Curve Model Quotes

We can always find each other, we girls with secrets.

With right fashion, every female would be a flame.

It's time to shop high heels if your fiance kisses you on the forehead.

Fashion doesn't make you perfect, but it makes you pretty.

Her shining tresses, divided in two parts, encircle the harmonious contour of her white and delicate cheeks, brilliant in their glow and freshness. Her ebony brows have the form and charm of the bow of Kama, the god of love, and beneath her long silken lashes the purest reflections and a celestial light swim, as in the sacred lakes of Himalaya, in the black pupils of her great clear eyes. Her teeth, fine, equal, and white, glitter between her smiling lips like dewdrops in a passion-flower's half-enveloped breast. Her delicately formed ears, her vermilion hands, her little feet, curved and tender as the lotus-bud, glitter with the brilliancy of the loveliest pearls of Ceylon, the most dazzling diamonds of Golconda. Her narrow and supple waist, which a hand may clasp around, sets forth the outline of her rounded figure and the beauty of her bosom, where youth in its flower displays the wealth of its treasures; and beneath the silken folds of her tunic she seems to have been modelled in pure silver by the godlike hand of Vicvarcarma, the immortal sculptor.

Dresses won't worn out in the wardrobe, but that is not what dresses are designed for.

Dresses don't look beautiful on hangers.

We women are a lot more powerful if we see ourselves as fighters on the same side. But it’s easier to judge others - their choices and their bodies - than to think about the struggles we share.

During the shoot in November 2003, I was vaguely aware of the stylist’s sulky demeanor and eye-rolling vibe, but I blocked her out. Some fashion people are snotty drama queens; this is not news. Whatever was going on with her, I was determined to be positive and not get infected by her energy. Later, Fiorella told me that the entire time I was in makeup, the stylist had been clomping up and down the hall, sputtering into her cell phone, “I can’t believe I have to style a FAT GIRL!” Believe it, bitch.

In one universe, they are gorgeous, straight-teethed, long-legged, wrapped in designer fashions, and given sport cars on their sixteenth birthdays, Teachers smile at them and grade them on the curve. They know the first names of the staff. They are the pride of the school. In Universe #2, they throw parties wild enough to attract college students. They worship stink of Eau de Jocque. They rent beach houses in Cancun during Spring Break and get group-rate abortions before the prom. But they are so cute. And they cheer on our boys, inciting them to violence and, we hope, victory. They’re are our role models- the Girls Who Have It All. I bet none of them ever stutter or screw up or feel like their brains are dissolving into marshmallow fluff.

Ms. Terwilliger didn’t have a chance to respond to my geological ramblings because someone knocked on the door. I slipped the rocks into my pocket and tried to look studious as she called an entry. I figured Zoe had tracked me down, but surprisingly, Angeline walked in. "Did you know," she said, "that it’s a lot harder to put organs back in the body than it is to get them out?" I closed my eyes and silently counted to five before opening them again. “Please tell me you haven’t eviscerated someone.” She shook her head. “No, no. I left my biology homework in Miss Wentworth’s room, but when I went back to get it, she’d already left and locked the door. But it’s due tomorrow, and I’m already in trouble in there, so I had to get it. So, I went around outside, and her window lock wasn’t that hard to open, and I—” "Wait," I interrupted. "You broke into a classroom?" "Yeah, but that’s not the problem." Behind me, I heard a choking laugh from Ms. Terwilliger’s desk. "Go on," I said wearily. "Well, when I climbed through, I didn’t realize there was a bunch of stuff in the way, and I crashed into those plastic models of the human body she has. You know, the life size ones with all the parts inside? And bam!" Angeline held up her arms for effect. "Organs everywhere." She paused and looked at me expectantly. "So what are we going to do? I can’t get in trouble with her." "We?" I exclaimed. "Here," said Ms. Terwilliger. I turned around, and she tossed me a set of keys. From the look on her face, it was taking every ounce of self-control not to burst out laughing. "That square one’s a master. I know for a fact she has yoga and won’t be back for the rest of the day. I imagine you can repair the damage—and retrieve the homework—before anyone’s the wiser.” I knew that the “you” in “you can repair” meant me. With a sigh, I stood up and packed up my things. “Thanks,” I said. As Angeline and I walked down to the science wing, I told her, “You know, the next time you’ve got a problem, maybe come to me before it becomes an even bigger problem.” "Oh no," she said nobly. "I didn’t want to be an inconvenience." Her description of the scene was pretty accurate: organs everywhere. Miss Wentworth had two models, male and female, with carved out torsos that cleverly held removable parts of the body that could be examined in greater detail. Wisely, she had purchased models that were only waist-high. That was still more than enough of a mess for us, especially since it was hard to tell which model the various organs belonged to. I had a pretty good sense of anatomy but still opened up a textbook for reference as I began sorting. Angeline, realizing her uselessness here, perched on a far counter and swing her legs as she watched me. I’d started reassembling the male when I heard a voice behind me. "Melbourne, I always knew you’d need to learn about this kind of thing. I’d just kind of hoped you’d learn it on a real guy." I glanced back at Trey, as he leaned in the doorway with a smug expression. “Ha, ha. If you were a real friend, you’d come help me.” I pointed to the female model. “Let’s see some of your alleged expertise in action.” "Alleged?" He sounded indignant but strolled in anyways. I hadn’t really thought much about asking him for help. Mostly I was thinking this was taking much longer than it should, and I had more important things to do with my time. It was only when he came to a sudden halt that I realized my mistake. "Oh," he said, seeing Angeline. "Hi." Her swinging feet stopped, and her eyes were as wide as his. “Um, hi.” The tension ramped up from zero to sixty in a matter of seconds, and everyone seemed at a loss for words. Angeline jerked her head toward the models and blurted out. “I had an accident.” That seemed to snap Trey from his daze, and a smile curved his lips. Whereas Angeline’s antics made me want to pull out my hair sometimes, he found them endearing.

If you ask me, it's all these skinny models that make girls anorexic," she went on, to Auntie Barbara. "I can't think why they don't use real girls with a few curves." "Stands to reason, Jenny." Auntie B. was as pinkly flushed as Mum. "All the designers are gay—they don't want bosoms in their clothes, or bottoms, either. Not proper, girls' bottoms.

As he walked out into the North Carolina sunshine, Lola's hand in his, a smile curved one corner of his lips. Not so long ago, he'd stood on the burned-out bridge of the Dora Mae, thinking himself cursed with a beautiful underwear model and her sissy little dog. He'd always believed Lola Carlyle would be the death of him. "We never did get around to watching Pride and Prejudice," she said, a teasing glint in her beautiful eyes. Yeah, she would most definitely be the death of him, but what a way to go.

So we pour in data from the past to fuel the decision-making mechanisms created by our models, be they linear or nonlinear. But therein lies the logician's trap: past data from real life constitute a sequence of events rather than a set of independent observations, which is what the laws of probability demand.[...]Even though many economic and financial variables fall into distributions that approximate a bell curve, the picture is never perfect.[...]It is in those outliers and imperfections that the wildness lurks.

She had Jessica Rabbit's curves and full lips that made him wish he was a tube of ChapStick.

It doesn’t have to be black and white. You have a structured workout and sure that makes your life easier. You have a template to follow. But if you don’t have 45 minutes to do that workout, you can do 10 minutes of it. If you don’t have time to train, you can take your dog for a walk. There’s so many ways you can make these incremental changes that will lead to overall better habits.

