Solving Equations Quotes

A human being should be able to change a diaper, plan an invasion, butcher a hog, conn a ship, design a building, write a sonnet, balance accounts, build a wall, set a bone, comfort the dying, take orders, give orders, cooperate, act alone, solve equations, analyze a new problem, pitch manure, program a computer, cook a tasty meal, fight efficiently, die gallantly. Specialization is for insects.

Ladies and gentlemen of the class of '97: Wear sunscreen. If I could offer you only one tip for the future, sunscreen would be it. The long-term benefits of sunscreen have been proved by scientists, whereas the rest of my advice has no basis more reliable than my own meandering experience. I will dispense this advice now. Enjoy the power and beauty of your youth. Oh, never mind. You will not understand the power and beauty of your youth until they've faded. But trust me, in 20 years, you'll look back at photos of yourself and recall in a way you can't grasp now how much possibility lay before you and how fabulous you really looked. You are not as fat as you imagine. Don't worry about the future. Or worry, but know that worrying is as effective as trying to solve an algebra equation by chewing bubble gum. The real troubles in your life are apt to be things that never crossed your worried mind, the kind that blindside you at 4 p.m. on some idle Tuesday.

I do believe in simplicity. It is astonishing as well as sad, how many trivial affairs even the wisest thinks he must attend to in a day; how singular an affair he thinks he must omit. When the mathematician would solve a difficult problem, he first frees the equation of all incumbrances, and reduces it to its simplest terms. So simplify the problem of life, distinguish the necessary and the real. Probe the earth to see where your main roots run.

She was a genius on paper. But not a team player. She was quick to loathe others. But not against loving. She was a complicated equation that didn't need to be solved.

Whoever you are, bear in mind that appearance is not reality. Some people act like extroverts, but the effort costs them energy, authenticity, and even physical health. Others seem aloof or self-contained, but their inner landscapes are rich and full of drama. So the next time you see a person with a composed face and a soft voice, remember that inside her mind she might be solving an equation, composing a sonnet, designing a hat. She might, that is, be deploying the powers of quiet.

School literally doesn’t care about you unless you’re good at writing stuff down or you’re good at memorising or you can solve bloody maths equations. What about the other important things in life?

Ladies and gentlemen of the class of '97: Wear sunscreen. If I could offer you only one tip for the future, sunscreen would be it. The long-term benefits of sunscreen have been proved by scientists, whereas the rest of my advice has no basis more reliable than my own meandering experience. I will dispense this advice now. Enjoy the power and beauty of your youth. Oh, never mind. You will not understand the power and beauty of your youth until they've faded. But trust me, in 20 years, you'll look back at photos of yourself and recall in a way you can't grasp now how much possibility lay before you and how fabulous you really looked. You are not as fat as you imagine. Don't worry about the future. Or worry, but know that worrying is as effective as trying to solve an algebra equation by chewing bubble gum. The real troubles in your life are apt to be things that never crossed your worried mind, the kind that blindside you at 4 pm on some idle Tuesday. Do one thing everyday that scares you. Sing. Don't be reckless with other people's hearts. Don't put up with people who are reckless with yours. Floss. Don't waste your time on jealousy. Sometimes you're ahead, sometimes you're behind. The race is long and, in the end, it's only with yourself. Remember compliments you receive. Forget the insults. If you succeed in doing this, tell me how. Keep your old love letters. Throw away your old bank statements. Stretch. Don't feel guilty if you don't know what you want to do with your life. The most interesting people I know didn't know at 22 what they wanted to do with their lives. Some of the most interesting 40-year-olds I know still don't. Get plenty of calcium. Be kind to your knees. You'll miss them when they're gone. Maybe you'll marry, maybe you won't. Maybe you'll have children, maybe you won't. Maybe you'll divorce at 40, maybe you'll dance the funky chicken on your 75th wedding anniversary. Whatever you do, don't congratulate yourself too much, or berate yourself either. Your choices are half chance. So are everybody else's. Enjoy your body. Use it every way you can. Don't be afraid of it or of what other people think of it. It's the greatest instrument you'll ever own. Dance, even if you have nowhere to do it but your living room. Read the directions, even if you don't follow them. Do not read beauty magazines. They will only make you feel ugly. Get to know your parents. You never know when they'll be gone for good. Be nice to your siblings. They're your best link to your past and the people most likely to stick with you in the future. Understand that friends come and go, but with a precious few you should hold on. Work hard to bridge the gaps in geography and lifestyle, because the older you get, the more you need the people who knew you when you were young. Live in New York City once, but leave before it makes you hard. Live in Northern California once, but leave before it makes you soft. Travel. Accept certain inalienable truths: Prices will rise. Politicians will philander. You, too, will get old. And when you do, you'll fantasize that when you were young, prices were reasonable, politicians were noble, and children respected their elders. Respect your elders. Don't expect anyone else to support you. Maybe you have a trust fund. Maybe you'll have a wealthy spouse. But you never know when either one might run out. Don't mess too much with your hair or by the time you're 40 it will look 85. Be careful whose advice you buy, but be patient with those who supply it. Advice is a form of nostalgia. Dispensing it is a way of fishing the past from the disposal, wiping it off, painting over the ugly parts and recycling it for more than it's worth. But trust me on the sunscreen.

I'm an equation that only she solves, these X's and Y's by other names called. My way of dividing is desperately flawed as I multiply the days without her" - Page 165

I am an equation that only she solves, These X's and Y's by other names called, My way of division is desperatley flawed, while I multiply days without her.

Enjoy the power and beauty of your youth; oh nevermind; you will not understand the power and beauty of your youth until they have faded. But trust me, in 20 years you’ll look back at photos of yourself and recall in a way you can’t grasp now how much possibility lay before you and how fabulous you really looked….You’re not as fat as you imagine. Don’t worry about the future; or worry, but know that worrying is as effective as trying to solve an algebra equation by chewing bubblegum. The real troubles in your life are apt to be things that never crossed your worried mind; the kind that blindside you at 4pm on some idle Tuesday. Do one thing everyday that scares you Sing Don’t be reckless with other people’s hearts, don’t put up with people who are reckless with yours. Floss Don’t waste your time on jealousy; sometimes you’re ahead, sometimes you’re behind…the race is long, and in the end, it’s only with yourself. Remember the compliments you receive, forget the insults; if you succeed in doing this, tell me how. Keep your old love letters, throw away your old bank statements. Stretch Don’t feel guilty if you don’t know what you want to do with your life…the most interesting people I know didn’t know at 22 what they wanted to do with their lives, some of the most interesting 40 year olds I know still don’t. Get plenty of calcium. Be kind to your knees, you’ll miss them when they’re gone. Maybe you’ll marry, maybe you won’t, maybe you’ll have children,maybe you won’t, maybe you’ll divorce at 40, maybe you’ll dance the funky chicken on your 75th wedding anniversary…what ever you do, don’t congratulate yourself too much or berate yourself either – your choices are half chance, so are everybody else’s. Enjoy your body, use it every way you can…don’t be afraid of it, or what other people think of it, it’s the greatest instrument you’ll ever own.. Dance…even if you have nowhere to do it but in your own living room. Read the directions, even if you don’t follow them. Do NOT read beauty magazines, they will only make you feel ugly. Get to know your parents, you never know when they’ll be gone for good. Be nice to your siblings; they are the best link to your past and the people most likely to stick with you in the future. Understand that friends come and go,but for the precious few you should hold on. Work hard to bridge the gaps in geography and lifestyle because the older you get, the more you need the people you knew when you were young.

