Math Positive Quotes

Yeah, but I’m the second most fucked up person I know, and when you put two negatives together, you get a positive. That’s math, Caleb. Math is the language of the universe. You can’t argue with the universe.

In life two negatives don't make a positive. Double negatives turn positive only in math and formal logic. In life things just get worse and worse and worse.

We have the oddest conversations.” “I find this conversation more than odd. It’s positively shocking.” “Why? Because I understand the principle of a logarithm? I know you’re used to speaking to me in small, simple words, but I did have the finest education England can offer a young aristocrat. Attended both Eton and Oxford.” “Yes, but . . . somehow, I never pictured you earning high marks in maths.

The lottery is a tax on poor people and on people who can’t do math. Rich people and smart people would be in the line if the lottery were a real wealth-building tool, but the truth is that the lottery is a rip-off instituted by our government. This is not a moral position; it is a mathematical, statistical fact. Studies show that the zip codes that spend four times what anyone else does on lottery tickets are those in lower-income parts of town. The lottery, or gambling of any kind, offers false hope, not a ticket out.

So, if I'm no cheerleader of sports, why write a chapter about it? Sports do have some positive impact on society. They solve problems, such as how to get inner-city kids to spend $175 on shoes. They serve as a backdrop for some of our most memorable commercials. And they remain the one and only relevant application of math. Not only that, but we have sports to thank for most of the last century's advances in manliness. The system starts in school, where gym class separates the men from the boys. Then those men are taught to be winners, or at least, losers that hate themselves.

students who were told to think about the happiest day of their lives right before taking a standardized math test outperformed their peers.19 And people who expressed more positive emotions while negotiating business deals did so more efficiently and successfully than those who were more neutral or negative.

The algebraic sum of all the transformations occurring in a cyclical process can only be positive, or, as an extreme case, equal to nothing. [Statement of the second law of thermodynamics, 1862]

It is India that gave us the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit. But its very simplicity and the great ease which it has lent to computations put our arithmetic in the first rank of useful inventions; and we shall appreciate the grandeur of the achievement the more when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest men produced by antiquity.

Conventional wisdom nor scientific, mathematical prove of randomness in life could do nothing to deter human's curiosity for the unknown, however small the chance of a positive outcome maybe.

We tend to see math and science as a steady state of facts rather than as the accumulated knowledge of linear traditions. As Korzybski put it, we see further because we “stand on the shoulders”5 of the previous generation. The danger of such a position is that we can forget to put our own feet on the ground.

(Actually, languages can be very tricky in this respect. The eminent linguistic philosopher J. L. Austin of Oxford once gave a lecture in which he asserted that there are many languages in which a double negative makes a positive but none in which a double positive makes a negative—to which the Columbia philosopher Sidney Morgenbesser, sitting in the audience, sarcastically replied, “Yeah, yeah.

There is nothing." Philosophy That can't be done." Religion Two negatives equals a positive." Math

Try doing a few situps, pushups, or jumping jacks. A little physical exertion can have a surprisingly positive effect on your ability to understand and recall.

Is it possible that the Pentateuch could not have been written by uninspired men? that the assistance of God was necessary to produce these books? Is it possible that Galilei ascertained the mechanical principles of 'Virtual Velocity,' the laws of falling bodies and of all motion; that Copernicus ascertained the true position of the earth and accounted for all celestial phenomena; that Kepler discovered his three laws—discoveries of such importance that the 8th of May, 1618, may be called the birth-day of modern science; that Newton gave to the world the Method of Fluxions, the Theory of Universal Gravitation, and the Decomposition of Light; that Euclid, Cavalieri, Descartes, and Leibniz, almost completed the science of mathematics; that all the discoveries in optics, hydrostatics, pneumatics and chemistry, the experiments, discoveries, and inventions of Galvani, Volta, Franklin and Morse, of Trevithick, Watt and Fulton and of all the pioneers of progress—that all this was accomplished by uninspired men, while the writer of the Pentateuch was directed and inspired by an infinite God? Is it possible that the codes of China, India, Egypt, Greece and Rome were made by man, and that the laws recorded in the Pentateuch were alone given by God? Is it possible that Æschylus and Shakespeare, Burns, and Beranger, Goethe and Schiller, and all the poets of the world, and all their wondrous tragedies and songs are but the work of men, while no intelligence except the infinite God could be the author of the Pentateuch? Is it possible that of all the books that crowd the libraries of the world, the books of science, fiction, history and song, that all save only one, have been produced by man? Is it possible that of all these, the bible only is the work of God?

Having neurons wire together can be a good thing. A positive experience with a math teacher can lead to neural connections that link math with pleasure, accomplishment, and feeling good about yourself as a student. But the opposite is equally true. Negative experiences with a harsh instructor or a timed test and the anxiety that accompanies it can form connections in the brain that create a serious obstacle to the enjoyment not only of math and numbers, but exams and even school in general.

If college admissions officers are going to encourage kids to take the same AP math class, why not statistics? Almost every career (whether in business, nonprofits, academics, law, or medicine benefits from proficiency in statistics. Being an informed, responsible citizen requires a sound knowledge of statistics, as politicians, reporters, and bloggers all rely on "data" to justify positions. [p.98]

We’re pretty far from perfect, Kitten. I’m the most fucked up person you know.” “Yeah, but I’m the second most fucked up person I know, and when you put two negatives together, you get a positive. That’s math, Caleb. Math is the language of the universe. You can’t argue with the universe.” Her grin was patently ridiculous. I love you so goddamn much.

To emphasize only the beautiful seems to me to be like a mathematical system that only concerns itself with positive numbers.

Not my grade in math, not my blood type, but my favourite quote "Be Positive".

The math of the matter changed with the situation, but, broadly speaking, an attempted steal had to succeed about 70 percent of the time before it contributed positively to run totals.

Research from the HeartMath Institute (heartmath.org) shows that when you have a feeling in your heart, it goes to every cell in the body, then outward—and other people up to 10 feet away can sense feelings transmitted by your heart. This means that each day you are broadcasting to your team how you feel. You are either broadcasting positive energy or negative energy, apathy or passion, indifference or purpose.

It is noted that from 1967 to 1995 essays on negative emotions far outnumbered those on positive emotions in the psychological literature. The ratio was 21:1. Even those supreme perpetrators of pop nihilism, The New York Times and The Washington Post, have a better ratio than psychological literature. They average 12 negative stories to every one that might be construed to be non-negative. Many of their non-negative stories, however, cover success in sports and entertainment. I demand that the purveyors of despair who pretend to be dispassionate observes of the human condition go ahead and disclose that the 10 most beautiful words in the English languages are chimes, dawn, golden, hush, lullaby, luminous, melody, mist, murmuring, and tranquil; that Java sparrows prefer the music of Back over that of Schoenberg; that math experts have determined there are 1/96 trillion ways to lace up your shoes; that the Inuit term for making love is translated as ‘laughing together in bed;' and that according to Buckminster Fuller, “pollution is nothing but resources we’re not harvesting.

Do you know what the foundation of mathematics is?" I ask. "The foundation of mathematics is numbers. If anyone asked me what makes me truly happy, I would say: numbers. Snow and ice and numbers. And do you know why?" He splits the claws with a nutcracker and pulls out the meat with curved tweezers. "Because the number system is like human life. First you have the natural numbers. The ones that are whole and positive. The numbers of a small child. But human consciousness expands. The child discovers a sense of longing, and do you know what the mathematical expression is for longing?" He adds cream and several drops of orange juice to the soup. "The negative numbers. The formalization of the feeling that you are missing something. And human consciousness expands and grows even more, and the child discovers the in between spaces. Between stones, between pieces of moss on the stones, between people. And between numbers. And do you know what that leads to? It leads to fractions. Whole numbers plus fractions produce rational numbers. And human consciousness doesn't stop there. It wants to go beyond reason. It adds an operation as absurd as the extraction of roots. And produces irrational numbers." He warms French bread in the oven and fills the pepper mill. "It's a form of madness.' Because the irrational numbers are infinite. They can't be written down. They force human consciousness out beyond the limits. And by adding irrational numbers to rational numbers, you get real numbers.

