Reasoning Math Quotes

The best way to be appreciative for your life is to live it; don't die for any other reason but love. Dreams are what guide us, art is what defines us, math is makes it all possible, and love is what lights our way.

Math can explain the reason there's one out of four chance that I'd have blue eyes. But it doesn't explain why me.

There are other reasons we use math in physics. Besides keeping us honest, math is also the most economical and unambiguous terminology that we know of. Language is malleable; it depends on context and interpretation. But math doesn’t care about culture or history. If a thousand people read a book, they read a thousand different books. But if a thousand people read an equation, they read the same equation.

Befuddlement is a healthy part of the learning process. When students approach a problem and don’t know how to do it, they’ll often decide they’re no good at the subject. Brighter students, in particular, can have difficulty in this way—their breezing through high school leaves them no reason to think that being confused is normal and necessary. But the learning process is all about working your way out of confusion. Articulating your question is 80 percent of the battle. By the time you’ve figured out what’s confusing, you’re likely to have answered the question yourself!” —Kenneth R. Leopold, Distinguished Teaching Professor, Department of Chemistry, University of Minnesota

We both had done the math. Kelly added it all up and... knew she had to let me go. I added it up, and knew that I had... lost her. 'cos I was never gonna get off that island. I was gonna die there, totally alone. I was gonna get sick, or get injured or something. The only choice I had, the only thing I could control was when, and how, and where it was going to happen. So... I made a rope and I went up to the summit, to hang myself. I had to test it, you know? Of course. You know me. And the weight of the log, snapped the limb of the tree, so I-I - , I couldn't even kill myself the way I wanted to. I had power over *nothing*. And that's when this feeling came over me like a warm blanket. I knew, somehow, that I had to stay alive. Somehow. I had to keep breathing. Even though there was no reason to hope. And all my logic said that I would never see this place again. So that's what I did. I stayed alive. I kept breathing. And one day my logic was proven all wrong because the tide came in, and gave me a sail. And now, here I am. I'm back. In Memphis, talking to you. I have ice in my glass... And I've lost her all over again. I'm so sad that I don't have Kelly. But I'm so grateful that she was with me on that island. And I know what I have to do now. I gotta keep breathing. Because tomorrow the sun will rise. Who knows what the tide could bring?

Sophie Germain proved to the world that even a woman can accomplish something in the most rigorous and abstract of sciences and for that reason would well have deserved an honorary degree.

The best way to be appreciative for your life is to live it; don’t die for any other reason but love. Dreams are what guide us, art is what defines us, math is what makes it all possible, and love is what lights our way.” ~ Mike Norton

The primary math of the real world is one and one equals two. The layman (as, often, do I) swings that every day. He goes to the job, does his work, pays his bills and comes home. One plus one equals two. It keeps the world spinning. But artists, musicians, con men, poets, mystics and such are paid to turn that math on its head, to rub two sticks together and bring forth fire. Everybody performs this alchemy somewhere in their life, but it’s hard to hold on to and easy to forget. People don’t come to rock shows to learn something. They come to be reminded of something they already know and feel deep down in their gut. That's when the world is at its best, when we are at our best, when life feels fullest, one and one equals three. It’s the essential equation of love, art, rock ’n’ roll and rock ’n’ roll bands. It’s the reason the universe will never be fully comprehensible, love will continue to be ecstatic, confounding, and true rock ’n’ roll will never die.

Remember your math: an anecdote is not a trend. Remember your history: the fact that something is bad today doesn't mean it was better in the past. Remember your philosophy: one cannot reason that there's no such thing as reason, or that something is true or good because God said it is. And remember your psychology: much of what we know isn't so, especially when our comrades know it too. Keep some perspective. Not every problem is a Crisis, Plague, Epidemic, or Existential Threat, and not every change is the End of This, the Death of That, or the Dawn of a Post-Something Era. Don't confuse pessimism with profundity: problems are inevitable, but problems are solvable, and diagnosing every setback as a symptom of a sick society is a cheap grab for gravitas. Finally, drop the Nietzsche. His ideas may seem edgy, authentic, baad,while humanism seems sappy, unhip, uncool But what's so funny about peace, love, and understanding?

...but numbers didn't lie. That was the reason I loved math. It was the only pure form of honesty left in this world.

Some mathematics problems look simple, and you try them for a year or so, and then you try them for a hundred years, and it turns out that they're extremely hard to solve. There's no reason why these problems shouldn't be easy, and yet they turn out to be extremely intricate. [Fermat's] Last Theorem is the most beautiful example of this.

Language as putative science. - The significance of language for the evolution of culture lies in this, that mankind set up in language a separate world beside the other world, a place it took to be so firmly set that, standing upon it, it could lift the rest of the world off its hinges and make itself master of it. To the extent that man has for long ages believed in the concepts and names of things as in aeternae veritates he has appropriated to himself that pride by which he raised himself above the animal: he really thought that in language he possessed knowledge of the world. The sculptor of language was not so modest as to believe that he was only giving things designations, he conceived rather that with words he was expressing supreame knowledge of things; language is, in fact, the first stage of occupation with science. Here, too, it is the belief that the truth has been found out of which the mightiest sources of energy have flowed. A great deal later - only now - it dawns on men that in their belief in language they have propagated a tremendous error. Happily, it is too late for the evolution of reason, which depends on this belief, to be put back. - Logic too depends on presuppositions with which nothing in the real world corresponds, for example on the presupposition that there are identical things, that the same thing is identical at different points of time: but this science came into existence through the opposite belief (that such conditions do obtain in the real world). It is the same with mathematics, which would certainly not have come into existence if one had known from the beginning that there was in nature no exactly straight line, no real circle, no absolute magnitude.

So how does one go about proving something like this? It's not like being a lawyer, where the goal is to persuade other people; nor is it like a scientist testing a theory. This is a unique art form within the world of rational science. We are trying to craft a "poem of reason" that explains fully and clearly and satisfies the pickiest demands of logic, while at the same time giving us goosebumps.

The probability of an event is the reason we have to believe that it has taken place, or that it will take place. The measure of the probability of an event is the ratio of the number of cases favourable to that event, to the total number of cases favourable or contrary, and all equally possible.

As for methods I have sought to give them all the rigour that one requires in geometry, so as never to have recourse to the reasons drawn from the generality of algebra.

If other people thought art was important, then it would be required to graduate. But no, I don’t have to take art. I do have to take math, which is just a waste of time because the numbers get all switched up in my brain, plus, calculators exist for a reason. I do have to take history, which is basically memorizing tariff acts till your brain bleeds. I do have to take four years of gym class with a bunch of jerks who punch me if they don’t like what I say. But art? Optional. Even though art and music and literature and all that are what make us human. Algebra doesn’t make us human. Games don’t make us human.

We think there's a reason for everything, as if life was supposed to make sense. It's not exactly math. People aren't numbers. Everybody knows life doesn't make any sense at all, so we just better deal with the whole mess. Have a beer. Have a cup of coffee. Have a piece of cake. Go out to a movie. Enjoy the Popcorn.

Many parents have asked me: What is the point of my child explaining their work if they can get the answer right? My answer is always the same: Explaining your work is what, in mathematics, we call reasoning, and reasoning is central to the discipline of mathematics.

Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality. Though different traditions may emphasize different aspects, it is only the interplay of these antithetic forces and the struggle for their synthesis that constitute the life, usefulness, and supreme value of mathematical science.

Why do any of us do what we don't want to do?" I don't respond, unsure what answer he's looking for. He smiles, but it's sad. "Because we're afraid of what will happen if we don't." I always considered fear to be a motivator or a reason not to do something, but I never considered it a reason to continue an ongoing behavior. This opens a vault full or questions about my own life. I've always assumed I'm afraid to engage in activities because I'm afraid of what might happen. But maybe I'm looking at it all wrong. Maybe I should be asking myself if I'm really afraid of leaving what makes me comfortable.