So the next time you see a person with a compose face and a soft voice, remember that inside her mind she might be solving an equation, composing a sonnet, designing a hat. She might, that is, be deploying the powers of quiet.

In one equation you can solve all the puzzles of life. It is the equation of giving.

I feel like I'm playing some giant video game, or trying to solve a really complicated math equation. 'One girl is trying to avoid forty raiding parties of between fifteen to twenty people each, spread out across a radius of seven miles. If she has to make it 2.7 miles through the center, what is the probablitiy she will wake up tomorrow morning in a jail cell? Please feel free to round pi to 3.14'.

Don't worry about the future. Or worry, but know that worrying is as effective as trying to solve an algebra equation by chewing bubble gum. The real troubles in your life are apt to be things that never crossed your worried mind, the kind that blindside you at 4 p.m. on some idle Tuesday.

Worrying about the future is as effective as trying to solve an algebra equation by chewing bubble gum. The real troubles in your life will always be things that never crossed your worried mind.

I could solve all the Diophantine equations, extend Newton’s work on infinite series, complete Euler's analysis of prime numbers, and it wouldn’t matter.” She looked at Isabelle. “Ella is the beauty. You and I are the ugly stepsisters. And so the world reduces us, all three of us, to our lowest common denominator.

How did you know?” “I…” Thomas swallowed hard, his attention fixed on the painting. “The truth?” “Please.” “You’ve got a dress with orchid blossoms embroidered on it. Ribbons in the deepest purple. You favor the color, but not nearly as much as I find myself favoring you.” He took a deep breath. “As to the stars? Those are what I prefer. More than medical practices and deductions. The universe is vast. A mathematical equation even I have no hope of solving. For there are no limits to the stars; their numbers are infinite. Which is precisely why I measure my love for you by them. An amount too boundless to count.

As to the stars? Those are what I prefer. More than medical practices and deductions. The universe is vast. A mathematical equation even I have no hope of solving. For there are no limits to the stars; their numbers are infinite. Which is precisely why i measure my love for you by them An amount too boundless to count.

If you choose to try to make a life with another person, you will live by that choice. You'd find yourself having to choose again and again to remain rather than run. It helps if you enter into a committed relationship prepared to work, ready to be humbled and willing to accept and even enjoy living in that in-between space, bouncing between the poles of beautiful and horrible, sometimes in the span of a single conversation, sometimes over the course of years. And inside of that choice and those years you'll almost certainly come to see that there is no such thing as a 50-50 balance, instead it will be like beads on an abacus, sliding back and forth, the maths rarely tidy, the equation never quite solved....

His lips are soft and warm and fit mine like the answer to an equation I didn't know I was trying to solve.

One degree of longitude equals four minutes of time the world over, but in terms of distance, one degree shrinks from sixty-eight miles at the Equator to virtually nothing at the poles.

In all things in this life, we are told "It's okay if you don't make it the first time!", "It's fine if you don't get it right the first time, just try again and again!" We are told this in learning how to ride a bike, in learning how to bake a cake, in solving our math equations...in everything. Except marriage. Why are we all expected to get such an enormous and weighty thing right, the very first time, and if we don't we're considered as failures? I beg to differ! This is a stupidity!

We, however, have all kinds of different ideas about what happiness is. Some must go bungee jumping to experience a rush of joy, while others find bliss staying home. Some are happy in a concert hall, listening to classical music, while children on a playground could be music to the ears of others. Some people experience elation when they solve a complicated equation, while for others a cancelled math class is a happy childhood memory.

The key point to keep in mind, however, is that symmetry is one of the most important tools in deciphering nature's design.

As my physics teacher always said, “My dear students! Just remember that money solves all problems, even differential equations.

I think what's happened, Marlee, is that you've realized the world isn't an addition problem. We tell kids that sometimes. We pretend the world is straightforward, simple, easy. You do this, you get that. You're a good person and try your best, and nothing bad will happen. But the truth is, the world is much more like an algebraic equation. With variables and changes, complicated and messy. Sometimes there's more than one answer, and sometimes there is none. Sometimes we don't even know how to solve the problem. But usually, if we take things step by step, we can figure things out. You just have to remember to factor the equation, break it down into smaller parts.

As with Randall Terry and other anti-abortion leaders, women simply did not figure into [Roeder's] equations. If all the abortion providers were dead, the problem would be solved, and he'd never have to think about those who sought to end their pregnancies through illegal or dangerous means.

The reason Dick's physics was so hard for ordinary people to grasp was that he did not use equations. The usual theoretical physics was done since the time of Newton was to begin by writing down some equations and then to work hard calculating solutions of the equations. This was the way Hans and Oppy and Julian Schwinger did physics. Dick just wrote down the solutions out of his head without ever writing down the equations. He had a physical picture of the way things happen, and the picture gave him the solutions directly with a minimum of calculation. It was no wonder that people who had spent their lives solving equations were baffled by him. Their minds were analytical; his was pictorial.

LIFE=UNCONDITIONAL LOVE If you can feel this equation. I said IF you can FEEL this equation you can solve any mystery of life..

But life is not evens and odds and solving for x. And sadness? Sadness is an equation made of all variables.

goal-directed self-imposed delay of gratification" is perhaps the essence of emotional self-regulation: the ability to deny impulse in the service of a goal, whether it be building a business, solving an algebraic equation, or pursuing the Stanley Cup. His finding underscores the role of emotional intelligence as a meta-ability, determining how well or how poorly people are able to use their other mental capacities.

It was like trying to solve a math equation with a poem.

It’s not clear when people started equating solving emotional issues with retracing your steps in order to find your car keys, but if you retrace your steps to uncover the ultimate source of your problems, you won’t usually find it. On the plus side, you might find your sunglasses.

Finding this,” he says, his voice soft as he pats the cover of my notebook, “was so”—his eyebrows pull together—“it was so extraordinarily painful.” He finally looks at me and he looks like a completely different person. Like he’s trying to solve a tremendously difficult equation. “It was like meeting a friend for the very first time.

