Line Graph Quotes

It surprised him that his grief was sharper than in the past few days. He had forgotten that grief does not decline in a straight line or along a slow curve like a graph in a child's math book. Instead, it was almost as if his body contained a big pile of garden rubbish full both of heavy lumps of dirt and of sharp thorny brush that would stab him when he least expected it.

I still remember the day I got my first calculator Teacher: All right, children, welcome to fourth grade math. Everyone take a calculator out of the bin. Me: What are these? Teacher: From now on we'll be using calculators. Me: What do these things do? Teacher: Simple operations, like multiplication and division. Me: You mean this device just...does them? By itself? Teacher: Yes. You enter in the problem and press equal. Me: You...you knew about this machine all along, didn't you? This whole time, while we were going through this...this charade with the pencils and the line paper and the stupid multiplication tables!...I'm sorry for shouting...It's just...I'm a little blown away. Teacher: Okay, everyone, today we're going to go over some word problems. Me: What the hell else do you have back there? A magical pen that writes book reports by itself? Some kind of automatic social studies worksheet that...that fills itself out? What the hell is going on? Teacher: If a farmer farms five acres of land a day-- Me: So that's it, then. The past three years have been a total farce. All this time I've been thinking, "Well, this is pretty hard and frustrating but I guess these are useful skills to have." Meanwhile, there was a whole bin of these things in your desk. We could have jumped straight to graphing. Unless, of course, there's some kind of graphing calculator! Teacher: There is. You get one in ninth grade. Me: Is this...Am I on TV? Is this a prank show? Teacher: No.

The graph of life is not a straight line— Initiatives climax to gradually decline. The world is infused with greed and hate— Where innocent errors may alter one's fate. Where the fulfillment of desires fails to satiate— Where turbulence is a constant state.

Whether we accept it or not, this will likely be the century that determines what the optimal human population is for our planet. It will come about in one of two ways: Either we decide to manage our own numbers, to avoid a collision of every line on civilization's graph - or nature will do it for us, in the form of famines, thirst, climate chaos, crashing ecosystems, opportunistic disease, and wars over dwindling resources that finally cut us down to size.

Progress isn't linear, though. If you plotted it onto a graph, it wouldn't be this straight line up towards happiness. It would wiggle backwards, then forwards, up and down. You might feel worse in a month from now than you did a few weeks after it happened. But that doesn't mean you're not healing. It just means that we all experience emotions at different times.

Though blessed with the enviable properties of a mink coat—graceful, unreasonable, and impractical no matter what she was draped over—she was nevertheless one of those people whose personality proved to be the bane of modern mathematicians. She was neither a flat nor solid shape. She showed no symmetry at all. Trigonometry, Calculus and Statistics all proved useless. Her Pie Chart was a muddle of arbitrary wedges, her Line Graph, the silhouette of the Alps. And just when one listed her under Chaos Theory—Butterfly Effects, Weather Predictions, Fractals, Bifurcation diagrams and whatnot—she showed up as an equilateral triangle, sometimes even a square.

Past the flannel plains and blacktop graphs and skylines of canted rust, and past the tobacco-brown river overhung with weeping trees and coins of sunlight through them on the water downriver, to the place beyond the windbreak, where untilled fields simmer shrilly in the A.M. heat: shattercane, lamb's-quarter, cutgrass, sawbrier, nutgrass, jimsonweed, wild mint, dandelion, foxtail, muscadine, spinecabbage, goldenrod, creeping charlie, butter-print, nightshade, ragweed, wild oat, vetch, butcher grass, invaginate volunteer beans, all heads gently nodding in a morning breeze like a mother's soft hand on your cheek. An arrow of starlings fired from the windbreak's thatch. The glitter of dew that stays where it is and steams all day. A sunflower, four more, one bowed, and horses in the distance standing rigid and still as toys. All nodding. Electric sounds of insects at their business. Ale-colored sunshine and pale sky and whorls of cirrus so high they cast no shadow. Insects all business all the time. Quartz and chert and schist and chondrite iron scabs in granite. Very old land. Look around you. The horizon trembling, shapeless. We are all of us brothers. Some crows come overhead then, three or four, not a murder, on the wing, silent with intent, corn-bound for the pasture's wire beyond which one horse smells at the other's behind, the lead horse's tail obligingly lifted. Your shoes' brand incised in the dew. An alfalfa breeze. Socks' burrs. Dry scratching inside a culvert. Rusted wire and tilted posts more a symbol of restraint than a fence per se. NO HUNTING. The shush of the interstate off past the windbreak. The pasture's crows standing at angles, turning up patties to get at the worms underneath, the shapes of the worms incised in the overturned dung and baked by the sun all day until hardened, there to stay, tiny vacant lines in rows and inset curls that do not close because head never quite touches tail. Read these.

People always spoke of healing as if it were predictable and progressive, a decisive diagonal line pointing from the lower left-hand corner of a graph to the upper right.

Look at that," he said. "How the ink bleeds." He loved the way it looked, to write on a thick pillow of the pad, the way the thicker width of paper underneath was softer and allowed for a more cushiony interface between pen and surface, which meant more time the two would be in contact for any given point, allowing the fiber of the paper to pull, through capillary action, more ink from the pen, more ink, which meant more evenness of ink, a thicker, more even line, a line with character, with solidity. The pad, all those ninety-nine sheets underneath him, the hundred, the even number, ten to the second power, the exponent, the clean block of planes, the space-time, really, represented by that pad, all of the possible drawings, graphs, curves, relationships, all of the answers, questions, mysteries, all of the problems solvable in that space, in those sheets, in those squares.

Spare’s drawings were always inspired by the New Aesthetic, the New Sexuality. They amount almost to masturbation in line; the line coils and curls upon itself and mounts the steep incline of ecstasy as the amazing sigils are woven into a complex web of dream. To follow closely the line of some of his Sabbatic drawings is to leave earth and dive obliquely between those spaces that Lovecraft celebrated in his nightmare tales. Such drawings are themselves the gateway to the Sabbath; one is drawn into a vortex and whirled down the funnel of consciousness which explodes into unknown worlds. Spare would not reveal the magical graphs that unsealed the cells of these eldritch dimensions…

The truth is staggering, colossal, unfathomable, so we cling to our bite-sized lies. We organize knowledge into bulleted lists and line graphs while the wisdom of the present moment sits patiently at the doors of our perception. Tackling

Some people engage in retail therapy, buying new things to make themselves feel more secure, and others engage in knowledge therapy, amassing new ideas to make themselves feel like they know something. We consume for comfort. We rely on certainty to shield us from the pain of confusion. The truth is staggering, colossal, unfathomable, so we cling to our bite-sized lies. We organize knowledge into bulleted lists and line graphs while the wisdom of the present moment sits patiently at the doors of our perception.

What the ethnographer is in fact faced with—except when (as, of course, he must do) he is pursuing the more automatized routines of data collection—is a multiplicity of complex conceptual structures, many of them superimposed upon or knotted into one another, which are at once strange, irregular, and inexplicit, and which he must contrive somehow first to grasp and then to render. And this is true at the most down-to-earth, jungle field work levels of his activity; interviewing informants, observing rituals, eliciting kin terms, tracing property lines, censusing households … writing his journal. Doing ethnography is like trying to read (in the sense of “construct a reading of”) a manuscript—foreign, faded, full of ellipses, incoherencies, suspicious emendations, and tendentious commentaries, but written not in conventionalized graphs of sound but in transient examples of shaped behavior.

