Combined Maths Quotes

Forty-six point two billion dollars, I thought, my heart attacking my rib cage and my mouth sandpaper-dry. Tobias Hawthorne was worth forty-six point two billion dollars, and he left his grandsons a million dollars, combined. A hundred thousand total to his daughters. Another half million to his servants, an annuity for Nan... The math in this equation did not add up. It couldn't add up. One by one, the other occupants of the room of the room turned to stare at me. 'The remainder of my estate,' Mr. Ortega read, 'including all properties, monetary assets, and worldly possessions not otherwise specified, I leave to Avery Kylie Grambs.

He walked straight out of college into the waiting arms of the Navy. They gave him an intelligence test. The first question on the math part had to do with boats on a river: Port Smith is 100 miles upstream of Port Jones. The river flows at 5 miles per hour. The boat goes through water at 10 miles per hour. How long does it take to go from Port Smith to Port Jones? How long to come back? Lawrence immediately saw that it was a trick question. You would have to be some kind of idiot to make the facile assumption that the current would add or subtract 5 miles per hour to or from the speed of the boat. Clearly, 5 miles per hour was nothing more than the average speed. The current would be faster in the middle of the river and slower at the banks. More complicated variations could be expected at bends in the river. Basically it was a question of hydrodynamics, which could be tackled using certain well-known systems of differential equations. Lawrence dove into the problem, rapidly (or so he thought) covering both sides of ten sheets of paper with calculations. Along the way, he realized that one of his assumptions, in combination with the simplified Navier Stokes equations, had led him into an exploration of a particularly interesting family of partial differential equations. Before he knew it, he had proved a new theorem. If that didn't prove his intelligence, what would? Then the time bell rang and the papers were collected. Lawrence managed to hang onto his scratch paper. He took it back to his dorm, typed it up, and mailed it to one of the more approachable math professors at Princeton, who promptly arranged for it to be published in a Parisian mathematics journal. Lawrence received two free, freshly printed copies of the journal a few months later, in San Diego, California, during mail call on board a large ship called the U.S.S. Nevada. The ship had a band, and the Navy had given Lawrence the job of playing the glockenspiel in it, because their testing procedures had proven that he was not intelligent enough to do anything else.

A Nonstandard Graph, Elements and Operations, a Card Game Dialect A combination of the Mold dialects and Sandwich graphs, backed by axiomatic math, creates a unique space of science and fantasy.

The thing with the Rolexes is amazing, amazing, Ivan wrote. Light, he said, seemed to sweep, but quantum theory said it ticked. Waves were the combination of sweeping and ticking. Could true sweeping ever happen on this Earth of ours? Maybe one could do sweeping math, og sweeping sex. Sweeping was beautiful, but powerless. Energy came from ticking - the capacity for rapid change. Immortality was sweeping. Lives coming and going, generations, years, minutes, seconds: all are on the fake Rolex.

Social media is biased, not to the Left or the Right, but downward. The relative ease of using negative emotions for the purposes of addiction and manipulation makes it relatively easier to achieve undignified results. An unfortunate combination of biology and math favors degradation of the human world. Information warfare units sway elections, hate groups recruit, and nihilists get amazing bang for the buck when they try to bring society down. The unplanned nature of the transformation from advertising to direct behavior modification caused an explosive amplification of negativity in human affairs.

If you hate math and English, then you’ll really hate Algebra, with its numbers and letters, because it combines BOTH. To survive in life you must pivot, which is why I'm now tutoring at Used Duck Prices.

Littlewood, on Hardy's own estimate, is the finest mathematician he has ever known. He was the man most likely to storm and smash a really deep and formidable problem; there was no one else who could command such a combination of insight, technique and power.

Part of the process of getting to know my children is helping them figure out what they're passionate about. And when I say passionate, I don't mean just, "What do you love?" I also want to know, "What angers you? What angers you about the world? What breaks your heart?" Pay attention to all the strong emotions, whether they're good or bad, because intensity shows how genuinely they care about something. If I can get my kids to pinpoint what really makes them *feel* and then combine that with who they are-- hyper, talkative, patient, great at math--I can help them begin to map out what they're meant to do with their lives.

