#kepler conjecture

[garadinervi]

Johannes Kepler, December 27, 1571 / 2022

(images: Johannes Kepler, Strena seu de Nive sexangula, Godfried Tampach, Frankfurt am Main, 1611. Milestones of Science Books, Ritterhude)

#graphic design #crystallography #mathematics #kepler conjecture #book #cover #book cover #johannes kepler #birthday anniversary #godfried tampach #1570s #1610s #2020s

[spacenutspod]

A quarter century ago, physicist Juan Maldacena proposed the AdS/CFT correspondence, an intriguing holographic connection between gravity in a three-dimensional universe and quantum physics on the universe’s two-dimensional boundary. This correspondence is at this stage, even a quarter century after Maldacena’s discovery, just a conjecture. A statement about the nature of the universe that seems to be true, but one that has not yet been proven to actually reflect the reality that we live in. And what’s more, it only has limited utility and application to the real universe. Still, even the mere appearance of the correspondence is more than suggestive. It’s telling that there is something deeply fundamental to the hologram, that the physics of the volume of the universe might just translate to the physics on the surface, and that there is more to be learned there. It’s one thing to cast problems of physics in a new language, even a new set of dimensions, to make them easier to solve. After all, physics abounds with such mathematical tricks and games that practitioners employ to solve challenging problems and move on to the next one. But the AdS/CFT correspondence, and the more general holographic principle that it represents, is so much more than a mathematical curiosity. Remember that the essential goal here is to describe gravity, which for centuries we believed to be just another force of nature, just one more interaction that entities in the cosmos can use to interact with each other. But gravity does stand alone and unique among all the forces, even beyond its quantum intractability. Gravity is the only force emitted and felt by every single entity in the cosmos. Anything with mass, anything with energy, creates a gravitational influence around it. And so too does anything with mass, anything with energy, anything with what we call existence respond to that gravitational influence. Kepler was right to discern something special about the motions of the heavenly objects and connect those motions to our lives here on Earth. Newton was right to label it a force, a set of invisible strings that connect all of creation. Einstein was right to cast gravity not in terms of pushes and pulls, but in terms of the very fabric of spacetime itself. The holographic principle, whether applied to the surface of a black hole and its mysterious contents or the relationship between string theory and quantum physics, is also telling us something meaningful about gravity. But Einstein already taught us what gravity is, it’s no mere force, but the natural response we living entities experience when we encounter the bends and wrinkles of spacetime. Gravity is the spacetime playground that we all exist within. Another name for general relativity is geometrodynamics – the dynamics of geometry itself. Gravity is space and time and matter and energy all rolled into one breathing, vibrant system. What we call the universe is simply the container for all that activity, all the breadth fo space and depth of time and complexity that fills it. We have failed to find a quantized theory of gravity. We have no description of what truly happens at the boundary of a black hole. But we have learned in our quantum wanderings that physical, three-dimensional entities are not exactly what they appear to be. Indeed, they are shallower: black holes may truly be described only by their surfaces, their boundaries, their edges, rather than their full extents. And when we apply this same chain of reasoning, that holography is a vital component to the quantum gravitational puzzle, out comes the AdS/CFT correspondence and a potential path to string theory glory. The post Why the Universe Might be a Hologram appeared first on Universe Today.

#space #astronomy #news #science

[jeffreyrobertpalinjr]

Theories (doesn't mean each theory) can be disproved into being no longer theories. If a theory is considered a theory despite that theory being "inaccurate or 100% accurate", it's because that theory hasn't yet been confirmed as being such. Correct?

Both of these answers (1 and 2), that two different people wrote on Quora, are good:

1. Theories (doesn't mean each theory) can be disproved into being no longer theories.

Falsified by evidence, you mean, not disproved. Like Copernicus and others displacing geocentric cosmology, yes. The history of science supplies plenty of other examples.

If a theory is considered a theory despite that theory being "inaccurate or 100% accurate",

Theories do not cease to be theories at the first sign of trouble. We hang on until we have a replacement that we cannot falsify. Some hang on longer, like Einstein with quantum uncertainty.

it's because that theory hasn't yet been confirmed as being such. Correct?

No. This turns out not to be the case.

Theories cannot be confirmed. Newton did not prove his supposed inverse-square gravitational force was real. He only proved that the equation for such a force predicted Kepler’s conic section orbits. Centuries later the hypothesis of such a force was falsified by both observation and Einstein’s curved spacetime model.

Quantum Mechanics (QM) and General Relativity (GR) are our two best theories in physics. Within the current limits of observation, both have stood up to every attempt to falsify them. Much of the time they get along together fine, as in the GPS. But we know that they are not compatible in the cores of black holes and at the beginning of the Big Bang.

In both of those cases, GR by itself predicts an unphysical singularity (aka a point mass), and QM says no, nothing can be confined in a region smaller than its wavelength .Thus we are searching for a viable theory of Quantum Gravity, one we can test thoroughly., falsifying all alternatives. We have some interesting but currently untestable conjectures.

2. Yes, that is correct. In science, a theory is a well-substantiated explanation of some aspect of the natural world, based on a body of facts that have been repeatedly confirmed through observation and experiment. Theories are not guesses or hunches; they are based on evidence.

A theory can be disproved if new evidence is found that contradicts it. For example, the theory of geocentrism, which held that the Earth was the center of the universe, was disproved by the discovery of other planets and stars.

If a theory is not disproved, it is considered to be true until new evidence comes along that suggests otherwise. This is why theories are often referred to as "working hypotheses." They are not 100% accurate, but they are the best explanation we have for the natural world based on the evidence we have.

Here are some examples of theories that have been disproved:

* The theory of geocentrism

* The theory of spontaneous generation

* The theory of phlogiston

Here are some examples of theories that are still considered to be true, even though they are not 100% accurate:

* The theory of evolution

* The theory of gravity

* The theory of relativity

Theories are an important part of science. They allow us to explain the natural world and make predictions about how it will behave. Theories are not perfect, but they are the best way we have to understand the world around us.

#question #questionbox #questions

[trolledu]

BOLOGNA, THE MANHATTAN OF THE MIDDLE AGES

 Bologna is a town in northern Italy which was once nicknamed ‘La Turrita’ on account of its 150+towers – of which only twenty-two remain today. Most took the name of the families who in the 12th and 13th century ordered their construction in a kind of competition to show who was the wealthiest and most powerful, though they also provided protection and clean air in an already congested city.  They were so many that the ground destabilized, causing a large number to lean so dangerously that they either collapsed or were demolished.  The last round of demolitions – now regretted – happened in 1917 along with parts of the 14th century city walls. Of the towers that remain today, the most famous are the 47-meters-tall Garisenda and the 97-meters Asinelli. Built next to each other in the centre of the old city, they are a perfect landmark under which to meet. The Garisenda was once taller, but the top 12 meters were removed when the ground yielded in the 1300s. It now leans more than the Tower of Pisa by 0.1 degree. Dante Alighieri saw it while it was still at its full height, and in his Divine Comedy compared it to the doubled-over giant Antaneus. It was acquired in the 15th century by the Corporation of the Drapers, which had their headquarters in front of the tower and used the outside square as a market. It became a property of the city at the end of the 19th century. The Asinelli was turned over to the city after the partial collapse of the Grisenda, and was then used as a prison and small stronghold connected to the Grisenda by a small wooden bridge. It is from this tower that some of Galileo’s conjectures about gravity and the acceleration of falling bodies were finally demonstrated through repeated, consistent, and precise experiments which could be reproduced by other scientists.  This was done by dropping objects of different weights, shapes and materials from the top of the tower, rigorously at night when there were no passers-by. The time it took for them to reach the ground was kept with the help of a precisely constructed pendulum and a small chorus of Jesuits chanting in unison to provide an audible timer – not a perfect method, but the most reliable that could be used at the time. Through it he was able to refute Aristotele’s claim that “an iron ball of one hundred pounds falling from a height of one hundred cubits reaches the ground before a one-pound ball has fallen a single cubit” asserting instead that objects of different masses and composition actually fall at the same speed – i.e. what is called the equivalence principle.  Unfortunately, he could not prove his principle because in fact, the smaller ball reached the earth two ‘finger-breadths’ later. That’s because air resistance works against gravity to change the actual terminal velocity of an object, a concept he understood but could not explain. Kepler and Newton performed more experiments, Einstein came up with the formulas, but the equivalence principle has only been proven in 2017 thanks to a small satellite launched by the French space agency CNES. Inside it are two cylindrical shells a few centimetres long, the outer made of a titanium and aluminium alloy, the inner of much denser platinum and rhodium. As the spacecraft orbits Earth, the cylinders are in continuous free fall. Electrodes monitor their position and keep them cantered by applying tiny electrostatic voltages that can be measured to compute the falling rate – which has been the same during 2,400 orbits. This proved the equivalence principle to one part in a quadrillion (10 to the power of 15). Sounds like a lot, but scholars want even more accurate proof and an Italian team is now working on a satellite that would test equivalence to a precision of 10 to the power of 17 partly by spinning rapidly and isolating any signal from other effects.  Meanwhile, researchers at Stanford University in Palo Alto, California, have proposed a satellite that aims to reach 10 to the power of 18 by using noise-reducing cryogenics. Still other researchers hope to use Bose-Einstein condensates—clouds of cold atoms that behave as a single quantum wave—to reach even tighter limits.  Not that I understand what these experiments are all about, but the idea that they are being run fills me with wonder. Because of their ingenuity, of course, but also because of the continuity of intent, from Galileo throwing stones off the Asinelli tower to Palo Alto scientists planning to send noise-reducing cryogenics into space.  The first picture is a rendition of what Bologna looked like in the 1100s, the second is what it looks like today Location: https://goo.gl/maps/keD5tkmJcBq7PL6v6  if you go to street view you get an idea of the stupefying height.

Copyright Simonetta Gatto - author - 

https://www.facebook.com/simonettagattoauthor/

#trolleng #trolledu #speaking #reading #writing #history #italy #bologna #interesting #facts

[wednesdaysat7]

Post n 52 | 3/4/5 Fictional Summer Sessions

Published on August 4rd 2022

Third Fictional Summer Session / July 22nd

I ‘ve dropped a last minute zoom invitation on the whatsapp group and Gia and George joined. It was very good to know each other bit better and we had so many things in common.

Brian Cox, who is Gia’s partner, made a brilliant short documentary for BBC on Bees and why do they make hexagonal cells. There is maths model that seems to justify this choice, it is called the Honeycomb Conjecture.

From Wikipedia: “The honeycomb conjecture states that a regular hexagonal grid or honeycomb has the least total perimeter of any subdivision of the plane into regions of equal area. The conjecture was proven in 1999 by mathematician Thomas C. Hales.” I have done some digging on him, he seems to work on a field of mathematics called “discreet geometry”, I’m not sure to understand what that means but I like the sound of it. His long term research includes both Kepler & Honeycomb conjectures.

After watching the documentary and reading (and struggling to understand the maths) of the Honeycomb Conjecture I came out of it with a question, quite simple I guess.

So, are bees able to calculate angles? Do they use their body to build

How is it possible that they just know that?

Of course it is something that someone else already investigated. So honey Bees dance to communicate where to find food or the new hive.  From the experimen called the “Schafberg Experiment”:

The only source of food for a colony was placed on the far side of the mountain and the bees could not fly over the mountain.   When they communicated where the food was to be found, they communicated this angle exactly across the mountain, relative to themselves, even though it was an angle they had never flown to the food source.

Food finding dances:  a Honey Bees will dance on a comb surface and consists of the bee turning in circles; on each revolution the bee will bisect the circle at an angle;  the angle with respect to the 12 o’clock represents the angle to fly with respect to the sun.   If the bee ran from 6 to 12 o’clock, this would mean fly straight forward towards the sun; 7 to 1 o’clock would mean fly just to the right of the sun; 12 to 6 o’clock, fly directly away from the sun.

Because these little dances can take a really long time, the angle of the sun will have changed in the meantime. So while doing the dance, the bee actually calculates the change in angle based on where the sun is right now with respect to the hive.   So if it’s at night when they are doing the dance, they calibrate the angles to associate with where the sun is right in the moment, even if it is on the other side of the World.   Likewise, when the bees are following the instructions and flying towards the food, they calibrate what they learned based on where the sun is right now vs when the instructions were given.  

