Claire Keane
@theartofmadeline
DEAR READER
RMH
Xuebing Du
Jules of Nature
Today's Document
Monterey Bay Aquarium
No title available
Janaina Medeiros
hello vonnie
ojovivo
Lint Roller? I Barely Know Her
Alisa U Zemlji Chuda
almost home
Product Placement
let's talk about Bridgerton tea, my ask is open
No title available
Kiana Khansmith
i don't do bad sauce passes
seen from Germany
seen from Türkiye
seen from Portugal
seen from United States
seen from Saudi Arabia
seen from Vietnam
seen from United States
seen from United States
seen from United States
seen from United Kingdom
seen from United States
seen from Türkiye
seen from United States
seen from Türkiye
seen from Italy
seen from Malaysia
seen from United States
seen from United States
seen from Canada
seen from Canada
@eyesfromhell
I was mugged by snow white and the seven dwarves the other day. six dwarves now, I suppose. kneed dipshit or dopey or whatever he was called in the eye socket so hard he died before his limp body hit the ground. they all scattered after that. I'll never forget how they wailed his name
When Martha and Monsignor Wicks leave the confessional I assumed she sucked his dick
Could Jacket be Kira?
Never caught or suspected
Suspected but never caught
Suspected only by whoever caught them
Suspected and eventually caught
Caught almost instantly
Known, but can't be caught
Jacket, after being killed, will be killed as a murderous maniac and not as Kira.
If I was gonna write an evil genocide guy with a cartoonishly evil sounding name I wouldn't not name him Bezalel Smotrich. By the way the literal meaning of Bezalel is "in the shadow of god". If I wanted to be really on the nose.
In 2020, right after Covid kicked off in earnest, I wrote a snippet for a creative writing class. It was set in that zombie setting I'm always tinkering with, and it was about a bunch of zombies who've figured out how to hunt on the interstate by throwing themselves in front of cars and then swarming the drivers when they get out to help- the effect of which is a grimly pragmatic, comically anti-pedestrian turn in American driving culture. About an hour after submitting this story I got a heartfelt and sincere note back from the TA about how if current events were getting to me there were a lot of campus resources available, to which I replied cheerfully, no, I'm fine, pandemic had nothing to do with this I just really like stories about killing and dying and violence and so on. Not in those words, I can read the room, I know when I'm in a kettle with the burner on. Ultimately one of several examples of how that space (I think largely expecting attempts at lit fic) was just really not acclimated to my baseline proclivities as a writer
Tuco Salamanca: Thinker 5, vague precog/dangersense for big problems and conspiracies against him and his family, but blind against the immediate, improvised attacks (season 2 episode 2 "Grilled" 19m 10s). Trigger likely involved a feeling of inevitable doom that was tragically fulfilled despite his efforts to stop it.
Walter White/Heisenberg: after decades of trying to solve a problem with a tangential chemistry flavour, capped with getting a cancer that requires chemotherapy, Walter does get the chemical-based Tinker 6 power that he dreamed of. However, as the actual problem he was trying to solve was a contradiction between cultural individualism/toxically masculine self sufficiency vs being repeatedly put in positions of pity and community reliance, his power forces him to rely on others in order to get results. In order to enter a tinker fugue state he's forced to surrender to the help of another pair of hands- hands that seemingly always end up clumsier and stupider than he'd like. This reliance on another collaborator and the intensified frustrations with both himself and his lab partner after every tinkering session has lead some to argue he should have a 0 or -1 master rating.
Saul Goodman/Jimmy McGill: Lightning Blaster 4-7 as previously established by other researchers. Very possibly a cauldron cape as he has little enough shard influence to avoid using his powers completely.
In the early twenty-first century, a "rational number" is any number that can be expressed as the ratio between two integers. For example, 0.5 is a rational number because it can be represented as 1 divided by 2 (or be 2 divided by 4, or by negative 7 divided by negative 14). Pi, famously, is NOT a rational number, nor is the square root of 2.
"Countably infinite" is a way to describe the size of a set. If a set has an infinite number of elements AND if it can be reached if they are "counted" one at a time forever, it is "countably infinite." For example, the counting numbers are trivially countably infinite, because you can just count. As long as there is a process that will EVENTUALLY reach any given element in an infinite set given some arbitrary finite amount of time, the set is countably infinite. The set of all real numbers, notably, is not countably infinite, because there is no process that will produce any arbitrary real number in finite time.
Proving the set of rational numbers is countably infinite is relatively easy. Imagine a number line of all counting numbers, from 1 towards infinity, going out to the right. Now, imagine a line of all counting numbers, from 1 towards infinity, going down. The two sequences form a grid.
Now, draw a series of diagonal lines, akin to pattern shown in the baking gif. For each point on the grid you cross, use the column number from the infinite line as the numerator, and the row number from the infinite line as the denominator. By definition, this process, following this traced line forever will eventually get you EVERY possible rational number (with many duplicates, but that isn't a problem). Technically, one would also need to include the number 0, and would need to ALSO include the negative version of each number, but this is ultimately the same.
