Proof by Counter Example

I still think about math, sometimes. But I yell at computers more frequently.

[whimsicallywiddershins]

Reading Artifical Conditon again is so funny. Imagine you are a young scientist who has decided to hire a security specialist to help you in a risky endeavor that could break or make your career. You are worried that you cannot afford any security specialist, let alone a competent one. To your surprise, you get a specialist who is extremely good at their job, willing to accept a low pay, saves your life many times, goes above and beyond to help you, and is also gentle and kind. You cannot understand how you got this lucky.

You do not realize your security specialist is two bots in a trench coat, pretending to be human for the first time ever.

[hyperoperationfractallisation]

[xyymath]

Things Math Professors Say

"The proof is trivial." (Oh, cool. Guess I’m just an idiot then.)

"Left as an exercise." (Translation: You’ll never solve this in a million years.)

"It’s obvious, really." (Sure, if you’re a demigod.)

"By inspection." (Stares harder at problem… still nothing.)

"For small values of epsilon." (How small? Subatomic? Microscopic? Vibes?)

"WLOG (Without Loss of Generality)." (Oh, we’re just assuming it doesn’t matter now? Alright.)

"Details omitted." (Because apparently, you don’t need to understand it.)

"By the usual argument." (Which you somehow don’t know because you weren’t born in 1702.)

"Assume the rest holds." (That’s some impressive optimism right there.)

"The usual abuse of notation." (Why does this feel like an emotional wound?)

"Almost surely correct." (But also possibly wrong? Cool, thanks for the clarity.)

"A non-rigorous approach." (I thought math was supposed to be precise?!)

"Assume it’s obvious." (Buddy, NOTHING about this is obvious.)

"The reader may verify." (No, the reader may CRY.)

"To the interested reader." (Guess I’m not interested enough, huh?)

"Well-behaved functions only." (We’re function-shaming now?)

"Obvious to the trained eye." (Guess I’ll never make it out of amateur league.)

"A trivial case analysis." (Trivial to WHO??)

"Integrate by parts, twice." (Bold of you to assume I got it the first time.)

"As you can clearly see." (Oh, I clearly see my FAILURE, alright.)

"It works in practice too." (Unlike me, who barely works at all.)

"Assume a spherical cow." (Are we doing math or abstract sculpture?)

"A standard result." (Not in my standards, pal.)

"We skip the tedious algebra." (No, no, please—I wanted to suffer MORE.)

"Assume non-zero solutions exist." (Okay, now we’re just assuming life works out.)

"The usual topology." (Bro, I don’t even know the unusual topology.)

"Finitely many cases left." (Just kidding, there’s 72.)

"By virtue of symmetry." (Virtue? I have none left.)

"Don’t worry about the constant." (The constant is probably my GPA dropping.)

"Assume continuity." (I’m assuming my brain is breaking.)

"Smooth functions only." (Guess I’ll leave, I’m clearly not smooth enough.)

"The simplest non-trivial case." (Simplest? NON-TRIVIAL? Pick a side!)

"Epsilon goes to zero." (Epsilon isn’t the only one losing it.)

"And the rest follows." (Where? Straight to my breakdown?)

[ironpour]

so. how does anyone ever have the time or energy

[copperbadge]

Executive function Georg, who lives in a cave and accomplishes 10,000 tasks per day, is an outlier adn should not be counted. 

[futurebogbody]

How does he have time between eating spiders?

[echoes-bookshelf]

The task is eating spiders

[copperbadge]

This is the quality content I come to Tumblr to see.

[yoneda-emma]

I think one fun side effect of studying uni level math is that simultaneously the complex numbers start seeming simpler than you thought but at the same time the real numbers are *way* more fucked up than you thought

[yoneda-emma]

in your first math lecture you will have this moment of shock when you find out the set of natural numbers and the set of rational numbers have the same cardinality and I just had that same moment of shock finding out that the set of *computable* numbers also has the same cardinality

the set of the real numbers would be exactly as big as the set of natural numbers if it wasn't for the infinitely larger amount of unknowable eldritch horror numbers that slumber in the void between the real numbers that you can actually use for math

[yoneda-emma]

its sad actually, most of these little creatures will be forever out of reach of being properly hugged and loved and appreciated by mathematicians

[dragon-daemon]

This is one of my favorite things in math ever.