Equally important was the fact that the interpretation provided the model for how Tianming had hidden his message in the three stories. He employed two basic methods: dual-layer metaphors and two-dimensional metaphors. The dual-layer metaphors in the stories did not directly point to the real meaning, but to something far simpler. The tenor of this first metaphor became the vehicle for a second metaphor, which pointed to the real intelligence. In the current example, the princess’s boat, the He’ershingenmosiken soap, and the Glutton’s Sea formed a metaphor for a paper boat driven by soap. The paper boat, in turn, pointed to curvature propulsion. Previous attempts at decipherment had failed largely due to people’s habitual belief that the stories only involved a single layer of metaphors to hide the real message. The two-dimensional metaphors were a technique used to resolve the ambiguities introduced by literary devices employed in conveying strategic intelligence. After a dual-layer metaphor, a single-layer supporting metaphor was added to confirm the meaning of the dual-layer metaphor. In the current example, the curved snow-wave paper and the ironing required to flatten it served as a metaphor for curved space, confirming the interpretation of the soap-driven boat. If one viewed the stories as a two-dimensional plane, the dual-layer metaphor only provided one coordinate; the supporting single-layer metaphor provided a second coordinate that fixed the interpretation on the plane. Thus, this single-layer metaphor was also called the bearing coordinate. Viewed by itself, the bearing coordinate seemed meaningless, but once combined with the dual-layer metaphor, it resolved the inherent ambiguities in literary language. “A subtle and sophisticated system,” a PIA specialist said admiringly. All the committee members congratulated Cheng Xin and AA. AA, who had always been looked down on, saw her status greatly elevated among the committee members. Cheng

College does not equal job security. Entrepreneurship does not equal job security. For heaven's sake, "job security" does not equal job security. So what do you do? Don't be a one-trick pony. Add real value in everything you do. But most of all, study and apply business models. No matter what discipline you come from. Learn how to add value so that value can flow in the form of money to you. That, my friends, is job security. Learn where money comes from and you'll know where to turn when life throws a curve.

This example highlights two aspects of choice that the standard model of indifference curves does not predict. First, tastes are not fixed; they vary with the reference point. Second, the disadvantages of a change loom larger than its advantages, inducing a bias that favors the status quo.

What can you prove about space? How do you know where you are? Can space be curved? How many dimensions are there? How does geometry explain the natural order and unity of the cosmos? These are the questions behind the five geometric revolutions of world history. It started with a little scheme hatched by Pythagoras: to employ mathematics as the abstract system of rules that can model the physical universe.

As shown in figure 2-2, to break the trade-off between differentiation and low cost and to create a new value curve, there are four key questions to challenge an industry’s strategic logic and business model: Which of the factors that the industry takes for granted should be eliminated? Which factors should be reduced well below the industry’s standard? Which factors should be raised well above the industry’s standard? Which factors should be created that the industry has never offered?

Her shining tresses, divided in two parts, encircle the harmonious contour of her white and delicate cheeks, brilliant in their glow and freshness. Her ebony brows have the form and charm of the bow of Kama, the god of love, and beneath her long silken lashes the purest reflections and a celestial light swim, as in the sacred lakes of Himalaya, in the black pupils of her great clear eyes. Her teeth, fine, equal, and white, glitter between her smiling lips like dewdrops in a passion-flower’s half-enveloped breast. Her delicately formed ears, her vermilion hands, her little feet, curved and tender as the lotus-bud, glitter with the brilliancy of the loveliest pearls of Ceylon, the most dazzling diamonds of Golconda. Her narrow and supple waist, which a hand may clasp around, sets forth the outline of her rounded figure and the beauty of her bosom, where youth in its flower displays the wealth of its treasures; and beneath the silken folds of her tunic she seems to have been modelled in pure silver by the godlike hand of Vicvarcarma, the immortal sculptor.

If you are going to use probability to model a financial market, then you had better use the right kind of probability. Real markets are wild. Their price fluctuations can be hair-raising-far greater and more damaging than the mild variations of orthodox finance. That means that individual stocks and currencies are riskier than normally assumed. It means that stock portfolios are being put together incorrectly; far from managing risk, they may be magnifying it. It means that some trading strategies are misguided, and options mis-priced. Anywhere the bell-curve assumption enters the financial calculations, an error can come out.

...Women have preserved this `baby look' for as long as possible so as to make the world continue to believe in the darling, sweet little girl she once was, and she relies on the protective instinct in man to make him take care of her. As with everything a woman undertakes on her own initiative, this whole maneuvre is as incredible as it is stupid. It is amazing, in fact, that it succeeds. It would appear very shortsighted to encourage such an ideal of beauty. For how can any woman hope to maintain it beyond the age of twenty-five? Despite every trick of the cosmetics industry, despite magazine advice against thinking or laughing (both tend to create wrinkles), her actual age will inevitably show'- through in the end. And what on earth is a man to do with a grown-up face when he has been manipulated into considering only helpless, appealing little girls to be creatures of beauty? What is a men to do with a woman when the smooth curves have become flabby tires of flesh, the skin slack and pallid, when the childish tones have grown shrill and the laughter sounds like neighing? What is to become of this shrew when her face no longer atones for her ceaseless inanities and when the cries of `Ooh' and Ah' begin to drive him out of his mind? This mummified `child' will never fire a man's erotic fantasy again. One might think her power broken at last. But no, she still manages to get her own way - and for two reasons. The first is obvious: she now has children, who enable her to continue feigning helplessness. As for the second - there are simply not enough young women to go around. It is a safe bet that, given the choice, man would trade in his grown-up child-wife for a younger model, but, as the ratio between the sexes is roughly equal, not every man can have a younger woman. And as he has to have a wife of some sort. he prefers to keep the one he already possesses. This is easy to prove. Given the choice, a man will always choose a younger woman.

With so much knowledge written down and disseminated and so many ardent workers and eager patrons conspiring to produce the new, it was inevitable that technique and style should gradually turn from successful trial and error to foolproof recipe. The close study of antique remains, especially in architecture, turned these sources of inspiration into models to copy. The result was frigidity—or at best cool elegance. It is a cultural generality that going back to the past is most fruitful at the beginning, when the Idea and not the technique is the point of interest. As knowledge grows more exact, originality grows less; perfection increases as inspiration decreases. In painting, this downward curve of artistic intensity is called by the sug- gestive name of Mannerism. It is applicable at more than one moment in the history of the arts. The Mannerist is not to be despised, even though his high competence is secondhand, learned from others instead of worked out for himself. His art need not lack individual character, and to some connoisseurs it gives the pleasure of virtuosity, the exercise of power on demand, but for the critic it poses an enigma: why should the pleasure be greater when the power is in the making rather than on tap? There may be no answer, but a useful corollary is that perfection is not a necessary characteristic of the greatest art.

School teaches us that life is a game to win against our peers. We’re graded on a uniform scale no matter our background, our strengths and weaknesses, or our future goals. Sometimes we’re even graded on a curve relative to our peers. This inane, pointless system of competition is baked into the twentieth-century educational model. We’re taught that life is a game of musical chairs and that if we don’t hustle, we’re going to be left standing without a seat. This in-it-to-win-it mentality is the polar opposite of a creative mindset, which is abundant, resilient, and full of potential. Aiming to be “better” is a dead end because it means you’re walking in someone else’s footsteps and trying to catch up.

The bust of the General was unquestionably the finest bust I ever saw. For your life you could not have found a fault with its wonderful proportion. This rare peculiarity set off to great advantage a pair of shoulders which would have called up a blush of conscious inferiority into the countenance of the marble Apollo. I have a passion for fine shoulders, and may say that I never beheld them in perfection before. The arms altogether were admirably modeled. Nor were the lower limbs less superb. These were, indeed, the ne plus ultra of good legs. Every connoisseur in such matters admitted the legs to be good. There was neither too much flesh, nor too little,—neither rudeness nor fragility. I could not imagine a more graceful curve than that of the os femoris, and there was just that due gentle prominence in the rear of the fibula which goes to the conformation of a properly proportioned calf. I wish to God my young and talented friend Chiponchipino, the sculptor, had but seen the legs of Brevet Brigadier General John A. B. C. Smith.

