How Learning Some Basic Math Will Help You Look Smarter: A true Story (sorta)
Excerpted from Look Smart: How To Appear Intelligent (When You’re Not).
Let’s face it; before mathematics, everything we knew came from religious texts. It didn’t matter if you were Mayan, Muslim, or Manichean, you had a question? Open the scriptures. What should I wear? Scriptures. Who should I marry? Scriptures. Which hand should I wipe with? How should I genuflect? You get the picture. But at some point this began to change, and there emerged a new way of approaching the world: As Roger Bacon pointed out in a cheeky, almost heretical, way in the twelfth century: “The things of this world cannot be made known without a knowledge of mathematics.” Scribes everywhere put down their quills, rubbed their inky hands on their hair shirts, and said “Wait, what?” (Rather like Baby Boomers do today when Millennials point out that they can watch TV shows on their phones).
But it wasn’t just one medieval philosopher who got that math was important to looking smart. I asked my brainy friend Jeff about what looks intelligent, and one of the first answers he gave, as he changed out of his scrubs, was: “Use percentages. If something is common, use a number around 85%. If something is uncommon go with near 15%.” He scratched his egg-like head, and added, sounding more and more like a sage every second: “Try using small ranges with slightly unusual numbers like 12–16%. Don’t use “always” or “never”…this leaves you unprotected.”
“What, never?” I asked. He stopped to think, frowning. “No, never!”
Now Jeff might not be Roger Bacon, but he understands that data is a dish best served hard. If it’s soft it’s probably not cooked. Hard data is reliable, and it happens to be the realm of mathematics. But Bacon (the Roger kind) was a bit early for the Renaissance, when logic and reasoning really became trendy, and most of his colleagues were still mired in the Bible, like ants stuck in honey. But by the seventeenth century some of the Bible’s answers were looking seriously questionable, and the mathematical way of thinking — what became the Scientific Revolution — was really underway. Ants, everywhere, were beginning the slow process of extricating themselves from stickiness.
Now that we were off to the races, another quick-witted Brit (where have they all gone?), Sir Isaac Newton, wrote a super-brainy book called The Mathematical Principles of Natural Philosophy. Although I personally found it a bit hard to read, it was apparently the cornerstone of this new mathematical way of thinking, and was key in producing a shift in what was generally considered “knowledge,” from God’s word to logic, reason, and…yes, Mathematics.
The point of this little foray into history is mostly to show you how erudite I am. And how I rock at Google. But I also want to highlight math’s role in our epic struggle to appear intelligent. To be honest, back in medieval times, I would probably have remained one of the ants in honey, scribbling away, day-in, day-out, in isolation, with ink-black fingers, in some dark granite tower in Florence (though this might have been mitigated by some nice rigatoni or perhaps homemade gnocchi for lunch).
This is because maths (as they call it in Jolly Olde England, apparently liking its plural form more) was always my weak point. In school I just didn’t really get it. By the age of 107 I was routinely being dragged into extra maths sessions with Mr. Moore, a stodgy old fart with a ram-rod back and an unsmiling demeanor. This was annoying and humiliating, but, having applied myself, I did eventually gain sufficient mastery of the subject to limp along until such time as I no longer needed any maths at all. This was at the age of about 15, when in my English education, I was allowed to abandon it at “O levels.” I did not use any maths until after college, when I sat the GREs to get into an American graduate school (which I did, having totally flunked the math section, but it was deemed unnecessary for a degree in Middle Eastern Studies — where they only practice equations, such as the enemy of my enemy=my friend.)
And those of us in the humanities have a somewhat jaundiced view of what intelligence and knowledge actually is. Most people like me mosey through an arts or humanities degree fuelled only by rhetoric — and end up as writers, or teachers, or worse…lawyers. As I’ve said already (chapters 1–9) intelligence is not easily quantifiable, so being an intelligent student in a humanities department is a case of persuading one’s teachers and peers of one’s intelligence — by rhetoric. What do humanities students actually do? Well, they read books, discuss them with other students and their professors, and essentially blurt out opinions about them. This is true in equal measure for English, History, Art History, Geography, or many any of the social sciences (many of which use statistics which is pretty math-y). If your rhetoric is of sufficient quality, you can persuade your professors to give you a good grade.