I love you. As the same value, as the same expression, with the same pride and the same meaning as I love my work, my mills, my Metal, my hours at a desk, at a furnace, in a laboratory, in an ore mine, as I love my ability to work, as I love the act of sight and knowledge, as I love the action of my mind when it solves a chemical equation or grasps a sunrise, as I love the things I've made and the things I've felt, as *my* product, as *my* choice, as a shape of my world, as my best mirror, as the wife I've never had, as that which makes all the rest of it possible: as my power to live.

Can’t you make yourself likeable? Can’t you even try?” Something shifted in Tavi then. She was always so flippant, trailing sarcasm behind her like a duchess trailing furs. But not this time. Hugo had pierced her armor and blood was dripping from the wound. “Try for whom, Hugo?” she repeated, her voice raw. “For the rich boys who get to go to the Sorbonne even though they’re too stupid to solve a simple quadratic equation? For the viscount I was seated next to at a dinner who tried to put his hand up my skirt through all five courses? For the smug society ladies who look me up and down and purse their lips and say no, I won’t do for their sons because my chin is too pointed, my nose is too large, I talk too much about numbers?” “Tavi …” Isabelle whispered. She went to her, tried to put an arm around her, but Tavi shook her off. “I wanted books. I wanted maths and science. I wanted an education,” Tavi said, her eyes bright with emotion. “I got corsets and gowns and high-heeled slippers instead. It made me sad, Hugo. And then it made me angry. So no, I can’t make myself likeable. I’ve tried. Over and over. It doesn’t work. If I don’t like who I am, why should you?

In an age defined by a chasm between those who have power and those who don’t, elites have spread the idea that people must be helped, but only in market-friendly ways that do not upset fundamental power equations. The society should be changed in ways that do not change the underlying economic system that has allowed the winners to win and fostered many of the problems they seek to solve. The broad fidelity to this law helps make sense of what we observe all around: the powerful fighting to “change the world” in ways that essentially keep it the same, and “giving back” in ways that sustain an indefensible distribution of influence, resources, and tools.

...books change lives, in big ways and small, from the simple desire to spend a few quiet hours in a comfy chair, swept away by a story, to the profound realization that the reader is not alone in the world, that there is someone else like him or her, someone who has faced the same fears, the same confusions, the same grief, the same joys. Reading is a way to live more lives, to experience more worlds, to meet people we care about and want to know more about, to understand others and develop a compassion for what they confront and endure. It is a way to learn how to knit or build a house or solve an equation, a way to be moved to laughter and wonder and to learn how to live...in all our fascination with technology we've forgotten that a simple book can make a difference.

I tell my students they can procrastinate as long as they follow three rules: 1. No going onto the computer during their procrastination time. It’s just too engrossing. 2. Before procrastinating, identify the easiest homework problem. (No solving is necessary at this point.) 3. Copy the equation or equations that are needed to solve the problem onto a small piece of paper and carry the paper around until they are ready to quit procrastinating and get back to work. “I have found this approach to be helpful because it allows the problem to linger in diffuse mode—students are working on it even while they are procrastinating.” —Elizabeth Ploughman, Lecturer of Physics, Camosun College, Victoria, British Columbia

In order to solve this differential equation you look at it till a solution occurs to you.

Everyone hated Calculus. Quadratic equations, parabolas, logarithms, trigonometry - you name it. It was like floating in an endless, frictionless void traveling at x miles per hour at a descension rate of one half the speed of gravity. Solve for x.

How would I say in Japanese, ‘I solve the Dirac Equation’?” They said such-and-so. “OK. Now I want to say, ‘Would you solve the Dirac Equation?’—how do I say that?” “Well, you have to use a different word for ‘solve,’” they say. “Why?” I protested. “When I solve it, I do the same damn thing as when you solve it!

IQ is a statistical method for quantifying specific kinds of problem-solving ability, mathematically convenient but not necessarily corresponding to a real attribute of the human brain, and not necessarily representing whatever it is that we mean by ‘intelligence’.

The arts and humanities are not mere entertainment, to be turned to for relaxation after a busy day spent solving differential equations; they are our templates for living, for governing ourselves and our societies. Nor can science offer any help with the knottier problems besetting the human race. It can remedy bad smells, bad pains, and bad roads, but not bad behavior, bad government, or bad ideas.

They were very upset when I said that the thing of greatest importance to mathematics in Europe was the discovery by Tartaglia that you can solve a cubic equation-which, altho it is very little used, must have been psychologically wonderful because it showed a modern man could do something no ancient Greek could do, and therefore helped in the renaissance which was the freeing of man from the intimidation of the ancients-what they are learning in school is to be intimidated into thinking they have fallen so far below their super ancestors.

The degree of the pain will be proportional to the price you will be able to charge (more on this in the Value Equation chapter). When they hear the solution to their pain, and inversely, what their life would look like without this pain, they should be drawn to your solution. I have a saying I use to train sales teams “The pain is the pitch.” If you can articulate the pain a prospect is feeling accurately, they will almost always buy what you are offering. A prospect must have a painful problem for us to solve and charge money for our solution.

We knew it was all wrong. We knew we were diminishing ourselves in ways we couldn't even name, and we wept sometimes at memories of better days, but we no longer saw a choice. We were doing our best to survive. The equations at the roots of our problems were complex, and we were far too exhausted to solve them.

Writing is like solving a creative equation.

Other people might need to add in friends or sports or money or something else, but my equation is already solved.

Aunt Anne's lips quirked up in a smile. "Life is not a neat equation to be solved," she said. "It's messy and wild and unpredictable. That's the heartbreak of it, but that's also the glory of it.

...it's as if I have just solved Skivver's predictive equations, or even better, as if I have intuited the One Equation, seen the numbers behind the moon and the stars, behind mountains and history, art and death and yearning, as if my comprehension is large enough that it can encompass universes, from the beginning to the end of time.

So the next time you see a person with a composed face and a soft voice, remember that inside her mind she might be solving an equation, composing a sonnet, designing a hat. She might, that is, be deploying the powers of quiet.

I don't create my images as visual equations to be solved, but rather, i create them as internal landscapes that the viewer can explore. I enjoy sharing the why behind the what, of my creations... but my way, isn't the only way, to experience them. There is no correct way to interpret them. Perception is reality and yours may be different from mine and that's okay.

I remembered my father coaching me before I took my GCE exam and how he said, as I stalled in solving a long equation, 'Yes, you're getting there. Don't doubt yourself. Don't stop.' Is that why I believe now in always trying? It is, of course, too easy to draw simple causative lines. It was the wholeness of him that formed me, but it was also these incidents, slice by slice.

It's simply not the case that people use one particular lobe, or a circumscribed area of the brain, to read a novel, or write an essay, or solve an equation, or calculate the angle of a triangle. And, unfortunately, neuroscience has yet to reach the stage at which it can peer into the brain and determine capacity for solving simultaneous equations or readiness to learn calculus.

