"All truths are easy to understand..."

The scientist Galileo Galilei once said, "All truths are easy to understand once they are discovered; the point is to discover them."  The process of discovery requires, first and foremost, a certain level of intellectual curiosity.  To this end, another scientist, Max Planck, said, "Scientific discovery and scientific knowledge have been achieved only by those who have gone in pursuit of it without any practical purpose whatsoever in view."  In other words, at least according to Galileo and Planck, most major advances in science and technology have come when individuals seek to find new knowledge simply for the sake of learning new things. 

I have talked about Harvard Business School professor, Amy C. Edmondson in a number of previous blog posts.  She is perhaps best known for her work on the concept of psychological safety (see, for example, her most recent book entitled "The Fearless Organization").  What is less known about Dr. Edmondson is her early work as Chief Engineer for the architect and inventor Buckminster Fuller in the early 1980's.  Her first book, in fact, explained some of Fuller's contributions to the world of mathematics, architecture, and design called "A Fuller Explanation: The Synergetic Geometry of R. Buckminster Fuller" in "conventional language" that a lay person could understand.  On a whim, I checked her book out at the local public library and tried to read it.  To be honest, there was little in the book that I could understand, so I never finished it.

My point is this - and it's a point that I have made before on a number of occasions - we should read broadly outside our own individual specialties, if for no other reason than to exercise our brains and stretch the limits of our comprehension.  Imagine having the intellectual brainpower to not only understand a highly technical concept outside of your own discipline, but also to be able to write an entire book on the subject!  Most of us - including me - are a long way from being able to do that.  The important thing is that we continue to learn new things, even if outside our intellectual comfort zones.

With all of this in mind, I'd like to recommend a great book by the mathematician Leonard M. Wapner, called "The Pea and the Sun: A Mathematical Paradox".  Here's another book that I checked out from our public library that discusses another esoteric concept called the "Banach-Tarski Paradox".  Simply stated, the Banach-Tarski Paradox suggests that a solid ball can be broken up into as few as five pieces which can then be assembled back together again to form two equally sized solid balls!  The title of Wapner's book comes from a slightly different version of the Banach-Tarski Paradox that suggests that a small sphere, say a pea, can be cut into five different pieces and reassembled together to form a new, much larger sphere, say the size of the sun! 

It sounds really fantastic, and when I first learned of this paradox, my initial response was "Are you kidding me?!?!"  I won't spoil your fun and explain the paradox any further here.  Wapner does a great job explaining the paradox through brief sketches on the lives of several other famous mathematicians, including Georg Cantor, Kurt Gödel, Paul Cohen, and of course, Stefan Banach and Alfred Tarski.  Read the book and you will also find out about the so-called "Axiom of Choice" and Hilbert's Infinity Hotel.  The book can get heavy in parts, but I really enjoyed it, and I think you will too.

There is almost certain that I will never have an opportunity to use or even talk about the Banach-Tarski Paradox in my own line of work.  That's not the point.  Learning knowledge for knowledge's sake - that is what matters.  Even if you don't end up reading a book about making a sun out of the different pieces of a pea, please take the time to read something that you will likely never use in your professional life.  Just read to learn, and learn just for the sake of knowledge.  Trust me, you will be better for it.