He longed for the years when it was enough to simply be in his room with his hand moving over a piece of graph paper, before the years of decisions and identities, when his parents made his choices for him, and the only thing he had to concentrate on was the clean blade stroke of a line, the ruler’s perfect knife edge.

based on a single variable! Every single line on this graph

Do you realise that it is God who chose you, in Christ Jesus, before he put the earth together? His ultimate goal is to make you holy & completely blameless, by the time he has finished working with you. It's not always a quick process, following a quick line fit on a graph. You are on a journey, full of ups and downs, stopping and waiting; as God develops character in you. The specific characteristics, which God wants to develop in your life are: patience; long suffering; and trust. And God may need to make several attempts at developing these characteristics in all of our lives. Have you ever wondered why the journey with God, to develop such characteristics in our lives, takes so long? It's because such characteristics will stay with us for eternity.

Saintey asks me to breathe in time with the blue bar—five seconds in as it fills, five seconds out as it drains. Then something striking happens. Within a few seconds, the difference between my lowest and highest heart rate is much larger than before—varying from about 60 to 90 beats per minute. And the line on the graph transforms from ugly random spikes into a smooth, snake-like curve.

And in an essential way, this was what he was most ashamed of: not his poor understanding of sex, not his traitorous racial tendencies, not his inability to separate himself from his parents or make his own money or behave like an autonomous creature. It was that, when he and his colleagues sat there at night, the group of them burrowed deep into their own ambitious dream-structures, all of them drawing and planning their improbable buildings, he was doing nothing. He had lost the ability to imagine anything. And so every evening, while the others created, he copied: he drew buildings he had seen on his travels, buildings other people had dreamed and constructed, buildings he had lived in or passed through. Again and again, he made what had already been made, not bothering to improve them, just mimicking them. He was twenty-eight; his imagination had deserted him; he was a copyist. It frightened him. JB had his series. Jude had his work, Willem had his. But what if Malcolm never again created anything? He longed for the years when it was enough to simply be in his room with his hand moving over a piece of graph paper, before the years of decisions and identities, when his parents made his choices for him, and the only thing he had to concentrate on was the clean blade stroke of a line, the ruler's perfect knife edge.

The Theorem reste upon the validity of my longstanding argument that the world contains precisely two kinds of people: Dumpers and Dumpees. Everyone is predisposed to being either one or the other, but of course not all people are COMPLETE Dumpers and Dumpees. Hence the bell curve:" The majority of people fall somewhere close to the vertical dividing line with the occasional statisticaly outliner (e.g., me) representing a tiny percentage of overall individuals. The numerical expression of the graph can be something like 5 being extreme Dumper, and 0 being me. Ergo, if the Great One was a 4 and I am a 0, total size of the Dumper/Dumpee differetial = -4 (Assuming negative numbers if the guy is more of a Dumpee; positive if the girl is.)

A calculation, in fact, demonstrates that without nodes, physical space has no volume. In other words, it is in the nodes of the graph, not in the lines, that the volume of space "resides." The lines "link together" individual volumes sitting at the nodes.

He had forgotten that grief does not decline in a straight line or along a slow curve like a graph in a child's math book. Instead, it was almost as if his body contained a big like of garden rubbish full both of heavy lumps of dirt and of harp thorny brush that would stab him when he least expected it.

If you plot perceived value on a graph, with the horizontal axis as time and the present as zero, then you will see the line representing value curve sharply upward the closer it comes to the zero point, reaching its zenith as it hits the vertical axis. By comparison, value in the far future goes low quickly, changing hardly at all between a year and two years distant. A hyperbola. When humans and most living creatures consider the value of something, they tend to see its future value diminish hyperbolically. In other words, our system of evaluation isn't exponentioally logical, it's hyperbolically illogical.

The difference between the long-term average of the graph and the ice age, 12,000 years ago, is just over 3°C. The IPCC 2001 report suggests that the line of the hockey stick graph might rise a further 5°C during this century. This is about twice as much as the temperature change from the ice age to pre-industrial times.

For the years 1749 to 1926, Alexander Chizhevsky compared the annual number of important political and social events with increased solar activity. On the graph, the blue line illustrates sun flares and the red line relates to human excitability. Notice that every time there is high solar activity, there is a correlation with heightened human events.

In the three years I spent working on this book, making dozens of line graphs, reading campus newspapers, and listening to the stories and opinions of young people during in-depth interviews, I’ve realized this: iGen’ers are scared, maybe even terrified. Growing up slowly, raised to value safety, and frightened by the implications of income inequality, they have come to adolescence in a time when their primary social activity is staring at a small rectangular screen that can like them or reject them. The devices they hold in their hands have both extended their childhoods and isolated them from true human interaction. As a result, they are both the physically safest generation and the most mentally fragile.

It surprised him that his grief was sharper than in the past few days. He had forgotten that grief does not decline in a straight line or along a slow curve like a graph in a child’s math book. Instead, it was almost as if his body contained a big pile of garden rubbish full both of heavy lumps of dirt and of sharp thorny brush that would stab him when he least expected it.

Americans already believed Carter was wasting too much time on the Middle East when there were more pressing problems at home. The country was experiencing double-digit inflation coupled with high unemployment and anemic growth—a confounding phenomenon tagged “stagflation.” As for the president’s job performance, the two dreaded lines on the graph finally crossed in the spring of 1978, with more Americans disapproving

In reality, when you look closely at the graph for most successful people, there are always ups and downs. When viewed over a longer period of time, however, the line generally moves up and to the right. When you’re in a down cycle, it’s sometimes hard to see that the temporary dip is actually a setup for the next rise. In fact, the slope of the upward line is often steeper after a down cycle, meaning you’re really achieving more than if you had stayed on a steady, predictable path.

There is no linear way out of grief, and life after loss is not an event with a finish line. While you may notice recurring themes or experiences in your grief, they don’t always appear in order, and they don’t always make sense to your brain. Grief is more like a zigzagging mountain trail than a line on a graph. It’s a mix of uphill and downhill paths, with some switchbacks tossed in for good measure. Know that it’s okay to feel like you’re “back at square one,” because in grief, there are no squares at all.

I had a firm policy never to charge up my team on an emotional level. I believe that for every artificial peak you may create there is a valley, and i don't like valleys. Games can be lost in valleys. The ideal is an ever-mounting graph line that peaks with your final performance. There will be difficulty and adversity to overcome, but that is necessary to become stronger. Other coaches believe in charging a team up. I never did and never will. I sought a calm assurances in our dressing room, and a calm assurance warming up on the floor, and ad calm assurance in my final remarks before going out to play.

One day, Carmona had an idea. Axcom had been employing various approaches to using their pricing data to trade, including relying on breakout signals. They also used simple linear regressions, a basic forecasting tool relied upon by many investors that analyzes the relationships between two sets of data or variables under the assumption those relationships will remain linear. Plot crude-oil prices on the x-axis and the price of gasoline on the y-axis, place a straight regression line through the points on the graph, extend that line, and you usually can do a pretty good job predicting prices at the pump for a given level of oil price.

History too has an inertia. In the four dimensions of spacetime, particles (or events) have directionality; mathematicians, trying to show this, draw what they call “world lines” on graphs. In human affairs, individual world lines form a thick tangle, curling out of the darkness of prehistory and stretching through time: a cable the size of Earth itself, spiraling round the sun on a long curved course. That cable of tangled world lines is history. Seeing where it has been, it is clear where it is going – it is a matter of simple extrapolation. For what kind of Δ v would it take to escape history, to escape an inertia that powerful, and carve a new course? The hardest part is leaving Earth behind.

