Maths Tables Quotes

My “Best Woman” speech Good evening everyone, my name is Rosie and as you can see Alex has decided to go down the non-traditional route of asking me to be his best woman for the day. Except we all know that today that title does not belong to me. It belongs to Sally, for she is clearly his best woman. I could call myself the “best friend” but I think we all know that today that title no longer refers to me either. That title too belongs to Sally. But what doesn’t belong to Sally is a lifetime of memories of Alex the child, Alex the teenager, and Alex the almost-a-man that I’m sure he would rather forget but that I will now fill you all in on. (Hopefully they all will laugh.) I have known Alex since he was five years old. I arrived on my first day of school teary-eyed and red-nosed and a half an hour late. (I am almost sure Alex will shout out “What’s new?”) I was ordered to sit down at the back of the class beside a smelly, snotty-nosed, messy-haired little boy who had the biggest sulk on his face and who refused to look at me or talk to me. I hated this little boy. I know that he hated me too, him kicking me in the shins under the table and telling the teacher that I was copying his schoolwork was a telltale sign. We sat beside each other every day for twelve years moaning about school, moaning about girlfriends and boyfriends, wishing we were older and wiser and out of school, dreaming for a life where we wouldn’t have double maths on a Monday morning. Now Alex has that life and I’m so proud of him. I’m so happy that he’s found his best woman and his best friend in perfect little brainy and annoying Sally. I ask you all to raise your glasses and toast my best friend Alex and his new best friend, best woman, and wife, Sally, and to wish them luck and happiness and divorce in the future. To Alex and Sally!

I still remember the day I got my first calculator Teacher: All right, children, welcome to fourth grade math. Everyone take a calculator out of the bin. Me: What are these? Teacher: From now on we'll be using calculators. Me: What do these things do? Teacher: Simple operations, like multiplication and division. Me: You mean this device just...does them? By itself? Teacher: Yes. You enter in the problem and press equal. Me: You...you knew about this machine all along, didn't you? This whole time, while we were going through this...this charade with the pencils and the line paper and the stupid multiplication tables!...I'm sorry for shouting...It's just...I'm a little blown away. Teacher: Okay, everyone, today we're going to go over some word problems. Me: What the hell else do you have back there? A magical pen that writes book reports by itself? Some kind of automatic social studies worksheet that...that fills itself out? What the hell is going on? Teacher: If a farmer farms five acres of land a day-- Me: So that's it, then. The past three years have been a total farce. All this time I've been thinking, "Well, this is pretty hard and frustrating but I guess these are useful skills to have." Meanwhile, there was a whole bin of these things in your desk. We could have jumped straight to graphing. Unless, of course, there's some kind of graphing calculator! Teacher: There is. You get one in ninth grade. Me: Is this...Am I on TV? Is this a prank show? Teacher: No.

It was on the table when I got here," Matt said in his defense. Josh eyed the open [Cosmo] magazine. "You don't already know how to satisfy your boyfriends in bed?" Matt ignored this. "Did either of you know there's ninety-nine ways to give a blow job? That's ninety-nine nights of blow jobs." "Look at you with the math skills," Josh said. Matt flipped him off while Ty flipped the page. "'How to Give Your Hoo-Ha a Spa Day.' Huh," he said. "I didn't know a woman's hoo-ha needed a spa day.

You can be a rich person alone. You can be a smart person alone. But you cannot be a complete person alone. For that you must be part of, and rooted in, an olive grove. This truth was once beautifully conveyed by Rabbi Harold S. Kushner in his interpretation of a scene from Gabriel García Márquez’s classic novel One Hundred Years of Solitude: Márquez tells of a village where people were afflicted with a strange plague of forgetfulness, a kind of contagious amnesia. Starting with the oldest inhabitants and working its way through the population, the plague causes people to forget the names of even the most common everyday objects. One young man, still unaffected, tries to limit the damage by putting labels on everything. “This is a table,” “This is a window,” “This is a cow; it has to be milked every morning.” And at the entrance to the town, on the main road, he puts up two large signs. One reads “The name of our village is Macondo,” and the larger one reads “God exists.” The message I get from that story is that we can, and probably will, forget most of what we have learned in life—the math, the history, the chemical formulas, the address and phone number of the first house we lived in when we got married—and all that forgetting will do us no harm. But if we forget whom we belong to, and if we forget that there is a God, something profoundly human in us will be lost.

Russell is reputed at a dinner party once to have said, ‘Oh, it is useless talking about inconsistent things, from an inconsistent proposition you can prove anything you like.’ Well, it is very easy to show this by mathematical means. But, as usual, Russell was much cleverer than this. Somebody at the dinner table said, 'Oh, come on!’ He said, 'Well, name an inconsistent proposition,’ and the man said, 'Well, what shall we say, 2 = 1.’ 'All right,’ said Russell, 'what do you want me to prove?’ The man said, 'I want you to prove that you’re the pope.’ 'Why,’ said Russell, 'the pope and I are two, but two equals one, therefore the pope and I are one.

No one had ever told her this basic fact: not everyone got to be loved. It was like those stupid bell curves they'd had to study in math class. There was the big, swollen, happy middle, a whale lump full of blissful couples and families eating around a big dining room table and laughing. And then, at the tapered ends, there were the abnormal people, the weirdos and freaks, and zeros like her.

pretend you’re an electron and orbit a nearby table. As

As a reader, she was an omnivore, devouring science, math, history, plays, and poetry. Her bookshelves ran over, so her vanity table was a mixture of pink blush and Dorothy Parker, mascara and Montaigne. Her armoire held Horace and high heels, stockings and Steinbeck. Her love of books and her love for me imbued my being like the amber scent of Shalimar she dabbed behind our ears.

It was on the table when I got here," Matt said in his defense. Josh eyed the open magazine. "You don't already know how to satisfy your boyfriends in bed?" Matt ignored this. "Did either of you know there's ninety-nine ways to give a blow job? That's ninety-nine nights of blow jobs." "Look at you with the math skills," Josh said. Matt flipped him off while Ty flipped the page. "'How to Give Your Hoo-Ha a Spa Day.' Huh," he said. "I didn't know a woman's hoo-ha needed a spa day.

My prolonged study of these photographs led me to appreciate the importance of preserving certain moments for prosperity, and as time moved forwards I also came to see what a powerful influence these framed scenes exerted over us as we went about our daily lives. To watch my uncle pose my brother a maths problem, and at the same time to see him in a picture taken thirty-two years earlier; to watch my father scanning the newspaper and trying, with a half-smile, to catch the tail of a joke rippling across the crowded room, and at that very same moment to see a picture of him to me that my grandmother had framed and frozen these memories so that we could weave them into the present.When, in the tones ordinarily preserved for discussing the founding of a nation, my grandmother spoke of my grandfather who had died so young, and pointed at the frames on the tables and the walls, it seemed that she, like me, was pulled in two direction , wanting to get on with life but also longing to capture the moment of perfection, savouring the ordinary life but still honouring the ideal. But even as I pondered these dilemmas-if you plucked a special moment from life and framed it, were you defying death, decay and the passage of time, or were you submitting to them? - I grew very bored with them.

