by Brian Katz
I recently read a great book by Leonard Mlodinow (sometimes coauthor of Steven Hawking), called The Drunkard’s Walk: How Randomness Rules Our Lives about “the kinds of misconceptions of randomness that fuel many of the common fallacies” (p7). I think this book is excellent for several reasons and for several groups of readers.
Mathematics is revisionist history, perhaps more so than any other discipline. We blithely re-derive old theorems from new definitions, we present clean definitions as though they were born fully-formed, and we largely abhor any substantive historical perspective in the ways we structure our courses. Although Mlodinow’s book is far from a history of probability and statistics, he does an excellent job of treating ideas within their historical contexts in an honest, respectful, and authentic manner. Many of the big ideas that he presents are contextualized in the peculiar life-stories of their creators (and often their gambling habits), and many of those life stories are embedded in the the sets of cultural values that made them possible. I think this contextualized development is highly valuable for young teachers of probability and statistics who don’t have much context to call upon and for students who have inappropriate beliefs about mathematics as a discipline.
Mlodinow also reframes statistics as a human endeavor in search of understanding, claiming that “we all create our own view of the world and then employ it to filter and process our perceptions, extracting meaning from the ocean of data that washes over us in daily life” (ix). This allows him to tie psychological phenomena like the confirmation bias and the “Law of Small Numbers” to logical errors like the prosecutor’s fallacy. Mlodinow and others (like Michael Shermer of the Skeptic Society) claim that there are evolutionary reasons for these errors in the human perception of the world. Mlodinow’s goal is to help the ideas from our community trickle into the common psyche because he feels that “once we understand the nature of random process, we can alter the way we perceive the events that happen around us” (218). If this direction interests you, you should try to find the brilliant BBC video entitled “The Secret Life of Chaos” and the illuminating and entertaining article “Are Birds Smarter than Mathematicians?” in the Journal of Comparative Psychology by Herbranson and Schroeder.
If we, as humans, make these kinds of errors “naturally”, then the study of probability and statistics is the codification of common sense in a way that it can be verified and and validated. Mlodinow somehow strikes a subtle balance between intuitive presentation of new ideas and the technical language to articulate them appropriately. He is able to motivate the basic laws in an honest fashion that can lead to discussion of questions that range from subtle meaning to subtle computation. For example, he is able to set up the Monty Hall Dilemma in such as way that 18 of my 20 students found the correct solution convincing (as opposed to the usual tiny handful). Moreover, he provides an articulate and compelling distinction between probability and statistics that helped my students clarify the process of making meaning from data and all the components therein.
I was attracted to math by the beautiful, crystaline clarity of Algebra, and I’ll admit that I have avoided learning any applied mathematics or statistics. But this summer I read “The Drunkard’s Walk: How Randomness Rules Our Lives” by the fantastic Leonard Mlodinow, and this fall I used this book as the mathematical component in my first-year seminar. If you are ashamed by your lack of familiarity with statistics, oblivious to most of the history of mathematics, or frustrated by how hard it is to convince students that statistics is a discipline devoted to making meaning not busy-work, then perhaps you found my brief journey encouraging.
creative mathematics