#Logarithm rules

[forgottenbones]

The iPhone of Slide Rules - Numberphile

[saintkevorkian]

[existinglimits]

Learn your properties of logarithms

Just... just do it. Before you take calculus is best, but as soon as possible if you're in the middle of calculus.

You're not going to be able to do "logarithmic differentiation" if you aren't comfortable with log rules.

Below the cut are..

a link to Khan Academy Algebra 2 Unit 8: Logarithms

"Logarithms explained Bob Ross Style"

"What is the number 'e' and where does it come from?"

Link to Khan Academy Algebra 2 Unit 8: Logarithms

You can skip to "Properties of logarithms" if you're short on time, but most people who struggle with properties of logarithms do so because they don't understand logarithms.

Logarithms are the inverse of exponentials, so the rules are closely related but inverted. If you're REALLY struggling with logarithms, you may want to examine how comfortable you feel with properties of exponents.

Logarithms explained Bob Ross Style

What is the number "e"?

[transhuman-priestess]

I've been wanting to try this film for a while. It's Lomography Fantôme Kino, also available as Wolfen DP31.

It's an ultra-low-speed Black And White film. It has an ISO of 8. Not 800, not 80, 8. So it's got incredibly high contrast, incredibly long exposure times, and it looks bitchin.

Film speed is logarithmic, every time you double the number, it doubles the sensitivity. Your standard walkabout film back in the day was 400, decently good for outdoor photography and indoor with flash. Your phone camera now is usually around ISO 800 at a minimum if you're indoors. (As a side note, ISO is not a unit, it's a rating. It's not correct to say a film has "8 ISOs")

Based on the above, this film requires about 7x as much light as my phone to make a good picture. This lets you slow down your shutter speed even in bright daylight to get long-exposure shots like the one in Row 3.

I'm surprised it shot so well with flash indoors.

I'm definitely buying this film again. It fucking rules.

P.S. I traded in my old canon A2 for a slightly newer Canon EOS 33 and it slaps. These were all taken on that one.

[vintagerpg]

What a fun and welcoming box set! This is the second edition of DC Heroes (1989) from Mayfair games. I’ve never encountered the first edition, but my impression of this box is as an attempt to make a fairly tricky system as welcoming and accessible as possible without, you know, tossing out the original system. Which is a clever system, based on logarithms — the same thing is under the hood of Underground. I understood it for a brief moment in time despite my deficiencies in math (but lordy, no, I did not retain it, nor do I wish to re-learn), and it struck me as a clever way to handle the divergent power levels present in a superhero game. It is, however, clearly not as user-friendly as, for instance, TSR’s Marvel RPG.

There’s a lot in the box — a brief intro pamphlet with a solo adventure, a rulebook for the GM, a player’s guide, a screen, a group adventure featuring the Justice League International, a little wheel that makes resolving rolls much easier (not quite so easy as the Universal Table in Marvel, but close). There’s a beefy dossier of characters accompanied by a stack of full-color character cards, which are a nifty, fidgety addition that doesn’t really add much to play.

The 15-page chapter on running games has some of the best advice I’ve encountered from the period — focused on collaborative play, encouraging roleplay and generally putting fun ahead of rules. One section has the header “You are the Player’s Senses” and I think that might be one of the best summaries of the GM’s role I’ve ever read. It certainly feels miles ahead of just about anything else from the period that comes to mind, with the possible exception of Rolemaster’s Campaign Law.

This box wants so desperately to be a game anyone can play. I don’t think it quite gets there, but I think the way it tried was influential — over the course of the ’90s, we’d start to see more and more supportive text in RPG books that sound like they spin right out of this GM’s section.

[starryhutcherson]

clapton davis fic where hes just like, super flirty and its really cute and the reader is oblivious to this but eventually clapton is like "damn it why cant you get the hint" so he opens up to the reader?&;&:& tysmm

━━ UNSUBTLE SUBTILITY

'୧ ‧₊ pairing: clapton davis x reader warnings: swearing, brief depictions of blood word count: 2500+ ⋆ ✩‧₊

The presence of Spring in Grizzly Lake brought a lot of things; including sporadic bursts of heaven-yellow sunlight, greenery spiraled across branches of previously barren tree skeletons, and, most importantly for students of Grizzly Lake High School, the promise of the Spring Fling Formal that was set to occur in the midst of May. 

For Clapton, this prom meant one thing; achieving his goal that’s been looming over him since freshman year — ask you out. Theoretically it’s a simple process, but if it was truly as easy as it sounds it would have occurred the very moment his eyes landed on your figure that first day in beginner spanish. 

You were the embodiment of perfection, punctuated through your gleaming smile that enraptured anyone in a ten mile radius, and the way the sun seemed to spread across the expanse of your cheeks, soaking you in the rays of heaven itself. Clapton was about ready to propose that day, and he didn’t even know your name. 

