#How To Learn Math for Machine Learning

[hackeocafe]

How To Learn Math for Machine Learning FAST (Even With Zero Math Background)

I dropped out of high school and managed to became an Applied Scientist at Amazon by self-learning math (and other ML skills). In this video I'll show you exactly how I did it, sharing the resources and study techniques that worked for me, along with practical advice on what math you actually need (and don't need) to break into machine learning and data science.

[superchat]

cannot get over how dumb the "education is training you to be a mindless work slave"

i think its mostly there to teach you critical thinking

[corvidcrafts273]

lmao

'People are panicking about AI tools the same way they did when the calculator was invented, stop worrying' cannot stress enough the calculator did not forcibly pervade every aspect of our lives, has such a low error rate it's a statistical anomaly when it does happen, isn't built on mass plagiarism, and does not obliterate the fucking environment when you use it. Be so fucking serious right now

[whencartoonsruletheworld]

candace flynn is THE most teenage girl character of all time. she is at level 100 anxiety 24/7. she shows her love for her brothers by trying to get them in trouble constantly. her neck is as long as her forearm. she features on a blues album after having an allergic reaction. she has a shrine to her boyfriend in her room. she can't live without her phone. she has a panic room in the basement. she plays 20 instruments that all start with the letter B. she read all of sherlock holmes in one night. she's seen their platypus running around as a secret agent more than once, assumed she was hallucinating each time, and moved on with her life while telling no one. she likes wrestling video games. she was rutabaga princess. she has a billion people to email memes to but when she's trying to think of friends she can only think of four people and one of them is her mom. most animals hate her except monkeys. she invented grilled cheese flavored ice cream. she pretended to be irish for a week. she's autistically obsessed with her universe's version of barney. she writes marvel fanfiction. she does parkour. there's an entire archive of her voice actress screaming just in case her voice ever gave out while recording. she sees her brothers build time machines and rollercoasters every day but doesn't believe in santa. when she starts scheming the wicked witch of the west theme starts playing in the background. she was elected queen of mars. she won a "mayor for the day" essay competition. there's a random person in town who's been avoiding her to the point she doesn't know he exists. she learned how to parallel park by driving a monster truck. she thinks the plural of moose is "meese." she tracks her mom with a GPS. she doesn't know her little brother's full name. she's scared of heights, spiders, and the number seven. when her boyfriend told her he'd call "soon" she started doing complex math to try and figure out when exactly that would be. her first thought upon seeing her royal doppelganger was to go to the laundromat and fill all the dryers with cheese. she earned 50 not-girl-scout patches in one day through sheer determination. she can run fast enough to catch up to moving cars. she can sense when ground is broken in the backyard and when people are judging her. one time she got her face caught in the sink. her brothers carved her into mount rushmore. every now and again a magical zebra appears, calls her kevin, and then disappears again. she killed 99% of an alien invasion with a t-shirt cannon. in an alternate universe she's leading a regime-destroying resistance at the age of 15. she's being accidentally gaslit every day of her life.

[bandedbulbussnarfblat]

I made a post the other day that mentioned IEPs. So I wanted to make a post as someone who was worked for the american school system, and explain IEPs versus 504s. I double checked by looking online just to make sure I wasn't spreading misinformation. (Or just the way my severely underfunded county did things, bc they cut corners) And I found this site above that gives a great break down. It offers a pdf with a chart that compares the two. There is a video that explains it as well. There's also video, a podcast, and the transcription available here . That link also has a few links to other resources.

I'm going add a quick summary of the most important details below regarding IEPs vs 504s. I'm also to going to add a link for parents/guardians who either don't speak/have limited English. (Unfortunately the pdf is in English, but you could probably put it through a one of online translators and the gist of what it saying.)

Most important differences between an IEP and a 504:

IEP: Is always written. Includes related services and specially designed instruction.

Generally much more in depth.

Requires any changes made to the IEP are given to parents/guardians in writing before the IEP team meets and makes any changes. You are automatically part of your child's IEP team. You have to right to attend these meetings. They will send a letter, by snail mail, telling you of a time and date they would like to meet. (If your kid has a good teacher, they will call and try to find a date that works for you. If not, you can contact the school and request a different day. Most schools are willing to be accommodating.)

Written consent from parents/guardians is required before evaluation and before the IEP is put into affect. HOWEVER, the student has to fall under one the 13 disability categories.

Typically includes modifications of the what the student is expected to know and learn. (For example, if the student has an intellectual disability, their learning goals will be established by the IEP team.)

This doesn't mean the student will not be presented with general education grade level concepts, just that they will be modified to meet the student's capability.

IEPs have annual goals that are measurable. These goals are made by the IEP team, including parents/guardians. (Aka, there is a lot of progress monitoring.)

Usually teachers will send out a progress report every two weeks. However, most teachers send out less formal methods of progress monitoring weekly or daily. Sometimes it's just a chart in a file folder where the teacher will jot a note of anything that the student was doing well with, or anything the were struggling on. Sometimes it's their complete work for the week sent home, excluding anything the teacher is keeping for records.

An IEP team has to include at least one gen ed teacher, one special education teacher (special education is usually called EC these days) a school psychologist/specialist, a district representative, and the parent/guardian of the student.

An IEP team is required to meet at least once a year, and the student is reevaluated at least once every three years. (Typically they are reevaluated and deemed still in need of an IEP. Though there are cases when students (mostly in high school) have received enough support that they no longer feel the need an IEP)

An IEP is a legal agreement. You have the right to sue the hell out of the school system if they fail to meet it.

504s:

Doesn't include specially designed instruction. Is meant to help student remain in general education.

Doesn't have to be a written document. (Though typically most schools do write documents. Bc otherwise they would not be able to keep track of what students need, bc there are so many).

Usually provides accomadations/assistive technology, but not related services of modifications. (Though sometimes these are also provided, especially if a student fails to qualify for an IEP, but still needs services and/or modifications)

Requires a student have a disability that impacts their education

Much easier to obtain than an IEP bc less requirements

No specific set of rules of who is on the student's plan team. Generally includes the parents/guardians, the student's general education teacher, (in the event the student has multiple teachers, the teacher will probably be their 'homeroom' teacher, and/or the teacher(s) of whatever subject/area your student is struggling in) and someone from administration, such as the principal or assistant/vice principal. Hopefully also someone from EC who has been trained to teach students with exceptional needs.

Parent/guardian consent is needed to evaluate the child, but this consent does not have to be written. (Many schools will still send some sort of consent form, bc the school system believes in documenting everything.)