The primary math of the real world is one and one equals two. The layman (as, often, do I) swings that every day. He goes to the job, does his work, pays his bills and comes home. One plus one equals two. It keeps the world spinning. But artists, musicians, con men, poets, mystics and such are paid to turn that math on its head, to rub two sticks together and bring forth fire. Everybody performs this alchemy somewhere in their life, but it’s hard to hold on to and easy to forget. People don’t come to rock shows to learn something. They come to be reminded of something they already know and feel deep down in their gut. That when the world is at its best, when we are at our best, when life feels fullest, one and one equals three. It’s the essential equation of love, art, rock ’n’ roll and rock ’n’ roll bands. It’s the reason the universe will never be fully comprehensible, love will continue to be ecstatic, confounding, and true rock ’n’ roll will never die.

Nature seems to take advantage of the simple mathematical representations of the symmetry laws. When one pauses to consider the elegance and the beautiful perfection of the mathematical reasoning involved and contrast it with the complex and far-reaching physical consequences, a deep sense of respect for the power of the symmetry laws never fails to develop.

Like Molière’s M. Jourdain, who spoke prose all his life without knowing it, mathematicians have been reasoning for at least two millennia without being aware of all the principles underlying what they were doing. The real nature of the tools of their craft has become evident only within recent times A renaissance of logical studies in modern times begins with the publication in 1847 of George Boole’s 'The Mathematical Analysis of Logic'.

Most of today’s educational systems are built upon the same learning hierarchy: math and science at the top, humanities in the middle, art on the bottom. The reason for this is because these systems were developed in the nineteenth century, in the midst of the industrial revolution, when this hierarchy provided the best foundation for success. This is no longer the case. In a rapidly changing technological culture and an ever-growing information-based economy, creative ideas are the ultimate resource. Yet our current educational system does little to nourish this resource.

If scientific reasoning were limited to the logical processes of arithmetic, we should not get very far in our understanding of the physical world. One might as well attempt to grasp the game of poker entirely by the use of the mathematics of probability.

No matter how limited their powers of reason might have been. still they must have understood that living like that was just murder, a capital crime - except it was slow, day-by-day murder. The government (or humanity) could not permit capital punishment for one man, but they permitted the murder of millions a little at a time. To kill one man - that is, to subtract 50 years from the sum of all human lives - that was a crime; but to subtract from the sum of all human lives 50,000,000 years - that was not a crime! No, really, isn't it funny? This problem in moral math could be solved in half a minute by any ten-year-old Number today, but they couldn't solve it. All their Kant's together couldn't solve it (because it never occurred to one of their Kant's to construct a system of scientific ethics - that is, one based on subtraction, addition, division, and multiplication).

People were her greatest fear, and in the simple math of her reasoning, there were more here, around them, going slowly insane.

I’ve been banging away at this thing for 30 years. I think the simple math is, some projects work and some don’t. There’s no reason to belabor either one. Just get on to the next.

People are always saying these things about how there's no need to read literature anymore-that it won't help the world. Everyone should apparently learn to speak Mandarin, and learn how to write code for computers. More young people should go into STEM fields: science, technology, engineering, and math. And that all sounds to be true and reasonable. But you can't say that what you learn in English class doesn't matter. That great writing doesn't make a difference. I'm different. It's hard to put into words, but it's true. Words matter.

Good Stories Always Beat Good Spreadsheets” “Whether you are raising money, pitching your product to customers, selling the company, or recruiting employees, never forget that underneath all the math and the MBA bullshit talk, we are all still emotionally driven human beings. We want to attach ourselves to narratives. We don’t act because of equations. We follow our beliefs. We get behind leaders who stir our feelings. In the early days of your venture, if you find someone diving too deep into the numbers, that means they are struggling to find a reason to deeply care about you.

Why did math matter so much? Some reasons were practical: More and more jobs required familiarity with probability, statistics, and geometry. The other reason was that math was not just math. Math is a language of logic. It is a disciplined, organized way of thinking. There is a right answer; there are rules that must be followed. More than any other subject, math is rigor distilled. Mastering the language of logic helps to embed higher-order habits in kids’ minds: the ability to reason, for example, to detect patterns and to make informed guesses. Those kinds of skills had rising value in a

It’s simple math, you know. Classic bell curve. Normal distribution. Most people are going to pile up in the middle, not going anywhere, but there’ll be a handful of outliers that go high and low, often for inexplicable reasons. Point is, even survivors don’t really understand why they survive—they just do.

It’s easy to forget that teaching is holy work. We forget that building up the intellect- teaching our children to really think- does not happen by the might of human reason, but rather by the grace of God. On an ordinary day, you and I likely have a set of tasks we've scheduled for our kids. But it's more than math. It's more than history. It's the building up of our children's minds and hearts, and we can only do that if we realize that this is how we thank Him for the graces He so lavishly pours out on us.

IT WAS EASIER FOR PEOPLE to be good at something when more of us lived in small, rural communities. Someone could be homecoming queen. Someone else could be spelling-bee champ, math whiz or basketball star. There were only one or two mechanics and a couple of teachers. In each of their domains, these local heroes had the opportunity to enjoy the serotonin-fuelled confidence of the victor. It may be for that reason that people who were born in small towns are statistically overrepresented among the eminent.68 If

Mathematics is not arithmetic. Though mathematics may have arisen from the practices of counting and measuring it really deals with logical reasoning in which theorems—general and specific statements—can be deduced from the starting assumptions. It is, perhaps, the purest and most rigorous of intellectual activities, and is often thought of as queen of the sciences.

The good Lord, in his infinite wisdom, did not make us all the same. Goodness gracious, if he had, this would be a boring world, don't you think? You are different from each other in height, weight, background, intelligence, talent, and many other ways. For that reason, each one of you deserves individual treatment that is best for you. I will decide what that treatment will be.

Remember your math: an anecdote is not a trend. Remember your history: the fact that something is bad today doesn't mean it was better in the past. Remember your philosophy: one cannot reason that there's no such thing as reason, or that something is true or good because God said it is. And remember your psychology: much of what we know isn't so, especially when our comrades know it too.

A distinguished writer [Siméon Denis Poisson] has thus stated the fundamental definitions of the science: 'The probability of an event is the reason we have to believe that it has taken place, or that it will take place.' 'The measure of the probability of an event is the ratio of the number of cases favourable to that event, to the total number of cases favourable or contrary, and all equally possible' (equally like to happen). From these definitions it follows that the word probability, in its mathematical acceptation, has reference to the state of our knowledge of the circumstances under which an event may happen or fail. With the degree of information which we possess concerning the circumstances of an event, the reason we have to think that it will occur, or, to use a single term, our expectation of it, will vary. Probability is expectation founded upon partial knowledge. A perfect acquaintance with all the circumstances affecting the occurrence of an event would change expectation into certainty, and leave neither room nor demand for a theory of probabilities.

To your party I'll bring my World-Famous Leftover Duck Meatloaf. It's from 1999, and the only reason I have it in my possession is because my old high-school math teacher called me up to come remove it from my old locker, because it was making his class smell like Savage Garden.

I always considered fear to be a motivator or a reason not to do something, but I never considered it a reason to continue an ongoing behavior. This opens a vault full of questions about my own life. I’ve always assumed I’m afraid to engage in activities because I’m afraid of what might happen. But maybe I’m looking at it all wrong. Maybe I should be asking myself if I’m really afraid of leaving what makes me comfortable.

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

Godly education means that the sovereignty of God is the baseline fact of all further knowledge, so that even elementary addition problems—two plus two equals four—follow not from any internal logic but...an acknowledgment that Jesus invented and rules over math, that He is in fact "the reason for" math.