The Babylonians had achieved great competence in arithmetic, using a number system based on 60 rather than 10. They had also developed some simple techniques of algebra, such as rules (though these were not expressed in symbols) for solving various quadratic equations.

most schools also focus too much on providing students with a set of predetermined skills, such as solving differential equations, writing computer code in C++, identifying chemicals in a test tube, or conversing in Chinese. Yet since we have no idea what the world and the job market will look like in 2050, we don’t really know what particular skills people will need. We might invest a lot of effort teaching kids how to write in C++ or speak Chinese, only to discover that by 2050 AI can code software far better than humans, and a new Google Translate app will enable you to conduct a conversation in almost flawless Mandarin, Cantonese, or Hakka, even though you only know how to say “Ni hao.

We all know on some level that it is important to love ourselves. But when people say that “all you have to do is love yourself,” it’s kind of like telling a child in kindergarten that he or she has to solve a college physics equation. Like that bewildered child, we have no idea where to begin. We are standing in a place where we don’t love ourselves and haven’t for some time. We simply have no idea where to start and where to go from here.

mass times its acceleration—is a differential equation because acceleration is a second derivative with respect to time. Equations involving derivatives with respect to time and space are examples of partial differential equations and can be used to describe elasticity, heat, and sound, among other things.

At first I would be taken aback by that observation, then I would think of them seeing other drummers on television, often faking it or playing less physically demanding music, and understood why they had that impression. I guess drumming wasn't hard work for every drummer, but it certainly was for me, the way I liked to play — as hard as I could, as fast as I could, as long as I could, and as well as I could. Playing a Rush concert was the hardest job I knew, and took everything I had, mentally and physically. I once compared it to running a marathon while solving equations, and that was a good enough analogy.

Simple problems are hard to solve, Because they need common sense. Simple problems are made complex. Complex things are solved using patterns. Coefficient is introduced along with variable to create a pattern, But coefficient is a constant. To find coefficient, We again use complex patterns to make it look constant.

When Dirac was an old man, younger physicists often asked him how he felt when he discovered the [Dirac] equation. From his replies, it seems that he alternated between ecstasy and fear: although elated to have solved his problem so neatly, he worried that he would be the latest victim of the 'great tragedy of science' described in 1870 by Thomas Huxley; 'the slaying of a beautiful theory by an ugly fact'. Dirac later confessed that his dread of such an outcome was so intense that he was 'too scared' to use it to make detailed predictions of the energy levels of atomic hydrogen - a test that he knew it had to pass. He did an approximate version of the calculation and showed that there was acceptable agreement but did not go on to risk failure by subjecting his theory to a more rigorous examination.

Solve the problem; find the solution. It's a simple equation.

Life=Unconditional love If you can feel this equation. I said IF you can FEEL this equation you can solve any mystery of life and finally you will understand life is not a mystery.

If you’re having trouble with a math problem, plug the equation into WolframAlpha.com and it will solve it for you.

The most important equation to solve in life is the human equation.

Dr. Ransome marked the exercises in the algebra textbook and gave him two strips of rice-paper bandage on which to solve the simultaneous equations. As he stood up, Dr. Ransome removed the three tomatoes from Jim's pocket. He laid them on the table by the wax tray. 'Did they come from the hospital garden?' 'Yes.' Jim gazed back frankly at Dr. Ransome. Recently he had begun to see him with a more adult eye. The long years of imprisonment, the constant disputes with the Japanese had made this young physician seem middle-aged. Dr. Ransome was often unsure of himself, as he was of Jim's theft. 'I have to give Basie something whenever I see him.' 'I know. It's a good thing that you're friends with Basie. He's a survivor, though survivors can be dangerous. Wars exist for people like Basie.' Dr. Ransome placed the tomatoes in Jim's hand. 'I want you to eat them, Jim. I'll get you something for Basie.

The combination of Bayes and Markov Chain Monte Carlo has been called "arguably the most powerful mechanism ever created for processing data and knowledge." Almost instantaneously MCMC and Gibbs sampling changed statisticians' entire method of attacking problems. In the words of Thomas Kuhn, it was a paradigm shift. MCMC solved real problems, used computer algorithms instead of theorems, and led statisticians and scientists into a worked where "exact" meant "simulated" and repetitive computer operations replaced mathematical equations. It was a quantum leap in statistics.

So the next time you see a person with a composed face and a soft voice, remember that inside her mind she might be solving an equation, composing a sonnet, designing a hat. She might, that is, be deploying the powers of quiet. We know from myths and fairy tales that there are many different kind of powers in this world. One child is given a light saber, another a wizard's education.

Even today, I am in total awe of the following wondrous chain of ideas and interconnections. Guided throughout by principles of symmetry, Einstein first showed that acceleration and gravity are really two sides of the same coin. He then expanded the concept to demonstrate that gravity merely reflects the geometry of spacetime. The instruments he used to develop the theory were Riemann's non-Euclidean geometries-precisely the same geometries used by Felix Klein to show that geometry is in fact a manifestation of group theory (because every geometry is defined by its symmetries-the objects it leaves unchanged). Isn't this amazing?

We’ve now established three things. First, we don’t need willpower when we don’t desire to do something, and it isn’t a thing some of us have in excess and some of us don’t have at all. It’s a cognitive function, like deciding what to eat or solving a math equation or remembering your dad’s birthday. Willpower is also a limited resource; we have more of it at the beginning of the day and lose it throughout the day as we use it to write emails or not eat cookies. When you automate some decisions or processes (through forming habits), you free up more brain power. Second, for us to make and change a habit, we need a cue, a routine, and a reward, and enough repetition must occur for the process to move from something we have to think about consciously (“I need to brush my teeth,” “I don’t want to drink wine”) to something we do naturally, automatically. Third, throughout the day, we must manage our energy so that we don’t blow out and end up in the place of no return—a hyperaroused state where the only thing that can bring us down is a glass (or a bottle) of wine. Maybe

The ”Dean of science fiction writers” Robert A. Heinlein once said: “A human being should be able to change a diaper, plan an invasion, butcher a hog, conn a ship, design a building, write a sonnet, balance accounts, build a wall, set a bone, comfort the dying, take orders, give orders, cooperate, act alone, solve equations, analyse a new problem, pitch manure, program a computer, cook a tasty meal, fight efficiently, die gallantly. Specialisation is for insects.

All right,” Malcolm said. “Let’s go back to the beginning.” He paused, staring at the ceiling. “Physics has had great success at describing certain kinds of behavior: planets in orbit, spacecraft going to the moon, pendulums and springs and rolling balls, that sort of thing. The regular movement of objects. These are described by what are called linear equations, and mathematicians can solve those equations easily. We’ve been doing it for hundreds of years.” “Okay,” Gennaro said. “But there is another kind of behavior, which physics handles badly. For example, anything to do with turbulence. Water coming out of a spout. Air moving over an airplane wing. Weather. Blood flowing through the heart. Turbulent events are described by nonlinear equations. They’re hard to solve—in fact, they’re usually impossible to solve. So physics has never understood this whole class of events. Until about ten years ago. The new theory that describes them is called chaos theory.