Now, roughly two years later, he was still amidst the same dilemma, the one in which he actually had to do the asking-out part. He was sure by now you would have picked up on his inherently obvious attempts to entice you, but you remained oblivious, so he decided he’d have to fully commit if he wanted to capture your attention. The art of unsubtle subtility, if you will. 

And so, forty three minutes into the depths of an agonizingly dull pre-calculus lesson, he confidently taps your shoulder with a fractionally tense hand, and indulges the tug on his heartstrings when you turn around, framed by the delicate glow of mid-morning spring that he adores so much. 

“Something wrong, Clapton?” Your voice cleaves through the classroom ambience of idle chatter and textbook pages being flipped. He flashes a boyish smile in hopes to flutter your heart in the same way you flutter his. 

“Do you get any of these questions?” 

“Yeah, they’re not too bad,” you reply, offering an ephemeral that renders his throat tight. 

He glanced down momentarily at his worksheet, adorned in scrawls and scribbles, yet lacking a single legible answer. His vision trains up back to you though, as it always does. He thought you’d easily detect the unspoken question for your help, but you remained stationary in your seat, as if waiting for him to say it. He couldn’t tell if you were genuinely that heedless, or if you were toying with him. Cat and mouse. 

“Seriously? When did they even teach us all this?”

You shrug mindlessly, and a lock of hair shifts from its position on your shoulder. He’d give anything to rope his fingers through it. “A while back. Why, you need some help?” 

Yes. He’d like your help, your compassion, your hand in marriage…

“Wanna walk me through it?” He tosses you a hopeful expression, and you answer back with a simple nod, sliding your chair along the cheap linoleum floor with a scrape, until the pair of you are sharing his desk, impossibly close. 

Your velvet voice is stringing sentences right down the expanse of his spine, though your attempts to help him understand logarithmic differentiation were ultimately futile— how was he supposed to concentrate on anything when he could feel your words blooming on his skin? See every freckle and divot etched into your face? He could taste his own heartbeat as it melded against his throat.

“So, this helps to avoid complications like the product rule and the quotient rule when— Clapton?”

He cocks his head up, trying to ignore the swell in his stomach when he hears the way his name sounds braided between your sentences, it suits your voice so well.

“Yeah? What’s up?” 

“Are you even listening?”  

Shit, no he absolutely wasn’t. How could he? Your proximity allowed him to see you. Like, properly see you. 

“Yeah. Totally. Logaramic thingyation,” he murmurs with overt certainty, and a puppylike grin. 

You snicker. “Couldn’t even get the name right?” 

He’s internally collapsing, though he manages to force some words out of his struggling brain. 

“Hard to think when you’re here.” He doesn’t dare sever the eye contact between you, hoping to hone the tension as long as possible, until he shatters you. His lopsided grin shrinks in a moment of brevity; you’re so close and he can smell you and your very essence. He’s sure that his ulterior motive is conveyed, through the way his eyes explore the breadth of your figure, never leaving, never faltering— yet to his pure irritation, all he gets is a blank expression and a confused chuckle. 

“Why is that?” You ask, and he wants to grab you by your shoulders and shake you. Are you really that dense? Your face is about as expressive as a rock, and you seem not even partially affected by the flirty wink he sent your way moments prior. 

“You’re kidding, right? Come on.” He fires back, raising a brow with a daring smirk. He wants you to inquire. You don’t. He realizes that trying to get you to take a fucking hint was about as impossible as teaching him calculus. 

You force out an awkward laugh that makes his skin crawl with defeat, but he doesn’t back down. “Come on what?” 

He refrains from the urge to say “me”, and instead huffs a sharp exhale through his nose. He’s moments away from spouting some lame compliment when the shrill cry of the bell interrupts his train of thought, and a tide of students eject eagerly from their seats and spill out into the corridor for lunch. 

Your friend approaches the desk with a quirked brow, reaching for your arm and mumbling something into your ear that’s intelligible to Clapton, tugging on you to try and steer you away from the classroom. And from him. You nod in response to her comment, before momentarily glancing back over to Clapton.

“I gotta go, Clapton. See you soon though, see you in History!” You send him a parting wave with a gentle flick of your wrist, before turning off and disappearing down the long stretch of corridor beside the classroom. His eyes follow you for as long as possible before your figure is consumed by the wandering horde of students, and he lets a grumbly sigh escape his parted lips before he packs up his belongings. This was going to be harder than he anticipated. 

*:･.・゜゜・

Clapton’s second attempt at alluring you resulted in more or less the same outcome. He’d entered the cafeteria, instantly bathed in the overwhelming odor of lysol and lard. His prior plan was to grab a doctor pepper, maybe a sandwich, and head over to his typical table to talk a painfully uninterested Sander’s ear off about you, but he scrapped it upon spotting you waiting in the cafeteria line, immediately changing course and veering over in hopes of a successful conversation.