Naturals, integers, rationals: yeah, easy.

Computable irrationals: ok, we can work with that. You want 20000 digits of pi? One million? Coming right up.

A single uncomputable number: uuh, it's basically six point two something, but we can never know the something. It's beyond mortal comprehension. Don't worry about it.

[salt-and-bramble]

goldenrod, swallowtail, thistle, finch monarch, buckeye, sunflower (idk which 😔)

[cellobuster]

Whoever invented "open in app" links that redirect you to the app store instead of actually opening the app even when you already have the app installed on your phone should be involuntarily turned into a beanbag chair

[someguyiguess-deactivated202511]

spiders have got to figure out contracting I need to be able to call my local spiders union and be like "hey can you send a guy out for a few days the fruit flies are back" and then pay it in spider currency. I'll learn the conversion rates. I'll be generous with my rounding. please.

[delicatuscii-wasbella102]

Paul Harvey, Kingfisher

[bibliolithid]

Out with the "stand up" meeting, in with the "deep squat" meeting, even more pressure to finish quickly before your knees give out!

[sigmaleph]

precariously balanced on a tightrope meeting

bed of hot coals meeting

gom jabbar meeting

[alexanderwales]

I'm a big fan of wizards-as-programmers, but I think it's so much better when you lean into programming tropes.

A spell the wizard uses to light the group's campfire has an error somewhere in its depths, and sometimes it doesn't work at all. The wizard spends a lot of his time trying to track down the exact conditions that cause the failure.

The wizard is attempting to create a new spell that marries two older spells together, but while they were both written within the context of Zephyrus the Starweaver's foundational work, they each used a slightly different version, and untangling the collisions make a short project take months of work.

The wizard has grown too comfortable reusing old spells, and in particular, his teleportation spell keeps finding its components rearranged and remixed, its parts copied into a dozen different places in the spellbook. This is overall not actually a problem per se, but the party's rogue grows a bit concerned when the wizard's "drying spell" seems to just be a special case of teleportation where you teleport five feet to the left and leave the wetness behind.

A wizard is constantly fiddling with his spells, making minor tweaks and changes, getting them easier to cast, with better effects, adding bells and whistles. The "shelter for the night" spell includes a tea kettle that brings itself to a boil at dawn, which the wizard is inordinately pleased with. He reports on efficiency improvements to the indifference of anyone listening.

A different wizard immediately forgets all details of his spells after he's written them. He could not begin to tell you how any of it works, at least not without sitting down for a few hours or days to figure out how he set things up. The point is that it works, and once it does, the wizard can safely stop thinking about it.

Wizards enjoy each other's company, but you must be circumspect about spellwork. Having another wizard look through your spellbook makes you aware of every minor flaw, and you might not be able to answer questions about why a spell was written in a certain way, if you remember at all.

Wizards all have their own preferences as far as which scripts they write in, the formatting of their spellbook, its dimensions and material quality, and of course which famous wizards they've taken the most foundational knowledge from. The enlightened view is that all approaches have their strengths and weaknesses, but this has never stopped anyone from getting into a protracted argument.

Sometimes a wizard will sit down with an ancient tome attempting to find answers to a complicated problem, and finally find someone from across time who was trying to do the same thing, only for the final note to be "nevermind, fixed it".

[mother-sauces]

"This spell causes the hair to fall off cats." "It works with my tome"

"This spell causes the hair to fall off cats." "That's fixed in Xaranthius' latest publication, you just have to rewrite your entire spellbook for compatibility."

"This spell causes the hair to fall of cats." "Magister Olaus of Writhington uses it to help with his allergies. WORKING AS INTENDED."

[foone]

I want to see wizards snarking at each other over different magical languages/scripts, the same way programmers do it over different languages.

Sure, "High Tower is a powerful language, but it's such a pain to write. I just use Unity* as it's simple to write and can do nearly everything I need" "cranky because you can't memorize all the conjugations and declensions, aren't you?" "LOOK MAN, I CAN MEMORIZE ANYTHING, INCLUDING THE FACE OF YOUR MOTHER IN ECSTASY. IN FACT, BEHOLD!" *a little time window appears between them, demonstrating exactly that. The first wizard (seen through the window) turns around and winks at the "camera".

