Maths Related Quotes

I am encouraged as I look at some of those who have listened to their "different drum": Einstein was hopeless at school math and commented wryly on his inadequacy in human relations. Winston Churchill was an abysmal failure in his early school years. Byron, that revolutionary student, had to compensate for a club foot; Demosthenes for a stutter; and Homer was blind. Socrates couldn't manage his wife, and infuriated his countrymen. And what about Jesus, if we need an ultimate example of failure with one's peers? Or an ultimate example of love?

We don't have a gun problem; we have a math problem: ZERO GUNS = ZERO GUN-RELATED DEATHS.

The importance of C.F. Gauss for the development of modern physical theory and especially for the mathematical fundament of the theory of relativity is overwhelming indeed; also his achievement of the system of absolute measurement in the field of electromagnetism. In my opinion it is impossible to achieve a coherent objective picture of the world on the basis of concepts which are taken more or less from inner psychological experience.

At the federal level, this problem could be greatly alleviated by abolishing the Electoral College system. It's the winner-take-all mathematics from state to state that delivers so much power to a relative handful of voters. It's as if in politics, as in economics, we have a privileged 1 percent. And the money from the financial 1 percent underwrites the microtargeting to secure the votes of the political 1 percent. Without the Electoral College, by contrast, every vote would be worth exactly the same. That would be a step toward democracy.

Todd, trust math. As in Matics, Math E. First-order predicate logic. Never fail you. Quantities and their relation. Rates of change. The vital statistics of God or equivalent. When all else fails. When the boulder's slid all the way back to the bottom. When the headless are blaming. When you do not know your way about. You can fall back and regroup around math. Whose truth is deductive truth. Independent of sense or emotionality. The syllogism. The identity. Modus Tollens. Transitivity. Heaven's theme song. The night light on life's dark wall, late at night. Heaven's recipe book. The hydrogen spiral. The methane, ammonia, H2O. Nucleic acids. A and G, T and C. The creeping inevibatility. Caius is mortal. Math is not mortal. What it is is: listen: it's true.

The philosophers make still another objection: "What you gain in rigour," they say, "you lose in objectivity. You can rise toward your logical ideal only by cutting the bonds which attach you to reality. Your science is infallible, but it can only remain so by imprisoning itself in an ivory tower and renouncing all relation with the external world. From this seclusion it must go out when it would attempt the slightest application.

If you don’t make a point of repeating what you want to remember, your “metabolic vampires” can suck away the neural pattern related to that memory before it can strengthen and solidify.

In an era of weaponized sensitivity, participation in public discourse is growing so perilous, so fraught with the danger of being caught out for using the wrong word or failing to uphold the latest orthodoxy in relation to disability, sexual orientation, economic class, race or ethnicity, that many are apt to bow out. Perhaps intimidating their elders into silence is the intention of the identity-politics cabal — and maybe my generation should retreat to our living rooms and let the young people tear one another apart over who seemed to imply that Asians are good at math.

By now, at age thirty-three, comparing myself to my mother had become an increasingly unnerving habit. Every year I’d do the math, calculating where I was in relation to where she’d been, and then, on the prediction that I’d also die when she had, figure out how many years I had left.

I think a strong claim can be made that the process of scientific discovery may be regarded as a form of art. This is best seen in the theoretical aspects of Physical Science. The mathematical theorist builds up on certain assumptions and according to well understood logical rules, step by step, a stately edifice, while his imaginative power brings out clearly the hidden relations between its parts. A well constructed theory is in some respects undoubtedly an artistic production. A fine example is the famous Kinetic Theory of Maxwell. ... The theory of relativity by Einstein, quite apart from any question of its validity, cannot but be regarded as a magnificent work of art.

Habits can be good and bad. Habit, after all, is simply when our brain launches into a preprogrammed “zombie” mode. You will probably not be surprised to learn that chunking, that automatically connected neural pattern that arises from frequent practice, is intimately related to habit.1 Habit is an energy saver for us. It allows us to free our mind for other types of activities

What? Would I do a ridiculous amount of relativistic math to calculate our relative velocity at any given moment as perceived by my inertial reference frame and then do Lorentz transformations to figure out when the light from his engines will drop out of the Petrovascope’s perception range? Just so I know how much longer I can see my friend in the distance? Wouldn’t that be kind of pathetic? Yeah.

Einstein, twenty-six years old, only three years away from crude privation, still a patent examiner, published in the Annalen der Physik in 1905 five papers on entirely different subjects. Three of them were among the greatest in the history of physics. One, very simple, gave the quantum explanation of the photoelectric effect—it was this work for which, sixteen years later, he was awarded the Nobel prize. Another dealt with the phenomenon of Brownian motion, the apparently erratic movement of tiny particles suspended in a liquid: Einstein showed that these movements satisfied a clear statistical law. This was like a conjuring trick, easy when explained: before it, decent scientists could still doubt the concrete existence of atoms and molecules: this paper was as near to a direct proof of their concreteness as a theoretician could give. The third paper was the special theory of relativity, which quietly amalgamated space, time, and matter into one fundamental unity. This last paper contains no references and quotes to authority. All of them are written in a style unlike any other theoretical physicist's. They contain very little mathematics. There is a good deal of verbal commentary. The conclusions, the bizarre conclusions, emerge as though with the greatest of ease: the reasoning is unbreakable. It looks as though he had reached the conclusions by pure thought, unaided, without listening to the opinions of others. To a surprisingly large extent, that is precisely what he had done.

There are chunks related to both concepts and procedures that reinforce one another. Solving a lot of math problems provides an opportunity to learn why the procedure works the way it does or why it works at all. Understanding the underlying concept makes it easier to detect errors when you make them.

A synthesis—an abstraction, chunk, or gist idea—is a neural pattern. Good chunks form neural patterns that resonate, not only within the subject we’re working in, but with other subjects and areas of our lives. The abstraction helps you transfer ideas from one area to another. That’s why great art, poetry, music, and literature can be so compelling. When we grasp the chunk, it takes on a new life in our own minds—we form ideas that enhance and enlighten the neural patterns we already possess, allowing us to more readily see and develop other related patterns. Once we have created a chunk as a neural pattern, we can more easily pass that chunked pattern to others, as Cajal and other great artists, poets, scientists, and writers have done for millennia, Once other people grasp that chunk, not only can they use it, but also they can more easily create similar chunks that apply to other areas in their lives—an important part of the creative process.

Stanford University's psychologist Carol Dweck and her colleagues have discovered that what you believe about intellectual ability—whether you think it's a fixed gift, or an earned ability that can be developed—makes a difference to your behavior, persistence, and performance. Students who see ability as fixed—as a gift—are more vulnerable to setbacks and difficulties. And stereotypes, as Dweck rightly points out, "are stories about gifts—who has them and who doesn't." Dweck and her colleagues are shown that when students are encouraged to see math ability as something that grows with effort—pointing out, for example, that the brain forges new connections and develops better ability every time they practice a task—grades improve and gender gaps diminish (relative to groups given control interventions).

Always preoccupied with his profound researches, the great Newton showed in the ordinary-affairs of life an absence of mind which has become proverbial. It is related that one day, wishing to find the number of seconds necessary for the boiling of an egg, he perceived, after waiting a minute, that he held the egg in his hand, and had placed his seconds watch (an instrument of great value on account of its mathematical precision) to boil! This absence of mind reminds one of the mathematician Ampere, who one day, as he was going to his course of lectures, noticed a little pebble on the road; he picked it up, and examined with admiration the mottled veins. All at once the lecture which he ought to be attending to returned to his mind; he drew out his watch; perceiving that the hour approached, he hastily doubled his pace, carefully placed the pebble in his pocket, and threw his watch over the parapet of the Pont des Arts.

A synthesis—an abstraction, chunk, or gist idea—is a neural pattern. Good chunks form neural patterns that resonate, not only within the subject we’re working in, but with other subjects and areas of our lives. The abstraction helps you transfer ideas from one area to another.15 That’s why great art, poetry, music, and literature can be so compelling. When we grasp the chunk, it takes on a new life in our own minds—we form ideas that enhance and enlighten the neural patterns we already possess, allowing us to more readily see and develop other related patterns.