When you do the math and examine how much energy is produced per atomic union, you find that fusing anything to iron’s twenty-six protons costs energy. That means post-ferric fusion* does an energy-hungry star no good. Iron is the final peal of a star’s natural life.

But the “jobs of the future” do not need scientists who have memorized the periodic table. In fact, business leaders say they are looking for creative, independent problem solvers in every field, not just math and science. Yet in most schools, STEM subjects are taught as a series of memorized procedures and vocabulary words, when they are taught at all. In 2009, only 3% of high school graduates had any credits in an engineering course. (National Science Board, 2012) Technology is increasingly being relegated to using computers for Internet research and test taking.

What if everything about me is totally made up? What if I’m actually…I don’t know. A wanted fugitive in the States.” “Julia.” He reached across the table and grabbed her hand. “Nobody makes up being a high school math teacher.” “That’s why it’s the perfect disguise!” He shook his head. “Nobody.

It went exactly according to my plan. That is, until my period was a week late and I realized I ate an entire loaf of bread and seven sticks of string cheese while I sat at the kitchen table looking at the calendar and wishing I'd paid more attention to math in kindergarten because there was no f**king way I counted right.

No one had ever told her this basic fact: Not everyone gets to be loved. It was like those stupid bell curves they'd had to study in math class. There was the big, swollen, happy middle, a whale hump full of blissful couples and families eating around a big dining room table and laughing. And then, at the tapered ends, there where the abnormal people, the weirdo's and freaks and zero's like her.

Mr. Editor, we are bound to be the slaves of those who have power to destroy us. I am not speaking of Strawforth any more. I knew him at school. We played ping-pong at the Reynolds Club. He had a white buttocky face with a few moles, and fat curling thumbs that put a cheating spin on the ball. Clickety-clack over the green table. I don’t believe his I.Q. was so terribly high, though maybe it was, but he worked hard at his math and chemistry. While I was fiddling in the fields.

I wasn’t planning on eating with them. For one, carbs are my frenemy. Second, this is supposed to be a players’ bonding dinner and sitting at a table with six football players, listening to them discuss strategy and film, isn’t my idea of a good time. Especially when, out of the six, two are feuding quarterbacks, four are competing wide receivers, two have been in my panties, and only one remembers it. Math has never been my strong point and even I can figure out this word problem.   But hey, how could that possibly go wrong?

People fluent in two languages can lose either one after trauma, since first and second languages* draw on distinct neural circuits. Language deficits can even interfere with math. We seem to have a natural “number circuit” in the parietal lobe that handles comparisons and magnitudes—the basis of most arithmetic. But we learn some things (like the times tables) linguistically, by rote memorization. So if language goes kaput, so too will those linguistically based skills. More strikingly, some people who struggle to string even three words together can sing just fine.

Deacon met my glare with an impish grin. “Anyway, did you celebrate Valentine’s Day when you were slumming with the mortals?” I blinked. “Not really. Why?” Aiden snorted and then disappeared into one of the rooms. “Follow me,” Deacon said. “You’re going to love this. I just know it.” I followed him down the dimly-lit corridor that was sparsely decorated. We passed several closed doors and a spiral staircase. Deacon went through an archway and stopped, reaching along the wall. Light flooded the room. It was a typical sunroom, with floor-to-ceiling glass windows, wicker furniture, and colorful plants. Deacon stopped by a small potted plant sitting on a ceramic coffee table. It looked like a miniature pine tree that was missing several limbs. Half the needles were scattered in and around the pot. One red Christmas bulb hung from the very top branch, causing the tree to tilt to the right. “What do you think?” Deacon asked. “Um… well, that’s a really different Christmas tree, but I’m not sure what that has to do with Valentine’s Day.” “It’s sad,” Aiden said, strolling into the room. “It’s actually embarrassing to look at. What kind of tree is it, Deacon?” He beamed. “It’s called a Charlie Brown Christmas Tree.” Aiden rolled his eyes. “Deacon digs this thing out every year. The pine isn’t even real. And he leaves it up from Thanksgiving to Valentine’s Day. Which thank the gods is the day after tomorrow. That means he’ll be taking it down.” I ran my fingers over the plastic needles. “I’ve seen the cartoon.” Deacon sprayed something from an aerosol can. “It’s my MHT tree.” “MHT tree?” I questioned. “Mortal Holiday Tree,” Deacon explained, and smiled. “It covers the three major holidays. During Thanksgiving it gets a brown bulb, a green one for Christmas, and a red one for Valentine’s Day.” “What about New Year’s Eve?” He lowered his chin. “Now, is that really a holiday?” “The mortals think so.” I folded my arms. “But they’re wrong. The New Year is during the summer solstice,” Deacon said. “Their math is completely off, like most of their customs. For example, did you know that Valentine’s Day wasn’t actually about love until Geoffrey Chaucer did his whole courtly love thing in the High Middle Ages?” “You guys are so weird.” I grinned at the brothers. “That we are,” Aiden replied. “Come on, I’ll show you your room.” “Hey Alex,” Deacon called. “We’re making cookies tomorrow, since it’s Valentine’s Eve.” Making cookies on Valentine’s Eve? I didn’t even know if there was such a thing as Valentine’s Eve. I laughed as I followed Aiden out of the room. “You two really are opposites.” “I’m cooler!” Deacon yelled from his Mortal Holiday Tree room

Why this girl? Why had this girl crawled right under his skin and made an uncomfortable home there? Why did he want to make things good for her, to see her smile, to make her face and her voice make all those interesting shapes and noises? Why did he want to stay up late with her when he knew she should be sleeping, just to hear her talk about maths and politics and the state of the world? This was not Quentin. Quentin did not like skinny girls. He didn’t like serious girls. And he really hated bossy girls. Quentin loved curvy, fun, uncomplicated girls; girls who laughed at his jokes and took off their bras when they danced on tables. If they wore bras at all. Yet here he was, washing up and mopping and feeling like five kinds of an arsehole over hurting the feelings of some skinny, serious, bossy girl.

Aunt Maxie giggled. ‘What can he be thinking about so hard?’ ‘Best not to know,’ his mother said. She tsked. ‘One day that boy’ll go too far.’ ‘Something serious. Look at him. He can’t even hear us talking about him. What can it be?’ ‘Complex numbers,’ Garvie said, without taking his eyes off the table. ‘Oh.’ With a suspicious glance at her son, Garvie’s mother asked Aunt Maxie about the new locl convenience store, and they settled into a conversation about the scandalous rising prices of food. Garvie carried on thinking. a + bi, where i has the property i squared = -1. The product of a real number and an imaginary number. You don’t compute complex numbers, you rotate them. You move them into an imaginary dimension and the answer is an unexpected jolt from the blue. ‘Garvie? Garvie?’ He looked up at his aunt. ‘Alex is lying,’ he said.

