What would Hippasus do?
This week I’d like to delve into the history of math, all the way back to the sixth centur B.C., and discuss the legend of a group of mathematicians and philosophers called the Pythagoreans, who can teach us a few important lessons about today’s world.
The Pythagoreans practiced what is called number mysticism. In fact, their motto was “God is Number”. They believed that by studying mathematics and philosophy, which were quite closely entwined at the time, they would discover the foundation for a moral life. By “number” the Pythagoreans meant whole numbers (one, two, three, etc.) and their ratios or fractions.
One day, when experimenting with their now-famous theorem about the relationship between the sides of right triangles, they discovered something that threatened to undermine their entire system of beliefs. When the number “one” is used for both ‘a’ and ‘b’ in the theorem’s equation (a^2 + b^2 = c^2) the resulting ‘c’ is the square root of two. It is relatively easy to prove that it is impossible to write root two as a ratio of whole numbers. The Pythagoreans found such a number to be unnatural, and were not willing to accept it after having built their whole system of belief on the assumption that all numbers are ratios of whole numbers.
Legend has it that the cult’s founder, Pythagoras, forbid anyone from releasing news of the discovery to the outside world.
Fortunately for all of us, one brave cult member, Hippasus, defied orders and spread the news of the discovery of what would come to be called an irrational number. Today, irrational numbers play an enormously important role in many branches of mathematics. If you’ve been reading my column for the last year and a half, you know mathematics affects our lives every day.
Actually though, this isn’t another one of those articles about how math is all around us all the time. I believe, particularly right now, that there is a bigger lesson we can learn from the story of the Pythagoreans, and especially from Hippasus.
The Pythagoreans had built a life for themselves based on a series of assumptions about the world around them—something I believe we all do. For instance, I grew up assuming that the police force will protect me, and that my wedding day will be something of a fairy tale, full of love and joy.
However, just as the Pythagoreans had the foundation of their beliefs tested, over the past few years my assumptions have been challenged as well. Moving from small-town, rural, Pennsylvania to Philadelphia, becoming immersed in the Jesuit mission of promoting social justice, and spending four months living abroad, I’ve had opportunities to observe and interact with a wide variety of people and also been exposed to a broad range of new experiences.
Over time, I’ve realized that many of my assumptions stem from places of privilege; by privilege, I mean advantages given to me by nature of who I am and the circumstances into which I was born. Looking back to the previous example of assumptions, it is easy to see now how my view of law enforcement has been shaped by the privilege of being born white, and how my vision of my wedding day has been molded by heterosexual and heteronormative privilege.
Although these past assumptions may be true with regard to my own experiences, I have now come to realize that for those who don’t share my particular set of privileges, these notions might be completely incorrect.
This idea then puts me at a crossroads, not unlike the one the Pythagoreans found themselves at some 2,500 years ago. I could easily choose the path of Pythagoras, and ignore the discovery that there are lives being affected by factors beyond the narrow sphere of my own privilege and continue to live under the assumptions it affords me.
My other choice is to take the path of Hippasus and confront my own biases, interacting with the world outside my privileged sphere. Perhaps I might even change this world, just as Hippasus changed forever the world of mathematics.
This crossroads is something that we all face every day. Each one of us has a set of assumptions based on our unique privileges, whether those stem from our race, religion, gender, sexuality, socioeconomic status, or other factors. Particularly in regard to recent acts of hate across our nation, our city, and even on our own campus, it is more imperative than ever that we realize when we are at an intersection between our comfort zones and the wider world. We must stop to consider the possible directions we may take.
Will we continue on, surrounded by the secure bubble of our comfort zone and old assumptions, or will we move beyond it and attack our own attitudes and fight the injustices we’ve identified?