She had always consciously or unconsciously formed fear into a simple equation: fear = unknown. And to solve the equation, one simply reduced the problem to simple algebraic terms, thus: unknown = creaky board (or whatever), creaky board = nothing to be afraid of. In the modern world all terrors could be gutted by simple use of the transitive axiom of equality. Some fears were justified, of course (you don’t drive when you’re too plowed to see, don’t extend the hand of friendship to snarling dogs, don’t go parking with boys you don’t know – how did the old joke go? Screw or walk?), but until now she had not believed that some fears were larger than comprehension, apocalyptic and nearly paralyzing. This equation was insoluble. The act of moving forward at all became heroism.

One of the ideas of this book is to give the reader a possibility to develop problem-solving skills using both systems, to solve various nonlinear PDEs in both systems. To achieve equal results in both systems, it is not sufficient simply “to translate” one code to another code. There are numerous examples, where there exists some predefined function in one system and does not exist in another. Therefore, to get equal results in both systems, it is necessary to define new functions knowing the method or algorithm of calculation.

Through the works of Weinberg, Glashow, and Salam on the electroweak theory and the elegant framework developed by the physicists David Gross, David Politzer, and Frank Wilczek for quantum chromodynamics, the characteristic group of the standard model has been identified with a product of three Lie groups denoted by U(1), SU(2), and SU(3). In some sense, therefore, the road toward the ultimate unification of the forces of nature has to go through the discovery of the most suitable Lie group that contains the product U(1) X SU(2) x SU(3).

When {Born and Heisenberg and the Göttingen theoretical physicists} first discovered matrix mechanics they were having, of course, the same kind of trouble that everybody else had in trying to solve problems and to manipulate and to really do things with matrices. So they had gone to Hilbert for help and Hilbert said the only time he had ever had anything to do with matrices was when they came up as a sort of by-product of the eigenvalues of the boundary-value problem of a differential equation. So if you look for the differential equation which has these matrices you can probably do more with that. They had thought it was a goofy idea and that Hilbert didn't know what he was talking about. So he was having a lot of fun pointing out to them that they could have discovered Schrödinger’s wave mechanics six month earlier if they had paid a little more attention to him.

How can one tell if a being has free will? If one encounters an alien, how can one tell if it is just a robot or it has a mind of its own? The behavior of a robot would be completely determined, unlike that of a being with free will. Thus one could in principle detect a robot as a being whose actions can be predicted. As we said in Chapter 2, this may be impossibly difficult if the being is large and complex. We cannot even solve exactly the equations for three or more particles interacting with each other. Since an alien the size of a human would contain about a thousand trillion trillion particles even if the alien were a robot, it would be impossible to solve the equations and predict what it would do. We would therefore have to say that any complex being has free will—not as a fundamental feature, but as an effective theory, an admission of our inability to do the calculations that would enable us to predict its actions.

I’ll be honest with you. The variables that construct my existence are confusing. Like handwritten math equations jammed together on a sloppy page of homework. They don’t make any sense. One math problem leads to another, and then another and so it goes. One day you realize that your life is one whole page of problems and nothing ever gets solved. One ongoing equation with no equal sign at the end. But it occurred to me, beneath the canopy of a starlight heaven, that I’d been looking at my life all wrong. It wasn’t a math equation. Things weren’t supposed to add up. There was no solution. In fact, there was no problem. Life’s variables and numbers and pages of chicken scratch weren’t mathematical marks. They were art. A drawing. An abstract painting. It was meant to be beautiful, not sensical. And embedded within the mess of it all were miracles. Small ones. I’d never paid attention to them because I was too busy, but it didn’t make them less real.

Enjoy the power and beauty of your youth; oh never mind; you will not understand the power and beauty of your youth until they have faded. But trust me, in 20 years you’ll look back at photos of yourself and recall in a way you can’t grasp now how much possibility lay before you and how fabulous you really looked. You’re not as fat as you imagine. Don’t worry about the future; or worry, but know that worrying is as effective as trying to solve an algebra equation by chewing bubblegum. The real troubles in your life are apt to be things that never crossed your worried mind; the kind that blindside you at 4pm on some idle Tuesday. Do one thing everyday that scares you. Sing. Don’t be reckless with other people’s hearts, don’t put up with people who are reckless with yours. Floss. Don’t waste your time on jealousy; sometimes you’re ahead, sometimes you’re behind, the race is long, and in the end, it’s only with yourself. Remember the compliments you receive, forget the insults; if you succeed in doing this, and tell me how. Keep your old love letters; throw away your old bank statements. Stretch. Don’t feel guilty if you don’t know what you want to do with your life.

Lao-tzu advised, “As soon as you have a thought, laugh at it,” because reality is not what we think. We perceive the world through a window colored by beliefs, interpretations, and associations. We see things not as they are but as we are. The same brain that enables us to contemplate philosophy, solve math equations, and create poetry also generates a stream of static known as discursive thoughts, which seem to arise at random, bubbling up into our awareness. Such mental noise is a natural phenomenon, no more of a problem than the dreams that appear in the sleep state. Therefore, our schooling aims not to struggle with random thoughts but to transcend them in the present moment, where no thoughts exist, only awareness. Our mind’s liberation awaits not in some imagined future but here and now.

Forget it, we can do it another time.” I turn around to go back into my parents’ room, but Mom catches my hand. She knows I may never feel ready to do this, that I may keep finding excuses to push this off until long after my dad is gone, and then maybe I’ll go to his grave and come out. But the time has to be now so I can feel as comfortable in my home as I am chilling with Collin. “Mark,” Mom says again. His eyes are still on the TV. I take a deep breath. “Dad, I hope you’re cool with this, but I sort of, kind of am dating someone and . . .” I can already see him getting confused, like I’m challenging him to solve an algebraic equation with no pen, paper, or calculator. “And that someone is my friend Collin.” Only then does Dad turn toward us. His face immediately goes from confused to furious. You would think the Yankees not only lost the game but also decided to give up and retire the team forever. He points his cigarette at Mom. “This is all your doing. You have to be the one to tell him he’s wrong.” He’s talking about me like I’m not even in the room. “Mark, we always said we would love our kids no matter what, and—” “Empty fucking promise, Elsie. Make him cut it out or get him out of here.” “If there’s something about homosexuality you don’t understand, you can talk to your son about it in a kind way,” Mom says, maintaining a steady tone that’s both fearless for me and respectful toward Dad. We all know what he’s capable of. “If you want to ignore it or need time, we can give that to you, but Aaron isn’t going anywhere.” Dad places his cigarette in the ashtray and then kicks over the hamper he was resting his feet on. We back up. I don’t often wish this, but I really, really wish Eric were here right now in case this gets as ugly as I think it might. He points his finger at me. “I’ll fucking throw him out myself.