Two mathematicians were having dinner. One was complaining: ‘The average person is a mathematical idiot. People cannot do arithmetic correctly, cannot balance a checkbook, cannot calculate a tip, cannot do percents, …’ The other mathematician disagreed: ‘You’re exaggerating. People know all the math they need to know.’ Later in the dinner the complainer went to the men’s room. The other mathematician beckoned the waitress to his table and said, ‘The next time you come past our table, I am going to stop you and ask you a question. No matter what I say, I want you to answer by saying “x squared.”‘ She agreed. When the other mathematician returned, his companion said, ‘I’m tired of your complaining. I’m going to stop the next person who passes our table and ask him or her an elementary calculus question, and I bet the person can solve it.’ Soon the waitress came by and he asked: ‘Excuse me, Miss, but can you tell me what the integral of 2x with respect to x is?’ The waitress replied: ‘x squared.’ The mathematician said, ‘See!’ His friend said, ‘Oh … I guess you were right.’ And the waitress said, ‘Plus a constant.

For things to change, somebody somewhere has to start acting differently. Maybe it’s you, maybe it’s your team. Picture that person (or people). Each has an emotional Elephant side and a rational Rider side. You’ve got to reach both. And you’ve also got to clear the way for them to succeed. In short, you must do three things: → DIRECT the Rider FOLLOW THE BRIGHT SPOTS. Investigate what’s working and clone it. [Jerry Sternin in Vietnam, solutions-focused therapy] SCRIPT THE CRITICAL MOVES. Don’t think big picture, think in terms of specific behaviors. [1% milk, four rules at the Brazilian railroad] POINT TO THE DESTINATION. Change is easier when you know where you’re going and why it’s worth it. [“You’ll be third graders soon,” “No dry holes” at BP] → MOTIVATE the Elephant FIND THE FEELING. Knowing something isn’t enough to cause change. Make people feel something. [Piling gloves on the table, the chemotherapy video game, Robyn Waters’s demos at Target] SHRINK THE CHANGE. Break down the change until it no longer spooks the Elephant. [The 5-Minute Room Rescue, procurement reform] GROW YOUR PEOPLE. Cultivate a sense of identity and instill the growth mindset. [Brasilata’s “inventors,” junior-high math kids’ turnaround] → SHAPE the Path TWEAK THE ENVIRONMENT. When the situation changes, the behavior changes. So change the situation. [Throwing out the phone system at Rackspace, 1-Click ordering, simplifying the online time sheet] BUILD HABITS. When behavior is habitual, it’s “free”—it doesn’t tax the Rider. Look for ways to encourage habits. [Setting “action triggers,” eating two bowls of soup while dieting, using checklists] RALLY THE HERD.

What Cantor's Diagonal Proof does is generate just such a number, which let's call R. The proof is both ingenious and beautiful-a total confirmation of art's compresence in pure math. First, have another look at the above table. We can let the integral value of R be whatever X we want; it doesn't matter. But now look at the table's very first row. We're going to make sure R's first post-decimal digit, a, is a different number from the table's a1. It's easy to do this even though we don't know what particular number a1 is: let's specify that a=(a1-1) unless a1 happens to be 0, in which case a=9. Now look at the table's second row, because we're going to do the same thing for R's second digit b: b=(b2-1), or b=9 if b2=0. This is how it works. We use the same procedure for R's third digit c and the table's c3, for d and d4, for e and e5, and so on, ad inf. Even though we can't really construct the whole R (just as we can't really finish the whole infinite table), we can still see that this real number R=X.abcdefhi... is going to be demonstrably different from every real number in the table. It will differ from the table's 1st Real in its first post-decimal digit, from the 2nd Real in its second digit, from the 3rd Real in its third digit,...and will, given the Diagonal Method here, differ from the table's Nth Real in its nth digit. Ergo R is not-cannot be-included in the above infinite table; ergo the infinite table is not exhaustive of all the real numbers; ergo (by the rules of reductio) the initial assumption is contradicted and the set of all real numbers is not denumerable, i.e. it's not 1-1 C-able with the set of integers. And since the set of all rational numbers is 1-1C-able with the integers, the set of all reals' cardinality has got to be greater than the set of all rationals' cardinality. Q.E.D.*

En honorant l'école à l'excès, c'est toi [l'élève excellent] que tu flattes en douce, tu te poses plus ou moins consciemment en élève idéal. Ce faisant, tu masques les innombrables paramètres qui nous font tellement inégaux dans l'acquisition du savoir : circonstances, entourage, pathologies, tempérament… Ah ! l'énigme du tempérament ! « Je dois tout à l'école de la République ! » Serait-ce que tu voudrais faire passer tes aptitudes pour des vertus ? (Les unes et les autres n'étant d'ailleurs pas incompatibles…) Réduire ta réussite à une question de volonté, de ténacité, de sacrifice, c'est ça que tu veux ? Il est vrai que tu fus un élève travailleur et persévérant, et que le mérite t'en revient, mais c'est, aussi, pour avoir joui très tôt de ton aptitude à comprendre, éprouvé dès tes premières conforntations au travail scolaire la joie immense d'avoir compris, et que l'effort portait en lui-même la promesse de cette joie ! À l'heure où je m'asseyais à ma table écrasé par la conviction de mon idiotie, tu t'installais à la tienne vibrant d'impatience, impatience de passer à autre chose aussi, car ce problème de math sur lequel je m'endormais tu l'expédiais, toi, en un tournemain. Nos devoirs, qui étaient les tremplins de ton esprit, étaient les sables mouvants où s'enlisait le mien. Ils te laissaient libre comme l'air, avec la satisfaction du devoir accompli, et moi hébété d'ignorance, maquillant un vague brouillon en copie définitive, à grand renfort de traits soigneusement tirés qui ne trompaient personne. À l'arrivée, tu étais le travailleur, j'étais le paresseux. C'était donc ça, la paresse ? Cet enlisement en soi-même ? Et le travail, qu'était-ce donc ? Comment s'y prenaient-ils, ceux qui travaillaient bien ? Où puisaient-ils cette force ? Ce fut l'énigme de mon enfance. L'effort, où je m'anéantissais, te fut d'entrée de jeu un gage d'épanouissement. Nous ignorions toi et moi qu'« il faut réussir pour comprendre », selon le mot si clair de Piaget, et que nous étions, toi comme moi, la vivante illustration de cet axiome. (p. 271-272)