The school has to tell you of any big changes to the plan, but they do not require your consent before starting them. Generally you'll be sent a letter of those changes in the mail. (If your students team is good at their job, they'll contact you before. Like, the teacher will call and say we are planning on starting x thing on y date, or email you if that's your preferred method of contact.)

504s don't track annual progress or create annual goals. (Though usually teachers will keep their own form of progress monitoring, bc a student with a 504 could be reevaluated and found they meet the criteria of an IEP. For that reason, many schools treat 504s as if they IEPs. Some schools suck though.)

For parents/guardians with limited or no English language known.

Most importantly, if you have a language barrier, your school must provide a competent translator/interpreter. They should NOT expect your child to work as translator for you.

And there is a lot of times where the translator isn't available that teachers will ask a bilingual staff member to translate for them. How you feel about that is up to you. A lot of parents don't mind in my area, bc we are severely understaffed when it comes to translators, and they want a quick response. If it's something you absolutely don't want, be sure to tell the school. You don't have to do so verbally; send a letter in your language stating your wishes. The school will find someone to interpret it. Keep a back-up copy for yourself.

Just as a general rule to all parents/guardians, keep documentation of everything the school sends you. You never know when you may need it.

[missjessefantastico]

who's surprised? nobody!

[physalian]

Avoiding Plot Holes by Seeding Doubt

Having an “expert” character conveniently fuck up right when the plot needs it to happen, when they otherwise would never, always loudly looks like the hand of the author sabotaging things. Which is exactly what’s happening.

However, if you set up that scene in a way where that fuckup is possible and warranted, you can turn “this is so contrived” to “omg I knew that was going to happen”.

Some suggestions!

Firstly, if we’re dealing with humans, humans are not machines. Variability in skill even at the expert level happens. Go watch the Olympics or any professional sporting event and people have terrible days all the time.

In fiction, a conveniently terrible day because that’s just how this works doesn’t fly. Diablos ex machinas tend to go over easier than deus ex machinas, but a character failing at a critical challenge in the narrative for no reason screws with a lot of the tension and expectations. “For no reason” takes no effort by the author to set up and pay off, and it reads as cheap.

Behavioral variables

I am a novice archer. I write expert archers. I do not write supernaturally accurate archers. From the very beginning of my story, my expert, with four centuries of experience, isn’t nailing perfect kill shots with every hit. A) he doesn’t need to and B) leaving his enemy to die slowly and painfully is a low he will absolutely stoop to if he thinks it’s warranted.

He’s as good as he has to be and if he gets the job done, he doesn’t care if it’s a little messy. Him being messy and overconfident is what gets him in the end, too. If he’s trying, he’ll do better, but most of the time “eh, I got close enough, they’ll die eventually” is his mindset.

“Expert” in fiction being “this is a character who will reliably pass the challenges set up for them by the narrative”.

So if you have an “expert,” allowing them to get a little bit lazy and overconfident, or simply not think of themselves as needing to be perfect in a given situation, you allow yourself a lot of wiggle room for them to majorly fuck up.

Doesn’t work very well if I throw my archer into an archery tournament, but I haven’t done that, and I’ll get to that later.

Environmental variables

Using the archery example once again: Archery is finnicky and precision is key. So if you’ve got your archer, or any marksman, in a windy environment, they have to work that much harder to factor in the wind when setting up their shot.

If it’s rainy, or the sun’s in their face, or it’s dark, or it’s loud and they can’t focus, these things aren’t exact data points the audience is going to do the math on. Or, if they and their enemy are moving, which, in combat, is highly likely.

Physiological variables

Maybe your character didn’t get enough sleep, or they’re stressed about this moment, they’re cracking under the pressure, they’re doubting themselves, the enemy got into their head, or they’re distracted worrying about something else. Or they got drunk the night before, they ate too much or too little. They’re sick, their hands are sweaty, they’ve got a sinus headache. They’ve got cramps, or hot flashes, or earlier they pulled a muscle and it still tweaks.

These are all, once again, introducing doubt into the narrative so that, when they fuck up as the plot demands, the audience should consider “well they weren’t at their best, I believe it”.

—

The sloppy way to do this is to go, in the moment:

“But because it was windy, X missed his shot”.

Is this the first time the reader is learning that it’s windy? Pretty convenient to introduce it right as it becomes important.

Rather, establish your variable beforehand in a disconnected moment. Try to ground it to a different element, otherwise it might look like it’s being mentioned for no other reason than “this is important”. Or, if it’s environmental, bury it with the other sensory descriptors.

When establishing the scene and setting, casually mention how the wind is interacting with the characters—making their hair a mess, throwing pollen everywhere, making skirts billow, etc.

Have another character complain about this variable bothering them

Have the character instantly regret the decision they made the night before for unrelated reasons. Like, if they got drunk, now they’ve still got a headache.

Depends on the story and the audience, of course, but I personally think having the narrator explicitly call out the variable fuckery going on reads a bit hammy. I like letting the audience figure out what went wrong with the clues I give.

If the scene demands, I'll also let my characters get annoyed and upset about their shots going wrong and blaming the environment. So long as it's not "hand of the author here to tell you what went wrong" you've got options.

I wouldn’t pull this trick too many times, otherwise your “expert” ends up consistently not an expert and then their sudden success looks suspect and contrived.

If you are writing some sort of tournament where this character is deliberately setting themselves up for success and is considering all these variables… a great example I like is Todoroki vs Bakugo in My Hero Academia season 2.

Dude is an uncertain mess throughout the rest of his tournament once his “fuck you dad I’m gonna win by half-assing it” suddenly isn’t enough to beat Midoriya. He’s forced to face some Tragic Backstory and it throws him off his game—establishes doubt.

He has a string of successes once he starts taking baby steps with the other half of his powers, and in the finale, he’s up against someone where he really does have to give it his all if he wants to win. His brute force powers are up against someone who has honed his very specific and powerful abilities for a decade.

And he can’t do it.

The final fight stops being a matter of power metrics and who would win if they both were competing at their best with all the tricks in their playbook available, which is what most of the tournament had been up to this point.

Basically—it stops being a numbers game, and starts being an emotional one. If you have a character you need to fail at something, but who wouldn’t otherwise, consider shifting the battle from external to internal, so the task failure is just the catalyst for the real meat of the story: what this loss means to this person in the long run.

**Side note there are of course a ton of anime tournament fights probably better than this one, Rock Lee’s whole arc against Gaara is one of them, I just don’t remember it well enough to comment on it.

