Are you innumerate?

A person who cannot read or write is said to be illiterate. Similarly, someone who is incapable of dealing with simple numerical ideas is referred to as innumerate. Innumeracy turns its victims into sitting ducks in a world of greedy commercialism, agressive marketing schemes and politicians who overwhelm voters with figures and statistics.

         Innumeracy is so common that marketing experts and salespeople seem to take it for granted. The car sales representatives that stalk innocent passersby at shopping malls in Mexico City are a case in point. Allow me to illustrate with a personal experience.

         One day I was at a Mexico City shopping mall, innocently passing by, when I was accosted by a car sales representative who offered me a financing scheme he thought I could not refuse. I decided (foolishly) to indulge him and sat down at his table. With a wide PR smile on his treacherous little face he then explained that his company´s financing plan was equivalent to placing a certain amount of money in the bank and paying the monthly instalments for the car off the interest.

         "So," he concluded triumphantly, "in the end you don´t really pay for the car!"

         There is a well known law of physics that establishes that in any and all physical processes energy is neither created nor destroyed, only transformed. This is the time-honored law of conservation of energy. A similar law --which we might call the law of conservation of money-- applies to commercial transactions. In any such transaction money is neither created nor destroyed; it merely flows from someone´s pocket to somebody else´s bank account, which means generally that no one makes money out of nothing. I´m sure the salesman was not aware that I was a physicist, and thus conversant with the not-really-too-arcane principle of monetary conservation (nothing in my appearance or demeanor gave away the fact), so I almost actually forgave him his trying  to bamboozle me.  I just gave him a knowing glance.

         "Oh, yeah?" quoth I. "Then why don´t I just take the car with me right away?"

         The guy looked confused. He blushed and chuckled uncomfortably.

         "I´m afraid that´s impossible, sir," he replied. It was obvious that the possibility of a prospective customer getting wise to the scam had not been contemplated in his training. I´m not even sure he was himself aware that his financing scheme, or at least his claim that you got the car for free, was pure baloney. This anecdote goes to prove that innumeracy is pervasive enough for these people to take it for granted.

         Here is another example of innumeracy. An acquaintance of mine (and a college graduate, mind you) is convinced that, if the average daily number of accidents in the Periférico is, say, ten --and if  there have already been ten accidents during a given day--, then he need not drive carefully for the rest of that day because he can´t possibly have an accident. Many years ago I sent this case to A.K. Dewdney, a columnist for Scientific American who wrote about innumeracy in the March 1990 issue of the magazine. In reply Dewdney told me about a businessman who always carried a bomb in his suitcase when flying because he had read that the odds for there being two bombs on the same plane were practically zero. (If you think this is a good idea, think again.) "The examples of math abuse," wrote Dewdney in November 1990, "are but symptoms of a general ignorance of mathematics --indeed, of science as a whole."

         People who imagine they "almost” hit the lotto because their ticket was just a few numbers away from the winning number display the same kind of misunderstanding of probability as my college-graduate innumerate friend. Can you tell what´s wrong with these examples of math abuse?