One of the most extraordinary stories of reframing is that of Roger Bannister, the first person to run a mile in less than four minutes. Bannister was a medical school student who couldn’t afford a trainer or a special runner’s diet. He didn’t even have time to run more than thirty minutes a day, squeezed in around his medical studies. Yet Bannister did not focus on all the reasons why he logically had no chance of reaching his goal. He instead refocused on accomplishing his goal in his own way. On the morning he made world history, he got up, ate his usual breakfast, did his required hospital rounds, and then caught a bus to the track.

Biot, who assisted Laplace in revising it [The Mécanique Céleste] for the press, says that Laplace himself was frequently unable to recover the details in the chain of reasoning, and if satisfied that the conclusions were correct, he was content to insert the constantly recurring formula, 'Il est àisé avoir' [it is easy to see].

Why were American kids consistently underestimated in math? In middle school, Kim and Tom had both decided that math was something you were either good at, or you weren’t, and they weren’t. Interestingly, that was not the kind of thing that most Americans said about reading. If you weren’t good at reading, you could, most people assumed, get better through hard work and good teaching. But in the United States, math was, for some reason, considered more of an innate ability, like being double-jointed.

The primary thing we need to learn is not just maths or spelling, but how to be good: we need to learn about courage, self-control, reasonableness, independence and calm.

_Yes _No 12. Did you get a reasonable night’s sleep before the test? (If your answer is no, your answers to 1–11 may not matter.)

give a reasonable priority to your sleep time, since it will greatly boost your brain skills, your ability to focus and even your problem solving and stress management abilities.

Teaching is a dialogue, and it is through the process of engaging students that we see ideas taken from the abstract and played out in concrete visual form. Students teach us about creativity through their personal responses to the limits we set, thus proving that reason and intuition are not antithetical. Their works give aesthetic visibility to mathematical ideas.

REAL MATHEMATICS is not about just computing but it is about figuring out… Figuring out the truthfulness, reasoning behind specific event, patterns, determinism in chaotic processes etc.

On Rachel's show for November 7, 2012: Ohio really did go to President Obama last night. and he really did win. And he really was born in Hawaii. And he really is legitimately President of the United States, again. And the Bureau of Labor statistics did not make up a fake unemployment rate last month. And the congressional research service really can find no evidence that cutting taxes on rich people grows the economy. And the polls were not screwed to over-sample Democrats. And Nate Silver was not making up fake projections about the election to make conservatives feel bad; Nate Silver was doing math. And climate change is real. And rape really does cause pregnancy, sometimes. And evolution is a thing. And Benghazi was an attack on us, it was not a scandal by us. And nobody is taking away anyone's guns. And taxes have not gone up. And the deficit is dropping, actually. And Saddam Hussein did not have weapons of mass destruction. And the moon landing was real. And FEMA is not building concentration camps. And you and election observers are not taking over Texas. And moderate reforms of the regulations on the insurance industry and the financial services industry in this country are not the same thing as communism. Listen, last night was a good night for liberals and for democrats for very obvious reasons, but it was also, possibly, a good night for this country as a whole. Because in this country, we have a two-party system in government. And the idea is supposed to be that the two sides both come up with ways to confront and fix the real problems facing our country. They both propose possible solutions to our real problems. And we debate between those possible solutions. And by the process of debate, we pick the best idea. That competition between good ideas from both sides about real problems in the real country should result in our country having better choices, better options, than if only one side is really working on the hard stuff. And if the Republican Party and the conservative movement and the conservative media is stuck in a vacuum-sealed door-locked spin cycle of telling each other what makes them feel good and denying the factual, lived truth of the world, then we are all deprived as a nation of the constructive debate about competing feasible ideas about real problems. Last night the Republicans got shellacked, and they had no idea it was coming. And we saw them in real time, in real humiliating time, not believe it, even as it was happening to them. And unless they are going to secede, they are going to have to pop the factual bubble they have been so happy living inside if they do not want to get shellacked again, and that will be a painful process for them, but it will be good for the whole country, left, right, and center. You guys, we're counting on you. Wake up. There are real problems in the world. There are real, knowable facts in the world. Let's accept those and talk about how we might approach our problems differently. Let's move on from there. If the Republican Party and the conservative movement and conservative media are forced to do that by the humiliation they were dealt last night, we will all be better off as a nation. And in that spirit, congratulations, everyone!

Svetlana said that I thought of myself as a robot who could act only negatively. She said I had cynical ideas about language. “You think language is an end in itself. You don’t believe it stands for anything. No, it’s not that you don’t believe—it’s that you don’t care. For you, language itself is a self-sufficient system.” “But it is a self-sufficient system.” “Do you see what you’re saying? This is how you get yourself involved with the devil incarnate. Ivan sensed this attitude in you. He’s cynical in the same way you are only more so, because of math. It’s like you said: math is a language that started out so abstract, more abstract than words, and then suddenly it turned out to be the most real, the most physical thing there was. With math they built the atomic bomb. Suddenly this abstract language is leaving third-degree burns on your skin. Now there’s this special language that can control everything, and manipulate everything, and if you’re the elite who speaks it—you can control everything. “Ivan wanted to try an experiment, a game. It would never have worked with someone different, on someone like me. But you, you’re so disconnected from truth, you were so ready to jump into a reality the two of you made up, just through language. Naturally, it made him want to see how far he could go. You went further and further—and then something went wrong. It couldn’t continue in the same way. It had to develop into something else—into sex, or something else. But for some reason, it didn’t. The experiment didn’t work. But by now you’re so, so far from all the landmarks. You’re just drifting in space.

Things were changing; I was changing. All swelling limbs and sweating brain, suddenly I had more body than I knew what to do with. Arms and legs became the prey of low desktops and narrow corridors, were ambushed by sharp corners. Mr Baxter ignored my plight. Bodies were inimical to mathematics, or so we were led to believe. Bad hair, acrid breath, lumpy skin, all vanished for an hour every Tuesday and Thursday. Young minds in the buff soared into the sphere of pure reason. Pages turned to parallelograms; cities, circumferences; recipes, ratios. Shorn of our bearings, we groped our way around in this rarefied air.

five suggestions that can work to open mathematics tasks and increase their potential for learning: Open up the task so that there are multiple methods, pathways, and representations. Include inquiry opportunities. Ask the problem before teaching the method. Add a visual component and ask students how they see the mathematics. Extend the task to make it lower floor and higher ceiling. Ask students to convince and reason; be skeptical.

Math can explain the reason there’s a one out of four chance that I’d have blue eyes. But it doesn’t explain why me. And science or math can’t explain what makes one person lucky, or what makes a person lucky enough to survive.

Research has established that one aspect of reading does need to be taught and practiced as a set of skills, much like math: decoding, the part that involves matching sounds to letters. The problem is that the other aspect of reading—comprehension—is also being taught that way. While there’s plenty of evidence that some instruction in some comprehension strategies can be helpful for some children, there’s no reason to believe it can turn struggling readers into accomplished ones.

Even the most complex math can be broken into a sequence of trivial steps. Each of these slaves has been trained to complete specific equations in an assembly-line fashion. When taken together, this collective human mind is capable of remarkable feats." Holtzman surveyed the room as if he expected his solvers to give him a resounding cheer. Instead, they studied their work with heavy-lidded eyes, moving through equation after equation with no comprehension of reasons or larger pictures.