Not every reader is going to be savvy enough to go “well that’s going to be important later”. Use betas and editors to help gauge how vague or obvious your foreshadowing is.

But even if you have readers sussing out your foreshadowing: Part of the fun is figuring out how the journey will end, even if we know when and where. Otherwise tragedies and prequels wouldn’t be made.

The dramatic irony of knowing variable fuckery is at play when the character is unaware can be so fun as the audience. Horror films are kind of built on it.

[sunarryn]

DP X Marvel #17

One week. One fucking week. That’s how long it took before the universe’s reality collapsed in on itself like a toddler knocking over a block tower made of cosmic rules, and Danny Fenton—sorry, High King Phantom of the Infinite Realms, Keeper of Balance, Ghost King of All Dimensions, Supreme Bureaucratic Overlord of Death and Souls, or whatever other bullshit title Clockwork slapped on him—was done. He was so done. With everything. With life. With afterlife. With bureaucracy. With math. Goddamn, he hated math.

He phased through the ceiling of what was left of the Avengers compound without so much as a knock because, frankly, he didn’t care anymore. People were dead. Everyone was dead. Half a fucking universe. And universes are fucking infinite. Literally. He’d been counting. Or trying to. But the math broke somewhere around “nine trillion decillion” and his brain short-circuited.

Inside, the Avengers were scattered around like bad leftovers. Steve was slouched in a chair like someone told him America lost the war. Thor was cradling a bottle like it was the last warmth in the world. Natasha looked like she hadn’t blinked in hours. Banner was trying to fix a coffee machine that had already given up on life. Tony—oh, Tony—Tony looked like he’d been held together with duct tape and sarcasm, and not the good kind.

“Yo,” Danny said, arms folded, crown floating behind him, cape swishing dramatically like it had beef with gravity. “Which one of you assholes thought wiping out half an entire goddamn universe was a great idea?”

They blinked. Steve slowly got to his feet. “Uh… who—?”

“No. Shut up. Don’t talk. I’m not in the mood. I haven’t slept in a week. Time doesn’t even exist in the Infinite Realms, and I somehow managed to be late to ten meetings that haven’t happened yet. Do you know what kind of eldritch administrative nightmare I’m dealing with? Do you?”

Tony blinked. “Not really, no.”

Danny whipped around to face him, pointing a glowing finger. “I don’t care, Stark. I don’t care that your kid sidekick is dead. I don’t care that half your team is sad. I don’t care that your billionaire ass is depressed and growing a sad beard like you’re auditioning for ‘Survivor: Superhero Edition’. I have literal oceans of paperwork made out of the screams of the damned piling up in my inbox because some purple California Raisin thought committing universal homicide was a vibe.”

“Hold on,” Natasha said, standing now, brows furrowed. “Who even are you?”

“I’m the janitor,” Danny deadpanned. “Of death. And you—you are all on my shit list.”

Steve opened his mouth.

“NO. I said no talking. Do you know how many souls half a universe is? Do you? BECAUSE I DON’T. THAT NUMBER DOESN’T EXIST. That’s not even math anymore, that’s heresy. There are species no one even knows about! I had to learn seven extinct galactic dialects in five minutes just to sign their death certificates!”

“Wait—wait,” Bruce said, cautiously stepping in like someone trying to defuse a bomb made of feelings. “You’re… the King of the Afterlife?”

“Infinite Realms,” Danny corrected. “Afterlife implies one dimension. I’ve got infinite. One of them is just an endless IKEA. You think you’re in hell? Try getting lost in that one for eternity.”

Tony blinked. “That explains the floating crown.”

“Oh, you noticed?” Danny snapped, sarcasm thick. “Yeah, the crown’s real subtle. You know what else I’m wearing? These.”

He held up his fingers. On them gleamed the actual Infinity Stones. Not the ones Thanos used. No, these were the OG versions—before the universe dumbed them down for mortal brains.

“I’m wearing multiversal cosmic artifacts as fucking accessories, Stark. I clapped death back into submission on my way here. I threatened Time itself with a lawsuit. I am so tired.”

Everyone was staring now. Thor slowly lowered his bottle.

“I have one question,” Thor said, eyes narrowing. “Can you bring them back?”

Danny didn’t respond immediately. He paced, muttering under his breath about soul processing queues and spectral overflow reports and ghost union strikes.

Then he turned, threw up his hands, and shouted, “Fine! Fine! But only because if I see one more Ectoplasmic Reconciliation Form I’m going to scream my own name and rip reality in half!”

Tony raised a cautious hand. “Just to clarify… you’re not doing this out of the goodness of your heart?”

Danny glared at him. “I am doing this because your collective idiocy has backed up the Infinite Realms so badly, I have ancient god-beasts getting angry Yelp reviews for not guiding souls fast enough.”

Bruce choked. “You get… Yelp reviews?”

“Do not ask. Do not google ‘Spiritual Bureaucracy Yelp.’ You’re not ready. It’s worse than you can even imagine.”

He clapped his hands. The power reverberated like a sonic boom made of lightning and bass drops. Light cracked through the floor, time folded, and space rewrote itself. In an instant, everything was back. People. Planets. Souls. Loved ones. Unsnapped. Safely. No one reappeared in traffic or mid-air. They were all fine.

Everyone stared.

Tony gasped. “…Peter?”

Somewhere in the compound, Peter Parker screamed, “MR. STARK I THINK I DIED?!”

Danny muttered, “Yeah, well, get in line, kid.”

Tony looked like he might cry. Steve looked like he might cry. Even Thor blinked back tears.

Danny didn’t give them a second to bask.

“Listen to me and listen hard, because I am only going to say this once. The next time you idiots let some glorified space grape get his hands on cosmic power and kill half the universe, I’m not bringing anyone back.”

Natasha stepped forward. “Wait—what—?”

“I said,” Danny growled, eyes glowing green and crown sparking violently, “the next time this happens, I am going to let the universe rot. I don’t care if it’s your kid, or your moms, or your emotional support dog. You will live with it. You will suffer. Because I’m not spending another week cleaning up your mess like the goddamn galactic janitor!”

Tony muttered, “Kinda thought you said you were the janitor.”

“I will kick your kneecaps off.”

Tony shut up.

Danny took a deep breath, pinching the bridge of his nose. “I’m going home. Do not call me again unless the universe is actually ending. And even then, it better be certified by at least three gods and signed in triplicate.”