She unbuttoned her coat, carried it to the closet, and hung it up. This gave him his first chance to have a good long look at her. Rachael's proportions, he noticed once again, were odd; with her heavy mass of dark hair her head seemed large, and because of her diminutive breasts her body assumed a lank, almost childlike “stance. But her great eyes, with their elaborate lashes, could only be those of a grown woman; there the resemblance to adolescence ended. Rachael rested very slightly on the fore-part of her feet, and her arms, as they hung, bent at the joint. The stance, he reflected, of a wary hunter of perhaps the Cro-Magnon persuasion. The race of tall hunters, he said to himself. No excess flesh, a flat belly, small behind and smaller bosom - Rachael had been modeled on the Celtic type of build, anachronistic and attractive, Below the brief shorts her legs, slender, had a neutral, nonsexual quality, not much rounded off in nubile curves. The total impression was good, however. Although definitely that of a girl, not a woman. Except for the restless, shrewd eyes.

Not long ago I was in Istanbul, Turkey. While there I toured the Topkapi Palace—the former royal palace of the Ottoman sultans and center of the Ottoman Empire. Among the many artifacts collected throughout the centuries and on display was an item I found quite remarkable—the sword of the prophet Muhammad. There, under protective glass and illuminated by high-tech lighting, was the fourteen-hundred-year-old sword of the founder of Islam. As I looked at the sword with its curved handle and jeweled scabbard, I thought how significant it is that no one will ever visit a museum and be shown a weapon that belonged to Jesus. Jesus brings freedom to the world in a way different from Pharaoh, Alexander, Caesar, Muhammad, Napoleon, and Patton. Jesus sets us free not by killing enemies but by being killed by enemies and forgiving them … by whom I mean us. Forgiveness and cosuffering love is the truth that sets us free—free from the false freedom inflicted by swords ancient and modern. Muhammad could fight a war in the name of freedom to liberate his followers from Meccan oppression, but Jesus had a radically different understanding of freedom. And lest this sound like crass Christian triumphalism, my real question is this: Do we Christians secretly wish that Jesus were more like Muhammad? It’s not an idle question. The moment the church took to the Crusades in order to fight Muslims, it had already surrendered its vision of Jesus to the model of Muhammad. Muhammad may have thought freedom could be found at the end of a sword, but Jesus never did. So are Christians who most enthusiastically support US-led wars against Muslim nations actually trying to turn Jesus into some version of Muhammad? It’s a serious question.

The Memory Business Steven Sasson is a tall man with a lantern jaw. In 1973, he was a freshly minted graduate of the Rensselaer Polytechnic Institute. His degree in electrical engineering led to a job with Kodak’s Apparatus Division research lab, where, a few months into his employment, Sasson’s supervisor, Gareth Lloyd, approached him with a “small” request. Fairchild Semiconductor had just invented the first “charge-coupled device” (or CCD)—an easy way to move an electronic charge around a transistor—and Kodak needed to know if these devices could be used for imaging.4 Could they ever. By 1975, working with a small team of talented technicians, Sasson used CCDs to create the world’s first digital still camera and digital recording device. Looking, as Fast Company once explained, “like a ’70s Polaroid crossed with a Speak-and-Spell,”5 the camera was the size of a toaster, weighed in at 8.5 pounds, had a resolution of 0.01 megapixel, and took up to thirty black-and-white digital images—a number chosen because it fell between twenty-four and thirty-six and was thus in alignment with the exposures available in Kodak’s roll film. It also stored shots on the only permanent storage device available back then—a cassette tape. Still, it was an astounding achievement and an incredible learning experience. Portrait of Steven Sasson with first digital camera, 2009 Source: Harvey Wang, From Darkroom to Daylight “When you demonstrate such a system,” Sasson later said, “that is, taking pictures without film and showing them on an electronic screen without printing them on paper, inside a company like Kodak in 1976, you have to get ready for a lot of questions. I thought people would ask me questions about the technology: How’d you do this? How’d you make that work? I didn’t get any of that. They asked me when it was going to be ready for prime time? When is it going to be realistic to use this? Why would anybody want to look at their pictures on an electronic screen?”6 In 1996, twenty years after this meeting took place, Kodak had 140,000 employees and a $28 billion market cap. They were effectively a category monopoly. In the United States, they controlled 90 percent of the film market and 85 percent of the camera market.7 But they had forgotten their business model. Kodak had started out in the chemistry and paper goods business, for sure, but they came to dominance by being in the convenience business. Even that doesn’t go far enough. There is still the question of what exactly Kodak was making more convenient. Was it just photography? Not even close. Photography was simply the medium of expression—but what was being expressed? The “Kodak Moment,” of course—our desire to document our lives, to capture the fleeting, to record the ephemeral. Kodak was in the business of recording memories. And what made recording memories more convenient than a digital camera? But that wasn’t how the Kodak Corporation of the late twentieth century saw it. They thought that the digital camera would undercut their chemical business and photographic paper business, essentially forcing the company into competing against itself. So they buried the technology. Nor did the executives understand how a low-resolution 0.01 megapixel image camera could hop on an exponential growth curve and eventually provide high-resolution images. So they ignored it. Instead of using their weighty position to corner the market, they were instead cornered by the market.

In 1950, a thirty-year-old scientist named Rosalind Franklin arrived at King’s College London to study the shape of DNA. She and a graduate student named Raymond Gosling created crystals of DNA, which they bombarded with X-rays. The beams bounced off the crystals and struck photographic film, creating telltale lines, spots, and curves. Other scientists had tried to take pictures of DNA, but no one had created pictures as good as Franklin had. Looking at the pictures, she suspected that DNA was a spiral-shaped molecule—a helix. But Franklin was relentlessly methodical, refusing to indulge in flights of fancy before the hard work of collecting data was done. She kept taking pictures. Two other scientists, Francis Crick and James Watson, did not want to wait. Up in Cambridge, they were toying with metal rods and clamps, searching for plausible arrangements of DNA. Based on hasty notes Watson had written during a talk by Franklin, he and Crick put together a new model. Franklin and her colleagues from King’s paid a visit to Cambridge to inspect it, and she bluntly told Crick and Watson they had gotten the chemistry all wrong. Franklin went on working on her X-ray photographs and growing increasingly unhappy with King’s. The assistant lab chief, Maurice Wilkins, was under the impression that Franklin was hired to work directly for him. She would have none of it, bruising Wilkins’s ego and leaving him to grumble to Crick about “our dark lady.” Eventually a truce was struck, with Wilkins and Franklin working separately on DNA. But Wilkins was still Franklin’s boss, which meant that he got copies of her photographs. In January 1953, he showed one particularly telling image to Watson. Now Watson could immediately see in those images how DNA was shaped. He and Crick also got hold of a summary of Franklin’s unpublished research she wrote up for the Medical Research Council, which guided them further to their solution. Neither bothered to consult Franklin about using her hard-earned pictures. The Cambridge and King’s teams then negotiated a plan to publish a set of papers in Nature on April 25, 1953. Crick and Watson unveiled their model in a paper that grabbed most of the attention. Franklin and Gosling published their X-ray data in another paper, which seemed to readers to be a “me-too” effort. Franklin died of cancer five years later, while Crick, Watson, and Wilkins went on to share the Nobel prize in 1962. In his 1968 book, The Double Helix, Watson would cruelly caricature Franklin as a belligerent, badly dressed woman who couldn’t appreciate what was in her pictures. That bitter fallout is a shame, because these scientists had together discovered something of exceptional beauty. They had found a molecular structure that could make heredity possible.