"you kids today with your lizardman. How can you get anything done in a language without gendered pronouns? It's like fingerpainting. Sure you can learn on it but once you've got the basics you should switch over to a REAL language"

"the Kalic have been here already. We better get out before the rest of their army marches in." "how can you be sure?" "you see that teleport?" "no" "well, if you COULD see it, you'd see it's written in Adevic Yevi. That's the Kalic magic language." "couldn't it be someone else? We saw those Monon traders, maybe one of them..." "no. No one writes Adevic Yevi unless they're being paid to. It's a language written by committee."

Wizards going on a quest to get the spellbooks for a lost spell, only to find out that it was written in skydove cant. No one can read that shit! The creator must have been one of those weird "functional wizards". (They're obsessed with making sure their spells have no side effects)

There's a small library on the outskirts of Freeport which tries to collect versions of basic spells in every language. The Adevic Yevi version of "fireball" takes up 7 pages, mostly boilerplate setting up the interfaces with fire and explosions and ExplodingMagicalBallFactorySingletons. The Lizardman version is basically "AHAHAHA, YOU GO BOOM!"

There's a bunch of wizard apprentices working on porting an old "Summon Bread and Fishes" spell from the absolutely archaic language it was written in. Once it's in Unity, it'll be easy to modify and teach to more wizards, which'll obviously be good for disaster areas. It's just too expensive to keep paying the ancient guys who can still do magic in TRAN-FOR.

Eccentric wizards keep inventing new languages for spells. You look at them and they're neat, but it'll never catch on. And either you're right, or the next time you're applying to be a court wizard, the advisors want to know if you have at least 5 years experience in Tilted Runic and you're like "it only came out 2 years ago!" "aren't you a chronomancer?" "oh good point. Yeah I've been using it for 20-30 years."

There's wizards who will spend incredible amounts of time doing silly things with spells in strange ways. There's this guy (Vorth) who made his own language where there's only one basic spell: fireball. Everything else is basic magic glue tying multiple fireballs together. So like, he's got a breakfast spell. Stand back (good advice for all his spells), and you'll see a fish get knocked out of the local pond, flung through the air by successive explosions, and eventually it lands on his plate, nicely cooked and deboned, if slightly charred (the glass of milk is harder to explain). His magical door locks involve a quicksilver sphere and molten lead changing shape when heated... It's tricky but it seems to work. He's working on a teleport spell, but so far it's mainly just killed test subjects (primarily sheep from a nearby farm).

* so the funny thing here is that this isn't a reference to the unity game engine. The main country in my One Hundred and One Magical Pistols setting is called "the union" and their language is called "unity".

[foone]

It's wands vs staves vs bare hands.

Wanders are like "they're available everywhere and once you learn how to do it it's so powerful!"

Staffguys always talk about how you can do ANYTHING with a staff. Wanders claim it's a pain to carry around an overpowered device that can do ANYTHING when you just need to cast fireball or a simple one man teleport.

Meanwhile the bare wizards are showing off how they don't need any magical tools and can just do hand motions.

Wanders and staffguys retort that when a spell goes wrong, THEY need to go to store for a new magical tool. YOU need new hands.

[phantomrose96]

Funny to me to think about the whole "oh you say you don't like <insert website> but you'll gladly reblog content FROM <insert website>" as like... trade exports between nations that all a little bit don't like each other.

"Come try these grapes. They're from Tiktok." "OH Tiktok? Wonderful. They grow the best grapes. We just don't have the right terrain for them here." "I agree. Lovely grapes. Wretched country though, I'd never live there." "Oh me neither. They cancel their peasants in the town square. Speaking of, have you seen the new textiles boypussydilf is selling in the town square? Imported from Instagram!" "Oh amazing textiles, Instagram has. Wretched country though." "Absolutely wretched."