If you have a library of concepts and solutions internalized as chunked patterns, you can more easily skip to the right solution to a problem by listening to the whispers from your diffuse mode. Your diffuse mode can also help you connect two or more chunks together in new ways to solve unusual problems. There are two ways to solve problems—first, through sequential, step-by-step reasoning, and second, through more holistic intuition. Sequential thinking, where each small step leads deliberately toward the solution, involves the focused mode. Intuition, on the other hand, often seems to require a creative, diffuse mode linking of several seemingly different focused mode thoughts. Most difficult problems are solved through intuition, because they make a leap away from what you are familiar with.24 Keep in mind that the diffuse mode’s semi-random way of making connections means that the solutions it provides with should be carefully verified using the focused mode. Intuitive insights aren’t always correct!25

Ethan’s parents constantly told him how brainy he was. “You’re so smart! You can do anything, Ethan. We are so proud of you, they would say every time he sailed through a math test. Or a spelling test. Or any test. With the best of intentions, they consistently tethered Ethan’s accomplishment to some innate characteristic of his intellectual prowess. Researchers call this “appealing to fixed mindsets.” The parents had no idea that this form of praise was toxic. 　　Little Ethan quickly learned that any academic achievement that required no effort was the behavior that defined his gift. When he hit junior high school, he ran into subjects that did require effort. He could no longer sail through, and, for the first time, he started making mistakes. But he did not see these errors as opportunities for improvement. After all, he was smart because he could mysteriously grasp things quickly. And if he could no longer grasp things quickly, what did that imply? That he was no longer smart. Since he didn’t know the ingredients making him successful, he didn’t know what to do when he failed. You don’t have to hit that brick wall very often before you get discouraged, then depressed. Quite simply, Ethan quit trying. His grades collapsed. What happens when you say, ‘You’re so smart’ 　　Research shows that Ethan’s unfortunate story is typical of kids regularly praised for some fixed characteristic. If you praise your child this way, three things are statistically likely to happen: 　　First, your child will begin to perceive mistakes as failures. Because you told her that success was due to some static ability over which she had no control, she will start to think of failure (such as a bad grade) as a static thing, too—now perceived as a lack of ability. Successes are thought of as gifts rather than the governable product of effort. 　　Second, perhaps as a reaction to the first, she will become more concerned with looking smart than with actually learning something. (Though Ethan was intelligent, he was more preoccupied with breezing through and appearing smart to the people who mattered to him. He developed little regard for learning.) 　　Third, she will be less willing to confront the reasons behind any deficiencies, less willing to make an effort. Such kids have a difficult time admitting errors. There is simply too much at stake for failure. 　　  　　What to say instead: ‘You really worked hard’ 　　What should Ethan’s parents have done? Research shows a simple solution. Rather than praising him for being smart, they should have praised him for working hard. On the successful completion of a test, they should not have said,“I’m so proud of you. You’re so smart. They should have said, “I’m so proud of you. You must have really studied hard”. This appeals to controllable effort rather than to unchangeable talent. It’s called “growth mindset” praise.

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.

there is any moral to this story, it’s that, when you are writing code, remember that someone may have to comb through it and check everything when it is being repurposed in the future. It could even be you, long after you have forgotten the original logic behind the code. For this reason, programmers can leave “comments” in their code, which are little messages to anyone else who has to read their code. The programmer mantra should be “Always comment on your code.” And make the comments helpful. I’ve reviewed dense code I wrote years before, to find the only comment is “Good luck, future Matt.

Jane Russell! My physical therapist had never heard of her. “Gentlemen Prefer Blondes,” I said. “Not in my experience,” she replied. Bina’s younger; perhaps that’s it. All this was earlier today; before I could argue with her, she laced one of my legs over the other, capsized me onto my right side. The pain left me breathless. “Your hamstrings need this,” she assured me. “You bitch,” I gasped. She pressed my knee to the floor. “You’re not paying me to go easy on you.” I winced. “Can I pay you to leave?” Bina visits once a week to help me hate life, as I like to say, and to provide updates on her sexual adventures, which are about as exciting as my own. Only in Bina’s case it’s because she’s picky. “Half the guys on these apps are using five-year-old photos,” she’ll complain, her waterfall of hair poured over one shoulder, “and the other half are married. And the other half are single for a reason.” That’s three halves, but you don’t debate math with someone who’s rotating your spine.

The solution to a math problem is not a number: it's an argument, a proof. We're trying to create these little poems of pure reason. Of course, like any other form of poetry, we want our work to be beautiful as well as meaningful. Mathematics is the art of explanation, and consequently, it is difficult, frustrating, and deeply satisfying.

There are seven billion people on this planet. As many as six billion pray and meditate, and never look at a book on reason, logic and math. Imagine if, instead, these six billion people were literate in reason, logic and math. If that were the case, we would already be building starships and making Star Trek for real rather than as a TV show.

Just as we talk of poetic beauty, so we should also talk of mathematical beauty and medicinal beauty. But we do not talk like that for the very good reason that we know what the object of mathematics is, namely proof; and what the object of medicine is, namely cure; but we do not know what constitutes the attraction which is the object of poetry.

science and reason, which has found itself in recent decades under attack on many fronts: right-wing ideologues who do not understand science; religious-right conservatives who fear science; left-wing postmodernists who do not trust science when it doesn’t support progressive tenets about human nature; extreme environmentalists who want to return to a prescientific and preindustrial agrarian society; antivaxxers who wrongly imagine that vaccinations cause autism and other maladies; anti-GMO (genetically modified food) activists who worry about Frankenfoods; and educators of all stripes who cannot articulate why Science, Technology, Engineering, and Math (STEM) are so vital to a modern democratic nation.

This is one of the reasons science has made such dramatic progress. An undergraduate science major today knows more about science and math than did Sir Isaac Newton, one of the most renowned scientists who ever lived. Even in this introductory astronomy course, you will learn about objects and processes that no one a few generations ago even dreamed existed.

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

Having described the basic methods of Hindu-Arabic arithmetic in the first seven chapters, Leonardo devoted most of the remainder of the book to practical problems. Chapters 8 and 9 provide dozens of worked examples on buying, selling, and pricing merchandise, using what we would today call reasoning by proportions—the math we use to check the best deal in the supermarket.

Remember your math: an anecdote is not a trend. Remember your history: the fact that something is bad today doesn’t mean it was better in the past. Remember your philosophy: one cannot reason that there’s no such thing as reason, or that something is true or good because God said it is. And remember your psychology: much of what we know isn’t so, especially when our comrades know it too.

Q: What are in your eyes the major defects in the West? A: The West has come to regard the values of freedom, the yardstick of human rights, as something Western. Many of them [westerns] specially in Europe take the values and the institutions on freedom, the institutions on science, curiosity, the individual, i mean, the rule of law and they’ve come to take that all for granted that they are not aware of the threat against it and not aware of the fact that you have to sustain it day by day as with all man made things. I mean, a building for example, the roof will leak, the paint will fall and you have to repaint it, you have to maintain it all the time it seems that people have forgotten that and perhaps part of the reason is because the generation that is now enjoying all the freedoms in the West is not the generations that built it; these are generations that inherited and like companies, family companies, often you’ll see the first generation or the second generation are almost always more passionate about the brand and the family company and name and keeping it all int he family and then the third generation live, use, take the money and they are either overtaken by bigger companies, swallowed up or they go bankrupt and I think there is an analogy there in that the generations after the second world war living today in Europe, United States may be different but I’m here much too short to say anything about it, is that there are people who are so complacent, they’ve always been free, they just no longer know what it is that freedom costs and for me that would be making the big mistake and you can see it. The education system in Europe where history is no longer an obligatory subject, science is no longer an obligatory subject, school systems have become about, look at Holland, our country where they have allowed parents, in the name of freedom, to build their own schools that we now have schools founded on what the child wants so if the child wants to play all day long then that is an individual freedom of the child and so it’s up to the child to decide whether to do math or to clay and now in our country in Holland, in the name of freedom of education, the state pays for these schools and I was raving against muslim schools and i thought about this cuz i was like you know ok in muslin schools at least they learn to count.

