I recently finished a book called The Number Mysteries (A Mathematical Odyssey Through Everyday Life) by Marcus du Sautoy. He's a professor of Mathematics at the University of Oxford among other things. Even though I'm not a big fan of math in general, I found it an interesting read.
In it's five chapters he discusses prime numbers, shapes that occur in the natural world and how they relate to numbers, mathematics in relation to gambling, how math is used in codes, and how math can be used to predict the future.
From his introduction (in the book) I'll give you a brief description of each chapter:
Chapter 1: The Curious Incident of the Never-Ending Primes - It takes, as its theme, the most basic object of mathematics: numbers. Du Sautoy introduces us to primes - the most important numbers in mathematics but also the most enigmatic. As he says, primes are indivisible numbers which are the building blocks of all other numbers - the hydrogen and oxygen of the world of mathematics.
Some interesting prime number facts - 1) The odds of having a 7-digit, prime number phone number is 1 in 15. The odds of having a 10-digit, prime number phone number is 1 in 22. You can enter your number here and see if you like. 2) At the time of printing, the largest prime number discovered was 12,978,189 digits. It was discovered by Edson Smith at UCLA on August 23rd, 2008. On offer is a prize of $150,000 if you can find a prime number with more than 100 million digits. $200,000 goes to the person who can find a prime number with more than a billion digits.
Chapter 2: The Story of the Elusive Shape - This chapter presents the A to Z of nature's wierd and wonderful shapes: from the six-pointed snowflake to the spiral of DNA, from the radial symmetry of a diamond to the complex shape of a leaf. Why are bubbles spherical? How does the body make such hugely complex shapes like the human lung? What shape is our universe? Math is at the heart of understanding how and why nature makes such a variety of shapes, and it gives us the power to create new shapes, as well as the ability to say where there are no more shapes to be discovered.
Why are bubbles spherical? Du Sautoy writes, take a piece of wire and bend it into the shape of a square. Dip it in bubble mixture and blow. Why isn't it a cube shaped bubble that comes out the other side? It's because nature is lazy and a sphere is nature's easiest shape. The bubble tries to find the shape that uses the least amount of energy, and that energy is proportional to the surface area.
Chapter 3: The Secret of the Winning Streak - Du Sautoy shows you how the mathematics of logic and probability can give you the edge when it comes to playing games. Whether you like playing with Monopoly money or gambling with real cash, mathematics is often the secret to coming out on top.
How math can help you win at Monopoly - Monopoly appears to be a pretty random game, but do you know what the most visited square on the board is? It's Jail. Why? Well, you could just throw the dice and find yourself visiting, or you might find that the dice takes you to the square directly opposite, where a policeman tells you to go to jail. You might even be unlucky enough to pick up one of the Chance or Community Chest cards that send you there. As a result players find themselves visiting the Jail square about three times more often than most other squares on the board.
Now that won't be much help to you because you can't "buy" jail. But, which squares do players end up on next most often? The answer would be Community Chest which is seven squares from Jail. The odds of rolling a seven are 6 in 36 of rolling a combination of 7 with two dice. Since you can't buy Community Chest either, the next two properties you can purchase are the two oranges ones (Tennessee Avenue and St. James Place) to either side. There's a 5 in 36 chance of rolling a total of 6. The same goes with rolling a total of 8. So those are the properties to buy and load up with hotels if you're lucky enough to get the chance to do so.
Chapter 4: The Case of the Uncrackable Code - Ever since people first learned to communicate they've been finding ever more fiendish ways to hide messages from their enemies. But codes aren't only for keeping things secret: they also make sure that information is communicated without errors. We can use mathematics to create ingenious ways to guarantee that the message that is received is the same as the message that was sent - which is vitally important in this age of electronic transactions.
I was going to talk a bit about secure transactions over the internet, but it's a bit too complicated to break down. Let's just say there's nothing to worry about transmitting sensitive information over the net. Part of cracking the code involves finding the two prime factors (numbers) for extremely huge numbers - in the hundreds of digits range. So confident were the mathematicians who invented the code that for many years they offered a $200,000 prize for the person who could find the two prime factors of a 617 digit number (which I won't bother typing out). If you tried cracking the code one prime number at a time, you'd need to work through more numbers than there are atoms in the universe before you got to them. Needless to say, the prize was never claimed and the offer eventually withdrawn.
Chapter 5: The Quest to Predict the Future - In this chapter du Sautoy explains how the equations of mathematics are the best fortune-tellers. They predict eclipses, explain why boomerangs come back, and ultimately tell us what the future holds for our planet.
One organization that definitely cares about the long run is the casino. Their profit depends on long-term probabilities. For every throw of the dice or spin of the roulette wheel, they rely on your failing to predict how the dice or ball will land. Well, in March of 2004 one Hungarian woman and two Serbian men used mathematics to make a killing in the London Ritz casino. Using a laser scanner hidden inside a mobile phone linked to a computer, they recorded the spin of the roulette wheel relative to the ball over two rotations. The computer worked out a region of six numbers within which it predicted the ball would fall. During the third rotation of the wheel, the gamblers placed their bets, thus increasing their chances of winning from 37:1 to 6:1. The first night they netted £100,000, the second £1.2 million. Despite being arrested they were eventually released. Legal teams determined they had done nothing to tamper with the wheel.
I have to say, I rather enjoyed the book. Though some of the mathematics discussed was beyond my ability of comprehension I found it a fascinating read. 2:1 says you will too.
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