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.

The Greeks were the real inventors of what we call math, because-again-they were the first people to treat numbers and their relations as abstractions rather than as properties of collections of real things.

Einstein, however, had a better intuition for physics than for math, and he did not yet appreciate how integrally the two subjects would be related in the pursuit of new theories. During his four years at the Polytechnic,

In one study, elite violinists had separated themselves from all others by each accumulating more than 10,000 hours of practice by age 20. Thus the rule. Many elite performers complete their journey in about ten years, which, if you do the math, is an average of about three hours of deliberate practice a day, every day, 365 days a year. Now, if your ONE Thing relates to work and you put in 250 workdays a year (five days a week for 50 weeks), to keep pace on your mastery journey you’ll need to average four hours a day. Sound familiar? It’s not a random number. That’s the amount of time you need to time block every day for your ONE Thing. More than anything else, expertise tracks with hours invested. Michelangelo once said, “If the people knew how hard I had to work to gain my mastery, it wouldn’t seem wonderful at all.” His point is obvious. Time on a task, over time, eventually beats talent every time. I’d say you can “book that,” but actually you should “block it.

But by 1912, Einstein had come to appreciate that math could be a tool for discovering—and not merely describing—nature’s laws. Math was nature’s playbook. “The central idea of general relativity is that gravity arises from the curvature of spacetime,” says physicist James Hartle. “Gravity is geometry.

Baseball also has statistical rigor. Its gurus have an immense data set at hand, almost all of it directly related to the performance of players in the game. Moreover, their data is highly relevant to the outcomes they are trying to predict. This may sound obvious, but as we’ll see throughout this book, the folks building WMDs routinely lack data for the behaviors they’re most interested in. So they substitute stand-in data, or proxies. They draw statistical correlations between a person’s zip code or language patterns and her potential to pay back a loan or handle a job. These correlations are discriminatory, and some of them are illegal.

If the only thing I did for the rest of my life was treat others kindly, file manila folders, and sit on the porch watching the grass grow it would be enough. It had to be. I did the math. The number of people who actually achieve a significant legacy is trifling compared to the vast number who go from birth to death living relatively unremarkable lives (at least on the surface). And maybe that wasn't the failure I'd been conditioned to believe. Maybe there was something to be said in praise of an outwardly unremarkable life. Maybe there were deep everyday forms of magic that had nothing to do with profound acomplishments or a Twitter feed that resonated down through the ages.

Would I do a ridiculous amount of relativistic math to calculate our relative velocity at any given moment as perceived by my inertial reference frame and then do Lorentz transformations to figure out when the light from his engines will drop out of the Petrovascope’s perception range? Just so I know how much longer I can see my friend in the distance

Je me rends parfaitement compte du desagreable effet que produit sur la majorite de l'humanité, tout ce qui se rapporte, même au plus faible dègré, á des calculs ou raisonnements mathematiques. I am well aware of the disagreeable effect produced on the majority of humanity, by whatever relates, even at the slightest degree to calculations or mathematical reasonings.

The nausea is related to these aspects of grief, but its true source, I think, is the realization that made my son cry on the last day of third grade: What once was will never be again. Never again this teacher, never again this particular configuration of classmates, never again will you learn long division for the first time (even if you don’t care very much for math).

A synthesis—an abstraction, chunk, or gist idea—is a neural pattern. Good chunks form neural patterns that resonate, not only within the subject we’re working in, but with other subjects and areas of our lives. The abstraction helps you transfer ideas from one area to another. That’s why great art, poetry, music, and literature can be so compelling. When we grasp the chunk, it takes on a new life in our own minds—we form ideas that enhance and enlighten the neural patterns we already possess, allowing us to more readily see and develop other related patterns. Once we have created a chunk as a neural pattern, we can more easily pass that chunked pattern to others, as Cajal and other great artists, poets, scientists, and writers have done for millennia, Once other people grasp that chunk, not only can they use it, but also they can more easily create similar chunks that apply to other areas in their lives—an important part of the creative process.

When one day Lagrange took out of his pocket a paper which he read at the Académe, and which contained a demonstration of the famous Postulatum of Euclid, relative to the theory of parallels. This demonstration rested on an obvious paralogism, which appeared as such to everybody; and probably Lagrange also recognised it such during his lecture. For, when he had finished, he put the paper back in his pocket, and spoke no more of it. A moment of universal silence followed, and one passed immediately to other concerns.

A third positive result even further from the traditional tool kit of financial incentives comes from a recent randomized control trial conducted in the U.K., using the increasingly popular and low-cost method of text reminders. This intervention involved sending texts to half the parents in some school in advance of a major math test to let them know that their child had a test coming up in five days, then in three days, then in one day. The researchers call this approach “pre-informing.” The other half of parents did not receive the texts. The pre-informing texts increased student performance on the math test by the equivalent of one additional month of schooling, and students in the bottom quartile benefited most. These children gained the equivalent of two additional months of schooling, relative to the control group. Afterward, both parents and students said they wanted to stick with the program, showing that they appreciated being nudged. This program also belies the frequent claim, unsupported by any evidence, that nudges must be secret to be effective.

In fact, as these companies offered more and more (simply because they could), they found that demand actually followed supply. The act of vastly increasing choice seemed to unlock demand for that choice. Whether it was latent demand for niche goods that was already there or a creation of new demand, we don't yet know. But what we do know is that the companies for which we have the most complete data - netflix, Amazon, Rhapsody - sales of products not offered by their bricks-and-mortar competitors amounted to between a quarter and nearly half of total revenues - and that percentage is rising each year. in other words, the fastest-growing part of their businesses is sales of products that aren't available in traditional, physical retail stores at all. These infinite-shelf-space businesses have effectively learned a lesson in new math: A very, very big number (the products in the Tail) multiplied by a relatives small number (the sales of each) is still equal to a very, very big number. And, again, that very, very big number is only getting bigger. What's more, these millions of fringe sales are an efficient, cost-effective business. With no shelf space to pay for - and in the case of purely digital services like iTunes, no manufacturing costs and hardly any distribution fees - a niche product sold is just another sale, with the same (or better) margins as a hit. For the first time in history, hits and niches are on equal economic footing, both just entries in a database called up on demand, both equally worthy of being carried. Suddenly, popularity no longer has a monopoly on profitability.

Like kind learning environments, a kind world is based on repeating patterns. “It’s perfectly fine,” she said, “if you stay in the same village or the same savannah all your life.” The current world is not so kind; it requires thinking that cannot fall back on previous experience. Like math students, we need to be able to pick a strategy for problems we have never seen before. “In the life we lead today,” Gentner told me, “we need to be reminded of things that are only abstractly or relationally similar. And the more creative you want to be, the more important that is.

THE TRUTH ABOUT PUBLIC SCHOOL EDUCATION • American fifteen-year-olds rank thirty-fifth out of fifty-seven developed countries in math and literacy. • 30 percent of public school students don’t graduate from high school. • Every day, 7,000 kids drop out of high school. • Of the 50 million children currently in public school, 15 million of them will drop out. • 25 percent of all public school math teachers did not major in mathematics or a math-related subject at a college or university. • Less than two-thirds of high school graduates are accepted to college every year. • One half...