Sitting with some of the other members of the Scholastic Decathlon team, quiet, studious Martha Cox heard snatches of the lunchtime poetry. Her ears instantly pricked up. "What's going on?" she asked, her eyes bright. Betty Hong closed her book and leaned close. "Taylor McKessie told me all about it," she whispered. Betty told Martha about next week's poetry-reading assembly and how Taylor was trying to help half the starting basketball team locate their muse. "That's totally fresh!" Martha cried. "Too bad I'm not in Ms Barrington's English class." Betty made a face. "You like poetry stuff? I thought you were into maths and science." "I like it all," Martha replied. "I love astronomy and hip-hop-" Betty rolled her eyes. "Not hip-hop again." "Word, girl," Martha replied. "You know I've been bustin' out kickin' rhymes for years. It helps me remember lessons, like last night's astronomy lecture." "No," Betty said. "You didn't make up a rap to that." "Just watch," Martha cried. Leaping out of her chair, she began to chant, freestyle: "At the centre of our system is the molten sun, A star that burns hot, Fahrenheit two billion and one. But the sun, he ain't alone in the heavenly sphere, He's got nine homeys in orbit, some far, some near. Old Mercury's crowding in 'bout as close as he can, Yo, Merc's a tiny planet who loves a tan.... Some kids around Martha heard her rap. They really got into it, jumping up from their tables to clap and dance. The beat was contagious. Martha started bustin' some moves herself. She kept the rap flowing, and more kids joined the party.... "Venus is next. She's a real hot planet, Shrouded by clouds, hot enough to melt granite. Earth is the third planet from the sun, Just enough light and heat to make living fun. Then comes Mars, a planet funky and red. Covered with sand, the place is pretty dead. Jupiter's huge! The largest planet of all! Saturn's big, too, but Uranus is small. So far away, the place is almost forgotten, Neptune's view of Earth is pretty rotten. And last but not least, Pluto's in a fog, Far away and named after Mickey's home dog. Yo, that's all the planets orbiting our sun, But the Milky Way galaxy is far from done!" When Martha finished her freestyle, hip-hop flow, the entire cafeteria burst into wild applause. Troy, Chad, Zeke, and Jason had been clapping and dancing, too. Now they joined in the whooping and hollering. "Whoa," said Chad. "Martha's awesome.

NICK [smiles at MARTHA. Then, to GEORGE, indicating a side table near the hall]: May I leave my drink here? GEORGE [as NICK exits without waiting for a reply]: Yeah . . . sure . . . why not? We've got half-filled glasses everywhere in the house, wherever Martha forgets she's left them...in the linen closet, on the edge of the bathtub....I even found one in the freezer, once. MARTHA [Amused in spite of herself]: You did not! GEORGE: Yes I did. MARTHA [ibid.]: You did not! GEORGE [Giving HONEY her brandy]: Yes I did. [To HONEY] Brandy doesn't give you a hangover? HONEY: I never mix. And then, I don't drink very much, either. GEORGE [Grimaces behind her back]: Oh...that's good. Your...your husband was telling me about the ...chromosomes. MARTHA [Ugly]: The What? GEORGE: The chromosomes, Martha...the genes, or whatever they are. [To HONEY] You've got quite a ...terrifying husband. HONEY [As if she's being joshed]: Ohhhhhhhhh.... GEORGE: No, really. He's quite terrifying, with his chromosomes, and all. MARTHA: He's in the Math Department. GEORGE: No, Martha...he's a biologist. MARTHA [Her voice rising]: He's in the Math Department! HONEY [Timidly]: Uh...biology. MARTHA [Unconvinced]: Are you sure? HONEY [With a little giggle]: Well, I ought to. [Then as an afterthought] Be. MARTHA [Grumpy]: I suppose so. I don't know who said he was in the Math Department. GEORGE: You did, Martha. MARTHA [By way of irritable explanation]: Well, I can't be expected to remember everything. I meet fifteen new teachers and their goddamn wives...present company outlawed, of course...[HONEY nods, smiles sillily]...and I'm supposed to remember everything. [Pause] So? He's a biologist. Good for him. Biology's even better. It's less...abstruse. GEORGE: Abstract. MARTHA: ABSTRUSE! In the sense of recondite. [Sticks her tongue out at GEORGE] Don't you tell me words. Biology's even better. It's...right at the meat of things. [NICK re-enters] You're right at the meat of things, baby. NICK [Taking his drink from the side table]: Oh? HONEY [With that giggle]: They thought you were in the Math Department. NICK: Well, maybe I ought to be. MARTHA: You stay right where you are...you stay right at the...meat of things. GEORGE: You're obsessed with that phrase, Martha....It's ugly. MARTHA [Ignoring GEORGE...to NICK]: You stay right there. [Laughs] Hell, you can take over the History Department just as easy from there as anywhere else. God knows, somebody's going to take over the History Department, some day, and it ain't going to be Georgie-boy, there...that's for sure. Are ya, swampy...are ya, Hunh? GEORGE: In my mind, Martha, you are buried in cement, right up to your neck. [MARTHA giggles] No...right up to your nose...that's much quieter.

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.

Through the judicious employment of symbols, diagrams, and calculations, mathematics enables us to acquire significant facts about extremely significant things (universal laws, even), not by first forging out into the cosmos with teams of scientists, but rather from the comforts and confines of coffee tables in our living rooms! p. 72

Problem Solving Toolbox • Draw a diagram or picture. • Act the problem out, step by step. • Make a systematic list, chart, or table. • Look for a pattern. • Simplify the problem. (Try it with smaller numbers.) • Restate the problem in another way, or look for a related problem. • Think about “Before” and “After” situations. • Work backwards. • Guess and check. (Try something to see if it works.)

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

…if there’s one thing that novelists love to talk about, it’s how to make things real when, obviously, they are not. This in turn leads naturally into something novelists like to talk about even more: the terrible struggle of writing itself. (My favourite line about writers: “Writers are people who find writing more difficult than other people.”) Now we’re really getting going. Metaphors rise from the table like disturbed lepidoptera. Writing a novel is like attempting to solve an extremely complicated maths equation, which seeks to represent reality, and through which you are trying to lead the public without them ever getting wind that said equation is, in fact, impossible to solve or that, actually, it might not represent reality at all. We are getting carried away. Deciding to write a novel is like visiting an obscure, half-forgotten and slowly-evaporating planet entirely comprised of swimming pools and deciding that what is needed is… yes, another swimming pool! But, for obscure reasons, a swimming pool that must be built single-handedly from scratch and then filled using only a syringe.

Memorizing multiplication tables may be a seminal school experience, among the few that kids today share with their grandparents. But a Stanford University professor says rapid-fire math drills are also the reason so many children fear and despise the subject.

