Have you ever called a doctor's office or a company and had to punch in the answers to five questions before being put on hold? Have you then waited for several minutes to the accompaniment of irritating music, only to find that you need to answer the same five questions again? If so, you've been subjected to an elementary and malignant version of the mathematical spirit. And if the experience left you fuming, what have you done about it?
Our civilization has become increasingly mathematical. Math is involved in national defense, medical diagnoses, measurements of intelligence, credit cards, census sampling, managing stock portfolios, encryption, designing new cars -- the list could be extended indefinitely. There is every reason to think that the trend will continue for the foreseeable future.
Does the ordinary person, therefore, need a better understanding of mathematics? It doesn't take a Ph.D. in math to understand what the product scanner at the supermarket accomplishes, though many Ph.D.'s -- going way back in history -- may have contributed to its design. Because the mathematical content of many devices is located deep within their hardware and software, we may not realize that it is there. We can wade through our mathematical society reasonably comfortably, except perhaps at income-tax time.
It might seem, then, that the mathematical education we all received in school was sufficient. But in fact, we need a heightened awareness of how math has invaded our daily lives so that we can counteract some of the horrors that have resulted.
I am not calling for more of the sort of publicity that math usually gets -- about low average math grades in schools, major national or international competitions in math, or the solution of difficult problems that puzzled mathematicians for decades. Nor am I advocating more attention to math in novels and plays, along the lines of David Auburn's Proof, which is now being performed in New York. Publicity and dramatizations like those only confirm the public's long-held opinion that mathematicians are a bunch of brilliant but crazy nerds who do things that are impossible to understand. So why bother even trying?
What we need instead is an appreciation of how mathematical ideas affect society. Math is created by humans and exhibits human frailties. It consists of structures of thought. Such structures often lead to actions and, like physical or social structures, they can support us or constrain us.
Putting economic, social, or even physical theories into mathematical terms does not make them more objective. Thinking, say, of history and politics in terms of the numbers of soldiers killed or votes cast can program us to view the world in certain ways.
Mathematics is no longer merely an academic discipline. The methods and programs it suggests have become products to be marketed, sold, and applied. As such, they are subject to commercial, political, and legal pressures.
Consider, for example, the question of how to count the population ofthe United States for the census. Mathematics proposes a number of schemes, including simple counting and counting along with sampling. Each method has pluses and minuses. The ultimate choice is not a mathematical decision, but a political and legal one. Everyone agrees that simple counting results in the underrepresentation of certain groups, whose members are hard to count. Yet the Supreme Court unanimously ruled that a simple count is what will determine congressional reapportionments.
We have encouraged the spread of math in daily life by our enthusiastic and often uncritical acceptance of mathematical products. Now it is time for us to look at them critically and to humanize them.
What should you do when you are irritated by the treatment you receive when you call your doctor's office? Punch 0 and hope you can reach a warm body? Get another doctor? Hire a hacker and tell him to muck up the offending system? Urge Congress to pass a law requiring every software product to carry an 800 number at which users can register their complaints? (Now that mathematics is packaged, it should be on a par with the can of sardines that carries such a number.)What should you do if you believe strongly that the system Americans use to elect a president -- a piece of political math -- needs reform? Start an anti-electoral-college Web site? Organize a march on Washington?
The answers depend on the individual cases. But all the solutions begin with the same first step: Making people aware of how mathematics affects society. With that awareness, new choices and courses of action will turn out to be possible.
Philip J. Davis is an emeritus professor of applied mathematics at Brown University.