It’s important to note, as we endeavor to understand relative harms, that they are entirely dependent on context. For example, if a high-risk score for a given defendant qualified him for a reentry program that would help him find a job upon release from prison, we’d be much less worried about false positives. Or in the case of the child abuse algorithm, if we are sure that a high-risk score leads to a thorough and fair-minded investigation of the situation at home, we’d be less worried about children unnecessarily removed from their parents. In the end, how an algorithm will be used should affect how it is constructed and optimized.

counterfactual emotions,” or the feelings that spurred people’s minds to spin alternative realities in order to avoid the pain of the emotion. Regret was the most obvious counterfactual emotion, but frustration and envy shared regret’s essential trait. “The emotions of unrealized possibility,” Danny called them, in a letter to Amos. These emotions could be described using simple math. Their intensity, Danny wrote, was a product of two variables: “the desirability of the alternative” and “the possibility of the alternative.” Experiences that led to regret and frustration were not always easy to undo. Frustrated people needed to undo some feature of their environment, while regretful people needed to undo their own actions. “The basic rules of undoing, however, apply alike to frustration and regret,” he wrote. “They require a more or less plausible path leading to the alternative state.” Envy was different. Envy did not require a person to exert the slightest effort to imagine a path to the alternative state. “The availability of the alternative appears to be controlled by a relation of similarity between oneself and the target of envy. To experience envy, it is sufficient to have a vivid image of oneself in another person’s shoes; it is not necessary to have a plausible scenario of how one came to occupy those shoes.” Envy, in some strange way, required no imagination. Danny spent the

Why? This is our world of habituation, where nothing is ever as good as that first time. Unfortunately, things have to work this way because of our range of rewards.86 After all, reward coding must accommodate the rewarding properties of both solving a math problem and having an orgasm. Dopaminergic responses to reward, rather than being absolute, are relative to the reward value of alternative outcomes. In order to accommodate the pleasures of both mathematics and orgasms, the system must constantly rescale to accommodate the range of intensity offered by particular stimuli. The response to any reward must habituate with repetition, so that the system can respond over its full range to the next new thing.

If you're now noticing a certain family resemblance among this no-successive-instant problem, Zeno's Paradoxes, and some of the Real Line crunchers described in Paragraph 2c and -e, be advised that this is not a coincidence. They are all facets of the great continuity conundrum for mathematics, which is that (Infinity)-related entities can apparently be neither handled nor eliminated. Nowhere is this more evident than with 1/(Infinity)s. They're riddled with paradox and can't be defined, but if you banish them from math you end up having to posit an infinite density to any interval, in which the idea of succession makes no sense and no ordering of points in the interval can ever be complete, since between any two points there will be not just some other points but a whole infinity of them. Overall point: However good calculus is at quantifying motion and change, it can do nothing to solve the real paradoxes of continuity. Not without a coherent theory of (Infinity), anyway.

Mandana Misra was a great scholar and authority on the Vedas and Mimasa. He led a householder’s life (grihastha), with his scholar-philosopher wife, Ubhaya Bharati, in the town of Mahishi, in what is present-day northern Bihar. Husband and wife would have great debates on the veracity of the Vedas, the Upanishads, the Gita and other philosophical works. Scholars from all over Bharatavarsha came to debate and understand the Shastras with them. It is said that even the parrots in Mandana’s home debated the divinity, or its lack, in the Vedas and Upanishads. Mandana was a staunch believer in rituals. One day, while he was performing Pitru Karma (rituals for deceased ancestors), Adi Shankaracharya arrived at his home and demanded a debate on Advaita. Mandana was angry at the rude intrusion and asked the Acharya whether he was not aware, as a Brahmin, that it was inauspicious to come to another Brahmin’s home uninvited when Pitru Karma was being done? In reply, Adi Shankara asked Mandana whether he was sure of the value of such rituals. This enraged Mandana and the other Brahmins present. Thus began one of the most celebrated debates in Hindu thought. It raged for weeks between the two great scholars. As the only other person of equal intellect to Shankara and Mandana was Mandana’s wife, Ubhaya Bharati, she was appointed the adjudicator. Among other things, Shankara convinced Mandana that the rituals for the dead had little value to the dead. Mandana became Adi Shankara’s disciple (and later the first Shankaracharya of the Sringeri Math in Karnataka). When the priest related this story to me, I was shocked. He was not giving me the answer I had expected. Annoyed, I asked him what he meant by the story if Adi Shankara himself said such rituals were of no use to the dead. The priest replied, “Son, the story has not ended.” And he continued... A few years later, Adi Shankara was compiling the rituals for the dead, to standardize them for people across Bharatavarsha. Mandana, upset with his Guru’s action, asked Adi Shankara why he was involved with such a useless thing. After all, the Guru had convinced him of the uselessness of such rituals (Lord Krishna also mentions the inferiority of Vedic sacrifice to other paths, in the Gita. Pitru karma has no vedic base either). Why then was the Jagad Guru taking such a retrograde step? Adi Shankaracharya smiled at his disciple and answered, “The rituals are not for the dead but for the loved ones left behind.

As I was completing this book, I saw news reports quoting NASA chief Charles Bolden announcing that from now on the primary mission of America’s space agency would be to improve relations with the Muslim world. Come again? Bolden said he got the word directly from the president. “He wanted me to find a way to reach out to the Muslim world and engage much more with dominantly Muslim nations to help them feel good about their historic contribution to science and math and engineering.” Bolden added that the International Space Station was a kind of model for NASA’s future, since it was not just a U.S. operation but included the Russians and the Chinese. Bolden, who made these remarks in an interview with Al-Jazeera, timed them to coincide with the one-year anniversary of Obama’s own Cairo address to the Muslim world.3 Bolden’s remarks provoked consternation not only among conservatives but also among famous former astronauts Neil Armstrong and John Glenn and others involved in America’s space programs. No surprise: most people think of NASA’s job as one of landing on the moon and Mars and exploring other faraway destinations. Even some of Obama’s supporters expressed puzzlement. Sure, we are all for Islamic self-esteem, and seven or eight hundred years ago the Muslims did make a couple of important discoveries, but what on earth was Obama up to here?

A more complex way to understand this is the method used by Hermann Minkowski, Einstein’s former math teacher at the Zurich Polytechnic. Reflecting on Einstein’s work, Minkowski uttered the expression of amazement that every beleaguered student wants to elicit someday from condescending professors. “It came as a tremendous surprise, for in his student days Einstein had been a lazy dog,” Minkowski told physicist Max Born. “He never bothered about mathematics at all.”63 Minkowski decided to give a formal mathematical structure to the theory. His approach was the same one suggested by the time traveler on the first page of H. G. Wells’s great novel The Time Machine, published in 1895: “There are really four dimensions, three which we call the three planes of Space, and a fourth, Time.” Minkowski turned all events into mathematical coordinates in four dimensions, with time as the fourth dimension. This permitted transformations to occur, but the mathematical relationships between the events remained invariant. Minkowski dramatically announced his new mathematical approach in a lecture in 1908. “The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength,” he said. “They are radical. Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.”64 Einstein, who was still not yet enamored of math, at one point described Minkowski’s work as “superfluous learnedness” and joked, “Since the mathematicians have grabbed hold of the theory of relativity, I myself no longer understand it.” But he in fact came to admire Minkowski’s handiwork and wrote a section about it in his popular 1916 book on relativity.

In 2012, the U.S. government estimated that 660,000 Americans were using heroin and more than 3,000 dying of it every year because Mexico was boosting the supply.22 About a quarter of all people who try heroin will become dependent on it, according to government estimates,23 and the precise appeal of methamphetamine to Mexico’s Sinaloa drug cartel was that it was “ragingly addictive,” according to the New York Times.24 Forbes reports that there is “little doubt” that the heroin that killed Philip Seymour Hoffman came from Mexico.25 These aren’t “big city” problems: They’re Mexico-is-on-our-border problems. Missouri had 18 heroin overdose deaths in 2001; ten years later, there were 245.26 Heroin deaths in Minnesota shot from 3 to 98 between 1999 and 2013.27 Michigan saw fatal heroin overdoses surge from a few dozen a year in 2002 to more than 100 a year starting in 2009.28 In just one year, heroin-related fatalities in Connecticut nearly doubled, to 257 in 2013.29 Between 2007 and 2012, heroin use in the United States is estimated to have increased by almost 80 percent.30 And that’s just heroin. More than 40,000 Americans were killed from all illegal drug use in 2010, surpassing car accidents and shootings as a cause of death.31 The addicts who die may be the lucky ones. In 2001, a seventeen-year-old boy in New Jersey who scored 700 on the math SAT took a heroin overdose that left him unable to stand, walk, or bathe himself. His mother, a globetrotting executive with Citibank, was forced to quit her job and become his full-time caretaker. After a year of hospitalization and more than a decade of therapy, he still needs his mother to carry him to the toilet. He has no recollection of taking an overdose, but packets of heroin and marijuana were found stored in a secret compartment in his bedroom.32

