Dec 072018

There are Universes in our midst, but assumptions can prevent us from experiencing their extraordinary wisdom, beauty, and elegance.

What number would you multiply by itself to arrive at -1? Early mathematicians assumed such a number was useless. They referred to it in a derogatory way as imaginary.

A visual depiction of the Mandelbrot Set

In the 18th century, mathematicians relinquished that assumption and began to give structure and meaning to imaginary numbers. They used the letter “i ” to denote the square root of -1. But it wasn’t until the 1980s that “super computers” enabled Benoit Mandelbrot to peer into a yet undiscovered universe. Named for him, the Mandelbrot Set is one of the most famous images in all of Mathematics. You can expand the Mandelbrot Set billions of times and elemental structures emerge again and again. (Play the short video at, listen to the music and imagine yourself peering into eternity.) We are blind to this breathtaking universe until we surrender the assumption that the square root of -1 is meaningless.

At the time Benoit Mandelbrot was peering into infinity, I was teaching Mathematics at a private boarding school near Princeton, New Jersey. I lived in the dorm and was advisor to several freshmen.

One Spring evening, David, one of my advisees, came to my apartment looking sad and frightened. He was about to complete French 1 with an elderly, kindly member of the faculty…one whose demands were minimal. That afternoon, David discovered he would be learning French 2 from an excellent, very demanding teacher. “Mr. Breisch,” he whispered in tears, “you have to let me out of her class. I’m not prepared. I’ll fail!” My heart broke, but since David was one of my (favorite) algebra students, I knew him to be diligent, intelligent and determined. I was certain he would succeed. In one of the most heart-wrenching moments of my time as a teacher, I looked him in the eye, told him of my confidence and that I would not let him shy away from this challenge. I sent him back to his room alone and in tears. The following year, after each French test, David returned to my apartment and we would, together, celebrate his success.

I have lost track of David, but my hope is that, by surrendering assumptions about his inability, he began to peer into a breathtaking personal universe that was, until that moment, inaccessible to him.

Not long ago, I spoke with a young woman suffering from lupus, a disease that could end her life. Her mother, she told me, constantly lamented the myriad experiences her daughter would never enjoy—everything from a glass of wine to having children. The young woman explained that, while she sometimes finds the disease difficult, she had a deep appreciation for the life that resulted from it. She tried to find words that would enable her mother to witness the wholeness of her life rather than its perceived brokenness. One day, when her Mother once again began to focus on all her daughter would miss, this young woman turned to her and said, “Mom, what you refuse to see is all you have missed by not having lupus!”

It was a stunning moment. I felt as though this woman had given me new eyes. My old eyes, when in the presence of a person who may lack abilities, were blinded by assumptions of what they were missing in their lives. The eyes she gifted me, by surrendering those assumptions, began to see worlds that were always there, but to which I was blind—Universes in which others are not lacking in abilities; they are given capabilities, capacities and wisdom I can never have. By peering through their eyes, hearts and souls, I can experience wisdom, beauty, and elegance in Universes in which it is I who is less-than-able in very profound ways.