As was foreshadowed in Paragraphs 1 and 4, Cantor, and Dedekind's near-simultaneous appearance in math is more or less the Newton + Leibniz thing all over again, a sure sign that the Time Was Right for (Infinity)-type sets. Just as striking is the Escherian way the two men's work dovetails. Cantor is able to define and ground the concepts of 'infinite set' and 'transfinite number,' and to establish rigorous techniques for combining and comparing different types of (Infinity)s, which is just where Dedekind's def. of irrationals needs shoring up. Pro quo, the schnitt technique demonstrates that actually-infinite sets can have real utility in analysis. That, in other words, as sensuously and cognitively abstract as they must remain, (Infinity)s can nevertheless function in math as practical abstractions rather than as just weird paradoxical flights of fancy.

Anywhere you find the combination of great need and ignorance, you’ll likely see predatory ads. If people are anxious about their sex lives, predatory advertisers will promise them Viagra or Cialis, or even penis extensions. If they are short of money, offers will pour in for high-interest payday loans. If their computer is acting sludgy, it might be a virus inserted by a predatory advertiser, who will then offer to fix it. And as we’ll see, the boom in for-profit colleges is fueled by predatory ads.

Take pride in your choices, not your gifts. ... This is something that's super-important for young people to understand, and for parents to preach to young people. It's really easy for a talented young person to take pride in their gifts: "I'm really athletic," or "I'm really smart," or "I'm really good at math." That's fine. You should celebrate your gifts. You should be happy. But you can't be proud of them ... What you can be proud of is your choices. How did you decide to use your gifts? Did you study hard? Did you work hard? Did you practice? The people who excel combine gifts and hard work, and the hard work part is a choice. You get to decide that. And that is something that when you're looking back on your life, you will be very proud of.

I occasionally return to some very basic, mathematical thoughts: There are only so many letters in our Roman alphabet. It is then by the power of the math—the infinite (or not strictly infinite, but huge) number of combinations of letters—that we have so many words. But then, further expanding the number of possibilities, truly to infinity, one word (one combination of letters) can have multiple meanings. Further multiplying the number of meanings, even within one given dictionary definition of a word, is the effect of its context, both immediate and larger, which can endow it with, again, an infinite number of subtly differing shades of meaning. Further enriching the single word, within and beyond its contexts, is one’s own personal associations with it, either from one’s reading or from one’s life experiences. And even in one’s own native language, there are a great many words, meanings, and shades of meaning that one simply doesn’t know and may never encounter.

Do you believe in God, Aunt Elner?” “Sure I do, honey, why?” “How old were you when you started believing, do you remember?” Aunt Elner paused for a moment. “I never thought about not believing. Never did question it. I guess believing is just like math: some people get it right out of the chute, and some have to struggle for it. (...) Oh, I know a lot of people struggle, wondering is there really a God. They sit and think and worry over it all their life. The good Lord had to make smart people but I don’t think he did them any favors because it seems the smart ones start questioning things from the get go. But I never did. I’m one of the lucky ones. I thank God every night, my brain is just perfect for me, not too dumb, not too bright. You know, your daddy was always asking questions.” “He was?” “I remember one day he said, ‘Aunt Elner, how do you know there is a God, how can you be sure?’ ” “What did you tell him?” “I said, ‘Well, Gene, the answer is right on the end of your fingertips.’ He said, ‘What do you mean?’ I said, ‘Well, think about it. Every single human being that was ever born from the beginning of time has a completely different set of fingerprints. Not two alike. Not a single one out of all the billions is ever repeated.’ I said, ‘Who else but God could think up all those different patterns and keep coming up with new ones year after year, not to mention all the color combinations of all the fish and birds.’ ” Dena smiled. “What did he say?” “He said, ‘Yes, but, Aunt Elner, how do you know that God’s not repeating old fingerprints from way back and reusing them on us?’ ” She laughed. “See what I mean? Yes, God is great, all right. He only made one mistake but it was a big one.” “What was that?” “Free will. That was his one big blunder. He gave us a choice whether or not to be good or bad. He made us too independent … and you can’t tell people what to do; they won’t listen. You can tell them to be good until you’re blue in the face but people don’t want to be preached at except at church, where they know what they are getting and are prepared for it.” “What’s life all about, Aunt Elner? Don’t you ever wonder what the point of the whole thing is?” “No, not really; it seems to me we only have one big decision in this life, whether to be good or bad. That’s what I came up with a long time ago. Of course, I may be wrong, but I’m not going to spend any time worrying over it, I’m just going to have a good time while I’m here. Live and let live.