[book to read: The Dance Language and Orientation of Bees https://www.hup.harvard.edu/catalog.php?isbn=9780674418776&content=toc | I really need help to understand what I need to read from this book]

I believe we had very quality time, we also discussed about identity/representation/recognition (Gia) and time (George)

George also mentioned Power of Ten & Mandelbrot set

Fourth Fictional Summer Session / July 29th

I have spent two hours at Kew Botanical Garden, in the area where is

Wolfgang Buttress’s installation Hive. Well, there is so much to say about this work.

First, what could I do more on this topic after a monumental and popular art installation? I could criticise it and pretend that I could do better, different etc. The only comment that I feel to make is that after three decades since it was made, seems to underline the impact of antropocene in nature but Kew Garden, despite how it looks it is not nature but still a human shaped environment. So it is already antropocene and the art installation is an interpretation of nature in a human made creation.

Observing the whole area I really value the presence of wild herbs and flowers to feed pollinators. I’ve spent half hour to observe a relatively small spot to see how many of those insects and I was very pleased to see so many overflies. They were so beautiful and fun to see.

The installation itself creates two or three areas of interest and engagement. The most obvious is the internal space of the structure but people seem to enjoy also a quick check on the ground area and of course the two paths that surround the installation.

The work represent the activities of a bee colony so people experience visual and sound stimulations and this gives an accurate / spectacular idea of the complexity of a bee hive.

Do I feel an empathetic connection with the bee of the colony that is connected to the installation? (I have loved the hoverflies the most!)

It doesn’t explain much the relationship between the activity of bees and its environment, the importance of biodiversity and the threaten the bees are experiencing.

How can I bring in my research this *entertainment factor and coniugate it to an empathetic and experimental investigation?

Until now my research on bees was meant to inform myself with what’s going on with the pesticides, the impact on biodiversity and what we don’t largely know about those amazing animals.

My drypoint series has been so far mainly preparatory to something else to come. Again, more experimental, more engaging and successfully loud.

UPDATE

If I wasn't feeling lost enough at The Hive I have visited Back To Nature at the Serpentine Gallery. The exhibition includes

This is the sentence that introduces her environmental site specific installation “Pollinator Pathmaker”: “I want to make an artwork for pollinators, not about them”. Seems very radical, definitive to me. Like if everyone else before have just made artworks to the art system or just for human beings. I’m not against what she claims. I perceive challenging that she is using artificial intelligence to address the topic I feel so close to me at the moment.

Her installation consists of a field in which the artificial intelligence designed the scheme in which the plant and the flours meant to attract and feed pollinators. It doesn’t lookalike much different from the field of wild herbs and flowers surrounding The Hive in Kew Garden.

I believe the difference between the two in the methodology that the two artists have used to conceive and realise their works. A side from the massive and articulate (very anthropoce style) structure of The Hive, the fields around are impressively full of all kind of pollinators, not only bees! I have been able to observe hoverflies, hundreds of them but I’m not good / fast enough to take photos of them (they fly much faster than bees and also the way they catch the nectar is very different because hoverflies have a very short tongue compared to bees and buterflies - this is why you can see them only on flat flowers).

So I believe Ginsberg is aimed to cross the platforms of art and design not to produce something beautiful on the eyes of the public, instead she seems to be interested on bringing people together on the campaign behind the production of the environmental installation.

In other words, the installation is for the pollinators and not for us, while we are potentially a community of creators and activists and together, through this initiative we have the opportunity of thinking collaboratively on the change that may occur. This sounds very Joseph Beuys to me!

  Fifth Fictional Summer Session / August 4rd

Today I have worked with some late victorian microscope and magic lantern slides concerning bee anatomy, especially mouth and tongue. I’m making a good use of the information I’m getting from them. I have collected tens of digital pictures, some even HD images but nothing is compared to have those pieces in my hand. Especially the Magic Lantern glass slide is so incredibly detailed. They were all produced by a company established in the XIX century. I have now three more drypoint in progress.

My current reflexion (i.e frustration) is: after reading F. Huber’s book and other classical researches on bees I’m wondering what is point for me to observe bees and produce a body of work on anatomical details of all those pollinators? I mean this has been already done two century ago. On one hand I need it for myself; while drawing this details or observing bees or hoverflies seem that I understand deeply and I get more compassionate to them. On the other hand I fear that I’m losing time because I don’t have years to complete this research, in few moths I should have finished something which seems still far to be. So I need part of this but also I don’t want to replicate the XVIII / XX centuries approach to insects and I don’t want to produce another series of engravings representing bees, hoverflies or details of them. I’d like to push it further. ++I’ll back on this soon++  

W. Watson and Son was an optical instrument maker. In 1837, the William Watson business was established in London for the manufacture of optical instruments. By the 1840s, the company moved into lanterns, slides and associated equipment. In 1868, the name was changed to W. Watson & Son and by this time were located at 313 High Holborn, London.  On 9 January 1881 William Watson died. In 1883, the name of the company was changed to W. Watson & Sons as the son, Charles Henry Watson joined the business. In 1908, the firm became W. Watson & Sons Ltd.

So my Magic Lantern slide, has the label W. Watson and Sons, which means that was produced between 1883 and 1908.

[cagestark]

Introduction to Ink//4

Chapter One | Chapter Two | Chapter Three | Chapter Four

don’t even pretend like i edited this lmao

-

It’s three in the morning when Toni feels confident enough to slip out from between the soft cotton sheets of one of Natasha’s guest bedrooms. It has been forty-five minutes since she heard the last stirring coming from the room beside her’s—Sam is apparently a bit of an insomniac. The cool air of the room on her bare legs has her shivering along with the thrill of anxious-excitement in her stomach. She isn’t doing anything wrong by sneaking out of her own room and into Bucky’s, but having it all take place in the dead of night with everyone asleep certainly makes her feel illicit. 

She takes a long moment to assess herself in the mirror above the dresser. Her hair has just begun to dry from the shower she took. When she presses some of the damp tendrils to her nose, all she can smell is acacia instead of smoke. The nightgown she’s wearing is hardly that, just one of Rhodey’s old shirts that falls past the crease where her thigh meets her ass. Beneath it are the only clean panties she had packed, sensible cotton ones. Nothing like the scraps of lace and silk that she’s seen in Natasha’s drawers and laundry hamper, but she doesn’t think Bucky will mind. And if he does mind? Then he’ll just have to peel them off of her. 

Reaching down, she softly traces her fingers over the cotton crotch of the underwear, noting the damp heat. Ever since Bucky had shed his pale t-shirt under the warm glow of the fairy lights, Toni had been wet. When she finished stomping her way through the woods after Wanda’s interruption, she’d had to disappear off to the bathroom to wipe away her own slick before it could drip down her thighs. Sitting there on the closed porcelain toilet seat, two fingers pressed flat against her clit, she’d been tempted to finish herself off. 

To use the two fingers Bucky had sucked clean (God, she could still see his face burned behind her eyelids, the way his stormy eyes had rolled back like he was licking ambrosia off of her instead of cum). 

But Toni didn’t like to do anything in halves. She would cum with Bucky tonight, or not at all. 

Creeping on silent, bare feet over to the door, she twists the doorknob and pulls the door inward. The hinges don’t squeak, nor does the floor as she slips out of the guestroom, careful to close the door behind herself less anyone pass in the night and see she isn’t there. When Natasha had directed them all to bedrooms, she had told Bucky to take his ‘usual room’, the one at the end of the hallway. That’s where Toni creeps, past Sam, past Clint. She holds her breath as she takes the cool doorknob in her palm.

Is he asleep already? She wonders. It would be thrilling to slip between the sheets with him, to wake him with her body pressed against his hard one. Maybe he’s awake like her, though, trying to convince himself to slip his way into her room. Toni only opens the door as wide as she needs to get inside. Then, she stares at the bed, eyes widening because—

Bucky isn’t there. 

Dread coils in her stomach. Had he left? He hadn’t been drunk like the others. What if he had decided to avoid any more interaction with Toni altogether, to slip out of the house and off into the night like some womanizing vagabond from her mother’s romance novels? He had gotten his, after all. Isn’t that all men ever want? Maybe with the blood back in his brain instead of his cock, he realized that he was out of Toni’s league.

Toni shuts Bucky’s door and nearly returns to her own room. But then she remembers the way he had wandered off outside, how he had seemed like he needed to put distance between himself and the others. With expectations low, she pads silently to the stairs, feeling her way down them carefully in the dark. 

She isn’t disappointed. 

There he is, seated in one armchair, his head leaned back and one tattooed arm thrown over his eyes. An afghan that had been draped over the back of the couch is in a heap on the floor. Either Bucky is an insomniac like Sam or there is something keeping him from sleeping. 

Toni must make some noise on the stairs because Bucky’s arm jerks away from over his eyes and he is staring at her with wide, bloodshot eyes. At the sight of her, he makes a noise in the back of his throat and returns to covering his eyes. 

“Shouldn’t you be in your room?” he asks. His voice is low but not a whisper, and Toni can’t help the way her heart jumps into her throat, turning to glance back up the stairs as if expecting one of the others to come bursting from their room to inspect the noise. When no one comes, she takes a steadying breath and takes the last few steps down the stairs. Sightless in the armchair, Bucky adds: “That sounds like the wrong direction for your room.” 

“I’m not going to my room,” Toni says, matching the low pitch of his voice. 

Sighing, Bucky sits up. He has shed his shirt again for comfort while he attempts to sleep. His skin looks carved from marble in the moonlight, the pale expanse only interrupted by the ink that divides him up and decorates him. His jeans have ridden low, belt off and left by his shirt, and it gives Toni a few more precious inches of the tattoos that rest at either hipbone: bold, encircled stars. 

“If you were smart, you would,” says Bucky, his eyes glued to her legs. 

“If I were smart? I solved the Kepler Conjecture when I was six.” 

Bucky winces, seeming to understand his insulting words. “I mean, I know you’re smart. Doctorate in engineering—goddamn you’re smart. But there’s more to being smart than numbers.” 

All his talk, but he isn’t working to get away from her. He doesn’t lift a finger to stop her while she takes slow, purposeful steps towards him until she’s standing inches from him, their knees nearly touching, bare skin to denim. Still, he stares at her legs, at her tanned thighs. She wonders what would happen if—

Letting her arms raise in a stretch, the shirt rides up and up. Bucky’s eyes open wider and wider until he’s staring at her white cotton panties with a stricken expression, the shadow of her well-trimmed pubic hair just barely visible. His throat bobs with a painful swallow as her arms fall back to their neutral position. Toni feels infused with power, drunk with it. While she didn’t doubt the existence of feminine sexuality (she lives with Nat, doesn’t she?), Toni had never considered her own ability to wield it. The way Bucky looks at her makes her slick between her legs, makes her head feel light.

Makes her bold. 

“Do you not want to have sex?” she asks. “Because I want to have sex.” 

“It’s not about what I want,” he rasps. “It’s about what’s right. You don’t know what you’re getting into, and it’d be wrong of me to take advantage of that while you’re drunk.” 

Toni places her palm in the center of his chest over his pounding heart and pressing him firmly back into his seat. She plants one knee beside him, wedged between the chair and his thigh, and then climbs fully onto his lap. His breath comes full and slow, like he’s counting them. The rasp of his jeans against her sensitive inner thighs has her clit aching. 

“First of all,” she says. “I’m not some sort of child; I’m a virgin. There’s a difference, believe it or not. I don’t know what I’m getting into? Unless you have a second cock which I somehow missed, I know exactly what I’m getting into. Or rather what I’d like to get into me. Second, I had two beers, and one shot before I followed you. That was five hours ago. If you’re scared and trying to come up with an excuse to keep from fucking me, you’ll need to think harder than that. The only thing wrong about this situation is that I haven’t cum yet. So let’s talk about solutions.” 

After her monologue, she is left panting, their faces so close that their breaths mingle. 

Bucky reaches out and cups one of her jaws, pulling her face down towards his own. Her eyes flutter shut on instinct, preparing for a kiss (their first, she thinks with a giddiness that is downright embarrassing), but instead he holds her face there inches from his own. When her eyes open, she narrows in on the furrow of his brows and the frown of his mouth. Beneath her, there is a growing bulge in his jeans that makes her thighs clench around his own. 

His eyes rake across her face with an intensity she could never hope to match. 

“You really are sober,” he murmurs. His thumb traces the line of her chin with tenderness.

“You know what else I am?” Toni asks. With a trembling hand, she reaches down between her legs. The shirt has ridden up dangerously high on her thighs and her wrist pulls it up the rest of the way while she cups her sex over her underwear. “I’m wet.” 

In an instant, Bucky grabs her hand and drags it to his face, breathing in like he’s smelling her (thank God she has showered, she thinks breathlessly, even though he had done more than smell her—he had fucking tasted her just hours ago out in the woods). The groan he lets out has her heart skipping. 