He cuts in front of an unsuspecting freshman, ignores the irritated “What’s your deal man?”, and ‘accidentally’ brushes up to you until your bodies knock, and you spin around in confusion. 

Your face mildly relaxes in recognition, and he takes this as progress.

 “Hey. Getting lunch?”

“What else would I be doing?” You ask. Swing and a miss. 

He clears his throat a fraction, not allowing this to throw him off his game. 

“I dunno, maybe you just really like standing in lines,” he teases, and you laugh back. 

“Especially if the line is for overpriced cafeteria food,” you add with a grin.

The pair of you share a laugh, and Clapton marvels at the fact that you can look so irresistible even in the harsh fluorescence of the cafeteria’s artificial lighting. The pair of you fall into a partially awkward silence, and he follows your line of vision, watching as you observe some students hanging a hand painted banner advertising prom for the entirety of the cafeteria to see. ‘Spring Fling Formal, get your tickets now!’ glistens in white gold lettering. He prays he can take the banner up on that offer. 

“Are you doing anything for it?” A bit of a jump from the casual conversation, but he was itching to entice you and couldn’t risk missing his chance. 

“Hm? For what?” His lips twitch into a gradually familiar downwards smile. “Prom,” he says, gesturing at the banner, obnoxiously pink in hue and decorated with scatterings of hastily painted daisies. 

“Oh. Maybe— I’m not sure, it’s kinda ages away.” Yup. An impossibly distant period of two weeks. Clapton’s jaw ticks uncomfortably at the prospect of the narrowing window of time. He can’t afford to screw this up.

“Right. Sure. Are you… interested in anyone in particular though?” He probes, hoping that you notice the searing spark of desperation that lingers in the loop of his irises.

“Eh. Not really. Are you?”

His ego suffers a blow at your total ignorance to his pining. He’s on the brink of combustion; unable to endure the cosmic irony of having you so close yet so far. He pictures you for the umpteenth time, glittering in a dress that matched your eyes and his tie. A slow dance to a Sting song, his eager hands situated either side of your waist. You’d stare up at him with a dazzled guise, illuminated by the scintillation of indigo disco lights, and his tongue would delve into yours as he soaked up the saccharine flavor of the fruit punch lingering on your lips. 

“Yeah.” He states bluntly, staring at you as if you hung each and every star. “Yeah, I’m interested in someone.” 

You raise a brow. “Oh yeah? Who?”

He clears his throat. “Someone special. Someone super special.”

“You should ask them!” “Easier said than done,” he chuckles humorlessly. 

Your lips part as you go to investigate further, but are interrupted by the scowl of the lunch lady barking at you for your order. He notes it, mac and cheese plus a diet sprite— you’re handed it moments later, and your vision is torn from him and towards your small circle of friends seated across the cafeteria, who are waving you down. You’re gonna leave again? 

“I better go sit down, but, uh, you should definitely ask that person to prom. Be upfront and everything. Y’know, you only live once, and all that, right?” 

He swears he’s going to implode at the unbridled irony of this entire situation. Be upfront. He’s been upfront! 

“You know it,” he quips weakly as you slink away. 

He’s been showering you in signals for months, and you’d always abandon them, his attempts for your acknowledgement left festering as sour memories in his head, things that made him roll over with shame in bed at night, and all for what?

He brainlessly orders his doctor pepper with a monotone grumble, feeling the frigid prick of the can’s condensation gather in his palm as he wonders what the hell it’s gonna take for you to take a damn hint. 

*:･.・゜゜・

After yet another failed interaction, Clapton had spent the span of the rest of the week stripping his words to the marrow. Every conversation he indulged in with you involved his inner thoughts spouted in their rawest form— cocky compliments, lingering touches, looks of intense pining and yet somehow you continued to miss them. Every. Last. One. 

He was nearing his wits end, teetering on the cliff of insanity and seconds away from taking the plunge. Maybe he was the one who needed to take a hint. Maybe you were trying to tell him that you weren’t interested and he wasn’t giving it up. It was a sickening notion, one that thrashes wildly in his stomach. He didn’t know much, but he did know that he’d never be satisfied until he knew your stance on him for certain.  

He was just gonna say it. 

In hindsight, it wasn’t Clapton’s smartest move to deliver the question in the midst of a dodgeball game, but his thoughts were warped and he decided now was as good as ever. His voice was barely even audible beside you over the screech of tennis sneakers scraping the gym floor and the continuous sound of rubber balls coming into contact with student flesh. 

“Hey!” He exclaims. 

