Fractals of Holiness ~ Beresheet ~ 27 Tishrei 5780 / 26 October 2019
Oct 26th 2019

This has been another great week at Beth Tzedec. Yom Tov with a musically superb Hallel and our special Hattan and Kallah for Simhat Torah. Shemini Atzeret Yizkor with Cantor Ezer’s special touch and Rabbi Fryer Bodzin’s poignant and powerful sermon: from now on, each of us will think of chairs in a different way. And a spectacular cantorial concert on Thursday evening.

We are also anticipating a dynamic month here with lunch-time education and public affairs programs resuming, evening classes beginning, a new healing service, our Holocaust Education program, welcoming the IDF soldiers for Peace of Mind and then the induction and installation of our two new rabbis. I’ll be leaving tomorrow for our Morocco tour with many congregants and then going on to Israel for the birth of a grandchildI”YH.

All this sounds good. Yet, around the world, we are aware of uncertainty and division, challenge and conflict: in Canada and America, in Israel and Britain, in Kurdistan and Syria. Closer in, tomorrow will be Pause with Pittsburgh, to remember the attack on three congregations — Dor Hadash, New Light and Tree of Life * Or L’Simcha— and the murder of 11 Jews at prayer.

Even as we recognize our increased vulnerability, we must not allow the haters and anti-Semites to win. We shall double down with our commitments to prayer, study and tzedakah, as Rabbi Wernick has encouraged, and share the teachings and insights of Judaism with the wider world.

With all this going on in contemporary life, I’d like to speak with you today about what might appear to be abstract, but is actually quite salient for today: the mathematics of prayer, Genesis and our planet.

As we move toward winter, I think of the magen david of nature — snowflakes. Ice crystallizes around a speck of dust in the atmosphere and the shape of the water molecules results in a six-sided symmetry. If you were to place a small equilateral triangle inside each of the six points, you could do this again — forever.

There are other objects in nature that display similarity through a full range of scale — they look the same no matter how big or how small they are. Pineapples and chambered nautiluses, tree branches and river deltas, human veins and DNA. In 1975, Benoit Mandelbrot, a Polish Jew whose family left for France and then America, called this phenomenon a fractal. He said that things typically considered to be "rough", a "mess" or "chaotic", like clouds or shorelines, actually had a "degree of order.”

Fractals are the design principles of nature. They exhibit great complexity driven by simplicity — some of the most complicated and beautiful fractals can be created with a simple equation. Super-efficient, fractals allow plants to maximize exposure to sunlight and blood systems to efficiently transport oxygen to all parts of the body. The closer in you go, or the farther you zoom out, the pattern remains the same. Other natural examples are ferns,romanesco, cauliflower, planetary orbits, ocean waves, lightning, and the seashore.

Rabbi Jonathan Sacks was the first to notice that the structure of tefillah containsfractals.The weekday amidah contains within it a three-part structure: praise, request and thanks. But if you zoom in closer, you find that each individual blessing within replicates the same pattern—praise, request, thanks.

The blessings of Sh’ma evoke three themes—Creation in time and space, the Revelation of Torah and the Redemption of the Jewish people through the miracles of history. The weekday morning service follows the same fractal pattern: peseukei d’zimra, the verses of praise, use the psalms to evoke the majesty of creation. When we recite the Sh’ma and Amidah, we re-enact the revelation of the Divine Presence. As we conclude our prayers, we speak of a redeemer who will come to Zion and hope for a messianic redemption as we recite Aleinu.

The same pattern is found in our Shabbat prayers. The amidah for Friday night speaks of Shabbat as a sign of Creation, zekher l’ma’aseh v’reisheet. Shabbat morning highlights the mitzvah of Shabbat as part of the giving of Torah. During Minhah, we note the fullness of time and the hope for mashi’ah and historical redemption.

Sacks calls fractals “the scientific equivalent of the mystical ability to sense the great in the small.” He quotes William Blake:

To see a World in a Grain of Sand

And a Heaven in a Wild Flower,

Hold Infinity in the palm of your hand

And Eternity in an hour.

As Dr. Lisi Levinsohn puts it, “This kind of infinity is held in a moment of Tefillah; and a moment of Tefillah is part of a great infinity.”

Numbers have always fascinated people. My father’s yahrzeit is this weekend, 38 years to the date — on both the Gregorian and the Hebrew calendars — after the death of his first wife, my aunt, who passed away when she was 38. From Mesopotamia, the home country of Abraham our Founder, our culture has inherited the 12 month calendar, the 24 hour clock, the 60 minute hour, the 60 second minute and the 360 degree circle.

Yet our Torah does not organize time around six. Instead, The Torah of our God structures time around the idea of the one after six. As Rabbi Sacks writes: “Judaism acknowledges the six part structure of time and space but adds that God exists beyond time and space. Hence seven — the one beyond six — became the symbol of the holy.”

Take a look at the first chapter of Genesis.

Genesis 1.1 has seven words.

Genesis 1.2 has 2x7 words.

The description of Shabbat in Genesis 2.1-3 consist of 5x7 words.

The term for God, Elohim, appears 5x7 times in the Creation narrative.

The phrase heaven and earth, shmayim v’aretz, recurs 3x 7 times.

Va’yaar elohim, God saw, repeats seven times, as does the term “and it was so,” Va’yehee khen.

We frame the week as six days plus Shabbat.

There are seven holy days identified in the Torah:

  Pesah 1 and Pesah 7


  Rosh Hashanah and Yom Kippur

  Sukkot and Shemini Atzeret

The six holy days look toward the seventh, Yom Kippur, the Shabbat of Sabbaths.

And the annual cycle involves six years of planting, plus the seventh year when the land lies fallow. From small to large, seven recurs throughout the Torah and Jewish life. This prime number becomes the fractal of holiness.

Just as we celebrated so much at Beth Tzedec, but carry the shadow of anti-Semitism with us, we can and should celebrate the delicate intricacy of the natural world, the fragile equilibrium of the environment, the careful balance of our biosphere. And we should be aware of the dark shadow of climate change.

Recent studies in Israel indicate that the climate of the country has been changing. The temperature has increased ½ degree in the past decade — it previously went up 1 degree in the past century. This is leading to increased evaporation, more flooding, greater danger of fires and more extreme weather. What is going on in Israel is, as we know, occurring elsewhere on this planet. If this continues, the Fertile Crescent, the breadbasket of humanity, may lose the capacity to produce grain. As we read about Creation and anticipate the Flood of Noah, we should bear in mind the careful and sensitive balance of the natural world.

During Sukkot, we read from the scroll of Kohelet. A rabbinic commentary to Ecclesiastes portrays God as leading Adam and Eve around the Garden of Eden. Speaking to the first humans, God says: “Look at my works! …See to it that you do not spoil and destroy My world; for if you do, there will be no one else to repair it.”(Ecclesiastes Rabbah 7:13).

Just as anti-Semitism was under control and then manifested itself in terrible ways, so our world has been in careful balance and could be thrown out of wack. The fractals of nature and the holiness of one beyond six are all in a sacred equilibrium. As Jews, we must remind ourselves and others of the sacred task of protecting this planet and maintaining its sustainability.

“Look at My works! ... See to it that you do not spoil and destroy My world; for if you do, there will be no one else to repair it.”

Jonathan Sacks, Introduction, The Koren Sacks Siddur: A Hebrew / English Prayerbook