Fractals in nature

When I returned to college in my mid-forties to finish earning my bachelor’s degree, I knew my biggest challenge wasn’t going to be my age. It was math. Never good at math, I dreaded the one additional class standing between me and that degree. So, I decided to take math the first semester. Get it out of the way.

However, on the first exam, everything seemed, as always, to just fly out of my head. When my professor handed me the graded exam, alongside the F at the top was a note to come to her office.

“What happened?” She asked. “You did well on the homework.”

“I clinched. That was my first exam in twenty-five years.”

During our discussion, where she learned my forte is English and writing, she told me I’d have a chance to make up for the failed grade later in the semester with a paper on a mathematician.

When the time came, the professor arbitrarily assigned each student a different mathematician. No two of us had the same person. Our mission was to explore the mathematician’s life and how their math contribution applied to our everyday life. My guy was one Benoit Mandelbrot.

Armed with enthusiasm and curiosity, I sifted through the offerings at Michigan State’s huge main library. About all I could find on Mandelbrot was a reference to fractals, a type of art based upon his formulas. Frustrated, I turned to the still-in-its infancy internet. A search gleaned a mere page about fractals.

On a sunny February Saturday, Martin accompanied me to the Math Library at MSU to continue my search. There, I found a few worn, tattered books written by Mandelbrot. Leafing through his math theories I managed to figure out he was all about chaos geometry. But, aside from the mathematical formulas, I found nothing else. I also couldn’t imagine what this contributed to my everyday life.

As we walked down the steps of the Math Library into the cold sunlight, I asked myself how someone who is supposedly such a great mathematician has nothing written about them. Suddenly, I stopped, did an about face, heading back up the steps.

“Where are you going?” Martin asked as I raced up to the door.

“He’s alive!” I cried over my shoulder.

Inside, I pulled one of his math books from the stacks, opening it to the copyright page. There it was _ B. 1924 followed by a dash, then nothing. No date of death.  An oh-so-brief notation said he worked for IBM. I knew there was an IBM facility at Johnson City, NY.

When I told my professor I’m going to call Mandelbrot, she said, “Don’t expect much. I hear he’s a snob. He probably won’t even take your call.”

Ignoring her discouraging remark, Monday afternoon I called information. But, dialing the number for IBM, I wondered if he was even still there. Maybe my teacher’s right and he won’t take my call. Maybe I won’t be able to get past an assistant or secretary or whoever is the gatekeeper. Maybe this is just lofty thinking. Maybe. Maybe. Maybe.

Now a receptionist greeted me. “IBM, how may I direct your call?” I gave her his name. She says he’s at the Ossining facility and tells me to hold while she connects me.

I can hear my heart beating in my ears. My mouth is suddenly dry. Then I hear the Polish accent.

“Dr. Mandelbrot here.”

I am now on the phone with one of the greatest minds of the twentieth century.

We’ve all been in situations during our lifetime where we think we can do something, but someone else is standing in the wings to discourage us. Whenever that happens in my life, I think of Mandelbrot and me.

Though there are many other instances in my life when I went my own way despite the naysayers, this is one which always stands out for me. Perhaps it’s because I was in a learning environment and teachers are supposed to encourage, not discourage. So, this is also always the very instance I remember when I need to catch myself from discouraging another. Especially someone very young who has yet to experience a Mandelbrot and me moment to add to their arsenal of self-confidence.

As aged adults we have many experiences, and hopefully wisdom, to pass on to younger generations. Having an older, wiser adult encouraging them to follow their dreams, to believe in their instincts is a key component to building self-confidence. A good dose of self-confidence leads to success. Does everything always work out the way we want or expect? No, sometimes, it’s even better.

After I got over my surprise at Mandelbrot answering his phone that day, I learned his secretary had a doctor’s appointment. What luck! He not only talked openly with me, but gave me his email address, asked for mine as well as my home address, where he sent me copies of numerous articles about his life and contributions to the world. Over the next couple of weeks I interviewed him for additional information and exchanged many emails. This man was no snob.

One of the other reasons I always think of Mandelbrot when someone discourages me or I’m tempted to discourage, is because he was an outlier. Shunned for decades by the mathematical establishment as wasting his time on chaos geometry, he went on with his work, believing in his theories. IBM obviously believed in them, too. As computers became faster and faster with calculating the data, the relevancy of his work became apparent. He eventually walked into a mathematical conference to a standing ovation.

So, what did he contribute to our everyday lives? Mandelbrot’s formulas are used in medicine, financial markets, geology, astronomy, engineering, graphics and, oh yes, art. It’s used in the maps you look at, in the prescription you took this morning, in the forecasts of the stock market, in the movie you watched last night. There is hardly a person on the planet who has not been touched by this man’s work, work he refused to be discouraged from doing.

As for me? After asking my permission, my professor read my A paper out loud to the class, citing it as the best paper she ever received from a student. She apologized for discouraging me from calling Mandelbrot. I finished the class with a respectable B average. More importantly, I learned not to discourage others from following their heart and I learned to dance more often to the beat of my own drum.