In both cultures, wealth is no longer a means to get by. It becomes directly tied to personal worth. A young suburbanite with every advantage—the prep school education, the exhaustive coaching for college admissions tests, the overseas semester in Paris or Shanghai—still flatters himself that it is his skill, hard work, and prodigious problem-solving abilities that have lifted him into a world of privilege. Money vindicates all doubts. They’re eager to convince us all that Darwinism is at work, when it looks very much to the outside like a combination of gaming a system and dumb luck. In both of these industries, the real world, with all of its messiness, sits apart. The inclination is to replace people with data trails, turning them into more effective shoppers, voters, or workers to optimize some objective. This is easy to do, and to justify, when success comes back as an anonymous score and when the people affected remain every bit as abstract as the numbers dancing across the screen. More and more, I worried about the separation between technical models and real people, and about the moral repercussions of that separation. In fact, I saw the same pattern emerging that I’d witnessed in finance: a false sense of security was leading to widespread use of imperfect models, self-serving definitions of success, and growing feedback loops. Those who objected were regarded as nostalgic Luddites.

When you measure a single spiked wave, such as that in Figure 8.9, the device registers the spike's location. If it's spiked at Strawberry Fields, that's what the device reads; if you look at the result, your brain registers that location and you become aware of it. If it's spiked at Grant's Tomb, that's what the device registers; if you look, your brain registers that location and you become aware of it. When you measure the double spiked wave in Figure 8.10, Schrodinger's math tells you to combine the two results you just found. But, says Everett, be careful and precise when you combine them. The combined result, he argued, does not yield a meter and a mind each simultaneously registering two locations. That's sloppy thinking. Instead, proceeding slowly and literally, we find that the combined result is a device and a mind registering Strawberry Fields, and a device and a mind registering Grant's Tomb. And what does that mean? I'll use broad strokes in painting the general picture, which I'll refine shortly. To accommodate Everett's suggested outcome, the device and you and everything else must split upon measurement, yielding two devices, two yous, and two everything elses-the only difference between the two being that one device and one you registers Strawberry Fields, while the other device and the other you registers Grant's Tomb. As in Figure 8.12, this implies that we now have two parallel realities, two parallel worlds. To the you occupying each, the measurement and your mental impression of the result are sharp and unique and thus fell like life as usual. The peculiarity, of course, is that there are two of you who feel this way.

The math is simple, and laid out in Table 5.6. From 20 million traffic stops, 2.4 percent lead to a search. Of those, just 33 percent led to contraband (0.8 percent of stops), and just 12 percent of the searches led to a contraband-arrest combination (0.29 percent of stops). That is, 99.7 percent of traffic stops fail to generate a drug or contraband arrest. The “sheer numbers game” the California trooper describes is a bad gamble.

What the HeartMath experiment demonstrates is that the quantum field doesn’t respond simply to our wishes—our emotional requests. It doesn’t just respond to our aims—our thoughts. It only responds when those two are aligned or coherent—that is, when they are broadcasting the same signal. When we combine an elevated emotion with an open heart and a conscious intention with clear thought, we signal the field to respond in amazing ways. The quantum field responds not to what we want; it responds to who we are being.

The first bell went off just as I got to my locker. After spinning the combination into the padlock, I yanked on the handle while pressing my shoulder into the door. It was my usual routine whenever I visited my locker so none of my stuff would fall out. Sure, we have a locker clean out every two weeks, but you know how life can get busy sometimes, right? That and I was pretty sure I was feeding a small family of rodents living at the bottom of it. I’m not sure I could live with myself if I did anything to take food off their table. Squeezing my fingers into the cold, dark, and somehow damp locker, I managed to scrape the top of my math book just enough so that it would tip into my hand. “Gotcha!” I exclaimed as I slid the book out slowly. After it was free from the locker, I slammed the door shut with my knee since that was the spot where it clicked shut. Suddenly, like she materialized out of thin air, Naomi was standing