“Hey?” You say back, turning to him momentarily. Yet again, he wonders how you do it. Hair blown back effortlessly, skin glistening with a fragile sheen of moisture that is hardly off-putting, if doing something it aids to soften your otherworldly glow. Meanwhile, he was panting like an old dog, hair matted to his forehead in sodden chunks beneath his obnoxious sweatband. 

“I needa ask you something!” It’s sink or swim. His teeth graze the inside of his cheek for a moment, his gaze varying between you and the opposing court, to prevent a dodgeball to the head. 

“Yeah?” Sink or swim sink or swim sink or swim. “What’s up?” He melts at the sight of your semi-breathless smile.

“Are you still dateless? Like, to prom?”

Your forehead creases, and you return the sideways glance. “Um, yeah. Why?”

With a delayed exhale that rings heavy in the pits of his lungs, he turns his entire body to face you, which in turn makes you face him as well. 

“Look, I’ve been trying to say this for months. Well, not months. Maybe weeks. Whatever– point is, it’s been a while. Like seriously, a long fucking time. And I swear I’ve been so obvious, but clearly not obvious enough because you’re still, like, totally unaware or whatever. But, like, basically, I was wondering— I’ve been wondering if—” “Clapton!” You exclaim hurriedly, splintering his stammered sentence in an instant. He barely has time to cast his visage front on, before a dodgeball with an extremely strayed trajectory soars gracefully through the current of the air and hits Clapton square in the face. Guess he wasn’t paying enough attention after all. 

An expletive leaves his lips, muffled by the wail of your gym teacher’s whistle. His head is temporarily a warped whirlwind resembling TV static, though the feeling fades fairly quickly.

You turn to him in a mild panic, noting the faint trickle of glossy crimson that has started to spill from his nose. “Holy shit! You’re bleeding! Lemme take you to the nurse.” 

He can’t help but twist his lips up to form a slight smirk as you place a worried hand on his bicep. The touch scars on his nerves, your fingers like an angel’s caress. 

In all honesty, he feels fine, but you offered to take him to the nurse— was he going to give up that delightful invitation? No. He was not. 

The pair of you are excused from the gym, trekking down the hallway in an atmosphere of silence so thick it’s practically tangible. Upon arrival at the nurse, Clapton’s seated in a shitty plastic chair, holding a paper towel held to his nose and tipping his head slightly backward. He couldn’t believe that his one chance of actually spitting his desperate question out was interrupted by a stray dodgeball. A goddamn stray dodgeball. 

You linger in the doorframe, taut as a coiled spring. The nurse, underpaid and painfully unsympathetic, leaves the pair of you once she deems Clapton to be ‘good enough’, in her exact words. 

You approach him, taking the scarlet-spotted tissue and holding it to his face for him, a gesture which turns his insides in on themselves. 

“Hey Clapton? What were you saying before?”

Shit. 

“What?” He croaks gutturally, trying and failing to play dumb. He knew damn well what he was saying. Prom with him. 

“You were asking me something. Before you got, y’know, obliterated by a flying dodgeball.”

He snickers feebly, even if for a moment. “Oh, yeah.”

You open your eyes wider as if to say, “Well?”

The climate in the room seems to sink heavier, cradling the scent of antiseptic and drying blood. Clapton’s words fizzle out on his tongue no matter which way he arranges them in his head, but he knows he just has to get it out—- rip off the band-aid, break the ice, all of that. 

His eyes, big and wide and drinking in your face so dangerously close to his, melt into an unmistakable question. He counts himself down in his head. Now or never. 

“Prom. I was asking if you wanna go to prom.” He takes a staggered breath. “With me, I mean.”

Oh. 

Oh. 

The genuine beam you erupt in subsequent to his words is enough to ease his nerves. It’s enough to make him soar, actually. 

“Why didn’t you say anything?” That wasn’t a no. That wasn’t a no. His heart hurts with hope. 

“I tried to. You’re just… you kinda suck at taking hints.” He chuckles. 

You roll your eyes, picturing every moment leading up to this one that you spent with him. Upon further reflection—- yeah. Yeah, you clearly did. People don’t look at friends the way he looked at you.

“Shit, I kinda definitely do,” you murmur. 

He doesn’t let the quiet last long.

“So…?”

“Oh. Right, yeah. Clapton, I’d love to go to prom with you.”

The smile he wears is irresistibly contagious. Finally. Finally. Two long years of craving you; two years of memorizing every quirk and curve and contour. He knows it’s sort of ridiculous to get so elated about some forgettable high school dance, but the image he can see so vividly in his head; the lights and the dress and the swarm of butterflies that comes with your killer smile… it’s worth every awkward exchange, every word that’s fallen on deaf ears.

“Seriously?” He asks, reaching for your hand and wallowing in the way you so brainlessly accept the touch.

“Seriously.”

“Good. You won’t regret it.” 