During my time in India, the commitment level of the believers there shocked me. I visited thousands of Christians who had been beaten or watched relatives murdered for their faith. At one point, I said to one of the leaders, “Every believer seems so serious about his or her commitment to Christ. Aren’t there people who just profess Christ but don’t really follow Him?” He answered by explaining that nominal Christianity doesn’t make sense in India. Calling yourself a Christian means you lose everything. Your family and friends reject you, and you lose your home, status, and job. So why would anyone choose that unless he or she is serious about Jesus? I witnessed that same passion during my time in mainland China. The highlight was attending a meeting with underground church members training to become missionaries. The way they prayed and gave testimony about being persecuted was convicting and encouraging. The most surprising part of our time together was when they asked me about church in America. They laughed hysterically when I told them that church for Americans tends to focus on buildings and that people will sometimes switch churches based on music, child care, preaching, or disagreements with other believers. I honestly was not trying to be funny. They laughed in disbelief at our church experiences, thinking it was ridiculous that we would call this Christianity. Keep in mind that the population of China is over 1.3 billion, and in India it’s over 1.2 billion. Meanwhile, there are around 300 million people in the United States. This means that we are a small minority. Our views of “Christianity” are peculiar to the vast majority of the world. I used to think of those “radical believers” overseas as the strange ones. Some simple math revealed to me that in actuality we are the weird ones. The majority of believers on this earth find it laughable that we could reduce the call to follow Jesus and make disciples to an invitation to sit in church service.

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.

SOCIAL AND EMOTIONAL FUNCTIONING Another coexisting regulatory problem may be how the child feels about himself and relates to other people. • Poor adaptability: The child may resist meeting new people, trying new games or toys or tasting different foods. He may have difficulty making transitions from one situation to another. The child may seem stubborn and uncooperative when it is time to leave the house, come for dinner, get into or out of the bathtub, or change from a reading to a math activity. Minor changes in routine will readily upset this child who does not “go with the flow.” • Attachment problem: The child may have separation anxiety and be clingy and fearful when apart from one or two “significant olders.” Or, she may physically avoid her parents, teachers, and others in her circle. • Frustration: Struggling to accomplish tasks that peers do easily, the child may give up quickly. He may be a perfectionist and become upset when art projects, dramatic play, or homework assignments are not going as well as he expects. • Difficulty with friendships: The child may be hard to get along with and have problems making and keeping friends. Insisting on dictating all the rules and being the winner, the best, or the first, he may be a poor game-player. He may need to control his surrounding territory, be in the “driver’s seat,” and have trouble sharing toys. • Poor communication: The child may have difficulty verbally in the way she articulates her speech, “gets the words out,” and writes. She may have difficulty expressing her thoughts, feelings, and needs, not only through words but also nonverbally through gestures, body language, and facial expressions. • Other emotional problems: He may be inflexible, irrational, and overly sensitive to change, stress, and hurt feelings. Demanding and needy, he may seek attention in negative ways. He may be angry or panicky for no obvious reason. He may be unhappy, believing and saying that he is dumb, crazy, no good, a loser, and a failure. Low self-esteem is one of the most telling symptoms of Sensory Processing Disorder. • Academic problems: The child may have difficulty learning new skills and concepts. Although bright, the child may be perceived as an underachiever.

I stood straight and calm, though every part of me wanted to blast the crap out of the room. No one moved, no one spoke. I barely breathed. I didn’t know how much time had passed when Ty finally broke the silence. “If we’re demigods and you are demigods, which gods are our grandparents?” Tyde asked, snapping me out of my funk. Why hadn’t it occurred to me to ask that? My parents were the children of gods. All Mer were thought of as children of Poseidon in some respects, but this was different. “Well, your father’s father is Apollo,” Mom said, “And my father is… Zeus.” Whoa, that was big. Zeus was our grandfather. How does someone wrap their mind around that? “So our grandfathers are Apollo and Zeus, but aren’t they related? Wouldn’t that make you and Dad…” Ty couldn’t finish that thought and I was grateful. I was now grossed out. I couldn’t do the math on that messed up family tree. Yuck. “It doesn’t really work that way with the gods,” Mom said, catching on to what Ty was hinting at. “They are so ancient that their blood, while it will carry power, doesn’t carry much else in terms of genealogy. Our DNA comes mostly from our mortal parents. Our powers come from our godly parents but that’s it. It’s complicated, but your father and I are not related. So if you were worried… stop. You’re not the product of kissing cousins

In practice, Bacon’s method doesn’t bother scientists, or most reasonable people, because the chances of being wrong, while present, are usually in a practical sense very small. It is, for example, theoretically possible that chemical processes taking place in your body could cause you to spontaneously combust, but we don’t live our lives worrying about it because the probability is extremely small. That is why math and statistics have become such important parts of science: they quantify the relative probability that a conclusion is true or false.

Certainly prevents some believers from being compassionate, sympathetic, or even tolerant of others who are not as certain in their faith. Their arrogance turns them into the "frozen chosen," consciously or unconsciously excluding others from their cozy, believing world. This is the crabbed, joyless, and ungenerous religiosity that Jesus spoke against: spiritual blindness. There is a more subtle danger for this group: a complacency that makes one's relationship with God stagnate. Some people cling to ways of understanding their faith learned in childhood that might not work for an adult. For example, you might cling to a childhood notion of a God who will never let anything bad happen. When tragedy strikes, since your youthful image of God is not reflected in reality, you may abandon the God of your youth. Or you may abandon God completely. An adult life requires an adult faith. Think of it this way: you wouldn't consider yourself equipped to face life with a third-grader's understanding of math. Yet people often expect the religious instruction they had in grammar school to sustain them in the adult world. In his book A Friendship Like No Other, the Jesuit spiritual writer William A. Barry invites adults to relate to God in an adult way. Just as an adult child needs to relate to his or her parent in a new way, he suggest, so adult believers need to relate t God in new ways as they mature. Otherwise, one remains stuck in a childlike view of God that prevents fully embracing a mature faith.

The entropy of a system is related to the number of indistinguishable rearrangements of its constituents, but properly speaking is not equal to the number itself. The relationship is expressed by a mathematical operation called a logarithm; don't be put off if this brings back bad memories of high school math class. In our coin example, it simply means that you pick out the exponent in the number of rearrangements-that is, the entropy is defined as 1,000 rather than 2^1000.

I'm still just as slow… At the end of the eleventh grade, I took the measure of the situation, and came to the conclusion that rapidity doesn't have a precise relation to intelligence. What is important is to deeply understand things and their relations to each other. This is where intelligence lies. The fact of being quick or slow isn't really relevant. (Schwartz, 2001)

Much science in many disciplines consists of a toolkit of very simple mathematical models. To many not familiar with the subtle art of the simple model, such formal exercises have two seemingly deadly flaws. First, they are not easy to follow. […] Second, motivation to follow the math is often wanting because the model is so cartoonishly simple relative to the real world being analyzed. Critics often level the charge ‘‘reductionism’’ with what they take to be devastating effect. The modeler’s reply is that these two criticisms actually point in opposite directions and sum to nothing. True, the model is quite simple relative to reality, but even so, the analysis is difficult. The real lesson is that complex phenomena like culture require a humble approach. We have to bite off tiny bits of reality to analyze and build up a more global knowledge step by patient step. […] Simple models, simple experiments, and simple observational programs are the best the human mind can do in the face of the awesome complexity of nature. The alternatives to simple models are either complex models or verbal descriptions and analysis. Complex models are sometimes useful for their predictive power, but they have the vice of being difficult or impossible to understand. The heuristic value of simple models in schooling our intuition about natural processes is exceedingly important, even when their predictive power is limited. […] Unaided verbal reasoning can be unreliable […] The lesson, we think, is that all serious students of human behavior need to know enough math to at least appreciate the contributions simple mathematical models make to the understanding of complex phenomena. The idea that social scientists need less math than biologists or other natural scientists is completely mistaken.

