36 Arguments for the Existence of God - [85]
“Here is how they are singing. This is their niggun. Find the biggest prime maloych. Call it Acharon, for the last, and stand him at the end of a line, with all the prime maloychim that came before him. Here is 2 and 3 and 5 and 7 and 11 and 13 and 17 and 19 and 23 and 29 and 31 and 37 and 41 and 43 and on and on, all of the prime maloychim up until Acharon, the last. Do to them like this. Take 2 three times and then take that number five times, and then take that number seven times, and then take that number eleven times, and if the Cambridger Rebbe asks me how long this goes on, he knows what I will say: take it each time by another, the next in line, all the way up to the last and biggest of the prime maloychim, Acharon. And then…” He threw his arms out and up into the air, a little Valdener in ecstasy. “Add one more to Acharon! That is a new maloych. His name is Acharay Acharon, the One Who Comes After the Last. And Acharay Acharon can’t be! You see! If there is Acharon, there is Acharay Acharon, and it can’t be, so there is no last, l’olam va-ed!”
He stood stock-still, an extraordinary expression on his face, entranced with what he was seeing. The look was replicated around the tish, up and down the bleachers, all motions stilled, snuffing the last blink and breath.
His father broke the silence with a question:
“Do you know the niggun of the prime maloychim? Can you sing it?”
“That was the niggun, Tata. I tried to sing it.”
“A beautiful niggun. But now sing us one of yours, tateleh.”
The child began to sing. The dense room pressed itself forward, trying to get as close as possible, even if they didn’t outwardly move, the lines of invisible force drawing them down to the foamy rectangle on which the Rebbe’s small son floated. His singing was beautiful, as could have been guessed from his speaking voice, and his pitch was perfect. He raised his little hands and gestured like his father, turning his palms up and then over. The Valdeners let him sing the pretty melody through once, and then, when he began it again, they joined in.
Ever since the Ba’al Shem Tov, the master of the Good Name, rebelled against the intellectualized strain of Judaism prevailing in his day, the Hasidim have cultivated a worship of the divine that is experiential, sensual, ecstatic. This is why they dance. This is why they sing. But the Valdeners of New Walden possessed a path to ecstasy that was theirs alone, and it was obvious on every face up and down the tiers. The Rebbe’s son was their ecstasy. They understood little of his words, but the melody they could understand, and they knew that they were in the presence of the divine. Their arms were linked again as they swayed, and many had tears overrunning their eyes, trickling down faces as enraptured as Azarya’s own face had been, a few moments ago, while he was contemplating the beautiful proof that there is no largest prime number.
He hadn’t bothered to go through the last steps of the proof. He had taken them far enough and pointed and expected that they all would see the wondrous thing that he was seeing.
Assume that there is a largest prime number. Give it a name, as Azarya had. Call it P. And now take all the prime numbers that precede P and multiply them together, just as Azarya had said: 2 times 3 times 5 times 7… times P. Take that product and add 1 to it. Call that new number Q. Is Q a prime or not? Since P has been assumed to be the largest prime number and Q comes after P, Q can’t be a prime. But then Q must be divisible by a prime number, because all non-prime numbers, or composites, are divisible by a prime. As Azarya had seen, composite numbers are all the products of primes. So there must be, at least, one prime number that is a perfect divisor of Q. None of the prime numbers less than Q can be a divisor of Q, because 1 had been added to the product of all of them in order to construct Q. So there has to be a prime number larger than P to be Q’s divisor, which contradicts the statement that P is the largest prime number. And so there cannot be a largest prime number.
Cass recognized the proof from Men of Mathematics. It was Euclid who first discovered it, though his proof had been slightly different, more geometrical than Azarya’s. And the Alexandrian giant had not been six years old.
The angels pour their beauty down on us, Azarya had said. They are above, yes, but also here, in everything. 36 descends from on high to sit at the Rebbe’s tish. It carries the beauty of its own composition, and of its invisible bonds with the immaculate others of its realm, transporting this beauty down to us to grace our humble table. As it is, so it must be, and that is the nature of the beauty. In every row, in every tier, in the whole assembled crush of Valdeners, carried on cantillated waves of explosive love, blasted with their gratitude for having been born Valdeners, there are numbers, and this very room, filled with so much shifting strangeness, which before had been an undifferentiated black and bubbling sea, and then had resolved into individual men, now yields its surface again so that Cass can glimpse the silent presence of Azarya’s angels conspiring with one another to bring about what is, because as it is, then so it must be, and this is the nature of the beauty.