The first bell went off just as I got to my locker. After spinning the combination into the padlock, I yanked on the handle while pressing my shoulder into the door. It was my usual routine whenever I visited my locker so none of my stuff would fall out. Sure, we have a locker clean out every two weeks, but you know how life can get busy sometimes, right? That and I was pretty sure I was feeding a small family of rodents living at the bottom of it. I’m not sure I could live with myself if I did anything to take food off their table. Squeezing my fingers into the cold, dark, and somehow damp locker, I managed to scrape the top of my math book just enough so that it would tip into my hand. “Gotcha!

Anywhere you find the combination of great need and ignorance, you’ll likely see predatory ads. Why, specifically, were they targeting these folks? Vulnerability is worth gold. The customers’ ignorance, of course, is a crucial piece of the puzzle. Once the ignorance is established, the key for the recruiter, just as for the snake-oil merchant, is to locate the most vulnerable people and then use their private information against them. This involves finding where they suffer the most, which is known as the “pain point.” It might be low self-esteem, the stress of raising kids in a neighborhood of warring gangs, or perhaps a drug addiction. Many people unwittingly disclose their pain points when they look for answers on Google or, later, when they fill out college questionnaires.

Woz was equal parts programming genius and mischievous prankster, known around the San Francisco Bay Area for running his own dial-a-joke phone number. In computers, Woz found the perfect place to combine his humor and his math skills, creating a game that flashed the message "Oh Shit" on the screen when the player lost a round. Jobs recruited Woz to design Breakout, a new game for Atari. This alchemy of Jobs's entrepreneurial vision and Woz's programming ingenuity gave birth to their company, Apple. Created in 1976, the first Apple computer was essentially a prototype for the Homebrew crowd, priced devilishly at $666.66.

Social media is biased, not to the Left or the Right, but downward. The relative ease of using negative emotions for the purposes of addiction and manipulation makes it relatively easier to achieve undignified results. An unfortunate combination of biology and math favors degradation of the human world. Information warfare units sway elections, hate groups recruit, and nihilists get amazing bang for the buck when they try to bring society down.

Innovations are happening in conventional schooling. Some people will read the chapters to come and respond that their own children’s schools are incorporating evidence-based changes, making them more like Montessori schools—eliminating grades, combining ages, using a lot of group work, and so on. One could take the view that over the years, conventional schooling has gradually been discovering and incorporating many of the principles that Dr. Montessori discovered in the first half of the 20th century. However, although schooling is changing, those changes are often relatively superficial. A professor of education might develop a new reading or math program that is then adopted with great fanfare by a few school systems, but the curricular change is minute relative to the entire curriculum, and the Lockean model of the child and the factory structure of the school environment still underlie most of the child’s school day and year. “Adding new ‘techniques’ to the classroom does not lead to the developmental of a coherent philosophy. For example, adding the technique of having children work in ‘co-operative learning’ teams is quite different than a system in which collaboration is inherent in the structure” (Rogoff, Turkanis, & Bartlett, 2001, p. 13). Although small changes are made reflecting newer research on how children learn, particularly in good neighborhood elementary schools, most of the time, in most U.S. schools, conventional structures predominate (Hiebert, 1999; McCaslin et al., 2006; NICHD, 2005; Stigler, Gallimore, & Hiebert, 2000), and observers rate most classes to be low in quality (Weiss, Pasley, Smith, Banilower, & Heck, 2003). Superficial insertions of research-supported methods do not penetrate the underlying models on which are schools are based. Deeper change, implementing more realistic models of the child and the school, is necessary to improve schooling. How can we know what those new models should be? As in medicine, where there have been increasing calls for using research results to inform patient treatments, education reform must more thoroughly and deeply implement what the evidence indicates will work best. This has been advocated repeatedly over the years, even by Thorndike. Certainly more and more researchers, educators, and policy makers are heeding the call to take an evidence-based stance on education. Yet the changes made thus far in response to these calls have not managed to address to the fundamental problems of the poor models. The time has come for rethinking education, making it evidence based from the ground up, beginning with the child and the conditions under which children thrive. Considered en masse, the evidence from psychological research suggests truly radical change is needed to provide children with a form of schooling that will optimize their social and cognitive development. A better form of schooling will change the Lockean model of the child and the factory structure on which our schools are built into something radically different and much better suited to how children actually learn.