Adam: Adam was a young man whose anxiety turned into a monster. Where Shelly had a very mild case of social anxiety, Adam’s case could only be called severe. Over a period of several years, his underlying social fears developed into a full-blown school phobia. A quiet, unassuming person, Adam had never stood out in the classroom. Through elementary school and on into high school, he neither excelled nor failed his subjects. By no means a discipline problem, the “shy” Adam kept to himself and seldom talked in class, whether to answer a teacher’s question or chat with his buddies. In fact, he really had no friends, and the only peers he socialized with were his cousins, whom he saw at weekly family gatherings. Though he watched the other kids working together on projects or playing sports together, Adam never approached them to join in. Maybe they wouldn’t let him, he thought. Maybe he wasn’t good enough. Being rejected was not a chance he was willing to take. Adam never tried hard in school either. If he didn’t understand something, he kept quiet, fearful that raising his hand would bring ridicule. When he did poorly on an exam or paper, it only confirmed to him what he was sure was true: He didn’t measure up. He became so apprehensive about his tests that he began to feel physically ill at the thought of each approaching reminder of his inadequacy. Even though he had studied hard for a math test, for example, he could barely bring himself to get out of bed on the morning it was to take place. His parents, who thought of their child as a reserved but obedient boy who would eventually grow out of this awkward adolescent stage, did not pressure him. Adam was defensive and withdrawn, overwrought by the looming possibility that he would fail. For the two class periods preceding the math test, Adam’s mind was awash with geometry theorems, and his stomach churning. As waves of nausea washed over him, he began to salivate and swallowed hard. His eyes burned and he closed them, wishing he could block the test from his mind. When his head started to feel heavy and he became short of breath, he asked for a hall pass and headed for the bathroom. Alone, he let his anxiety overtake him as he stared into the mirror, letting the cool water flow from the faucet and onto his sweaty palms. He would feel better, he thought, if he could just throw up. But even when he forced his finger down his throat, there was no relief. His dry heaves made him feel even weaker. He slumped to the cold tile and began to cry. Adam never went back to math class that day; instead, he got a pass from the nurse and went straight home. Of course, the pressure Adam was feeling was not just related to the math test. The roots of his anxiety went much deeper. Still, the physical symptoms of anxiety became so debilitating that he eventually quit going to school altogether. Naturally, his parents were extremely concerned but also uncertain what to do. It took almost a year before Adam was sufficiently in control of his symptoms to return to school.

Adam: Of course, the pressure Adam was feeling was not just related to the math test. The roots of his anxiety went much deeper. Still, the physical symptoms of anxiety became so debilitating that he eventually quit going to school altogether. Naturally, his parents were extremely concerned but also uncertain what to do. It took almost a year before Adam was sufficiently in control of his symptoms to return to school. Clearly, he was working to avoid the pain of any kind of interaction, because he was so afraid of rejection or humiliation. His social anxiety became so extreme that he feared the symptoms as much as the stressor itself; in fact, his fear of interaction developed into a full-blown phobia. Adam’s anxiety profile obviously featured all the physical symptoms on the list (especially shortness of breath, accelerated heartbeat, dizziness, and depersonalization). They surfaced almost daily and were extremely incapacitating, affecting him to a high degree whenever he was actually in the situation that caused them. Of course, when Adam avoided these situations, their frequency and severity diminished, but their degree of interactive interference increased until it was at level 5. The symptoms were so bad that they were preventing him from interacting, all the way to the point of incapacity. Obsessive thought patterns were a contributing factor as well: “Am I good enough?” “Will they like me?” Adam even had these recurring thoughts when he was alone in his room, looking out on the street at the neighborhood kids playing below.

And I love math because there's always a right answer. It's not interpretive; it's not subjective. There is a correct destination, even if you have to hack through confusing parts to get there. That's not always true in life.

A third positive result even further from the traditional tool kit of financial incentives comes from a recent randomized control trial conducted in the U.K., using the increasingly popular and low-cost method of text reminders. This intervention involved sending texts to half the parents in some school in advance of a major math test to let them know that their child had a test coming up in five days, then in three days, then in one day. The researchers call this approach “pre-informing.” The other half of parents did not receive the texts. The pre-informing texts increased student performance on the math test by the equivalent of one additional month of schooling, and students in the bottom quartile benefited most. These children gained the equivalent of two additional months of schooling, relative to the control group. Afterward, both parents and students said they wanted to stick with the program, showing that they appreciated being nudged.

The brain researchers concluded that automaticity should be reached through understanding of numerical relations, achieved through thinking about number strategies (Delazer et al., 2005).

This led them to a simple equation. There will be no math questions in the quiz at the end of this book, but I thought you might like to cast your eyes upon it. Ready? Don’t flinch, don’t worry, don’t blink: R0 = βN/(α + b + v) In English: The evolutionary success of a bug is directly related to its rate of transmission through the host population and inversely but intricately related to its lethality, the rate of recovery from it, and the normal death rate from all other causes.

We have heard that when it arrived in Europe, zero was treated with suspicion. We don't think of the absence of sound as a type of sound, so why should the absence of numbers be a number, argued its detractors. It took centuries for zero to gain acceptance. It is certainly not like other numbers. To work with it requires some tough intellectual contortions, as mathemati­cian Ian Stewart explains. "Nothing is more interesting than nothing, nothing is more puzzling than nothing, and nothing is more important than nothing. For mathematicians, nothing is one of their favorite topics, a veritable Pandora's box of curiosities and paradoxes. What lies at the heart of mathematics? You guessed it: nothing. "Word games like this are almost irresistible when you talk about nothing, but in the case of math this is cheat­ing slightly. What lies at the heart of math is related to nothing, but isn't quite the same thing. 'Nothing' is ­well, nothing. A void. Total absence of thingness. Zero, however, is definitely a thing. It is a number. It is, in fact, the number you get when you count your oranges and you haven't got any. And zero has caused mathematicians more heartache, and given them more joy, than any other number. "Zero, as a symbol, is part of the wonderful invention of 'place notation.' Early notations for numbers were weird and wonderful, a good example being Roman numerals, in which the number 1,998 comes out as MCMXCVIII ­one thousand (M) plus one hundred less than a thousand (CM) plus ten less than a hundred (XC) plus five (V) plus one plus one plus one (III). Try doing arithmetic with that lot. So the symbols were used to record numbers, while calculations were done using the abacus, piling up stones in rows in the sand or moving beads on wires.

You can also think of them as “research” or “reference materials.” They are trends you are keeping track of, ideas related to your job or industry, hobbies and side interests, and things you’re merely curious about. These folders are like the class notebooks you probably kept in school: one for biology, another for history, another for math.

As educators, they realized that the game could teach without teaching. Basic math, spatial relations, narrative structure, predictive reasoning, and above all, human interaction. Things, in other words, that football or baseball offered, but without the physical boundaries. At the gaming table, you could be blind and missing both legs, but still lead your comrades to glory.

A holiday of any sort is a distraction They are all created by a system of domination They are all related to religion Do the math...Pay attention.

We are not individually much cleverer than the average animal, a heron or a mole, but the knack of our species lies in our capacity to transmit our accumulated knowledge down the generations. The slowest among us can, in a few hours, pick up ideas that it took a few rare geniuses a lifetime to acquire. Yet what is distinctive is just how selective we are about the topics we deem it possible to educate ourselves in. Our energies are overwhelmingly directed towards material, scientific and technical subjects – and away from psychological and emotional ones. Much anxiety surrounds the question of how good the next generation will be at maths; very little around their abilities at marriage or kindness. We devote inordinate hours to learning about tectonic plates and cloud formations, and relatively few fathoming shame and rage. The assumption is that emotional insight might be either unnecessary or in essence unteachable, lying beyond reason or method, an unreproducible phenomenon best abandoned to individual instinct and intuition. We are left to find our own path around our unfeasibly complicated minds – a move as striking (and as wise) as suggesting that each generation should rediscover the laws of physics by themselves.

