“Though the tone of Will You Be Alive 10 Years from Now is lighthearted and many of its puzzles and problems relevant, this book should be labeled: ‘For Experts Only.’”
Based on the difficulty of material, Will You Be Alive 10 Years from Now is not “popular mathematics.” Not for the faint of mathematical heart, Will You Be Alive 10 Years from Now is a probability workbook couched in the language of popular mathematics.
For this book to reach its target audience, that audience must be familiar with probability, probability’s mathematical notation, and have practice in solving probability problems and calculus. Some of the problems yield directly to analysis, while others are more quickly solved by Monte Carlo simulation. When a computer program is used the author provides Matlab pseudocode. Sometimes when a solution is presented, the solution is only for the specific instance of the specific problem where this reviewer would have preferred the author identify how to go about generalizing solutions to cover a wider range of cases.
Given those drawbacks, what makes this book different from (and perhaps better than) other probability workbooks is that it does not provide the same-old, same-old probability problems of typical workbooks such as picking M white balls from a jar of R white and Q black balls but instead provides a different and often more relevant set of problems pertaining to gambling, sports, medicine, and law.
The introduction is accessible to readers of all mathematical abilities. The first chapter is a historiography, of interest for its discussion of famous (dead) mathematicians taken from historical documents. The mathematics of probability goes back to the desire to know the odds for gambling. All gamblers have to know the odds, and the branch of mathematics we know today as probability was started by those early mathematician-gamblers.
The start of the analytical approach to gambling—that is, solution by exact formula rather than guesswork—began with Antoine Gombaud. Gombaud presented questions to Blaise de Pascal in the 17th century concerning games of chance, though Gerolamo Cardano may have been the first to write on the mathematics of games in the 16th century his book wasn’t published until much later.
Nahin adds an aside (In case anyone is actually keeping score) that Cardano claimed probability was driven by supernatural forces. Will You Be Alive 10 Years from Now includes several of the problems first posed 400 years ago.
The types of more modern problems in Will You Be Alive 10 Years from Now are wide ranging, from calculating the probability of accuracy in radio direction-finding, to the odds that a glass rod randomly broken into three pieces can form a triangle, to the average number of stops an elevator will make in travelling from the lobby to the fifth floor, to calculating gambling odds for dice, to calculating the odds in the Jewish children’s game of Dreidel.
Also presented are probability puzzles from various sports including football, darts, ping-pong and squash. Nahin notes the similarity (when there are more than two choices and more than one round) between getting a majority and winning a trophy. He calculates the probability of finding additional misprints by additional proofreadings, the probability that the chain will be broken in a chain letter, and yes, the probability that you will be alive ten years from now.
Despite this, Nahin’s writing is always clear and concise, though for one problem the lead-in is fanciful to the extreme, reading almost like a screenplay. The problem begins, “Shortly after his death in Biloxi, Mississippi, in a tragic bungee-jumping accident, the following preliminary movie workup was found in the papers of famed Hollywood director Irving Nutso . . . While it remains unclear if the film will ever be made, Nutso’s preliminary workup does present us with an interesting math problem.” The problem that follows is truly a gem of imagination, a movie workup that is also a math problem wrapped in an epidemic caused by unsanitary buttered popcorn dispensers.
Nahan to his credit also presents several medical probability problems in a more serious frame of mind. In one, the reader discovers that population size in drug trials has a significant impact on determining the efficacy of treatment. In another, the probability of false positives and false negatives determines whether or not even to give a medical diagnostic.
There is an exploration of the “telephone game” to determine the probability of a message arriving correctly when repeaters may be liars, which can be used as a model for noise in data communication. Nahin also provides problems relevant to product maintenance and warrantees. For example, given N toasters used concurrently with a given failure rate, when will the last toaster fail?
Of the solution the author says, “One of the curious things about how a collection of seemingly identical things fail is that it can take a very long time, relative to the average failure rate for an individual thing, for the very last failure to occur.” Nahin also provides a variation of this problem where instead of concurrent operation each toaster is used serially; a new toaster being used only after the previous one has failed.
A probability problem of immediate social relevance is in determining the odds that a police stop to check citizenship will turn up an illegal alien. Nahin simplifies the problem by mapping people into two different colored balls (citizen and not citizen), placing the balls into an urn and then pulling them out at random.
The problem in real-life is two-part. One, how many people do you have to stop at random before you actually find an illegal alien and two, how annoying will this be for everyone else? After showing how mathematics can aid rational decision-making, Nahin downplays the place of mathematics in politics, “Whether or not any of these numbers are ‘acceptable’ in the context of police stopping people at random to find undocumented aliens is not a question that can be answered in our analysis. Math gives us numbers but people have to make the decision.” To this reviewer that disclaimer sounds like wanting to have your cake and eat it, too.
The last problem in Will You Be Alive 10 Years from Now is a problem so well known it has its own Wikipedia entry, and remains an open challenge. Nahin claims, “If you solve it, fame is guaranteed”, though he adds that some mathematicians don’t believe it is a true probability problem. A clue to the problem’s nature may be gleaned from a poem provided by Nahan, authored by Danish scientist Piet Hein. Nahin concedes, “. . . what could be a better note than that on which to end a book of probability puzzles?”
A bit beyond perceptions reach
I sometimes believe I see
That life is two locked boxes, each
Containing the other’s key.
Final notes: This reviewer, having last worked probability problems more than 30 years ago, found much of the mathematics difficult to follow. What would have made Will You Be Alive 10 Years from Now a much more useful book for a wider audience would have been to provide tutorial material in an appendix.
Though the tone of Will You Be Alive 10 Years from Now is lighthearted and many of its puzzles and problems relevant, this book should be labeled: “For Experts Only.”