Google had a built-in disadvantage in the social networking sweepstakes. It was happy to gather information about the intricate web of personal and professional connections known as the “social graph” (a term favored by Facebook’s Mark Zuckerberg) and integrate that data as signals in its search engine. But the basic premise of social networking—that a personal recommendation from a friend was more valuable than all of human wisdom, as represented by Google Search—was viewed with horror at Google. Page and Brin had started Google on the premise that the algorithm would provide the only answer. Yet there was evidence to the contrary. One day a Googler, Joe Kraus, was looking for an anniversary gift for his wife. He typed “Sixth Wedding Anniversary Gift Ideas” into Google, but beyond learning that the traditional gift involved either candy or iron, he didn’t see anything creative or inspired. So he decided to change his status message on Google Talk, a line of text seen by his contacts who used Gmail, to “Need ideas for sixth anniversary gift—candy ideas anyone?” Within a few hours, he got several amazing suggestions, including one from a colleague in Europe who pointed him to an artist and baker whose medium was cake and candy. (It turned out that Marissa Mayer was an investor in the company.) It was a sobering revelation for Kraus that sometimes your friends could trump algorithmic search.

We love Mary for one reason: because we love Jesus. The more we love Jesus, the more we love Mary. If we could grade Catholics on a scale of sainthood, a kind of spiritual graph, three lines would be almost identical in height or depth: how saintly you are, how much you love Jesus, and how much you love Mary. That’s the empirical fact. Here comes the explanation. Look at the Hail Mary prayer. It stops halfway through. The speaker has to take a silence break before and after the name “Jesus.” He’s at the heart of that prayer as He was at the heart of her body, her womb. Look at the title we give her in that prayer: “Mother of God.” Unbelievable, astonishing, incredible, amazing, infinitely wonderful! What? Jesus in Mary, Jesus incarnating, Jesus coming down to us in Mary. Suppose He had chosen to come in another way. He could have. He could have appeared instantly as a full-grown man descending from the sky, the reverse of the Ascension. He could have come down on a mountaintop, or in the Temple. And if he had, every Christian in the world who adored Him would make a pilgrimage to that mountain or that Temple. They would love that place above all places in the universe. They would make a very big deal of it. Why? Because they make a very big deal about Him.

Although Israel is targeted by terrorists much more frequently than the United States, Israelis do not live in fear of terrorism. A 2012 survey of Israeli Jews found that only 16 percent described terrorism as their greatest fear81—no more than the number who said they were worried about Israel’s education system. No Israeli politician would say outright that he tolerates small-scale terrorism, but that’s essentially what the country does. It tolerates it because the alternative—having everyone be paralyzed by fear—is incapacitating and in line with the terrorists’ goals. A key element in the country’s strategy is making life as normal as possible for people after an attack occurs. For instance, police typically try to clear the scene of an attack within four hours of a bomb going off,82 letting everyone get back to work, errands, or even leisure. Small-scale terrorism is treated more like crime than an existential threat. What Israel certainly does not tolerate is the potential for large-scale terrorism (as might be made more likely, for instance, by one of their neighbors acquiring weapons of mass destruction). There is some evidence that their approach is successful: Israel is the one country that has been able to bend Clauset’s curve. If we plot the fatality tolls from terrorist incidents in Israel using the power-law method (figure 13-8), we find that there have been significantly fewer large-scale terror attacks than the power-law would predict; no incident since 1979 has killed more than two hundred people. The fact that Israel’s power-law graph looks so distinct is evidence that our strategic choices do make some difference.

Perhaps the elements of memory in plants are superficially treated," he writes, "but at least there they are in black and white! Yet no one calls his friends or neighbors, no one shouts in a drunken voice over the telephone: Have you heard the news? Plants can feel! They can feel pain! They cry out! Plants remember everything!" When Soloukhin began to telephone his own friends in excitement he learned from one of them that a prominent member of the Soviet Academy of Sciences, working in Akademgorodok, the new town inhab­ ited almost exclusively by research scientists on the outskirts of Siberia's largest industrial center, Novosibirsk, had stated: Don't be amazed! We too are carrying out many experiments of this kind and they all point to one thing: plants have memory. They are able to gather impressions and retain them over long periods. We had a man molest, even torture, a geranium for several days in a row. He pinched it, tore it, pricked its leaves with a needle, dripped acid on its living tissues, burned it with a lighted match, and cut its roots. Another man took tender care of the same geranium, watered it, worked its soil, sprayed it with fresh water, supported its heavy branches, and treated its burns and wounds. When we electroded our instruments to the plant, what do you think? No sooner did the torturer come near the plant than the recorder of the instrument began to go wild. The plant didn't just get "nervous"; it was afraid, it was horrified. If it could have, it would have either thrown itself out the window or attacked its torturer. Hardly had this inquisitor left and the good man taken his place near the plant than the geranium was appeased, its impulses died down, the recorder traced out smooth­ one might almost say tender-lines on the graph.

Starting a little over a decade ago, Target began building a vast data warehouse that assigned every shopper an identification code—known internally as the “Guest ID number”—that kept tabs on how each person shopped. When a customer used a Target-issued credit card, handed over a frequent-buyer tag at the register, redeemed a coupon that was mailed to their house, filled out a survey, mailed in a refund, phoned the customer help line, opened an email from Target, visited Target.com, or purchased anything online, the company’s computers took note. A record of each purchase was linked to that shopper’s Guest ID number along with information on everything else they’d ever bought. Also linked to that Guest ID number was demographic information that Target collected or purchased from other firms, including the shopper’s age, whether they were married and had kids, which part of town they lived in, how long it took them to drive to the store, an estimate of how much money they earned, if they’d moved recently, which websites they visited, the credit cards they carried in their wallet, and their home and mobile phone numbers. Target can purchase data that indicates a shopper’s ethnicity, their job history, what magazines they read, if they have ever declared bankruptcy, the year they bought (or lost) their house, where they went to college or graduate school, and whether they prefer certain brands of coffee, toilet paper, cereal, or applesauce. There are data peddlers such as InfiniGraph that “listen” to shoppers’ online conversations on message boards and Internet forums, and track which products people mention favorably. A firm named Rapleaf sells information on shoppers’ political leanings, reading habits, charitable giving, the number of cars they own, and whether they prefer religious news or deals on cigarettes. Other companies analyze photos that consumers post online, cataloging if they are obese or skinny, short or tall, hairy or bald, and what kinds of products they might want to buy as a result.