Whenever a state of featureless equilibrium loses stability—for whatever reason, and by whatever physical, biological, or chemical process—the pattern that appears first is a sine wave, or a combination of them.

One night, Hayes went home after work and decided he would cook dinner for them. Ainsworth, stuck at work on a conference call, was running late. When she finally got home, dinner was nearly ready, but Ainsworth was wiped out and declared that she wanted to decompress in a bath. “Give me ten minutes,” she said. After a while, Hayes went upstairs to the bathroom to see what was taking so long. Ainsworth was still soaking in the tub. Hayes was hungry. He’d prepared a shepherd’s pie, a casserole-style combination of ground beef, mashed potatoes, and peas, and he wanted to eat it before it got cold. Ainsworth asked for a few more minutes. Ten minutes passed. Hayes marched back upstairs and dumped the pie into the water. Ainsworth, stunned, sat in the bath, peas bobbing around her. At work the next day, Davies asked Hayes how his night had been. Hayes took the casual question literally, and without reserve or the slightest sense of faux pas told Davies what had happened. Within days, the pie-in-the-bath story had bounced all over the City’s trading and brokerage floors. It would continue to circulate for more than a decade.

First, there’s mathematics. Obviously, you’ve got to be able to handle numbers and quantities—basic arithmetic. And the great useful model, after compound interest, is the elementary math of permutations and combinations. That was taught in my day in the sophomore year in high school. I suppose by now, in great private schools, it’s probably down to the eighth grade or

The Daisy he knew was young and innocent and had fully embraced her position on the high school geek squad. Her clothes had been quirky and weird, a mix of accessories, colors, patterns, and fandoms that she'd combined into a unique geek-chic style. She'd tied her long, dark hair in a ponytail so it didn't get in the way when she was helping the freshmen with their computer programs, mixing chemicals for science fair projects, or studying for the latest math competition.

Flower of life: A figure composed of evenly-spaced, overlapping circles creating a flower-like pattern. Images of the Platonic solids and other sacred geometrical figures can be discerned within its pattern. FIGURE 3.14 FLOWER OF LIFE The Platonic solids: Five three-dimensional solid shapes, each containing all congruent angles and sides. If circumscribed with a sphere, all vertices would touch the edge of that sphere. Linked by Plato to the four primary elements and heaven. FIGURE 3.15 PENTACHORON The applications of these shapes to music are important to sound healing theory. The ancients have always professed a belief in the “music of the spheres,” a vibrational ordering to the universe. Pythagorus is famous for interconnecting geometry and math to music. He determined that stopping a string halfway along its length created an octave; a ratio of three to two resulted in a fifth; and a ratio of four to three produced a fourth. These ratios were seen as forming harmonics that could restore a disharmonic body—or heal. Hans Jenny furthered this work through the study of cymatics, discussed later in this chapter, and the contemporary sound healer and author Jonathan Goldman considers the proportions of the body to relate to the golden mean, with ratios in relation to the major sixth (3:5) and the minor sixth (5:8).100 Geometry also seems to serve as an “interdimensional glue,” according to a relatively new theory called causal dynamical triangulation (CDT), which portrays the walls of time—and of the different dimensions—as triangulated. According to CDT, time-space is divided into tiny triangulated pieces, with the building block being a pentachoron. A pentachoron is made of five tetrahedral cells and a triangle combined with a tetrahedron. Each simple, triangulated piece is geometrically flat, but they are “glued together” to create curved time-spaces. This theory allows the transfer of energy from one dimension to another, but unlike many other time-space theories, this one makes certain that a cause precedes an event and also showcases the geometric nature of reality.101 The creation of geometry figures at macro- and microlevels can perhaps be explained by the notion called spin, first introduced in Chapter 1. Everything spins, the term spin describing the rotation of an object or particle around its own axis. Orbital spin references the spinning of an object around another object, such as the moon around the earth. Both types of spin are measured by angular momentum, a combination of mass, the distance from the center of travel, and speed. Spinning particles create forms where they “touch” in space.