Film and TV V.I.P, seeker of the peace, part time chandelier cleaner, a legend in his own time, oppressor of champions, soldier of fortune, world traveller, bonvivant, all round good guy, international lover, casual hero, philosopher, wars fought, bears wrestled, equations solved, virgins enlightened, revolutions quelled, tigers castrated, orgies organised, bars quaffed dry, governments run, test rockets flown, life president of the Liquidarian Society of Great Britain and Ireland.

We have already seen that gauge symmetry that characterizes the electroweak force-the freedom to interchange electrons and neturinos-dictates the existence of the messenger electroweak fields (photon, W, and Z). Similarly, the gauge color symmetry requires the presence of eight gluon fields. The gluons are the messengers of the strong force that binds quarks together to form composite particles such as the proton. Incidentally, the color "charges" of the three quarks that make up a proton or a neutron are all different (red, blue, green), and they add up to give zero color charge or "white" (equivalent to being electrically neutral in electromagnetism). Since color symmetry is at the base of the gluon-mediated force between quarks, the theory of these forces has become known as quantum chromodynamics. The marriage of the electroweak theory (which describes the electromagnetic and weak forces) with quantum chromodynamics (which describes the strong force) produced the standard model-the basic theory of elementary particles and the physical laws that govern them.

In a nation still stuck in an old Jim Crow mind-set - which equates racism with white bigotry and views racial diversity as proof the problem has been solved- a racially diverse police department invites questions like: "How can you say the Oakland Police Department's drug raids are racist? There's a black police chief, and most of the officers involved in the drug raids are black." If the caste dimensions of mass incarceration were better understood and the limitations of cosmetic diversity were better appreciated, the existence of black police chiefs and black police officers would be no more encouraging today than the presence of black slave drivers and black plantation owners hundreds of years ago. When meaningful change fails to materialize following the achievement of superficial diversity, those who remain locked out can become extremely discouraged and demoralized, resulting in cynicism and resignation. Perhaps more concerning, though, is the fact that inclusion of people of color in power structures, particularly at the top, can paralyze reform efforts.

August 29th WANT NOTHING = HAVE EVERYTHING “No person has the power to have everything they want, but it is in their power not to want what they don’t have, and to cheerfully put to good use what they do have.” —SENECA, MORAL LETTERS, 123.3 Is there a person so rich that there is literally nothing they can’t afford? Surely there isn’t. Even the richest people regularly fail in their attempts to buy elections, to purchase respect, class, love, and any number of other things that are not for sale. If obscene wealth will never get you everything you want, is that the end of it? Or is there another way to solve for that equation? To the Stoics, there is: by changing what it is that you want. By changing how you think, you’ll manage to get it. John D. Rockefeller, who was as rich as they come, believed that “a man’s wealth must be determined by the relation of his desires and expenditures to his income. If he feels rich on $10 and has everything he desires, he really is rich.” Today, you could try to increase your wealth, or you could take a shortcut and just want less.

Feynman said, “If, in some cataclysm, all of scientific knowledge were to be destroyed, and only one sentence passed on to the next generations of creatures, what statement would contain the most information in the fewest words? In that one sentence, you will see, there is an enormous amount of information about the world, if just a little imagination and thinking are applied” Our sentence would be: “The Monadology asserts that the fundamental units of existence are INFINITE, dimensionless, living, thinking points – monads, ZEROS, souls – each of which has INFINITE energy content, all controlled by a single equation – Euler’s Formula – and the collective energy of this universe of mathematical points creates a physical universe of which every objective value is ZERO, but, through a self-solving, self-optimizing, dialectical, evolving process, the universe generates a final, subjective value of INFINITY – divinity, perfection, the ABSOLUTE.” For ours is the religion of zero and infinity, the two numbers that define the soul and the whole of existence. As above, so below.

Surprisingly, palindromes appear not just in witty word games but also in the structure of the male-defining Y chromosome. The Y's full genome sequencing was completed only in 2003. This was the crowning achievement of a heroic effort, and it revealed that the powers of preservation of this sex chromosome have been grossly underestimated. Other human chromosome pairs fight damaging mutations by swapping genes. Because the Y lacks a partner, genome biologists had previously estimated that its cargo was about to dwindle away in perhaps as little as five million years. To their amazement, however, the researchers on the sequencing team discovered that the chromosome fights withering with palindromes. About six million of its fifty million DNA letters form palindromic sequences-sequences that read the same forward and backward on the two strands of the double helix. These copies not only provide backups in case of bad mutations, but also allow the chromosome, to some extent, to have sex with itself-arms can swap position and genes are shuffled. As team leader David Page of MIT has put it, "The Y chromosome is a hall of mirrors.

We have written the equations of water flow. From experiment, we find a set of concepts and approximations to use to discuss the solution--vortex streets, turbulent wakes, boundary layers. When we have similar equations in a less familiar situation, and one for which we cannot yet experiment, we try to solve the equations in a primitive, halting, and confused way to try to determine what new qualitatitive features may come out, or what new qualitative forms are a consequence of the equations. Our equations for the sun, for example, as a ball of hydrogen gas, describe a sun without sunspots, without the rice-grain structure of the surface, without prominences, without coronas. Yet, all of these are really in the equations; we just haven't found the way to get them out. ...The test of science is its ability to predict. Had you never visited the earth, could you predict the thunderstorms, the volcanoes, the ocean waves, the auroras, and the colourful sunset? A salutary lesson it will be when we learn of all that goes on on each of those dead planets--those eight or ten balls, each agglomerated from the same dust clouds and each obeying exactly the same laws of physics. The next great era of awakening of human intellect may well produce a method of understanding the qualitative content of equations. Today we cannot. Today we cannot see that the water flow equations contain such things as the barber pole structure of turbulence that one sees between rotating cylinders. Today we cannot see whether Schrodinger's equation contains frogs, musical composers, or morality--or whether it does not. We cannot say whether something beyond it like God is needed, or not. And so we can all hold strong opinions either way.

I love you. As the same value, as the same expression, with the same pride and the same meaning as I love my work, my mills, my Metal, my hours at a desk, at a furnace, in a laboratory, in an ore mine, as I love my ability to work, as I love the act of sight and knowledge, as I love the action of my mind when it solves a chemical equation or grasps a sunrise, as I love the things I’ve made and the things I’ve felt, as my product, as my choice, as a shape of my world, as my best mirror, as the wife I’ve never had, as that which makes all the rest of it possible: as my power to live.

