If you study math enough, something happens to the way you think and the way to interpret the world around you. When I’m explaining this to students, I use the metaphor that learning math gives you an additional sense. I was very startled and pleased to learn who else had this thought. Charles Darwin, the discoverer of evolution, had the following thought in a letter:
“In after year I have deeply regretted that I did not proceed far enough at least to understand something of the great leading principles of mathematics, for men thus endowed seem to have an extra sense.”
Darwin’s observation suggests that my thought that math is like an added sense is not mere whimsy. In Starman Jones, one of Robert Heinlein’s young adult novels, the main character manages to get a position on a starship with falsified records. When he gets caught, he asks his superior what gave him away. This is the superior’s reply:
“Jones, I deal in figures and my mind can no more help manipulating them for all the information they contain than I can help breathing. This record says you went to space a year before your uncle retired – I remember what year that was. But you told me that your uncle had trained you at home and your performance bore out that statement. Two sets of alleged facts were contradictory; need I add that I was already fairly sure of the truth?”
While many things are not quantified or governed by logic, many things are. Training and practice in mathematics develop your ability to notice logical contradictions and to literally notice when things don’t add up.
In the most recent provincial election here in Ontario, candidate Tim Hudak had a central goal of creating 1,000,000 jobs in the province over eight years. When his opponents said it was impossible, no one paid much attention. When economist after economist looked at the plan and said is was “riddled with errors” people began to have concerns. While there were many problems in the plan, the biggest error was confusing man-years of employment with jobs. Since the plan was for job creation over eight years, that meant that it over-estimated by eight fold the number of jobs created.
Hudak spent weeks trying to defend his plan, even after the big, simple error came to light. Tim Hudak is not a stupid man, but he is clearly unable to deal with simple mathematics. I don’t mean that he cannot do simple mathematics, rather he refuses to do simple mathematics when it leads somewhere he doesn’t like. Unlike Starman Jones fictional superior, Tim Hudak cannot manipulate the numbers in his own political plan for very simple information it obviously contains. A good place to wrap up this example is to note that he lost the election.
Wishful thinking is the enemy of prosperity and even survival. Learning math does not prevent wishful thinking, but it does make it harder and reduces its impact. Examples of dangerous wishful thinking appear in the design of the the Maginot Line, in several market bubbles from the famous tulip mania through the great depression in the 1930’s to the more recent collapse in 2008. Another wonderful example of wishful thinking is the cold fusion debacle in the late 1980s and early 1990s.
Wishful thinking requires refusing to consider, or even notice, contrary evidence. I was at CalTech, as a graduate student, during the cold fusion debacle. A team of physicists at CalTech looked at the data and generated a report. Their report started with a satellite photo of the campus where the cold fusion experiments were talking place. The presence of green plants near the building where the experiments were taking place was conclusive evidence that the cold fusion reaction could not possibly be producing neutrons at the rate reported. This means the cold-fusion experimenters were able to report a lethal radiation density without noticing all the living creatures around them, apparently unaffected by the radiation.
Its time to explain how the added sense that arises from mathematical study functions to help you avoid wishful thinking.
The best metaphor I can find the the “spidey sense” that the Marvel comic’s Spider Man(tm) has. It warns him by causing a tingling sensation when he is about to be attacked. Similarly, if your math sense is engaged, you get a sense that something is wrong when the logic or quantitative information available don’t support a plan or a proposed course of action.
The math sense is not as reliable as the spidey sense, but the more you use it and the more math you learn, the more reliable it gets. It also helps to make simple checks of figures, something that used to be called a back-of-the-envelope calculation.
Tim Hudak’s plan to get elected Premier of Ontario by creating a bunch of jobs was founded on, and foundered because of, simple errors in the supporting figures. Other political programs founded on faulty mathematics have gotten prime ministers and presidents elected and have resulted in economic and social problems of varying magnitude. Sometimes the errors are honest but more often the bad math is a smoke screen. Supply side economics, for example, didn’t produce a rising tide that lifted all boats, but it did put a bunch of money in the pockets of its wealthy supporters.
Occupy Math believes that if everyone kicks up their mathematical game a bit, then it will be harder to mess with them. This isn’t hard. You can check claims made by candidates during elections. The numbers might be right, they might be wrong, or they may be missing. You can read the contract for you new car or insurance policy – and insist on having confusing terms explained. You can estimate the cost of the `protection plan’ for your new cellphone or toaster when deciding if you want to pay for it. Most advertising and sales talks are based on fear and deception. Math gives you a tool to resist.
I hope I see you here again.
Department of Mathematics and Statistics
University of Guelph, Ontario, Canada