And something inside you tells you that he’s absolutely right. 

reminder, my requests are always open

masterlist

✩‧₊˚

[foone]

fun fact: You wanna know how you calculated trigonometric functions and logarithms (very handy for complex multiplications!) before calculators?

You had tables!

yeah it's just a book of lots of numbers. these were worked out by hand. It's hundreds of pages. This (along with your slide-rule) was essential to every math student.

This one is a 1959 reprint of a 1943 original

[whats-another-song-contest]

For many years there has been intense discussion on the role and legitimacy of the jury vs the televote in the Eurovision Grand Final. The problem is that many of the arguments I see made are based on nothing but people's gut feeling and snap judgements from watching the show. And humans are notoriously terrible at intuiting statistics.

That's why I wanted to provide some actual data to give context to the more eye-catching examples people tend to use, and hopefully encourage some critical thought. I spent the afternoon updating my eurovision excel file with data from the 2024 and 2025 Grand Finals, and can now present these graphs of jury results plotted against the televote. As far as eurovision statistics go, this is one of the simplest charts you could make, and should hopefully be as simple to understand.

Terms: I use the term televote to refer to the entire public vote - this includes all votes from calls, texts, websites etc.

The axes: These show percentages out of the total number of jury or televote points awarded overall in a given show. Using this measure instead of the actual point scores ensures that results from different years are comparable, despite the fact that the number of Grand Final entries and overall points to be distributed between them varies from year to year (depending on the number of voting countries) .

Reference line: This shows where an entry would land if the juries and televote respectively awarded it an equal percentage of their available points. Data points that land above this line means the jury awarded the entry a greater proportion of its available points as compared to the televote, and vice versa. I find it interesting to see which entries land near this line, and then compare them to entries that stray further from it, in either direction. I also like to see where my favourites ended up, and consider how that can be understood in the context of the previous comparison.

First chart: Here each data point represents an individual entry in the Eurovision Grand Finals from 2016 to 2025 (aka every year with the current split scoring system). Data source: eurovisionworld.com

Second chart: These data points represent the average percentage out of the total jury/televote points each country was awarded between 2016 and 2025 (for the years that they made it to the Grand Final, that is).

Beware: For countries that made it to the final more times there are more data points to average, while for others there are as few as two results to work from.

Also beware: Averages can obscure variance - a country with epic highs and lows might end up looking similar one with stable middle-of-the-road results, despite their actual experiences being very different. That is to say: there are lots of outliers included in these averages - Spiders Georg has set up his cave and now lives in this chart. With his entire spider farm. Look at it. It's on the web.

Also-also beware: This chart makes the assumption that nationality is the most relevant variable to investigate in relation to the final result. But that remains an unproven assumption; before drawing any conclusions about potential biases the public or juries might have for certain countries, these results should be compared to charts where other factors are accounted for, to rule them in or out as compounding factors. Such factors could be running order, when the voting opens, genre, vocal ability, dancing ability, stage precence, visual production, creative cohesion etc.

In short, this chart doesn't rule anything in or out on its own—but it makes a good starting point for further investigation.

Country letter codes, for reference:

Not sure how viewable these charts will be on smaller screens, but for the lower scores on the detailed breakdown to be visible at all I needed to make them huge. Might fuck around and make the scale logarithmic at some point, to show more detail in the lower range without cutting off the upper. I also have more data tables with more complex calculations going on in this excel file. I might make charts of those at a later date, if I can first work out whether they provide any useful insights at all or were just fun to make. ¯\_(ツ)_/¯

Thanks for reading!

[a-dinosaur-a-day]

Think of Megafauna as the evolutionary equivalent of The Rich

no no no, hold on with me a second

matter and energy are finite. an ecosystem is, essentially, a group of organisms in a particular location balancing each other out in order to allow for matter and energy to flow in a constant cycle

that balance requires each species to reproduce to the best of its ability, and all the species around it to take advantage of that reproduction to the best of their abilities

the larger you are, the more energy and matter you need to survive. yes, if you're bigger, you can have an advantage over other species in getting food (either by being able to reach more of it, or overpower things to get to it, that kind of thing). but you have to make up for it by eating more. a LOT more. it scales up logarithmically.

because bigger species need more resources to exist, they aren't able to spend as many on reproduction, meaning that - as a rule - bigger species have smaller populations. which is an evolutionary disadvantage. but not their only one.

in a way, they are hoarding matter and energy in the bodies of a select few, that gained larger size in order to access more matter and energy. which, yes, every species tries to do, but at smaller sizes, its sustainable.

smaller species have larger populations, which then speciate more so that more offspring can live and occupy new niches, which then leads to more speciation because niches beget niches, and so on

yes, bigger species can also strike that balance, but they sit on the top of a precarious peak. they rely on that entire system to continue to function in order to fuel their large size and successful populations.