This process is known as diagonalization, because of the diagonal lines being drawn. Similar proofs can be used to establish that real numbers are UNcountably infinite.
This is an extremely obscure topic, despite being pretty simple for those in the field. It would likely be taught at college level in the early twenty-first century. Most people would not get the joke.
small point: this is not diagonalisation! it does involve diagonals though, so I get the confusion.
the technique of diagonalisation, as was originally implemented by Cantor to prove the uncountability of the real numbers, is as follows:
suppose for now that the reals were countable. we would like to show that this leads to a contradiction, and therefore cannot be true. by our assumption, there is some way to count the reals one by one (not necessarily in their usual order - in the same way that our counting method for the rationals didn't go from "smallest" to "largest"). we can number the reals using this counting method: the first real we encounter will be assigned "first place", the next one "second place", and so on. suppose we start writing out this list, writing one real in each line of the list - so for example the list might start "1st. π, 2nd. 5.4, 3rd. -301.665..." and so on. we can use this list to define a real number that will never appear in the list; first, we make sure it's not equal to π=3.14..., by choosing the first digit 1. then we make it different from 5.4 by choosing the second digit (=first digit after the decimal point) to also be 1. we go on like this - to define the n-th decimal digit of our new number, we look at the n-th digit of whichever number is n-th place in the list, and define our digit to be different from that one - so if the n-th digit of the n-th place number is anything other than 1, we say our number's n-th digit is 1. otherwise, we say it's 2.
by assuming we had a method to count all real numbers, we've constructed a new real number that our method will never count (because it differs in at least one digit from each of the ones we will ever count), contradicting our assumption, and therefore showing that the assumption was false - the reals cannot be counted one-by-one. this is exactly what we wanted to prove.
the name "diagonalisation" comes from the fact that this technique also uses a diagonal - that of the "n-th digit of the n-th place number". this term has since been generalised to refer to any of a bunch of similar proofs, all using a list to define an object that doesn't belong to that list; for example, another proof that I think was also published by Cantor, shows that in general every set is strictly smaller in cardinality than its set-of-subsets (="powerset"). more succinctly, this is "K < 2^K".
I considered going into detail about diagonalization with regard to infinite strings or halting problem or (as I touched upon) the real number proof. But at a certain point I need to stop the explanation for a given topic. Moreover, the post I reblogged used the term "diagonalization," as a tag. I would not have brought it up at all if not for such.
It's interesting in the moment to moment distinction, to think about language as a changing with every use. I made a deliberate decision in the moment to expand a definition, thus opening me up for rightful criticism. By continuing with a modified definition, the community has the opportunity to (correctly) reject it and maintain the prescriptive meaning, or to accept it just as I had in the moment, which would also be a correct choice (in my opinion). And this is a continued, iterative process. After all, it is not wrong to want to keep definitions as people before us understood. And, after all, it is not wrong to want to accept reasonable changes in definitions.
Actual diagonalization proofs are just plain fun. They are so cool when you learn about them the first time. Should the proof of countably infinite rational numbers be accepted among their number? It is not for you or me to decide, but for everyone. Perhaps we might cleave between "diagonalization" and "Cantor diagonalization." Or perhaps we should rigidly accept the definition, for the sake of communicating with people 300 years from now.
Close enough welcome back Cherish from Parahumans
I had a friend who was seriously injured from walking behind one of those
he also told me he did war crimes in Gaza so ¯\_(ツ)_/¯
Worm would be 70% better if we got a whole interlude about parahuman taxes.
This is for the Valentine's Day event on Cauldron. My gift recipient was Distraktion. His prompt: Thomas Calvert's power actually works against him when it comes to dating...
have you ever been told you look like a celebrity?
yes (who? 👀)
no
have you ever been told you look like a celebrity?
yes (who? 👀)
no
while we're talking about character appearance headcanons
*after watching Bullet Train* I think Lisa is more of a Diesel. I mean her whole schtick (other than collecting information) is causing trouble
Having an extremely specific problem after trying a traditional pencil crayon look for an older Tattletale portrait. Somehow, during the slow work from grubby sketch to rendering, she became way too hot. And said traditional art style means I can’t change this with regular digital tools, I have to redraw sections of her face entirely.
That I did with optical colour mixing using hatching and a limited palette.
Do I roll with hot Tattletale or do I suffer?
Well, here’s accidentally hot Tattletale. It was that smug grin, I tell you.
Speedpaint under the cut so you can see her clown beginnings.
I FORGOT THE FRECKLES
Emma moments before taunting Taylor for crying after her mom died:
this drawing made me realize Tattletale mirrors Emma and Taylor-as-a-bully was there from day 2 when she condoned Tattletale's antics. (I am that drawing of a story's point going over a reader's head)
realizing that armsmaster's trigger was definitely a situation where he was overwhelmed with a bunch of different issues and unable to triage. granting him the ability to actually have a solution for every problem means that he doesn't have an excuse *not* to.
Just found out citrine is a gem.
thought she had yellow powers so decided to be citrus themed and I mean, an Ambassador can't wear oranges so she's citrus themed only in color
(on further googling 'citrine' means citrus-colored, and the gem is called that because it is citrus colored)