I have no problem with being fabulous. My problem comes when you won't allow yourself to be an ordinary woman with a decent apartment and an okay job. When only the mom is allowed to be boring—because her life is so rich with meaning. When I carefully choreographed the story of how amazing I was, I was acting like one of those helicopter parents—you know, the ones who refuse to admit that their Jackson might suck at math or Stella might not be the world's greatest violinist. 'You are special! You are special!' they cry to their children, hoping this will boost their confidence. But the real message is one of panic: You must be special. Ordinary is not okay. When I walked into a party projecting the Shiny Girl—she of the lighthearted flings and glitzy job—I was essentially doing the same thing.

Further, the same Arguments which explode the Notion of Luck, may, on the other side, be useful in some Cases to establish a due comparison between Chance and Design: We may imagine Chance and Design to be, as it were, in Competition with each other, for the production of some sorts of Events, and many calculate what Probability there is, that those Events should be rather be owing to the one than to the other.

C-minus in algebra; A plus in coolology. See, popularity is complicated, yo. You have to spend a lot of time thinking about liking; you have to really like being liked, and also sorta like being disliked." And reason three," Lindsey said, "is I gotta teach you how to shoot so you don't embarass yourself." "Shoot a gun"? A shotgun. I put one in your trunk this afternoon." Colin nervously glanced toward the back.

The leader sighed. It was a resigned kind of sigh. He was clearly put upon. It didn’t have to be like this. But now his hands were tied. “You seem like a reasonable man. Do the math.” “It’s not about math. And yes, normally I’m reasonable enough. But this is what you might call an emotionally difficult time of the year for me. I’m irritable, out of eggnog, and one of my freeloading creatures ate my cookies. You should leave while you still can.

There is little reason to believe that previously colonized people have any use for a postcolonial Theory or decoloniality that argues that math is a tool of Western imperialism,48 that sees alphabetical literacy as colonial technology and postcolonial appropriation,49 that views research as the production of totalizing meta-texts of colonial knowledge,50 or that confronts France and the United States about their understanding of big black butts.

On the SB5 Stanford-Binet intelligence test Isaiah’s reasoning scores were near genius levels. His abilities came naturally but were honed in his math classes. He was formally introduced to inductive reasoning in geometry, a tenth-grade subject he took in the eighth. His teacher, Mrs. Washington, was a severe woman who looked to be all gristle underneath her brightly colored pantsuits. Lavender, Kelly green, peach. She talked to the class like somebody had tricked her into it. “All

I have no reason to believe that the social scientists at Facebook are actively gaming the political system. Most of them are serious academics carrying out research on a platform that they could only have dreamed about two decades ago. But what they have demonstrated is Facebook’s enormous power to affect what we learn, how we feel, and whether we vote. Its platform is massive, powerful, and opaque. The algorithms are hidden from us, and we see only the results of the experiments researchers choose to publish.

I spoke off the record to a database consultant who was working with a company in Italy. They had a lot of clients, and their database would generate a client ID for each one by using something like the current year, the first letter of the client company name and then an index number to make sure each ID was unique. For some reason their database was losing companies whose names started with the letter E. It was because they were using Excel and it was converting those client IDs to be a scientific notation number, which was no longer recognized as an ID.

This success permits us to hope that after thirty or forty years of observation on the new Planet [Neptune], we may employ it, in its turn, for the discovery of the one following it in its order of distances from the Sun. Thus, at least, we should unhappily soon fall among bodies invisible by reason of their immense distance, but whose orbits might yet be traced in a succession of ages, with the greatest exactness, by the theory of Secular Inequalities. [Following the success of the confirmation of the existence of the planet Neptune, he considered the possibility of the discovery of a yet further planet.]

Never forget – there is nothing other than mathematics. The reason why you imagine that the universe is not mathematical is that your mind experiences the information carried by mathematics – its empirical Content – but you don’t regard this as math. Yet it is. It’s just the other side of the ontological mathematical coin It’s mathematical Content rather than mathematical Form, but it’s math all the same. Mathematics is Janus-faced. It looks two ways at once: empirically and rationally. You have been brainwashed to think that only the rational Form is math – and that it’s cold and abstract, with nothing to do with reality. In fact, both sides of the coin are fully mathematical. That’s what it means to say that mathematics is ontological.

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.

Homework _Yes _No 1. Did you make a serious effort to understand the text? (Just hunting for relevant worked-out examples doesn’t count.) _Yes _No 2. Did you work with classmates on homework problems, or at least check your solutions with others? _Yes _No 3. Did you attempt to outline every homework problem solution before working with classmates? Test Preparation The more “Yes” responses you recorded, the better your preparation for the test. If you recorded two or more “No” responses, think seriously about making some changes in how you prepare for the next test. _Yes _No 4. Did you participate actively in homework group discussions (contributing ideas, asking questions)? _Yes _No 5. Did you consult with the instructor or teaching assistants when you were having trouble with something? _Yes _No 6. Did you understand ALL of your homework problem solutions when they were handed in? _Yes _No 7. Did you ask in class for explanations of homework problem solutions that weren’t clear to you? _Yes _No 8. If you had a study guide, did you carefully go through it before the test and convince yourself that you could do everything on it? _Yes _No 9. Did you attempt to outline lots of problem solutions quickly, without spending time on the algebra and calculations? _Yes _No 10. Did you go over the study guide and problems with classmates and quiz one another? _Yes _No 11. If there was a review session before the test, did you attend it and ask questions about anything you weren’t sure about? _Yes _No 12. Did you get a reasonable night’s sleep before the test? (If your answer is no, your answers to 1–11 may not matter.) _Yes _No TOTAL

It's specifically this Z = 2^(Aleph0) that he couldn't prove. Ever. Despite years of unimaginable doodling. Whether it's what unhinged him or not is an unanswerable question, but it is true that his inability to prove the C.H. caused Cantor pain for the rest of his life; he considered it his great failure. This too, in hindsight, is sad, because professional mathematicians now know exactly why G. Cantor could neither prove nor disprove the C.H. The reasons are deep and important and go corrosively to the root of axiomatic set theory's formal Consistency, in rather the same way that K. Godel's Incompleteness proofs deracinate all math as a formal system. Once again, the issues here can be only sketched or synopsized (although this time Godel is directly involved, so the whole thing is probably fleshed out in the Great Discoveries Series' Godel booklet).

I have both some good news and some bad news for you: there is little that is unique or special about your problems. That’s why letting go is so liberating. There’s a kind of self-absorption that comes with fear based on an irrational certainty. When you assume that your plane is the one that’s going to crash, or that your project idea is the stupid one everyone is going to laugh at, or that you’re the one everyone is going to choose to mock or ignore, you’re implicitly telling yourself, “I’m the exception; I’m unlike everybody else; I’m different and special.” This is narcissism, pure and simple. You feel as though your problems deserve to be treated differently, that your problems have some unique math to them that doesn’t obey the laws of the physical universe. My recommendation: don’t be special; don’t be unique. Redefine your metrics in mundane and broad ways. Choose to measure yourself not as a rising star or an undiscovered genius. Choose to measure yourself not as some horrible victim or dismal failure. Instead, measure yourself by more mundane identities: a student, a partner, a friend, a creator. The narrower and rarer the identity you choose for yourself, the more everything will seem to threaten you. For that reason, define yourself in the simplest and most ordinary ways possible. This often means giving up some grandiose ideas about yourself: that you’re uniquely intelligent, or spectacularly talented, or intimidatingly attractive, or especially victimized in ways other people could never imagine. This means giving up your sense of entitlement and your belief that you’re somehow owed something by this world. This means giving up the supply of emotional highs that you’ve been sustaining yourself on for years. Like a junkie giving up the needle, you’re going to go through withdrawal when you start giving these things up. But you’ll come out the other side so much better.