“If you want me, I’m yours,” he says, nuzzling against her palm. “Can’t say no to you. Don’t want to say no to you, ever.” 

His consent overwhelms her. She lowers herself the last few inches until her cunt is pressed flush against his jean-clad erection, and God it feels so good. Reaching out to steady herself with his shoulders, she lets her body lead the way, back arching on instinct so that she can grind against his hardness. Bucky’s hands ghost up her thighs before taking her hips in his broad hands, encouraging her to make long, hard strokes. Her body sags forward as she buries her face in his neck, breaths shaking. 

Already, she feels the heat inside her building. 

“I—I could cum like this,” she admits into the junction between his shoulder and neck. “Should I stop?” 

Bucky groans. His fingers tighten their grip on her. “The hell should you stop for? Show me, honey. Show me how you can cum like this.” 

“Bucky,” she gasps, body shivering at his words. 

Using his feet on the floor as leverage, he drives his hips upwards. If his jeans and her underwear weren’t in the way, they would be fucking. But even this is good, so good, so much better than her fingers. Even better is his voice in her ear muttering the filthiest things: “There you go. Chase yours, honey. Your body knows what to do, doesn’t it? Come on, Toni, tilt your hips, oh yes, there you go. That’s right against your clit, isn’t it? That feel good?” 

The coil inside her winds tighter and tighter, throat constricting until she feels like she can hardly breathe much less answer his questions. His hands slide from her hips back towards her ass, fingers slipping beneath the fabric until he’s digging his fingers into the flesh where the curve of her ass becomes the curve of her vulva, pulling her apart until the lips of her sex spread and her clit has to take the brunt of the thrusts. 

The coil snaps. For a moment her entire body goes still, frozen in time. Then the pressurized ball of pleasure that’s been condensing bursts, all her muscles stiffening and unstiffening as if she’s in the throes of a seizure. Bucky whispers the dirtiest encouragement to her, his hands drifting back to her hips to help smooth her jerky, desperate thrusts. She hardly recognizes the sounds that pour from her mouth and feels helpless to stop them as the sweetest pleasure floods from her pelvis outward, washing over her in waves that she feels helpless against. 

“—so good, Jesus, Toni, the noises you make drive me insane. Come on, lean back, show me your face—” 

And she can’t imagine what he could want to see her face for, but she does as he asks anyway, tipping herself back into a seated position so that he can look at her. She’s too busy looking at him to wonder what he might be seeing, to think that her expression might be mimicked on his face, the glossy heated eyes, the flush that’s trailing down his inked collar bones. 

Suddenly she is overcome with the need to feel that inked skin with her mouth, to trace it with her tongue, to rub her lips against the smooth skin until they are raw and swollen. Still overcome with twitching aftershocks, it feels good to keep rubbing against his cock so she does, the simplicity of chasing feel-good sensations overwhelming her higher functioning. Parting her mouth, she places a wet kiss to the honeycomb on his throat. Above her, he makes a tortured sound, trailing his hands gently from her thighs over her flank and up the arch of her back. 

His skin is warm and clean, tasting faintly of the scent of whatever masculine body wash Nat keeps stocked in the guest bathrooms. A helpless noise slips past her lips as she lets her mouth drift up to the wasp just beneath his ear to suck. 

“God,” he rasps, voice buzzing the skin beneath her mouth. “You gonna mark me up? Suck harder, honey, I can take it. I’m gonna be covered in you before the night’s through, in more ways than one.” 

Harder? she thinks. A tendril of righteous fury unwinds in her belly—he kept her waiting for so long, wielded his morals like a shield against her obvious affection. And while there is a sensible part of her that sees these are good things, a part of her that is even glad he did those things, she feels overcome with the need for pleasurable vengeance. She opens her mouth wider and bites him, sinking her teeth into skin, body thrumming when he jerks and groans. 

The sounds of him, his smell, his flesh against her tongue stokes the fire that had just been smothered, igniting coals inside of her. 

“Can I have your cock now?” she asks. “I feel—empty.” 

Bucky’s head tips back until it rests against the headrest of the armchair. His face catches the moonlight, and Toni can just barely see the blooming mark on his throat outlined by the crescents of her teeth. 

Then he is shaking his head. “Not yet,” he says. “Need to get you naked, first. Here, get up—” 

Toni stands coltish in front of him. His eyes scan her from head to toe, stopping where her nipples are visible through the thin shirt. He reaches out and fists a hand in the fabric and tugs her forward until he is nuzzling against her sternum. Then he gathers the excess and tugs it tight across the modest swell of her breasts. Suddenly she is hyper-aware of how her breasts ache, nipples tight desperate points. Then he leans forward and takes one clothed tip into his mouth, sucking at her through the cotton. 

She slaps a hand over her mouth to keep from crying out and waking the house. His other fingers toy with the neglected peak, strumming the pad of his thumb over it. It feels like there is a direct connection between her nipples and her clit and that when he teases one, it teases the other. 

When he pulls his mouth away, the cotton of her shirt is damp and see-through. She shivers as it cools, leaving goosebumps on her skin—but then he is switching to the other breast and he lights her on fire all over again. 

“Bucky,��� she whines. 

He parts his mouth from her reluctantly, lapping at the cotton one last time. His hands skim down the curve of her hips until his palms reach the hem of her shirt. Pale eyes flash burning hot when he glances up in question. Toni barely manages to keep from rolling her eyes; instead, she reaches down for the hem and in one simple motion strips it from her body. 

Bucky groans. Beneath the shirt, she is naked except for her soaked panties. Toni has no illusions of her physical appearance: she is average at best. But Bucky still looks at her like he wants to eat her whole, one of his hands reaching down to rub at his erection. Emboldened, she reaches down and slides the panties off too, lets them pool at her ankles before stepping out of them delicately. 

“Lookit you,” Bucky murmurs. 

“I hope you’ll do more than look.” 

When he stands from the armchair, he towers over her, but any intimidation she felt for him was left in the woods outside, was shed from her the moment he shed his shirt just to let a naive young woman sate her curiosity in his body. His hands ghost over her form, giving her phantom tingles. He turns his hand over and lets the back of his fingers brush against the dark curls between her legs. 

“Spread them,” he says. 

“What?” 

“Your legs, spread them.” 

Flushing, Toni does. Then he drags one knuckle up the seam of her cunt. It’s electrifying, brushing over her clit in a touch that has her gasping, parting her lips around his finger so that he can nestle it against her opening. God, it makes her realize just how hungry it feels. Seeing no reason to deny her instincts or what feels good, Toni lets her hips jerk forward, his knuckle just pressing past her entrance, a stretch that has her whining. 

Bucky pulls back, ignoring her noise of displeasure. Even in the moonlight, it glistens, wet with her cum. 

“That all for me?” he wonders. 

Toni snorts. “I don’t see anyone else here.” 

“Wouldn’t put it past you to have better eyesight than I do,” he teases, smiling. Then he lifts his hand to his mouth and licks her wetness from his finger. 

Toni is suddenly struck with the knowledge that she has never tasted herself. Reaching down, she uses one finger to mimic the path that Bucky had taken, shivering at the slick heat and the roughness of her curls. Then she brings it to her own mouth, brows furrowed. It is almost tasteless, probably from her thorough shower. There’s a hint of musk, but she kind of likes it. More than anything, she likes Bucky’s reaction to her, his eyes going wider than she’s ever seen, his mouth parting in surprise. 

“It’s not bad,” Toni says. Her eyes fall to his lap. “When do I get to taste you?” 

Bucky groans. “Jesus, can’t believe you’re just asking me questions like that—” 

“What, am I breaking sex-etiquette?” 

His lips ghost into a smile. “No. There isn’t really any etiquette, except for the kind we decide on together, I guess. I like your mouth—the things you say, I mean, the, the way you say things without caring how they sound.”

“We’ll see how long that lasts,” she says somberly. Toni knows the effect her mouth has on people—and to date it has mostly been negative. There was a disastrous date (one Toni had been far too embarrassed to admit was her first) between herself and one of Nat’s classmates. By the end of the night, every time Toni opened her mouth, she saw the exasperated roll of her date’s eyes and spent the rest of the date in complete silence. 

He didn’t deserve my mouth, Toni thinks. But Bucky does. 

As Bucky presses her back towards the couch, Toni twists and slips from his grasp. 

“Stop,” she says. When Bucky freezes, she feels the thrill of being obeyed. He is like marble as she reaches out and runs her fingers down the hollow of his sternum. His piercings catch the light that streams in through the window and she feels like a magpie with how drawn she is to the tiny barbells. “Tell me if I hurt you.” 

Bucky exhales shakily, the only response. When Toni drags her thumb across his nipple, nudging the metal bead at one end and then the other, his head tilts back to bare his honeycomb throat, mouth parting. It’s a strange sensation to feel the metal beneath his skin, and she knows that she must be being far more cautious than she needs to as she rolls either nipple between her fingers. But he doesn’t seem to mind. His chest heaves with the breaths he takes and she follows the rapid rise and fall, refusing to give him a moment of reprieve. 

When it feels more like she’s teasing herself than teasing him, then she drags her fingers down between his pecs, down over the bare skin of his abdominals and down to the waistband of his jeans. The zipper is distorted obscenely by his erection, and he hisses and groans as she works the button free, giving him inadvertent stimulation. 

He isn’t wearing boxers beneath—maybe he abandoned them after the woods, maybe he threw them away in Nat’s guest bathroom. His cock springs free and it is bigger up close, a very decent length, an intimidating thickness, cut and flushed dark. The head is sticky, and when she traces a thumb over it, Bucky gasps. In her grasp, his cock jerks: an adorable bob that has her fighting a smile.

Bringing her thumb to her mouth, she wastes no time in pressing it past her lips and sucking it clean. His taste isn’t much like hers; instead it is stronger, muskier and with a hint of salt. All at once, she needs him in her mouth. 

“Let me suck you off,” Toni asks. 

“Toni,” Bucky groans. His cock jerks again in her hand. “You don’t have to do that.” 

“I want to. Do you want me to? You said you liked my mouth. Would you—like it on your cock?” 

If he thinks that the dirty talk rolls stilted from her mouth, he doesn’t show it. All he does is mutter expletives and nod jerkily. Bucky strips himself of his jeans and sits on the center couch cushion. 

Bare to her. Completely. 

With reverence, Toni kneels, running her palms across his thighs. The hairs there are fairer and more sparse. His legs are inked as well, pictures that she traces with her fingertips. Above her, he sits patient and still, only twitching when she presses her mouth to the sensitive skin of his inner thigh. With a hand on either knee, she coaxes him to spread wider. Her eyes rake over him eagerly. It isn’t the first cock she’s ever seen (though it is the first in-person). If only the lights were on, she would be able to explore him better. In the dark, she can only really rely on one exploratory sense: touch. 

The skin of his cock feels like hot silk when she runs her fingers down the length of him. It has ridges that are perfect for her tongue to trace, veins running paths from the flared head down to his sac. Bucky must prefer to keep himself well-groomed, because he is hairless here the same way he is on his chest. She presses his cock up towards his stomach, noting the way precum leaks from the tip at her firm touch. Her other hand cups his balls, tracing one and then the other, running her fingers gently over the soft, wrinkled skin. 

“You’re gonna kill me,” says Bucky brokenly.

Leaning forward, she presses her closed lips to the very base of his cock. Beside him on the couch, his hands tighten into fists, knuckles standing out white. Encouraged, Toni begins to press gentle kisses up the shaft, gradually letting her mouth open so that she can stroke her tongue along the silken skin. When she reaches the head, she takes it past her lips and lets it rest on her tongue. Her eyes fall shut so that she can concentrate on the smoothness of his skin, the sharp taste of his cum. When she suckles at the head of him, Bucky groans, the muscles of his thighs clenching and unclenching. 

“Dear god,” he rasps with a voice like sandpaper. “This won’t last long at all, sugar, I, oh fucking hell, your mouth—” 

She startles at the feeling of his fingers touching her hair. When he sinks them deep into the damp tresses and takes hold firmly, something inside of her positively burns. Opening her jaw so wide it aches, she takes more of him into her mouth. If he stretches her open here, what will it be like when he sinks his cock inside her sex? The thought makes her whine around him, spit running down the inches of his shaft she can’t swallow down. It makes the slide of her hand easier when she wraps her slim fingers around the base and begins to jerk off the excess. 