He started floating upward, preparing to phase out, when Steve blurted, “Wait, thank you. Really.”

Danny paused mid-air, sighed, and turned around. “You’re welcome. I guess. But seriously. If another genocidal space maniac so much as coughs on the timeline, I’m filing a restraining order on this entire dimension. Bye.”

And with that, he vanished in a swirl of ectoplasmic smoke, leaving the Avengers staring at each other in the awkward silence that followed a divine ass-whooping.

Thor finally muttered, “I liked him.”

Tony sat down, blinked a few times, then said, “He just wore the Infinity Stones as rings. Like mood jewelry.”

Bruce nodded solemnly. “He’s not paid enough.”

“Was he even paid at all?” Steve asked.

And somewhere in the realms between life and death, Danny Phantom screamed into his pillow made of souls: “I AM NOT GETTING PAID FOR THIS BULLSHIT!!!”

[glitteringcrab]

Morty is so dumb that...

1. He regularly disarms Rick's neutrino bombs. The first time he did it it was completely on the fly, no prior experience. Yet, he did it.

2. He has a knack for learning alien languages... as for the tree people in the battery dimension, it was obviously done without any sort of translator or support. (And he took over as their leader)

3. He's quick on his feet and can think his way out in a stressful situation, figuring out things that Rick can't and coming up with innovative solutions.

4. He figured out how to use a portal gun.

5. He can figure out how machines he's never seen nor used before work, and employ them successfully.

6. Beat Rick (smartest man in the universe?) in a board game.

7. Can manipulate said "smartest man in the universe", if he so chooses.

8. Became a successful stock broker. Out of the blue. Just did it.

9. Run. Whole. Freaking. Civilizations (and also toppled them as Marta)

10. Pitches good ideas that Rick typically ignores

11. When suddenly becomes motivated to try, he is good at math

12. His ideas were good enough that he would have gotten a deal for a movie production...!

13. His default intelligence is maxed out.

...At this point, it's only a matter of time before he starts making his own inventions, Eyepatch-Morty-style.

GUYS.

The only reason we've been thinking that Morty is stupid is that Rick has been calling him stupid repeatedly.

Sure, Morty does plenty of dumb stuff, but so does Rick. Rick has the emotional intelligence of a four year old and throws tantrums of cosmic proportions whenever slighted (vat of acid? submit to the selfie?), while often going ahead with complicated, innovative ideas... that in reality solve nothing and are a waste of time (Pickle Rick?? Leg Rick?? Cloning his own daughter? The dumb time-loop in his own dimension? Replacing himself with a robot? Creating a robot ghost to scary Mr Poopybutthole instead of just telling him to leave??) Not to mention his many incredibly lame jokes.

Everyone does dumb stuff occasionally!!! No one is an impeccable genius of non-stop moments of brightness!! (even Eyepatch Morty, the most cautious character, the character who has made basically NO MISTAKES up to now, sounds dumb a couple of times: "I'm gonna do the thing I wanna do, with the curve thing" and "My biggest fear is other people being afraid. Of fear. Itself." lol).

If Rick hadn't been calling Morty a freaking idiot with every breath available, we wouldn't be thinking "oh look haha the moron became a stock broker, what a joke, must be some sort of fluke"; we would be thinking "what an incredibly gifted kid".

We would attribute Morty's many mistakes to lack of experience, to lack of wisdom, to youth, to enthusiasm, to idealism, to teenager hormones, to acting hastily.

We would wish to see him eventually mature, apply his time and effort to worthwhile endeavors instead (mainly) of inane teenage stuff. We would wish to see him do well in school, we would wish to see him reach his full potential and succeed in great things.

Only Rick keeps pounding our heads with how stupid Morty is, and all of Morty's successes are never mentioned again, but getting lost to oblivion in comparison to Rick's (who has 60+ years more experience) genius.

WE VIEWERS ARE BEING UNWITTINGLY MANIPULATED THE EXACT SAME WAY MORTY IS.

[ramblings-of-a-chaotic-neutral]

Ok, I don't really post here, but there's a Merlin AU idea that's been rattling around in my skull like it's a pinball machine and I need to get it out, so here we go:

Imagine an AU where Balinor doesn't die and banishes Kilgarrah before sneaking away so Uther doesn't catch him and can't put his newfound son in danger. Of course, both he and Merlin are heartbroken about having to be separated again after just finding each other, but they work out a way to keep in touch and occasionally meet in secret.

And this is all well and good, and everything in the show just kinda proceeds as normal up until about season 4, where we have the knights of the round table well-established in Camelot.

It'd make sense that after a few years of travelling around with Kilgarrah, Balinor would be pretty well-known and well-feared throughout all the five kingdoms as "that dragonlord who escaped the purge and now travels around on the back of a giant dragon", and people all over Albion are kinda terrified of the guy.

Rumors say that he never smiles, that he can kill a man in a split second without even utterring a spell, and can decimate kingdoms with the dragon under his total command. That makes for a formidable figure!

And then one day, Balinor is trying to sneak into Camelot to visit his son (he heard Merlin got hit by a dorocha and wants to make sure he's ok!), and the knights see him and freak out because holy shit that's one of the deadliest guys in Albion!

They're in a tense standoff, with Balinor threatening to call down the dragon on them if they don't let him through. The knights are all ready to give their lives to at least buy the people in the castle time to evacuate, when suddenly Merlin and Arthur make it to the standoff. Arthur immediately starts strategizing with his knights on how they're going to negociate with the sorcerer in an attempt to make sure that they aren't all slaughtered.

Meanwhile, Merlin just laughs and pushes through the rows of knights blocking Balinor's path to the castle. The knights, being very fond of Merlin and not wanting to see their kind little friend be brutally murdered by one of the most terrifying men in exsistence, are trying to grab Merlin and pull him back to safety or shouting at him to get back, but Merlin manages to avoid them as he walks up to Balinor.

For a horrifying moment, the knights and Arthur think that Merlin is about to sacrifice himself for them, but Merlin breaks into a huge grin, yells "Dad!", and runs right into Balinor's arms.

(Merlin and Balinor reason that now that Arthur's king, they might as well start easing him into some of Merlin's less shocking secrets)

And even more shockingly to the knights, Balinor hugs him back, asking Merlin all about how he's been doing, how are his studies under Gaius, etc etc.

And all of the knights just bluescreen. Because the math isn't mathing on this one. Hunith + Balinor = MERLIN?! Does not compute.