In Oppenheimer's view, it would be a waste of his precious time, or of mine, to concern ourselves with the details of particular solutions. This was how the philosophy of reductionism led Oppenheimer and Einstein astray. Since the only purpose of physics was to reduce the world of physical phenomena to a finite set of fundamental equations, the study of particular solutions such as black holes was an undesirable distraction from the general goal. Like Hilbert, they were not content to solve particular problems one at a time. They were entranced by the dream of solving all the basic problems at once. And as a result, they failed in their later years to solve any problems at all.

if consumer demand should increase for the goods or services of any private business, the private firm is delighted; it woos and welcomes the new business and expands its operations eagerly to fill the new orders. Government, in contrast, generally meets this situation by sourly urging or even ordering consumers to “buy” less, and allows shortages to develop, along with deterioration in the quality of its service. Thus, the increased consumer use of government streets in the cities is met by aggravated traffic congestion and by continuing denunciations and threats against people who drive their own cars. The New York City administration, for example, is continually threatening to outlaw the use of private cars in Manhattan, where congestion has been most troublesome. It is only government, of course, that would ever think of bludgeoning consumers in this way; it is only government that has the audacity to “solve” traffic congestion by forcing private cars (or trucks or taxis or whatever) off the road. According to this principle, of course, the “ideal” solution to traffic congestion is simply to outlaw all vehicles! But this sort of attitude toward the consumer is not confined to traffic on the streets. New York City, for example, has suffered periodically from a water “shortage.” Here is a situation where, for many years, the city government has had a compulsory monopoly of the supply of water to its citizens. Failing to supply enough water, and failing to price that water in such a way as to clear the market, to equate supply and demand (which private enterprise does automatically), New York’s response to water shortages has always been to blame not itself, but the consumer, whose sin has been to use “too much” water. The city administration could only react by outlawing the sprinkling of lawns, restricting use of water, and demanding that people drink less water. In this way, government transfers its own failings to the scapegoat user, who is threatened and bludgeoned instead of being served well and efficiently. There has been similar response by government to the ever-accelerating crime problem in New York City. Instead of providing efficient police protection, the city’s reaction has been to force the innocent citizen to stay out of crime-prone areas. Thus, after Central Park in Manhattan became a notorious center for muggings and other crime in the night hours, New York City’s “solution” to the problem was to impose a curfew, banning use of the park in those hours. In short, if an innocent citizen wants to stay in Central Park at night, it is he who is arrested for disobeying the curfew; it is, of course, easier to arrest him than to rid the park of crime. In short, while the long-held motto of private enterprise is that “the customer is always right,” the implicit maxim of government operation is that the customer is always to be blamed.

But you don’t really think wearing a low-cut top to the boys’ party will solve all your problems, do you?” she asked. “Of course not. I think wearing a low-cut top to the boys’ part will show Sean I’m ready for him.” “Lori, no girl is ever ready for a boy like Sean. How were finals?” Clearly she wanted to change the subject to impress upon me that boys were not all there was to a teenage girl’s life. As if. “Finals?” I asked. “Yes, finals. To graduate from the tenth grade? You took them yesterday.” Wow, it was hard to believe I’d played hopscotch with the quadratic equation only twenty-seven hours ago. Thinking back, it seemed like I’d sleepwalked through the past nine months of school, compared with everything that had happened today. Time flew when you were having Sean.

As a civilization progresses, it goes through wars, pandemics, catastrophes. those that survive grow more astute, more perceptive, more advanced. Diseases are conquered, infirmity eliminated. Life spans increase. Suffering becomes largely a memory. "Meanwhile, their explorers and historians find evidence of past cultures, and cultures before that. At first it is exciting. But all they keep finding are ruins. And slowly, either through science or history, every advanced civilizations becomes aware of a disturbing possibility -- that their futures may end in ruin too. "The civilization then rushes to probe other stars, even other galaxies; it increases its research, attempting to manipulate space, time, in the hope that somewhere, someone might have found an escape, a loophole. "But eventually, the find, and solve, the mathematical equation that explains the entire universe." "I think our scientists are working on something like that too," Shizuka said. Lan shook her head. "They'll need to find the Grand Unified Theory a few more times before they can even begin to understand what 'everything' is -- sorry, I didn't mean to offend your civilization." Shizuka shrugged. "No offense taken." "Still, should your civilization survive, it will eventually find the same equation. And that will be your death sentence. For in that equation, there will be no forever, no eternity. Nothing. "And this collapse, and all its attendant despair, is the Endplague." Shizuka was puzzled. Space aliens, she could understand. Purple skin? Cute. Two elbows? Weird, but fine. Galactic warfare? Frankly, expected. Being a refugee? Of course. But how could the mere concept of mortality be enough to topple advanced civilizations? People live, people die, and so what?

It is the best of times in physics. Physicists are on the verge of obtaining the long-sought theory of everything. In a few elegant equations, perhaps concise enough to be emblazoned on a T-shirt, this theory will reveal how the universe began and how it will end. The key insight is that the smallest constituents of the world are not particles, as had been supposed since ancient times, but “strings”—tiny strands of energy. By vibrating in different ways, these strings produce the essential phenomena of nature, the way violin strings produce musical notes. String theory isn’t just powerful; it’s also mathematically beautiful. All that remains to be done is to write down the actual equations. This is taking a little longer than expected. But, with almost the entire theoretical-physics community working on the problem—presided over by a sage in Princeton, New Jersey—the millennia-old dream of a final theory is sure to be realized before long. It is the worst of times in physics. For more than a generation, physicists have been chasing a will-o’-the-wisp called string theory. The beginning of this chase marked the end of what had been three-quarters of a century of progress. Dozens of string-theory conferences have been held, hundreds of new Ph.D.’s have been minted, and thousands of papers have been written. Yet, for all this activity, not a single new testable prediction has been made; not a single theoretical puzzle has been solved. In fact, there is no theory so far—just a set of hunches and calculations suggesting that a theory might exist. And, even if it does, this theory will come in such a bewildering number of versions that it will be of no practical use: a theory of nothing. Yet the physics establishment promotes string theory with irrational fervor, ruthlessly weeding dissenting physicists from the profession. Meanwhile, physics is stuck in a paradigm doomed to barrenness.

The biggest stumbling block that has traditionally plagued all the unification endeavors has been the simple fact that on the face of it, general relativity and quantum mechanics really appear to be incomprehensible. Recall that the key concept of quantum theory is the uncertainty principle. When you try to probe positions with an ever-increasing magnification power, the momenta (or speeds) start oscillating violently. Below a certain minuscule length known as the Planck length, the entire tenet of a smooth spacetime is lost. This length (equal to 0.000...4 of an inch, where the 4 is at the thirty-fourth decimal place) determines the scale at which gravity has to be treated quantum mechanically. For smaller scales, space turns into an ever-fluctuating "quantum foam." But the very basic premise of general relativity has been the existence of a gently curved spacetime. In other words, the central ideas of general relativity and quantum mechanics clash irreconcilably when it comes to extremely small scales.