Convert the following fractions into % (percentages). Press/select the answer with the correct combination from the 3 given options: a) 50%, 25%, 30%, 20% b) 1/2%, 12%, 60%, 20% c) 50%, 75%, 60%, 20%

What are the missing numbers in the boxes labelled a, b, c, and d. Press/select the answer with the correct combination from the 4 given options: a) 3, 51, 27, 49 b) 3, 68, 27, 49 c) 3, 51, 27, 49 d) 3, 68, 29, 49

Ignition and deep practice work together to produce skill in exactly the same way that a gas tank combines with an engine to produce velocity in an automobile

Why do things happen the way they do? Is there some kind of order in all this chaos that we just don't see, or is it all, as the mathematically minded people would like us to believe, just random coincidence? If you put one hundred apes in a room, they'll tell you, with one hundred typewriters, and given an infinite amount of time and bananas, one of them would eventually churn out the complete Oxford dictionary. It's all statistical math and probability. The odds of winning the lottery are greater than the odds of getting struck by lightning, but someone wins, don't they? And people get hit by lightning disturbingly more often that you would think. Their point is, eventually all things happen. No matter how philosophically unprejudiced you are, you can't argue with statistical probabilities. But you can certainly give the mathematicians some substantial cud to chew on, can't you? For instance, sure, everything may be eventual from a statistical point of view, but what happens to the formula if you plug in when a particular thing happens? The fortuitousness of the timing? Or combine a particular coincidence with other seemingly non-related coincidences that might have occurred within the same general time frame? We've all had it happen. It's one of our favorite phrases: "Why me? Why now?" Well, when you take the "when" into account, all kinds of very interesting and un-mathematical things begins to happen. The coincidence becomes too coincidental to be a coincidence.

Making is a way of bringing engineering to young learners. Such concrete experiences provide a meaningful context for understanding abstract science and math concepts. For older students, making combines disciplines in ways that enhance the learning process for diverse student populations and opens the doors to unforeseen career paths.

Kenzie Denune pedaled the bicycle harder, her thighs burning from the exertion. Thanks to a car that refused to start, she was going to be late for her job interview at Iverson Loch Manor. Grunting and pounding from the shrubs ahead, near the road's edge, snagged her attention. Naked shoulders glistened in the afternoon sun. Back muscles bulged and undulated with every thrust. “Bloody hell. Come fer me. Come.” In all of Mathe Bay in the Scottish Highlands, only one deep masculine voice had the power to raise the hair on her arms like this. A man with braided russet-colored hair that brushed broad shoulders inked with a bear's claw marks, woven into an intricate tribal design - Bryce Matheson. Damn him to hell. Who's he shagging in broad daylight? Out in the open, no less. Has he no shame? ... “I canna keep pounding at ye like this all bloody day. Me back is about to give out.” Bryce moaned and groaned again, obviously in the throes of ecstasy. The bear-shifting bastard. She eased up on the brakes to whiz past his love nest of bushes and brambles. “I'll not give up until I get ye wild cherry. Let me push both me thumbs and most of me fingers in here and....." My God, what's he doing to her? Kenzie couldna resist one fleeting glance over her shoulder. Her front wheel plunged into a pothole and the bike pitched... as she toppled across the grit. The force of the impact, combined with the slant of the narrow road, caused her to roll toward Bryce and his current conquest. No! No, God, no!

On the SAT exam, boys who took the test during 1988–89 at Permian had a combined average score of 915 (433 verbal, 482 mathematical), 19 points below the national average for boys. Girls had a combined score of 840 (404 verbal, 436 mathematical), 75 points below their male counterparts at Permian and 35 points below the national average for girls. Of the 132 girls who took the test during the 1988–89 school year, there wasn’t one who got above a 650 in either the math or verbal portions of the exam.

