Mathematics Monkey Business
Despite his admitted early troubles with arithmetic, Dr. Edward Burger encourages everyone he meets to think like a mathematician.
Currently the Francis Christopher Oakley Third Century Professor of Mathematics at Williams College and president-elect of Southwestern University, Burger is one of the most renowned mathematics educators in the U.S. During his presentation in March for Angelo State’s West Texas Medical Associates Distinguished Lectureship in Science Honoring Dr. Roy E. Moon, Burger explained how math is filled with life lessons.
“It’s no wonder most people don’t like math,” Burger said, “even the most basic math exercises are called ‘problems.’ You look in a math book, and all you find are ‘problems.’”
“But just like every other discipline we can explore,” he added, “math offers a lens through which to see the world and, even better, to see ourselves. So, long after you’ve forgotten all the technical stuff and even the names of your instructors, your life will have changed because you now have a new lens through which to see things, analyze issues and think.”
Using the wit and personality that previously got him a job as a contract writer for Jay Leno in the 1980s, Burger iterated that the first life lesson to learn from mathematicians is to embrace surprises and even put yourself in a position to be surprised. But, his most important life lesson is, “when you are faced with a really great challenge, don’t do it.”
“In the frontiers of math and science, we do not face difficult challenges head on,” Burger said. “Instead, we create easier questions that allow for intuition, realization and ‘a-ha’ moments. Through that process, we can ask another question, and then another question. Soon, paradoxically, the original daunting challenge is whittled down to something that becomes common-sensical.”
“It’s no wonder most people don’t like math, …. You look in a math book, and all you find are ‘problems.’”
To illustrate that point, Burger proposed to prove a theorem utilizing the rather uncommon mathematical tool of monkeys.
“Suppose you have a whole bunch of monkeys in a room, and you give each monkey a typewriter or keyboard,” Burger said. “Then, just have the monkeys bash away on the keys. If we wait long enough, will one of the monkeys accidentally produce ‘Hamlet,’ the entire play, without any typographical errors? The answer is, in fact, ‘Yes.’”
Since he promised prior to his presentation to not confound the audience with any advanced mathematical equations, Burger used a common six-sided die to illustrate the laws of probability and prove that if a million monkeys simultaneously hit one random keystroke every second, eventually one of them would type “Hamlet”—though it would take, on average, the number of years equal to 10 to the 60th power (that is a 1 followed by 60 zeros!) just to get the phrase, “To be or not to be, that is the question.”
“This is a frivolous example, but one that actually serves a mathematical lesson,” Burger said. “The lesson is that if you continue to repeat something, and if there is even a tiny chance of a particular outcome—if you wait long enough, it will eventually happen.”
“Take an idea and push it to its absolute limits,” he added, “and all of a sudden, things that seemed surprising at first become totally intuitive. By doing that and by constantly being surprised, asking questions and extending ideas, you will embrace a mindset where you are always asking questions of yourself and others, and you will all of a sudden see worlds that otherwise you wouldn’t have seen.”
To make sure the audience took his message home after the lectureship, Burger also handed out copies of his latest book, The 5 Elements of Effective Thinking, which further illustrates his mathematics-based philosophies.
“Remember that just because schooling is over, that doesn’t mean our education is over,” Burger said. “It is now our job to figure out how to provoke thought, even if that provocation has to come from within. We are all life-long learners.”