Positive thoughts and feelings add energy to our system. An optimistic perspective, a feeling of appreciation, or a gesture of kindness, for example, are energy assets. Negative thoughts and feelings deplete our store of energy. Anger, jealousy, and judgmental thoughts, for example, are energy deficits.

specific link between our emotional states and our heart rhythms. When we have negative emotions (such as anger and fear), our heart rhythms become erratic and disorganized. In contrast, positive emotions (love and joy, for instance) produce highly ordered, coherent patterns that HeartMath researchers refer to as heart coherence.

To the average mathematician who merely wants to know his work is securely based, the most appealing choice is to avoid difficulties by means of Hilbert's program. Here one regards mathematics as a formal game and one is only concerned with the question of consistency ... . The Realist position is probably the one which most mathematicians would prefer to take. It is not until he becomes aware of some of the difficulties in set theory that he would even begin to question it. If these difficulties particularly upset him, he will rush to the shelter of Formalism, while his normal position will be somewhere between the two, trying to enjoy the best of two worlds.

To the average mathematician who merely wants to know his work is securely based, the most appealing choice is to avoid difficulties by means of Hilbert's program. Here one regards mathematics as a formal game and one is only concerned with the question of consistency ... . The Realist position is probably the one which most mathematicians would prefer to take. It is not until he becomes aware of some of the difficulties in set theory that he would even begin to question it. If these difficulties particularly upset him, he will rush to the shelter of Formalism, while his normal position will be somewhere between the two, trying to enjoy the best of two worlds.

I smiled despite myself. "We're pretty far from perfect, Kitten.'m the most fucked up person you know." "Yeah but I'm the most fucked up person I know, and when you put two negatives together, you get a positive. That's Math Caleb. Math is the language of universe. You can't argue with the universe." Her grin was patently ridiculous.

Among other things, HeartMath research tests theories about the electromagnetic field of the human heart using machines that measure faint magnetic fields, such as those that are often used in MRIs and cardiologic tests. Remarkably, the heart’s toroidally shaped electrical field is sixty times greater than that of the brain, and its magnetic field is 5,000 times greater than that of the brain. The heart generates the strongest electromagnetic field in the body, and its pumping action transmits powerful rhythmic information patterns containing neurological, hormonal, and electromagnetic data to the brain and throughout the rest of the body. The heart actually sends more information to the brain than the brain sends to the heart. In other words, the heart has a mind of its own. Studies reveal this electromagnetic field seems to pick up information in the surrounding environment and also broadcasts one’s emotional state out from the body. Their measurements reveal that the field is large enough to extend several feet (or more) outside our bodies. Positive moods such as gratitude, joy, and happiness correlate to a larger, more expanded heart field, while emotions such as greed, anger, or sadness correlate to a constricted heart field.

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.

Twice a day the small white compact moved, for meals, she guessed, or bathroom breaks, and about four times a day the Hummer and the Charger swapped positions, but there was apparently no coordination between the agencies, because once a day in the early morning everyone was missing at the same time, for about twenty minutes. Zero agents, zero hour. The street went back to its normal self. Some kind of logic issue, she supposed, or simple math, like in class, with x number of cars, and y number of locations, and z number of hours to cover. Something had to give.

Tools of the Mind, by contrast, doesn’t focus much on reading and math abilities. Instead, all of its interventions are intended to help children learn a different kind of skill: controlling their impulses, staying focused on the task at hand, avoiding distractions and mental traps, managing their emotions, organizing their thoughts. The founders of Tools of the Mind believe that these skills, which they group together under the rubric self-regulation, will do more to lead to positive outcomes for their students, in first grade and beyond, than the traditional menu of pre-academic skills.

We become more successful when we are happier and more positive. For example, doctors put in a positive mood before making a diagnosis show almost three times more intelligence and creativity than doctors in a neutral state, and they make accurate diagnoses 19 percent faster. Optimistic salespeople outsell their pessimistic counterparts by 56 percent. Students primed to feel happy before taking math achievement tests far outperform their neutral peers. It turns out that our brains are literally hardwired to perform at their best not when they are negative or even neutral, but when they are positive.

I suddenly remember being about seven, riding beside him in the car, and asking him how grown-ups found their way to places. After all, I had never seen him pull out a map. "I guess we just get used to taking the same turns," he said, but I wasn't satisfied. "Then what about the first time you go somewhere?" "Well," he said, "we get directions." But what I want to know is who got them the very first time? What if no one's ever been where you're going? "Dad?" I ask, "is it true that you can use stars like a map?" "Yeah, if you understand celestial navigation." "Is it hard?" I'm thinking maybe I should learn. A backup plan, for all those times I feel like I'm just wandering in circles. "It's pretty jazzy math—you have to measure the altitude of a star, figure out its position using a nautical almanac, figure out what you think the altitude should be and what direction the star should be in based on where you think you are, and compare the altitude you measured with the one you calculated. Then you plot this on a chart, as a line of position. You get several lines of position to cross, and that's where you go." My father takes one look at my face and smiles. "Exactly," he laughs. "Never leave home without your GPS.

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.

Being good at something feels great. Playing ninja turtles with two little boys for hours on end is sometimes less great. It’s so easy to hop on a plane or say yes to one more meeting or project, to get that little buzz of being good at something, or the pleasure bump of making someone happy, or whatever it is that drives you. And many of us continue to pretend we don’t have a choice—the success just happened, and we’re along for the ride. The opportunities kept coming, and anyone in our position would have jumped to meet them. But we’re the ones who keep putting up the chairs. If I work in such a way that I don’t have enough energy to give to my marriage, I need to take down some chairs. If I say yes to so many work things that my kids only get to see tired mommy, I need to take down some chairs. I know I’ve let my work win sometimes. I know I’ve gotten the math wrong, sometimes unwittingly, believing I could fit in more than I could. There have been times I’ve hidden behind my work, because work is easier to control than a hard conversation with someone you love. That’s part of the challenge of stewarding a calling, for all of us: you get it wrong sometimes. And part of stewarding that calling is sometimes taking down some chairs. We have more authority, and therefore, more responsibility than we think. We decide where the time goes. There’s so much freedom in that, and so much responsibility

Philosopher Nick Bostrom takes things one step further by asking whether we are a “real” species or a simulation created by an intelligent civilization that came before. This idea comes from the simple fact that we will someday be able to create software simulations that believe they are real creatures. And when we achieve that level of technical proficiency, we’re unlikely to stop with one simulation of that type. In the long run, you could expect far more simulated realities than the real one that started it all. So the math of it says we are far more likely to be a simulation than an original species. The interesting thing here is that neither the real species nor the simulations would be in a position to know which one they are.