IN THE SCHOOLS Memorizing multiplication tables may be a seminal school experience, among the few that kids today share with their grandparents. But a Stanford University professor says rapid-fire math drills are also the reason so many children fear and despise the subject. Moreover, the traditional approach to math instruction — memorization, timed testing and the pressure to speedily arrive at answers — may actually damage advanced-level skills by undermining the development of a deeper understanding about the ways numbers work. “There is a common and damaging misconception in mathematics — the idea that strong math students are fast math students,” says Jo Boaler, who teaches math education at the California university and has authored a new paper, “Fluency Without Fear.” In fact, many mathematicians are not speedy calculators, Boaler says. Laurent Schwartz, the French mathematician whose work is considered key to the theory of partial differential equations, wrote that as a student he often felt stupid because he was among the slowest math-thinkers in class.

After the publication of a report in 1967 by Bridget Plowden, an amateur educationalist, describing primary schooling, Britain’s education system had become an ideological battleground. Masked by a scattering of platitudes about improving schools, Plowden recommended the destruction of traditional education. Children, she wrote, should no longer sit in rows of desks but instead gather in groups around tables to encourage self-learning. She also recommended that the eleven-plus examination, a three-part test (English, maths and intelligence) taken in one day that irrevocably determined a child’s educational fate – either to blossom in a grammar school or be consigned to failure in a secondary modern school – should be abandoned. Grammar schools should be replaced by non-selective comprehensives that mixed children of all standards. With cross-party support, successive Labour and Conservative governments implemented her recommendations.

Forget it once. *** Knock, knock! Who's there? Accordion! Accordion who? Accordion to the TV, it's going to rain tomorrow. *** Yo momma so stupid she tried to commit suicide by jumping off a building but got lost on the way down. *** Teacher: Why is the Mississippi such an unusual river? Student: Because it has four eyes and can't see! *** Teacher: "Why are you on the floor?" Johnny: "Because you said to do this math problem without tables!" *** How do you make an elephant float? Take one elephant, two tons of ice cream, and one ton of soda. Blend. *** In

Of course he was there, a removed audience of my redemption songs from beyond the grave, the way Kafka and his father continued to shadow-box, long after they quit staring at each other at the dinner table.

For things to change, somebody somewhere has to start acting differently. Maybe it’s you, maybe it’s your team. Picture that person (or people). Each has an emotional Elephant side and a rational Rider side. You’ve got to reach both. And you’ve also got to clear the way for them to succeed. In short, you must do three things: → DIRECT the Rider FOLLOW THE BRIGHT SPOTS. Investigate what’s working and clone it. [Jerry Sternin in Vietnam, solutions-focused therapy] SCRIPT THE CRITICAL MOVES. Don’t think big picture, think in terms of specific behaviors. [1% milk, four rules at the Brazilian railroad] POINT TO THE DESTINATION. Change is easier when you know where you’re going and why it’s worth it. [“You’ll be third graders soon,” “No dry holes” at BP]               → MOTIVATE the Elephant FIND THE FEELING. Knowing something isn’t enough to cause change. Make people feel something. [Piling gloves on the table, the chemotherapy video game, Robyn Waters’s demos at Target] SHRINK THE CHANGE. Break down the change until it no longer spooks the Elephant. [The 5-Minute Room Rescue, procurement reform] GROW YOUR PEOPLE. Cultivate a sense of identity and instill the growth mindset. [Brasilata’s “inventors,” junior-high math kids’ turnaround]                             → SHAPE the Path TWEAK THE ENVIRONMENT. When the situation changes, the behavior changes. So change the situation. [Throwing out the phone system at Rackspace, 1-Click ordering, simplifying the online time sheet] BUILD HABITS. When behavior is habitual, it’s “free”—it doesn’t tax the Rider. Look for ways to encourage habits. [Setting “action triggers,” eating two bowls of soup while dieting, using checklists] RALLY THE HERD. Behavior is contagious. Help it spread. [“Fataki” in Tanzania, “free spaces” in hospitals, seeding the tip jar] ————— OVERCOMING OBSTACLES ————— Here we list twelve common problems that people encounter as they fight for change, along with some advice about overcoming them. (Note

France had recently switched to the metric system of measurement. This gave scientists a much-needed standardized system to measure and compare results, but it also required a whole new set of calculating tables. The sheer number of calculations was beyond what could be accomplished by all the mathematicians in France, so Riche established calculating 'factories' to manufacture logarithms the same way workers manufactured mercantile goods. Each factory employed between 60 and 80 human 'computers.' But they weren’t trained mathematicians; they were mostly out-of-work hairdressers who had found their skill at constructing elaborate pompadours for aristocrats much less in demand after so many former clients lost their heads at the height of the French Revolution. Riche had hit upon a rote system of compiling results based on a set of given values and formulas, and the workers just cranked out the answers in what must have been the world’s first mathematical assembly line. Babbage figured that if an army of untrained hairdressers could make the calculations, so could a computing 'engine.

Teacher: "Why are you on the floor?" Johnny: "Because you said to do this math problem without tables!

I’m smart, right? I should be able to come up with a solid plan as to how I can get back to the twenty-first century. The trouble is I’m lost without Wikipedia and Google. I know all sorts of things, of course, but none of it is useful: the periodic table of elements, how to factor a math equation with four different variables, the symbiotic relationship between the great white shark and the remora fish. Completely useless, random information. Even a year of advanced chemistry isn’t going to do me any good; it’s not like there’s a chapter in there about time travel. I get up off the bed and creep to the door and peek out. No one is around. I’ll just explore the house. Maybe there really is a phone hidden somewhere that will prove Emily is lying about 1815. Or maybe I’ll find a servant in some Old Navy jeans.

Mr. Max jumped up out of his chair. It fell behind him and crashed on the floor with a loud thud. “We’re leaving,” he said to Melissa. His chest heaved up and down like it couldn’t get enough air. “Put the cat down.” Melissa set PJ on the floor and stood. “Uncle Max,” she said, “I told you about PJ.” She put her hands on her head. “He really did help me with my math homework.” “Let’s calm down,” my mom said. “We can talk about this.” She didn’t take her eyes off Mr. Max. He looked around the table at all of us. “I thought it was just a story. You know, for fun.” He cleared his throat and said to Melissa, “I forbid you from coming here anymore. I have to talk to your father. Let’s go. Now.” Melissa put hands in the air. “These are my friends. Don’t do this.” She shrugged her shoulders at me.