Script for “Did I Ever Tell You About the Time . . . ?” Identify the essence of your child’s struggle. (Is it hard for her to feel happy for other people’s accomplishments? Hard to stay engaged when math feels hard and frustrating?) Take on the problem as your own: remember a moment, in the recent past or when you were a child, when you struggled with something similar. Talk to your child not in the heat of the moment but when things are calm, starting with, “Did I ever tell you about the time . . . ?,” and share a story about yourself having a similar struggle. Engage your child in this story, ideally one where you didn’t come up with a quick fix but struggled and just kind of got through it. Do not end your story by directly relating it to your child. There’s no need to spell out, “Isn’t that just like when you . . . ?” Allow the story and moment to stand on their own, trusting that it will reach the part of your child that needed connection.

During the 1919 solar eclipse, people go out to measure the positions of the stars and they find exactly what Einstein predicted. Einstein gets a telegram saying this, and somebody asked him, Professor Einstein, what would you have said if the observations didn’t agree with what your prediction of general relativity said should be happening? And Einstein said, “I’d be sorry for the dear lord; the theory is correct.” What he meant by that is the math is just so elegant, so beautiful, so powerful, that almost seemingly it can’t possibly be wrong.

The field of knowledge that can not be related or expressed with number can not be the mathematical branch. Quantification, Quantification & quantification is the ultimate aim of mathematics.

The key point is that, in principle, interest income is the change in price associated with the passage of time. Capital gains and losses are the changes in price related to changes in value—for bonds that means a change in the yield. We'll see in Chapter 4 when we get into bond taxation how well these economic principles hold up in practice.

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.

Advantage of Playing Educational Games: Kids Learn With Fun Kids Game play has mentally worth profit because games have been shown to enhance attention, focus, and interval. Games have motivational profit because they encourage associate progressive, instead of an entity theory of intelligence. Games have emotional profit as a result of they induce positive mood states; additionally, there's speculative proof that games might support children develop flexible feeling regulation. Games have social profit because gamers area unit able to translate the prosocial skills that they learn from co-playing or multiplayer gameplay to “peer and family relations outside the gambling atmosphere. DIFFERENT GAMES FOR DIFFERENT GOALS. But it’s a little ​twisted​ to say that Educational games are “good for kids.” Kids games are not like fruits and vegetables. Don’t think them as if they were know about vegetable and fruits name that help kids grow into healthy adults. Like all forms of media, it depends on the particular games and how they are used. Kids Learn With Fun Present Different games such as Learn Vehicles for Kids,1 to 100 Spelling learning,123 number for kids,Maths Practice,Puzzle Games,Real Birds Game,Toodle Alphabets Puzzle and many more available at : kidslearnwithfun dot com Play Kids Learn with Fun Game : Make your kid’s mind Creative. Educational Kids games that ​inspire​ creative expression, such as Maths Practice Game and Puzzle game, push kids to think outside the norm and consider ​different methods of explanation. Exploring and expanding creativity through such kids games can also help with nurturing self-​prize,self-love,self-habit​ and self-acceptance, and they inspire a greater connection between personality and activity. In the end,​ sticking with a kids game through it can help kids develop patience and maturity in 0 to 5 year age.

Nobody is, was, will be born smart. But for you to be smart, and act smart, you need to think smart always. It is not a subject of your alma mater, it is the side and fries of what the genius within can comprehend, comply and captivate. In every beginning has a twelve kick start, promotion of the relativity of your new thinking, the story of a bunch of math and the spirit of a wonder apple.

Grades may be useful for communicating where students are in relation to each other, and it is fine to give them at the end of a semester or term, but if they are given more frequently than that, they will reduce the achievement of many.

Take a look at the following list of numbers: 4, 8, 5, 3, 9, 7, 6. Read them out loud. Now look away and spend twenty seconds memorizing that sequence before saying them out loud again. If you speak English, you have about a 50 percent chance of remembering that sequence perfectly. If you're Chinese, though, you're almost certain to get it right every time. Why is that? Because as human beings we store digits in a memory loop that runs for about two seconds. We most easily memorize whatever we can say or read within that two-second span. And Chinese speakers get that list of numbers—4, 8, 5, 3, 9, 7, 6—right almost every time because, unlike English, their language allows them to fit all those seven numbers into two seconds. That example comes from Stanislas Dehaene's book The Number Sense. As Dehaene explains: Chinese number words are remarkably brief. Most of them can be uttered in less than one-quarter of a second (for instance, 4 is "si" and 7 "qi"). Their English equivalents—"four," "seven"—are longer: pronouncing them takes about one-third of a second. The memory gap between English and Chinese apparently is entirely due to this difference in length. In languages as diverse as Welsh, Arabic, Chinese, English and Hebrew, there is a reproducible correlation between the time required to pronounce numbers in a given language and the memory span of its speakers. In this domain, the prize for efficacy goes to the Cantonese dialect of Chinese, whose brevity grants residents of Hong Kong a rocketing memory span of about 10 digits. It turns out that there is also a big difference in how number-naming systems in Western and Asian languages are constructed. In English, we say fourteen, sixteen, seventeen, eighteen, and nineteen, so one might expect that we would also say oneteen, twoteen, threeteen, and five- teen. But we don't. We use a different form: eleven, twelve, thirteen, and fifteen. Similarly, we have forty and sixty, which sound like the words they are related to (four and six). But we also say fifty and thirty and twenty, which sort of sound like five and three and two, but not really. And, for that matter, for numbers above twenty, we put the "decade" first and the unit number second (twentyone, twenty-two), whereas for the teens, we do it the other way around (fourteen, seventeen, eighteen). The number system in English is highly irregular. Not so in China, Japan, and Korea. They have a logical counting system. Eleven is ten-one. Twelve is ten-two. Twenty-four is two- tens-four and so on. That difference means that Asian children learn to count much faster than American children. Four-year-old Chinese children can count, on average, to forty. American children at that age can count only to fifteen, and most don't reach forty until they're five. By the age of five, in other words, American children are already a year behind their Asian counterparts in the most fundamental of math skills. The regularity of their number system also means that Asian children can perform basic functions, such as addition, far more easily. Ask an English-speaking seven-yearold to add thirty-seven plus twenty-two in her head, and she has to convert the words to numbers (37+22). Only then can she do the math: 2 plus 7 is 9 and 30 and 20 is 50, which makes 59. Ask an Asian child to add three-tensseven and two-tens-two, and then the necessary equation is right there, embedded in the sentence. No number translation is necessary: It's five-tens-nine. "The Asian system is transparent," says Karen Fuson, a Northwestern University psychologist who has closely studied Asian-Western differences. "I think that it makes the whole attitude toward math different. Instead of being a rote learning thing, there's a pattern I can figure out. There is an expectation that I can do this. There is an expectation that it's sensible. For fractions, we say three-fifths. The Chinese is literally 'out of five parts, take three.' That's telling you conceptually

String theory is potentially the next and final step in this progression. In a single framework, it handles the domains claimed by relativity and the quantum. Moreover, and this is worth sitting up straight to hear, string theory does so in a manner that fully embraces all the discoveries that preceded it. A theory based on vibrating filaments might not seem to have much in common with general relativity's curved spacetime picture of gravity. Nevertheless, apply string theory's mathematics to a situation where gravity matters but quantum mechanics doesn't (to a massive object, like the sun, whose size is large) and out pop Einstein's equations. Vibrating filaments and point particles are also quite different. But apply string theory's mathematics to a situation where quantum mechanics matters but gravity doesn't (to small collections of strings that are not vibrating quickly, moving fast, or stretched long; they have low energy-equivalently, low mass- so gravity plays virtually no role) and the math of string theory morphs into the math of quantum field theory.

when I look back on my first two years at McKinsey, a solid 80 percent of my managers’ feedback related to communication skills. They rarely gave me any feedback on my math skills, quantitative analysis skills, spreadsheets, or models.

