Provoking Thought

What do you think?  How do you think?  And can you think even better? I’ve spent nearly ten years focusing on these and related questions. The result is a recently-published book, co-authored with Michael Starbird from The University of Texas at Austin, entitled The 5 Elements of Effective Thinking (Princeton University Press, 2012).  It’s a tiny, practical book offering concrete action items and specific habits you can adopt to help generate new ideas, innovate, and maximize your creative abilities. While these elements of thinking derive from how mathematicians look at the world and make new discoveries, these same thinking techniques transcend math and can be applied to any discipline and any issue.

The five elements we introduce to provoke thinking are: (1) Challenge yourself to understand issues deeply rather than superficially.  Wherever your understanding currently lies, you can always go even deeper.  (2) Fail as a way to uncover hidden insights and to intentionally engineer new epiphanies. In fact, deliberately failing often leads to novel solutions faster than if you carefully tried to navigate around the minefield of missteps. (3) Create questions as a way of becoming an active participant in life’s adventures rather than a passive audience member.  By forcing yourself to create questions, you will get more out of discussions, lectures, concerts, exhibits, movies, and the like. Even if you don’t ask those questions, you’ll see hidden gems. (4) Realize that no idea resides in a vacuum. Every idea naturally came from some previous idea and will lead to another idea.  This basic realization helps us to understand ideas better because they no longer are a series of discrete objects to be memorized, but rather a string of pearls that logically follow one after the other to reveal the entire story. Moreover, the habit of seeing a new idea as a beginning—asking, “What comes next?” will allow you to generate new generalizations, extensions, or variations.

The last element is the meta-element of all education: Change.  The point of education is to transform lives, and in this context, we see that by embracing the mindset of the first four elements, you will be a different person—you’ll still be you, but just your best version of you (think: “You 2.0”). In addition to offering specific action items for each of these elements to allow you to make these strategies your own, we also connect them with the five classical elements of the ancient Greeks (Earth, Fire, Air, Water, and the Quintessential Element), so you’ll be able to remember these thought-provoking items.

If you want to read about how these ideas can be applied to the election, check out this blog.  If you you’re interested in how these relate to psychology, have a look at this blog. If you would like to see this focus on thinking at an institutional level, see this story, and if you want to read more about failure, check out this story or this one. Here at Williams, a number of mathematics professors are highlighting some or all of these techniques as part of their courses.  It will be exciting to see what they and their students think! If you try some of these techniques for yourself, I’d love to hear what results.  Feel free to share your stories with me.

Edward B. Burger is Francis Christopher Oakley Third Century Professor of Mathematics at Williams College.