I approached a small table at the far corner of the Sky Garden and saw Akemi sitting nearby, studying a math textbook. She wore a demure, long-sleeved, knee-length white lace dress, black patent leather Mary Jane shoes, and on the floor was her school backpack that said "ICS-Tokyo" and was adorned with pastel ribbons, bows, and lace.

packed in steamer trunks.” “Good. How many trunks?” She glanced at the nearby tables, which were empty. “A typical steamer trunk filled with hundred-dollar bills will hold about fifteen million dollars, and weigh about four hundred pounds.” “Okay . . . one in each hand, two people, that’s sixty million.” She ignored my math and said, “But there are also fifty-dollar bills, and twenties, so there are more than four trunks.” “How many?” “My grandfather said ten.” “Each weighing four hundred pounds?” “Yes. A twenty-dollar bill weighs the same as a hundred-dollar bill.” “Right. That’s four thousand pounds of steamer trunks.” “Give or take.” If I’d known this in Key West I would have gone to the gym. “How about the gold and jewels?” “The gold may be too heavy to take. But there are four valises of jewelry which we’ll take.” “Always room for jewelry. And how about the property deeds that you mentioned?” “That’s another steamer trunk.” I pointed out, “This could be a bit of a logistical problem. You know, getting the trunks out of the cave, onto a truck, then to the boat.” “Carlos has a plan.” “Well, thank God. Would you like another cup of coffee?” She stared at me. “We wouldn’t be doing this if we didn’t think we could do it.” “Right.” A pretty waitress cleared our plates and smiled at me. It was almost 8 A.M. and people from various tour groups were making their way toward the lobby. We stood and I left two CUCs on the table, and Sara said, “That’s three days’ pay.” “She worked hard.” “And she had a nice butt.” “Really?” The Yale group was already boarding and Sara and I got on the bus together, said good morning to José, Tad, Alison, Professor Nalebuff, and our travel mates as we made our way toward the rear and found a seat together. The efficient Tad did a head count and announced, “We’re all here.” Antonio hopped aboard and called out, “Buenos días!” Everyone returned the greeting so we could get moving. “We will have a beautiful day!” said Antonio. Sí, camarada. CHAPTER 20 The bus wound its way out of Havana and again I had the impression of a once vibrant city that was suffocating under the weight of a rotting corpse. Hemingway’s house, Finca Vigía, was a handsome Spanish Colonial located about fifteen kilometers from Havana,

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

The conviction lodged in her head, that American children learned nothing in elementary school, and it hardened when he told her that his teacher sometimes gave out homework coupons; if you got a homework coupon, then you could skip one day of homework. Circles, homework coupons, what foolishness would she next hear? And so she began to teach him mathematics—she called it “maths” and he called it “math” and so they agreed not to shorten the word. She could not think, now, of that summer without thinking of long division, of Dike’s brows furrowed in confusion as they sat side by side at the dining table, of her swings from bribing him to shouting at him. Okay, try it one more time and you can have ice cream. You’re not going to play unless you get them all right. Later, when he was older, he would say that he found mathematics easy because of her summer of torturing him. “You must mean summer of tutoring,” she would say in what became a familiar joke that, like comfort food, they would reach for from time to time.

Without moving apart, Zev moaned and whispered into Jonah’s mouth, “Damn, Blondie, you’re a great kisser.” Jonah moved his arms up to Zev’s back, wrapping the young man in his embrace and stroking his smooth, firm skin. “You’re not so bad yourself, Hassick. You been practicing this with someone without me knowing?” Zev snickered. “You jealous?” Jonah didn’t return the smile. He looked into Zev’s eyes and answered without any guile, “Yeah. I’m jealous of anyone who got to touch you.” Instead of looking freaked out, as Jonah had half expected, Zev remained completely calm. He gazed into Jonah’s eyes with such powerful emotion that Jonah’s heart raced and his breath hitched. “Unless you can manage being jealous of yourself, you don’t have to worry. Like I told you yesterday, I haven’t ever thought about anyone else—girls or guys—let alone touched anyone else. It’s just you, Blondie. It’s always been you.” Zev let his words sink in, then he reversed the tables on the discussion. “What about you? Been hiding out behind the bleachers sneaking kisses with cheerleaders?” Jonah snorted more than laughed. “Uh, Zev, I was teasing about the whole not-so-smart thing earlier, but now I’m thinking I may have been on to something. That hardness you feel against your stomach isn’t a banana. That’s me happy to see you, or feel you, in this case. And you’re a guy. With that background in place, we can add two and two together here and even someone with your limited math skills can come up with the correct answer. I’m gay. I’ve got no deep dark cheerleader secrets in my past.” Zev was amazed at how easily Jonah said the words. He admired how his friend so completely accepted this part of himself. No shame, no hesitation. Just a matter-of-fact statement. In that moment, Zev decided he’d take the same approach. He knew it’d shock his parents. Hell, it’d rock his whole community. But he was attracted to a man. He had a male mate. That meant he was gay. Zev Hassick was a gay shifter. The pack would just have to find a way to deal with that truth even though they’d always believed it to be impossible. “And in case you’re wondering,” Jonah continued, his hand still rubbing Zev’s back but now moving lower, skating over his ass, “I don’t have any deep dark football player secrets, either. I’ve had a crush on one guy for as long as I can remember and I kinda put all my eggs in that basket.” Zev took another kiss, slow, soft and sweet this time. “I better be the egg-basket guy in that story, Blondie, or the tickles are coming back in full force.

I sat at the kitchen table, next to their youngest son, eleven-year-old Amir, chirpy, polite and fluent in English, who was busy alternating between his maths homework and sketching the fascinations of a contemporary Iranian boy: luxury sports cars, the BMW roundel and masked gun-toting terrorists. ‘These are the speciality of Yazd,’ said Sara. For a moment I thought she was referring to her son’s artwork, but was relieved to find her presenting us with a plate of tiny decorated sweets and pastries.

He traced a groove in the melamine counter. "I had some of the best times sitting around your table, throwing out math problems for you to solve or talking hockey with Sanjay and your dad." He pointed to the dent. "Do you remember this?" Daisy put the pastries in the microwave and took down two mugs from the cupboard. "What is it?" "It's where I dropped a bowl of pakoras when you walked into the kitchen wearing a tight green dress that Layla had bought for you because she was dragging you to a school dance. You were sixteen, and you looked amazing. Your dad and Sanjay went crazy. Sanjay insisted you wear a winter jacket. Layla had to run interference. That was the day I realized you weren't a little girl anymore and I couldn't treat you like you were.

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

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

Come find us at lunch. We sit at the back table next to the biggest window.” She turns away without waiting for an answer, blond hair sweeping across her shoulders. Ezra watches them leave with a bemused expression, then turns to me. “I have a really strong feeling that on Wednesdays, they wear pink.” Ezra and I have most of the same classes that morning, except for right before lunch, when I head to AP calculus and Ezra goes to geometry. Math isn’t his strong suit. So I end up going to the cafeteria on my own. I make my way through the food line assuming that he’ll join me at any minute, but when I exit with a full tray, he’s still nowhere in sight.

We can mathematically prove the periodic table is a matrix, thus our reality is all made from maths. The Fibonacci sequence is interwoven into the basics of reality, thus everything is formulated from a central Source.