Nature vs. nurture is part of this—and then there is what I think of as anti-nurturing—the ways we in a western/US context are socialized to work against respecting the emergent processes of the world and each other: We learn to disrespect Indigenous and direct ties to land. We learn to be quiet, polite, indirect, and submissive, not to disturb the status quo. We learn facts out of context of application in school. How will this history, science, math show up in our lives, in the work of growing community and home? We learn that tests and deadlines are the reasons to take action. This puts those with good short-term memories and a positive response to pressure in leadership positions, leading to urgency-based thinking, regardless of the circumstance. We learn to compete with each other in a scarcity-based economy that denies and destroys the abundant world we actually live in. We learn to deny our longings and our skills, and to do work that occupies our hours without inspiring our greatness. We learn to manipulate each other and sell things to each other, rather than learning to collaborate and evolve together. We learn that the natural world is to be manicured, controlled, or pillaged to support our consumerist lives. Even the natural lives of our bodies get medicated, pathologized, shaved or improved upon with cosmetic adjustments. We learn that factors beyond our control determine the quality of our lives—something as random as which skin, gender, sexuality, ability, nation, or belief system we are born into sets a path for survival and quality of life. In the United States specifically, though I see this most places I travel, we learn that we only have value if we can produce—only then do we earn food, home, health care, education. Similarly, we learn our organizations are only as successful as our fundraising results, whether the community impact is powerful or not. We learn as children to swallow our tears and any other inconvenient emotions, and as adults that translates into working through red flags, value differences, pain, and exhaustion. We learn to bond through gossip, venting, and destroying, rather than cultivating solutions together. Perhaps the most egregious thing we are taught is that we should just be really good at what’s already possible, to leave the impossible alone.

Rich Purnell sipped coffee in the silent building. Only his cubicle illuminated the otherwise dark room. Continuing with his computations, he ran a final test on the software he'd written. It passed. With a relieved sigh, he sank back in his chair. Checking the clock on his computer, he shook his head. 3:42am. Being an astrodynamicist, Rich rarely had to work late. His job was the find the exact orbits and course corrections needed for any given mission. Usually, it was one of the first parts of a project; all the other steps being based on the orbit. But this time, things were reversed. Iris needed an orbital path, and nobody knew when it would launch. A non-Hoffman Mars-transfer isn't challenging, but it does require the exact locations of Earth and Mars. Planets move as time goes by. An orbit calculated for a specific launch date will work only for that date. Even a single day's difference would result in missing Mars entirely. So Rich had to calculate many orbits. He had a range of 25 days during which Iris might launch. He calculated one orbital path for each. He began an email to his boss. "Mike", he typed, "Attached are the orbital paths for Iris, in 1-day increments. We should start peer-review and vetting so they can be officially accepted. And you were right, I was here almost all night. It wasn't that bad. Nowhere near the pain of calculating orbits for Hermes. I know you get bored when I go in to the math, so I'll summarize: The small, constant thrust of Hermes's ion drives is much harder to deal with than the large point-thrusts of presupply probes. All 25 of the orbits take 349 days, and vary only slightly in thrust duration and angle. The fuel requirement is nearly identical for the orbits and is well within the capacity of EagleEye's booster. It's too bad. Earth and Mars are really badly positioned. Heck, it's almost easier to-" He stopped typing. Furrowing his brow, he stared in to the distance. "Hmm." he said. Grabbing his coffee cup, he went to the break room for a refill. ... "Rich", said Mike. Rich Purnell concentrated on his computer screen. His cubicle was a landfill of printouts, charts, and reference books. Empty coffee cups rested on every surface; take-out packaging littered the ground. "Rich", Mike said, more forcefully. Rich looked up. "Yeah?" "What the hell are you doing?" "Just a little side project. Something I wanted to check up on." "Well... that's fine, I guess", Mike said, "but you need to do your assigned work first. I asked for those satellite adjustments two weeks ago and you still haven't done them." "I need some supercomputer time." Rich said. "You need supercomputer time to calculate routine satellite adjustments?" "No, it's for this other thing I'm working on", Rich said. "Rich, seriously. You have to do your job." Rich thought for a moment. "Would now be a good time for a vacation?" He asked. Mike sighed. "You know what, Rich? I think now would be an ideal time for you to take a vacation." "Great!" Rich smiled. "I'll start right now." "Sure", Mike said. "Go on home. Get some rest." "Oh, I'm not going home", said Rich, returning to his calculations. Mike rubbed his eyes. "Ok, whatever. About those satellite orbits...?" "I'm on vacation", Rich said without looking up. Mike shrugged and walked away.

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.

And who knows (there is no saying with certainty), perhaps the only goal on earth to which mankind is striving Free eBooks at Planet eBook.com lies in this incessant process of attaining, in other words, in life itself, and not in the thing to be attained, which must always be expressed as a formula, as positive as twice two makes four, and such positiveness is not life, gentlemen, but is the beginning of death. Anyway, man has always been afraid of this mathematical certainty, and I am afraid of it now. Granted that man does nothing but seek that math- ematical certainty, he traverses oceans, sacri ces his life in the quest, but to succeed, really to nd it, dreads, I assure you. He feels that when he has found it there will be noth- ing for him to look for. When workmen have nished their work they do at least receive their pay, they go to the tavern, then they are taken to the police-station—and there is oc- cupation for a week. But where can man go? Anyway, one can observe a certain awkwardness about him when he has attained such objects. He loves the process of attaining, but does not quite like to have attained, and that, of course, is very absurd. In fact, man is a comical creature; there seems to be a kind of jest in it all. But yet mathematical certainty is a er all, something insu erable. Twice two makes four seems to me simply a piece of insolence. Twice two makes four is a pert coxcomb who stands with arms akimbo bar- ring your path and spitting. I admit that twice two makes four is an excellent thing, but if we are to give everything its due, twice two makes ve is sometimes a very charming thing too. And why are you so rmly, so triumphantly, convinced that only the normal and the positive—in other words, only what is conducive to welfare—is for the advantage of man? Notes from the Underground Is not reason in error as regards advantage? Does not man, perhaps, love something besides well-being? Perhaps he is just as fond of su ering? Perhaps su ering is just as great a bene t to him as well-being? Man is sometimes extraor- dinarily, passionately, in love with su ering, and that is a fact. ere is no need to appeal to universal history to prove that; only ask yourself, if you are a man and have lived at all. As far as my personal opinion is concerned, to care only for well-being seems to me positively ill-bred. Whether it’s good or bad, it is sometimes very pleasant, too, to smash things. I hold no brief for su ering nor for well-being either. I am standing for ... my caprice, and for its being guaran- teed to me when necessary. Su ering would be out of place in vaudevilles, for instance; I know that. In the ‘Palace of Crystal’ it is unthinkable; su ering means doubt, negation, and what would be the good of a ‘palace of crystal’ if there could be any doubt about it? And yet I think man will never renounce real su ering, that is, destruction and chaos. Why, su ering is the sole origin of consciousness. ough I did lay it down at the beginning that consciousness is the great- est misfortune for man, yet I know man prizes it and would not give it up for any satisfaction. Consciousness, for in- stance, is in nitely superior to twice two makes four. Once you have mathematical certainty there is nothing le to do or to understand. ere will be nothing le but to bottle up your ve senses and plunge into contemplation. While if you stick to consciousness, even though the same result is attained, you can at least og yourself at times, and that will, at any rate, liven you up. Reactionary as it is, corporal punishment is better than nothing.

new research in psychology and neuroscience shows that it works the other way around: We become more successful when we are happier and more positive. For example, doctors put in a positive mood before making a diagnosis show almost three times more intelligence and creativity than doctors in a neutral state, and they make accurate diagnoses 19 percent faster. Optimistic salespeople outsell their pessimistic counterparts by 56 percent. Students primed to feel happy before taking math achievement tests far outperform their neutral peers. It turns out that our brains are literally hardwired to perform at their best not when they are negative or even neutral, but when they are positive.