You are familiar with The Decline of the West, in which Oswald Spengler takes note of the current decadence of painting, as well as literature and music, and concludes that the end of our cultural epoch has arrived. He is a philosopher, but one descended from the natural sciences. He arranges observations, he records insights and knowledge. He takes a graphic view of history. And if he sees that a line curves downward, he considers the trend a proven fact, so that zero must be reached at a particular time and place. And that moment represents the end, the decline of the West! "But his graphing has no bearing on any of my ideas and plans as architect and politician. I study the reasons why the line curves downward, and I try to remove the causes. But at the same time, I examine the reasons why at an earlier time the line curved upward! And then I set out to restore the conditions of that day, to awake anew the creative wall of that time, and to bring about a new crest in the constantly fluctuating curve of history. "No doubt about it! Our culture has entered on stagnation, it looks like old age. But the reasons for this state do not lie in the fact that it has genuinely passed its manhood, but rather that the upholders of this culture, the Germanic-European peoples, have neglected it and have turned their attention to material tasks, to technology, industry, to hunger for material possessions, to rapacity, and to an economic egocentrism that overwhelms everything else. All their thinking and striving reaches its only climax in account books and in the outward show of the worldly goods they possess. "I am overcome with disgust, a vexing scorn, when I see the way such people live and behave! [ . . . ] But thank God, it is only the top ten thousand who think along these lines. It is true that the whole of the bourgeoisie is already strongly infected and sickly. But bourgeois youth are still healthy and can be shown the way back to nature, to a higher development, to new cultural will, provided only that they do not become enmeshed in the treadmill of meaningless and wholly materialistic contemporary life, only to drown either in the cupidity of business or in the tedium of the middle-class workaday routine or in the corruption of the big city. “If we succeed in replacing the egocentric cupidity of business with a socialist communal wall and a work-affirming responsibility for the common-weal; in abolishing the tedium of middle-class workaday monotony by substituting for it the potential enjoyment of personal liberty, the beauty of nature, the splendor of our own Fatherland and the thousandfold diversity of the rest of the world; and if we put an end to the corruption of omnipresent degeneracy, bred in the warrens of buildings and on the asphalt streets of the cities of millions - then the road is clear to a new life, to a new creative will, to a new flight of the free, healthy spirit and mind. And then, my dear Herr Roselius, your bricks will form themselves into entirely new shapes all by themselves. Temples of life will be built, cathedrals of a higher cult will be raised, and even thousands of years later, the walls will bear witness to the exalted times out of which even more exalted ones were bom!” When Roselius had left Hitler’s room with me, he took my hand and said: “Wagener, I thank you for having made this hour possible. What a man! And how small we feel, concerned as we are with those things that preoccupy us! But now I know' what I have to do! In spite of my sixty years, I have only one goal: to join in the work of helping the young people and the German Volk to find internal and external freedom!

In the three years I spent working on this book, making dozens of line graphs, reading campus newspapers, and listening to the stories and opinions of young people during in-depth interviews, I’ve realized this: iGen’ers are scared, maybe even terrified.

Activities to Develop the Visual System Making Shapes—Let your child draw or form shapes, letters, and numbers in different materials, such as playdough, finger paint, shaving cream, soap foam, sand, clay, string, pudding, or pizza dough. Mazes and Dot-to-Dot Activities—Draw mazes on paper, the sidewalk, or the beach. Have the child follow the mazes with his finger, a toy car, a crayon, a marker, or chalk. On graph paper, make dot-to-dot patterns for the child to follow. Peg Board—Have the child reproduce your design or make his own. Cutting Activities—Provide paper and scissors and have your child cut fringe and strips. Draw curved lines on the paper for her to cut. Cutting playdough is fun, too. Tracking Activities—Lie on your backs outside and watch birds or airplanes, just moving your eyes while keeping your heads still. Jigsaw Puzzles! Block Building!!

The rounded, transparent covers from the growth capsules radiated a warm bluish-white light in the darkened hall, and inside each lay a naked body attached to a ghostly face. Affixed to the control panel of every capsule were lines containing air and liquid nourishment, pumping and maintaining the lives within while creating a constant hum that vibrated faintly throughout the room. The scientists shuffled amongst them. They spoke quietly and checked the ever-present dials, blinking lights and graphs, as they constantly monitored the life signs of the valuable occupants inside each chamber.

The scaling curve applies to every blitzscaler, regardless of industry or geography. The same multiple S-curve graph that describes Facebook or Apple also describes Tencent, which launched with QQ, then added a second curve for WeChat after QQ reached maturity in 2010. Just when you’ve finished blitzscaling one business line, you need to blitzscale the next to maintain your company’s upward trajectory. And as blitzscaling continues to spread, established companies with mature business lines should consider turning to intrapreneurs to blitzscale new business units.

When we add these two waves together, we find that there are some places where they are in phase, and add up to give a bigger wave. In other places, they’re out of phase, and cancel each other out. The wavefunction we get from adding them together (the solid line in the figure) has lumps in it—there are places where we see waves, and places where we see nothing. When we square that to get the probability distribution, we get the bottom graph: The dashed curves in the top graph show the wavefunctions for the two different wavelengths (shifted up so you can see them clearly). The solid curve shows the sum of the two wavefunctions. The bottom graph shows the probability distribution resulting from adding them together (the square of the solid curve in the top graph).

The trajectory curves produced by the ball thrown into the air or the orbital curves of the planets orbiting the sun were of great interest to mathematicians. Treating algebraic systems was developed by medieval Islam scholars. Descartes showed how to use the algebraic term (x, y) to describe a geometric shape, showing what is known as Cartesian coordinates and how they were drawn using x, y and graphs. A straight line graph has characteristics that are easy to calculate. 카톡【AKR331】텔레【RDH705】라인【SPR331】위커【SPR705】 저희는 7가지 철칙을 바탕으로 거래를 합니다. 고객들과 지키지못할약속은 하지않습니다 1.정품보장 2.총알배송 3.투명한 가격 4.편한 상담 5.끝내주는 서비스 6.고객님 정보 보호 7.깔끔한 거래 포폴,에토미,수면제 팔아요 The known formula from the Babylonian times was able to calculate the area under the straight line. This slope (the rate of change represented by the slope of the straight line) is the value of the y coordinate divided by the change of the associated x coordinate. However, these values ​​are more difficult to calculate in the curve. Before Newton, mathematicians realized that one way to do this was to calculate an approximation. Calculate the curve as continuous straight lines, and the area under the curve as continuous squares and triangles. Using more or less rectangles and triangles, you can get a more accurate approximation, but this is still only an approximation. Newton began challenging this problem before he reached Ulussof. In February 1665 he was still in the third year of college. He knew that the French mathematician Fermat and his mentor Bera both explained the formula for a particular curve. He began to wonder if they could be generalized to all curves. "I got a hint about this method from how to draw Fermat's tangents and generalized it," he later said. The key to this problem was his ability to use infinite water. Newton realized this. Instead of adding to infinity, the sum associated with an infinite series is similar to a finite set of goals or limits. And we could use this to find the curve as a rectangle. Effective using infinite numbers and giving small squares to the area under the curve. This is 'integral'.

I almost always use dark grey for the graph title. This ensures that it stands out, but without the sharp contrast you get from pure black on white (rather, I preserve the use of black for a standout color when I’m not using any other colors). A number of preattentive attributes are employed to draw attention to the “Progress to date” trend: color, thickness of line, presence of data marker and label on the final point, and the size of the corresponding text.

grief does not decline in a straight line or along a slow curve like a graph in a child’s math book.

Graphically, residuals are the vertical distances between the observed values and the fitted values. On the graph, the line represents the fitted values from the regression model. We call this line . . . the fitted line! The lines that connect the data points to the fitted line represent the residuals. The length of the line is the value of the residual.