“You sure you’ve never done this before?” he breathes. “Because you’re a natural. Thirty seconds in and I want to shoot down your throat. Goddamn, Toni—” 

Toni is sure that her own slick must be dripping down her legs at this point. As curious as she is to explore his body and reactions, she has never been patient: she wants him inside her. Pulling off of his cock, she says, “I don’t want you to cum down my throat. I want you to cum inside me.” 

Bucky hisses. He has to reach down and grip the base of his cock to keep from cumming, eyes squeezed shut in concentration. “I can’t do that. I don’t have any condoms.” 

“What good would it be for you to cum in me if you’re wearing a condom?” Toni snarks. “I want it dripping down my legs when I go up the stairs back to your room. I’ve had the implant since I was fifteen years old, neither of us need to worry about any souvenirs.”

“You don’t even know if I’m clean,” he says. He looks down at her with his jaw clenched and eyes narrowed, high on his moral outrage. “That’s what I mean about smarts being more than just numbers. You should never fuck a guy bare unless you’ve seen that he’s clean.” 

“I know you’re clean,” she snaps. 

“How the hell do you know that? Read a book on STD’s?” 

“You let me put your cock in my mouth. You think that can’t spread disease? Yeah. You weren’t thinking about it then, were you? Because you know you’ve got nothing bad to give me. I know that you’re clean because if you weren’t, you would have stopped me.” 

Now he looks downright tortured, staring down at her with his face twisted in sadness and anger. “You don’t know that. There are people out there who don’t care if they hurt you as long as they can stick their dicks inside of you. You can’t go thinkin’ the best of everyone.”

“I’m not thinking the best of everyone,” Toni admits. “I’m thinking the best of you. In science, theories are accepted as true until proven false. The only thing you’ve done since we’ve met is try to protect me. An infuriating though noble motive. You are a good man, and until you prove otherwise—I’m going to believe in you. In the good in you.” 

Bucky’s head tilts back to rest against the couch. His throat works as he takes several slow breaths. Much like when playing chess, Toni knows when to press and when to let pieces alone; she lets him turn over her words without any more fuel from her. Instead, she leans her cheek against his knee and waits, refusing to breathe lest she vibrates out of her skin with impatience. At last, he lets his head fall forward again and he nods with comical graveness. 

“Come here,” he says. “Up on my lap.” 

Her heart pounds, blood thrumming with anticipation. The size difference between them is only emphasized as she straddles his thighs. Elevated as she is, they can look at each other eye-to-eye. Toni is struck all over again by how handsome he is, the perfect symmetry from his face, the low brows that give him an intensity that threatens to take her breath away. 

“Can I kiss you?” he asks. When his hand reaches for her, thumb ghosting along the line of her jaw, it trembles.

“Yes,” she whispers. His fingers make contact, and he brings her forward.

It’s her first kiss. While there is an instinctive fluidity to it, the mechanics aren’t as simple as her erotica novels made it out to be. It helps to be hungry for him and to feel his thinly veiled hunger in return. His lips are soft and eager, and when they part to adjust the angles of their faces, his mouth returns to her parted, tongue lapping at the seam of her lips until she opens. A soft aching sound slips past her lips, and she’s glad that both of their eyes are shut so that he can’t see the embarrassed flush that burns her face. 

Wait, his eyes are shut, right?

She peaks. 

They are shut. She shuts hers quickly lest he catch her looking, but then he takes her entire bottom lip between his own and sucks at it softly and the thoughts leak from her ears. Bucky kisses with a dual nature; sometimes he is prone to long moments of softness as if he is sipping sweetly from her mouth. Other times, she can’t help but feel like he wants to split her open, drink deeply and sate his thirst of her. A quick learner, she mimics his actions. The noise he makes when she nips at his full bottom lip goes right between her legs. 

It is much like taking a poker to the softly smoldering coals of a fire. Toni burns. Thighs trembling from the effort it takes to hover over his lap, she lowers herself only find that his hard cock brushes against her curls. Bucky pulls away, hissing. 

“Sorry,” Toni murmurs. 

“Feels good,” he pants. He looks debauched, mouth red and swollen. From me, she thinks. “Remember what I told you in the woods? About you rubbing yourself off on me? Feels good for the both of us, honey.” 

“Put it inside me.”

He laughs too loud. Toni glances up towards the stairs, still dark and empty. 

“Fingers first,” says Bucky. “Put your arms around my neck and let me know if anything hurts.” 

Toni buries her face in his neck. With one large hand, he cups the entirety of her naked sex. Just the warmth of his hand has her mouth parting, when he lets two middlemost fingers press forward to touch her opening, she groans. 

“You play with yourself here?” he asks her. His fingers make no move to enter her, just rub and circle around her entrance. Toni is beyond words, chest tight with anticipation, so all she can do is nod in confirmation. Bucky groans, cock jerking where it is pressed flush between their naked bellies. 

For a long time, all he does is trace the line of her: fingers gathering the slick at her entrance and dragging it up to her swollen clit. Most passes, he avoids touching that knot of throbbing nerves, but sometimes he takes it between his two fingers and applies the slightest pressure until she is gasping and her hips are trembling in his grasp. 

“Relax,” he says. 

She bites his neck.

“Jesus,” he groans, flinching away from her teeth. “I should spank the hell out of you for that.” 

Toni arches her back until the hand steadying her hip slips back and takes a firm hold of her ass. He must feel as if she is panting in his ear, her breaths are coming so fast. Usually, Toni skimmed over spanking scenes in erotica or watched with ambivalence, eager to get to the good parts. Why the thought of Bucky doing that—of disciplining her—turns her on so much, she won’t even begin to guess. Her degree is in engineering and not psychology; leave the soft sciences to the soft scientists. 

“Is that supposed to scare me?” she mocks. 

“No,” he says. His fingers press with more firmness at her entrance, stretching her just barely. “I don’t need to scare you to get you to behave.” 

With slow and steady movements, he lets one finger slip inside her. Toni sighs happily. In a rare moment of penance, she kisses the bruise left on his throat in the shape of her mouth. 

“God you feel good,” Bucky says. “That hurtin’ you?” 

Toni rolls her eyes. “No. I usually use two fingers, anyway.” 

“I’d die to see that,” he sighs. “Is that what you were doing up there in your room for so long? Working two fingers in an’ out of this pretty pussy?” 

“No. I wanted to wait—for you.” 

It’s Bucky’s turn to lean in to her, his lips pressing against her throat. His voice is wrecked when he says, “There isn’t a single part of you, not a single thing you say or do that doesn’t drive me insane.” 

Without another word, he withdraws from her and then two fingertips are nudging at her entrance. The stretch makes her suck in a breath even though there is plenty of wetness to ease his way. 

“Okay?” he asks. His breathing has picked up, either mimicking her unconsciously or noticing the tension in her form. “You feel—real tight.”

“Your fingers are bigger than mine,” she theorizes. “It doesn’t hurt though. Keep going.”

Bucky presses in to his last knuckle. He uses his thumb to rub at her clit and when she clenches around his fingers, they both groan. Impatient, Toni draws her hips back to feel the slide as his fingers come free, dragging against the sensitive rim of her entrance. 

“Go ahead,” he pants. “If it feels good, go ahead honey.”

She keeps her thrusts slow. Her hips are unused to the movement, and when he spreads his fingers to open her wide, it almost hurts. 

“How the hell am I going to get inside you,” Bucky mutters. 

Toni hopes that’s rhetorical. 

More and more, he opens her up. She never stops the rolling of her hips, but sometimes he pins her to him so that he can focus on her clit, strumming his thumb back and forth over it until she feels liable to cum and more slick drips out of her. Then he stretches his fingers again. It goes on forever, the slick sounds growing more and more obscene until there is no more ache. When he slips a third finger inside, it doesn’t hurt at all, just burns in a deeply satisfying way. 

“I want you on top, just like this,” he says. “That way you’re in control and if somethin’ hurts, you can stop right away. Got it?” 

“Got it, it’s gotten,” Toni answers. Her thighs tremble, cunt pulsing emptily when he pulls his fingers free and goes to lick them clean. Toni stops him with a hand around his wrist. His eyes stare at the way her fingers can’t touch for the thickness of him. Without thought, she says, “That’s mine.” 

He blinks. “I—know?”

“So it’s mine,” she says, tugging his hand towards her mouth. When he realizes that she means to lick her slick off of his fingers, his eyes fall shut, cock jerking between them. 

His throats clicks when he swallows. “But, you’re a good girl, right? You’re gonna share, aren’t you?” 

“If you ask nicely,” she whispers, buzzing on the high of his submission. 

His eyes are so heated, they pin her in place. Never has she been so thankful for her eidetic memory. He’s the most beautiful person she’s ever seen, and the sight of him with his swollen mouth and inked skin and burning eyes is one that she commits to memory again and again. Unwilling to part from it. 

“Please,” begs Bucky. 

“Do better.” 

“Please share. Two tastes tonight aren’t enough. I’d gladly spend the rest of my life with my mouth to your pussy, that’s how bad I want it. Even just one finger, honey, let me have one.” 

She is positively shaking when she brings his wrist towards her—and takes all three fingers into her mouth. Bucky makes a sound like he’s been punched, but he bites down on any protests, gritting his teeth. He presses down on her tongue, the barest bite of his nails until she shuts her teeth around his fingers in warning. When any semblance of her essence is gone, she lets go of his wrist. 

“You’re cruel,” he rasps. 

“That’s what you get for thinking I’m a good girl.” 

“I take it back.” 

Toni shifts up, her hand reaching between them for his cock. It is slick with precum that has smeared against his abs. As soon as the flared head rests against her entrance, she realizes the discrepancy between three fingers and his cock. 

“Just take it slow,” he says, breaths unsteady. “For both our sakes.” 

She lowers herself just an inch. The stretch as the head slips past her entrance burns in the best way. Once she doesn’t need to guide him anymore, she lets her thin arms wrap around his shoulders, the fingers of one hand burying themselves in his hair in a grip that must be painful even if he doesn’t mention it. Another inch disappears inside her, and it pinches in a way that has her wincing. Instead of pressing forward, she raises her hips up until he nearly slips free from her before taking him back in. 

“Jesus,” Bucky whispers as she fucks herself on the tip alone. 

“Don’t rush me,” she laughs. 

“I’m not, I swear,” he says. “Just trying not to blow my load, you’re so tight—fuck, I felt that. You squeeze my dick like that again and I’m finished, honey, holy shit.” 

“I can’t help it,” Toni gasps. It feels so good to use those muscles, feels so good to clench against him as he’s filling her up. The next inch comes easier, and the next after that. She lets herself lower those last few inches until he’s completely inside of her. It doesn’t make sense: how it feels so foreign but how it feels so right. He’s touching places inside of her that her fingers never could, that even his fingers never could, filling her in a way she’s never been full. It’s overwhelming all at once. Whining into his throat, she says, “God, it feels like you’re in my throat.” 

Inside of her, his cock twitches and makes her squeak—an altogether indignant sound that she will take to the grave. 

“Just sit there for a minute,” Bucky pants. “Please Joseph, Mary, and Jesus, don’t fucking move.” 

“Don’t tell me that; now I want to move even more.” 

He tightens his grip on her hips, unrelenting. Now, even when she shifts against him, she can’t move an inch. The knowledge stokes the heat inside her higher, pulling a moan from deep in her chest. She feels his lips press to her shoulder, a soft and sweet touch that maybe she wasn’t even meant to notice. A smile blooms where no one can see it, and she forces herself to relax and wait for him. 

After an endless minute, he finally releases his bruising hold of her hips. “Okay,” he says. 

“Okay? I can move?”  

He nods. “Do whatever feels best.” 

In for a penny, in for a pound. Toni lifts herself up, lamenting the loss of him just so that she can bring her hips down hard in a thrust that shakes her to her core. If she had any breath in her lungs, she might have shouted; even Bucky seems shattered, groaning expletives that are far too loud. At the apex of his thrust, he touches a spot inside her that feels so sensitive it nearly hurts. She wants to feel that hurt again and again and again. The pace she sets nearly breaks the both of them. She has never been able to cum from internal stimulation alone, but when he hits that spot deep inside, she feels like maybe she could. 

When her legs begin to shake from overexertion, he shifts them until he lies flat on the couch, coaxing her to lean forward and let some of her weight be borne by her palms on the armrest his head lays on. It changes the angle, and she leans forward and then backward to experience every sensation.

“Look at you,” Bucky breathes. “Taking my cock so well. Just chasing what feels good, aren’t you honey? Tell me how it feels.” 

“Good,” Toni whines, digging her fingers into the fabric of the armrest. He thrusts his hips up like a reward and she cries out. When she leans forward, she finds that she can grind her clit against the base of his cock. 