I've got two smart boys," she'd say. "Two mighty smart boys." .... "First thing you're going to do is memorize your times tables." .... I learned the times table. I just kept repeating them until they fixed themselves in my brain... Within days of learning my times table, math became so much easier that my test scores soared.... "I've decided you boys are watching too much television," she said one evening, snapping off the set in the middle of a program... "From now on, you boys can watch no more than three programs a week." .... Mother had already decided how we would spend our free time when we weren't watching television. "You boys are going to go to the library and check out books. You're going to read at least two books every week. At the end of each week you'll give me a report on what you read." .... Slowly the realization came that I was getting better in all my school subjects. I began looking forward to. my trips to the library. The staff got to know Curtis and me, offering suggestions on what we might like to read.... By reading so much, my vocabulary improved along with my comprehension. Soon I became the best student in math when we did story problems. .... The final week of fifth grade we had a long spelling bee in which Mrs. Williamson made us go through every spelling word we were supposed to have learned that year. As everyone expected, Bobby Farmer won the spelling bee. But to my surprise, the last word he spelled correctly to win was agriculture. I can spell that word, I thought with excitement. I had learned it just the day before from my library book. As the winner sat down, a thrill swept through me--a yearning to achieve--more powerful than ever before. "I can spell agriculture," I said to myself. "and I'll bet I can learn to spell any other word in the world." .... I can learn about flax or any subject through reading. It is like Mother says--if you can read, you can learn just about anything.... As I continued to read, my spelling, vocabulary, and comprehension improved, and my classes became much more interesting.

Double-entry accounting was popularized in Europe toward the end of the fifteenth century, and most scholars believe it set the table for the flowering of the Renaissance and the emergence of modern capitalism. What is far less well understood is the why. Why was something as dull as bookkeeping so integral to a complete cultural revolution in Europe? Over nearly seven centuries, “the books” have become something that, in our collective minds, we equate with truth itself—even if only subconsciously. When we doubt a candidate’s claims of wealth, we want to go to his bank records—his personal balance sheet. When a company wants to tap the public markets for capital, they have to open their books to prospective investors. To remain in the market, they need accountants to verify those books regularly. Well-maintained and clear accounting is sacrosanct. The ascendance of bookkeeping to a level equal to truth itself happened over many centuries, and began with the outright hostility European Christendom had to lending before double-entry booking came along. The ancients were pretty comfortable with debt. The Babylonians set the tone in the famous Code of Hammurabi, which offered rules for handling loans, debts, and repayments. The Judeo-Christian tradition, though, had a real ax to grind against the business of lending. “Thou shalt not lend upon usury to thy brother,” Deuteronomy 23:19–20 declares. “In thee have they taken gifts to shed blood; thou hast taken usury and increase, and thou hast greedily gained of thy neighbors by extortion, and hast forgotten me, saith the Lord God,” Ezekiel 22:12 states. As Christianity flourished, this deep anti-usury culture continued for more than a thousand years, a stance that coincided with the Dark Ages, when Europe, having lost the glories of ancient Greece and Rome, also lost nearly all comprehension of math. The only people who really needed the science of numbers were monks trying to figure out the correct dates for Easter.

Al-Khwarizmi fell into the taboo that humans refused to fall into throughout their history, not because of their stupidity, nor their lack of attention to the presence of a number here that has an impact, but because they preferred not to deal with it at all unless they fully understood it, they ignored it rather than building the world around them on a wrong frame of reference. So, you have to ask now what if we decided to change the zero and give it its value that we know for sure, which is the unknown. We do not know it, we do not understand it, and not knowing is better than building everything on the wrong frame of reference Any number multiplied by zero equals an unknown The sum of any number with zero equals an unknown The result of any number divided by zero equals an unknown The result of subtracting any number with zero equals an unknown Are you starting to feel the problem and see the size of the unknown that is inside our calculations and our whole life! Infiltrating it without knowing anything about it! The clear is clear, that zero is not only divisible, but also summation, subtraction, and multiplication, because it is unknown, and no matter how much we try to patch the tables to fit the calculations, the division keeps breaking our back and telling us, you are wrong. Despite all this, our strongest strength remains, our winning ball, which has never failed us, is the power of creative adaptation. We are not like viruses, we settle in an environment that we drain and then move to others, nor like animals, we go into an environment and adapt to it and adapt ourselves according to its capabilities. That is why when we hit zero, we got creative and innovated, and decided to change the law of the entire universe, made it a hypothetical effect inspired by our imagination, and built the world on this basis. And the crazy thing is that everything around us is working perfectly. And what is even crazier, is that if we decide to change the effect of zero, so that one multiplied by zero equals twenty, then everything around us will reset, and it will work perfectly as well. Even if we decide to change all the math tables, this universe will mutate to suit our thinking.

Stage 3: Consciously competent. The kid thinks, “I’ve studied really hard, I know my math, this test will be fine.” He’s right. We’re delighted when our kids get here. This is the dream, people. Stage 4: Unconsciously competent. Fast-forward twenty years, and that kid is now a parent. He’s been doing math for so long that he doesn’t even have to think about it anymore. He can’t really understand why his daughter is struggling so much with something that’s become like breathing to him. (Incidentally, this is why older kids often make better tutors than parents. They learned their times tables not so long ago themselves, so they remember all the steps it took before it really sunk in.) Kids might become unconsciously competent in some areas—like reading or tying their shoelaces—while they’re still living at home, but for the most part, you don’t need to worry about Stage 4 except to note when you yourself might be in it.

people fear sobriety because without booze, you’re forced to see Clockwork Orange style that you’re bad at relationships, and bad at vulnerability, and bad at honesty, and your rants about life’s injustices are generally not cute. and if you see all that you have to give up the dream that some brave soul is gonna show up and extend themselves to you even though your arms are crossed and your back is turned. you have to stop pretending and actually start earning your keep, it’s basic human math, you gotta bring something to the table, you can’t just show up empty-handed and expect to be fed.

I have confirmed from my many years of teaching abstract mathematics to art students that I am not the only one who prefers to use abstract ideas to illuminate concrete examples rather than the other way round. Many of these art students consider that they’re bad at math because they were bad at memorizing times tables, because they’re bad at mental arithmetic, and they can’t solve equations. But this doesn’t mean they’re bad at math—it just means they’re not very good at times tables, mental arithmetic and equations, an absolutely tiny part of mathematics that hardly counts as abstract at all. It turns out that they do not struggle nearly as much when we get to abstract things such as higher dimensional spaces, subtle notions of equivalence, and category theory structures. Their blockage on mental arithmetic becomes irrelevant.

But before she read the article in Popular Science she had never been intrigued by mathematics or even thought about the fact that the multiplication table was math. It was something she memorized one afternoon at school, and she never understood why the teacher kept going on about it for the whole year.

