Our Days Are Numbered: How Mathematics Orders Our Lives

Our Days Are Numbered: How Mathematics Orders Our Lives

by Jason Brown
     
 

A revealing and entertaining look at the world, as viewed through mathematical eyeglasses.

From the moment our feet touch the floor in the morning until our head hits the pillow, numbers are everywhere. And yet most of us go through each day unaware of the mathematics that shapes our lives.

In fact, many people go through life fearing and avoiding mathematics,

…  See more details below

Overview

A revealing and entertaining look at the world, as viewed through mathematical eyeglasses.

From the moment our feet touch the floor in the morning until our head hits the pillow, numbers are everywhere. And yet most of us go through each day unaware of the mathematics that shapes our lives.

In fact, many people go through life fearing and avoiding mathematics, making choices that keep it at arm’s length or further. Even basic math — like arithmetic — can seem baffling.

In Our Days Are Numbered, Jason Brown leads the reader through a typical day, on a fascinating journey. He shows us the world through a mathematician's eyes and reveals the huge role that mathematics plays in our lives. It lies hidden within the electronics we use, the banking we do, and even the leisure activities we enjoy. Whether we’re putting a down payment on a new car, reading the financial pages, or listening to our favourite songs, math is behind it all.

At once entertaining and informative, Our Days Are Numbered covers an array of mathematic concepts and explores the hidden links between mathematics and everyday life. Brown reveals that a basic understanding of math can make us more creative in the way we approach the world.

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Editorial Reviews

From the Publisher
"Professor Brown's mathematical meanderings provide more than just entertainment. . . . Brown takes the mystery out of calculating interest on your money, converting Fahrenheit to Celsius and interpreting daily values on food labels. You'll enjoy numerous other examples of the fascinating use of numbers ranging from risk analysis to how GPS works. You can count on it."
— Dr. Joe Schwarcz

Product Details

ISBN-13:
9780771016974
Publisher:
McClelland & Stewart Ltd.
Publication date:
04/27/2010
Pages:
296
Product dimensions:
5.20(w) x 7.90(h) x 0.70(d)

Read an Excerpt

YOU BET!

Some probabilities are easy to determine. Tossing a fair coin is a 50—50 proposition: half the time it comes up heads and half the time it comes up tails. Many games of chance rely on the fact that each possible outcome is equally likely. In poker, each hand of five cards is equally likely to be dealt. In roulette, the ball is equally likely to drop into any one of the 38 pockets. When all outcomes are equally likely, the probability of any one outcome occurring is simply 1 divided by the number of possible outcomes.

The mathematics of such games is well understood. In all casino games the probability of winning is always less than the probability of losing, that is, of the house winning. The odds of winning are the probability of winning compared to losing, written with a colon instead of a division sign. The odds of losing are the reverse. Mathematically speaking, if my odds of winning are m:n then my chances of winning are m/(m+n) while my probability of losing is n/(m+n) (and so the odds of losing are n:m). So odds of 2:3 indicate that my chances of winning are only 2/(2+3)=2/5, or 40%, while my chances of losing are 3/5, or 60%.

Now the odds offered for winning are not the same as the odds for losing, though they would be in a fair game. Craps is a popular game in which one person, the “shooter,” rolls a pair of dice repeatedly. There are a variety of different outcomes to bet on. Let’s examine one of these: For rolling “craps,” that is, a 2, 3, or 12, on a single roll of the dice (but not the first opening roll of the dice), there is one way to roll 2 (namely ones on each of the two dice) and one way to roll a 12 (two sixes). There are two waysto roll a 3 (a 2 on the first die, a 1 on the second, or vice versa). So in total there are four ways to roll craps. Since there are 36 different, equally likely outcomes for rolling two dice (six choices for the first die and six for the second), the probability of rolling craps on a single roll of two dice is 4/36, which is 1/9, or about 11%. The probability of not rolling craps on a single roll of two dice is therefore 1—1/9=8/9, or about 89%. The ratio of not throwing craps to rolling craps is (8/9)/(9/1) = 8/9 × 9/1 = 8/1=8. (Remember that to divide by a fraction you invert and multiply.)

Thus the odds of not throwing a 2, 3, or 12 in a single roll are 8:1. In a fair game your payment if craps came up would be 8:1 as well, that is, for every dollar wagered, you would win $8. But what you will find typically in a casino is that, if you bet on craps coming up in a single roll of the dice, your winnings are 7:1, meaning that for every dollar you wagered you could win $7. Over the long term, repeatedly making the same bet, what you can expect to win is $7, 1/9th or about 11% of the time (when a 2, 3, or 12 does come up) and you can expect to lose $1, 8/9ths or about 89% of the time. Letting amounts we win be positive, and amounts we lose be negative, on average, I’d earn 7× 1/9 +(—1)× 8/9 = 7/9 — 8/9=—1/9 , which is about —0.11. (In mathematics, this calculation — adding up the winnings and losses multiplied by their respective probabilities — is called expectation.) In the long haul, I can expect to lose about 11 cents on each dollar bet. On any one $1 bet, I might lose the dollar or win $7, but over, say, 100 such $1 bets, I would expect to lose about $11.

It is this spread that keeps casinos in the black. On any individual bet, the casino might win or lose. The probability of this happening is not usually crucial to the casino; what is vital is the payouts that are paid for winning. Casinos make sure that on every type of bet, there is enough of a spread (that is, enough of a difference) between the odds of losing and the payout odds so that, in the end, they make money. That’s all there is to it.

Of course, the lower the payout odds are, compared with the odds of losing, the more money a casino would expect to make. So why don’t casinos give, say, 5:1 payouts for rolling craps? The key is that casinos want the odds to be in their favour, but only slightly, so that individuals will lose their money more slowly, and feel they have a chance at winning. If the payout odds are 5:1 instead of 7:1 for rolling craps, on average, I’d lose about 33 cents per each dollar bet, rather than 11 cents per bet. I’d run through my money faster, and get less enjoyment from gambling. And the gambling establishments want me to keep coming back.

Is there a way to beat the house? In reality, no. The only way not to lose is not to play!

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Meet the Author

Jason I. Brown is a professor of mathematics in the Department of Mathematics and Statistics at Dalhousie University, and a former vice-president of the Canadian Mathematical Society. His mathematical research decoded the famous opening chord of The Beatles’s “A Hard Day’s Night,” and this discovery was featured in the news media throughout North America. He lives in Halifax.

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