Many teachers felt that no matter how creative they were in the classroom, it wouldn’t make a difference anyway. They talked about a devastating erosion in standards, how the students of today bore no resemblance to the students of even ten or fifteen years ago, how their preoccupations were with anything but school. It was hard for teachers not to feel depressed by the lack of rudimentary knowledge, like in the history class in which students were asked to name the president after John F. Kennedy. Several students meekly raised their hands and proffered the name of Harry Truman. None gave the correct answer of Lyndon Johnson, who also happened to have been a native Texan. In 1975, the average SAT score on the combined math and verbal sections at Permian was 963. For the senior class of 1988–89, the average combined SAT score was 85 points lower, 878. During the seventies, it had been normal for Permian to have seven seniors qualify as National Merit semi-finalists. In the 1988–89 school year the number dropped to one, which the superintendent of schools, Hugh Hayes, acknowledged was inexcusable for a school the size of Permian with a student body that was rooted in the middle class. (A year later, with the help of $15,000 in consultant’s fees to identify those who might pass the required test, the number went up to five.)

Rebecca Gleeson (an everyday schoolgirl on her way to school on the Monday morning eight o’clock train.) The Kingdom of Nought is a time tale legacy: accompanying her on the train Rebecca’s arch nemeses Rona Chadwick, the school bully. Rebecca a fan of poetry and fairy tales. “Tales of kindness and friendship.” She would say to herself. Rebecca was a reader of wonderful books that have a cult following. Unknown to Rebecca far away at the start of the universe dark and evil forces start to unbalance the natural order of day and night, good and evil. Weird things begin to happen as both Rebecca and Rona are transported back in time to The Kingdom of Nought to reinstate the benevolent balance within the kingdom. The adventure for the schoolgirls starts out strange and gets stranger, in the best way possible. Their meeting with the witch Sycorax is as creepy and evocative as you’d hope. The story combines mathematical realism with fantasy, blurring the edges in a way that high-lights that place where stories and real life convene, where magic contains truth. As you open the book and turn the pages you enter a strange place out-side time with amazing creatures and spectacular landscapes. An extremely addictive story that will take you to a magical place with a most unusual conclusion.

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.

The findings that were deemed believable enough to be published, however, revolutionized ethologists’ thinking. Ethologists began to speak less often of a chasm between man and ape; they began to speak instead of a dividing “line.” And it was a line that, in the words of Harvard primatologist Irven De Vore, was “a good deal less clear than one would ever have expected.” What makes up this line between us and our fellow primates? No longer can it be claimed to be tool use. Is it the ability to reason? Wolfgang Kohler once tested captive chimps’ reasoning ability by placing several boxes and a stick in an enclosure and hanging a banana from the high ceiling by a string. The animals quickly figured out that they could get to the banana by stacking the boxes one atop the other and then reaching to swat at the banana with a stick. (Once Geza Teleki found himself in exactly this position at Gombe. He had followed the chimpanzees down into a valley and around noon discovered he had forgotten to bring his lunch. The chimps were feeding on fruit in the trees at the time, and he decided to try to knock some fruit from nearby vines with a stick. For about ten minutes he leaped and swatted with his stick but didn’t manage to knock down any fruit. Finally an adolescent male named Sniff collected a handful of fruit, came down the tree, and dropped the fruit into Geza’s hands.) Some say language is the line that separates man from ape. But this, too, is being questioned. Captive chimpanzees, gorillas, and orangutans have been taught not only to comprehend, but also to produce language. They have been taught American Sign Language (ASL), the language of the deaf, as well as languages that use plastic chips in place of words and computer languages. One signing chimp, Washoe, often combined known signs in novel and creative ways: she had not been taught the word for swan, but upon seeing one, she signed “water-bird.” Another signing chimp, Lucy, seeing and tasting a watermelon for the first time, called it a “candy-drink”; the acidic radish she named “hurt-cry-food.” Lucy would play with toys and sign to them, much as human children talk to their dolls. Koko, the gorilla protegee of Penny Patterson, used sign language to make jokes, escape blame, describe her surroundings, tell stories, even tell lies. One of Biruté’s ex-captives, a female orangutan named Princess, was taught a number of ASL signs by Gary Shapiro. Princess used only the signs she knew would bring her food; because she was not a captive, she could not be coerced into using sign language to any ends other than those she found personally useful. Today dolphins, sea lions, harbor seals, and even pigeons are being taught artificial languages, complete with a primitive grammar or syntax. An African grey parrot named Alex mastered the correct use of more than one hundred spoken English words, using them in proper order to answer questions, make requests, do math, and offer friends and visitors spontaneous, meaningful comments until his untimely death at age 31 in 2007. One leading researcher, Ronald Schusterman, is convinced that “the components for language are present probably in all vertebrates, certainly in mammals and birds.” Arguing over semantics and syntax, psychologists and ethologists and linguists are still debating the definitions of the line. Louis Leakey remarked about Jane’s discovery of chimps’ use of tools that we must “change the definition of man, the definition of tool, or accept chimps as man.” Now some linguists have actually proposed, in the face of the ape language experiments, changing the definition of language to exclude the apes from a domain we had considered uniquely ours. The line separating man from the apes may well be defined less by human measurement than by the limits of Western imagination. It may be less like a boundary between land and water and more like the lines we draw on maps separating the domains of nations.