The consequence model, the logical one, the amoral one, the one which refuses any divine intervention, is a problem really for just the (hypothetical) logician. You see, towards God I would rather be grateful for Heaven (which I do not deserve) than angry about Hell (which I do deserve). By this the logician within must choose either atheism or theism, but he cannot possibly through good reason choose anti-theism. For his friend in this case is not at all mathematical law: the law in that 'this equation, this path will consequently direct me to a specific point'; over the alternative and the one he denies, 'God will send me wherever and do it strictly for his own sovereign amusement.' The consequence model, the former, seeks the absence of God, which orders he cannot save one from one's inevitable consequences; hence the angry anti-theist within, 'the logical one', the one who wants to be master of his own fate, can only contradict himself - I do not think it wise to be angry at math.

The PSR gives rise to ontological mathematics, which is just the exploration of all the different ways in which x = 0 can be explored, and x can be any expression at all, provided it can ultimately be reduced to zero. There are infinite mathematical tautologies, all of which are consistent with the PSR and Occam’s razor. Nothing can be simpler in hypothesis than requiring everything to equal zero, and nothing could be richer in phenomena than this strict requirement since there are infinite ways to generate mathematical expressions that equal zero. So, the law of ultimate simplicity leads, inevitably, to endless variety ... all thanks to mathematics and the equals sign. There is no contradiction whatsoever between total simplicity and infinite variety ... that’s exactly why math is so powerful, and can produce the incredibly varied universe we live in ... all of which is simply “nothing” expressed in different ways. Is that not the ultimate miracle? But it’s not a miracle at all. It is the direct consequence of the PSR, hence is the most rational thing of all.

What the fuck is going on?” Sloane asks, worry etched in her features, the green hues of her hazel eyes more vibrant against the bloodshot evidence of the worried tears she must have shed during her drive here. “I thought you hated Lachlan. You can’t be serious about marrying him.” “What gave you the impression I hate him?” “You saying, ‘Lachlan is a dickhead, I really hate that guy,’ might be one reason.” I let out an unsteady laugh as I try not to fidget with the bouquet clutched in my iron grip. “Well, he can kind of be a dickhead, sure, but hate might be a bit strong.” Sloane turns toward me, the car still idling in park. “Tell me what the fuck is going on, Lark. You’re my best friend. You’re the most impetuous person I know, but this? A random-as-fuck wedding to Lachlan Kane when you’ve spoken to each other what, like, five times? And all those times have been some kind of miserable? There has to be a reason for this sudden one-eighty.” She shakes her head as fresh tears well at her lash line. Her voice is barely more than a strained squeak when she says, “The math. It ain’t mathin’.

My mother loved giving me math challenges. At Kmart or Winn-Dixie, she’d have me pick out books and model cars and trucks and buy them for me if I was able to mentally add together their prices. Over the course of my childhood, she kept escalating the difficulty, first having me estimate and round to the nearest dollar, then having me figure out the precise dollar-and-cents amount, and then having me calculate 3 percent of that amount and add it on to the total. I was confused by that last challenge—not by the arithmetic so much as by the reasoning. “Why?” “It’s called tax,” my mother explained. “Everything we buy, we have to pay three percent to the government.” “What do they do with it?” “You like roads, buddy? You like bridges?” she said. “The government uses that money to fix them. They use that money to fill the library with books.” Some time later, I was afraid that my budding math skills had failed me, when my mental totals didn’t match those on the cash register’s display. But once again, my mother explained. “They raised the sales tax. Now you have to add four percent.” “So now the library will get even more books?” I asked. “Let’s hope,” my mother said.

[J.Ivy:] We are all here for a reason on a particular path You don't need a curriculum to know that you are part of the math Cats think I'm delirious, but I'm so damn serious That's why I expose my soul to the globe, the world I'm trying to make it better for these little boys and girls I'm not just another individual, my spirit is a part of this That's why I get spiritual, but I get my hymns from Him So it's not me, it's He that's lyrical I'm not a miracle, I'm a heaven-sent instrument My rhythmatic regimen navigates melodic notes for your soul and your mental That's why I'm instrumental Vibrations is what I'm into Yeah, I need my loot by rent day But that is not what gives me the heart of Kunte Kinte I'm tryina give us "us free" like Cinque I can't stop, that's why I'm hot Determination, dedication, motivation I'm talking to you, my many inspirations When I say I can't, let you or self down If I were of the highest cliff, on the highest riff And you slipped off the side and clinched on to your life in my grip I would never, ever let you down And when these words are found Let it been known that God's penmanship has been signed with a language called love That's why my breath is felt by the deaf And why my words are heard and confined to the ears of the blind I, too, dream in color and in rhyme So I guess I'm one of a kind in a full house Cuz whenever I open my heart, my soul, or my mouth A touch of God reigns out [Chorus] [Jay-Z (Kanye West)] Who else you know been hot this long, (Oh Ya, you know we ain't finished) Started from nothing but he got this strong, (The ROC is in the building) Built the ROC from a pebble, pedalled rock before I met you, Pedalled bikes, got my nephews pedal bikes because they special, Let you tell that man I'm falling, Well somebody must've caught him, Cause every fourth quarter, I like to Mike Jordan 'em, Number one albums, what I got like four of dem, More of dem on the way, The Eight Wonder on the way, Clear the way, I'm here to stay, Y'all can save the chitter chat, this and that, this and Jay, Dissin' Jay 'ill get you mased, When I start spitting them lyrics, niggas get very religious, Six Hail Maries, please Father forgive us, Young, the Archbishop, the Pope John Paul of y'all niggas, The way y'all all follow Jigga, Hov's a living legend and I tell you why, Everybody wanna be Hov and Hov still alive.

Henry had taught Eddie how to play basketball in the playground near the apartment building where they lived--this was in a cement suburb where the towers of Manhattan stood against the horizon like a dream and the welfare check was king. Eddie was eight years younger than Henry and much smaller, but he was also much faster. He had a natural feel for the game; once he got on the cracked, hilly cement of the court with the ball in his hands, the moves seemed to sizzle in his nerve-endings. He was faster, but that was no big deal. The big deal was this: he was BETTER than Henry. If he hadn't known it from the results of the pick-up games in which they sometimes played, he would have known it from Henry's thunderous looks and the hard punches to the upper arm Henry often dealt out on their way home afterwards. These punches were supposedly Henry's little jokes--"Two for flinching!" Henry would cry cheerily, and then whap-whap into Eddie's bicep with one knuckle extended--but they didn't FEEL like jokes. They felt like warnings. They felt like Henry's way of saying You better not fake me out and make me look stupid when you drive for the basket; you better remember that I'm Watching Out for You. The same was true with reading...baseball...Ring-a-Levio...math...even jump-rope, which was a girl's game. That he was better at these tings, or COULD be better, was a secret that had to be kept at all costs. Because Eddie was the younger brother. Because Henry was Watching Out for him. But the most important part of the underneath reason was also the simplest: these things had to be kept secret because Henry was Eddie's big brother, and Eddie adored him.

Still, the appeal of regressive ideas is perennial, and the case for reason, science, humanism, and progress always has to be made. When we fail to acknowledge our hard-won progress, we may come to believe that perfect order and universal prosperity are the natural state of affairs, and that every problem is an outrage that calls for blaming evildoers, wrecking institutions, and empowering a leader who will restore the country to its rightful greatness. I have made my own best case for progress and the ideals that made it possible, and have dropped hints on how journalists, intellectuals, and other thoughtful people (including the readers of this book) might avoid contributing to the widespread heedlessness of the gifts of the Enlightenment. Remember your math: an anecdote is not a trend. Remember your history: the fact that something is bad today doesn’t mean it was better in the past. Remember your philosophy: one cannot reason that there’s no such thing as reason, or that something is true or good because God said it is. And remember your psychology: much of what we know isn’t so, especially when our comrades know it too. Keep some perspective. Not every problem is a Crisis, Plague, Epidemic, or Existential Threat, and not every change is the End of This, the Death of That, or the Dawn of a Post-Something Era. Don’t confuse pessimism with profundity: problems are inevitable, but problems are solvable, and diagnosing every setback as a symptom of a sick society is a cheap grab for gravitas. Finally, drop the Nietzsche. His ideas may seem edgy, authentic, baaad, while humanism seems sappy, unhip, uncool. But what’s so funny about peace, love, and understanding?

