Beautiful Equations – Shavu’ot, 5777

Close your eyes. Think for a moment about somebody you love. Think about what makes them special, what brings you pleasure when you are in their presence, what makes them unique, what you have learned from them, the good times you have shared.

It is always difficult to encapsulate why you love somebody in a few sentences or thoughts. It is the very nature of relationships that they can seldom be relegated to finite descriptors. We are much more likely to rely on our feelings, which are hard to put into words.

If you could describe the essential features of a lover, a companion, a spouse, a friend, a child, a sibling, a parent, what words would you use?

Comfort / Safety / Security / Shared experiences / Memories / Partnership / Simplicity / Warmth / Mutuality / Ezer kenegdo (sometimes translated as “helpmeet”; Gen. 2:18)

***

Many of you know that, as a recovering engineer, I am always looking for metaphors that come from science to help us understand ourselves and our various relationships, including our relationship with the Qadosh Barukh Hu (God). So when I spot such metaphors or stories in articles or podcasts, I make note of them.

One such piece appeared in a recent article in the New York Times, which struck me as particularly fascinating. It was about how some people find mathematical equations aesthetically beautiful.

My father is one of those people. He has a doctorate in mathematics, and he has always found all things related to math quite captivating. When he was in elementary school, he would deliberately misbehave, because the teacher would “punish” him by giving him math problems. But the joke was on her, because my father enjoyed doing these problems. Today, my dad will talk your ear off about Fibonacci numbers, or why integration is never taught well, or how much fun he had trying to solve a mathematical puzzle. He’s been retired for a decade or so, but has recently taken to tutoring students over the internet. He gets paid for it, but I’m pretty sure he’s not doing it for the money.

So I understand people who like math. I’m kind of in that category myself, and of all the holidays of the Jewish year, Shavu’ot is the mathematician’s holiday. Its date is set by counting off  forty-nine, that is, seven-squared days from the first day of Pesah. Its very name, meaning, “weeks,” is derived from this. It’s a holiday on which we read about Aseret HaDibberot, the “Ten Commandments” (although really there are 13 or 14, depending on how you count), and we also read and meditate on Ezekiel’s vision of a four-sided chariot that descends from heaven. In fact, the very name “Shavu’ot,” meaning weeks, is derived from the Hebrew word for seven, sheva.

This article in the Times referenced a recent study that compared the relative beauty of mathematical equations. The researchers did this by hooking up a bunch of mathematicians to fMRI scanners, and watching their medial orbitofrontal cortices “light up” when they saw certain equations. This area of the brain, right behind the eyes, shows a lot of activity when people respond positively to aesthetic experiences, like music or art.

So they were able to measure which equations the mathematicians found most beautiful. And the one that they loved the most was Euler’s Identity:

eulers identity

Now, I must confess, that is one staggeringly beautiful equation. It’s just so darned cool: e (Euler’s number, the base of the natural logarithm) is an irrational number equal to approximately 2.71828; π, the ratio between a circle’s diameter and its circumference, is also irrational. The other number, i, is the strangest of them all: it is an imaginary number that corresponds to the mathematically impossible solution of the square root of -1.

(My wife Judy reads all my sermons, and at this point she started inserting lots of question marks and exclamation points. So I’m going to apologize right now if you did not understand any of that – I don’t have the time to explain all of those things, and it’s not really that important. But very cool, nonetheless.)

And yet, somehow, when you throw all three of these mystical, seemingly unrelated numbers together, they magically resolve themselves to simplicity. Euler’s identity seems completely counter-intuitive, and yet it yields the most fascinating statement of math: that there is always an elegant solution. That’s one reason my father always cited for his love of math: that if you have done it right, there will always be an answer.

You might say that people are sort of like equations: we take in information about the world, mix it up within ourselves, and give back. We relate to others through variables and constants and operators. Right?

Or maybe not. OK, so people are not really like equations. We are much more complex. We rarely accept simple solutions. We have many more inputs and outputs, variables and constants. Most of the time we are difficult to understand. Our word problems are never so easily or elegantly solved. Our lives are not airtight, removed from all the other environmental factors around us. There is not always an answer; in fact, one of the most beautiful and agonizing aspects of humanity is that most of the time the answers evade us.

But sometimes, in the context of some relationships, the simplicity of our love for one another is striking. Sometimes we appreciate the others around us in a way that is absolutely indescribable, that cannot be put into words. I suspect that if you’d take a human subject, hook them up to the fMRI and paraded in front of them images of various people in their lives, their medial orbitofrontal cortices would “light up.”

As a regular part of my work as a rabbi, I sit with people all the time to discuss their relationships. It happens in the context of preparing for a wedding, when I ask the couples to talk about what makes their relationship successful. Or when I meet with a family in advance of a bar/bat mitzvah, when I ask the other members of the family to speak about the nascent 13-year-old. Or when I meet with the family who has just lost a loved one, in preparation for a funeral.

I am often struck by how difficult it is for us to talk about our closest relations, the people with whom we share the deepest, most complex bonds. How do you capture the richness of give-and-take between siblings? How do you acknowledge the massive burden of unpaid gratitude we owe to our parents?

And yet, we all know and intuitively understand, without trying to label it with words or ideas, the very deep connection we have with those whom we love, just as those mathematicians unwittingly revealed their appreciation of those gorgeous, elegant equations.

The great early-20th-century Jewish philosopher Martin Buber is perhaps best known for his essential work of modern theology, I and Thou. His message in that short, yet powerful, text is that our relationship with God is the most unconditional relationship we have. We cannot put any conditions on God, says Buber, and God puts no conditions on us. All human relationships are subject to the complexities of expectations met and missed, of the ideal vs. the imperfect reality.

And yet, at the core of every relationship is that fundamental sense of connection – not a logical one, not a checklist of “these are the things I love about you,” but a taste of the Unconditional. That’s where the Godliness seeps into each of our relationships. That’s where the holiness lies.

On this day when we actively remember those whom we have loved who have left this world, I think it is easier to rely on that unconditional, deeply emotional bond that we share with them. We feel that love for them in a way that is beyond logical. And particularly after the equations of our lives have ceased to function, after they have exhausted all the data, what remains is a kind of snapshot of their lives that lives forever inside of us, a shortcut that represents the many ways we knew them, the rich roster of experiences that we shared.

As we turn now to recall those whom we have lost, I ask you to remember how they taught you, how they raised you, how they gave you wisdom and love and companionship and everything else that they gave. And I ask you to recall the deeper things that made your relationship special, the indescribable ways that you loved them, the moments when you just took a look at that person and subconsciously acknowledged their inner beauty.

 

~

Rabbi Seth Adelson

(Originally delivered at Congregation Beth Shalom, 2nd day of Shavuot, June 1, 2017.)

 

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Filed under Festivals, Sermons, Yizkor

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