“Do better,” he says, mocking her earlier words. Another sharp thrust upwards, that sharp, bright ache—my cervix, she thinks with a thrill. That’s what that is. He’s just long enough to touch it. 

“If cumming means that you won’t be able to keep fucking me like this, then you’re never allowed to cum,” she says. “Ever.” 

Bucky laughs so hard he wheezes. “Yeah?” he says when he catches his breath. “You want to put a ring on me, use my cock like it’s a toy for your convenience? How many times could you cum on my dick before I blow my load even with the ring on, huh? Nothing could keep me from cummin’ inside you. A pussy this sweet? Let’s be glad I’ve lasted this long.” 

Toni clenches her muscles tight until he hisses. 

“Let’s start counting,” she says. “Make me cum, Bucky, please.” 

He groans. One of his hands goes to her breast, taking her pebbled nipple between his fingers while the other drifts down to where they’re connected. For a moment, he ignores her aching clit and instead lets his fingers trace where she’s stretched around his cock. He mutters something foul, filthy, hot and then he presses the pad of his thumb against her clit, rubbing briskly, working to follow her thrusts even as they stutter and grow erratic. 

“Oh God,” Toni breathes, toes curling. “Please don’t stop, please don’t stop, please—” 

When she cums, it’s explosive—never has she cum while so full, while being filled. Hypersensitive to his cock, it feels huge where he thrusts in and out of her, cunt gripping him tight. Every thrust drags her orgasm on and on, his thumb never growing lenient where it toys with her clit until she feels like she could cum again, which has never happened, never—

The second is slower and deeper, her entire body seizing up above him. Both of her legs cramp, but it doesn’t matter. Nothing fucking matters. Nothing except for his thumb on her clit and that burst of pleasure so deep inside her so keen that it almost hurts. 

When her brain finally begins to function again, her lashes are wet, her throat is raw, and Bucky has a hold of her hips, gently humping upwards into the cradle of her hips. The wet sounds of their sex almost make her flush, but then she realizes that he is whispering to her frantically: 

“—please, I’ve got to cum, can’t hold off anymore. Did you mean it, that you want, you want it inside?” 

“God, yes,” Toni says, voice wrecked. “Inside me, please. Do it inside me—” 

He grows still beneath her, the music staff across his chest expanded from the force of his inhalation. His eyes are squeezed shut, the expression on his face looking almost pained. Then she feels it: his cock twitching where it’s buried deep inside of her, a flush of warmth and wetness. He groans, teeth clenched tight. 

“I can feel that,” she says in wonder. 

And when his eyes open, misty and dazed and looking for her own so that he can smile up at her, all she can think is, I want to feel that again. 

-

Nat creeps back up from where she had crouched on the stairs low enough to catch a glimpse of the living room below. A noise down the hallway draws her attention, but it is just Wanda, her head poking out questioningly from one of the guest rooms. Wanda points a finger towards the stairs and then takes that same finger and thrusts it into a hole loosely formed by her other fist. 

Nat makes a circle with her thumb and forefinger. 

Yes! Wanda mouths, pumping her fist. She holds up her hand and Natasha gives her a phantom high-five before disappearing back into her bedroom, taking extra care to close the door without a single sound. Steve is sound asleep where she left him, but when she crawls back into bed, he reaches for her even in sleep to wrap an arm around her. 

All in a day’s work. 

-

Hours after the sun has ridden, Natasha is the first awake. The living room is empty with no sign of any late-night scandalous activities. She hadn’t checked Toni’s guestroom, but she would guarantee that it was empty. It puts her in a good mood, and she hums while he starts an extra-large pot of coffee. In the quiet early morning, Natasha is struck by a rare moment of complete contentment. So many of the people she loves under one room, safe, happy, sated. 

If only life could be like this all the time, she thinks.

One by one the others begin to wake and come down. Bucky arrives first. Natasha passes him a mug of coffee without a word, ignoring the sight of the vivid bruise against his neck. They must have staggered their arrivals to avoid suspicion, because Toni arrives only a few minutes later, hair wet from a shower. 

“Are you hungover?” Natasha asks, letting her face crumple into a concerned expression. “God, T, you look like you didn’t sleep a wink. Was it the bed? Those guest rooms—” 

“The bed was fine,” Toni says primly. Her face barely twists when she sits on the stool at the kitchen island. 

“Gimme that,” Bucky mutters, taking the mug meant for Toni from her hands. Looking her dead in the eye, he says lowly enough so that only she can hear: “You aren’t slick, Nat.” 

“Toni sure was,” she says, barely moving her lips. 

Bucky snorts, turning away to take Toni the coffee. Natasha turns her back to them, making herself busy with breakfast on the stove so that no one can see her smile while she listens to them bicker over the best way to take their coffee. Steve is suddenly there, pressed flush against her back so that he can place a kiss at the crown of her head. 

“Everything okay?” he asks under his breath. 

And it’s not a lie when she looks up at him and says: “Perfect.” 

#winteriron #female!tony stark #toni stark #cagewrites #iti

[puzzlescore]

Kepler is the newest puzzle designed by Felix Ure @felix_ure . ⠀ ✅ The approach to the puzzle naming is enough to earn the title. Johannes Kepler is a very important figure in the scientific revolution of the 17th century. And there’s another thing – Kepler Conjecture. It’s a mathematical theorem about sphere packing (I’m already giving you a hint). frustrating. ⠀ ✅ The Kepler puzzle consists of a container, 11 balls and a lid. It’s made of brass and aluminum: screws and a lid are made of brass and the box is produced in aluminum. ⠀ ✅ The objective is to insert all 11 balls into the box so that the lid closes. As usual, it sounds simple, but don’t be flattered till you start solving the puzzle. Also remember that the lid should be flat against the top of the container. ⠀ The Kepler Puzzle is an ode to intelligence, science and observation. Its witty solution will make you be happy like a child. But be careful, it has one side effect: its quality causes true tactile euphoria. ⠀ More Puzzles on our website. Link in bio👆 ⠀ #puzzlescore #puzzle #metalart https://www.instagram.com/p/CLrPIrIDWj7/?igshid=1c3fqsdc2rqws

#puzzlescore #puzzle #metalart

[myassignmenthelperonline-blog]

Do my math assignment Service by the Mathematics Experts

Our math homework done for you service has empowered pupils to achieve who feels completing assignment as a daunting task. Marketplace leaders work with genuine college students to show the importance of learning mathematics. Procedural skill and mathematical understanding are important and are assessable currently with mathematical tasks of riches that are adequate. The A Math’s Dictionary for Kids is an animated, interactive mathematics dictionary for students which explains over 630 ordinary mathematical terms and math phrases in language with practice, examples, activities, definitions, and calculators. 

Even the EOC mathematics tests measuring the 2016 Mathematics Standards of Learning will be implemented in the spring mathematics tests. Teach more about tasks and the people that produce UC Berkeley certainly one among the best places on earth for undergraduate, graduate and analysis study in math. Burton senior school math instructor Stephanie Hanson will work with a class of 11th-grade students. 

Returns the largest (closest to positive infinity) double value which is less than or equal to this debate and is equal to a mathematical integer. SOL Practice Items in TestNav 8 provide samples of their articles adapting to the 2016 Mathematics Standards of Learning and opportunities to practice together with the online tools and functions that can be found in TestNav 8 throughout SOL testing. The Mathematics Competitions certainly are a collection of curriculum materials and assessments that build abilities and wisdom at superior and center school students. 

Topology in all its many effects could have become the greatest growth location in 20thcentury math; it includes point-set topology, set-theoretic topology, algebraic topology, and topology specifically, instances of contemporary topology are metrizability principle, axiomatic set theory, homology theory, and Morse theory Topology also comprises the now solved Poincare conjecture, and also the nonetheless inland areas of the Hodge conjecture Other benefits in geometry and topology, including the 4 color theorem along with Kepler conjecture, are proved only with the assistance of pcs. 

We feel that if students come to be doers rather than passive consumers of mathematics these mathematical thinking's best benefits can be realized. 35 Its adjective is μαθηματικός (mathematics), which “associated with understanding" or “studious", which likewise further came to mean “mathematical". The Kumon Math Worksheets might assist your child understand expertise all the way. Next calendar year, also a study team and Boaler intend to recommend that California phase from the pathway in favor of math for most college students -- something she pitched around their country to training leaders. 

Another way to get assistance with your Math coursework that you search with I need help with math homework term for quality assignment help.

#math homework help #do math homework online

[kplr-radio]

Broadcast: Angelo Divine, 01/09/19

[Live a Little Kenny Chesney]

Angelo: Good morning Kepler, that was Kenny Chesney’s “Live A Little,” and what a mood to start the morning on! This is 103.5 KPLR radio, and we’ll get to the news after this word from our sponsor.

[Audio advertisement transcript: [haunting orchestral music] Have you ever heard a true story that couldn’t possibly be real? Or maybe seen something you couldn’t believe with your own two eyes? No? [music cuts off] Then you’re not living, my friend! Come on down to the Cryptonomica, we have centuries of hidden knowledge of the arcane and the mystical! Stories beyond suspicion, creatures beyond compare! We’re just off State Route 16055. The Cryptonomica: a museum for the mysterious.]

Angelo: Big thanks to the Cryptonomica for sponsoring us this week! And don’t forget to check out the Lamplighter, this week’s issue talks about Krampus and the history of goat creatures in horror. It’s a really good read even if you’re not into the supernatural side of it. Now let’s get to the news. Traffic is as uneventful as ever, and weather reports say we’re looking at clear skies for the rest of the week. Do be sure to watch out for ice on the roads, though. It’s still pretty chilly, so be sure to grab a coat before you head to work. There’s not a long going on this week, that cold weather is kinda pushing everyone inside, but the Kepler Cup is running down the last of their Christmas stock so be sure to get all that before it’s gone. I myself have a peppermint mocha right here, actually, it’s keeping me warm while I wait for the heater to get going. Let’s get back to the tunes! This is “I Want A Cowboy” by Reba McEntire.

[I Want A Cowboy Reba McEntire] [Take Me Home, Country Roads John Denver] [Personal Jesus Johnny Cash] [Islands in the Stream Kenny Rogers and Dolly Parton]

Alright, since there isn’t so much official news today, why don’t we look into some of the more extraordinary stuff? If any of you saw something noteworthy, why don’t you call in and tell me about it? Oh! Here we go. You’re on the air!

Caller: You know, I thought I saw Bigfoot but I got a bit closer and it turned out it was just Barclay from the lodge. He’s so ******* big . I asked him what he was doing in the woods and he said he likes night walks, and honestly yeah same I was doing a night walk too. And I said “Hey Barclay! Holy ****! I thought you were Bigfoot!” And then he choked on his own spit or something. I think he found it pretty funny. He was laughing a lot? I think? Anyway like holy ****! It’s so weird, he’s so tall and hairy, how many times have people seen Barclay and thought he was Bigfoot? How many sightings are just Barclay?

Angelo: Oh yeah, I wonder. Seems like half the sightings around here turn out to just be someone from town! What a strange place Kepler is. We’re still taking callers, if anyone else has any noteworthy sightings to report. Oh, looks like we got one! Hey!

Caller: Hello! It's great to be on the show, big fan! I ran into one a' those... Whaddya call it, hoke-mons? Okie-bombs? Somethin' like that. Saw a big monstrous lookin' one down in the park. Crazy what y'all can do with all them new-fangled technologies these days. Also Richard, if you're listenin', I love you!

Angelo: It’s great to have you! You might have seen a Pokémon, maybe? Strange that you would see one, uh, out and about. Maybe I’ll have to go down to the park sometime and check it out. Thanks for the info! Anyone else?

Caller: Angelo! Hey, Bonnie here, and I’m in the mood to be scared! You got any ghost stories?

Angelo: Well, uh, usually it’s y’all giving me the ghost stories, but I’ll do my best. [papers rustling] Here we go. This isn’t so much a story as a sort of summary, but I’ll read off my notes on the Nachtkrapp, an old Germanic bird monster. Shoutout to my coworker for helping me translate the information on this, not sure how he knows Old High German but we all have our hobbies, right? Anyways, the Nachtkrapp or “Night Raven” is described as a large raven, roughly the same size as an adult man, who acts as a boogeyman-type figure to scare children into going to sleep. In some versions of the legend, it imitates a human scream to either terrify them or lure them outside. In others, it has holes in its wings and no eyes, and just looking at the creature could make you sick or even kill you. There aren’t any recorded sightings of the creature as far as I can tell, but who knows? There’s a lot of area in northwestern Europe, it could be out there somewhere. Thanks so much to everyone who called in, but my producer says we gotta wrap this segment up. Hold onto those stories though, ‘cause I’m here every weekday and I love hearing them. This song up next is “Thank God I’m A Country Boy” by John Denver.