Our two taco specials get shoved up on the serving counter, crispy, cheesy goodness in brown plastic baskets lined with parchment paper, sour cream and guacamole exactly where they should be. On the side. There is a perfect ratio of sour cream, guac, and salsa on a shredded chicken tostada. No one can make it happen for you. Many restaurants have tried. All have failed. Only the mouth knows its own pleasure, and calibration like Taco Heaven cannot be mass produced. It simply cannot. Taco Heaven is a sensory explosion of flavor that defies logic. First, you have to eye the amount of spiced meat, shredded lettuce, chopped tomatoes, and tomatillos. You must consider the size and crispiness of the shells. Some people–I call them blasphemers–like soft tacos. I am sitting across from Exhibit A. We won’t talk about soft tacos. They don’t make it to Taco Heaven. People who eat soft tacos live in Taco Purgatory, never fully understanding their moral failings, repeating the same mistakes again and again for all eternity. Like Perky and dating. Once you inventory your meat, lettuce, tomato, and shell quality, the real construction begins. Making your way to Taco Heaven is like a mechanical engineer building a bridge in your mouth. Measurements must be exact. Payloads are all about formulas and precision. One miscalculation and it all fails. Taco Death is worse than Taco Purgatory, because the only reason for Taco Death is miscalculation. And that’s all on you. “Oh, God,” Fiona groans through a mouthful of abomination. “You’re doing it, aren’t you?” “Doing what?” I ask primly, knowing damn well what she’s talking about. “You treat eating tacos like you’re the star of some Mythbusters show.” “Do not.” “Do too.” “Even if I do–and I am notconceding the point–it would be a worthwhile venture.” “You are as weird about your tacos as Perky is about her coffee.” “Take it back! I am not that weird.” “You are.” “Am not.” “This is why Perky and I swore we would never come here with you again.” Fiona grabs my guacamole and smears the rounded scoop all over the outside of her soft taco. I shriek. “How can you do that?” I gasp, the murder of the perfect ratio a painful, almost palpable blow. The mashed avocado has a death rattle that rings in my ears. Smug, tight lips give me a grimace. “See? A normal person would shout, ‘Hey! That’s mine!’ but you’re more offended that I’ve desecrated my inferior taco wrapping with the wrong amount of guac.” “Because it’s wrong.” “You should have gone to MIT, Mal. You need a job that involves nothing but pure math for the sake of calculating stupid shit no one else cares about.” “So glad to know that a preschool teacher holds such high regard for math,” I snark back. And MIT didn’t give me the kind of merit aid package I got from Brown, I don’t add. “Was that supposed to sting?” She takes the rest of my guacamole, grabs a spoon, and starts eating it straight out of the little white paper scoop container thing. “How can you do that? It’s like people who dip their french fries in mayonnaise.” I shudder, standing to get in line to buy more guac. “I dip my french fries in mayo!” “More evidence of your madness, Fi. Get help now. It may not be too late.” I stick my finger in her face. “And by the way, you and Perky talk about my taco habits behind my back? Some friends!” I hmph and turn toward the counter.

How to live (forty pieces of advice I feel to be helpful but which I don’t always follow) 1. Appreciate happiness when it is there 2. Sip, don’t gulp. 3. Be gentle with yourself. Work less. Sleep more. 4. There is absolutely nothing in the past that you can change. That’s basic physics. 5. Beware of Tuesdays. And Octobers. 6. Kurt Vonnegut was right. “Reading and writing are the most nourishing forms of meditation anyone has so far found.” 7. Listen more than you talk. 8. Don’t feel guilty about being idle. More harm is probably done to the world through work than idleness. But perfect your idleness. Make it mindful. 9. Be aware that you are breathing. 10. Wherever you are, at any moment, try to find something beautiful. A face, a line out of a poem, the clouds out of a window, some graffiti, a wind farm. Beauty cleans the mind. 11. Hate is a pointless emotion to have inside you. It is like eating a scorpion to punish it for stinging you. 12. Go for a run. Then do some yoga. 13. Shower before noon. 14. Look at the sky. Remind yourself of the cosmos. Seek vastness at every opportunity, in order to see the smallness of yourself. 15. Be kind. 16. Understand that thoughts are thoughts. If they are unreasonable, reason with them, even if you have no reason left. You are the observer of your mind, not its victim. 17. Do not watch TV aimlessly. Do not go on social media aimlessly. Always be aware of what you are doing and why you are doing it. Don’t value TV less. Value it more. Then you will watch it less. Unchecked distractions will lead you to distraction. 18. Sit down. Lie down. Be still. Do nothing. Observe. Listen to your mind. Let it do what it does without judging it. Let it go, like Snow Queen in Frozen. 19. Don’t’ worry about things that probably won’t happen. 20. Look at trees. Be near trees. Plant trees. (Trees are great.) 21. Listen to that yoga instructor on YouTube, and “walk as if you are kissing the earth with your feet”. 22. Live. Love. Let go. The three Ls. 23. Alcohol maths. Wine multiplies itself by itself. The more you have, the more you are likely to have. And if it is hard to stop at one glass, it will be impossible at three. Addition is multiplication. 24. Beware of the gap. The gap between where you are and where you want to be. Simply thinking of the gap widens it. And you end up falling through. 25. Read a book without thinking about finishing it. Just read it. Enjoy every word, sentence, and paragraph. Don’t wish for it to end, or for it to never end. 26. No drug in the universe will make you feel better, at the deepest level, than being kind to other people. 27. Listen to what Hamlet – literature’s most famous depressive – told Rosencrantz and Guildenstern. “There is nothing either good or bad, but thinking makes it so.” 28. If someone loves you, let them. Believe in that love. Live for them, even when you feel there is no point. 29. You don’t need the world to understand you. It’s fine. Some people will never really understand things they haven’t experienced. Some will. Be grateful. 30. Jules Verne wrote of the “Living Infinite”. This is the world of love and emotion that is like a “sea”. If we can submerge ourselves in it, we find infinity in ourselves, and the space we need to survive. 31. Three in the morning is never the time to try and sort out your life. 32. Remember that there is nothing weird about you. You are just a human, and everything you do and feel is a natural thing, because we are natural animals. You are nature. You are a hominid ape. You are in the world and the world is in you. Everything connects. 33. Don’t believe in good or bad, or winning and losing, or victory and defeat, or ups and down. At your lowest and your highest, whether you are happy or despairing or calm or angry, there is a kernel of you that stays the same. That is the you that matters.

