You probably first met pi—the number used to calculate the circumference of a circle—when you were in school. If you aren’t mathematically inclined, you probably haven’t thought about it since then. But pi has practical applications for everyone as a real tool to better understand the universe and life itself. Without doing a lick of math.
In Visions of Infinity, mathematician Ian Stewart explains that it took about 2,000 years of great minds working at the problem of pi—moving from Euclidian geometry to algebraic calculations—to understand it as an irrational and transcendental number. In math terms, this means that pi cannot be represented by a fraction or an algebraic expression.
Numerically, pi is 3.14159, plus some. That added bit—the plus some—continues infinitely, a series of digits that never stop in a number sequence that doesn’t repeat, ever. In that infinite repetition lies pi’s greatest lesson.
On the surface, not knowing seems problematic
Computers have calculated pi to the trillions of digits. But pi isn’t really solved and doesn’t appear to be solvable. That makes it a fantastic philosophical tool, a reminder to both the mathematically and mystically inclined of all that cannot be finally understood despite great effort.
Pi is wonderful precisely because it can only ever be understood theoretically, never actually grasped in its entirety. The lack of solution can be liberating, a demonstration of a classic axiom: The wisest among us know only how little we know.
The greatest mathematical minds of the centuries made advances. Yet every step forward in comprehension and calculation also reveals the limitations of human knowledge. Pi shows that knowing, wholly, is an impossibility.
The more we know, the more apparent it is that there is much more to know. For each individual, and for humanity as a whole, there is always that added bit that simply can’t be figured out, no matter how much information or education we possess.
Existence transcends reason—it can’t be understood
Mysteries remain, always, and that can be a good thing. Like the digits of pi that have yet to be calculated and stretch on endlessly—“the plus some” that can’t be figured out—serves us. It is proof that calculations are necessarily imperfect and theoretical. Things we can’t imagine could still happen, for better and for worse.
Life and the universe, like pi, don’t make perfect sense. We may have a very good idea of what is likely to occur under a certain set of circumstances, applying all the information we have at a given time, and we may attempt to insure against all unknowns.
But mystery is a constant, a sliver containing infinite possibilities, in our math and in our lives. That is what pi demonstrates so certainly. Math is our guide. But not our master. It cannot provide all the answers.