Take Psychology, for example. Beginning with its forefathers — people like Sigmund Freud — it existed only as a bunch of theories and ideas — rhetoric, nothing more. Why are we so f…d up about sex? There is no definitive answer; maybe it’s because culture has repressed the natural, monkey-like instinct that wants to have it all the time, everywhere (see Civilization and its Discontents). Maybe its because uncle Leopold fiddled with us in the coat closet that New Year’s Eve. Maybe its because we want to have sex with our fathers and kill our mothers (or is it the other way around? — see chapter five for more on classical mythology).
Only now, very, very recently is psychology beginning to come in from the cold and develop some serious mathematically grounded, scientifically solid ideas and facts. God forbid, however, that you look at English, the rhetorical discipline par excellence. What, exactly, is Hamlet’s problem? Do women and men write differently? What is a “text?” The mathematician looks up wearily from her desk. “Excuse me,” she says (probably in a real smart, German accent). “I have some equations to solve, I don’t have time for your stories, interesting though they might be.”
And that’s the difference. The English departments will talk you silly (probably in a French accent, that may be sexy, but just won’t get to the point), giving you idea after idea. But when the scientists and mathematicians get together they test each others’ theories, and see if they can replicate their results, and reduce the lip-flapping vagaries of language to the more concrete idiom of mathematics, thus actually establishing some new knowledge. Being a student in this environment then is much harder…you have to get things right, not just fill your papers with pompous, sententious guff that sounds pretty!
So, to explain the title of this chapter, this is why you should master some basic mathematical operations and terms. You don’t have to actually become a mathematician, I simply mean that in the quest to appear intelligent you should be seen to have a working knowledge of the mathematical universe, and include in your flowery rhetoric some hard numbers. They stand out in conversation like crunchy M&Ms in a bowl of mushy yoghurt, and really make your conversation pop. This, according to Jeff, will give you an eighty-five per cent chance of sounding smarter (it’s a fact).
But which mathematical operations and terms?
Mathematical operations and terms are different things. Let’s take operations first. Here’s a good example. When you are out on a date and, assuming you are paying, you need to avoid dithering over the tip. You could look like a real dunce if you either get it wrong, and leave the restaurant with the waitstaff hexing you under their breath while your date looks on, thinking that you are a skinflint. Or you could look similarly dopey if you spent hours figuring it out, instead of jotting it down quickly and casually as if your mind is a calculating machine operating on all cylinders — and of course that you are a sophisticated, restaurant-eating urbanite who knows his or her way around.
Now, in most places in the US we like to tip a solid twenty per cent (assuming the waiter didn’t spill soup in your lap or act like a dick, and that they made at least an honest effort to provide decent food). So the easiest way to figure out the tip, in my humble opinion, is to start with the simplest of procedures, figuring out ten percent — by moving the decimal point. Make sure it’s going in the right direction — usually leftwards unless you are an Arab, and if you are a Gulf Arab you should be moving it two places to the right — and then doubling it.
So let’s say your bill came to $121.00. That means you are eating in a medium-to-high priced joint in an average American city which is full of foody options. You had a modest Californian Cabernet. Maybe you shared the appetizer (a warm Alpaca cheese and Goji berry salad, with cheese from our friends at New Life Farm, with local micro supergreens, and a balsamic reduction), and the desert (a pumpkin Tiramisu with a ball of house-made raspberry sorbet). You both had the sustainably-farmed and formerly-endangered Bison steak with mashed parsnips and shallots from our other friends at Sunshine Acres Farm. Throw in an espresso for good luck, and that’s not a bad price to pay for a full stomach, a satisfied date and a minimal impact on the environment. So, ah yes, back to the Math… Moving the decimal in the right direction gives you 12.10; times two, is about $24.
So far all this information is relatively easy to follow, but if you find this too much for your tiny brain then, OK, resort to the lowest form of behavior, and use your phone. However, in the spirit of sly methods of appearing intelligent, don’t just work it out in plain view. Oh no, that would not help our cause in the least. Instead, being a practiced student of the appearance of intelligence, you pretend that you have just received a text, and consulting your phone with a quizzical “hmm…who is that…?” you deftly open your calculator app and work it out while appearing to actually respond to the imaginary text. Hey, it’s not deception if it’s utilized in the cause of love.