[Thank God I’m A Country Boy John Denver] [High Note Mavis Staples] [God’s Gonna Cut You Down Johnny Cash] [A Working Man Can’t Get Nowhere Today Merle Haggard]

Angelo: Some excellent songs on the rotation this week, though I might be biased. Anyways, it’s time for what I’m sure is everyone’s favorite, Angelo’s Advice Hour. As usual, if you’re in need of some advice, call in! As a certified expert I can and will solve your problems for you.

[Disclaimer: Angelo Divine is not qualified to answer most questions definitively. All answers are purely conjecture and Angelo Divine is not liable for any negative results that may come from following his advice.]

Angelo: We got our first caller! Hello, listener!

Caller: What should I do if I have a crush on one of my sisters friends?

Angelo: Aw, I’ve been there. I mean, it really depends on how well you know that person. If you’re friends or you think they might like you back, definitely go the “secret relationship” route. Not because you should lie to your sister, but because it is very fun. If you don’t know them too well or they don’t know you enough, get your sister to introduce you! Unless your sister is a jerk, in which case you should definitely be obnoxious about it. Hope that answers your conundrum! Who’s next?

Caller: I think I might have joined a gang? How do I say I don’t want to join but I like the jacket?

Angelo: The classic “accidentally joined a gang” problem. Those Hornets are wily, huh? Here’s what I’ll say: stick with it for a little bit, and you might have fun, I dunno, I have no idea what kids are doing these days. If you don’t like it still, stop wearing the jacket and hide it away so they can’t steal it back, and then just kinda ghost on ‘em. They’ll definitely find you, but it should buy you some time to come up with a good excuse. It’s a great plan.

Caller: I’m stuck on the roof, can you help me?

Angelo: I know who this is and the answer is: you know I can’t. Also you aren’t stuck. Get down before station management goes looking for you. Consider that my official advice.

Caller: So, uh, listen, I know this isn’t really your thing, but your coworker, uh, Rob was his name? Whoever does the overnight. He mentioned that he was looking for someone, and I think I can help him.

Angelo: Oh, uh, alright, I’ll— listen, come by the station when you can, if I’m not here then Rob definitely will be. Does anyone out there have actual advice questions?

Caller: Yeah, so, uh, I got a lotta people coming through my store, and I try to be real friendly, but I’m gettin’ old and I can’t remember everyone’s names. Do you have any tips for remembering names?

Angelo: Yeah, for sure! I’m still getting the hang of everyone’s names here at the station, haha. The trick is associating that person with something, so when you see that thing you remember their name. Like my coworker J— Rob, he’s got this cool jacket so when I see his jacket I think “that’s Rob!” It doesn’t always work, sometimes you end up calling him “jacket guy” but it’s better than not addressing them at all! I do think that’s it for today, folks, my airtime’s almost up, so let me leave you with “Jolene” by Dolly Parton.

[Jolene Dolly Parton]

#broadcast #1/9/19 #angelo divine

[awholefuckinglifetimeofthis]

hang on its 4 am and I'm getting emotional. johannes kepler created a crutial conjecture for sphere-packing and described, for the first time ever, the hexagonal symmetry of snowflakes, as a new year's gift to a friend... the pamphlet was called "a new year's gift of hexagonal snow"....

#creation as a love language.... mathematics as art.... idk idk #btw im unironiaclly a kepler stan. favorite old mathematician and astonomer #txt

[telavivdelhi2]

Freud was at the time under the influence of his friend and collaborator Wilhelm Fliess, an ear, nose, and throat specialist. Fliess, whom Freud had called "the Kepler of biology", had developed theories today considered pseudoscientific, including the belief that sexual problems were linked to the nose by a supposed nasogenital connection. Fliess had been treating "nasal reflex neurosis" by cauterizing the inside of the nose under local anesthesia. Fliess conjectured that if temporary cauterization was useful, surgery would yield more permanent results. He began operating on the noses of patients he diagnosed with the disorder, including Eckstein and Freud.

His surgery proved disastrous, resulting in profuse, recurrent nasal bleeding – Fliess had left a half-metre of gauze in Eckstein’s nasal cavity, the subsequent removal of which left her permanently disfigured. Though aware of Fliess’s culpability – Freud fled from the remedial surgery in horror – he could only bring himself to delicately intimate in his correspondence to Fliess the nature of his disastrous role and in subsequent letters maintained a tactful silence on the matter or else returned to the face-saving topic of Eckstein’s hysteria. Freud ultimately reasserted his full confidence in Fliess's competence, making Eckstein responsible for the whole catastrophe by concluding that her post-operative hemorrhages were "wish-bleedings", caused by her hysterical longing for the affection of others.[

#emma eckstein nose job

[juniperpublishers-rr]

Laws of the Universe or Laws of Physics- Juniper Publishers

Abstract

It seems crucial to differentiate these two expressions: laws of the Universe and laws of physics. A law is supposed to be invariable, definitive, intangible, whereas there are many examples of evolution of physical laws; in such a way that we talk about the diachrony of physical laws. Diachrony, from the Greek dia (through), is a term of linguistics: it means change with time, not because of time, since we know that time is not a phenomenon [1].

Introduction

A modeling is an arrangement with physical reality, but not a substitute for it. However, it allows a description, a quantification, an evaluation, and a certain prediction. The observation, the experiments, the replication of findings, and the mathematical models of physics, lead to the formulation of laws. Therefore, the physical laws depend on the concepts and the models that are used; they depend on the progress of research and on the progress of thinking in general. A physical law is not discovered in nature, instead, it follows from a construction of the mind: thus, the observation of nature and the modelings lead to physical laws.

The Diachrony of Physical Laws

These remarks provide grounds for making the following observations:

a) The accuracy of laws is not absolute; they do their best (sic pro optima), but they inevitably convey inaccuracies.

b) The physical laws are not immutable. For Einstein, laws are only temporary solutions to our conceptions of reality [2].

The concepts and the models evolve independently of time; this evolution leads to changing laws. However, this does not cast shadow upon the genius of their initiators; to claim a century later that Einstein, Darwin, or Freud were mistaken is an anachronism. For these reasons, neither nature nor the Universe obeys our laws; They are not compelled to abide by our laws; they do not operate according to a law, ex lege in Cicero [3]; Our physical laws provide certain descriptions and they make some predictions possible, but they do not prescribe anything. The main feature of our physical laws is that they provide a temporary description rather than a permanent imperative. Repeated train or aircraft crashes often make people conjecture some law about series of accidents, but this is a mistake, because the essence of a law is to predict, while these events are not predictable. The economic cycle is not a law of economics, because collapse is unpredictable. Moreover, economists and politicians are unable to predict crises; they do not even agree among themselves about how to find a way out of a crisis. The principle of Roman law, lex imperat (the law dictates), is not true in physics; so, the ambition to circumscribe the Universe (totum, the whole, the totality) with a corpus of immutable laws within a final theory is utopic (i.e., in no place) and uchronic (i.e., never, at no time). Einstein gave up looking for a global picture of the Universe, explaining that he was not disavowing a principle, but applying a method [2].

More thorough observations, more accurate measurements, more advanced mathematical models, and new theories will lead to changing laws, to the rejection of some laws and the introduction of new laws. Some of the current laws will be done away with or modified like Kepler’s laws. The first law of the German astronomer Johannes Kepler (1571-1630) provides a simple illustration. It says that the Earth follows an elliptical orbit around the Sun. This law overturned the then consensus on astronomical knowledge. However, it turned out later that astronomy had to make some corrections, among which we find: The orbit followed by the Earth is disrupted by the revolution of the Moon; the Earth is shaken by the Moon, so that the ellipse is sinusoidal. In fact, it is the center of gravity of the couple Earth-Moon that follows an elliptical curve.

a) Moreover, the laws of physics have been developed with concepts of time and space, which are prevalent, although they remained undefined. Therefore, this quite legitimately raises a question concerning the progressive precarity of existing laws in favors of new ones which may not involve time and/or space, but some more efficient models, with more effective parameters.

b) Due to an infinitesimal deceleration, the center of gravity does not return to exactly the same place after one revolution: the curve is a converging spiral ellipse.

c) In conclusion, the curve followed by the Earth is a sinusoidal and converging spiral ellipse. This means that the accuracy of the Earth-Sun clock is limited.

Conclusion

Expressions such as laws of the Universe and laws of nature, The law of nature is in Cicero [3], are survivors from ancient divinations of Nature, which were considered superstitions by Lucretius [4]. These expressions are examples of epistemic immoderation which should be excluded from scientific semantics and replaced by more circumstantial expressions, such as laws of biology, laws of astronomy, laws of thermodynamics, laws of physics, or physical laws; provided that a physical law is always an interpretation, the consequence of an observation.

For more Open Access Journals in Juniper Publishers please click on: https://juniperpublishers.com

For more articles in Open Access Journal of Reviews & Research please click on: https://juniperpublishers.com/arr/index.php

To know more about Open Access Journals please click on: https://juniperpublishers.com/index.php

#Juniper Publishers Indexing Sites #Juniper Publishers #juniper publishers contact info #Juniper publishers publishing group #Juniper Publishers Review

[catholiccom-blog]

The Galileo Controversy

It is commonly believed that the Catholic Church persecuted Galileo for abandoning the geocentric (earth-at-the-center) view of the solar system for the heliocentric (sun-at-the-center) view. The Galileo case, for many anti-Catholics, is thought to prove that the Church abhors science, refuses to abandon outdated teachings, and is not infallible. For Catholics, the episode is often an embarrassment. It shouldn’t be. This tract provides a brief explanation of what really happened to Galileo.

Anti-scientific?

The Church is not anti-scientific. It has supported scientific endeavors for centuries. During Galileo’s time, the Jesuits had a highly respected group of astronomers and scientists in Rome. In addition, many notable scientists received encouragement and funding from the Church and from individual Church officials. Many of the scientific advances during this period were made either by clerics or as a result of Church funding. Nicolaus Copernicus dedicated his most famous work, On the Revolution of the Celestial Orbs, in which he gave an excellent account of heliocentricity, to Pope Paul III. Copernicus entrusted this work to Andreas Osiander, a Lutheran clergyman who knew that Protestant reaction to it would be negative, since Martin Luther seemed to have condemned the new theory, and, as a result, the book would be condemned. Osiander wrote a preface to the book, in which heliocentrism was presented only as a theory that would account for the movements of the planets more simply than geocentrism did—something Copernicus did not intend. Ten years prior to Galileo, Johannes Kepler published a heliocentric work that expanded on Copernicus’ work. As a result, Kepler also found opposition among his fellow Protestants for his heliocentric views and found a welcome reception among some Jesuits who were known for their scientific achievements.