Two-One Alpha, ready for you. Move it. We’re in kind of a hurry to find a quieter place!” Two wounded men were hauled to the helicopter first by four of their buddies, with the rest strafing the hill to keep the Taliban heads down. The fright and panic in the eyes and faces of the soldiers were clearly visible. Their screams rose above the thundering noise of the engines as they pushed the wounded in and then took up position outside the chopper to provide covering fire for the remaining men to get in. “All in. Let’s get out of here!” Leo shouted. “Grab tight. It’s going to be a rough ride boys!” John pulled the chopper into a steep climb while banking away from the hill. With no fire coming from the doorgun to keep them down, the full force and frustration of the enemy was now directed at the chopper and its occupants. They saw their prey escaping out of their hands right in front of their eyes. A burning pain shot through John’s back and legs as the body of the helicopter shuddered under the power of the two Rolls-Royce Gem turboshaft engines at full throttle. Smoke started to billow from the starboard engine. I have to get over that hill three miles away. Why am I dizzy? I have to get these boys out of trouble. I have to level the chopper and save power. I must get over that hill. I must get out of the reach of the bullets. “Doug! Doug! Can you hear me? What’s wrong man?” Leo screamed in a high-pitched, panicked voice. “Oh my God, you’ve been hit! Are you ok? Shit man, put the chopper down now. You’ll crash and kill us all!” “That hill … I have to get over it … out of range … I must get us there ...” Doug stuttered. “What was that? I can’t hear you. For God’s sake put the chopper down!” Leo shouted at the top of his voice. “Going down, going down … radio for help!” John whispered, a few seconds before everything went dark. The nightmare and the math Doug paid little heed to his passengers as he banked away from the canyon rim. Max was back there to help them. Doug had plenty on his mind, between the flashback to his crash in Afghanistan and wondering when whoever had shot two of his passengers would show up and try to shoot the chopper down here and now, over the Grand Canyon. Not to mention nursing the aging machine to do his bidding. Within minutes after takeoff from the canyon site, lying in the back of the chopper, JR and Roy were oblivious to their surroundings due to the morphine injection administered to them by Max Ellis – an ex-Marine medic and the third member of the Rossler boys’ rescue expedition. Others on the chopper had more on their minds. Raj was in his own world, eyes closed, wondering about his wife Sushma, their child, and the future. He and Sushma were not the outdoors adventure and camping types – living in a cave with other people was going to take some getting used to for them. They both grew up and had lived in the city all their lives. How was this going to work out

Positive emotions such as happiness, appreciation, compassion, care, and love not only change patterns of activity in the nervous system; they also reduce the production of the stress hormone cortisol.

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 real danger comes when the siblings just ignore each other. There may be less tension to deal with, but that’s also a recipe for a cold and distant relationship as adults. So if you want to develop close long-term relationships between your kids, think of it as a math equation, where the amount of enjoyment they share together should be greater than the conflict they experience. You’re never going to get the conflict side of the equation to zero. Siblings argue; they just do. But if you can increase the other side of the equation, giving them activities that produce positive emotions and memories, you’ll create strong bonds between them

Sometimes I feel compelled to do something, but I can only guess later why it needed to done, and I question whether I am drawing connections where none really exist. Other times I see an event – in a dream or in a flash of “knowing” – and I feel compelled to work toward changing the outcome (if it’s a negative event) or ensuring it (when the event is positive). At the times I am able to work toward changing or ensuring the predicted event, sometimes this seems to make a difference, and sometimes it doesn’t seem to matter. Finally, and most often, throughout my life I have known mundane information before I should have known it. For example, one of my favourite games in school was to guess what numbers my math teacher would use to demonstrate a concept, or to guess the words on a vocabulary test before the test was given. I noticed I was not correct all the time, but I was correct enough to keep playing the game. Perhaps partially because of the usefulness of this mundane skill, I was an outstanding student, getting straight As and graduating from college with highest honours in neuroscience and a minor in computer science. I was a modest drinker even in college, but I found I could ace tests when I was hungover after a night of indulgence. Sometimes I think I even did better the less I paid attention to the test and the more I felt sick or spacey. It was like my unconscious mind could take over and put the correct information onto the page without interruption from my overly analytical conscious mind. At graduate school in neuroscience, I focused on trying to understand human experience by studying how the brain processes pain and stress. I wanted to know the answer to the question: what’s going on inside people’s heads when we suffer? Later, as I finished my PhD in psychoacoustics, which is all about the psychology of sound, I became fascinated with timing. How do we figure out the order of sounds, even when some sounds take longer to process than others? How can drummers learn to decode time differences of 1/1,000 of a second, when most people just can’t hear those kinds of subtle time differences? At this point, I was using my premonitions as just one of the tools in my day-to-day toolkit, but I wasn’t thinking about them scientifically. At least not consciously. Sure, every so often I’d dream of the slides that would be used by one of my professors the next day in class. Or I’d realize that the data I was recording in my experiments followed the curve of an equation I’d dreamed about a year before. But I thought that was just my quirky way of doing things – it was just my good student’s intuition and it didn’t have anything to do with my research interests or my life’s work. What was my life’s work again?

She turned over and looked up. In the ceiling’s corner, she could see a small brown spider spinning a web and comforted herself by thinking of math—after all, the French mathematician Descartes’s inspiration for positions of points, coordinates, and the Cartesian plane had been a fly on the ceiling of his bedroom.

I woke up every morning at six to study—because it was easier to focus in the mornings, before I was worn out from scrapping. Although I was still fearful of God’s wrath, I reasoned with myself that my passing the ACT was so unlikely, it would take an act of God. And if God acted, then surely my going to school was His will. The ACT was composed of four sections: math, English, science and reading. My math skills were improving but they were not strong. While I could answer most of the questions on the practice exam, I was slow, needing double or triple the allotted time. I lacked even a basic knowledge of grammar, though I was learning, beginning with nouns and moving on to prepositions and gerunds. Science was a mystery, perhaps because the only science book I’d ever read had had detachable pages for coloring. Of the four sections, reading was the only one about which I felt confident. BYU was a competitive school. I’d need a high score—a twenty-seven at least, which meant the top fifteen percent of my cohort. I was sixteen, had never taken an exam, and had only recently undertaken anything like a systematic education; still I registered for the test. It felt like throwing dice, like the roll was out of my hands. God would score the toss. I didn’t sleep the night before. My brain conjured so many scenes of disaster, it burned as if with a fever. At five I got out of bed, ate breakfast, and drove the forty miles to Utah State University. I was led into a white classroom with thirty other students, who took their seats and placed their pencils on their desks. A middle-aged woman handed out tests and strange pink sheets I’d never seen before. “Excuse me,” I said when she gave me mine. “What is this?” “It’s a bubble sheet. To mark your answers.” “How does it work?” I said. “It’s the same as any other bubble sheet.” She began to move away from me, visibly irritated, as if I were playing a prank. “I’ve never used one before.” She appraised me for a moment. “Fill in the bubble of the correct answer,” she said. “Blacken it completely. Understand?” The test began. I’d never sat at a desk for four hours in a room full of people. The noise was unbelievable, yet I seemed to be the only person who heard it, who couldn’t divert her attention from the rustle of turning pages and the scratch of pencils on paper. When it was over I suspected that I’d failed the math, and I was positive that I’d failed the science. My answers for the science portion couldn’t even be called guesses. They were random, just patterns of dots on that strange pink sheet. I drove home. I felt stupid, but more than stupid I felt ridiculous. Now that I’d seen the other students—watched them march into the classroom in neat rows, claim their seats and calmly fill in their answers, as if they were performing a practiced routine—it seemed absurd that I had thought I could score in the top fifteen percent. That was their world. I stepped into overalls and returned to mine.

