On Saturday in Brooks-Rogers Recital Hall, Ed Burger, professor of math, gave a lecture titled, “Monkeys, Mathematics, and Mischief: What are the lifelong lessons of education?” The talk, held during Family Days, was eventually closed due to overflow and broadcast in the Brooks-Rogers lobby, where attendees were able to watch the lecture on video.
Burger delivered the lecture as part of the selection process for Baylor University’s 2010 Robert Foster Cherry Award for Great Teaching, for which he stands as one of three finalists. The award, named in honor of Robert Foster Cherry, a 1929 Baylor graduate, is meant to distinguish professors who are outstanding in communicating in the classroom and has been a biennial tradition since 1991.
Burger aptly began his Saturday morning talk with a math lesson. He introduced the audience to the monkey theorem, asking, “If you have enough monkeys at typewriters and they’re just bashing away at the keys at random, and if you wait long enough, will one of them actually produce Hamlet?”
It’s a concept Burger introduces in the book Coincidences, Chaos and All That Math Jazz: Making Light of Weighty Issues, which he co-wrote with Michael Starbird of the University of Texas. Burger used the famous monkey theorem as a launching pad for his following discussion on why we teach and learn math, when the majority of the audience admitted to not remembering the “stuff” on their last math final.
“The real lessons are the patterns of thinking that emerge from learning math [that allow] humans to see our world and ideally ourselves through the lens of mathematical thinking,” Burger said. And while people don’t often encounter monkeys with typewriters attempting to recreate Shakespearian tragedies, Burger admitted that people certainly would be surprised if this theorem were to find the monkey theorem proven true; he defined surprise as “when our intuition runs counter to reality” or when expectations are not fulfilled. “A surprise is a moment when learning can occur,” he said, adding that as lifelong learners we should, whenever possible, put ourselves in a situation where we can be surprised.
Burger unpacked the monkey theorem in realistic terms. He compared the puzzle to rolling a fair die and continuing to roll until it lands on, for example, a five. As the probability of this event is one in six â€“ a positive number â€“ it is an achievable end. Similarly, Burger supposed that approximately 70 characters (capital and lower-case letters, numbers and punctuation) would be necessary to re-write Hamlet and explained that while the probability of achieving this end is extremely small, it is nonetheless a positive number.
But, as to the time this task would take, Burger admitted that a million monkeys, each randomly hitting keys on the keyboard at one keystroke per second, would take 10 to the 60th power years merely to produce the famous sentence, “To be, or not to be, that is the question.” Burger also underscored the math lesson within the riddle. “If you keep repeating an act, and there is a positive chance of a repeated action (hitting the appropriate keys to form Hamlet, for example) … over time you will definitely see it,” he said.
“Things look complex because they are,” he said, and suggested that in addition to seeking out surprises as opportunities for learning, one should not tackle difficult problems, but rather strive to create easier questions. Slowly, the easy questions will lead to answering larger and more complicated problems, he said.
“What we’ll see within that simplicity is tremendous structure,” Burger said, which will in turn make the more difficult problem seem not so difficult after all. “Forget about solving for x, but look at the world as a puzzle,” he said. “Invisible lessons are not just within the department of mathematics.”
For those who do study within the math department, he suggested they should stop and ask themselves, “What are the invisible lessons that our professors are teaching us?” One of these lessons, according to Burger, is the power of failing. He said that unfortunately, educators as a whole do not teach how to fail, and good failure consists of the opportunity to develop some insight.
And while the monkey theorem, despite the time required to fulfill it, can be proven to be true, Burger acknowledged that clearly not all theorems were built in a day, and that failure was key in the construction of any successful conjecture. “If one can learn something from a failed attempt, then I would deem it as good,” he said.
The Cherry Award winner will be announced in the spring of 2010 and will receive $200,000, as well as $25,000 for his home department. Each of the three finalists will present a lecture series at Baylor University this fall, as well as a Cherry Award Lecture on their home campuses. The award winner will teach in residence at Baylor University during either the fall of 2010 or the spring of 2011. According to Baylor University’s Web site, the Cherry Award is the single largest award given to an individual for exceptional teaching.