Here was my first lesson: This type of skill development is hard. When I got to the first tricky gap in the paper’s main proof argument, I faced immediate internal resistance. It was as if my mind realized the effort I was about to ask it to expend, and in response it unleashed a wave of neuronal protest, distant at first, but then as I persisted increasingly tremendous, crashing over my concentration with mounting intensity. To combat this resistance, I deployed two types of structure. The first type was time structure: “I am going to work on this for one hour,” I would tell myself. “I don’t care if I faint from the effort, or make no progress, for the next hour this is my whole world.” But of course I wouldn’t faint and eventually I would make progress. It took, on average, ten minutes for the waves of resistance to die down. Those ten minutes were always difficult, but knowing that my efforts had a time limit helped ensure that the difficulty was manageable. The second type of structure I deployed was information structure—a way of capturing the results of my hard focus in a useful form. I started by building a proof map that captured the dependencies between the different pieces of the proof. This was hard, but not too hard, and it got me warmed up in my efforts to understand the result. I then advanced from the maps to short self-administered quizzes that forced me to memorize the key definitions the proof used. Again, this was a relatively easy task, but it still took concentration, and the result was an understanding that was crucial for parsing the detailed math that came next. After these first two steps, emboldened by my initial successes in deploying hard focus, I moved on to the big guns: proof summaries. This is where I forced myself to take each lemma and walk through each step of its proofs—filling in missing steps. I would conclude by writing a detailed summary in my own words. This was staggeringly demanding, but the fact that I had already spent time on easier tasks in the paper built up enough momentum to help push me forward. I returned to this paper regularly over a period of two weeks. When I was done, I had probably experienced fifteen hours total of deliberate practice–style strain, but due to its intensity it felt like much more. Fortunately, this effort led to immediate benefits. Among other things, it allowed me to understand whole swaths of related work that had previously been mysterious. The researchers who wrote this paper had enjoyed a near monopoly on solving this style of problem—now I could join them.

Here was my first lesson: This type of skill development is hard. When I got to the first tricky gap in the paper’s main proof argument, I faced immediate internal resistance. It was as if my mind realized the effort I was about to ask it to expend, and in response it unleashed a wave of neuronal protest, distant at first, but then as I persisted increasingly tremendous, crashing over my concentration with mounting intensity. To combat this resistance, I deployed two types of structure. The first type was time structure: “I am going to work on this for one hour,” I would tell myself. “I don’t care if I faint from the effort, or make no progress, for the next hour this is my whole world.” But of course I wouldn’t faint and eventually I would make progress. It took, on average, ten minutes for the waves of resistance to die down. Those ten minutes were always difficult, but knowing that my efforts had a time limit helped ensure that the difficulty was manageable. The second type of structure I deployed was information structure—a way of capturing the results of my hard focus in a useful form. I started by building a proof map that captured the dependencies between the different pieces of the proof. This was hard, but not too hard, and it got me warmed up in my efforts to understand the result. I then advanced from the maps to short self-administered quizzes that forced me to memorize the key definitions the proof used. Again, this was a relatively easy task, but it still took concentration, and the result was an understanding that was crucial for parsing the detailed math that came next. After these first two steps, emboldened by my initial successes in deploying hard focus, I moved on to the big guns: proof summaries. This is where I forced myself to take each lemma and walk through each step of its proofs—filling in missing steps. I would conclude by writing a detailed summary in my own words. This was staggeringly demanding, but the fact that I had already spent time on easier tasks in the paper built up enough momentum to help push me forward.

Math class was the worst. Those fucking graphing calculators! When my teachers handed out quizzes, I didn’t even try. I just handed them in blank.

When your self-image is as a math “nonperformer” and you’re challenged to learn a math skill, your brain uses up your intellectual energy by arguing with you that you really can’t do it, a kind of mental barricade on the road to accomplishment. You may inherently have the ability to learn it, but that ability is eroded by the roiling doubts that wear it away. Even girls who do well in math typically assess themselves as inferior to their male counterparts, self-stereotyping apparent in girls as young as seven. Shown to affect long-term achievement, it’s hard not to equate this with the relatively small numbers of women going into math, engineering, and computer science.

In 1919, a solar eclipse took place that settled that question once and for all. This is the eclipse during which Einstein's theory of relativity was proven, as Einstein's math perfectly predicted the position of Mercury observed in the eclipse.

As we’ve seen, Math is a grab bag of number-related utility functions, such as Math.max (maximum), Math.min (minimum), and Math.sqrt (square root).

Einstein completely failed to address the elephant in the room, namely that light – from its own perspective – isn’t in any inertial reference frame. We can therefore legitimately say that it obeys entirely different laws of physics – those of non-locality (singularities) rather than locality (spacetime) – and, in fact, actually the laws of pure mathematics. Light is the non-inertial container for all inertial reference frames, and ensures that they are all part of an absolute system, not a relative system. It imposes a principle of absolutism, not a principle of relativism!

Truth and beauty are closely related but not the same. You’re never sure that you have the truth. All you’re doing is striving towards better and better truths and the light that guides you is beauty.

Many females have a problem not only with stereotypes, but with other people’s opinions of them in general. They trust them too much... This vulnerability afflicts many of the most able, high-achieving females. Why should this be? When they’re little, these girls are often so perfect, and they delight in everyone’s telling them so. They’re so well behaved, they’re so cute, they’re so helpful, and they’re so precocious. Girls learn to trust people’s estimates of them. “Gee, everyone’s so nice to me; if they criticize me, it must be true.” Even females at the top universities in the country say that other people’s opinions are a good way to know their abilities. Boys are constantly being scolded and punished. When we observed in grade school classrooms, we saw that boys got eight times more criticism than girls for their conduct. Boys are also constantly calling each other slobs and morons. The evaluations lose a lot of their power. Even when women reach the pinnacle of success, other people’s attitudes can get them... The fixed mindset, plus stereotyping, plus women’s trust in people’s assessments: I think we can begin to understand why there’s a gender gap in math and science. That gap is painfully evident in the world of high tech. Julie Lynch, a budding techie, was already writing computer code when she was in junior high school. Her father and two brothers worked in technology, and she loved it, too. Then her computer programming teacher criticized her. She had written a computer program and the program ran just fine, but he didn’t like a shortcut she had taken. Her interest evaporated. Instead, she went on to study recreation and public relations. Math and science need to be made more hospitable places for women. And women need all the growth mindset they can get to take their rightful places in these fields.

Can we ever really know to what extent this man [Mark Twain] or his book [Adventures of Huckleberry Finn] was, or is, racist? When we identify racism in the book, aren't we really just identifying racism in the culture out of which it came? Is it fair to expect Twain to have vaulted himself out of his own time and place and arrive, clean-booted and upright, in our own? Isn't the book still funny and deep? Aren't I actually enjoying it? How does one do the complicated math of Ultimate Racism: If we determine that, relative to our own time, Twain was a 40 percent racist, while relative to his own, he was only a 12 percent racist, or was in fact a 0 percent racist--what do we know, really?

Like all of my friends, I’d seen the ubiquitous soft-core pornography on late-night German television that our English relatives found scandalous. Police interviews, maths lessons, doctors’ visits turning unexpectedly sexual and ending with grunting dry humping. But I’d never seen an erect penis that wasn’t my own, I’d never seen a pale pink circumcision scar, I’d never seen, piece by piece, how a man’s body joins up, how the landscape of skin and hair changes in texture and tone, from the folds of the lips to the folds of the testicles, the tufts of black on his toes to the perfect triangle of hair above his buttocks on his otherwise hairless back.

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.