This graph shows all the observations together with a line that represents the fitted relationship. As is traditional, the Y-axis displays the dependent variable, which is weight. The X-axis shows the independent variable, which is height. The line is the fitted line. If you enter the full range of height values that are on the X-axis into the regression equation that the chart displays, you will obtain the line shown on the graph. This line produces a smaller SSE than any other line you can draw through these observations. Visually, we see that that the fitted line has a positive slope that corresponds to the positive correlation we obtained earlier. The line follows the data points, which indicates that the model fits the data. The slope of the line equals the coefficient that I circled. This coefficient indicates how much mean weight tends to increase as we increase height. We can also enter a height value into the equation and obtain a prediction for the mean weight. Each point on the fitted line represents the mean weight for a given height. However, like any mean, there is variability around the mean. Notice how there is a spread of data points around the line. You can assess this variability by picking a spot on the line and observing the range of data points above and below that point. Finally, the vertical distance between each data point and the line is the residual for that observation.

a slender vinyl attaché case; the kind carried by State Department clerks, computer salesmen, and executive trainees. This, which she opened on her lap, had proved to contain such serious businesslike material as yellow-lined legal pads, ballpoint pens, graph paper, loose-leaf filler books, a cassette recorder, sharpened yellow pencils, and a slide rule. (I have always envied people who know what a slide rule is for. It’s not even the question of how you use it, it’s more basic than that; I am convinced there have been moments in my life which would have been made easier if I had been equipped with a handy slide rule and the mastery of its operation, but I’m so ignorant I don’t even know which moments those were. Never have I said, “Oh, if only I had a slide rule!” though surely there have been times when it was the appropriate thing to say.) But not at the moment for Ms. Scott. She’d taken from the attaché case only one legal pad and one ballpoint pen, then closed

Graphs show two or more timelines, for example, trailing 6-week and trailing 12-month. Trend lines for the short term can magnify small but important issues that are hard to spot when averaged out over longer periods.

FROM OTHER SOURCES Pre–race and Venue Homework Get hold of any history of past events at the venue, plus any information that the conducting club may have about weather and expected conditions. Go to the weather bureau and get history for the area. Speak to sailors from your class who have this venue as their home club or who have sailed there on a number of occasions. Boat, Sails, Gear Preparation Checklist Many times the outcome of a race is as dependent on what you have done prior to the race as to what you do out on the course. Sometimes no matter how good your tactics and strategy are a simple breakage could render all that useless. Hull – make sure that your hull is well sanded and polished, centreboard strips are in good condition, venturis if fitted are working efficiently, buoyancy tanks are dry and there are no extraneous pieces of kit in your boat which adds unwanted weight. Update any gear that looks tired or worn especially control lines. Mast, boom and poles – check that all halyards, stays and trapeze wires are not worn or damaged and that pins are secure, knots tight and that anything that can tear a sail or injure flesh is taped. Mark the full hoist position on all halyards. Deck hardware – check all cam cleats for spring tension and tape anything that may cause a sail tear or cut legs hands and arms. Check the length of all sheets and control lines and shorten anything that is too long. This not only reduces weight but also minimises clutter. Have marks on sheets and stick or draw numbers and reference scales for the jib tracks, outhaul and halyards so that you can easily duplicate settings that you know are fast in various conditions. Centreboard and rudder – ensure that all nicks and gouges are filled and sanded and the surfaces are polished and most importantly that rudder safety clips are working. Sails – select the correct battens for the day’s forecast. Write on the deck, with a china graph pencil, things like the starting sequence, courses, tide times and anything else that will remind you to sail fast. Tools and spares – carry a shackle key with screwdriver head on your person along with some spare shackles and short lengths of rope or different diameters. A tool like a Leatherman can be very useful to deal with unexpected breakages that can occur even in the best prepared boat.

Substandard work done efficiently or committed to a slick PowerPoint presentation, illustrated by colorful graphs, photographs, and even video patches, is still substandard work.

Display grid: displays gridlines in the graph. Plot area border: XY only: when this option is selected, lines for the X and Y axes are drawn. If this option is not selected, the plot area is enclosed in a rectangle.

SUMMARY A vast array of additional statistical methods exists. In this concluding chapter, we summarized some of these methods (path analysis, survival analysis, and factor analysis) and briefly mentioned other related techniques. This chapter can help managers and analysts become familiar with these additional techniques and increase their access to research literature in which these techniques are used. Managers and analysts who would like more information about these techniques will likely consult other texts or on-line sources. In many instances, managers will need only simple approaches to calculate the means of their variables, produce a few good graphs that tell the story, make simple forecasts, and test for significant differences among a few groups. Why, then, bother with these more advanced techniques? They are part of the analytical world in which managers operate. Through research and consulting, managers cannot help but come in contact with them. It is hoped that this chapter whets the appetite and provides a useful reference for managers and students alike. KEY TERMS   Endogenous variables Exogenous variables Factor analysis Indirect effects Loading Path analysis Recursive models Survival analysis Notes 1. Two types of feedback loops are illustrated as follows: 2. When feedback loops are present, error terms for the different models will be correlated with exogenous variables, violating an error term assumption for such models. Then, alternative estimation methodologies are necessary, such as two-stage least squares and others discussed later in this chapter. 3. Some models may show double-headed arrows among error terms. These show the correlation between error terms, which is of no importance in estimating the beta coefficients. 4. In SPSS, survival analysis is available through the add-on module in SPSS Advanced Models. 5. The functions used to estimate probabilities are rather complex. They are so-called Weibull distributions, which are defined as h(t) = αλ(λt)a–1, where a and 1 are chosen to best fit the data. 6. Hence, the SSL is greater than the squared loadings reported. For example, because the loadings of variables in groups B and C are not shown for factor 1, the SSL of shown loadings is 3.27 rather than the reported 4.084. If one assumes the other loadings are each .25, then the SSL of the not reported loadings is [12*.252 =] .75, bringing the SSL of factor 1 to [3.27 + .75 =] 4.02, which is very close to the 4.084 value reported in the table. 7. Readers who are interested in multinomial logistic regression can consult on-line sources or the SPSS manual, Regression Models 10.0 or higher. The statistics of discriminant analysis are very dissimilar from those of logistic regression, and readers are advised to consult a separate text on that topic. Discriminant analysis is not often used in public

categorical and the dependent variable is continuous. The logic of this approach is shown graphically in Figure 13.1. The overall group mean is (the mean of means). The boxplots represent the scores of observations within each group. (As before, the horizontal lines indicate means, rather than medians.) Recall that variance is a measure of dispersion. In both parts of the figure, w is the within-group variance, and b is the between-group variance. Each graph has three within-group variances and three between-group variances, although only one of each is shown. Note in part A that the between-group variances are larger than the within-group variances, which results in a large F-test statistic using the above formula, making it easier to reject the null hypothesis. Conversely, in part B the within-group variances are larger than the between-group variances, causing a smaller F-test statistic and making it more difficult to reject the null hypothesis. The hypotheses are written as follows: H0: No differences between any of the group means exist in the population. HA: At least one difference between group means exists in the population. Note how the alternate hypothesis is phrased, because the logical opposite of “no differences between any of the group means” is that at least one pair of means differs. H0 is also called the global F-test because it tests for differences among any means. The formulas for calculating the between-group variances and within-group variances are quite cumbersome for all but the simplest of designs.1 In any event, statistical software calculates the F-test statistic and reports the level at which it is significant.2 When the preceding null hypothesis is rejected, analysts will also want to know which differences are significant. For example, analysts will want to know which pairs of differences in watershed pollution are significant across regions. Although one approach might be to use the t-test to sequentially test each pair of differences, this should not be done. It would not only be a most tedious undertaking but would also inadvertently and adversely affect the level of significance: the chance of finding a significant pair by chance alone increases as more pairs are examined. Specifically, the probability of rejecting the null hypothesis in one of two tests is [1 – 0.952 =] .098, the probability of rejecting it in one of three tests is [1 – 0.953 =] .143, and so forth. Thus, sequential testing of differences does not reflect the true level of significance for such tests and should not be used. Post-hoc tests test all possible group differences and yet maintain the true level of significance. Post-hoc tests vary in their methods of calculating test statistics and holding experiment-wide error rates constant. Three popular post-hoc tests are the Tukey, Bonferroni, and Scheffe tests.