The Keeling Curve Courtesy the NASA Earth Observatory. NASA graph by Robert Simmon, based on data provided by the NOAA Climate Monitoring and Diagnostics Laboratory.   If the scientific story of global warming has one great hero, he is James Hansen, and not only because he is the most important climatologist of his era, whose massive computer models were demonstrating by the early 1980s that increased CO2 posed a dire threat.

My passing grade in modeling school was just because Evie'd dragged down the curve. She'd wear shades of lipstick you'd expect to see around the base of a penis. She'd wear so much eye shadow you'd think she was a product testing animal. Just from her hair spray, there's a hole in the ozone over the Taylor Robberts Modeling Academy.

THE CHASM – THE DIFFUSION MODEL WHY EVERYBODY HAS AN IPOD Why is it that some ideas – including stupid ones – take hold and become trends, while others bloom briefly before withering and disappearing from the public eye? Sociologists describe the way in which a catchy idea or product becomes popular as ‘diffusion’. One of the most famous diffusion studies is an analysis by Bruce Ryan and Neal Gross of the diffusion of hybrid corn in the 1930s in Greene County, Iowa. The new type of corn was better than the old sort in every way, yet it took twenty-two years for it to become widely accepted. The diffusion researchers called the farmers who switched to the new corn as early as 1928 ‘innovators’, and the somewhat bigger group that was infected by them ‘early adaptors’. They were the opinion leaders in the communities, respected people who observed the experiments of the innovators and then joined them. They were followed at the end of the 1930s by the ‘sceptical masses’, those who would never change anything before it had been tried out by the successful farmers. But at some point even they were infected by the ‘hybrid corn virus’, and eventually transmitted it to the die-hard conservatives, the ‘stragglers’. Translated into a graph, this development takes the form of a curve typical of the progress of an epidemic. It rises, gradually at first, then reaches the critical point of any newly launched product, when many products fail. The critical point for any innovation is the transition from the early adaptors to the sceptics, for at this point there is a ‘chasm’. According to the US sociologist Morton Grodzins, if the early adaptors succeed in getting the innovation across the chasm to the sceptical masses, the epidemic cycle reaches the tipping point. From there, the curve rises sharply when the masses accept the product, and sinks again when only the stragglers remain. With technological innovations like the iPod or the iPhone, the cycle described above is very short. Interestingly, the early adaptors turn away from the product as soon as the critical masses have accepted it, in search of the next new thing. The chasm model was introduced by the American consultant and author Geoffrey Moore. First they ignore you, then they laugh at you, then they fight you, then you win. Mahatma Gandhi

Near my feet is a glowing archway. The light is white and shimmery, like iridescent glitter, and it’s so tall the top nearly brushes the ceiling. Inside, instead of seeing the cement wall of the basement, I’m looking at evenly spaced wooden pillars and a reed-mat floor. Standing on that mat is a woman with curves that would make a Playboy model jealous. She’s wearing a long, butter yellow dress, and her white hair hangs down to her waist. She looks like an angel when she smiles at me, holding out her hands. “Hudson, come with me.” Her voice reminds me of the breeze rustling through the trees near the lake. Soft and subtle and calming. “Let me help you.” Did I die? Maybe the scratch on my side got infected. Maybe I’ve been slowly bleeding to death from internal injuries for the past week. Who knows? If this is death, if she’s what’s waiting for me on the other side, then fuck it. I’m letting go.

You have nothing to feel insecure about. It's a thing of beauty for a man to have a real woman to hold onto. All the models and actresses I've been with are so friggin' thin, I swear their chests are flatter than mine. But you, on the other hand, have one killer body. I can't keep my hands off you, baby, your curves drive me crazy.

learning—we have learned how to increase productivity, the outputs that can be produced with any inputs. There are two aspects of learning that we can distinguish: an improvement in best practices, reflected in increases in productivity of firms that marshal all available knowledge and technology, and improvements in the productivity of firms as they catch up to best practices. In fact, the distinction may be somewhat artificial; there may be no firm that has employed best practices in every aspect of its activities. One firm may be catching up with another in some dimension, but the second firm may be catching up with the first in others. In developing countries, almost all firms may be catching up with global best practices; but the real difference between developing and developed countries is the larger fraction of firms that are significantly below global best practices and the larger gap between their productivity and that of the best-performing firms. While we are concerned in this book with both aspects of learning, it is especially the learning associated with catching up that we believe has been given short shrift in the economics literature, and which is central to improvements in standards of living, especially in developing countries. But as we noted in chapter 1, the two are closely related; because of the improvements in best practices by the most innovative firms, most other firms are always engaged in a process of catching up. While the evidence of Solow and the work that followed demonstrated (what to many seems obvious) the importance of learning for increases in standards of living, to further explicate the role of learning, the first three sections of this chapter marshal other macro- and microeconomic evidence. In particular, we stress the pervasive gap between best practices and the productivity of most firms. We argue that this gap is far more important than the traditional allocative inefficiencies upon which most of economics has focused and is related to learning—or more accurately, the lack of learning. The final section provides a theoretical context within which to think about the sources of sustained increases in standards of living, employing the familiar distinction of movements of the production possibilities curve and movements toward the production possibilities curve. Using this framework, we explain why it is that we ascribe such importance to learning. Macroeconomic Perspectives There are several empirical arguments that can be brought to bear to support our conclusion concerning the importance of learning. The first is a simple argument: In theory, leading-edge technology is globally available. Thus, with sufficient capital and trained labor (or sufficient mobility for capital and trained labor), all countries should enjoy comparable standards of living. The only difference would be the rents associated with ownership of intellectual property rights and factor supplies. Yet there is an enormous divergence in economic performance and standards of living across national economies, far greater than can be explained by differences in factor supplies.1 And this includes many low-performing economies with high levels of capital intensity (especially among formerly socialist economies) and highly trained labor forces. Table 2.1 presents a comparison of formerly socialist countries with similar nonsocialist economies in the immediate aftermath of the collapse of the state-controlled model of economic activity. TABLE 2.1 Quality of Life Comparisons, 1992–1994 (U.S. $) Source: Greenwald and Khan (2009), p. 30. In most of these cases, at the time communism was imposed after World War II, the subsequently socialist economies enjoyed higher levels of economic development than

the bell curve serves as both a model and a fitting symbol of an archaic public education system. It describes a broad swath of mediocrity flanked by a sliver of excellence and a ribbon of failure” (Wallace & Graves, 1995, p. 24).

The S curve is not just important as a model in its own right; it’s also the jack-of-all-trades of mathematics. If you zoom in on its midsection, it approximates a straight line. Many phenomena we think of as linear are in fact S curves, because nothing can grow without limit. Because of relativity, and contra Newton, acceleration does not increase linearly with force, but follows an S curve centered at zero. So does electric current as a function of voltage in the resistors found in electronic circuits, or in a light bulb (until the filament melts, which is itself another phase transition). If you zoom out from an S curve, it approximates a step function, with the output suddenly changing from zero to one at the threshold. So depending on the input voltages, the same curve represents the workings of a transistor in both digital computers and analog devices like amplifiers and radio tuners. The early part of an S curve is effectively an exponential, and near the saturation point it approximates exponential decay. When someone talks about exponential growth, ask yourself: How soon will it turn into an S curve? When will the population bomb peter out, Moore’s law lose steam, or the singularity fail to happen? Differentiate an S curve and you get a bell curve: slow, fast, slow becomes low, high, low. Add a succession of staggered upward and downward S curves, and you get something close to a sine wave. In fact, every function can be closely approximated by a sum of S curves: when the function goes up, you add an S curve; when it goes down, you subtract one. Children’s learning is not a steady improvement but an accumulation of S curves. So is technological change. Squint at the New York City skyline and you can see a sum of S curves unfolding across the horizon, each as sharp as a skyscraper’s corner. Most importantly for us, S curves lead to a new solution to the credit-assignment problem. If the universe is a symphony of phase transitions, let’s model it with one. That’s what the brain does: it tunes the system of phase transitions inside to the one outside. So let’s replace the perceptron’s step function with an S curve and see what happens.