so bigger species tend to evolve in systems where there are not selection pressures for them to be economical. and most bigger species do not have much in the way of modern descendants.

because the minute their ecosystem starts to fall apart, they can't get enough food.

and they go extinct.

megafaunalism is just a different kind of specialization, and niche specialists have to be very lucky to survive mass extinctions.

we see this in every extinction. end ordovician, end devonian, end permian, end triassic, end cretaceous, the current one. megafauna go first.

the main difference between megafauna and Human Wealth Hoarders is that megafauna aren't making a conscious choice. Human Wealth Hoarders are.

and, much like megafauna, as the system they rely on collapses, they will be the first to go extinct. there's fewer of them, and they're more vulnerable. poorer people, much like smaller species, will lose many members - but, because there are more of us / smaller species are significantly more diverse, we'll/they'll ultimately get through it a lot easier.

the only reason we think megafauna = good is because *we're* megafauna. not only megafauna, but the highest trophic level (ie "top predators", which, given everything gets decomposed in the end, sure is an extremely revealing way to phrase it in terms of the psyche of the people inventing the term). we've convinced ourselves that being at the "end" (there is no end. we all get decomposed) of the "food chain" (it's a circular web) is best because that's where we are, and it gives us more power and control.

but just as toxins in water concentrate in "top predators", so do the stressors of ecological crises disproportionately affect megafauna. and us.

smaller is more diverse, more speciose, because they can. and evolutionarily speaking, more diverse = winning. because you're more likely to keep playing the game in the future.

so yeah. bigger is worse, actually.

[anglbunny]

Hey it's 🪼 anon I was wondering when requests will be open again since I NEED kiyora~ No lube, no protection, all night, all day,from the kitchen floor to the toilet seat, from the bathroom sink to the shower, vertically, horizontally, quadratic, exponential, logarithmic, while I gasp for air, scream and see the light, missionary, cowgirl, doggy, backwards, sideways, upside down, on the floor, In the bedroom, on the couch, on the chair, in a car, on a motorcycle, in the back of the truck, on a trampoline, in the pool, in the basement, against the window, having the most toe curling, back arching, mouth drooling, ass clenching, eyes watering, leg shaking, soul snatching, jaw dropping, hair pulling, moaning what a pretty, gorgeous, beautiful, attractive, admirable, adorable, alluring, angelic, appealing, beauteous, bewitching, captivating, charming, classy, comely, cute, dazzling, delicate, delightful, divine, elegant, enthralling, enticing, excellent, exquisite, fair, fascinating, fetching, fine, foxy, good-looking, graceful, grand, ideal, inviting, lovely, magnetic, magnificent, marvelous, mesmeric, nice, pleasing, pulchritudinous, radiant, ravishing, refined, resplendent, shapely, slightly, splendid statuesque, stunning, sublime, superb, symmetrical, breath taking, tantalizing, masterpiece, art, graceful, flawless, appealing, pleasant, drop dead, fascinating, breath taking, and perfect manyou're the apple of my eye, mango with my pie, palaman of my tinapay, niyog on my kalamay, ipin of my suklay, ring of my kamay, blood of my atay, bubbles of my laway, roof of my bahay, strength of my tulay, joy of my tagumpay, dream of my nanay, ube in my siomai, calcium in my kalansay, buhol of my tie, bituin of my sky, beauty in my tagaytay, ketchup in my frenchfries, wings when i fly, wind when i paypay, sipit of my sampay, tungkod when I'm pilay, shoulder when i cry, cure to my aray, answer to my why, love till I die, in short you're the center of my buhay.But believe me i closely calculated the formula of i love you oo po, very much, real, realest, relate, 100% I miss you baby, gorgeous beaitful extremely pretty pookie lookie cookie dooke wookie cookieswirlc bbg babygorl dookie lioke rookie very preciouspookie kitten witten cupcake sugarcake watermelon

I'm crying, at the end of the yr, I plan on doing my top 5 anons of the yr and this is going in at number one, I'm sorry, I dont make the rules. BUT, send in the req queen, it might take some time for me to get to but I'll do it, I have tons of requests, a lot from when I first started out, which I plan on doing after exams

[scotianostra]

On April 4th 1617 John Napier, the mathematician, died.

It’s said that Napier is the nearest Scotland has produced to a 'Renaissance Man', at least as far as mathematics and the sciences are concerned. To the philosopher David Hume he was "the person to whom the title of a great man is more justly due than any other whom his country ever produced". The historian Christopher Smout has listed his achievements as including "a new type of screw-drainage for coal mines", "the use of salt as an agricultural fertiliser", "military burning glasses" and "self-propelled armoured chariots like tanks".

His enduring fame rests on his 'discovery' of logarithms in 1614 which propelled him into the front rank of European scientists alongside his contemporaries Kepler and Tycho Brahe.