Key to the Pronunciations This dictionary uses a simple respelling system to show how entries are pronounced, using the symbols listed below. Generally, only the first of two or more identical headwords will have a pronunciation respelling. Where a derivative simply adds a common suffix such as -less, -ness, or -ly to the headword, the derivative may not have a pronunciation respelling unless some other element of the pronunciation also changes. as in hat //, fashion // as in day //, rate // as in lot //, father //, barn // as in big // as in church //, picture // as in dog //, bed // as in men //, bet //, ferry // as in feet //, receive // as in air //, care // as in soda //, mother /, her // as in free //, graph //, tough // as in get //, exist // as in her //, behave // as in fit //, women // as in time /t/, hire //, sky // as in ear //, pierce // as in judge //, carriage // as in kettle //, cut //, quick // as in lap //, cellar //, cradle // as in main //, dam // as in need //, honor //, maiden // as in sing //, anger // as in go //, promote // as in law //, thought //, lore // as in boy //, noisy // as in wood //, sure // as in food //, music // as in mouse //, coward // as in put //, cap // as in run //, fur //, spirit // as in sit //, lesson //, face // as in shut //, social // as in top //, seat //, forty // as in thin //, truth // as in then //, father // as in very //, never // as in wait //, quit // as in when //, which // as in yet //, accuse // as in zipper //, musician // as in measure //, vision // Foreign Sounds as in Bach // as in en route //, Rodin / / as in hors d’oeuvre //, Goethe // as in Lully //, Utrecht // Stress Marks Stress (or accent) is represented by marks placed before the affected syllable. The primary stress mark is a short, raised vertical line // which signifies that the heaviest emphasis should be placed on the syllable that follows. The secondary stress mark is a short, lowered vertical line // which signifies a somewhat weaker emphasis than on the syllable with primary stress. Variant Pronunciations There are several ways in which variant pronunciations are indicated in the respellings. Some respellings show a pronunciation symbol within parentheses to indicate a possible variation in pronunciation; for example, in sandwich //. Variant pronunciations may be respelled in full, separated by semicolons. The more common pronunciation is listed first, if this can be determined, but many variants are so common and widespread as to be ofequal status. Variant pronunciations may be indicated by respelling only the part of the word that changes. A hyphen will replace the part of the pronunciation that has remained the same. Note: A hyphen sometimes serves to separate syllables where the respelling might otherwise look confusing, as at reinforce //.

So what are you doing?” Paul said, tapping the diary. “Oh, um. Studying.” His gaze took in the suspect graph and time line, and he raised his eyebrows. “For what?” I blinked, at a loss for a response. I didn’t want to lie, but I couldn’t see telling him the truth. I’d been sitting here trying to visualize myself as Veronica Mars, all smart and badass. But in reality, I felt more like Inspector Gadget with my go-go button stuck in neutral.

Streamgraph,6 a comparative, flowing area graph developed as an improved way to compare large, changing datasets over time. Similarly, Edward Tufte’s Sparklines visualization7 concept (developed in the late 1990s) embedded short, intense line-graph metrics of a single changing metric within surrounding text. This type of visualization has become a common feature of online financial publications.

axis, all of those straight-ish lines would look like the first graph above of Andy’s tribble family—horizontal most of the way, then suddenly close to vertical at the end. And there would really be no way to graph them all together—the numbers involved are just too different. Logarithmic scaling takes care of these issues and allows us to get a clear overall picture of improvement in digital gear. It’s clear that many of the critical building blocks of computing—microchip density, processing speed, storage capacity, energy efficiency, download speed, and so on—have been improving at exponential rates for a long time. To understand the real-world impacts of Moore’s Law, let’s compare the capabilities of computers separated by only a few doubling periods. The ASCI Red, the first product of the U.S. government’s Accelerated Strategic Computing Initiative, was the world’s fastest supercomputer when it was introduced in 1996. It cost $55 million to develop and its one hundred cabinets occupied nearly 1,600 square feet of floor space (80 percent of a tennis court) at Sandia National Laboratories in New Mexico.10 Designed for calculation-intensive tasks like simulating nuclear tests, ASCI Red was the first computer to score above one teraflop—one trillion floating point operations* per second—on the standard benchmark test for computer speed. To reach this speed it used eight hundred kilowatts per hour, about as much as eight hundred homes would. By 1997, it had reached 1.8 teraflops.

Correlations made by big data are likely to reinforce negative bias. Because big data often relies on historical data or at least the status quo, it can easily reproduce discrimination against disadvantaged racial and ethnic minorities. The propensity models used in many algorithms can bake in a bias against someone who lived in the zip code of a low-income neighborhood at any point in his or her life. If an algorithm used by human resources companies queries your social graph and positively weighs candidates with the most existing connections to a workforce, it makes it more difficult to break in in the first place. In effect, these algorithms can hide bias behind a curtain of code. Big data is, by its nature, soulless and uncreative. It nudges us this way and that for reasons we are not meant to understand. It strips us of our privacy and puts our mistakes, secrets, and scandals on public display. It reinforces stereotypes and historical bias. And it is largely unregulated because we need it for economic growth and because efforts to try to regulate it have tended not to work; the technologies are too far-reaching and are not built to recognize the national boundaries of our world’s 196 sovereign nation-states. Yet would it be best to try to shut down these technologies entirely if we could? No. Big data simultaneously helps solve global challenges while creating an entirely new set of challenges. It’s our best chance at feeding 9 billion people, and it will help solve the problem of linguistic division that is so old its explanation dates back to the Old Testament and the Tower of Babel. Big data technologies will enable us to discover cancerous cells at 1 percent the size of what can be detected using today’s technologies, saving tens of millions of lives. The best approach to big data might be one put forward by the Obama campaign’s chief technology officer, Michael Slaby, who said, “There’s going to be a constant mix between your qualitative experience and your quantitative experience. And at times, they’re going to be at odds with each other, and at times they’re going to be in line. And I think it’s all about the blend. It’s kind of like you have a mixing board, and you have to turn one up sometimes, and turn down the other. And you never want to be just one or the other, because if it’s just one, then you lose some of the soul.” Slaby has made an impressive career out of developing big data tools, but even he recognizes that these tools work best when governed by human judgment. The choices we make about how we manage data will be as important as the decisions about managing land during the agricultural age and managing industry during the industrial age. We have a short window of time—just a few years, I think—before a set of norms set in that will be nearly impossible to reverse. Let’s hope humans accept the responsibility for making these decisions and don’t leave it to the machines.

The biggest shift was from a bar graph to a line graph. As we’ve discussed, line graphs typically make it easier to see trends over time. This shift also has the effect of visually reducing discrete elements, because the data that was previously five bars has been reduced to a single line with the end points highlighted. When we consider the full data being plotted, we’ve gone from 25 bars to 4 lines. The organization of the data as a line graph allows the use of a single x-axis that can be leveraged across all of the categories. This simplifies the processing of the information (rather than seeing the years in a legend at the left and then having to translate across the various groups of bars).

For each stop—each timbre, or type of sound, that the organ could make (viz. blockflöte, trumpet, piccolo)—there was a separate row of pipes, arranged in a line from long to short. Long pipes made low notes, short high. The tops of the pipes defined a graph: not a straight line but an upward-tending curve. The organist/math teacher sat down with a few loose pipes, a pencil, and paper, and helped Lawrence figure out why. When Lawrence understood, it was as if the math teacher had suddenly played the good part of Bach’s Fantasia and Fugue in G Minor on a pipe organ the size of the Spiral Nebula in Andromeda—

In every age, there have been thinkers who might broadly be described as Prophets of Doom. This does not necessarily mean that they are pessimists, but rather that they reject the notion that history is an inexorable march of improvement. History is not, in their view, a line on the graph going up and up ‘to infinity and beyond’, but a recurring pattern of rise and fall.