Leaning back in the couch, she let her mind relax. Think, Heather. Think. She visualized a grid containing the origin of a coordinate system. A perpendicular set of lines labeled “x axis” and “y axis” appeared to float before her. She drew a single point located right three ticks and up four ticks from the origin on the grid, then followed up with another point, connecting the two with a line. It was there, floating perfectly in the air before her. Right, she thought. She added another dimension to the grid to form a cube, and into this cube she drew spheres, ellipsoids, cubes, and pyramids. It was easy. The equations came faster and faster, as if she had fumbled around and found a switch in the dark. A part of her mind turned on, big time. Adding a fourth dimension was easy. She took her three-dimensional grid cube, shrank it to the size of a pinhead, then formed a line of these cubes. Five dimensions formed from a plane of the 3D grid cubes. Six: a cube made of cubes. Seven dimensions: a line made of the new cube of cubes. On and on the mental sequence spun from her mind. Easy. Oh so easy. She no longer had to think about the equations that represented the shapes. Merely visualizing the shape brought the corresponding equations to her mind. She didn’t have to solve them; she just knew them. It was beautiful beyond her wildest imaginings.

The properties that define a group are: 1. Closure. The offspring of any two members combined by the operation must itself be a member. In the group of integers, the sum of any two integers is also an integer (e.g., 3 + 5 = 8). 2. Associativity. The operation must be associative-when combining (by the operation) three ordered members, you may combine any two of them first, and the result is the same, unaffected by the way they are bracketed. Addition, for instance, is associative: (5 + 7) + 13 = 25 and 5 + (7 + 13) = 25, where the parentheses, the "punctuation marks" of mathematics, indicate which pair you add first. 3. Identity element. The group has to contain an identity element such that when combined with any member, it leaves the member unchanged. In the group of integers, the identity element is the number zero. For example, 0 + 3 = 3 + 0 = 3. 4. Inverse. For every member in the group there must exist an inverse. When a member is combined with its inverse, it gives the identity element. For the integers, the inverse of any number is the number of the same absolute value, but with the opposite sign: e.g., the inverse of 4 is -4 and the inverse of -4 is 4; 4 + (-4) = 0 and (-4) + 4 = 0. The fact that this simple definition can lead to a theory that embraces and unifies all the symmetries of our world continues to amaze even mathematicians.

The main ones are the symbolists, connectionists, evolutionaries, Bayesians, and analogizers. Each tribe has a set of core beliefs, and a particular problem that it cares most about. It has found a solution to that problem, based on ideas from its allied fields of science, and it has a master algorithm that embodies it. For symbolists, all intelligence can be reduced to manipulating symbols, in the same way that a mathematician solves equations by replacing expressions by other expressions. Symbolists understand that you can’t learn from scratch: you need some initial knowledge to go with the data. They’ve figured out how to incorporate preexisting knowledge into learning, and how to combine different pieces of knowledge on the fly in order to solve new problems. Their master algorithm is inverse deduction, which figures out what knowledge is missing in order to make a deduction go through, and then makes it as general as possible. For connectionists, learning is what the brain does, and so what we need to do is reverse engineer it. The brain learns by adjusting the strengths of connections between neurons, and the crucial problem is figuring out which connections are to blame for which errors and changing them accordingly. The connectionists’ master algorithm is backpropagation, which compares a system’s output with the desired one and then successively changes the connections in layer after layer of neurons so as to bring the output closer to what it should be. Evolutionaries believe that the mother of all learning is natural selection. If it made us, it can make anything, and all we need to do is simulate it on the computer. The key problem that evolutionaries solve is learning structure: not just adjusting parameters, like backpropagation does, but creating the brain that those adjustments can then fine-tune. The evolutionaries’ master algorithm is genetic programming, which mates and evolves computer programs in the same way that nature mates and evolves organisms. Bayesians are concerned above all with uncertainty. All learned knowledge is uncertain, and learning itself is a form of uncertain inference. The problem then becomes how to deal with noisy, incomplete, and even contradictory information without falling apart. The solution is probabilistic inference, and the master algorithm is Bayes’ theorem and its derivates. Bayes’ theorem tells us how to incorporate new evidence into our beliefs, and probabilistic inference algorithms do that as efficiently as possible. For analogizers, the key to learning is recognizing similarities between situations and thereby inferring other similarities. If two patients have similar symptoms, perhaps they have the same disease. The key problem is judging how similar two things are. The analogizers’ master algorithm is the support vector machine, which figures out which experiences to remember and how to combine them to make new predictions.

We also find *physics*, in the widest sense of the word, concerned with the explanation of phenomena in the world; but it lies already in the nature of the explanations themselves that they cannot be sufficient. *Physics* is unable to stand on its own feet, but needs a *metaphysics* on which to support itself, whatever fine airs it may assume towards the latter. For it explains phenomena by something still more unknown than are they, namely by laws of nature resting on forces of nature, one of which is also the vital force. Certainly the whole present condition of all things in the world or in nature must necessarily be capable of explanation from purely physical causes. But such an explanation―supposing one actually succeeded so far as to be able to give it―must always just as necessarily be burdened with two essential imperfections (as it were with two sore points, or like Achilles with the vulnerable heel, or the devil with the cloven foot). On account of these imperfections, everything so explained would still really remain unexplained. The first imperfection is that the *beginning* of the chain of causes and effects that explains everything, in other words, of the connected and continuous changes, can positively *never* be reached, but, just like the limits of the world in space and time, recedes incessantly and *in infinitum*. The second imperfection is that all the efficient causes from which everything is explained always rest on something wholly inexplicable, that is, on the original *qualities* of things and the *natural forces* that make their appearance in them. By virtue of such forces they produce a definite effect, e.g., weight, hardness, impact, elasticity, heat, electricity, chemical forces, and so on, and such forces remain in every given explanation like an unknown quantity, not to be eliminated at all, in an otherwise perfectly solved algebraical equation. Accordingly there is not a fragment of clay, however little its value, that is not entirely composed of inexplicable qualities. Therefore these two inevitable defects in every purely physical, i.e., causal, explanation indicate that such an explanation can be only *relatively* true, and that its whole method and nature cannot be the only, the ultimate and hence sufficient one, in other words, cannot be the method that will ever be able to lead to the satisfactory solution of the difficult riddles of things, and to the true understanding of the world and of existence; but that the *physical* explanation, in general and as such, still requires one that is *metaphysical*, which would furnish the key to all its assumptions, but for that very reason would have to follow quite a different path. The first step to this is that we should bring to distinct consciousness and firmly retain the distinction between the two, that is, the difference between *physics* and *metaphysics*. In general this difference rests on the Kantian distinction between *phenomenon* and *thing-in-itself*. Just because Kant declared the thing-in-itself to be absolutely unknowable, there was, according to him, no *metaphysics* at all, but merely immanent knowledge, in other words mere *physics*, which can always speak only of phenomena, and together with this a critique of reason which aspires to metaphysics." ―from_The World as Will and Representation_. Translated from the German by E. F. J. Payne. In Two Volumes, Volume II, pp. 172-173