People are not interchangeable. They come from a variety of backgrounds and with a varied set of personalities, strengths, and goals. To be the best manager, you must manage to the person, accounting for each individual’s unique set of characteristics and current challenges. Craft unique roles that amplify each individual’s strengths and motivations. Avoid the Peter principle by promoting people only to roles in which they can succeed. Properly delineate roles and responsibilities using the model of DRI (directly responsible individual). People need coaching to reach their full potential, especially at new roles. Deliberate practice is the most effective way to help people scale new learning curves. Use the consequence-conviction matrix to look for learning opportunities, and use radical candor within one-on-ones to deliver constructive feedback. When trying new things, watch out for common psychological failure modes like impostor syndrome and the Dunning-Kruger effect. Actively define group culture and consistently engage in winning hearts and minds toward your desired culture and associated vision. If you can set people up for success in the right roles and well-defined culture, then you can create the environment for 10x teams to emerge.

Programming languages, their features, readability, and interoperation Code reuse across platforms (server vs web vs mobile) Early error detection (compile-time vs runtime error detection, breadth of validation) Availability and cost of hiring the right talent; learning curve for new hires Readability and refactorability of code Approach to code composition, embracing the change Datastore and general approach to data modeling Application-specific data model, and the blast radius from changing it Performance and latency in all tiers and platforms Scalability and redundancy Spiky traffic patterns, autoscaling, capacity planning Error recovery Logging, telemetry, and other instrumentation Reducing complexity User interfaces and their maintainability External APIs User identity and security Hardware and human costs of the infrastructure and its maintenance Enabling multiple concurrent development workstreams Enabling testability Fast-tracking development by adopting third-party frameworks

This room contained, as well as many books, several painted wooden models of boats, which had been mounted to the walls. They were very intricately and beautifully made, down to the miniature coils of rope and tiny brass instruments on their sanded decks, and the larger ones had white sails arranged in curving attitudes of such tension and complexity that it did indeed seem as though the wind was blowing in them. When you looked more closely, you saw that the sails were attached to countless tiny cords, so fine as to make them almost invisible, which had fixed them in these shapes. It required only a couple of steps to move from the impression of wind in the sails to the sight of the mesh of fine cords, a metaphor I felt sure Clelia had intended to illustrate the relationship between illusion and reality, though she did not perhaps expect her guests to go one step further, as I did, and reach out a hand to touch the white cloth, which was not cloth at all but paper, unexpectedly dry and brittle. Clelia’s

Skin in the game can make boring things less boring. When you have skin in the game, dull things like checking the safety of the aircraft because you may be forced to be a passenger in it cease to be boring. If you are an investor in a company, doing ultra-boring things like reading the footnotes of a financial statement (where the real information is to be found) becomes, well, almost not boring. But there is an even more vital dimension. Many addicts who normally have a dull intellect and the mental nimbleness of a cauliflower—or a foreign policy expert—are capable of the most ingenious tricks to procure their drugs. When they undergo rehab, they are often told that should they spend half the mental energy trying to make money as they did procuring drugs, they are guaranteed to become millionaires. But, to no avail. Without the addiction, their miraculous powers go away. It was like a magical potion that gave remarkable powers to those seeking it, but not those drinking it. A confession. When I don’t have skin in the game, I am usually dumb. My knowledge of technical matters, such as risk and probability, did not initially come from books. It did not come from lofty philosophizing and scientific hunger. It did not even come from curiosity. It came from the thrills and hormonal flush one gets while taking risks in the markets. I never thought mathematics was something interesting to me until, when I was at Wharton, a friend told me about the financial options I described earlier (and their generalization, complex derivatives). I immediately decided to make a career in them. It was a combination of financial trading and complicated probability. The field was new and uncharted. I knew in my guts there were mistakes in the theories that used the conventional bell curve and ignored the impact of the tails (extreme events). I knew in my guts that academics had not the slightest clue about the risks. So, to find errors in the estimation of these probabilistic securities, I had to study probability, which mysteriously and instantly became fun, even gripping. When there was risk on the line, suddenly a second brain in me manifested itself, and the probabilities of intricate sequences became suddenly effortless to analyze and map. When there is fire, you will run faster than in any competition. When you ski downhill some movements become effortless. Then I became dumb again when there was no real action. Furthermore, as traders the mathematics we used fit our problem like a glove, unlike academics with a theory looking for some application—in some cases we had to invent models out of thin air and could not afford the wrong equations. Applying math to practical problems was another business altogether; it meant a deep understanding of the problem before writing the equations.

it has faced the challenge of establishing its relevance to baby boomers who reject the Leisure World model of late adulthood

The incremental mindset focuses on making something better, while the exponential mindset is focused on making something different,” he notes. “Incremental is satisfied with 10 percent. Exponential is out for 10X.”14 “The incremental mindset draws a straight line from the present to the future,” Bonchek continues. “A ‘good’ incremental business plan enables you to see exactly how you will get from here to there. But exponential models are not straight. They are like a bend in the road that prevents you from seeing around the corner, except in this case the curve goes up.

There are five ways technology can boost marketing practices: Make more informed decisions based on big data. The greatest side product of digitalization is big data. In the digital context, every customer touchpoint—transaction, call center inquiry, and email exchange—is recorded. Moreover, customers leave footprints every time they browse the Internet and post something on social media. Privacy concerns aside, those are mountains of insights to extract. With such a rich source of information, marketers can now profile the customers at a granular and individual level, allowing one-to-one marketing at scale. Predict outcomes of marketing strategies and tactics. No marketing investment is a sure bet. But the idea of calculating the return on every marketing action makes marketing more accountable. With artificial intelligence–powered analytics, it is now possible for marketers to predict the outcome before launching new products or releasing new campaigns. The predictive model aims to discover patterns from previous marketing endeavors and understand what works, and based on the learning, recommend the optimized design for future campaigns. It allows marketers to stay ahead of the curve without jeopardizing the brands from possible failures. Bring the contextual digital experience to the physical world. The tracking of Internet users enables digital marketers to provide highly contextual experiences, such as personalized landing pages, relevant ads, and custom-made content. It gives digital-native companies a significant advantage over their brick-and-mortar counterparts. Today, the connected devices and sensors—the Internet of Things—empowers businesses to bring contextual touchpoints to the physical space, leveling the playing field while facilitating seamless omnichannel experience. Sensors enable marketers to identify who is coming to the stores and provide personalized treatment. Augment frontline marketers’ capacity to deliver value. Instead of being drawn into the machine-versus-human debate, marketers can focus on building an optimized symbiosis between themselves and digital technologies. AI, along with NLP, can improve the productivity of customer-facing operations by taking over lower-value tasks and empowering frontline personnel to tailor their approach. Chatbots can handle simple, high-volume conversations with an instant response. AR and VR help companies deliver engaging products with minimum human involvement. Thus, frontline marketers can concentrate on delivering highly coveted social interactions only when they need to. Speed up marketing execution. The preferences of always-on customers constantly change, putting pressure on businesses to profit from a shorter window of opportunity. To cope with such a challenge, companies can draw inspiration from the agile practices of lean startups. These startups rely heavily on technology to perform rapid market experiments and real-time validation.

You may go through two, three, or more iterations of the product, and by the nth iteration, the model you created for the first iteration will be hopelessly inappropriate. Paradoxically, emphasizing a business model prematurely, you may block yourself from the best money-making opportunities.