They're all pondering how could someone as joyful, friendly, and kind as Merlin be the spawn of a terrifying man like Balinor?? They just cannot comprehend it. The manservant who they all know and love came from this sorcerer who's name is synonymous with the threat of death and destruction??

They're all jolted back to reality however when Balinor asks Merlin if he wants to come back to Balinor's newly-renovated stronghold in the mountains (that's only accessable by riding a dragon) to learn more about one day becoming a dragonlord. And suddenly, the knight understand why Balinor's here. He wants to kidnap Merlin from them and twist him into a terrifying sorcerer to carry on Balinor's legacy!

It all basically dissolves into a long game of high-stakes tug-of-war between Balinor and the knights + Arthur, and Merlin's just enjoying spending time with his father and his friends.

Balinor will just casually crash one of their quests while riding Kilgarrah and "kidnap" Merlin while the knights fight to keep Merlin with them.

Balinor eventually gives Merlin Aithusa so he can get practice raising dragons, and the knights see it as some evil scheme to make Merlin betray Camelot and attack it from within, but damn it Merlin's already adopted the damn thing so now they're stuck with a baby dragon.

IDK if I'd ever write a fic about it since I'm pretty busy writing another fic rn, but I thought that it was a funny idea to throw out there!

PS: if anyone wants to read my current project, where I'm giving Sir Leon more anxiety with each chapter after a kinda-botched magic reveal on Merlin's part (and Merlin may or may not be an eldritch god), feel free to check it out here: https://archiveofourown.org/works/54027337/chapters/136771564

Thank you all for sticking with my incoherent rambling! :D I hope you have a great day/night!

Also, please let me know if you guys wants to hear more of the ideas that pinball around in my head!

[reachartwork]

PLEASE JUST LET ME EXPLAIN REDUX

AI {STILL} ISN'T AN AUTOMATIC COLLAGE MACHINE

I'm not judging anyone for thinking so. The reality is difficult to explain and requires a cursory understanding of complex mathematical concepts - but there's still no plagiarism involved. Find the original thread on twitter here; https://x.com/reachartwork/status/1809333885056217532

A longpost!

This is a reimagining of the legendary "Please Just Let Me Explain Pt 1" - much like Marvel, I can do nothing but regurgitate my own ideas.

You can read that thread, which covers slightly different ground and is much wordier, here; https://x.com/reachartwork/status/1564878372185989120

This longpost will; Give you an approximately ELI13 level understanding of how it works Provide mostly appropriate side reading for people who want to learn Look like a corporate presentation

This longpost won't; Debate the ethics of image scraping Valorize NFTs or Cryptocurrency, which are the devil Suck your dick

WHERE DID THIS ALL COME FROM?

The very short, very pithy version of *modern multimodal AI* (that means AI that can turn text into images - multimodal means basically "it can operate on more than one -type- of information") is that we ran an image captioner in reverse.

The process of creating a "model" (the term for the AI's ""brain"", the mathematical representation where the information lives, it's not sentient though!) is necessarily destructive - information about original pictures is not preserved through the training process.

The following is a more in-depth explanation of how exactly the training process works. The entire thing operates off of turning all the images put in it into mush! There's nothing left for it to "memorize". Even if you started with the exact same noise pattern you'd get different results.

SO IF IT'S NOT MEMORIZING, WHAT IS IT DOING?

Great question! It's constructing something called "latent space", which is an internal representation of every concept you can think of and many you can't, and how they all connect to each other both conceptually and visually.

CAN'T IT ONLY MAKE THINGS IT'S SEEN?

Actually, only being able to make things it's seen is sign of a really bad AI! The desired end-goal is a model capable of producing "novel information" (novel meaning "new").

Let's talk about monkey butts and cigarettes again.

BUT I SAW IT DUPLICATE THE MONA LISA!

This is called overfitting, and like I said in the last slide, this is a sign of a bad, poorly trained AI, or one with *too little* data. You especially don't want overfitting in a production model!

To quote myself - "basically there are so so so many versions of the mona lisa/starry night/girl with the pearl earring in the dataset that they didn't deduplicate (intentionally or not) that it goes "too far" in that direction when you try to "drive there" in the latent vector and gets stranded."

Anyway, like I said, this is not a technical overview but a primer for people who are concerned about the AI "cutting and pasting bits of other people's artworks". All the information about how it trains is public knowledge, and it definitely Doesn't Do That.

There are probably some minor inaccuracies and oversimplifications in this thread for the purpose of explaining to people with no background in math, coding, or machine learning. But, generally, I've tried to keep it digestible. I'm now going to eat lunch.

Post Script: This is not a discussion about capitalists using AI to steal your job. You won't find me disagreeing that doing so is evil and to be avoided. I think corporate HQs worldwide should spontaneously be filled with dangerous animals.

Cheers!

[dykedvonte]

The new Vegas Tribes having to learn to read, write, do math, and every casino game on earth along with customer service etiquette in the span of like a month or else this gambling Walt Disney Knockoff they’ve never met is going to gun them down with big fuck machines they’ve seen for the first time in their life. Not to mention they have to learn how to tie a tie:

[izzyy-stuff]

heyy izzy! i don’t think ive ever sent in a request to you before but i absolutely love your work so i thought i’d send something in. could you please do a roommate!taehyun fic where he accidentally walks in on you while you’re in the shower but then decides to join you which then ends up in him fucking you while you’re pressed against the cold shower wall and one leg pulled over his shoulder so he can hit deep :)

𝐌𝐀𝐓𝐇 & 𝐂𝐇𝐄𝐌𝐈𝐒𝐓𝐑𝐘 - 𝐊𝐀𝐍𝐆 𝐓𝐀𝐄𝐇𝐘𝐔𝐍

roommate!taehyun x fem!reader

in which what originally was supposed to be just a quick shower to help him relax takes a different turn when he walks into the bathroom and sees you already in the shower, deciding to relieve his frustration differently than he originally intended to.

wc 2.5k

warnings shower sex, unprotected sex + creampie, vaginal fingering, tiny mention of nipple play, oral (f. receiving), overstimulation, pet names, softdom!taehyun, biting/marking

↪ izzy speaks... I can't believe tae had zero works until now... like that's insane. I'm glad I can finally show it to you though. The writing process for this was for someone reason extremely SLOW. Everyone thank serene for being my life saver again and helping me get through whatever writing block I was feeling while writing this.

Kang Taehyun must have been the safest choice for a roommate ever. 