There's a telos of self-improvement baked into the immigrant experience. As a teenager, I busied myself with the school newspaper or debate club because, unlike with math or science, I thought I could actually get better at these things. You flip through your father's old physics notebooks, and you know in your bones that these formulas and graphs will never make sense to you. But one day, you realize that your parents speak with a mild accent, and that they have no idea what passive voice is. The next generation would acquire a skill on their behalf -- one that we could also use against them. Commanding the language seemed like our only way of surpassing them. Home life took on a kind of casual litigiousness. The calm and composed children, a jaunty bounce to our sentences, laying traps with our line of questioning. The parents, tired and irritated, defaulting to the native tongue.

A linear relationship between two elements in a system can be drawn on a graph with a straight line. It’s a relationship with constant proportions. If I put 10 pounds of fertilizer on my field, my yield will go up by 2 bushels. If I put on 20 pounds, my yield will go up by 4 bushels. If I put on 30 pounds, I’ll get an increase of 6 bushels.

From extreme left to extreme right in Germany the political graph is not a straight line. It is a nearly complete circle.” And the center was weak.29

The bottom line, then, is that the evidence shows that vaccination programmes have not done the things they are credited with but have done most of the things they are blamed for. The decline in disease, the reduction in infant mortality rates and the increase in average life expectation are all due to improved living conditions. Cleaner water, efficient methods of removing sewage, fresher food, less poverty and less overcrowding are the real reasons why these improvements have taken place. Anyone who doubts this has only to look at graphs showing mortality rates and life expectation rates alongside graphs showing when vaccines were introduced. The graphs show clearly that the improvements took place before the vaccines were introduced. Study the evidence relating to whooping cough, tetanus, diphtheria, smallpox, polio and other diseases and it becomes clear that the incidence of these diseases, and number of deaths caused by them, were in decline long before the relevant vaccines were introduced.

label maker plus extra cartridge tape and batteries pad of lined paper, pad of graph paper pens, pencils, felt-tip pens, Sharpies®, and highlighters office necessities like a stapler, tape, paper clips, scissors, labels, calculator, sticky notes, etc. box cutter, letter opener zip ties, cable ties, or cable clips tape measure and small tools (hammer, screw driver, level) assortment of nails and picture-hanging supplies Moving

The mathematician Stanislaw Ulam once said that calling a problem nonlinear was like going to the zoo and talking about all the interesting nonelephant animals you see there. His point was that most animals are not elephants, and most equations are not linear. Linear equations describe simple, idealized situations where causes are proportional to effects, and forces are proportional to responses. If you bend a steel girder by two millimeters instead of one, it will push back twice as hard. The word linear refers to this proportionality: If you graph the deflection of the girder versus the force applied, the relationship falls on a straight line.

Stories can be incredibly powerful and beautiful devices that form and assist our perception and understanding of the world. However, according to twentieth-century American author Kurt Vonnegut, stories rarely tell the truth. After studying stories from an anthropological standpoint, examining the relationships with various cultures, Vonnegut found that stories and myths across many cultures share consistent similar shapes that can typically be broken down into just a few main categories. These shapes can be found graphing the course of a protagonist’s journey through a story along an axis of good and ill fortune. In all stories, someone or something starts somewhere, either in a good place, bad place, or neutral place. Then things happen related to that person which is conveyed as good or bad, bringing the character up and down the axis of fortune as they traverse forward through the story. Then, the story ends and its shape reveals itself. Vonnegut discovered that many popular stories follow common, consistent curves and spikes up and down the good/ill axis and that most end with the protagonist higher on the axis than where they started. However, what’s perhaps most interesting about Vonnegut’s analysis is this argument that these shapes, and consequently most stories, lie. Vonnegut proposed that a more honest, realistic story shape is simply a straight line. In a story of this shape, things still happen and characters still change, but the story maintains ambiguity around whether or not the events that occur are conclusively good or bad. According to Vonnegut, Hamlet is the closest literary representation of real life. “We are so seldom told the truth. In Hamlet-Shakespeare tells us that we don’t know enough about life to know what the good news is and the bad news is and we respond to that.” One story medium that seems to inadvertently coincide with this idea, is the medium of the television series. The goal of TV series is to keep viewers watching as long as possible. Each episode must be an engaging enough story to keep the viewer watching until the end, but each episode must also be left unresolved enough so the larger season-long and series-long stories continue and the viewer is interested in watching all the following episodes. In order to keep the whole thing going, none of the stories can reach a conclusion, and thus, the main characters can’t find ultimate peace or freedom from the uncertainty between good and ill-fortune. Of course, most shows don’t qualify as the straight-line shape in Vonnegut’s analysis, because most shows attempt to convey conclusively good and bad fortunes within them. However merely by the requirements of the medium TV series are forced to self-impose the same sort of universal truth that Vonnegut suggests. That neither the viewer nor the characters in a series can ever know what anything that’s so-called “good” or “bad” in one episode might cause in the next. And that on a fundamental level, the changes in each episode are futile because they are a part of a never-ending cycle of change through conflict and resolution, for the mere sake of its continuation, with no aim of a final resolution or reveal of what’s ultimately good or bad. Of course, eventually, a show reaches its series end when it stops working or runs its natural course. But the show fights its whole life to stay away from this moment. A good TV series, a series that we don’t want to end, is only a series that we don’t want to end because it can’t seem to resolve itself. In this, the format of Tv series also shows us that there is meaning, engagement, and entertainment within the endless cycle of change, regardless of its potential universal futility. And that perhaps change in life can exist not for the sake of some conclusion or ultimate state of peace, but a continuation of itself for the sake of itself. And perhaps the ability to be in this cycle of continued change for the sake of change is the actual good fortune.

I do have an interest in dissidents. My mother believes 5G may harm us, and I think she’s silly. But what of the nonconformist who warned back in 1940 that cigarettes kill? What of the contrarian who said the CIA was spying on Martin Luther King, Jr.? I mean, I’ve seen no evidence that 5G or the Covid vaccines are harmful. But have I done that research myself? No. I just trust the media would tell me if they were. My media. Whatever media my mom is consuming, they’re quoting “research, studies.” They’re slinging medical articles and YouTube videos of doctors saying that mRNA vaccines kill. A month before our road trip, she sent me one of these videos. It’s a clip of a longer talk, but even the clip is twelve minutes long. “Something to consider,” she wrote in the subject line. “Doctor calls out deadly vaccine!” Twelve minutes is annoyingly long for something I instinctively discredit, but short enough to give it a go. So I do. It’s a doctor on a stage with a PowerPoint. He has studies and graphs and lists of ingredients in tiny fonts and words like “embryonic stem cells.” I write my mom a long response. “OK I’m six minutes in and here are my thoughts: he’s using a lot of technical science speak that is above my pay grade. And so, what I’m doing is I’m trusting the lingo of an expert.

A parabola opens at a certain direction, allowing for infinitely many points to reside inside the area from which it opens. As a student, I do not like to specialize in a single discipline; specialization seems unfulfilling in my own mind. Hence, the graph of a straight line is not an appropriate analogy to the depths of my curiosity. A line only goes in one direction, and unlike a parabola, a line cannot encase that infinite amount of white space on a coordinate plane—it can only pass through it. Rather than being like a rigid line, I try to be more open to a wider variety of academic subjects. I do admit—a parabola still opens in a certain direction, and of course, my interests are still skewed toward particular subjects. However, the open curve of the parabola can still encompass infinitely many points as the graph extends, the same way my curiosity can still expand to multiple different subjects. This is why I see myself more in the curvaceous parabola than the rigid line.

