Pi – Rosh Hashanah 5759 (1998)

In Deuteronomy, we read, “You shall find God, if you search after Adonai with all your heart and all your soul.”

“But belief in God is irrational,” the atheists say.

“Probably right,” harmonize the agnostics.

“Belief in God is indisputable,” the fundamentalists say.

“How do you know?” ask the agnostics.

“Because the Bible tells us so.”

“So what?” press the agnostics.

“Well, the Bible is infallible.”


“Because God wrote it!”

“Ah,” the agnostics reply, condescendingly, leaving to dine with the atheists. “You were right,” they whisper, “belief in God is irrational.”

I agree. Belief in God is irrational.

Now, when you think of the word “irrational,” what do you think of? A deranged person, babbling. A confused person, muttering. Yes, these are examples of one kind of irrationality. But I have another kind of irrationality in mind: consider the number Pi.

Pi, you may remember from your early days of geometry, is a very special number. Pi is used to calculate the circumference of a circle, knowing its diameter. You may also remember that Pi has an infinite number of digits after the decimal point. It starts “3.14159…” and goes on and on forever. Scientists have contests to see how many millions of digits of Pi they can calculate.

Pi is an irrational number.

Formally, an irrational number is a number that cannot be formed by dividing one integer – for example, four – by another, say three. The irrational numbers (like Pi) live in a different world from the rational numbers: in many ways, you can say, “You can’t get there from here.”

Like those irrational people, Pi babbles on, randomly, without end. Pi is confusing, muttering its infinite sequences to the wind. Pi even makes some people uncomfortable, and I’m not just talking about math students.

In 1897, the Indiana House of Representatives passed a bill declaring Pi to be equal to “3.2” – nothing more, nothing less. No infinite digits, no difficult calculations. Just a nice, simple, rational “3.2”. It was their hope that they could simplify teaching, allow calculations to be less complicated, make the world of geometry a little easier. Oh, and yes, they hoped to make some money on the deal – but that is a different story.

The problem is, setting Pi equal to 3.2 doesn’t work. When you do that, you calculate circumferences that are too big, diameters that are too small. You find that areas of circles and ellipses are wrong; volumes of cylinders and spheres don’t work. Suddenly, all the simple objects that used to function so well aren’t right anymore, all because someone rounded up a few decimal points.

All because somebody tried to take an irrational number and make it rational.

Rabbi Nachman of Bratslav said, “We should believe in God through faith, not miracles.” I used to think that was because miracles – like parting the sea, stopping the sun in the sky, and so on – don’t seem to happen these days, and we could spend our lives waiting for such a miracle. But now I believe that Rabbi Nachman sensed a deeper truth.

A miracle gives us evidence. Evidence that can be used to convince us, and others, of the existence of God. Rational proof that God is real. So what’s wrong with that?

How many of you have ever tried to convince someone of something they didn’t want to believe? You can present all the evidence in the world, and chances are, you will still fail. Sigmund Freud recognized this when he wrote, “Humanity is in the highest degree irrational, so that there is no prospect of influencing it by reasonable arguments.”

But that’s not the real problem. The real problem is, using miracles to prove God’s existence is like setting Pi equal to 3.2: you are trying to make the irrational, rational.

Back in my days as a philosophy major, I took a course in the Philosophy of Mathematics with a fantastic scholar, Professor Benardete. He had a wonderful knack for making the subtlest of concepts understandable, without eliminating their mystery. Early in the course, it was necessary to explain the difference between rational and irrational numbers.

“Imagine a ruler: you can divide it into inches, or centimeters, any number of evenly-spaced units, marked with a hatch mark. No matter how many units per ruler you choose, there will always be hatch marks and spaces between them. The hatch marks are the rational numbers, the spaces the irrational.”

You cannot have the hatches without the spaces, you cannot have the spaces without the hatches. Rational numbers depend on irrational numbers for their existence, just as do the irrational on the rational.

And so it is with our rational and irrational lives, our scientific and spiritual selves. Albert Einstein wrote, “Science without religion is lame; religion without science is blind.” The spiritual world coexists with the scientific, each supporting the other. We can use science to explain the structure of a mountain, but not the spiritual experience of its beauty. As the poet Noah ben Shea has said, “Reason explains the darkness, but it is not a light.” The pursuit of science always leads to gaps, some of which cannot be filled with yet more science. And religion on its own offers a poor map of the world and its everyday challenges.

We cannot build great structures without numbers like Pi and numbers like 3.2: at least, not structures with the great curves of beauty, the rounded edges we find in all living things. We need both the rational and the irrational to manage our world; how much more so must we need them to manage our spirits?

As we enter this High Holy Day season, come and embrace both the rational and irrational, draw the science and magic together; make your world both predictable and mysterious, and in so doing, make your world one, as our God is one.

Shma, Yisrael, Adonai Eloheinu, Adonai Echad.


© 1998-2007 James F. Brulé