... Feynman's technique was simple. And he claimed that it was always successful. But it' not currently working for me. Not yet. What was it? Well, when he was building the first atomic bomb, he observed that scientists were so worried about forgetting the codes to their safes that they invariably used a memorable date as their combination. And if you do the maths on that, the first two numbers, the month in the American dating system, could only be 01 - 12 and having only twelve options instead of 99 made it far more manageable process when the next to numbers were likely to be between one and 31, and the last two were certainly a two-digit number from the previous 50 years. Basically, he cut the odds and could crack the code with brute force if he had to. But he rarely had to because he just found that people wrote the code down on a slip of paper or in a notebook somewhere near the safe in question. In a drawer or what not. Seriously, Tanika asked, that's the problem with magic tricks. If you look at the effect, Richard Feynman breaking into Robert Oppenheimer's safe, where the codes where the atomic bomb were kept, your dumbstruck. But explain your workings and it all becomes very hum-drum.

In all racial groups, students from wealthy households tend to score better than those who are poor, but income does not explain group differences. A study by McKinsey and Company found that white fourth graders living in poverty scored higher—by the equivalent of about half-a-year’s instruction—than black fourth graders who were not poor. These differences increase in high school. On the 2009 math and verbal SAT tests, whites from families with incomes of less than $20,000 not only had an average combined score that was 117 points (out of 1600) higher than the average for all blacks, they even outscored by 12 points blacks who came from families with incomes of $160,000 to $200,000. Educators and legislators have not ignored the problem. The race gap in achievement is such a preoccupation that in 2007, 4,000 educators and experts attended an “Achievement Gap Summit” in Sacramento. They took part in no fewer than 125 panels on ways to help blacks and Hispanics do as well as whites and Asians. Overwhelming majorities in Congress passed the No Child Left Behind Act in 2002 to improve student performance and bridge achievement gaps. The government budgeted $24.4 billion for the program for fiscal year 2007, and its requirements for “Adequate Yearly Progress” have forced change on many schools. This is only the latest effort in more than 25 years of federal involvement. The result? In 2009, Chester E. Finn, Jr., a former education official in the Reagan administration, put it this way: “This is a nearly unrelenting tale of woe and disappointment. If there’s any good news here, I can’t find it.

Social media is biased, not to the Left or the Right, but downward. The relative ease of using negative emotions for the purposes of addiction and manipulation makes it relatively easier to achieve undignified results. An unfortunate combination of biology and math favors degradation of the human world. Information warfare units sway elections, hate groups recruit, and nihilists get amazing bang for the buck when they try to bring society down.The unplanned nature of the transformation from advertising to direct behavior modification caused an explosive amplification of negativity in human affairs. We’ll return to the higher potency of negative emotions in behavior modification many times as we explore the personal, political, economic, social, and cultural effects of social media.

It is hard to overstate the beauty of this equation. It combines in one equation what are arguably the most important symbols and operations in mathematics. Along with the operations of addition, multiplication, and exponentiation, you have 0, the additive identity, 1, the multiplicative identity, i, the imaginary unit, and two of the most important mathematical constants, e and π. This equation is also integral to quantum computing. You will see eiθ all over the place in quantum computing, so you better get used to it!

If you have a set of vectors and you can create a linear combination of one of the vectors from a subset of the other vectors, then all of those vectors are linearly dependent.

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