Cantor's Corner by Eric Schulmiller

At opposite ends of this month of May (and spanning two Jewish months) are the holidays of Lag B’Omer and Shavuot – the Festival of Revelation. The former is a one-day respite from the anxious counting of days between Pesach and Shavuot, the early barley and late wheat harvest, the wandering in the desert and the revelation at Sinai. For a political view of the theme of counting, see this month’s social action column. But for now, I’d like to devote this month’s column to a look at Mandelbrot. No, not the delightfully almond-flavored Jewish version of biscotti! The incredibly influential Jewish mathematician, Benoit Mandelbrot (pronounced "Man-del-bro"). Born in 1924 in Warsaw to a Lithuanian Jewish family, his family moved to France in the 1930’s to escape the Nazi regime, and it was there that Benoit developed his historic contribution to the world of mathematics: fractal geometry. The key concept illustrated by the graphs of the equations developed by Mandelbrot (most famously known as the the “Mandelbrot Set”) is that they are self-similar on all scales. In other words, no matter how much you magnify a fractal, it always looks the same (or at least very similar).

As is often the case, an abstract mathematical principle can shed a surprising light on the deeper reality of our world. Perhaps this is why renowned 18th century Jewish scholar and leader known as the Vilna Gaon said, "To the degree that a person is lacking in the wisdom of mathematics they will lack one hundredfold in the wisdom of the Torah." Examples of fractal geometry abound in nature. Think of a tree, whose trunk and branches bare a startling similarity to the structure of veins on their leaves. Or to our own system of veins, arteries and capillaries, which are also strikingly self-similar on several levels of magnification. Snowflakes, rivers, sea-coasts, all provoke the same sense of awe at their fractal-like similarity at different viewpoints and distances.

The sages recognized that the Torah was also fractal in nature. Every day from Passover to Shavuot we study an excerpt from the Mishnah called Pirke Avot (Teachings of the Ancestors). In it, we read the words of 1st century Rabbi Ben Bag Bag who proclaimed, "Turn it, and turn it again and again, for everything you want to know is found within it." He may have been speaking of Torah – but Torah doesn’t just mean the five books of Moses, or the entire Bible, or even the Mishnah, Talmud, Kabbalah and Jewish law codes. Torah, in its most expansive sense, can be our own existence, which, as structural anthropologists have taught us, can be the most holy 'text' we can read. By reading creatively, playfully, closely this Torah, we come to see the wisdom of Ben Bag Bag and of Benoit Mandelbrot. In our lives, as in nature and in math, the parts mirror the whole. As we count each day, may we strive to make each day count, as we recognize ourselves as created in the Divine image – the Whole in each part, each part sacred, unique, yet echoing the deeper connection that runs through it all. This is the revelation which we celebrate on Shavuot – Hear, O Israel, The Eternal Our God, The Eternal is All One!