Though energy fields are invisible, they shape matter. Albert Einstein said that, “The field is the sole governing agency of the particle.” Many studies show that human beings are influenced by the energy fields of others. In a series of 148 1-minute trials involving 25 people, trained volunteers going into heart coherence were able to induce coherence in test subjects at a distance. They didn’t have to touch their targets to produce the effect. Their energy fields were sufficient. When you are in a heart coherent state, your heart radiates a coherent electromagnetic signal into the environment around you. This field is detectable by a magnetometer several meters away. When other people enter that coherent energy field, their heart coherence increases too, producing a group field effect. Not only are we affected by the fields of other people; we’re affected by the energies of the planet and solar system. A remarkable series of experiments, conducted by a research team led by Rollin McCraty, director of research at the HeartMath Institute, has linked individual human energy to solar cycles. McCraty and his colleagues track solar activity using large magnetometers placed at strategic locations on the earth’s surface. Solar flares affect the electromagnetic fields of the planet. The researchers compare the ebbs and flows of solar energy with the heart coherence readings of trained volunteers. They have found that when people are in heart coherence, their electromagnetic patterns track those of the solar system. 8.15. The heart coherence rhythms of a volunteer compared to solar activity over the course of a month. A later study of 16 participants over 5 months found a similar effect. McCraty writes: “A growing body of evidence suggests that an energetic field is formed among individuals in groups through which communication among all the group members occurs simultaneously. In other words, there is an actual ‘group field’ that connects all the members” together. The results of this research confirm a hypothesis McCraty and I discussed at a conference when I was writing Mind to Matter: Not only are these heart-coherent people in sync with large-scale global cycles, they’re also in sync with each other. McCraty continues, “We’re all like little cells in the bigger Earth brain—sharing information at a subtle, unseen level that exists between all living systems, not just humans, but animals, trees, and so on.” When we use selective attention to tune ourselves to positive coherent energy, we participate in the group energy field of other human beings doing the same. We may also resonate in phase with coherent planetary and universal fields. 8.16. The brain functions as receiver of information from the field. The Brain’s Ability to Detect Fields The idea of invisible energy fields has always been difficult for many scientists to swallow. Around 1900, when Dutch physician Willem Einthoven proposed that the human heart had an energy field, he was ridiculed. He built progressively more sensitive galvanometers to detect it, and he was eventually successful.

FIELD EFFECTS Emotional contagion is just one explanation for the growth of meditation. Another is field effects. Everything begins as energy, then works its way into matter. Though energy fields are invisible, they shape matter. Albert Einstein said that, “The field is the sole governing agency of the particle.” Many studies show that human beings are influenced by the energy fields of others. In a series of 148 1-minute trials involving 25 people, trained volunteers going into heart coherence were able to induce coherence in test subjects at a distance. They didn’t have to touch their targets to produce the effect. Their energy fields were sufficient. When you are in a heart coherent state, your heart radiates a coherent electromagnetic signal into the environment around you. This field is detectable by a magnetometer several meters away. When other people enter that coherent energy field, their heart coherence increases too, producing a group field effect. Not only are we affected by the fields of other people; we’re affected by the energies of the planet and solar system. A remarkable series of experiments, conducted by a research team led by Rollin McCraty, director of research at the HeartMath Institute, has linked individual human energy to solar cycles. McCraty and his colleagues track solar activity using large magnetometers placed at strategic locations on the earth’s surface. Solar flares affect the electromagnetic fields of the planet. The researchers compare the ebbs and flows of solar energy with the heart coherence readings of trained volunteers. They have found that when people are in heart coherence, their electromagnetic patterns track those of the solar system. 8.15. The heart coherence rhythms of a volunteer compared to solar activity over the course of a month. A later study of 16 participants over 5 months found a similar effect. McCraty writes: “A growing body of evidence suggests that an energetic field is formed among individuals in groups through which communication among all the group members occurs simultaneously. In other words, there is an actual ‘group field’ that connects all the members” together. The results of this research confirm a hypothesis McCraty and I discussed at a conference when I was writing Mind to Matter: Not only are these heart-coherent people in sync with large-scale global cycles, they’re also in sync with each other. McCraty continues, “We’re all like little cells in the bigger Earth brain—sharing information at a subtle, unseen level that exists between all living systems, not just humans, but animals, trees, and so on.” When we use selective attention to tune ourselves to positive coherent energy, we participate in the group energy field of other human beings doing the same. We may also resonate in phase with coherent planetary and universal fields. 8.16. The brain functions as receiver of information from the field. The Brain’s Ability to Detect Fields The idea of invisible energy fields has always been difficult for many scientists to swallow. Around 1900, when Dutch physician Willem Einthoven proposed that the human heart had an energy field, he was ridiculed. He built progressively more sensitive galvanometers to detect it, and he was eventually successful.

We intuitively know that the heart is the center of love and empathy, and studies are showing this to be true. In fact, empathy manifests in the electromagnetic field (EMF), which is generated by the heart in amounts greater than anywhere else in the body. The heart’s EMF emits fifty thousand femtoteslas (a measure of EMF), in contrast to the ten generated by the brain.37 Other research shows that when separated from the magnetic field, the heart’s electrical field is sixty times greater in amplitude than the brain’s field.38 Through this field, a person’s nervous system tunes in to and responds to the magnetic fields produced by the hearts of other people.39 The heart’s field is therefore one of the means by which a practitioner affects patients. This effect leads to the question, What do you want to share? To generate positive outcomes for a patient, a practitioner must hold positive feelings in his or her own heart. Not only does good will profit the client, but it also benefits the practitioner as a person. A set of studies by researcher Dr. Rollin McCraty of the HeartMath Institute in California, and described in his e-book, The Energetic Heart, helps explain the importance of positive energy.40 For decades, scientists have known that information is encoded in the nervous system in the time intervals between activities or in the pattern of electrical activity. Recent studies also reveal that information is captured in hormone pulses. Moreover, there is a hormone pulse that coincides with heart rhythms, which means that information is also shared in the interbeat intervals of the pressure and electromagnetic waves produced by the heart. Negative emotions such as anger, frustration, or anxiety disturb the heart rhythm. Positive emotions such as appreciation, love, or compassion produce coherent or functional patterns. Feelings, distributed throughout the body, produce chemical changes within the entire system. Do you want to be a healthy person? Be sincerely positive as often as you can. You thus “increase the probability of maintaining coherence and reducing stress, even during challenging situations.”41 What you as a practitioner believe will be shared—everywhere and with everyone you meet.

Chris Argyris, professor emeritus at Harvard Business School, wrote a lovely article in 1977,191 in which he looked at the performance of Harvard Business School graduates ten years after graduation. By and large, they got stuck in middle management, when they had all hoped to become CEOs and captains of industry. What happened? Argyris found that when they inevitably hit a roadblock, their ability to learn collapsed: What’s more, those members of the organization that many assume to be the best at learning are, in fact, not very good at it. I am talking about the well-educated, high-powered, high-commitment professionals who occupy key leadership positions in the modern corporation.… Put simply, because many professionals are almost always successful at what they do, they rarely experience failure. And because they have rarely failed, they have never learned how to learn from failure.… [T]hey become defensive, screen out criticism, and put the “blame” on anyone and everyone but themselves. In short, their ability to learn shuts down precisely at the moment they need it the most.192 [italics mine] A year or two after Wave, Jeff Huber was running our Ads engineering team. He had a policy that any notable bug or mistake would be discussed at his team meeting in a “What did we learn?” session. He wanted to make sure that bad news was shared as openly as good news, so that he and his leaders were never blind to what was really happening and to reinforce the importance of learning from mistakes. In one session, a mortified engineer confessed, “Jeff, I screwed up a line of code and it cost us a million dollars in revenue.” After leading the team through the postmortem and fixes, Jeff concluded, “Did we get more than a million dollars in learning out of this?” “Yes.” “Then get back to work.”193 And it works in other settings too. A Bay Area public school, the Bullis Charter School in Los Altos, takes this approach to middle school math. If a child misses a question on a math test, they can try the question again for half credit. As their principal, Wanny Hersey, told me, “These are smart kids, but in life they are going to hit walls once in a while. It’s vital they master geometry, algebra one, and algebra two, but it’s just as important that they respond to failure by trying again instead of giving up.” In the 2012–2013 academic year, Bullis was the third-highest-ranked middle school in California.194

The math says you can either know the position of an electron or the momentum, but never both.