So much for a basic mathematical operations. Now I want to turn to a major mathematical term — which can be the foundation for many operations. That term is “exponential growth.” If, like me, you are or were a math failure, you might have bandied this term around, not being fully cognizant of its real meaning. And if you were lucky, you might have escaped without having been outed as a charlatan, and even considered smart for using the term. However, if you actually use it in the right context, well then you will enjoy bonus points (which quickly add up — exponentially in fact).
Most people think of exponential growth as meaning really, really fast, growth. This is how you will most often hear it. In the Princess Bride, for example, Inigo Montoya says, “You keep on using that word. I don’t think you know what it means.” But even if you do use it to emphasize the nature of fast growth, that’s not the end of the world, as long as you can back it up…just a little.
An example of this fast growth is, of course, compound interest. You might remember from Mary Poppins, another intellectual masterpiece, that “If you invest your tuppence, wisely in the bank; safe and sound/That tuppence wisely invested in the bank will compound.” It is good enough for now, then, to understand the compound interest sense of exponential, which is little more than the doubling effect. Double two, no big deal, but keep doubling the sum of the doubling and at some point it really explodes. In slightly more mathematical terms you could say that the exponential function arises whenever a quantity grows — or declines — at a rate proportional to its current value. In other words if you have one and double it by itself you get two. Keep doing this and the current value of the quantity doubles, so the growth rate speeds up.
Ok, I can smell brains frying at this point (possibly mine), so I should probably switch to explaining this term via a personal story.
Once, when I was much younger, I invented a game I called “Chess.” This was when I was living in Persia (as Iran used to be called — just giving you some free general knowledge). The Shah, as the ruler was known, loved the game — he felt it was a great way to relax, while simultaneously sharpening his strategic thinking. As it happened his thinking needed some help, he having been descended from a long line of in-bred royals. I spent many evenings eating pistachios, drinking hibiscus tea, and moving my hand-carved miniature figures around the mother-of-pearl-inlaid board in the palace. Some nights the Shah couldn’t make it, because one of his wives was such a good story-teller, he could not resist creeping off to her room to hear the next instalment — at least that’s what he told me he was doing (or was that the Sultan in Baghdad? I get them mixed up). This happened hundreds, possibly even thousands of times, so as you can imagine I became very good over the years at practicing my openings (although I invented the game I still found that I could not quite master all its elements, I guess that was the genius of my invention).
The problem with the Shah was that, like many rulers, and perhaps some you know, he was a giant baby. If he didn’t get his way in everything he would throw a man-baby tantrum, desperately looking for people to blame his stupidity on. This is a clear sign of low-intelligence (and weak moral character, by the way.) But, like a true sycophant, I assuaged his sensitive ego by avoiding placing his king in check — the means I had devised for ending this funny little game I invented.
A few years into this period of my life, I received transfer orders, and I had to leave the capital. Needless to say, I left my chess set in the hands of the Shah, as a gift and memento, and moved on. However, before I left, the Shah summoned me to the palace.
“Hassan,” he said — never able to remember my name. “I have enjoyed our games of Chess so much! I want to reward you in some way. Not too much, of course, for you are, after-all, an infidel, and I never managed to convert you. But name a reward within reason and I swear on my forefather’s and the Prophet’s beard (Peace be Upon Him) that I shall grant it.”
Clearly, although a hapless tyrant, he actually admired people who he knew deep down were smarter than him, and this allowed him to go all sentimental from time to time. I thought about his offer for a moment: It was a difficult situation. Much easier, I thought, if he had just given me a bag of gold or a gift certificate to the souk. Or perhaps one of his concubines. But asking me to name my own reward? Was it a trap?
Finally I thought of something that would be to my benefit more than a gift certificate, and which would seem like a modest proposal to him, and since I knew he was only firing on two cylinders upstairs, I figured he might go for it.
“All I ask, you worshipfulness, is one grain of rice for the first square of the chessboard; two for the next, four the next, eight, and so on, doubling every square.”
“Ha!” Ejaculated the Shah, rocking back on his pillow with mirth. “A modest proposal indeed! I thought you were going to be a greedy little infidel and ask for one of my concubines (Layla, perhaps?)” He winked.
“Certainly not, your majesty,” I responded. “I would have to be Majnun to ask for her!” (That’s an in-joke that most of you won’t understand).
“Or at least an outrageously large gift certificate to the souk!” he said. “I’ll get your request right now!”