Unlike the other guys in your friend group, he was calm and knew when to shut up. Taehyun could cook, making your life a lot easier when he offered to make dinner as often as he could, and he was outside the dorm most of the time, too. If he wasn’t in the library studying after his lessons ended, you would find him in the gym, keeping in shape. 

He barely went straight to your dorm after school, so you had learned to get comfortable during your alone time. From using your living room for studying and making a mess with your papers and study books all over the floor, which he would have usually pointed out and told you to keep a system, to walking around the apartment with just your underwear.

So it wasn’t unusual when you sat on the couch in your living room in just panties and an oversized shirt you found at the bottom of your closet while cleaning up last week. You were surprised when you found it, confident you’ve never bought nor worn that shirt. But as you put it on, pushing your thoughts aside as there was no possible way of it being someone else’s if it was in your closet, you realized it was more comfortable than the garments you knew you owned. 

You have gone over the math formula hundreds of times and still feel like you see it for the first time every time your eyes land on it again. It doesn’t make sense. No matter how long you stare at it, the numbers and signs seem foreign. 

You sigh, slamming the math book shut and spreading out on the couch as a sign of giving up. You would have to ask Taehyun about it after dinner. But for now, you had other things on your to-do list for the day. 

Put your and Taehyun’s clothes into the washing machine (AND THANK HIM FOR DOING IT LAST TIME!!) 

Wash up 

Learn math 

Call your mom

You mentally cross out math, pretending it never existed. Still, you know you will have to come back to it. To this day, you weren’t sure why you decided to take another math semester when you didn’t have to. You were naive when you listened to your parents and signed up for “the only important class you will need in the future.” You had to scoff every time now when you remembered your mother’s words, knowing you wouldn’t ever need the formulas you were learning. 

Sighing, you get up from the couch and look around the living room. Looking at it now, you understand why Taehyun always wants you to have your work organized. It was a mess. 

Your fingers run through your hair before you pick up a few of your books and put them aside in the corner of the table so that other people can still use it. It also reminds you that you should clean around the house with Taehyun soon. 

But for now, there was the current to-do list you had to go through. 

You grab Taehyun’s clothes basket from his room, as you did many times before, kicking the door behind you so it would close before continuing towards your shared bathroom. 

Having a shared bathroom might have been the only disadvantage of living with Taehyun. You both tried to search for a bigger place so you could each get your own, but once you saw the prices, you both decided it was only a petite inconvenience. 

It doesn’t take you long to sort out all of his and your clothes by colors, leaving Tae’s underwear in the basket for him to do later on his own. You don't mind doing his laundry, just like he doesn't mind doing yours, but there are still limits to what you are willing to do for him. Even though those lines sometimes seem blurry in your eyes.

You aren't sure when or how it happened, but lately, you've found yourself wanting to step over some of the lines you had set for yourself when you first decided to room with Taehyun.

Maybe it was because of how comfortable you got with each other after half a year of living together. Perhaps it was because Tae had become your best friend over the years you knew him. Or, more likely, it was actually because of the amount of times you had seen him shirtless.

“We are friends, Ma. You don’t have to worry about me getting pregnant or something just because I am rooming with a guy. And you have met him many times. You know how Tae is.” You remember the call you had with your mom after you moved in, rethinking all your words. You were so sure back then that nothing could ever happen between the two of you, but a small part of you always wished for something else. 

You snap out of your thoughts, pressing the start button on your washing machine with a sigh. You step over the pile of white clothing you had prepared for the next wash, getting to the shower. You pull down your panties and shirt, hanging them on the empty peg beside your towel. 

♡⸝⸝ 

Taehyun was too exhausted to go to the gym tonight. He had enough. From missing lunch because he lost track of time while reviewing for his upcoming exam to completely forgetting about an assignment due last night. He just wanted to go home and relax for a bit before he would have to fall into the endless circle of studying again. 

So when he got through the door of your shared apartment, his first thought was to shower and go to sleep. He didn’t think much of what you were doing as he took down his shoes. Honestly, that was what he was the least worried about. 

Taehyun shakes his head as his eyes land on your books on the table, but then a smile creeps up his lips. You did listen when he scolded you about making a mess, after all. 

He looks around the apartment, trying to find you with his eyes. Eventually, his sight lands on your room, assuming you didn’t hear him coming in and were busy with your studies, so you didn’t come out to greet him. It wouldn’t be the first time. 

He doesn’t even properly register the sound of the washing machine as he walks toward the bathroom. For the first time in a while, his mind is finally blank, making him relax as he opens the door. 

Neither of you really realizes what’s going on until you drop down your shampoo, your eyes wide as you quickly try to cover your naked body upon noticing your roommate in the room. 

Taehyun’s cheeks could be mistaken for a tomato as his eyes travel from the bottom of your body to your face, swallowing everything he wants to say before even opening his mouth, stuttering. “I– shit, fuck– uhm, sorry,” he blurts out quickly, turning around so he wouldn’t face you. He doesn’t leave, though. 

 You can’t hear your own breath, nor his, as you stare at his back, your mind, unlike Tae’s, clouded with thoughts. “I wanted to shower. I’m– I didn’t know you were in here,” he says, you think. You’re unsure if any of the words actually reach your ears or if it’s all just in your head. Maybe he is just a figment of your imagination, too. He isn’t real. He isn’t standing in the bathroom with his back turned to you. 

“I’ve been so out of it today I just– I’m not sure what I am saying, to be honest. I didn’t mean to, though–” 

You cut him off, your words echoing in his ears. Still, he doesn’t believe what he just heard. “What?” He asks, his boba eyes making you feel weak in the knees as he turns around to face you again. “You wanted to shower and relax your mind, right?” You repeat half your question, your hands slowly falling to your sides. Taehyun bites his bottom lip, fighting all his inner demons to keep his eyes on yours. “Want to join me then?” 

You’re not sure what happens next. It’s all blurry in your mind. But the next thing you know, Taehyun’s hands are all over your body, “helping you to wash up,” as he said, but you both know that’s not what it really is when his hand just so innocently squeezes your breast. 

Your breath shakes as you feel him groan against your shoulder, sending shivers through your body. You tilt your head to the side, biting your bottom lip to prevent a moan from escaping your lips as he kisses your collarbone, his cold fingers playing with your nipples as if he had touched them thousands of times before, as if he wasn’t afraid at all of the sudden intimacy. 

“Tae,” you breathe out, and he only hums in response, his lips on your neck. “Are you okay with this?” He asks carefully, making it almost impossible for you to tell him no. So you nod, whining when his fingers trace down from your chest to your legs, making their way to your clit. “You’re so wet,” he mumbles. 