Clinging to Tradition? Anti-Catholics often cite the Galileo case as an example of the Church refusing to abandon outdated or incorrect teaching, and clinging to a "tradition." They fail to realize that the judges who presided over Galileo’s case were not the only people who held to a geocentric view of the universe. It was the received view among scientists at the time. Centuries earlier, Aristotle had refuted heliocentricity, and by Galileo’s time, nearly every major thinker subscribed to a geocentric view. Copernicus refrained from publishing his heliocentric theory for some time, not out of fear of censure from the Church, but out of fear of ridicule from his colleagues. Many people wrongly believe Galileo proved heliocentricity. He could not answer the strongest argument against it, which had been made nearly two thousand years earlier by Aristotle: If heliocentrism were true, then there would be observable parallax shifts in the stars’ positions as the earth moved in its orbit around the sun. However, given the technology of Galileo’s time, no such shifts in their positions could be observed. It would require more sensitive measuring equipment than was available in Galileo’s day to document the existence of these shifts, given the stars’ great distance. Until then, the available evidence suggested that the stars were fixed in their positions relative to the earth, and, thus, that the earth and the stars were not moving in space—only the sun, moon, and planets were. Thus Galileo did not prove the theory by the Aristotelian standards of science in his day. In his Letter to the Grand Duchess Christina and other documents, Galileo claimed that the Copernican theory had the "sensible demonstrations" needed according to Aristotelian science, but most knew that such demonstrations were not yet forthcoming. Most astronomers in that day were not convinced of the great distance of the stars that the Copernican theory required to account for the absence of observable parallax shifts. This is one of the main reasons why the respected astronomer Tycho Brahe refused to adopt Copernicus fully. Galileo could have safely proposed heliocentricity as a theory or a method to more simply account for the planets’ motions. His problem arose when he stopped proposing it as a scientific theory and began proclaiming it as truth, though there was no conclusive proof of it at the time. Even so, Galileo would not have been in so much trouble if he had chosen to stay within the realm of science and out of the realm of theology. But, despite his friends’ warnings, he insisted on moving the debate onto theological grounds. In 1614, Galileo felt compelled to answer the charge that this "new science" was contrary to certain Scripture passages. His opponents pointed to Bible passages with statements like, "And the sun stood still, and the moon stayed . . ." (Josh. 10:13). This is not an isolated occurrence. Psalms 93 and 104 and Ecclesiastes 1:5 also speak of celestial motion and terrestrial stability. A literalistic reading of these passages would have to be abandoned if the heliocentric theory were adopted. Yet this should not have posed a problem. As Augustine put it, "One does not read in the Gospel that the Lord said: ‘I will send you the Paraclete who will teach you about the course of the sun and moon.’ For he willed to make them Christians, not mathematicians." Following Augustine’s example, Galileo urged caution in not interpreting these biblical statements too literally. Unfortunately, throughout Church history there have been those who insist on reading the Bible in a more literal sense than it was intended. They fail to appreciate, for example, instances in which Scripture uses what is called "phenomenological" language—that is, the language of appearances. Just as we today speak of the sun rising and setting to cause day and night, rather than the earth turning, so did the ancients. From an earthbound perspective, the sun does appear to rise and appear to set, and the earth appears to be immobile. When we describe these things according to their appearances, we are using phenomenological language. The phenomenological language concerning the motion of the heavens and the non-motion of the earth is obvious to us today, but was less so in previous centuries. Scripture scholars of the past were willing to consider whether particular statements were to be taken literally or phenomenologically, but they did not like being told by a non-Scripture scholar, such as Galileo, that the words of the sacred page must be taken in a particular sense. During this period, personal interpretation of Scripture was a sensitive subject. In the early 1600s, the Church had just been through the Reformation experience, and one of the chief quarrels with Protestants was over individual interpretation of the Bible. Theologians were not prepared to entertain the heliocentric theory based on a layman’s interpretation. Yet Galileo insisted on moving the debate into a theological realm. There is little question that if Galileo had kept the discussion within the accepted boundaries of astronomy (i.e., predicting planetary motions) and had not claimed physical truth for the heliocentric theory, the issue would not have escalated to the point it did. After all, he had not proved the new theory beyond reasonable doubt.

Galileo "Confronts" Rome Galileo came to Rome to see Pope Paul V (1605-1621). The pope, weary of controversy, turned the matter over to the Holy Office, which issued a condemnation of Galileo’s theory in 1616. Things returned to relative quiet for a time, until Galileo forced another showdown. At Galileo’s request, Cardinal Robert Bellarmine, a Jesuit—one of the most important Catholic theologians of the day—issued a certificate that, although it forbade Galileo to hold or defend the heliocentric theory, did not prevent him from conjecturing it. When Galileo met with the new pope, Urban VIII, in 1623, he received permission from his longtime friend to write a work on heliocentrism, but the new pontiff cautioned him not to advocate the new position, only to present arguments for and against it. When Galileo wrote the Dialogue on the Two World Systems, he used an argument the pope had offered, and placed it in the mouth of his character Simplicio. Galileo, perhaps inadvertently, made fun of the pope, a result that could only have disastrous consequences. Urban felt mocked and could not believe how his friend could disgrace him publicly. Galileo had mocked the very person he needed as a benefactor. He also alienated his long-time supporters, the Jesuits, with attacks on one of their astronomers. The result was the infamous trial, which is still heralded as the final separation of science and religion.

Tortured for His Beliefs? In the end, Galileo recanted his heliocentric teachings, but it was not—as is commonly supposed—under torture nor after a harsh imprison- ment. Galileo was, in fact, treated surprisingly well. As historian Giorgio de Santillana, who is not overly fond of the Catholic Church, noted, "We must, if anything, admire the cautiousness and legal scruples of the Roman authorities." Galileo was offered every convenience possible to make his imprisonment in his home bearable. Galileo’s friend Nicolini, Tuscan ambassador to the Vatican, sent regular reports to the court regarding affairs in Rome. Many of his letters dealt with the ongoing controversy surrounding Galileo. Nicolini revealed the circumstances surrounding Galileo’s "imprisonment" when he reported to the Tuscan king: "The pope told me that he had shown Galileo a favor never accorded to another" (letter dated Feb. 13, 1633); " . . . he has a servant and every convenience" (letter, April 16); and "[i]n regard to the person of Galileo, he ought to be imprisoned for some time because he disobeyed the orders of 1616, but the pope says that after the publication of the sentence he will consider with me as to what can be done to afflict him as little as possible" (letter, June 18). Had Galileo been tortured, Nicolini would have reported it to his king. While instruments of torture may have been present during Galileo’s recantation (this was the custom of the legal system in Europe at that time), they definitely were not used. The records demonstrate that Galileo could not be tortured because of regulations laid down in The Directory for Inquisitors (Nicholas Eymeric, 1595). This was the official guide of the Holy Office, the Church office charged with dealing with such matters, and was followed to the letter. As noted scientist and philosopher Alfred North Whitehead remarked, in an age that saw a large number of "witches" subjected to torture and execution by Protestants in New England, "the worst that happened to the men of science was that Galileo suffered an honorable detention and a mild reproof." Even so, the Catholic Church today acknowledges that Galileo’s condemnation was wrong. The Vatican has even issued two stamps of Galileo as an expression of regret for his mistreatment.

Infallibility Although three of the ten cardinals who judged Galileo refused to sign the verdict, his works were eventually condemned. Anti-Catholics often assert that his conviction and later rehabilitation somehow disproves the doctrine of papal infallibility, but this is not the case, for the pope never tried to make an infallible ruling concerning Galileo’s views. The Church has never claimed ordinary tribunals, such as the one that judged Galileo, to be infallible. Church tribunals have disciplinary and juridical authority only; neither they nor their decisions are infallible. No ecumenical council met concerning Galileo, and the pope was not at the center of the discussions, which were handled by the Holy Office. When the Holy Office finished its work, Urban VIII ratified its verdict, but did not attempt to engage infallibility. Three conditions must be met for a pope to exercise the charism of infallibility: (1) he must speak in his official capacity as the successor of Peter; (2) he must speak on a matter of faith or morals; and (3) he must solemnly define the doctrine as one that must be held by all the faithful. In Galileo’s case, the second and third conditions were not present, and possibly not even the first. Catholic theology has never claimed that a mere papal ratification of a tribunal decree is an exercise of infallibility. It is a straw man argument to represent the Catholic Church as having infallibly defined a scientific theory that turned out to be false. The strongest claim that can be made is that the Church of Galileo’s day issued a non-infallible disciplinary ruling concerning a scientist who was advocating a new and still-unproved theory and demanding that the Church change its understanding of Scripture to fit his. It is a good thing that the Church did not rush to embrace Galileo’s views, because it turned out that his ideas were not entirely correct, either. Galileo believed that the sun was not just the fixed center of the solar system but the fixed center of the universe. We now know that the sun is not the center of the universe and that it does move—it simply orbits the center of the galaxy rather than the earth. As more recent science has shown, both Galileo and his opponents were partly right and partly wrong. Galileo was right in asserting the mobility of the earth and wrong in asserting the immobility of the sun. His opponents were right in asserting the mobility of the sun and wrong in asserting the immobility of the earth. Had the Catholic Church rushed to endorse Galileo’s views—and there were many in the Church who were quite favorable to them—the Church would have embraced what modern science has disproved.

#Catholic Answers #Catholic Answers Tracts #Galileo #Heliocentric #Geocentric

[fromthecommsroom]

Higher Ground

read it on the AO3 at http://bit.ly/2PVcV5K

by PunkHazard

Kepler passes out a folder to each crewmember, waiting for them to crack the files open before he speaks. "Our first order of business" he says, standing at the head of the table, "is getting a few programs out of the crossfire. Non-negotiable."

"Good afternoon to you too, Colonel." Jacobi grumbles, already reading. "How was your day, Jacobi? Oh, you know, same as always. Thanks for asking, sir, really makes us feel like you care."

Words: 3212, Chapters: 1/1, Language: English

Series: Part 5 of Kent

Fandoms: Wolf 359 (Radio)

Rating: Teen And Up Audiences

Warnings: No Archive Warnings Apply

Categories: Gen

Characters: Warren Kepler, Daniel Jacobi, Alana Maxwell, Isabel Lovelace, Renée Minkowski, Doug Eiffel, Miranda Pryce, Hera (Wolf 359)

Additional Tags: Post-Canon, Corporate Espionage, Slice of Life, alien doppelgänger funtimes, kepler getting to flex his 'artful lawyer' and 'encyclopedic bureaucrat' muscles, equal parts pure conjecture and suits AU

read it on the AO3 at http://bit.ly/2PVcV5K

#AO3 Feed #Wolf 359 fan fiction #Wolf 359 fic #Wolf 359

[geopolicraticus]

Nietzsche’s Secret Garden

Having made the case for the impersonality of science (if not the self-abnegation of the scientist) in Scientific Self-Abnegation, it now remains to make the case for the uniquely personal, private, and idiosyncratic side of science—if indeed there is any such side of science, or if there is any such case to make. 

What would an idiosyncratic scientific research program look like? It is not difficult to imagine, as for the greater part of the history of human science, scientific research programs were nothing more than the life work of a single man—an Archimedes, a Galileo, a Kepler, a Huygens, a Newton. This is the de facto condition of science in human history, but not necessarily the ideal of science, and not the reality of the large-scale research programs of big science that have come into being since the industrial revolution.

Scientific research programs in the time of Archimedes were the insights and ambitions of one man, but by the time of Newton there were printing presses, universities, scientific societies, and scientific journals (on which cf. Boundary Conditions of the Scientific Revolution). Newton had a community of scientific researchers to which he could communicate his work and from which he could anticipate an informed response. Even if Newton and his colleagues did not have the instantaneous global communications that we take for granted today, books did make their way around the world, and some scientists were well-traveled and worldly men in Newton’s day. And this was true to a much greater extent than was the case for Archimedes in classical antiquity.

Archimedes was a man a Syracuse, and his fate was tied to the fate of his city-state. The greatest institutions of learning of which we know from the pre-modern world—Plato’s Academy, the library at Alexandria, and the House of Wisdom in Baghdad—could be said to be regional centers of learning, or even centers on a civilizational scale that attracted the best minds within that civilization, but it is nothing like the international scientific collaboration of today.

Kenneth Clark made an astute observation related to this:

“The great churchmen of the eleventh and twelfth centuries came from  all over Europe. Anselm came from Aosta, via Normandy, to be Archbishop of Canterbury; Lanfranc had made the same journey, starting from Pavia. The list could be extended to almost every great teacher of the early Middle Ages. It couldn’t happen in the Church, or politics, today: one can’t imagine two consecutive archbishops of Canterbury being Italian. But it could happen—does happen—in the field of science; which shows that where some way of thought or human activity is really vital to us, internationalism is accepted unhesitatingly.” (Civilisation: A Personal View, Harper & Row, 1969, p. 35)

Clark is right to point out that the church was an international institution (regionally confined to Europe) in the Middle Ages, and similarly the Roman world had its international institutions in the Mediterranean Basin in its time (though the use of “international” here is misleading and unhistorical). However, these earlier international institutions did not involve science, and despite their internationalism they were confined within a geographical region.

Science today thrives on a planetary scale, and so its institutions are planetary-scale institutions. But science began as a regional institution within Europe—this was science during the scientific revolution, from Copernicus to the industrial revolution—and before science was a regional institution, it was only the institution of gifted individuals and their immediate circle, if indeed a gifted individual had any circle at all. Many did not.

Previously I wrote about Nietzsche’s secret garden in Philosophies of the Secret Garden, in which I quoted the following: 

“…out of my answers there grew new questions, inquiries, conjectures, probabilities—until at length I had a country of my own, a soil of my own, an entire discrete, thriving, flourishing world, like a secret garden the existence of which no one suspected. —Oh how fortunate we are, we men of knowledge, provided only that we know now to keep silent long enough!” (Nietzsche, On the Genealogy of Morals, translated by Walter Kaufmann, Preface, section 3) 

I strongly identify with this. I have been working on my philosophical ideas in isolation for so many years that I have layers upon layers of concepts that are my own, so that concepts that I worked out several years ago I have since used to work out additional concepts that presuppose these earlier concepts. I have iterated this process to several generations with my own ideas, and this makes it extraordinarily difficult to explain what I am doing to others. Any explanation would make use of concepts that would have to be explained in turn. 