There are many things the Chinese do differently from Westerners. There’s the question of extra credit, for example. One time, Lulu came home and told me about a math test she’d just taken. She said she thought it had gone extremely well, which is why she didn’t feel the need to do the extra-credit problems. I was speechless for a second, uncomprehending. “Why not?” I asked. “Why didn’t you do them?” “I didn’t want to miss recess.” A fundamental tenet of being Chinese is that you always do all of the extra credit all of the time. “Why?” asked Lulu, when I explained this to her. For me this was like asking why I should breathe. “None of my friends do it,” Lulu added. “That’s not true,” I said. “I’m 100% sure that Amy and Junno did the extra credit.” Amy and Junno were the Asian kids in Lulu’s class. And I was right about them; Lulu admitted it. “But Rashad and Ian did the extra credit too, and they’re not Asian,” she added. “Aha! So many of your friends did do the extra credit! And I didn’t say only Asians do extra credit. Anyone with good parents knows you have to do the extra credit. I’m in shock, Lulu. What will the teacher think of you? You went to recess instead of doing extra credit?” I was almost in tears. “Extra credit is not extra. It’s just credit. It’s what separates the good students from the bad students." "Aww - recess is so fun," Lulu offered as her final sally. But after that, Lulu, like Sophia. always did the extra credit. Sometimes the girls got more points on extra credit than on the test itself - an absurdity that would never happen in China. Extra credit is one reason that Asian kids get such notoriously good grades in the United States. Rote drilling is another. Once Sophia came in second on a multiplication speed test, which her fifth grade teacher administered every Friday. She lost to a Korean boy named Yoon-seok. Over the next week, I made Sophia do twenty practice tests (of 100 problems each) every night, with me clocking her with a stopwatch. After that, she came in first every time. Poor Yoon-seok. He went back to Korea with his family, but probably not because of the speed test.

Real Quick" [Intro:] Valuable lesson, man I had to grow up That's why I never ask for help I'll do it for you niggaz and do it for myself [Chorus:] I go 0 to 100 nigga, real quick Real quick, whole squad on that real shit 0 to 100 nigga, real quick Real quick, real fuckin quick nigga 0 to 100 nigga, real quick Real quick, whole squad on that real shit 0 to 100 nigga, real quick Real quick, real fuckin quick nigga! [50 Cent:] I'll run my blade 'cross a nigga ass {"real quick"} I'm so for real I'm on some real real nigga shit You playin boy I'll get you hit {"real quick"} You better hope the parademics come {"real quick"} Got me fucked up you think it's different now a nigga rich Before I get to cuttin know you niggaz better cut the shit Boy, you gon' have ya head popped, pull a trigger for me And my lil' niggaz trigger op' like it's legal homie No game when I bang, boy I empty the clip You run like a bitch, you ain't 'bout that shit Hey hey hey hey, I'll catch you another day day day day It's the Unit back to the bullshit [Tony Yayo:] Yeah! Nothin in life is out of bounds AK hold about a hundred rounds 60 shots like K.D. at the Rucker's Okay! When I see you on respirators Southside nigga 'til the day I'm gone Indulge in the violence when the drama on Yeah, these rap niggaz lukewarm I'm two sleeves of dope, when the mic on [Chorus] [Kidd Kidd:] Real quick, Rida Gang fuck nigga, huh! Don't Tweet me, see me when you see me Down to make the news just to say that I'm on TV (Kidd Kidd) This clip rated R, niggaz PG Them shells burn like a bootleg CD (huh?) Fuck love, I want the money When you get too much of it they gon' say you actin funny "Kidd, how you feel now that the Unit's back?" Like a million bucks, muh'fucker do the math! [Young Buck:] Cold-blooded, boy my heart don't feel shit Get with me, ask 50, I'll take the hit {"real quick"} Balenciagas, you can still get ya ass kicked Take a rapper nigga bitch and make a real flick I know I'm different from what you usually be dealin with Don't need a mic, give me some white to make a million with Single borough, six shots on the Brooklyn Bridge I'll let the nigga Drake tell you what I just did (yeah) [Chorus] [Lloyd Banks:] Nigga gettin money new to you (uh) I give a fuck if shit get ugly, there'll be a beautiful funeral You fit the script I'm gon' assume it's true Can't manuever through the street without a strategy, ain't nobody to tutor you And man was lucky Unit's through, you know why he flows 15 years, switchin dealers like casinos And my goon'll clip you on the arm (uhh) I'm out the country every week and dumpin ash out on the Autobahn Auto-pilot's always on Rather better livin, I've been [?] green bills callin me all day long This is homicide, more tears in your mama eyes More reason to wake up, real niggaz arrive [Chorus]

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.

So, what did you want to watch?’ ‘Thought we might play a game instead,’ he said, holding up a familiar dark green box. ‘Found this on the bottom shelf of your DVD cupboard … if you tilt the glass, the champagne won’t froth like that.’ Neve finished pouring champagne into the 50p champagne flutes she’d got from the discount store and waited until Max had drunk a good half of his in two swift swallows. ‘The thing is, you might find it hard to believe but I can be very competitive and I have an astonishing vocabulary from years spent having no life and reading a lot – and well, if you play Scrabble with me, I’ll totally kick your arse.’ Max was about to eat his first bite of molten mug cake but he paused with the spoon halfway to his mouth. ‘You’re gonna kick my arse?’ ‘Until it’s black and blue and you won’t be able to sit down for a week.’ That sounded very arrogant. ‘Really, Max, Mum stopped me from playing when I was thirteen after I got a score of four hundred and twenty-seven, and when I was at Oxford, I used to play with two Linguistics post-grads and an English don.’ ‘Well, my little pancake girlfriend, I played Scrabble against Carol Vorderman for a Guardian feature and I kicked her arse because Scrabble has got nothing to do with vocabulary; it’s logic and tactics,’ Max informed her loftily, taking a huge bite of the cake. For a second, Neve hoped that it was as foul-tasting as she suspected just to get Max back for that snide little speech, but he just licked the back of the spoon thoughtfully. ‘This is surprisingly more-ish, do you want some?’ ‘I think I’ll pass.’ ‘Well, you’re not getting out of Scrabble that easily.’ Max leaned back against the cushions, the mug cradled to his chest, and propped his feet up on the table so he could poke the Scrabble box nearer to Neve. ‘Come on, set ’em up. Unless you’re too scared.’ ‘Max, I have all the two-letter words memorised, and as for Carol Vorderman – well, she might be good at maths but there was a reason why she wasn’t in Dictionary Corner on Countdown so I’m not surprised you beat her at Scrabble.’ ‘Fighting talk.’ Max rapped his knuckles gently against Neve’s head, which made her furious. ‘I’ll remind you of that little speech once I’m done making you eat every single one of those high-scoring words you seem to think you’re so good at.’ ‘Right, that does it.’ Neve snatched up the box and practically tore off the lid, so she could bang the board down on the coffee table. ‘You can’t be that good at Scrabble if you keep your letters in a crumpled paper bag,’ Max noted, actually daring to nudge her arm with his foot. Neve knew he was only doing it to get a rise out of her, but God, it was working. ‘Game on, Pancake Boy,’ she snarled, throwing a letter rack at Max, which just made him laugh. ‘And don’t think I’m going to let you win just because it’s your birthday.’ It was the most fun Neve had ever had playing Scrabble. It might even have been the most fun she had ever had. For every obscure word she tried to play in the highest scoring place, Max would put down three tiles to make three different words and block off huge sections of the board. Every time she tried to flounce or throw a strop because ‘you’re going against the whole spirit of the game’, Max would pop another Quality Street into her mouth because, as he said, ‘It is Treat Sunday and you only had one roast potato.’ When there were no more Quality Street left and they’d drunk all the champagne, he stopped each one of her snits with a slow, devastating kiss so there were long pauses between each round. It was a point of honour to Neve that she won in the most satisfying way possible; finally getting to use her ‘q’ on a triple word score by turning Max’s ‘hogs’ into ‘quahogs’ and waving the Oxford English Dictionary in his face when he dared to challenge her.

There is an almost complete overlap between men and women’s math scores. The majority of women have a male math twin: a man with the same math score as they do.

Fiqh is man-made!" By that reasoning and applying your standards, so are logic, math, natural sciences, and virtually every single body of knowledge and its fruits. If being man made is sufficient reason to reject fiqh, it's more than sufficient reason to reject those, too. And before arguing that science is special, know that the epistemology and philosophy of science are also man-made. UPDATE. Pay particular attention to where it says the "body of knowledge." And if you want to eliminate that qualifier, read up a bit on antirealism.