“S-shut up,” your voice shakes as you try to grind against his fingers, muffling your moan when he removes his hand. Your pussy clenches around nothing when your name leaves his lips, his kisses moving lower on your back until you hear him kneel behind you. You swallow a lump in your throat when his hands wrap around your thighs, the water drops on your back sending shivers through your body. “Mind bending over for me, sweetheart?” 

It feels unreal. Your roommate’s head between your legs, eating you out as if you were supposed to be tonight’s dinner, was all a little too much. You weren’t sure how long you could last. “Wait– I’m–” you try to speak up but end up swallowing everything you wanted to say when his tongue gets replaced by his fingers. You gasp, your hand slowly sliding down on the bathroom tiles as you begin to lose strength. You don’t think he notices, or at least he doesn’t do anything about it. His fingers pump into you so effortlessly, too. Somehow, it feels like he has been in your cunt many times before. 

Your first orgasm of the night is on Taehyun’s fingers, preparing you for himself. “Doing so well,” he coos, slowly standing up. It takes no time for his lips to find your neck again, his thumb rubbing slow circles on your clit. “‘S too much,” you whine, turning your head around to see him. His boba eyes are soft, full of love even, you’d dare to say. 

“You’re so pretty,” he breathes out when his eyes land on yours, immediately kissing you. You fall into the kiss, turning around to face him. Taehyun takes a step forward, making you press your back against the wet tiles. The water dripping between the two of you doesn’t seem to bother him a bit as he wraps your leg around his waist. 

You are still kissing him when he aligns himself at your entrance, thrusting into you without a warning. You gasp, breaking the kiss. His lips chase after yours again, but you’re too busy trying to get used to him to kiss him back. “So good,” he praises you again, his mouth moving to your jaw and chin. You tilt your head to the side, trying to keep as quiet as possible as he thrusts into you again, starting slowly, with his eyes on yours to make sure you are okay. 

You nod to him instinctively, and he thrusts into you right away, this time faster, harsher. It doesn’t take long for him to set a comfortable speed, and you can feel all his stress in each thrust. “I needed this,” he mumbles. “Needed you.” 

It almost passes unnoticed by you, just some out-of-mind praises, but you catch onto it, and his words get stuck in your head. “N–Needed me?” Your question comes out as a broken moan, making him groan. “The whole day,” he agrees, only thrusting harder. “Everyone’s been getting on my nerves,” he explains. “Couldn’t wait to come home to you.” 

The ticklish feeling in your stomach makes you uneasy. You’re not sure if it’s another orgasm building up or just an after-effect of his words. Honestly, it might be both. But before you can think about it properly, another thrust comes in, with a few mumbles about how perfect you are before you feel his speed slowing down again, letting you know he is reaching his limit, too. 

It only takes a few more sloppy thrusts before he cums inside you, both of you too into the moment to realize he should pull out. Taehyun’s head falls onto your shoulder, but he doesn’t stop holding your leg up, assuring himself he still feels you on his body. “I’ve been waiting for this,” he breathes out, and before you can answer, you feel his teeth digging into the skin on your shoulder. 

You gasp, “What was that for?” He only hums in response, as if he had no idea what you were referring to. “A mark,” he finally mutters, making your eyes widen. “Wanted to mark you.” He says it so casually, while his hand slides between your bodies, circling your clit slowly again. You swallow a moan as his finger makes its way into your pussy again, feeling the mixture of his and your cum sliding down your thigh. You need another shower. 

You stay still for a bit, his head resting on your shoulder and your leg wrapped around his waist while your fingers play with his hair to assure him you are still there, not saying anything. 

You step out of the shower, wrapping a towel around yourself immediately. You keep your eyes on his naked body, rethinking your next moves. “I need your help with math,” you proclaim quietly like you normally would. “I’ll gladly help you,” he nods with a smile. So happy, and for what? He was never rude about it when you asked for his help, but it wasn’t like he would be excited, either. This time, however, he makes you question what’s going on in his mind. 

“Here,” he says, the same smile still on his lips as he hands you your shirt and panties. “I didn’t know you were already wearing my stuff, but I can’t say I would complain,” he teases you, and it all finally clicks. Of course, that’s why you didn’t remember owning the shirt. It wasn’t yours in the first place. “Uhm–” you panic, trying to find a good excuse, but it’s already too late because all Taehyun can think about is the adorable blush on your cheeks.

TXT ⋆✶ izzy's tags @beomiracles @seoulzie @adel222 @inkigayocamman @flowzel @love-be0m @virgo-and-libra @hwanghyunjinismybae @liaatiny @minaateez ✶⋆

Want to get notified? Join taglist here !

[i-cant-sing]

You know I'm giggling picturing Baldwin in readers time, no no no not him growing up but if that time machine brought us to the right time and him to modern times and just imagine reader was a massive geek loser with a bunch of posters having to explain to him😭

“Is this your chamber?” He asked as he walked into your room, while you scrambled to lock your door and pull down the curtains, lest anyone sees him.

“Is that me?” Your blood runs cold as you hear him faintly gasp from the bedroom and you dash in.

Baldwin’s unphased by your attempts at trying to push him away from your board, where there are multiple pictures of him pinned. “You have a shrine of me in your room.”

“This is not a shrine!” But it’s like he’s not even listening to a word you’re saying, his eyes glazed over at the board.

“This is devotion.”

“It’s not devotion, it’s like… aesthetic appreciation. Of history. With maybe a little bit of… admiration. And thirst. I MEAN THIRST FOR KNOWLEDGE—” Baldwin is grinning widely under his mask.

“Do you lie to all kings? Or just me?” He finally looks at you, further adding onto your embarrassment. “I do hope that I’m the only one privileged enough to be in your chambers.”

“Are you asking me if I bring other men into my bedroom?” You narrow your eyes, attempting to remove the attention from the board. “What, are you jealous?”

He stares into your eyes, no hint of amusement in them. Then, he slowly raises his hand to remove his mask, setting it aside and looks at you.

His lip quirks up. “I’m not jealous, angel. I see your devotion, and not just from my shrine there.” He leans down, closer to you. “I see it in your eyes. You dream of me.”

“Dreams? I have insomnia-” But he cuts off your attempts at brushing him off.

“You honor me with your heart, even if your tongue fears to confess it. Do you know what that does to a man unloved?” He whispers, and you try to shrink away until your back hits the wall.