It often happens that the bulk of a philosopher’s most original thoughts are to be found in their manuscripts. Probably every philosopher experiences what I have noted just above, and so holds back the strangest and least familiar flowers from his secret garden, instead presenting the public with only those arrangements that appear sufficiently conventional that they will not be rejected tout court.

Husserl wrote tens of thousands of pages in Gabelsberger shorthand, and Husserl’s industrious intellectual heirs have continued to transcribe, to edit, to publish, and to translate this enormous body of work almost a hundred years after this death. Godel’s notebooks, also written in Gabelsberger, are only now beginning to be transcribed and published (though they are already available in digitized form to anyone who can puzzle them out). I previously discussed these efforts in The arc of cognitive astrobiology is long, but it bends toward rationality. The impact of these philosophical efforts—the secret gardens of Husserl and Godel—will only be felt by the wider intellectual community in the coming century.

While philosophy in our time has started to follow the scientific model of international collaborative research, it is far behind science in this respect, and most philosophers doing truly original work do so in relative isolation, much as science was done in classical antiquity (though I might well argue that philosophy was an international collaboration in the ancient world, along the model that Clark described in the passage quoted above).

This is significant for science, because new scientific disciplines are suggested by novel philosophical research, and a new discipline in its nascent state is a fragile thing, easy destroyed if mishandled. It would be entirely understandable if a contemporary philosopher chose to work on ideas at the border of science and philosophy and kept this entirely to himself because this work would not likely be welcomed in either in the scientific community (being too philosophical) or in the philosophical community (being too scientific). Nevertheless, this is where most of the interesting ideas come from, and we tacitly and implicit rely on such efforts for the overall advancement of science.

I have often said that one of the advantages of the heightened individualism of western civilization is that it allows societies so organized to explore more possibilities at a lower social cost. Collectivist societies that insist upon joint social effort explore new possibilities at a high social cost, and failure can be catastrophic. This makes collectivist societies more risk averse than individualistic societies.

Additionally, the individualism of western civilization allows for the indulgence of eccentrics and splendid individuals, who, if they are successful, will be celebrated as individuals. And they may even be financially rewarded as individuals for their individual effort. Thus there is both a carrot and a stick for the individual researcher who attempts to make a contribution without being part of any wider research community.

The paradigm of “big science” represents a mainstreaming of a particular research program—a program that defines the wider research community—which enjoys disproportionately large social investments: university facilities, funding, personnel, equipment, etc. This has been crucial for the growth of what Kuhn called “normal science,” which is an enormous cooperative and collaborative effort. And with the conceptual framework of normal science being more comprehensive and more adequate than ever before in the past, normal science practiced as big science can continue almost indefinitely.

This potentially indefinite growth of normal science has been further facilitated by an awareness of Kuhnian philosophy of science, and this has meant that scientists are more clearly aware than at any previous time of the ellipses incorporated into the body of scientific knowledge, and many are open to considering alternative theories as long as those theories are competently expressed in the technical jargon of the discipline. We know that general relativity and quantum theory cannot be brought together in our current physics framework, and we know that we cannot explain large-scale cosmology (which often invokes “dark matter” and “dark energy,” which are merely ciphers that mean, “something to explain gravitational anomalies” and “something to explain the accelerating expansion of the universe”), so that the scientific community is actively seeking more adequate formulations of these problems.

Be that as it may, the most striking developments of science are likely to come out of the work of philosophical scientists (as indeed the theories of relativity and gravitation came out of Einstein’s work, and Einstein has rightly been called a “philosopher-scientist”), and these philosophical scientists will probably develop the most crucial and distinctive concepts that later serve to advance science in a Nietzschean secret garden of their own.

#Nietzsche #Friedrich Nietzsche #Kenneth Clark #science #history of science #scientific research program #individualism

[2whatcom-blog]

Okay, Possibly Proofs Aren't Dying After All

In my final column I recount how again within the 1990s two mathematicians named a geometrical object after me, the "Horgan surface," as revenge for "The Death of Proof." The column gave me an excuse to revisit my controversial 1993 article, which argued that advances in computer systems, the rising complexity of arithmetic and different developments have been undermining the standing of conventional proofs. As I wrote the column, it occurred to me that proofs generated by the Horgan floor contradict my death-of-proof thesis. I emailed a number of consultants to ask how they assume my death-of-proof thesis has held up. Listed below are responses from laptop scientist Scott Aaronson, mathematician-physicist Peter Woit and mathematics-software mogul Stephen Wolfram. (See Additional Studying for hyperlinks to my Q&As with them). -John Horgan Scott Aaronson response (which he additionally simply posted on his weblog): John, I such as you so I hate to say it, however the final quarter century has not been sort to your thesis about "the death of proof"! These mathematicians sending you the irate letters had a degree: there's been no basic change to arithmetic that deserves such a dramatic title. Proof-based math stays fairly wholesome, with (e.g.) an answer to the Poincare conjecture since your article got here out, in addition to to the Erdos discrepancy downside, the Kadison-Singer conjecture, Catalan's conjecture, bounded gaps in primes, testing primality in deterministic polynomial time, and so forth. -- simply to select a number of examples from the tiny subset of areas that I do know something about. There are evolutionary adjustments to mathematical follow, as there at all times have been. Since 2009, the web site MathOverflow has let mathematicians question the worldwide hive-mind about an obscure reference or a recalcitrant step in a proof, and get near-instant solutions. In the meantime "polymath" initiatives have, with reasonable success, tried to harness blogs and different social media to make advances on long-standing open math issues utilizing huge collaborations. Whereas people stay within the driver's seat, there are persistent efforts to extend the function of computer systems, with some notable successes. These embrace Thomas Hales's 1998 computer-assisted proof of the Kepler Conjecture (in regards to the densest potential solution to pack oranges) -- now absolutely machine-verified from begin to end, after the Annals of Arithmetic refused to publish a combination of conventional arithmetic and laptop code. It additionally contains William McCune's 1996 resolution to the Robbins Conjecture in algebra (the computer-generated proof was solely half a web page, however concerned substitutions so unusual that for 60 years no human had discovered them); and on the "opposite extreme," the 2016 resolution to the Pythagorean triples downside by Marijn Heule and collaborators, which weighed in at 200 terabytes (at the moment, "the longest proof in the history of mathematics"). It is conceivable that sometime, computer systems will exchange people in any respect features of mathematical analysis -- but it surely's additionally conceivable that, by the point they will do this, they will have the ability to exchange people at music and science journalism and the whole lot else! New notions of proof -- together with probabilistic, interactive, zero-knowledge, and even quantum proofs -- have seen additional growth by theoretical laptop scientists since 1993. To this point, although, these new kinds of proof stay both completely theoretical (as with quantum proofs), or else they're used for cryptographic protocols however not for mathematical analysis. (For instance, zero-knowledge proofs now play a serious function in sure cryptocurrencies, reminiscent of Zcash.) In lots of areas of math (together with my very own, theoretical laptop science), proofs have continued to get longer and more durable for anyone particular person to soak up. This has led some to advocate a break up method, whereby human mathematicians would discuss to one another solely in regards to the handwavy intuitions and high-level ideas, whereas the tedious verification of particulars could be left to computer systems. To this point, although, the large funding of time wanted to put in writing proofs in machine-checkable format -- for nearly no return in new perception -- has prevented this method's large adoption. Sure, there are non-rigorous approaches to math, which proceed to be extensively utilized in physics and engineering and different fields, as they at all times have been. However none of those approaches have displaced proof because the gold commonplace every time it is accessible. If I needed to speculate about why, I might say: if you happen to use non-rigorous approaches, then even when it is clear to you beneath what situations your outcomes could be trusted, it is most likely a lot much less clear to anyone else. Additionally, even when just one section of a analysis neighborhood cares about rigor, no matter earlier work that section builds on will must be rigorous as nicely -- thereby exerting fixed strain in that route. Thus, the extra collaborative a given analysis space turns into, the extra vital is rigor. For my cash, the elucidation of the foundations of arithmetic a century in the past, by Cantor, Frege, Peano, Hilbert, Russell, Zermelo, Godel, Turing, and others, nonetheless stands as one of many best triumphs of human thought, up there with evolution or quantum mechanics or the rest. It is true that the perfect set by these luminaries stays largely aspirational. When mathematicians say theorem has been "proved," they nonetheless imply, as they at all times have, one thing extra like: "we've reached a social consensus that all the ideas are now in place for a strictly formal proof that could be verified by a machine ... with the only task remaining being massive rote coding work that none of us has any intention of ever doing!" It is also true that mathematicians, being human, are topic to the complete panoply of foibles you would possibly count on: claiming to have proved issues they have not, squabbling over who proved what, accusing others of lack of rigor whereas hypocritically taking liberties themselves. However identical to love and honesty stay advantageous beliefs irrespective of how typically they're flouted, so too does mathematical rigor. Peter Woit response: What most strikes me pondering again to this debate from a quarter-century in the past is how little has modified. There's some huge cash and a focus now going to knowledge science, machine studying, AI and such, however apart from extra of our college students taking jobs in these areas, the impact on pure arithmetic analysis has been minimal. One change is that the Web has offered higher entry to high-quality arithmetic analysis supplies and discussions, with examples movies of talks, discussions on MathOverflow, and my colleague Johan deJong's Stacks Undertaking. This sort of change has individuals speaking a lot as they've at all times executed, simply extra effectively. On the identical time, computer systems proceed to solely not often have any function within the creation and checking of the proofs of mathematical theorems. The extraordinary debate surrounding Mochizuki's claimed proof of the abc conjecture offers an fascinating check case. The issues with understanding and checking the proof have concerned one of the best minds within the discipline engaged in a troublesome battle for comprehension, with computerized proof checking taking part in no function in any respect. There is no such thing as a proof that laptop software program is any nearer now than in 1993 to being to compete with Peter Scholze and different consultants who've labored on analyzing Mochizuki's arguments. If there is a new optimistic growth forward on this story, it is going to be progress in direction of deeper understanding coming from a flesh and blood mathematician, not a tech trade server farm. Stephen Wolfram response. Once I contacted Wolfram, creator of Mathematica and different merchandise, a publicist despatched me a hyperlink to Wolfram's latest essay "Logic, Explainability and the Future of Understanding." It's filled with provocative assertions in regards to the nature of arithmetic, logic, proof, computation and data typically. Wolfram claims, for starters, to have mapped out the house of all potential logical axioms, suggesting, he contends, that the axioms upon which we generally rely should not one way or the other optimum or mandatory however arbitrary. My takeaway is that the house of potential arithmetic, whereas infinite, could also be far more infinite than usually suspected. Wolfram additionally means that with the assistance of one among his innovations, Wolfram Language, laptop proofs needn't be black containers, which generate a outcome however little understanding. Right here is how he places it: At some stage I believe it is a quirk of historical past that proofs are usually right this moment introduced for people to know, whereas applications are often simply considered issues for computer systems to run... ne of the principle objectives of my very own efforts over the previous a number of many years has been to alter this--and to develop within the Wolfram Language a real "computational communication language" through which computational concepts could be communicated in a manner that's readily comprehensible to each computer systems and people. However Wolfram warns that we are going to at all times bump up in opposition to the boundaries of understanding: In arithmetic we're used to constructing our stack of data so that every step is one thing we will perceive. However experimental mathematics--as nicely as issues like automated theorem proving--make it clear that there are locations to go that will not have this characteristic. Will we name this "mathematics"? I believe we should always. However it's a special custom from what we have largely used for the previous millennium. It is one the place we will nonetheless construct abstractions, and we will nonetheless assemble new ranges of understanding. However someplace beneath there can be all types of computational irreducibility that we'll by no means actually have the ability to convey into the realm of human understanding. Additional Studying: The Horgan Floor and the Loss of life of Proof How William Thurston (RIP) Helped Convey About "The Death of Proof" Who Found the Mandelbrot Set? Was I Fallacious about The Finish of Science? Is Science Hitting a Wall? Magnificence Does Not Equal Fact, in Physics or Elsewhere Bayes's Theorem: What is the Huge Deal? Thoughts-Physique Issues (free on-line guide) See additionally Q&As with Scott Aaronson, Stephen Wolfram, Edward Witten and Peter Woit. Read the full article

#2what.com #it’s #mathematics #proof #proofs