Trespassing on Einstein's Lawn (41 page)

He was also on a constant search for words. I saw now that it was no accident Wheeler had coined so many terms and phrases, like “black hole,” “wormhole,” “quantum foam,” “the self-excited circuit,” and “the boundary of a boundary.” His desire to find the best words for such things bordered on mania. The journals were full of pages that were nothing but lists of words, hundreds upon hundreds of words, seemingly copied out of a dictionary: “Secret seek sought senses shadow shade shape shapeless shares shatter sharp sheen shelter shield shine shock shore shot show shuffle siege sink siren song skeleton skin sky slate slide slumber sight smoke smuggle snow sober soil sojourn soldier solid solitude solution solve …”

My father, reading my mind as usual, leaned over and whispered, “This guy had a serious case of OCD!”

I nodded. Ya think?

He even traveled with a thesaurus, a fact I gleaned from his packing lists, which cataloged every item that ever graced his suitcase along
with their respective weights. A fair amount of weight was allocated to books. On an average trip he brought two physics books, a few philosophy books, several volumes of poetry, and one thesaurus. Wheeler's parents had both been librarians. Clearly he had inherited their devotion to the written word and to cataloging.

“Spurn spyglass squeeze stable staccato stage stamp stand standing star start state stay steel steep steer steersman …”

My father and I read in silence, the massive journals propped up on foam wedges for support, carefully turning the brittle pages, which were all loosening from their bindings, weakened by the passing of time and by the weight of all the pictures, postcards, and papers Wheeler had glued to them. I wondered if Wheeler had developed his compulsion for gluing everything down after Eisenhower had personally scolded him for losing classified H-bomb documents on a train.

I soon came to recognize Wheeler's symbol for “the boundary of a boundary is zero”: ∂∂ ≡ 0. It popped up everywhere: “Of all regularities, the one to me most suggestive is ∂∂ ≡ 0.” “Everything from nothing ∂∂ ≡ 0.” He described it as “spacetime's grip on mass,” the “faint frown of space.” He wrote, “The principle of algebraic geometry that ‘the boundary of a boundary is zero' is dimension free. It would be difficult to find any simpler principle on which to build the laws of physics if, at bottom, these are all based on ‘law without law,' a universe of ‘higgledy-piggledy' construction. Therefore it is interesting to see that major portions of electromagnetism, gravitation, and the Yang-Mills theory of the quark-binding field are built exactly on this principle. However, in each case there is a part of the theory that has no equally simple structure.”

How were electromagnetism, gravity, and QCD built on the boundary of a boundary? It was clear that Wheeler saw it as the unifying principle of physics and a possible way to get something from nothing. But what the hell did it mean? And what was with the triple equals sign? I leaned over to ask my father.

“It's an identity,” he whispered.

Inside John Wheeler's journal (American Philosophical Society library)
A. Gefter

“Isn't that what a normal equals sign is?” I asked.

“An equals sign says these two things happen to be the same. The three lines mean they're identical, by definition.” Fair enough. I read on.

“Go anywhere, see anybody, ask any question,” Wheeler wrote—and he did. Many entries were written in transit as he traveled around the globe meeting with physicists, philosophers, mathematicians, and virtually anyone else who might have anything to contribute to his quest to understand the universe. At times, though, he grew frustrated. “All this traveling about trying out ideas—still it isn't clear how we're going to build up structure out of nothingness.”

Wheeler knew, I soon discovered, that such lofty philosophical ambitions were looked down upon by his colleagues, a fact that clearly bothered him but seemed to bother his wife, Janette, even more. On January 31, 1976, he wrote, “Janette and I arrived in Princeton.… Wonderful people. But on the whole they took a skeptical point of view
toward what I had to say. Janette was mortified she told me this morning when we woke, and said that at the meeting she almost burst out in tears. I was talking, she said, about the kind of thing college students discuss, incredibly naïve, vague comments about the nature of reality, lots of quotes but nothing hard to get one's teeth into. A happy manner of presentation didn't make up for lack of hard content. She thought she saw Gi[a]n Carlo Wick making a sniggering remark to I. I. Rabi sitting beside him, about halfway through my presentation. And I went overtime … Rabi after the session said to me, ‘I hear you're giving up physics for this sort of thing.' I expostulated, spoke of my paper on scattering theory for the Borgmann Festschrift. Lewis Thomas, too, was a bit anti-philosophical. Aage Peterson (Yeshiva) referred to my ‘beautifully poetic talk' but said there was one term in it, ‘quantum principle,' that might lead to confusion.”

The next day, Stephen Hawking had come to visit Wheeler in Princeton and invited him to speak at a conference in Cambridge. A downhearted Wheeler replied, “Maybe yes, maybe no.” “I brought up my problem about reactions I received to general ideas and desire I have for a low profile, and yet the problem that one can't think if one can't talk. He sympathized and says he talks about ideas ‘in formation' only in company of one or two others.”

