“Really?… Amazing that he saw The Confessions. What a coincidence.”
Hamish put some ice in his cocktail shaker. “He produced this theorem, the Incompleteness Theorem — that’s why we laughed. It was quite devastating.” He shook the shaker. “Changed the face of mathematics for all time.” He poured out two drinks and looked at me. “In fact I was going to write to you about it, try and explain Kurt’s theorem to you. It’s quite uncanny how it all fits together. Now you’re here, I can tell you about it.”
“Super,” I said.
Hamish handed me a glass.
“Good to see you, John.”
“Cheers.”
That night we had dinner in one of Zion’s better restaurants. I think we ate a kind of pot roast followed by ice cream. I can barely remember eating. Hamish talked constantly, and with the single-minded intensity of all lonely people, of quantum mechanics and its bizarre world of chance and supposition. He mentioned names: Einstein, Bohr, the Copenhagen Statement, de Broglie, thought experiments, Schrödinger’s cat. But he kept coming back to Werner Heisenberg and his Uncertainty Principle and how everything linked up with Kurt’s Incompleteness Theorem. Absolute truth, he said at one juncture, had been finally exposed as a chimera, an utterly vain ambition. In the sum of human knowledge there would always be crucial uncertainties. And Kurt had shown how even in the most abstract formal systems there would be holes, gaps and inconsistencies that could never be overcome.
Eventually we paid our bill and went outside. I felt stupid, my head stuffed with strange concepts. It was a warm night. I breathed slowly, deeply, as we walked back to the institute.
“Shifting sands, John. Shifting sands.”
“Yes?”
“We live in extraordinary times. They’ll call this the Age of Uncertainty. The Age of Incompleteness.”
“Yes,” I said again, simply.
“Strong stuff, isn’t it?” He paused. “Limits. Limits everywhere.”
“It’s rather depressing, in a way.”
“Why?” He seemed astonished at me. “There may be uncertainties, but don’t you think it’s better to live in the full knowledge of this than go on looking for illusory ‘truths’ that can never exist?”
“Well, yes. I suppose it is, actually.”
“It is, believe me. I find it all invigorating. Great gusts of fresh air. Like standing on top of Paulton Law. Remember?”
“God. Paulton Law.… I haven’t thought about the Academy in years.”
Hamish paused to light a cigarette. The flare of the match cast dark shadows in the rugged, pitted surface of his skin. I felt one of those epiphanic shudders of sadness pass through me — the sort that are meant to signal all manner of potential foreboding. I tried not to think of my future. What would be waiting for me up ahead? I hadn’t a clue.
“The Age of what did you say?” I asked.
“Of Uncertainty. The Age of Uncertainty and Incompleteness.”
“Seems pretty apt, now I come to think of it.”
“It is. Bang on.” He grinned. “That Kurt, he’s a clever old bugger. Set the cat among the pigeons. Remarkable.”
“I thought he seemed very nice.”
“I’m going to do some work on it, when I can find the time.”
“What?”
“Tying up Heisenbergs Uncertainty and Kurt’s Incompleteness.”
“Oh yes?”
“It’s all tremendously exciting.”
“I can see that.”
I blew cool air on my palms. For some reason they were suddenly hot and sweaty. We walked on in silence for a while.
“You’ll take care, won’t you, John?”
“What do you mean?”
“In Europe. The war. Don’t do anything, you know, foolhardy.”
I laughed. “No bloody fear, Hamish. No bloody fear.”
I left Hamish at Zion the next day. It had been a disquieting visit. We had gone back to his Quonset for a last drink and he went on talking for two more hours about Kurt and Heisenberg, Schrödinger and all that crowd. I felt slightly alarmed also: I was worried that he was becoming obsessed and he wanted me to share his obsession with him. I looked at his rows of calculating machines and asked him what he did with them all. He told me he was still working on prime numbers.
“Very, very big ones,” he said. “Enormous ones.” He thought he had found a way of devising an unbreakable cipher using these vast prime numbers. That explained why he was working for the government and why he had the rank of major.
He tapped out a number on a machine. It printed, “2,146,319,807.”
“That’s the largest prime number known to man,” he said. “I’m trying to find one half as big again.” He waved at the calculators. “With the help of these chaps. Once I’ve found that, I can make the code.”
He spent another hour explaining how the cipher would work, but it was all over my head.
I continued thinking about Kurt and his Incompleteness Theorem and its implications on the train back to New York. I was intrigued that the little man who loved my film had removed the foundations of certainty from the entire world of mathematics. How remarkable too that he had seen my film and how gratifying that it should have affected such an extraordinary man so. I felt a warm glowing surge of self-esteem within me. He was right, as well. The Confessions: Part I was a work of genius. It took one to recognize it. I knew its worth and I owed it to myself and to the world not to let it languish unfinished.
I looked out of the window at the New Jersey swamps. But first there was a war to get through.
17 The Invasion of St.-Tropez
Dateline, St.-Tropez, August 16, 1944. Yesterday, the South of France was invaded by three hundred thousand men from the U.S. and French armies. Operation Dragoon had begun. A vast armada of over twelve hundred vessels, the largest invasion fleet the Mediterranean had ever seen, assembled secretly off the golden beaches of the Riviera. Thousands of parachutists were dropped inland before dawn. Nine hundred fifty-nine aircraft pounded the coastal defenses on an invasion front that stretched from Cavalaire to Fréjus.…
I paused. I thought I had the tone just about right. I imagined it being read in an urgent “March of Time” voice, which I felt was just the sort of voice required. I did not find journalism at all easy.
I was sitting typing on the terrace of a ruined café situated on the quay at St.-Tropez Harbor. The Germans had blown up and largely demolished the port installations and had badly damaged most of the quayside buildings. The rest of the small ancient town was more or less untouched. The big white hotel — the Hôtel Sube et Continental — seemed to pulse with brightness in the midday sun. The old walls and fortifications of the citadel were sharp and distant against the washed-out blue of the sky. I drained the last of my beer, brought to me by the cheerful patron of the demolished café. Yesterday had been a very curious twenty-four hours.
The invasion force — General Patch’s Seventh Army — had been attacking three sectors of the coastline. Alpha Force was assaulting beaches at Cavalaire and St.-Tropez. Delta Force was concentrating on Ste.-Maxime, and Camel Force was divided between Fréjus and St.-Raphaël. I was assigned to a company of the 17th RCT (Regimental Combat Team), which was going in on Alpha Yellow Beach, the long strip of sand on the Baie de Pampelonne.
There was a heavy mist on August 15, so heavy it looked artificial. As I peered over the gunwale of the chugging LCI as we cruised steadily in towards Pampelonne Beach, I was reminded of that day at Nieuport when I had raised the false gas alarm. I wasn’t sure if that thick line of smog was mist or the dust raised by the bombers and the naval barrage. I suspect that whoever was at the helm was similarly inconvenienced because we landed somewhat off target, to the right of the beach in a small rocky shingled cove. I kept my eyes on Captain Loomis as he led the company off the front of the LCI into the water. It was eerily quiet for an invasion. No one was shooting at us.