“You- you weren’t unloved.” You say and a wave of softness washes over his face. “I was, until you came along…” he murmured.

Avoiding his blue eyes, you looked to the side as you told him how he was popular with time. “You’re… a legend. People have only ever spoken good about you. About your acts. You’re a hero-“

“Is that a painting of me without my top?”

“Stop-!” You try to cover his eyes with your hands but he just grabs them with one hand and pins you against the wall.

“It’s adorable to see myself through your eyes.” He smiles, his dimples appearing as he tucks a strand of your hair over your ear. “And to have an angel as my devotee… I’m honored.”

He sees your eyes widen before you narrow them and look away, your face turning red and he chuckles, pulling you to him as he hides your face in his chest.

“I’m not obsessed with you, you know?” You mumble. He hums, swaying you a bit as he pets your hair, consoling you. “Mmhm. I believe you, darling.” He kisses the top of your head. “Y/n?”

“Hm?”

“Why is my face on your pillow?”

Later:

Baldwin: “So why is my face on your pillow?”

Y/n: I use it. Wanna see?

Baldwin, lust washing over his eyes: I would be lucky-

Y/n, proceeds to punch pillow over and over again: so when I’m studying and I need to learn complicated things, I act like I’m teaching to this pillow- well you, and I’m the emotionally unavailable father who needs to teach you math😌

Baldwin:

Y/n:

Baldwin:

Y/n:

Baldwin: can you order me a pillow with your face on it? I think I can show you how to use it correctly😏 *gets smacked in the face by the pillow*

[merajsblog]

𓆩ᥫ᭡𓆪*ೃ༄

akaashi keji was quiet. it wasn’t that he was too shy or scared to speak, he just would rather not talk. he liked observing. he was sat at the back of the classroom, nose in a manga. his nose scrunched a little and his eyebrows slowly rose into a confused look as he read. his hand was propped up on the desk supporting his head as his dark hair soaked up the sunlight. he occasionally pushed his glasses up.

as you found your seat, and placed your bag on the proper hook, as you turn to meet other classmates.

as you just observed him, he likes to observe you. quietly placing his manga down, his gaze flits over to you. his gaze is intimate and soft enough that you don’t feel like anyone is staring at you. he observes how you stand, where your hands are, your posture from behind. it was easy to watch you. he was entranced to say the least.

at the end of class, he had grown confident enough to say hello to you before heading to lunch. you were sat there, hands in your hair staring with your brows furrowed at the marked paper in front of you. this class had been exceptionally tough for you. math was hard to understand and even harder if you didn’t have a good teacher.

“hello y/n” akaashi would say politely, while walking by your desk. you looked up your brows furrowed, still thinking about the problem. you had a slight frown on your face too. as you looked up at him he could swear his heart skipped a beat.

“hi akaashi!” you said, smiling after a bit. “i’m sorry, i was just trying to figure this out before lunch but it seems like ill be stuck here a while…” you said giving a half laugh. you look back down, expecting him to walk away.

“well, for this part you just have to take the anti derivative of the derivative. you should be able to get your answer after that.” he said, squatting down next to your desk.

you were startled. this was the last thing you were expecting. you were determined to learn this, determination overcoming you. as he pointed and helped you through each step, you felt more confident.

“you’re a life saver akaashi keji.” you say making direct eye contact with him. you’re met with startled grey eyes, and his mouth slightly open in awe. he did love how you said his name.

“anytime y/n.” he said with a soft smile.

“did you get lunch already?! i’ll buy you bread and a milk i promise. you can pick from the vending machine!” you say triumphly. he snickers before shaking his head.

“you’re gonna need the brain food so i won’t take you up on that. thank you though.” he said softly. “we can head down to the cafeteria together if you’d like!” he said, stepping back and signaling the way ahead for you. you step out, and start walking ahead.

[max1461]

One thing that was hard for me to get used to when I started learning math was what I call "static thinking". Math doesn't have any time evolution; everything either is or it isn't.

When non-mathematicians think about operations like addition, they think of them as "processes" that "occur": you take 2 and 8 and "combine them" to get 10. The expression "2+8" is like a sort of command, telling you to perform this process of addition. People think of math this way because it's basically how math is presented in schools.

To a mathematician, the expression "2+8" is not a command and it does not signify a process. "2+8" is merely another way of writing "10". They are two expressions with identical meaning. That's what "2+8=10" means, it means "these two expressions signify the same thing". There is no "process of addition" which "happens" and "results in 10". "10" and "2+8" are just alternate spellings of the same number.

For a more advanced example, consider the formal definition of a finite state machine. Intuitively, we think of a finite state machine as a network with various nodes and directed edges and so on, into which we input some string in the machine's alphabet. After inputting the string, it travels around the machine according to the transition functions before finally arriving (or not) at a final node, and by this process a computation is performed. Of course, mathematically, this is nonsense. A finite state machine is a network with various nodes and directed edges and so on, but the notion that you can "input a string" and it will "travel around the network via the transition functions" is bullshit. A string is recognized by the machine if and only if there exists a valid path for that string via the transition functions from an initial node to a final node. The string never actually travels the path, because such a notion does not exist in mathematics.

A finite state machine is not a machine, it never actually does anything. It sits there in the realm of abstractions, unmoving and static. Every string which it "recognizes" it recognizes by dint not of things that it does but of facts that simply are; every string recognized by the machine is so and has been so since the dawn of time, without the machine ever in fact going about the process of recognizing it.

This is philosophically a little bit trippy, but it can also confuse early math students in practice, too. As I mentioned at the top, I was very confused by it. For instance, in the finite state machine example, a perfectly ordinary statement to encounter in a proof might run something like

[Block of reasoning establishing that some string w is recognized by the machine M] [Block of reasoning establishing that all transition functions into a final node F of M have label x] ...since w is recognized by the machine M, there must exist a transition function T whose target is a final node and which sends w to that final node on the last character of w. Thus, since T must have label x, the final character of w is x.

To a mathematician this seems perfectly trivial. To me as a young math student, this kind thing seemed almost miraculous. We don't even know what w is, and yet we can run it through the machine? And from the fact that the machine recognized it, we can conclude things about what w is? We can tell its final character? How is that possible? I felt like this kind of thing involved "reaching into the future", reasoning about processes from the end when we haven't even begun them yet.

But, of course, we can do this, because there is no past or future in mathematics. The machine is simple there, the string is simply recognized or not, its last character simply is x or it isn't x. Nothing has to "happen".