "spell" satchel...
Torus:= {(sqrt(x2+y2)-R)2+z2<=r2}
R=0.05
r=0.01
A torus appears in the air, and Epsilon holds the neck of the bottle into its hole. The inner radius is still far too large to properly hold it, so she has to readjust her choice of R until, once she lets go, the bottle is only held up in the air by the torus.
"This is probably overcomplicating it... god, I really need to implement some control objects."
mov(Torus ∪ cuboid((-0.6, -0.5, -0.5), (-0.5, -0.4, -0.4)))
A cube appears behind Epsilon's shoulder, and suddenly, the bottle starts falling along with the cube and the torus, Before it can hit the ground, she catches it, then grabs the cube, and via a seemingly invisible connection between the cube and the torus, manages to dip the bottle into the cauldron without having to dip in her own hands. Though, because the cuboid dimensions she picked were so small, she only gets the bottle back out after some trial. She sets the bottle down on a table next to the cauldron, and lets her construction vanish.
"Yeah, that was definitely overcomplicating it. But fun!"
"What I don‘t like about measure theory is that you have to say 'almost everywhere' almost everywhere." - Attributed to Kurt Friedrichs
Albedo
Albedo puts his glove back on, stifling a laugh as he watches Epsilon bottle the potion. ”I believe most people would use metal tongs. But neither of us are most people, I suppose.” He puts the cap onto the potion he had bottled before. ”Here we are, one beginner strength potion.”
“You carry the aura of the stars, interesting...”
Extreme math nerd
"Right, metal prongs, of course." Epsilon chuckles. "So, potion making is that simple... Just put the right ingredients into- well, there's whatever the base was. What is the base that you start with, plain mineral water?"
"What I don‘t like about measure theory is that you have to say 'almost everywhere' almost everywhere." - Attributed to Kurt Friedrichs
Albedo
”I believe so. Starsilver, mostly. That said, I’m not the main person setting these up. Lisa has been doing most of the work here.” He nods. “Other than that, it’s quite the simple process indeed.”
“You carry the aura of the stars, interesting...”
Extreme math nerd
Epsilon grabs a cork and puts one on the bottle she filled. "I'd have imagined this to be more complicated. Like, in Harry Potter, a story from my homeworld, there are some really weird rules to potion making, like for some recipes stirring the ladle clockwise by thirty degrees or counterclockwise twice. And of course, you ask yourself how people would find these sorts of odd potion recipes to begin with. Sheer chance?" She shrugs. "Harry Potter is written for entertainment, I suppose, not for education."
Inkopolis
In an inconspicuous parking garage, on the third floor, is an inconspicuous blue van with the license plate "XTVRS". Its windows are completely darkened.
Okay, maybe this van is a bit suspicious.
Inside, a human girl with twintails and a jacket covered in all sorts of mathematical scribbles is hiding and waiting. She's also brought a shark plushie.
Edited by StepexNo2 on Apr 2nd 2024 at 11:30:11 AM
"What I don‘t like about measure theory is that you have to say 'almost everywhere' almost everywhere." - Attributed to Kurt Friedrichs
He takes the ingredients that had already been thrown into the pot, and rearranges them slightly. "Hmm..." Albedo proceeds to, without explaining, take the ingredients from Epsilon's hands and arrange them in a specific way. "There."
guy who is So not used to teaching things to people. he just forgot to to do the teaching part.
“You carry the aura of the stars, interesting...”