137 - Arthur I. Miller [129]
And more way out still, 137 is the foundation stone of a fiendishly complex “biblical mathematics” referred to by followers of “The Bible Wheel” as a “Holographic Generating Set.” It is based on three geometric forms: a cube, A, divided into 27 subcubes; a hexagon, B, divided into 37 subhexagons; and a star of David, C, divided into 73 circles Of course 27 + 37 + 73 = 137. From this “generating set” with its Pythagorean-geometric aura, aficionados of the Bible Wheel claim to be able to generate biblical passages and probe mystical numbers by multiplying A, B, and C in various ways.
Thus 137 continues to fire the imagination of everyone from scientists and mystics to occultists and people from the far-flung edges of society.
The last challenge
With World War II behind them, Heisenberg and Pauli resumed their scientific correspondence. But the days of their collaboration and the frequent exchange of letters seemed to have ended. After all, they had been on opposite sides in the war. And Heisenberg’s reputation was colored by the fact that he had remained in Germany and had ended up in charge of the German atomic bomb project. Most of his postwar colleagues, of course, had been involved in the Manhattan Project. Even Heisenberg’s brilliance was not enough to overcome this stain.
Then in 1957 Heisenberg wrote to Pauli that he had the germ of a theory that could explain the masses of elementary particles as well as most of the symmetries. In a preliminary test he was almost able to deduce the fine structure constant from his new theory. In his calculations it came to 1/250, which is not very far away from 1/137, in the same way as 1/3 is not far from 1/4, even though 3 is far from 4. This was extraordinary, given that Heisenberg’s theory was still in its formative stages. Pauli immediately took up Heisenberg’s suggestion to join him in his project.
“Never before or afterward have I seen [Pauli] so excited about physics,” Heisenberg later recalled. It seemed as if the old days had come back. The two giants of quantum physics were working together once again.
“The picture keeps shifting all the time. Everything in flux. Nothing for publication yet but it’s all bound to turn out magnificently,” Pauli wrote exuberantly to Heisenberg at the start of 1958. “This is powerful stuff…. The cat is out of the bag and has shown its claws: division of symmetry reduction. I have gone out to meet it with my antisymmetry—I gave it fair play—whereupon it made its quietus…. A very happy New Year. Let us march forward toward it. It’s a long way to Tipperary, it’s a long way to go.”
Heisenberg was equally excited. For him the theory was to be the culmination of his life’s work. Over the years he had become entranced by the power of mathematics to probe and understand the physical world. And he knew how to use it. “A wonderful combination of profound intuition and formal virtuosity inspired Heisenberg to conceptions of striking brilliance,” a colleague wrote. He had used his formidable insight and daring to apply mathematics to make his startling discoveries in quantum mechanics. These included the uncertainty principle; the first steps toward understanding the force that holds the nucleus together; and his attempts to produce a coherent theory of electrons and light, known as quantum electrodynamics.
The theory he was working on with Pauli was exactly what he was looking for. “The last few weeks have been full of excitement for me,” he wrote to his wife’s sister Edith in January 1958:
I have attempted an as yet-unknown-ascent to the fundamental peak of atomic theory with great efforts during the last five years. And now, with the peak directly ahead of me, the whole terrain of interrelationships in atomic theory is suddenly and clearly spread out before my eyes. That these interrelationships display, in all their mathematical abstraction, an incredible degree of simplicity, is a gift we can only accept humbly. Not even Plato could have believed them to be