Tag Archives: mathematics

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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The Memory Machine – Second Day Shavuot, 5776

Remembrance of those who have passed from this world is a universal human desire; we all feel the need to recall our family members and friends who are no longer with us.

Two decades ago, when I was an undergraduate at Cornell, I recall reading a statement about memory that has stuck with me.  It appeared in the campus newspaper, the Cornell Daily Sun, in the middle of a tongue-in-cheek article about something that I can’t remember.  But the statement that struck me read as follows:

“[So-and-so] is still trying to cope with the realization that he is a function of every person he has ever met and every book he has ever read.”

I remember thinking, hey, that’s me too.  I am also a function of every person I’ve ever met and every book I’ve ever read.  And here, the word “function” is used in its mathematical sense.  Perhaps some of you recall from junior high school algebra:

f(x)

or the diagram of the function machine:

function can be visualized as a "machine" that takes an input x and ...

A function is a box that performs some kind of action on data that is entered, such that what comes out is modified in a particular way.  So if f(x) is x-squared, then if I put in 2, the function turns it into 4.  If I put in 3, it becomes 9.  And so forth.

To say that we are functions of our life experience is a vast oversimplification, of course.  Our own function machines would have to be very, very complicated.  But on some level, this is not far off.  We are shaped by our experiences, from the moment we emerge from the womb, through schooling and relationships and work and success and failure and loss and happiness and sadness.

Perhaps a better way of understanding ourselves, then, is that we are  memory machines — sacks full of memory — that not only process our experiences through those memories, but also allow us to dig into our past, to re-examine, to think of the beautiful moments as well as the awkward ones that we wish had never happened. What we carry with us is invaluable; it is in fact who we are.

And it is really hard to wrap our brains around that.  We often measure people by the superficial stuff: how they appear, what car they drive, where they go to synagogue, when they go to synagogue, and so forth.

But what really makes us who we are is our own, personal, individual sack of memory. And in particular on a day like today, when we reflect back on how our lives were touched by those whom we remember.

The proper name from Yizkor, by the way, is Hazkarat Neshamot, the recalling of souls. What we do on this day is to attempt to bring up those shards of memory of those who have left us: who they were, what they stood for, what they taught us.

Perhaps this endeavor serves as a reminder on an ongoing basis of our obligation to treat others well, to remember that every interaction that we have with other people is logged in somebody’s memory.  And not only that, but also that many little actions can add up to a tidal wave of memories, memories that cross over from individuals to peoples.  Memory shapes not only individuals, but also cultures, politics, and nations.

I’m going to share with you a few examples from my own memory machine, memories that have shaped me as a contemporary Jew, as an American, and as a rabbi.

When I was in cantorial school, and before I had a cantorial position that required me to be at the same synagogue every Shabbat and holiday, I used to do a lot of “shul-hopping.”  That is, I would walk to different synagogue in Manhattan to listen to different hazzanim, to hear them practice their art.  One year on Shemini Atzeret, I walked to Fifth Avenue Synagogue, an Orthodox congregation on the East Side, to hear Cantor Joseph Malovany.  Unfortunately, he was not there that day, and his substitute was unremarkable.  But I was treated to something else that day: the author Elie Wiesel was there, sitting quietly in the front row on the rabbi’s side.  I did something that day that I was not accustomed to doing at the time: I stayed in the sanctuary for Yizkor, mostly so I could watch Elie Wiesel as he stood up to recite his own personal Yizkor prayers, recalling, I imagined, all of the things that he had recounted in his books: the loss of his family, his Romanian village, the loss of his faith upon arrival in Auschwitz.  He stood with his eyes closed, gently rocking side to side, his head cast slightly upward.  Where is he?  I wondered.  Where is he right now?

A different story: The summer of my seventeenth year I visited Israel for the first time.  I spent eight weeks there on an academic program called the Alexander Muss High School in Israel, where we learned Jewish history from ancient times until present day, and visited relevant sites all over Israel to put it in context.  It was amazing — much of what I learned that summer I have carried with me and used again and again.

Of course, when you have 40 seventeen-year-olds living together in a dorm for eight weeks, you learn a whole lot about the complexity of human relationships as well.  One thing that I remember from that summer was learning about how mean one Jew can be to another for the sake of one interpretation of Judaism.  One weekend, we had some free time in Jerusalem, and one of my female friends was caught inadvertently among a mob of Haredim (so-called ultra-Orthodox Jews, although I prefer not to use that misleading term) who were protesting the opening of certain cinemas on Shabbat.  She was wearing something that someone in that crowd deemed inappropriate, and so he spat upon her.  She was, as you can imagine, more than taken aback; the Jews among whom she had grown up and lived with and traveled around Israel with did not behave that way.

That was a memory that I am sure that she carries with her to this day, and so do I by proxy (even though I was not there when it happened).

Ladies and gentlemen, as a people we came through the Shoah together, laden with horrible memories, with martyrdom an essential feature of the modern Jewish psyche.  We established a Jewish state in our historical homeland.  We have empowered women to participate fully in Jewish life and mitzvot.  Many of us in this room remember all of these things personally, because you were there.  Our memories have shaped us as a people. And they will continue to help us move forward as a people into the bold, inchoate Jewish future.

Many of you have been to parlor meetings with me over the past year, and you know that part of the process is to tell a story about a Jewish memory, a meaningful Jewish experience. My goal in asking you to do so is not so that the others in the room might simply say, “Now that’s nice.” Rather, it is to (a) remind us of the power of memory, (b) create a sense of community through shared stories, and (c) try to connect who we are and how we live today as Jews with our past experiences. We fire up those memory machines to connect them with each other, and then with Congregation Beth Shalom.

On this second day of Shavuot, this day of remembering, it is upon us to look back not only on the people that have created deep personal memories for us, our parents, our siblings, our teachers, our friends, but also those among our people who have created salient cultural memories for us as Jews, and the community that we have inherited.

Memory makes us collectively stronger as individuals and as a qehillah. Turn on those memory machines; now is the time to actively remember.

 

~

Rabbi Seth Adelson

(Originally delivered at Congregation Beth Shalom, second day of Shavuot, 6/13/2016.)

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