Developed by E.M. Rogers in 1962, the S-curve model is an attempt to understand how, why, and at what rate ideas and products spread throughout cultures. Adoption is relatively slow at first, at the base of the S, until a tipping point, or knee of the curve, is reached. You then move into hypergrowth, up the sleek, steep back of the curve. This is usually at somewhere between 10 to 15 percent of market penetration. At the flat part at the top of the S, you've reached saturation, typically at 90 percent.

Chain code Labs to be able to Host an additional Run regarding Its Month-Long Bitcoin Html coding Class Chain code Labs, the newest York-based improvement company and also a major factor to Bitcoin Core, will be organizing an extra edition involving its Bitcoin residency put in the first weeks of 2018. The program expects to help designers overcome the particular steep understanding curve connected with becoming a protocol-level contributor for you to projects just like Bitcoin Key. In doing, therefore , Chaincode Amenities hopes to aid expand Bitcoin’s development neighborhood. “Last 12 months was the 1st run, ” Chaincode System developer David Newbery advised Bitcoin Journal. “We have today taken the favorable stuff from this and attempted to make it a lot more focused along with useful for occupants this year. ” The Residency Program Chain code Labs, inside collaboration together with Matt Corallo - who also worked from Blockstream this past year but became a member of Chaincode Facility since: organized typically the residency plan for the first time throughout September in addition to October connected with 2016. Another edition begins on The month of January 29, 2018, and will previous until Feb. 23. Newbery himself has been one of the guests of this initial residency software. He was afterward hired simply by Chaincode Amenities and has given that been the most prolific contributing factors to the Bitcoin Core job. Now, he or she is coordinating the next of a couple of legs in the new course. “Chaincode System exists to boost Bitcoin, ” said Newbery. “We do that by simply contributing to Bitcoin Core, yet each of people has a lot with the freedom to accomplish what we consider is important. As well as the main function of this residency program is always to try to improve the designer community. ” Specifically, classes will cover standard protocol design, adversarial thinking, risk models plus security things to consider, as well as deal with some of Bitcoin’s biggest problems, like climbing, fungibility and also privacy. Guests will mostly discover by doing and might even commence contributing to often the Bitcoin-Central project through the residency. Through the program will have them assisted from the entire Chaincode Labs crew - Alex Morcos, Suhas Daftuar, Shiny Corallo, Ruben Newbery along with Russ Yanofsky. There are often guest loudspeakers.

My company provides personal guarding services to foreign dignitaries, billionaires, politicians, sports teams, movie and Broadway stars---" "Movie and Broadway stars?" Zara grabbed his tie and yanked him forward until they were almost nose to nose. "Names. Give me names. Who have you guarded? A-list? B-list? Anyone from Hamilton?" Her full attention was on him now and it was hard not to get pulled into the depths of her liquid brown eyes. "Our client list is confidential." "Did you work for Lin-Manuel Miranda?" She tipped her head back and gave the kind of groan he'd only ever heard from a woman between the sheets. "What was he like? Tell me. No. Don't tell me. We're in public and I can't be responsible for what might happen if you do." His mouth opened but no words came out. He'd convinced himself there was no chemistry between them. But now, with her face only inches away, he was almost overwhelmed with the desire to taste the curve of her lips. "C'mon, Jay." She leaned close, the gold flecks in her eyes sparkling, her voice a husky purr that he felt as a throb in his groin. Had he ever met a woman with eyelashes so long? He could swear that every time she blinked, they swept over her cheeks. "Just one name," she pleaded. "One itty-bitty little name for me to fantasize about when I'm alone in bed tonight." She ran her tongue over her bottom lip, slow and sensual. "Or even better, an introduction. I'll make it worth your while." Jay swallowed hard, loosened his collar. Need, tightly controlled, began to unravel. He knew he shouldn't ask, but the words came out just the same. "What do you mean worth my while?" "What do you want, Jay?" Her breath whispered against his cheek. "What is your greatest desire? World domination? Ten glamor models in a limo? Your own island? An endless supply of samosas? Six blue silk ties? A perfectly balanced set of accounts? A night of hot sex, no strings attached...?

The same approaches will not always work. As we climb the evolution curve, we would need new tools, techniques and models to keep up with the evolution pace.

the discovery of a crumpled love note in Kazuko’s school locker. Kazuko had striking cheekbones. They glazed the sunshine and sliced the shadows into two parts: darker and lighter. Her eyes sat on top of her cheekbones with a curve, sliding into her temples. Boys stuttered at her; she could correct their grammar while all they could think about was kissing her pert lips. She enrolled in modelling school and learned about manicures, pedicures, skin massage points, creams and the secrets of a flawless complexion. “Look at me, Toyo-nesan!” she exclaimed with a heavy book balanced on her head, walking back and forth along the corridor. “This is how models walk.” Toyo lived with Ryu in the building that housed his menswear shop. From her window she could see customers entering and exiting, the traffic from the nearby train station ebbing and flowing as work began and finished. At first Ryu did not want her to assist in the shop. She could not see why and was affronted by his refusal even to let her come downstairs: “Get back up, Toyo! Don’t let the customers see you.” Kazuko told Toyo that he wanted to keep her beauty all to himself, that her entry into the Zhang family was already spreading like wildfire down the street, and the increased traffic past the menswear shop consisted, partially, of

Erlang himself, working for the Copenhagen Telephone Company in the early twentieth century, used it to model how much time could be expected to pass between successive calls on a phone network. Since then, the Erlang distribution has also been used by urban planners and architects to model car and pedestrian traffic, and by networking engineers designing infrastructure for the Internet. There are a number of domains in the natural world, too, where events are completely independent from one another and the intervals between them thus fall on an Erlang curve. Radioactive decay is one example, which means that the Erlang distribution perfectly models when to expect the next ticks of a Geiger counter. It also turns out to do a pretty good job of describing certain human endeavors—such as the amount of time politicians stay in the House of Representatives.

Regression: This is a well-understood technique from the field of statistics. The goal is to find a best fitting curve through the many data points. The best fitting curve is that which minimizes the (error) distance between the actual data points and the values predicted by the curve.  Regression models can be projected into the future for prediction and forecasting purposes.

Heterogeneous effects might be hidden because PD plots only show the average marginal effects. Suppose that for a feature half your data points have a positive association with the prediction – the larger the feature value the larger the prediction – and the other half has a negative association – the smaller the feature value the larger the prediction. The PD curve could be a horizontal line, since the effects of both halves of the dataset could cancel each other out. You then conclude that the feature has no effect on the prediction. By plotting the individual conditional expectation curves instead of the aggregated line, we can uncover heterogeneous effects.

I don’t want to hear it,” Sophie growled. “What kind of a husband are you? You can’t even get it up for this?” She thrust out one hip and ran a hand down her side, like a showroom model caressing the curves of a new car.

neutral stability normally occurs only at transitions, at critical settings of a system’s parameters (the “knobs” that control its properties). But the Kuramoto model was breaking this rule. Its incoherent state was doggedly staying neutrally stable, even as we widened the bell curve to make the population more diverse. Turning that knob over a wide range of parameters made no difference.

Ive’s design team had obsessed over the rounded corners of the phone and become advocates of Bézier curves, a concept from computer modeling used to eliminate the transition breaks between straight and curved surfaces. The Bézier geometry gave the iPhone rounded corners that arched like a sculpture. A standard rounded corner consists of a single-radius arch or a quarter circle, whereas their curves were mapped through a dozen points, creating a more gradual and natural transition. Meanwhile, Forstall used a standard three-point curve in the corners of iPhone apps. Each time Ive opened his iPhone, he could see the difference between the phone’s carefully crafted corners and the software’s clunky corners. He was powerless to change those features because Jobs excluded him from software design meetings. He could only look at them and fume.