Judith Richards (1993), a teacher in Cambridge, Massachusetts, recounts her experience in a third/fourth grade classroom of children of white and African-American professionals and working-class Haitian immigrants. When she structured a traditional math problem-solving activity, the children of professionals invariably took the lead. However, when she embedded the same type of math problem-solving activity in a traditional Haitian folk tale, the Haitian children took the lead. It seems reasonable that culturally responsive pedagogy would positively affect learning. In both instances, the cognitive task facing children from cultures that were different from mainstream culture was simplified when they did not have to deal with both an unfamiliar speech event and instructional content. Further, one can imagine that using a familiar communication style could possibly reduce cultural dissonance, create a sense of membership, and symbolically affirm children who are members of racial minority groups (Erickson 1987).

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.

Such results should prompt educators to abandon the traditional fixed ideas of the brain and learning that currently fill schools—ideas that children are smart or dumb, quick or slow. If brains can change in three weeks, imagine what can happen in a year of math class if students are given the right math materials and they receive positive messages about their potential and ability.

Nursing an infant, in the first few months, really sucks up the day. I never get over and am always totally taken aback by the amount of time in a day it takes to nurse a baby. When you are all and solely what they eat in the beginning of their lives, which I am in the habit of being for about the first year—Marco a little longer, Leone a little less—it could be, if you were a less driven and energetic person than myself, about the only thing you accomplished in a day. Certainly in a vacation day. But I imagine the total sensory pleasure for the kid—to pass out at the tap, belly full of that rich, sweet good stuff, and then he is in a little incomparable sleep coma with his cheeks still smashed up against the warm boob firmly and securely held in the arms of his mother—and so I tend to give my kids their twenty minutes of nursing and then their twenty minutes of post-hookup nap, undisturbed, in the very position they fell into it in, regardless of my own discomfort, arm cramps or list of shit to do that day. If you do the math of that, in pure forty-minute increments, factoring that an infant needs to be fed every couple of hours … well, an eight-hour day can really fly by, and what I used to accomplish in that time gets reduced to a maddening fraction. A whisper more than zilch.

In a study performed by Margaret Shih and her colleagues at Harvard, a group of Asian women were given similar math tests on two separate occasions.7 The first time around, they were primed to think about the fact that they were women, stereotypically worse at math than men. The second time around, they were told to focus on their identity as Asians, generally thought to be math whizzes compared to other ethnic groups. The result: The women performed far better in the second situation than they did in the first. Their math IQs hadn’t changed and neither had the difficulty of the questions. But in the second instance they believed more in their ability, and this was enough to make a substantive difference in performance.

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.

Someday Tatiana must tell Alexander how glad she is that her sister Dasha did not die without once feeling what it was like to love. Alexander. Here he is, before he was Tatiana’s, at the age of twenty, getting his medal of valor for bringing back Yuri Stepanov during the 1940 Winter War. Alexander is in his dress Soviet uniform, snug against his body, his stance at-ease and his hand up to his temple in teasing salute. There is a gleaming smile on his face, his eyes are carefree, his whole man-self full of breathtaking, aching youth. And yet, the war was on, and his men had already died and frozen and starved... and his mother and father were gone... and he was far away from home, and getting farther and farther, and every day was his last—one way or another, every day was his last. And yet, he smiles, he shines, he is happy. Anthony is gone so long that his daughters say something must have happened to him. But then he appears. Like his father, he has learned well the poker face and outwardly remains imperturbable. Just as a man should be, thinks Tatiana. A man doesn’t get to be on the President’s National Security Council without steeling himself to some of life’s little adversities. A man doesn’t go through what Anthony went through without steeling himself to some of life’s little adversities. In this hand Anthony carries two faded photographs, flattened by the pages of the book, grayed by the passing years. The kitchen falls quiet, even Rachel and Rebecca are breathless in anticipation. “Let’s see...” they murmur, gingerly picking up the fragile, sepia pictures with their long fingers. Tatiana is far away from them. “Do you want to see them with us, Grammy? Grandpa?” “We know them well,” Tatiana says, her voice catching on something. “You kids go ahead.” The grandchildren, the daughter, the son, the guests circle their heads, gaping. “Washington, look! Just look at them! What did we tell you?” Shura and Tania, 23 and 18, just married. In full bloom, on the steps of the church near Lazarevo, he in his Red Army dress uniform, she in her white dress with red roses, roses that are black in the monochrome photo. She is standing next to him, holding his arm. He is looking into the camera, a wide grin on his face. She is gazing up at him, her small body pressed into him, her light hair at her shoulders, her arms bare, her mouth slightly parted. “Grammy!” Rebecca exclaims. “I’m positively blushing. Look at the way you’re coming the spoon on Grandpa!” She turns to Alexander from the island. “Grandpa, did you catch the way she is looking at you?” “Once or twice,” replies Alexander. The other colorless photo. Tania and Shura, 18 and 23. He lifts her in the air, his arms wrapped around her body, her arms wrapped around his neck, their fresh faces tilted, their enraptured lips in a breathless open kiss. Her feet are off the ground. “Wow, Grammy,” murmurs Rebecca. “Wow, Grandpa.” Tatiana is busily wiping the granite island. “You want to know what my Washington said about you two?” Rebecca says, not looking away from the photograph. “He called you an adjacent Fibonacci pair!” She giggles. “Isn’t that sexy?” Tatiana shakes her head, despite herself glancing at Washington with reluctant affection. “Just what we need, another math expert. I don’t know what you all think math will give you.” And Janie comes over to her father who is sitting at the kitchen table, holding her baby son, bends over Alexander, leans over him, kisses him, her arm around him, and murmurs into his ear, “Daddy, I’ve figured out what I’m going to call my baby. It’s so simple.” “Fibonacci?” She laughs. “Why, Shannon, of course. Shannon.” The

The most important pillar behind innovation and opportunity—education—will see tremendous positive change in the coming decades as rising connectivity reshapes traditional routines and offers new paths for learning. Most students will be highly technologically literate, as schools continue to integrate technology into lesson plans and, in some cases, replace traditional lessons with more interactive workshops. Education will be a more flexible experience, adapting itself to children’s learning styles and pace instead of the other way around. Kids will still go to physical schools, to socialize and be guided by teachers, but as much, if not more, learning will take place employing carefully designed educational tools in the spirit of today’s Khan Academy, a nonprofit organization that produces thousands of short videos (the majority in science and math) and shares them online for free. With hundreds of millions of views on the Khan Academy’s YouTube channel already, educators in the United States are increasingly adopting its materials and integrating the approach of its founder, Salman Khan—modular learning tailored to a student’s needs. Some are even “flipping” their classrooms, replacing lectures with videos watched at home (as homework) and using school time for traditional homework, such as filling out a problem set for math class. Critical thinking and problem-solving skills will become the focus in many school systems as ubiquitous digital-knowledge tools, like the more accurate sections of Wikipedia, reduce the importance of rote memorization. For children in poor countries, future connectivity promises new access to educational tools, though clearly not at the level described above. Physical classrooms will remain dilapidated; teachers will continue to take paychecks and not show up for class; and books and supplies will still be scarce. But what’s new in this equation—connectivity—promises that kids with access to mobile devices and the Internet will be able to experience school physically and virtually, even if the latter is informal and on their own time.

