I recently found a pretty neat mathematical book entitled How not to be wrong: The power of mathematical thinking by Jordan Ellenberg. The author outlines real-life applications that show how mathematics makes them possible. This is a great STEM book that answers the question that many, many students ask, Why do I need to study math? How will I ever apply this stuff in real life in my future job?
Ellenberg states that not many people know what a logarithm is. So he says that the logarithm of a positive number N, called log N, is the number of digits it has! Well, not quite, but he goes on to explain that we can call the number of digits the “fake logarithm” or “flogarithm”. This is close to what the actual logarithm is. The flogarithm is a very slowly growing function, so that the flogarithm of a thousand is 4, the flogarithm of a million (a thousand times greater than a thousand) is 7, and the flogarithm of a billion is only 10.
Ellenberg safely reveals the true mathematical definition of Log N in a foot note at the bottom of the page, and I quote: It is that number x such that ex = N. Here e is Euler’s number whose value is about 2.71828….I say “e” and not “10” because the logarithm we mean to talk about is the natural logarithm, not the common or base-10 logarithm. The natural logarithm is the one you always use if you’re a mathematician or if you have e fingers.
So you will get Ellenberg’s dry humor like this throughout the book, but he will also reveal some really interesting mathematical ideas to you among some very witty “parables” on his journey to show the hidden beauty of the power of math and its powerful logic which you can use in life.
Another of many really neat math analyses in this book is a mathematical look at Powerball. He asks Is it wise to play Powerball? And immediately tells us that his father, a former president of the American Statistical Association, plays Powerball.
Ellenberg goes on to explain that a jackpot of $100 million looks enticing but let’s look at some mathematical facts. We will compute the expected value of a $2 ticket and your chances at winning the $100 million and other lower prizes:
1/175,000,000 chance of a $100 million jackpot
1/5,000,000 chance of a $1 million prize
1/650,000 chance of a $10,000 prize
1/19,000 chance of a $100 prize
1/12,000 chance of a different $100 prize
1/700 chance of a $7 prize
1/360 chance of a different $7 prize
1/110 chance of a $4 prize
1/55 chance of a different $4 prize
(Check Powerball’s website—these odds are there)
So now the expected amount you will win is:
100 million/175 million+1 million/5 million+10,000/650,000+100/19,000+100/12,000+7/700+7/360+4/110+4/55
That is just about $0.94. This says that your ticket is not even worth the $2 you spent for it.
He goes on to explain that as the jackpot goes up in other drawings in the future, like to $337 million; your $2 ticket is worth $2.29. But remember that when the jackpot gets higher, more people will play. Ellenberg than gives some best strategies for making money playing Powerball at the end of that discussion.
I highly recommend this book to math aficionados, engineers, students, gamblers (just kidding), and anyone who says Why do I need to know math?
Please let me know if you have read this book and what you think of it.