If dying and rising with Christ is the new normal, then when we encounter dying, we don’t have to collapse or withdraw into ourselves. We can be weak, even depressed. This frees us from our tendency to be depressed about our depression. Because depression avoidance is such a high value in our culture, when people are depressed, they think something is wrong. It’s a relief to realize that if we’re dealing with hard things, we should be depressed. Jesus models depression for us in his Passion as he is overcome by the weight of his coming death. Our modern obsession with creating a pain-free self lays a great burden on us.

Silicon Valley’s and China’s internet ecosystems grew out of very different cultural soil. Entrepreneurs in the valley are often the children of successful professionals, such as computer scientists, dentists, engineers, and academics. Growing up they were constantly told that they—yes, they in particular—could change the world. Their undergraduate years were spent learning the art of coding from the world’s leading researchers but also basking in the philosophical debates of a liberal arts education. When they arrived in Silicon Valley, their commutes to and from work took them through the gently curving, tree-lined streets of suburban California. It’s an environment of abundance that lends itself to lofty thinking, to envisioning elegant technical solutions to abstract problems. Throw in the valley’s rich history of computer science breakthroughs, and you’ve set the stage for the geeky-hippie hybrid ideology that has long defined Silicon Valley. Central to that ideology is a wide-eyed techno-optimism, a belief that every person and company can truly change the world through innovative thinking. Copying ideas or product features is frowned upon as a betrayal of the zeitgeist and an act that is beneath the moral code of a true entrepreneur. It’s all about “pure” innovation, creating a totally original product that generates what Steve Jobs called a “dent in the universe.” Startups that grow up in this kind of environment tend to be mission-driven. They start with a novel idea or idealistic goal, and they build a company around that. Company mission statements are clean and lofty, detached from earthly concerns or financial motivations. In stark contrast, China’s startup culture is the yin to Silicon Valley’s yang: instead of being mission-driven, Chinese companies are first and foremost market-driven. Their ultimate goal is to make money, and they’re willing to create any product, adopt any model, or go into any business that will accomplish that objective. That mentality leads to incredible flexibility in business models and execution, a perfect distillation of the “lean startup” model often praised in Silicon Valley. It doesn’t matter where an idea came from or who came up with it. All that matters is whether you can execute it to make a financial profit. The core motivation for China’s market-driven entrepreneurs is not fame, glory, or changing the world. Those things are all nice side benefits, but the grand prize is getting rich, and it doesn’t matter how you get there.

On the other hand, when a company’s value curve lacks focus, its cost structure will tend to be high and its business model complex in implementation and execution. When it lacks divergence, a company’s strategy is a me-too, with no reason to stand apart in the marketplace. When it lacks a compelling tagline that speaks to buyers, it is likely to be internally driven or a classic example of innovation for innovation’s sake with no great commercial potential and no natural take-off capability. A Company Caught in the Red Ocean When a company’s value curve converges with its competitors, it signals that a company is likely caught within the red ocean of bloody competition. A company’s explicit or implicit strategy tends to be trying to outdo its competition on the basis of cost or quality. This signals slow growth unless, by the grace of luck, the company benefits from being in an industry that is growing on its own accord. This growth is not due to a company’s strategy, however, but to luck. Overdelivery without Payback When a company’s value curve on the strategy canvas is shown to deliver high levels across all factors, the question is, Does the company’s market share and profitability reflect these investments? If not, the strategy canvas signals that the company may be oversupplying its customers, offering too much of those elements that add incremental value to buyers. To value-innovate, the company must decide which factors to eliminate and reduce—and not only those to raise and create—to construct a divergent value curve. Strategic Contradictions Are there strategic contradictions? These are areas where a company is offering a high level on one competing factor while ignoring others that support that factor. An example is investing heavily in making a company’s website easy to use but failing to correct the site’s slow speed of operation. Strategic inconsistencies can also be found between the level of your offering and your price. For example, a petroleum station company found that it offered “less for more”: fewer services than the best competitor at a higher price. No wonder it was losing market share fast.

I worry about our shrinking industrial base and the loss of a highly skilled workforce that has kept America the unchallenged aerospace leader since World War II. By layoffs and attrition we are losing skilled toolmakers and welders, machinists and designers, wind tunnel model makers and die makers too. And we are also losing the so-called second tier—the mom-and-pop shops of subcontractors who supplied the nuts and bolts of the industry, from flight controls to landing gears. The old guard is retiring or being let go, while the younger generation of new workers lucky enough to hold aerospace jobs has too little to do to overcome a steep learning curve any time soon.

Mathematics teaches us that the solution of the Malthus equation dx/dt = x is uniquely defined by the initial conditions (that is that the corresponding integral curves in the (t,x)-plane do not intersect each other). This conclusion of the mathematical model bears little relevance to the reality. A computer experiment shows that all these integral curves have common points on the negative t-semi-axis. Indeed, say, curves with the initial conditions x(0) = 0 and x(0) = 1 practically intersect at t = -10 and at t = -100 you cannot fit in an atom between them. Properties of the space at such small distances are not described at all by Euclidean geometry. Application of the uniqueness theorem in this situation obviously exceeds the accuracy of the model. This has to be respected in practical application of the model, otherwise one might find oneself faced with serious troubles.

THE KOCH SNOWFLAKE. “A rough but vigorous model of a coastline,” in Mandelbrot’s words. To construct a Koch curve, begin with a triangle with sides of length 1. At the middle of each side, add a new triangle one-third the size; and so on. The length of the boundary is 3 × 4/3 × 4/3 × 4/3…—infinity. Yet the area remains less than the area of a circle drawn around the original triangle. Thus an infinitely long line surrounds a finite area.

Jim Cramer’s Mad Money is one of the most popular shows on CNBC, a cable TV network that specializes in business and financial news. Cramer, who mostly offers investment advice, is known for his sense of showmanship. But few viewers were prepared for his outburst on August 3, 2007, when he began screaming about what he saw as inadequate action from the Federal Reserve: “Bernanke is being an academic! It is no time to be an academic. . . . He has no idea how bad it is out there. He has no idea! He has no idea! . . . and Bill Poole? Has no idea what it’s like out there! . . . They’re nuts! They know nothing! . . . The Fed is asleep! Bill Poole is a shame! He’s shameful!!” Who are Bernanke and Bill Poole? In the previous chapter we described the role of the Federal Reserve System, the U.S. central bank. At the time of Cramer’s tirade, Ben Bernanke, a former Princeton professor of economics, was the chair of the Fed’s Board of Governors, and William Poole, also a former economics professor, was the president of the Federal Reserve Bank of St. Louis. Both men, because of their positions, are members of the Federal Open Market Committee, which meets eight times a year to set monetary policy. In August 2007, Cramerwas crying outforthe Fed to change monetary policy in order to address what he perceived to be a growing financial crisis. Why was Cramer screaming at the Federal Reserve rather than, say, the U.S. Treasury—or, for that matter, the president? The answer is that the Fed’s control of monetary policy makes it the first line of response to macroeconomic difficulties—very much including the financial crisis that had Cramer so upset. Indeed, within a few weeks the Fed swung into action with a dramatic reversal of its previous policies. In Section 4, we developed the aggregate demand and supply model and introduced the use of fiscal policy to stabilize the economy. In Section 5, we introduced money, banking, and the Federal Reserve System, and began to look at how monetary policy is used to stabilize the economy. In this section, we use the models introduced in Sections 4 and 5 to further develop our understanding of stabilization policies (both fiscal and monetary), including their long-run effects on the economy. In addition, we introduce the Phillips curve—a short-run trade-off between unexpected inflation and unemployment—and investigate the role of expectations in the economy. We end the section with a brief summary of the history of macroeconomic thought and how the modern consensus view of stabilization policy has developed.