To successfully launch a product, generic drug companies must tread in reverse through this obstacle course. Once a generic company zeroes in on a molecule, and its scientists figure out how it operates in the body, its lawyers get to work to establish how well protected it is legally. The next step takes place in the laboratory: developing the active pharmaceutical ingredient by synthesizing it into ingredient form. That alone can take several years of trial and error. Once successful, the finished generic has to take the same form as the brand, whether that be pill, capsule, tablet, or injection. Formulating it requires additional ingredients known as excipients, which can be different, but might also be litigated. Then comes testing. In the lab, the in-vitro tests replicate conditions in the body. During dissolution tests, for example, the drug will be put in beakers whose contents mimic stomach conditions, to see how the drugs break down. But some of the most important tests are in-vivo—when the drug is tested on people. Brand-name companies must test new drugs on thousands of patients to prove that they are safe and effective. Generic companies have to prove only that their drug performs similarly in the body to the brand-name drug. To do this, they must test it on a few dozen healthy volunteers and map the concentration of the drug in their blood. The results yield a graph that contains the all-important bioequivalence curve. The horizontal line reflects the time to maximum concentration (Tmax) of drug in the blood. The vertical line reflects the peak concentration (Cmax) of drug in the blood. Between these two axes lies the area under the curve (AUC). The test results must fall in that area to be deemed bioequivalent. Every batch of drugs has variation. Even brand-name drugs made in the same laboratory under the exact same conditions will have some batch-to-batch differences. So, in 1992, the FDA created a complex statistical formula that defined bioequivalence as a range—a generic drug’s concentration in the blood could not fall below 80 percent or rise above 125 percent of the brand name’s concentration. But the formula also required companies to impose a 90 percent confidence interval on their testing, to ensure that less than 20 percent of samples would fall outside the designated range and far more would land within a closer range to the innovator product.

The bottom line is that when members of iGen arrived on campus, beginning in the fall of 2013, they had accumulated less unsupervised time and fewer offline life experiences than had any previous generation. As Twenge puts it, “18-year-olds now act like 15-year-olds used to, and 13-year-olds like 10-year-olds. Teens are physically safer than ever, yet they are more mentally vulnerable.”9 Most of these trends are showing up across social classes, races, and ethnicities.10 Members of iGen, therefore, may not (on average) be as ready for college as were eighteen-year-olds of previous generations. This might explain why college students are suddenly asking for more protection and adult intervention in their affairs and interpersonal conflicts. The second major generational change is a rapid rise in rates of anxiety and depression.11 We created three graphs below using the same data that Twenge reports in iGen.

The rate at which we can adapt is increasing,” said Teller. “A thousand years ago, it probably would have taken two or three generations to adapt to something new.” By 1900, the time it took to adapt got down to one generation. “We might be so adaptable now,” said Teller, “that it only takes ten to fifteen years to get used to something new.” Alas, though, that may not be good enough. Today, said Teller, the accelerating speed of scientific and technological innovations (and, I would add, new ideas, such as gay marriage) can outpace the capacity of the average human being and our societal structures to adapt and absorb them. With that thought in mind, Teller added one more thing to the graph—a big dot. He drew that dot on the rapidly sloping technology curve just above the place where it intersected with the adaptability line. He labeled it: “We are here.” The graph, as redrawn for this book, can be seen on the next page. That dot, Teller explained, illustrates an important fact: even though human beings and societies have steadily adapted to change, on average, the rate of technological change is now accelerating so fast that it has risen above the average rate at which most people can absorb all these changes. Many of us cannot keep pace anymore.

Teller arrived at our interview on Rollerblades, which is how he keeps up with his daily crush of meetings. He wasted no time before launching into an explanation of how the accelerations in Moore’s law and in the flow of ideas are together causing an increase in the pace of change that is challenging the ability of human beings to adapt. Teller began by taking out a small yellow 3M notepad and saying: “Imagine two curves on a graph.” He then drew a graph with the Y axis labeled “rate of change” and the X axis labeled “time.” Then he drew the first curve—a swooping exponential line that started very flat and escalated slowly before soaring to the upper outer corner of the graph, like a hockey stick: “This line represents scientific progress,” he said. At first it moves up very gradually, then it starts to slope higher as innovations build on innovations that have come before, and then it starts to soar straight to the sky.

having a good understanding of what the exponential mindset looks like. In a piece for the Harvard Business Review, Mark Bonchek, founder and chief epiphany officer of Shift Thinking, describes the linear mindset as a line appearing on a graph that rises gradually over time. He then juxtaposes this with a second line that curves upward, slowly at first, and then shooting over the other line before heading far off the graph. This is his visual depiction of the exponential mindset.

When God looks upon my life graph, he sees not jagged swerves toward good and bad but rather a steady line of good: the goodness of God’s Son captured in a moment of time and applied for all eternity.

Brendan Nyhan, assistant professor of government at Dartmouth College, found that when voters are misinformed, factual information only makes them become more rigid in their point of view! Nyhan found these instances of facts making people more rigid: -People who thought weapons of mass destruction were found in Iraq believed that misinformation even more strongly when they were shown a news story correcting that belief. -People who thought George W. Bush banned all stem cell research kept thinking he did that even after they were shown an article saying that only some federally funded stem cell work was stopped. -People who said the economy was the most important issue to them, and who disapproved of Barack Obama’s economic record, were shown a graph of nonfarm employment over the prior year. It included a rising line that indicated about one million jobs were added. They were asked whether the number of people with jobs had gone up, down, or stayed about the same. Many, looking straight at the graph, said down.

In the three years I spent working on this book, making dozens of line graphs, reading campus newspapers, and listening to the stories and opinions of young people during in-depth interviews, I’ve realized this: iGen’ers are scared, maybe even terrified. Growing up slowly, raised to value safety, and frightened by the implications of income inequality, they have come to adolescence in a time when their primary social activity is staring at a small rectangular screen that can like them or reject them. The devices they hold in their hands have both extended their childhoods and isolated them from true human interaction. As a result, they are both the physically safest generation and the most mentally fragile. They are more focused on work and more realistic than Millennials, grasping the certainty that they’ll need to fight hard to make it. They’re exquisitely tolerant and have brought a new awareness of equality, mental health, and LGBT rights, leaving behind traditional structures such as religion. iGen’ers have a solid basis for success, with their practical nature and their inherent caution. If they can shake themselves free of the constant clutch of their phones and shrug off the heavy cloak of their fear, they can still fly. And the rest of us will be there, cheering them on.

The first surveillance system K-129 encountered was called SOSUS by the Americans, an acronym for Sound Surveillance System. This system was a vast array of passive hydroacoustical listening devices called hydrophones, placed strategically around the Atlantic and Pacific oceans. It consisted of cable-connected, underwater phones planted along the bottom of the oceans to collect sounds generated from any source. These sounds were transmitted to shore stations where they were recorded in lines on continuous rolls of graph paper. Acoustic experts were able to read these sound patterns to distinguish between natural ocean sounds, ships, and submarines. The hydrophones were so sensitive that even aircraft noise from planes flying above the ocean and the sound of falling rain could be monitored.

expanded the graph with two fingers. The slight decline of the dotted testosterone line looked like a change one might hardly notice. While I was falling off the sheer face of a mountain, Harris would be ambling along a gently sloping country road with a piece of straw in the corner of his mouth, whistling.