Not much is known about his early life except for the fact that he was the son of a Scottish landowner and official and received a privileged upbringing. As a member of the nobility, he was tutored privately at home for a few years before being sent to St Salvator’s College, St Andrews. It was here that he first became deeply interested in theology though he did not acquire in-depth knowledge in mathematics until later.

For reasons unknown, he left the college before earning his degree and it is believed that he moved to some other educational institute for his higher studies. Eventually he began managing his estates and pursued mathematics as a hobby. Among his several contributions to the field, his invention of logarithms is regarded as his greatest.

In 1614 he wrote Mirifici Logarithmorum Canonis Descriptio which contained 90 pages of tables of natural logarithms and also contained theorems in spherical trigonometry known as Napier’s Rules of Circular Parts.

Now I can appreciate why these things are necessary in science etc I have to say, I hate maths, don’t mistake that with arithmetic, as I am quite adept at counting, the times table and division etc, trigonometry, algebra, logarithms can quite simple GTF.

Our archives at The National Library of Scotland has the original copies of Napiers memoirs, I will give you an example of his work;

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I mean come on, what kind of sorcery is this?

Which leads me to the final party of this post, John Napier was seen as a devoted and deeply religious family man, but in fact several members of John Napier’s family – respected and wealthy participants of Edinburgh society - were commonly known to be wizards or sorcerers. Their necromantic power was feared by nobles as well as peasants from far and wide.

This was at a time when James VI was actively attending and persecuting many poor people, mainly women, putting them to death after days and weeks of torture, had Napiers family not been landed gentry, they would have been the ideal candidates for these actions, money eh, changes everything.

Was John Napier involved in this? Well there is no proof of it, he was however a free thinker and thought outside the box, a very clever man, two examples of this here, initially caused the witchcraft tag to be be placed on him……

Rumours spread that he was a warlock after he enlisted the help of the cockeral to discover which if his servants had been stealing from him. Each servant was ordered to go into a darkened room and stroke the cockeral - the bird would crow, said Napier, when the guilty servant touched it.

The bird remained silent but Napier stunned the household by immediately identifying the culprit. Surely this was sorcery. But all he had done was put soot on the cockerel’s feathers - the innocent servants all had black on their hands, while the guilty one’s were clean because he was afraid to touch the bird.

At Merchiston, when pigeons belonging to a neighbouring landowner had been eating Napier’s grain, he threatened to restrain them. 'Do so, if you can catch them,’ scoffed his neighbour. Next morning, Napier’s servants could be seen stuffing hundreds of semi-conscious pigeons into sacks. Onlookers were convinced Napier had bewitched them - in fact he had simply scattered succulent peas soaked in wine to get the birds drunk and incapable.

But before his death Napier had left full details of how his logarithms had been calculated, and had left one final invention as a boon to the merchant classes. Napier’s Rods, or Napier’s Bones as they were called from the material they were made of, were in effect a powerful "pocket calculator”, as seen in the second pic.

Napier was twice married; first, in 1571, to Elizabeth, daughter of Sir James Stirling of Keir, by whom he had a son and a daughter; secondly, to Agnes, daughter of James Chisholm of Cromlix, by whom he had ten children. His eldest son, Archibald, who succeeded him, was raised to the rank of a baron by Charles I., in 1627, under the title of lord Napier, which is still borne by his descendants. A very elaborate life of him was published in 1835.

[anjelicawrites]

Oh michael is defo a dom! He gives me “pushes his glasses up on his nose eyes in his book telling y/n this dick aint gonna suck itself while paying hee no attention”

Yeah right??? And I might be absolutely off the mark, but he gives off these "distant dom" vibes???

I'm sorry for the filth so early in the morning

Like yes, he loves you and understands the importance of aftercare and being with you when you subdrop, but when the mood strikes, you're on your knees, observed from a distance, the same way he would a complicated logarithm. Whatever goal he wants for this session, he's doing the maths in his head: if I do this, then the outcome should be this, let's see if I'm right.

And he gives off the vibes of a very strict dom? There's no first, second or third strike with him: you're not following the rules? Are you being a brat? You get punished immediately and there's no way around it: you can say you're sorry, that's nice to hear, but you'd better get your arse over here, now, before he loses any more patience. And the punishment is not about pain, more fucking with your brilliant mind? Because you are smart, or you two wouldn't have clicked, but now you are sitting with your back against his chest, legs spread, three of his fingers deep inside of you and a simple math problem in front of your eyes and you can't focus, because he's too distracting and you need to find the solution before he makes you come, or you'll see what he has in store for you. But his thumb is on your clit, his fingers crooked that perfect way and your brain is unravelling. You are fighting, desperate to keep you orgasm at bay and he's just staring at you, half smile on his lips, cool and collected, just waiting for you to fail. Only then, you two will have some real fun.