So what’s the endgame? The upward cycle of curve upon curve can’t continue forever. Bodies age, congregations decline, and nations rise and fall. Certainly, we cannot launch curve after curve in perpetuity. But we can use this model to transfer momentum to the next generation. This is not about the ongoing existence of one particular church but the future health of Jesus’ church and the forward momentum of the gospel from one era to the next.

Table 14.1 also shows R-square (R2), which is called the coefficient of determination. R-square is of great interest: its value is interpreted as the percentage of variation in the dependent variable that is explained by the independent variable. R-square varies from zero to one, and is called a goodness-of-fit measure.5 In our example, teamwork explains only 7.4 percent of the variation in productivity. Although teamwork is significantly associated with productivity, it is quite likely that other factors also affect it. It is conceivable that other factors might be more strongly associated with productivity and that, when controlled for other factors, teamwork is no longer significant. Typically, values of R2 below 0.20 are considered to indicate weak relationships, those between 0.20 and 0.40 indicate moderate relationships, and those above 0.40 indicate strong relationships. Values of R2 above 0.65 are considered to indicate very strong relationships. R is called the multiple correlation coefficient and is always 0 ≤ R ≤ 1. To summarize up to this point, simple regression provides three critically important pieces of information about bivariate relationships involving two continuous variables: (1) the level of significance at which two variables are associated, if at all (t-statistic), (2) whether the relationship between the two variables is positive or negative (b), and (3) the strength of the relationship (R2). Key Point R-square is a measure of the strength of the relationship. Its value goes from 0 to 1. The primary purpose of regression analysis is hypothesis testing, not prediction. In our example, the regression model is used to test the hypothesis that teamwork is related to productivity. However, if the analyst wants to predict the variable “productivity,” the regression output also shows the SEE, or the standard error of the estimate (see Table 14.1). This is a measure of the spread of y values around the regression line as calculated for the mean value of the independent variable, only, and assuming a large sample. The standard error of the estimate has an interpretation in terms of the normal curve, that is, 68 percent of y values lie within one standard error from the calculated value of y, as calculated for the mean value of x using the preceding regression model. Thus, if the mean index value of the variable “teamwork” is 5.0, then the calculated (or predicted) value of “productivity” is [4.026 + 0.223*5 =] 5.141. Because SEE = 0.825, it follows that 68 percent of productivity values will lie 60.825 from 5.141 when “teamwork” = 5. Predictions of y for other values of x have larger standard errors.6 Assumptions and Notation There are three simple regression assumptions. First, simple regression assumes that the relationship between two variables is linear. The linearity of bivariate relationships is easily determined through visual inspection, as shown in Figure 14.2. In fact, all analysis of relationships involving continuous variables should begin with a scatterplot. When variable

relationships are nonlinear (parabolic or otherwise heavily curved), it is not appropriate to use linear regression. Then, one or both variables must be transformed, as discussed in Chapter 12. Second, simple regression assumes that the linear relationship is constant over the range of observations. This assumption is violated when the relationship is “broken,” for example, by having an upward slope for the first half of independent variable values and a downward slope over the remaining values. Then, analysts should consider using two regression models each for these different, linear relationships. The linearity assumption is also violated when no relationship is present in part of the independent variable values. This is particularly problematic because regression analysis will calculate a regression slope based on all observations. In this case, analysts may be misled into believing that the linear pattern holds for all observations. Hence, regression results always should be verified through visual inspection. Third, simple regression assumes that the variables are continuous. In Chapter 15, we will see that regression can also be used for nominal and dichotomous independent variables. The dependent variable, however, must be continuous. When the dependent variable is dichotomous, logistic regression should be used (Chapter 16). Figure 14.2 Three Examples of r The following notations are commonly used in regression analysis. The predicted value of y (defined, based on the regression model, as y = a + bx) is typically different from the observed value of y. The predicted value of the dependent variable y is sometimes indicated as ŷ (pronounced “y-hat”). Only when R2 = 1 are the observed and predicted values identical for each observation. The difference between y and ŷ is called the regression error or error term

The lovely young lady in the mirror was not a stranger, nor was she Lady Overlooked. Once again, Brierly had found some essential core of her model and designed the whole dress around it. Brierly had gathered Nissa’s brown hair in a loose pile on top of her head, with a curl spilling over here and there. The comb secured a single rose just verging on full bloom. Nissa still looked short and sturdy but—endearingly so. A friendly elf. Youthful, but not childish. The dress flattered and concealed the correct curves. Not even Aunt Perturbance would mistake her for fifteen tonight. Nissa blushed–ith pleasure at her appearance, yes–but mainly that her childhood heroine would think so highly of her as to craft such a masterpiece. That she would know her so well as to reflect the true Nissa, but love her so well as to reflect the best possible Nissa.

Fashion models today are so different from the women buying the clothes. That has not always been the case. If you look at issues of ‘Vogue’ or other fashion magazines from the 1950s, you’ll see models in possession of womanly (albeit spectacular) bodies and expressive, mature faces. Star models typically were over thirty, and they had curves. They just looked like extraglamorous versions of the women buying the dresses. It almost seems shocking now, when models are all in their teens and look as though they’re playing dress up. In 2011 there was a cover of French ‘Vogue’ featuring a ten-year-old model. Ten years old! Did she look ten? No, she looked twenty-five! What does that say to young people? I worry about the pressure this puts on teenagers and tweens.

Marilyn Monroe was pretty far along that curve, as close as one can come to dancing while still walking. In her classic 1953 movie Niagara she takes a legendary walk away from the camera, hips swinging—roiling—in a mode long since memorialized by catwalk models, drag queens, prima donnas, freaks and queers, street punks of all persuasions.

One study of America’s Fortune 500 companies found that the one quarter with the most female executives had a return on equity 35 percent higher than the quarter with the fewest female executives. On the Japanese stock exchange, the companies with the highest proportion of female employees performed nearly 50 percent better than those with the lowest. In each case, the most likely reason isn’t that female executives are geniuses. Rather, it is that companies that are innovative enough to promote women are also ahead of the curve in reacting to business opportunities. That is the essence of a sustainable economic model. Moving women into more productive roles helps curb population growth and nurtures a sustainable society.

That kind of Bible works, because that is our story, too. The Bible “partners” with us (so to speak), modeling for us our walk with God in discovering greater depth and maturity on our journey of faith, not by telling us what to do at each step, but by showing us a journey of hills and valleys, straight lanes and difficult curves, of new discoveries and insights, of movement and change—with God by our side every step of the way.

The Bible speaks of beauty in Psalm 27 as a characteristic of God, greatly to be desired. In fact, David says that to “gaze on the beauty of the Lord” is the one and only thing he really desires (Ps. 27:4). In another hint, the first example of God filling someone with his Spirit comes about in Exodus 31 when men are filled with God’s Spirit in order to create beautiful things for the tabernacle. A third indirect reference is when the Bible speaks of the beauty of creation and how that beauty reflects the glory of God (Ps. 19:1). These may not give us a Ten Commandments of beauty (always do this, never do that; blue is beautiful, green is not; straight lines are more beautiful than curved ones; or similar nonsense), but what these examples do is require us to consider the nature of beauty because the Scriptures teach that God is to be the fulfillment of our desire for beauty. God intends and empowers us to make beautiful things, and his glory is reflected in the beauty of his own handiwork, giving us a model to follow as men and women created in his image.

For infectious diseases, simulations rely on models based on bioinformatics, displaying the beginning and end of the curve, anticipating different waves of the epidemic (Mackenzie 2003).