Yet, they don’t know anything about who I am really… like I’m not sure if I know who I am…! They just see what they see. I’m not sure if Ray understands me completely or not, so how are they going to, just looking at my profile photos on their computers clicking away. They just want to feel the inside of me, not get inside of me. (Yah- know.) So anyway, at lunch today. Jenny is somewhat okay, that I want to be with Ray… so she said, at the table smelling through her teeth. The stipulation she gave was only if we keep on nodding terms, like with all the other guys or even girls I am with. So that means that I can have a full-blown relationship, whether I find them attractive if they're popular, hot, or not. That I can only hook up with a girl or boy, yet not stay with them. It made no sense to me. At the time I didn’t get it. Just like I didn’t get it when I saw Maddie was wearing bunny slippers, and a holy bathrobe to school today. Looking like, she was ridden hard and put away wet. I giggled so hard in math class today when she walked into the room; I think I snorted loudly.

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

Math isn’t about memorizing. It’s about knowing, knowing the language.” She looked at a billboard advertising a pawnshop. A car sped past. “Teachers shouldn’t quiz kids on multiplication tables.” Numbers weren’t something to regurgitate. They were a way to communicate and describe what was happening in the world around them. “Memorizing defeats the whole purpose.

It’s maths, Poe, not luck,’ she said without a trace of irony. ‘Toast usually falls from the table and is almost always butter side up when it does. Unless there are outside factors involved, the spin rate is rarely fast enough for it to go through a full revolution before it reaches the ground. If tables were ten feet high, we would say that toast always seems to land butter side up.

The fact of zero He added nonstop: Did you know that zero was not used throughout human history! Until 781 A.D, when it was first embodied and used in arithmetic equations by the Arab scholar Al-Khwarizmi, the founder of algebra. Algorithms took their name from him, and they are algorithmic arithmetic equations that you have to follow as they are and you will inevitably get the result, the inevitable result. And before that, across tens and perhaps hundreds of thousands of years, humans refused to deal with zero. While the first reference to it was in the Sumerian civilization, where inscriptions were found three thousand years ago in Iraq, in which the Sumerians indicated the existence of something before the one, they refused to deal with it, define it and give it any value or effect, they refused to consider it a number. All these civilizations, some of which we are still unable to decipher many of their codes, such as the Pharaonic civilization that refused to deal with zero! We see them as smart enough to build the pyramids with their miraculous geometry and to calculate the orbits of stars and planets with extreme accuracy, but they are very stupid for not defining zero in a way that they can deal with, and use it in arithmetic operations, how strange this really is! But in fact, they did not ignore it, but gave it its true value, and refused to build their civilizations on an unknown and unknown illusion, and on a wrong arithmetical frame of reference. Throughout their history, humans have looked at zero as the unknown, they refused to define it and include it in their calculations and equations, not because it has no effect, but because its true effect is unknown, and remaining unknown is better than giving it a false effect. Like the wrong frame of reference, if you rely on it, you will inevitably get a wrong result, and you will fall into the inevitability of error, and if you ignore it, your chance of getting it right remains. Throughout their history, humans have preferred to ignore zero, not knowing its true impact, while we simply decided to deal with it, and even rely on it. Today we build all our ideas, our civilization, our software, mathematics, physics, everything, on the basis that 1 + 0 equals one, because we need to find the effect of zero so that our equations succeed, and our lives succeed with, but what if 1 + 0 equals infinity?! Why did we ignore the zero in summation, and did not ignore it in multiplication?! 1×0 equals zero, why not one? What is the reason? He answered himself: There is no inevitable reason, we are not forced. Humans have lived throughout their ages without zero, and it did not mean anything to them. Even when we were unable to devise any result that fits our theorems for the quotient of one by zero, then we admitted and said unknown, and ignored it, but we ignored the logic that a thousand pieces of evidence may not prove me right, and one proof that proves me wrong. Not doing our math tables in the case of division, blowing them up completely, and with that, we decided to go ahead and built everything on that foundation. We have separated the arithmetic tables in detail at our will, to fit our calculations, and somehow separate the whole universe around us to fit these tables, despite their obvious flaws. And if we decide that the result of one multiplied by zero is one instead of zero, and we reconstruct the whole world on this basis, what will happen? He answered himself: Nothing, we will also succeed, the world, our software, our thoughts, our dealings, and everything around us will be reset according to the new arithmetic tables. After a few hundred years, humans will no longer be able to understand that one multiplied by zero equals zero, but that it must be one because everything is built on this basis.

seen. It swirled around with a life of its own and was an even deeper and brilliant gold than the outside casing of the stone. Lu had always admired it. When she had asked him where it came from, he only smiled and said that one day she would find out for herself. Now, he wrapped her hand around the stone and told her to go play in the gardens. After she left, he had drifted off to sleep, never to wake up. That had been one year ago, and Lu had companionless since. Now, her loneliness was compounded by drudgery. Every moment of her day was planned out for her, scripted like a play. Her father believed that a strict schedule produced a disciplined mind, and unfortunately, her tutors agreed. Every morning at dawn, she was awakened for breakfast in the garden and was then whisked off to horseback riding lessons in the family woods. This wouldn’t have been so bad except that her horseback riding instructor was also her science tutor and demanded she recite the Periodic Table of Elements at least once during each ride. Promptly at nine, her morning lessons of math, English, and science began. At noon, she had a short lunch break taken in the sunroom.

The << method starts with the character <, which appears lower in Table 5.3 than the character +, which is the first and only character of the + method. Thus << will have lower precedence than +, and the expression will be evaluated by first invoking the + method, then the << method, as in 2 << (2 + 2). 2 + 2 is 4, by our math, and 2 << 4 yields 32.

Mathematics works only with computationally reducible systems. Axioms and deductive logic are intended to provide shortcuts, to give general results that can compress a problem and provide insight into its workings so that it can be solved without having to take on the tedious task of running things through step by step. For example, the math behind ballistics tables allows an artillery gunner to calculate where the shell will land before it is fired. By contrast, there is no precalculated table to consult to determine the best path through rush hour traffic.

Knowledge of a subject doesn’t necessarily mean you can do anything with it. That would require skill. Likewise, a student can commit something to memory with no knowledge whatsoever. A grade-schooler, for example, might be able to recite the multiplication table perfectly, but still be unable to solve simple math problems. Coming to know something implies the goal of being able to use the knowledge, while being aware of facts or figures does not. Of

Problem Solve by Making a Table

At this age children love to carry heavy things. That is physics. And setting the table with a chair, plate, fork, for each person? That is math.

No one had ever told her this basic fact: Not everyone got to be loved. It was like those stupid bell curves they had to study in math class. There was the big, swollen, happy middle, a whale hump full of blissful couples and families eating around a big dining room table and laughing. And then, at the tapered ends, there were the abnormal people. The weirdos and freaks and zeroes. Like her.