by Shane L. Larson
Fifty years ago, on 2 March 1962, a number was indelibly printed on history: 100. On a basketball court in Hershey, Pennsylvania the great Wilt Chamberlain posted 100 points in the Philadelphia Warriors’ 169-147 win over the New York Knicks. Only 4100 people were in attendance to witness a feat that has never been repeated. On 15 October 1997, on the sun-kissed salt flats of the Black Rock Desert in Nevada, Andy Green set the land-speed record of 763.035 miles per hour, the first supersonic land-speed every attained. On 26 February 2012, Joe Ayoob in an aircraft hangar at McClellan Air Force Base in California, threw a paper airplane 226 feet and 10 inches, shattering the old record of 207 feet 4 inches that had stood since 2003.
By certain standards, these numbers are huge –– enormous compared to the average number of points you or I could score in a Saturday morning pick-up game, or the speed you can hit in your Honda Civic screaming down I-80, or the distance we could throw an average airplane folded out of last month’s cell phone bill. These numbers are symbolic representations that we use to measure and advertise our acheievements. This use of numbers, this appellation to a quantification of our skills, reflects a deeply inbred desire to have an infallible and unassailable method by which two of anything can be compared and contrasted. Numbers are the ticket.
Numbers fill our lives. Some numbers are small: your age; the distance you have to travel to work; the number of pet iguanas in your house. Some numbers are larger: the price tag on a new car; the square footage of your home; the number of miles you must travel to enjoy afternoon tea with your great aunt Myra. Some numbers you may be aware of, but never pay attention to: the amount of electricity you use in your house each month; the current mileage on your ‘85 Yugo; the number of “friends” you have on Facebook. Some numbers aren’t actually used as numbers: your phone number; your Social Security number; your credit card number. Some numbers you may have never even thought about, but could figure out with a little help from the source of all knowledge (Google/Wikipedia): the average number of hairs on a human head; the total amount of fresh water stored in lakes in North America; the number of tire shops within 120 miles of Winnemuca, Nevada. Some numbers are extreme and challenge the boundaries of our comprehension: the distance to the center of the Milky Way galaxy; the number of atoms in the visible Universe; the number of microbes currently inhabiting planet Earth.
More than any other concept from science, numbers pervade and drive our everyday lives. It has not always been this way. As recently as the height of the Roman Empire, the numbers as you know them did not even exist in Western culture. Famously, the number “0” was an uncertain concept to the Greeks and Romans, who couldn’t decide if it was indeed a number. Think about how flabbergasting that thought is. Could you get by without having the concept of “0” around? Imagine you’re at a pre-Superbowl party, laughing it up about the Broncos’ season (more numbers) and someone with a plate of snacks walks up to you and asks, “How many haggis and head-cheese cracker stackers would you like?” Unless you’re a very strange person, the answer is probably “ZERO!” Fortunately for the Romans, I don’t think they had been exposed to haggis, head cheese, or the punishing life of being a Denver Broncos fan.
I have an interesting book on my shelf called The Penguin Dictionary of Curious and Interesting Numbers (http://amzn.com/0140261494). It goes through the numbers in order, starting at -1, and details the most fascinating and dizzying array of facts, history and uses of everyday numbers you might encounter. Did you know that if the sum of the digits of any whole number is divisible by 3, then the number is divisible by three? Try it! My favorite entry is for 51, which the book claims is the first “uninteresting” number, which is of course interesting! 51 is the first number that is simultaneously interesting and uninteresting! Perusing the book one encounters many ideas about numbers that your middle school math teacher tried to convince you were important. One of these ideas, which you might not know plays a vital role in your everyday life, are the concepts of factors and prime numbers.
Do you remember factors? Factors are the numbers you have to multiply together to get another number. It has been 104 years since the Cubs have won a World Series (the last time being in 1908, against the Detroit Tigers); two “factors” of 104 are 8 and 13: 104 = 8 x 13. You use factors everyday. You’re standing in Target looking at new dinnerware, and want settings for 12. A box comes with 4 place settings, so you buy 3 boxes: 12 = 4 x 3. A prime number is a number with only two factors: itself and the number 1. An excellent example is 7. There is no way to multiply two whole numbers together to get 7 other than 7 x 1.
In an informal poll of my non-nerd friends, it seems many remember learning about prime numbers, but haven’t thought much about them since somewhere around the 8th grade. Yet there are some people who have been thinking a lot about prime numbers. Do you know who they are? Hackers. That’s because prime numbers are a core part of computer security. Hackers spend lots of time trying to figure out easy ways to figure out large prime numbers so they can steal your online identity and then order $25,000 worth of lurid, bust-bursting romance novels on your Amazon account.
What do prime numbers have to do with computer security? Every time your computer hooks up to a network, or talks to a secure site on the web, it goes through a mutual identification procedure known as a “handshake.” It is much like the handshake you do when you greet someone new at your wake for the Denver Broncos’ season: you introduce yourselves, look each other in the eye and file away identifying characteristics that will help you later identify your new friend: mullet, blue eyes, diamond on front tooth, eyepatch. In the case of your computer, one form of security utilizes large numbers which have two prime factors –– that is to say, the only factors of the large number are both themselves prime numbers. These prime factors are used to encode data; you must know the prime numbers to decode the data.
For exceedingly large numbers, the prime factors are hard to find –– they can be found, but only by using computers to multiply all known primes together to see if they give you the big number. For instance, why don’t you try and figure out what the two prime factors of 552,277,573 are. Don’t worry, I’ll wait…
Tired of multiplying numbers together yet? Well, the prime factors were 6007 x 91,939 = 552,277,573. In computer security, finding the prime factors in an encryption algorithm can take a lot of time, more time than most hackers are willing to spend. Mathematics is protecting your online life, every hour of every day.
We could go on at great length about the stupefyingly enormous list of ways that numbers influence us every day, just as prime numbers do. This exercise would make one thing abundantly clear: numbers are a special kind of magic. More than any other idea, they serve to capture our impressions, our knowledge, and our perceptions of the world around us. They give you a special kind of power to express yourself, to understand the world around you, and to protect yourself against the malevolent forces of darkness (hackers, or swindlers who want you to bet on the Broncos in next year’s football pool). Own that power, and never surrender it.