When it comes to our own well being, it is not a matter of doing the math, it is a matter of choosing the formula. When you add up the numbers, keep the primary factors in mind. Then multiply all sums by a positive outlook. The numbers will inevitably change and so will any undesirable equivalence. The math is merely the meter for the moment in an ever changing flux of the dynamic human equation.

In a powerful demonstration of this, psychologist Lisa Blackwell and her colleagues showed seventh-grade students how the brain grows and makes new connections when we learn, much like muscles becoming stronger. The exercise reminded the students that they can grow their intelligence. In subsequent testing, these students improved their math achievement across the difficult transition to junior high school, whereas another group of students, who had not been exposed to Blackwell’s lessons, showed a decline.

I smiled despite myself. Caleb: "We're pretty far from perfect, Kitten. I'm the most fucked up person you know." Livvie: "Yeah but I'm the second most fucked up person I know, and when you put two negatives together, you get a positive. That's Math Caleb. Math is the language of universe. You can't argue with the universe." Her grin was patently ridiculous.

Braid groups have many important practical applications. For example, they are used to construct efficient and robust public key encryption algorithms.7 Another promising direction is designing quantum computers based on creating complex braids of quantum particles known as anyons. Their trajectories weave around each other, and their overlaps are used to build “logic gates” of the quantum computer.8 There are also applications in biology. Given a braid with n threads, we can number the nails on the two plates from 1 to n from left to right. Then, connect the ends of the threads attached to the nails with the same number on the two plates. This will create what mathematicians call a “link”: a union of loops weaving around each other. In the example shown on this picture, there is only one loop. Mathematicians’ name for it is “knot.” In general, there will be several closed threads. The mathematical theory of links and knots is used in biology: for example, to study bindings of DNA and enzymes.9 We view a DNA molecule as one thread, and the enzyme molecule as another thread. It turns out that when they bind together, highly non-trivial knotting between them may occur, which may alter the DNA. The way they entangle is therefore of great importance. It turns out that the mathematical study of the resulting links sheds new light on the mechanisms of recombination of DNA. In mathematics, braids are also important because of their geometric interpretation. To explain it, consider all possible collections of n points on the plane. We will assume that the points are distinct; that is, for any two points, their positions on the plane must be different. Let’s choose one such collection; namely, n points arranged on a straight line, with the same distance between neighboring points. Think of each point as a little bug. As we turn on the music, these bugs come alive and start moving on the plane. If we view the time as the vertical direction, then the trajectory of each bug will look like a thread. If the positions of the bugs on the plane are distinct at all times – that is, if we assume that the bugs don’t collide – then these threads will never intersect. While the music is playing, they can move around each other, just like the threads of a braid. However, we demand that when we stop the music after a fixed period of time, the bugs must align on a straight line in the same way as at the beginning, but each bug is allowed to end up in a position initially occupied by another bug. Then their collective path will look like a braid with n threads. Thus, braids with n threads may be viewed as paths in the space of collections of n distinct points on the plane.10

All of this told of harm done, of a drug that made a child depressed, lonely, and filled with a sense of inadequacy, and when researchers looked at whether Ritalin at least helped hyperactive children fare well academically, to get good grades and thus succeed as students, they found that it wasn’t so. Being able to focus intently on a math test, it turned out, didn’t translate into long-term academic achievement. This drug, Sroufe explained in 1973, enhances performance on “repetitive, routinized tasks that require sustained attention,” but “reasoning, problem solving and learning do not seem to be [positively] affected.”26 Five years later, Herbert Rie was much more negative. He reported that Ritalin did not produce any benefit on the students’ “vocabulary, reading, spelling, or math,” and hindered their ability to solve problems. “The reactions of the children strongly suggest a reduction in commitment of the sort that would seem critical for learning.”27 That same year, Russell Barkley at the Medical College of Wisconsin reviewed the relevant scientific literature and concluded “the major effect of stimulants appears to be an improvement in classroom manageability rather than academic performance.”28 Next it was James Swanson’s turn to weigh in. The fact that the drugs often left children “isolated, withdrawn and overfocused” could “impair rather than improve learning,” he said.29 Carol Whalen, a psychologist from the University of California at Irvine, noted in 1997 that “especially worrisome has been the suggestion that the unsalutary effects [of Ritalin] occur in the realm of complex, high-order cognitive functions such as flexible problem-solving or divergent thinking.”30 Finally, in 2002, Canadian investigators conducted a meta-analysis of the literature, reviewing fourteen studies involving 1,379 youths that had lasted at least three months, and they determined that there was “little evidence for improved academic performance.”31

Teaching is a surprisingly powerful method of learning. In a meta-analysis of 16 studies, students who were randomly assigned to tutor their peers ended up earning higher scores in the material they were teaching. Students who taught reading improved in reading; those who taught math got dramatically better at math. The more time they spent tutoring, the more they learned. As one group of researchers concluded, “Like the children they helped, the tutors gained a better understanding of and developed more positive attitudes toward the subject matter covered in the tutorial program.” [*]

Perhaps the most unsettling thing is that a negative times a negative is a positive.

Teaching is a surprisingly powerful method of learning. In a meta-analysis of 16 studies, students who were randomly assigned to tutor their peers7 ended up earning higher scores in the material they were teaching. Students who taught reading improved in reading; those who taught math got dramatically better at math. The more time they spent tutoring, the more they learned. As one group of researchers concluded, “Like the children they helped, the tutors gained a better understanding of and developed more positive attitudes toward the subject matter covered in the tutorial program.”8,fn2 Psychologists call this the tutor effect.9 It’s even effective for novices: the best way to learn something is to teach it. You remember it better after you recall it10—and you understand it better after you explain it. All it takes is embracing the discomfort of putting yourself in the instructor’s seat before you’ve reached mastery. Even just being told you’re going to teach11 something is enough to boost your learning.

They are more satisfied at work and are viewed more positively by co-workers. They feel less regret and are better able to roll with the punches of life. In typically stressful events, like math tests or public speaking, they keep calm.

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.

Cellular biologist Glen Rein, Ph.D., conceived of a series of experiments to test healers’ ability to affect biological systems. [...] In Dr. Rein’s experiment, he first studied a group of ten individuals who were well practiced in using techniques that Heart-Math teaches to build heart-focused coherence. They applied the techniques to produce strong, elevated feelings such as love and appreciation, then for two minutes, they held vials containing DNA samples suspended in deionized water. When those samples were analyzed, no statistically significant changes had occurred. A second group of trained participants did the same thing, but instead of just creating positive emotions (a feeling) of love and appreciation, they simultaneously held an intention (a thought) to either wind or unwind the strands of DNA. This group produced statistically significant changes in the conformation (shape) of the DNA samples. In some cases the DNA was wound or unwound as much as 25 percent! A third group of trained subjects held a clear intent to change the DNA, but they were instructed not to enter into a positive emotional state. In other words, they were only using thought (intention) to affect matter. The result? No changes to the DNA samples. [...] Only when subjects held both heightened emotions and clear objectives in alignment were they able to produce the intended effect. An intentional thought needs an energizer, a catalyst—and that energy is an elevated emotion.

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.

When the church lives out its mission, it will be founded on the gospel, evidence true discipleship, positively impact society, and become the body of Christ in whatever cultural context it develops. Ministry will be done. Jesus will be worshiped as supreme above all else.