So saying, he summoned his vizier, Mohsen, and ordered him to bring out some rice, explaining my request to him. Mohsen looked a little doubtful, as the Shah explained what I had asked for. He was a bright fellow, there was no doubt about it. After all, he really pulled the strings in the palace, even if he was a eunuch (you can’t be too careful around the harem). He clearly understood what exponential growth meant. “Really, you highness?” He said, with his thick Egyptian accent, raising his bushy eyebrows.
“Don’t stand there questioning me, man!” said the Shah, brushing him aside. “Go and get the rice! A small bag should do.” The Shah was clearly chuffed that he had gotten away with such a cheap gift. This had me chortling inside. I had not actually done the math — couldn’t do the math I should say — but I knew that the number would get very large, very quickly.
Mohsen beetled off with a couple of houseboys to fetch the rice. He knew that it would require more than a “small bag!” Sure enough, the wily old technocrat came back ten minutes later with several carts loaded with rice bags.
“What in the name of Allah are you doing, you buffoon?” Roared the Shah, nearly falling of his silk pillow. “We don’t need the entire store house!”
“Apologies, your magnificence,” said Mohsen, glaring at me. “But I wanted to make absolutely sure I did not have to make another trip to the store house. I think this should be enough.” Mohsen motioned to the boys, and they lugged a big bag from the cart to the chess board where the Shah and I sat. One of them slit the bag open, and the Sultan put in a soft, chubby hand.
And this is how it went: The first square had one grain. So far so good. The second had two. Ok, no problem here. The third had four. The fourth eight, the fifth 16 the sixth 32. So far things were looking entirely manageable for the sultan. He beamed and he continued to measure out handfuls. But by the eighth (128) it was taking him much longer to count out, and he was clearly getting a little annoyed. He might also have been able to envisage where this was headed. But the time he reached the twelfth he was trying his best to squeeze 2048 grains of rice onto one square and it was getting messy. The board was already covered. So now he gave up fitting them into the squares and just measured out huge heaping bowlfuls onto the board, which overflowed. By 20, things were out of control, the Shah was moaning, as 524, 288 grains were measured out by his assistants. Mohsen was visibly sweating, the sweat running off his brow and dripping on his silk doublet. His fingers were fiddling with his abacus as he tried to calculate exactly how deep the Shah was going to have to dig.
Now the Shah’s expression was that of a sick child having to chug capfuls of horrible medicine: “Do I have to drink it all! Its yukky?” His moans turned into wails, like the lamentations of a grieving mother, like a greedy, power-hungry tyrant losing his shirt. But he had sworn on the Prophet’s beard. Maybe he wasn’t afraid of his forefathers, but the beard of the Prophet was not something you took lightly! By the early twenties we were into the millions. By the thirties it was billions. By now the Shah was apoplectic. He was ranting and raging and breaking things as the servants poured bag after bag of rice onto the floor. All the house servants, slaves and low ranking military personnel were summoned to help in the count. Mohsen ordered the houseboys back to the storehouse to load the cart again, even he had drastically underestimated the amount of rice needed for this operation. And yet what could he do? The beard! The beard! Thank heavens for the beard, was all I could think, for that hairy old chin belonging to God’s final messenger was all that was standing between me and a good old-fashioned beheading.
To make a long story short, I had Mohsen and the palace staff (all one hundred of them by now) re-bag all the rice, load it up on carts, and supply me with the mules to transport it. Once this was done (by that time the Shah had stormed off to sulk in his bedroom), I made off as soon as I could, before the Shah decided to forget his oath to the cursed beard and relieve me of my head. As you have guessed by now, I made it out of town head intact, although I swore never to go near the palace or the capital again. The funny thing is that I don’t even eat rice. Too many carbs. Thankfully, lots of other people do. But that, my friends, is the sneaky secret of exponential growth — the doubling factor — and, in short, perhaps the best reason that you, I and the rest of us dullards, should have a passing knowledge of mathematics, especially if you are a shah.
This concludes my attempt to persuade you to get down with the benefits of mathematics. Perhaps the final word should go to our friend Roger Bacon, philosopher, Franciscan Friar, and known apparently to some by the strange moniker Doctor Mirabilis. Had the Shah read his (frankly unreadable) book, he might have avoided that awful experience with me all those years ago. And if you had read this book before going on that date and humiliating yourself over the check, you might have sealed the deal that night with your date.
“If,” said Roger, “in other sciences we should arrive at certainty without doubt and truth without error, it behoves us to place the foundations of knowledge in mathematics.”