[transgenderer]

Re: universal science cooccurring w/capitalism

Invention/discovery of logarithms and books of them, and slide rules, etc. was important! I think. For computing things for navigation. I saw a whole YouTube video on this and everything. Almost 3D printed a slide rule about it

hmm see logarithms are important and all. but i feel like theres a very specific concept cluster, just barely emerging in newton and then gradually expanding until solidifying in the 19th century of behavior that looks like 20th century science. controlled experiments, mathematical models, all that jazz. and that particular cluster has been powerful in a very specific way. and it didnt exist before like, maybe the mid 18th century? which is around when you see the inklings of capitalism. which is weird

[porphyraminos]

Happy 413, this year I decided to convert the Vtubers in FSP EN into trolls. Because I need to blend my special interests for the sake of chasing dopamine.

This was also an opportunity for me to practice my digital art because I'm a Noob and you can actually see with each piece I get better and better. So that's cool. Thanks homestuck.

Let's get started.

I had to change and adjust their names to fit Troll name rules.

Twink incoming...

I tried to base their horns on their Oshi Marks. So for Rosco it's 🕹 and for Luci it's 🌙.

Cassian 🌿 was where I really started to improve and it's making me want to go back and redo Luci.

Gay-le, we love Gale 🍻, that is all chat.

My Kami-Oshi, Zander Netherbrand ♈️, you may be nobility in your lore. But you're an Aries so in this universe you're a peasant. 🤣

Malim’s jewellery can't sit with us. Nope. Incorporating his sign was a pain in the ass. Not as difficult as Zander's sign. But still. Love you Malim 🫖 but damn.

This one took days. It was far too much, far too overwhelming. Altus ⛈️ your design is too complex for us noobs... the clothes are too detailed... take them off-

I'm super proud of Nayu's eyes. The jacket details and shirt details took the wind out of me for a second, but this is Kiki Mamas boy. I gotta do him justice. I love Nayu 🧬.

no lube, no protection, all night, all day, from the kitchen floor to the toilet seat, from the dining table to the bedroom, from the bathroom sink to the shower, from the front porch to the balcony, vertically, horizontally, quadratic, exponential, logarithmic, while I gasp for air, scream and see the light, missionary, cowgirl, reverse cowgirl, doggy, backwards, sideways, upside down, on the floor, in the bed, on the couch, on a chair, being carried against the wall, outside, in a train, on a plane, in the car, on a motorcycle, the the bed of a truck, on a trampoline, in a bounce house, in the pool, bent over, in the basement, against the window, have the most toe curling, back arching, leg shaking, dick throbbing, fist clenching, ear ringing, mouth drooling, ass clenching, nose sniffling, eye watering, eye rolling, hip thrusting, earthquaking, sheet gripping, knuckles cracking, jaw dropping, hair pulling, teeth jitterbug, mind blogging, soul snatching, overstimulating, vile, sloppy,moan inducing, heart wrenching, spine tingling, back breaking, atrocious, gushy, creamy, beastly, lip biting, gravity defying, nail biting, sweaty, feet kicking, mind blowing, body shivering, orgasmic, bone breaking, world ending, black hole creating, universe destroying, devious, scrumptious, amazing, delightful, delectable, unbelievable, body numbing, bark worthy, can't walk, head nodding, soul evaporating, volcano erupting, sweat rolling, voice cracking, trembling, sheets soaked, hair drenched, flabbergasting, lip locking, skin peeling, eyelash removing, eye widening, nail scratching, back cuts, spectacular, brain cell desolving, hair ripping, show stopping, magnificent, unique, extraordinary, slendid, phenomenal, mouth foaming, heavenly, awakening, devils tango ever bro could cause a nuclear bomb inside me and I'd still ride...

Ahem, anyway, I'm proud of how Ryzar 🌋 turned out.

The last one and it shows. I even learnt how to add glow to things. The difference between Luci and Nix 🦾 is insane. This was a journey and I was so worried I wouldn't get it finished on time. But after two months of drawing with my finger on my phone in Ibis Paint X, I really feel like an artist now.

[needlesandnilbogs]

top 5 mathematical concepts?

assorted and not in order:

0) differentials and differential calc ESPECIALLY stokes’s theorem. It just made everything about calc 3 make so much more sense

sequences and series! Honestly sometimes especially with series this is a love hate relationship but they’re fun

logarithms. No real reason I just like the rules for them

All of number theory but especially elliptic curves. This probably should be first because it’s what I want to do with my life

set theory and group theory

[foone]

It is taking everything in me not to buy a little book of logarithmic and exponential tables just because I think it would be peak math major of me to pull it out of my pocket every time someone gets on the topic.

You should do it, but only if you also get a slide rule and learn to use it.