The great breakthrough that permitted man to count far beyond 10 with just ten different symbols was the invention of this turning point—a concept that mathematicians call positional notation. Positional notation means that each digit in a number has a particular value based on its position. In a decimal number, the first (farthest right) digit represents 1’s, the next digit 10’s, the next 100’s, and so on. The number 206 stands for six 1’s, no 10’s, and two 100’s: Add it all up: and you get 206. This number, incidentally, demonstrates why mathematicians consider the invention of a symbol that represents nothing (i.e., the number 0) to have been a revolutionary event in man’s intellectual history. Without zero, there would be no positional notation, because there would be no difference between 26 and 206 and 2,000,006. The Romans, for all their other achievements, never hit on the idea of zero and thus were stuck with a cumbersome system of M’s, C’s, X’s, and I’s which made higher math just about impossible. With

Corvallis and most of the other techies hated this idea because of its sheer bogosity, which was screamingly obvious to any person of technical acumen who thought about it for more than a few seconds. If their pattern-recognition software could identify the moving travelers and vectorize their body positions well enough to translate their movements into T’Rain, then it could just as easily notice, automatically, with no human intervention, when one of those figures was walking the wrong way and sound the alarm. There was no need at all to have human players in the loop. They should just spin out the pattern-recognition part of it as a separate business. Richard understood and acknowledged all of this—and did not care. “Did you, or did you not, tell me that this was all marketing? What part of your own statement did you not understand?” The purpose of the exercise was not really to build a rational, efficient airport security system. It was, rather (to use yet another of those portentous phrases cribbed from the math world), an existence proof. Once it was up and running, they could point to it and to its 100 percent success rate as vindicating the premise of APPIS, which was that real-world problems—especially problems that were difficult to solve because of hard-wired deficiencies of the human neurological system, such as the tendency to become bored when given a terrible job—could be tackled by metaphrasing them into Medieval Armed Combat scenarios, and then (here brandishing two searingly hip terms from high tech) putting them out on the cloud so that they could be crowdsourced.

Benevolent prejudice,” repeated the DS. “It’s where you’re racist but, like, in a positive way. Like, handing out food to black people because you think they’re all poor. Or, I don’t know, assuming Asians are all great at maths.

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.

We’re in a small boat with Russia, Hungary, and the Slovak Republic. Who’s at the very top? Shanghai, Hong Kong, Singapore, and Taiwan. According to the study, the math performance of fifteen-year-olds in Shanghai was “over two years . . . ahead of those . . . in Massachusetts,” even though "strong-performing U.S. states.” The somewhat comforting suggestion that our low scores were just the result of a high proportion of poor performers pulling down our average doesn’t work. The United States also has significantly fewer “top performers in math.” For instance, fewer than 9 percent of U.S. students scored “advanced” in math, compared to a whopping 55 percent of students in Shanghai, 40 percent in Singapore, and more than 16 percent in Canada. The lag in math scores in fifteen-year-old Americans can be traced, in stages, back to eighth grade, then to fourth grade, then to first grade and even kindergarten. Chinese children, on the other hand, have been shown to excel early on in math, in addition, subtraction, counting, and even the ability to position a specific number correctly on a line between 0 and 100. Chinese kindergarteners have been found to have skills similar to U.S. second graders for number estimation.

If you go around saying that something must be falsifiable, you are saying that it must be false since, by definition, nothing true can be falsifiable. The whole task of truthfully explaining reality is to arrive at rational positions that are 100% unfalsifiable (hence non-scientific). Mathematics is what lies behind science and is unfalsifiable.

The commonplace idea that math is a manmade language is comically dumb. We know what manmade languages are like: English, German, French, Spanish, Japanese, and so on. None of these has any resemblance whatsoever to math. How can a human being invent π or e? How can a human pluck Euler’s Formula out of nothing? The reason why people are so keen to say that math is manmade is because if they’re wrong then the converse is true: man is mathmade! That is, of course, exactly the position of ontological mathematics, and it represents the highest possible wisdom

techniques that had been developed by the Institute of HeartMath. These positive emotion-focused techniques help individuals learn to self-generate and sustain a beneficial functional mode known as psychophysiological coherence, characterized by increased emotional stability and by increased synchronization and harmony in the functioning of physiological systems.

in both academic and business settings, these same benefits persist throughout our adult lives. For instance, students who were told to think about the happiest day of their lives right before taking a standardized math test outperformed their peers.19 And people who expressed more positive emotions while negotiating business deals did so more efficiently and successfully than those who were more neutral or negative.20

Eight perfect shuffles will return a fifty-two-card deck to its original order, with every card having cycled back to its starting position.

The brain is not the source of anything. It is the conduit, the biological computer system, which responds to information stimuli and makes it conscious in terms of fivesense perception and behaviour. Different areas of the brain become activated, or ‘light up’, when energetic information is received that relates to their specific role in decoding and communicating information to the holographic conscious mind. The information can come from the heart and the greater Consciousness (what some call the soul), or it can come from direct Archontic possession and the endless Archontic programs such as education, science, medicine, media, politics etc., etc., etc. Once you open yourself to heart intelligence – innate intelligence, universal intelligence – the ‘opposition’ is routed and the heart and brain speak as one . The fact it is such a ‘revelation’ that the brain is changeable and malleable shows how far off the pace mainstream ‘science’ is and has been. The brain is a hologram and its base state is a 100 percent malleable waveform information field. When the field changes, the ‘physical’ brain must change and it is at the waveform and electromagnetic levels that Archontic possession takes place and the heart most powerfully interacts with the brain, although it does so electrically, too. For the most extreme possession to happen the heart’s influence must be seriously curtailed and that is why the Archons target the heart vortex in the way they have structured society and lock people into the emotional chakra in the gut. Positive feelings and perceptions like love and joy (high frequency) come from the heart while negative emotions like fear, anxiety, stress and depression (low frequency) come from the belly. The idea is to block the influence of the heart by giving people so many reasons to feel fear, anxiety, stress and depression. Stress causes heart disease because it stems the flow of energy through the heart chakra and causes it to form a chaotic field that becomes more intense the longer the stress continues. This distortion is transferred through to the holographic heart and there you have the reason why in a fearful and stressed society that heart disease is a mass global killer. What is called ‘heartache’ is when people feel the effect of the distorted heart-field. The effect of severe trauma, like losing a loved one, really can cause people to die of a ‘broken heart’ because of this. Research by the Institute of HeartMath has shown that the heart’s electromagnetic fields change in response to emotions and, given that the heart field can be measured several feet from the body, you can appreciate the fundamental effect – positive or negative – the nature of that field can have on mental, emotional and bodily health. The heart vortex and its massive electromagnetic field is where human perception has been most effectively hijacked and we need to reverse that. Nothing is more important than this for those who truly want to free themselves from Archontic tyranny. If people think they can meet this challenge with anger, hatred or violent revolution they should feel free to waste their time. No shift from gut to heart = global tyranny. Shift from gut to heart = game over. It is possible to override and bypass the brain altogether and in fact this must be done to go beyond ‘time and space’. I have been doing this since my experience in Peru and it gets more powerful and profound the more you do it. This is what Da Vinci, Bruno and the others were doing. Normally information enters what we call the conscious mind through the brain with all the potential interference, blocks and filters caused by belief, emotion and other programming. But if you move your point of attention from the body out into the infinity beyond the Matrix you can make a direct connection between expanded insight and your own conscious awareness.

Essentially, they and others have documented a specific link between our emotional states and our heart rhythms. When we have negative emotions (such as anger and fear), our heart rhythms become erratic and disorganized. In contrast, positive emotions (love and joy, for instance) produce highly ordered, coherent patterns that HeartMath researchers refer to as heart coherence.

We are now in a position to turn to problems of the definition of mathematics. The definition I advocate is briefly this: Mathematics is the science of formal systems.

If two bisexual disasters find each other, does that negate the whole disaster part? Like how two negatives equal a positive?" "It's so sexy when you talk math to me," he rasped.