[wilkpreriowy]

Northern coyotes (Canis latrans incolatus) Potter Hill, Alaska, USA

Photo by Eric Kilby

[bajoop-sheeb]

Mb with a patch on it’s coat that say “this machine kills fascists”

[kelssiel]

hate it when you experience something of better quality and then you’re doomed to no longer be satisfied

[kelssiel]

in my family we call this “getting the good bologna” because after my grandma got fancy bologna on sale she couldn’t go back

[koko-mochi]

Do y’all ever think about how absolutely bananas Lake Baikal is? It’s the world’s largest lake by volume. It’s the world’s deepest lake. It’s the world’s oldest lake. It contains nearly a quarter of the planet’s surface freshwater. It’s a rift lake, caused by the earth’s crust literally coming apart at the seams. It would be deeper than the Mariana Trench except the bottom is covered in a sediment layer that is miles deep. There are trains that have sunk to the bottom because Russia tried to build a railroad over the ice. The entire lake surface freezes for half the year. The lake is a focal point of multiple indigenous cultures. The lake has its own species of seal, which is the only exclusively freshwater pinniped in the world. There are unique ice formations formed by convection from the depths of the lake. There are 330 inflowing rivers.

I dunno, Lake Baikal sure is a thing.

[weaselle]

a truly unique and magnificent Feature on our planet, as singular and fascinating as Jupiter's Great Red Spot

[parkchanwoohoo]

a little kid came up to the desk (it came up to his like, collarbone) and very seriously asked me about baby name books, because he wanted to help name his new sibling. i guided him to the shelf (there were only two book of names) and pointed out the differences between them, and after some serious contemplation he went, “I think I should take both, just in case.” So I gave him both and he thanked me and went on his way.

And I went back to my desk and screamed into my arm for like 45 years because HE WAS SO FUCKING ADORABLE AAAAA

[parkchanwoohoo]

i love when little kids come to the reference desk alone because they want to be perceived as an adult and so they come up to you and very seriously inquire “Where are your books about dolphins? ò__ó”

and of course you have to very seriously show them your collection of dolphin books while they nod carefully at your explanations and it’s SO CUTE!!! THEY’RE SO CUTE AAAH

[andletforsakendidodie]

a kid came up to me to enquire about books on queen victoria, so I promptly guided him to the children’s history section, and we had a lovely chat flicking through horrible histories books, when I asked him what does he like about history. he grinned, and with a smooth, brilliant smile he said “My favourite thing about old times is torture.”

[wakingfromthewater]

One time I had a dad come in with his ~10 year old kid and go “Hi, we’re looking for, um…” at which point he trailed off and looked expectantly at the kid the way parents usually do when they can’t remember which Percy Jackson book comes next, but instead the kid looked up at me and very brightly and firmly announced, “The Federalist Papers!”

[platypusisnotonfire]

I had a kid come in all the time by herself after school, and she was hands down my favorite patron of all time. 5 years after I met her, she graduated 8th grade, so she was….8 or 9 when she first came in? Young enough that I was like “where is parent? I guess I am your mom now. you are safe in the library, child.”

The very first book she asked for was a book on Morse code. I was instantaneously enthralled with this child. Over the years, she took out books on first nations religions, the war of 1812, Ulysses by james joyce, books about tracking animals and identifying pawprints, basket weaving, loom weaving, the battle of Agincourt, honestly way too many things to remember. 

100% of the topics she was into were not typically “age-appropriate” (although I am a staunch believer in there being no age-appropriate subjects, just age-appropriate ways of explaining them) and about half of them required interlibrary loan requests because the topic was so esoteric the only books on it existed in some university library on the other side of the country. 

Some evenings she would come in after school and it would be a big snow day so there was hardly anyone there, and we’d just talk until the library closed, looking things up on google when she had a sudden inspiration to know something. Topics ranged from the physics behind a woodpecker’s tongue wrapping around its brain (she taught me about that one) to “Horrible bear bear” and the “bear circle” and the “anti-bear circle” (latin and greek roots of bear names and the Arctic.) She was just like, the coolest person. 

I really hope to meet up with her again someday because I really think these kinds of things have a circular effect- I’m thinking back to when I first moved to that town at 13 and went into that same library, marching up to the front desk and asking for books on astrophysics (probably looking even younger, I’m 26 now and people peg me for 14-16 consistently), and how the librarian- who later became my boss- must have felt about tiny me when she was putting in interlibrary loan requests for specific textbooks from MIT to go along with the OpenCourseWare courses I was taking online (which I gained much greater respect for when I became the interlibrary loan technician- holy Hannah that’s a lot of steps.) 

Anyway that was literally my favorite part about working at the library.

[certifiedlibraryposts]

Certified Library Post