One popular trend in education is to emphasize “STEM” subjects to such a degree that science, technology, engineering, and math dominate a child’s school career. There is nothing wrong with those studies, but if a child has no time to read poetry and stories, to experience art and music, to delve into history and learn to appreciate the heritage of the past, we have violated the principle that education is the science of relations. A person wants to know about many things and a child needs broad exposure to all kinds of knowledge, especially in the younger years. That wide exposure lays a good foundation for specializing later--in a STEM subject or anything else.

In fact, they are. In a remarkable experiment, Margaret Shin, Todd Pittinsky, and Nalini Ambady asked Asian-American women to take an objective math exam. But first they divided the women into two groups. The women in one group were asked questions related to their gender. For example, they were asked about their opinions and preferences regarding coed dorms, thereby priming their thoughts for gender-related issues. The women in the second group were asked questions related to their race. These questions referred to the languages they knew, the languages they spoke at home, and their family’s history in the United States, thereby priming the women’s thoughts for race-related issues. The performance of the two groups differed in a way that matched the stereotypes of both women and Asian-Americans. Those who had been reminded that they were women performed worse than those who had been reminded that they were Asian-American. These results show that even our own behavior can be influenced by our stereotypes, and that activation of stereotypes can depend on our current state of mind and how we view ourselves at the moment.

IT POPS, A new discovery, by: Jonathan Roy Mckinney IT POPS is relative to space time in that it has two major components that follow the 3 laws of thermodynamics. The PIrandom creator injects an object with the relative XYZ coordinates in a model view projection that are derived by utilizing the correct Matrix math 11,10,10,10. Once Injected, the two way hash coin creator in time will create the entropy required to derive random shapes and reverse or abstract them into full objects for a complete wire frame like Michaelangelo could carve an Angel out of marble.

Unit circle is one of the important math concepts that every student must learn and understand. There are numerous concepts related to Trigonometry and geometry that needs to understand basics before solving the problems. Unit circle is known as the foundation of projectile motion, sine, cosine, tangents, degrees and radians. If you are learning the concept of geometry and trigonometry then you must have a unit circle chart as reference sheet. Most of the school teachers us this sheet while teaching the concepts of applied mathematics. This basic circle will be helpful throughout your life. It is necessary to learn this Blank Unit Circle Printable by heart and to practice it regularly for a solid foundation.

These operations move memory around, perform some sort of basic math, or interrupt the processor to get it to do something else. In the end, that's all a computer processor can really do. But in the same way millions of books have been written using a relatively small alphabet of letters, an infinite number of possible programs can be created using a relatively small collection of machine instructions.

Contrary to Piaget’s theory, it turns out that babies come into this world with an innate, non-verbal “number sense” and the ability to “guesstimate” the relative number of things. Newborns just two days old are, in fact, even capable of doing a kind of numbers matching game. Researchers found that when they played a specific number of syllables to newborns, the babies were able to match it to the correct number of geometric shapes. For example, when the newborns were played “tuuuuu tuuuu tuuuu tuuu,” they would look longer at a picture with four squares; when twelve syllables were played, they looked longer at a picture with twelve squares. Even more impressive, the ability of infants to link the number of sounds to the number of objects at six months of age often predicted their eventual math ability.

The moment you treat math as an abstraction, as unreal, as manmade, as a branch of logic, as a technical game, as a bunch of axioms, as some mere formalism, you are lost. Math, ontologically, is energy, and the study of math is the study of the existence, relations, interactions and symmetries of energy. That’s exactly why math can replace science wholesale. Anyone who approaches math as anything other than noumenal, ontological energy – energy in itself – will never get anywhere with relating math to reality.

All one must do is remember basic math. If one system that administers medical payments require hundreds of duplicate services, equipment, software, & databases, and must make profits for passive investors, and must pay thousands of executives millions of dollars, then it is mathematically impossible for that system to be more efficient than one that must provide the same medical payments without those expenses and overhead. Not even an inordinate amount of waste and fraud in any single-payer system would likely match the legalized fraud of the private healthcare insurance system. It is simply basic math.

Hubble’s work confirmed his math—and refuted Einstein’s general theory of relativity. Furthermore, he deduced, if the universe was expanding equally in all directions, it must have initiated in a massive explosion from a single point. This meant that the universe is not infinitely old; it has a certain age, and that the moment of creation—which British astronomer Fred Hoyle later mockingly called the “big bang”—was analogous to God’s first command: Let there be light.

This is an encouraging finding on two fronts. It means that young black children have continued to make gains relative to their white counterparts. It also means that whatever gap remains can be linked to a handful of readily identifiable factors. The data reveal that black children who perform poorly in school do so not because they are black but because a black child is more likely to come from a low-income, low-education household. A typical black child and white child from the same socioeconomic background, however, have the same abilities in math and reading upon entering kindergarten.

Lies or Falsehood = NO Trust = NO Relation Anyway. Maths are Exact.

This is not to say that being born late into a big family automatically makes someone fast, any more than having a parent die early in life automatically makes one prime minister of England. But it does say that being fast, like any talent, involves a confluence of factors that go beyond genes and that are directly related to the intense, subconscious reaction to motivational signals that provide the energy to practice deeply and thus grow myelin.

With such an illustrious reputation, it would be easy to assume Einstein rarely made mistakes—but that is not the case. To begin with, his development was described as “slow,” and he was considered to be a below-average student.16 It was apparent from an early age that his way of thinking and learning was different from the rest of the students in his class. He liked working out the more complicated problems in math, for example, but wasn’t very good at the “easy” problems.17 Later on in his career, Einstein made simple mathematical mistakes that appeared in some of his most important work. His numerous mistakes include seven major gaffes on each version of his theory of relativity, mistakes in clock synchronization related to his experiments, and many mistakes in the math and physics calculations used to determine the viscosity of liquids.18 Was Einstein considered a failure because of his mistakes? Hardly. Most importantly he didn’t let his mistakes stop him. He kept experimenting and making contributions to his field. He is famously quoted as having said, “A person who never made a mistake never tried anything new.” What’s more, no one remembers him for his mistakes—we only remember him for his contributions.

The Lorentz transformations, when properly understood, are revealing a mathematical relation between mind and matter. Descartes argued that mind is unextended and matter extended, yet can interact with each other. The Lorentz transformations show how this actually works. Light is unextended, and matter is extended, yet matter is wholly defined relative to light, and cannot exist without light. Because light is absolute, it is eternal and necessary. Because matter is relative, it is temporal and contingent. It’s all in the math. The Lorentz transformations mathematically prove that idealism is true and materialism false. Idealism is absolute, and materialism relative (dependent, derived, created, caused)

I believe that what the vast majority of the masses call life is just fiction. A therapist's work ends up being trying to bring them into nonfiction. Although I feel that many are just replacing a novel by another. Too many people tell me: 'Why do you talk like you know the truth? There is no truth'. It is as if they felt that I'm destroying their inner world by being direct. They feel the need to project a defense mechanism to protect it. Another common phrase is: 'You don't know me better than I know myself'. This one is also interesting. Because it is as if the person was saying: 'You don't know my novel better than I do because I am the author of it.’ Life pretty much follows the same principles — gravity, air, water, fire, weight, hight; all of which is represented in maths, physics, and other sciences. But most people these days consider a personal attack when you make them observe something that may touch their inner world. It's the oversensitivity paradox in which we live today, for people want to feel more alive but are afraid to live at the same time. Allegorically speaking, they need to float like a bubble of steel. And many times they are perfectly fine in discussing others' issues until those issues are projected at them for self-analysis. Quite often, we are not really talking to a human being, but to his alter-ego. There's not much difference between the real self and the alternate version of that self for such person. And how ironic when both the therapist and the patient play the same game from different perspectives. This is why people don't want the truth anymore, but an alternate version of reality where they can merge themselves as if they were merely a chemical solution melting with another. They are too afraid of the truth because they have often been hurt when trying to find it. However, the concept of truth merges with the personality of the individual. And that is why having a personality is now an outdated concept, often falling into the realm of the abstract — Everything is relative, everything is fine, and everyone is everything you can decide for yourself. So why live if life has no meaning? Well, life does have a meaning, but won't be found by running away from it.