Wheeler worried, too, about the effect his quest might have on his loyal followers. On May 25, 1979, in his hotel room at the Hyatt Regency in New Orleans, he wrote, “Wheeler has been leading people along a trail. He can't abandon them at the bottom of a cliff. He has to show the way up. Many are staking their futures on the promise of the road he espouses. He can't let them down. He is under a tremendous obligation to deliver.”

When the library closed for the evening, my father and I headed back out to the cobblestone streets. It took a moment for my eyes to adjust and my mind to emerge from inside Wheeler's head. It was that feeling you get when you exit a movie theater and your brain has to snap out of the fictional world and back into reality, only this movie had lasted eight hours and featured the mind-bending ideas of a tortured genius.

I looked at my father with a grin. “Wow.”

“I know,” he said, looking dazed and exhilarated.

“They're not how I imagined they'd be. I always thought of him as this kind of cheery, lighthearted guy. I didn't imagine him to be so …”

“Relentless?”

“Yeah. Relentless. Determined. But it's not normal determination.”

My father nodded. “It's obsession.”

Over the next few days I discovered that Wheeler had one particular obsession: Kurt Gödel. “I argue that the Gödel business has to come into physics, and physics into the understanding of it, it is important to see the G.B. through and through,” Wheeler had scrawled in his journal on July 22, 1973. “My problem, I am afraid, is this, that after I've written down the circuit I see nothing next, and infinite number of things to do next, but nothing clearly sorted out in between.”

“The Gödel business,” I assumed, referred to Gödel's incompleteness theorem, which said that if a mathematical system is consistent, it can't be complete. Gödel had proven the theorem by creating a mathematical sentence that said, in numerical language, something to the effect of:
This sentence is not provable by this mathematical system.
If the system could prove it, then the statement would be rendered false and the system inconsistent for producing falsities. On the other hand, if the system couldn't prove it, then the statement would be true, keeping the system consistent but incomplete, unable to prove one of its own statements. If it was true it was false; if it was false it was true. A classic paradox.
This sentence is a lie.

But here's the thing: it's obvious that Gödel's sentence is actually true. The mathematical system can't prove it, because if it did the system would self-destruct. The sentence clearly speaks the truth. It's true but unprovable.
We
know the statement is true, even though the mathematical system making the statement doesn't. How? Because we have a vantage point the system doesn't:
we're on the outside.
From our God's-eye view outside the system, we can determine the truth or falsity of the sentence. From inside the system, it's nothing but paradox.

The whole mess came down to one word:
this.
The statement is
talking about itself. Self-reference is the root of the whole inside/outside problem. You can't assess the validity of statements about the system from inside the system—to determine their truth or falsity, you have to look down on them from some higher level of reality. Gödel's incompleteness theorem said that the minute self-reference is involved, there are limits to what we can know, unless we can step outside the thing. And if I had learned one thing about the universe, about reality, it was that
you can never step outside the thing.

A few months before writing that entry, Wheeler had approached Gödel at a cocktail party thrown by the Princeton economist Oskar Morgenstern. Wheeler and Gödel had a close friend in common: Albert Einstein. Wheeler explained to Gödel that he intuited some deep connection between Gödel's incompleteness theorem and Heisenberg's uncertainty principle, two principles that had been discovered within a few years of each other and placed sudden, disturbing limitations on what is knowable in the universe. Gödel didn't want to talk about it. When Wheeler asked why, he learned that Gödel wasn't exactly enthusiastic about quantum mechanics. As Wheeler put it, “He had walked and talked with Einstein enough to have been brainwashed out of any interest in quantum theory—to me a great tragedy, because Gödel's insight might be the key thing.”

Wheeler seemed convinced that hidden inside Gödelian incompleteness sat the meaning of quantum mechanics. But why? “Idea of isomorphism between calculus of propositions and pregeometry more interesting than ever,” he scribbled.

I knew that propositions were like the atoms of logic, simple statements that could be either true or false, such as “Snow is white” or “My pants are on fire,” and the calculus of propositions was just a set of logical rules that related the propositions to one another. And I knew that pregeometry, another Wheeler coinage, was some mysterious thing more fundamental than spacetime, the building material of reality, one presumably based on ∂∂ ≡ 0. But why there would be an isomorphic mapping from the calculus of propositions to some kind of pregeometry was beyond me.

I spotted a clue when Wheeler quoted mathematician Hans Freudenthal speaking about the calculus of propositions: “Our vocabulary
need not contain a single constant subject. The predicates are, as it were, floating in the air; they do not refer to anything.” Opposite this Wheeler had written, “How entrancing—almost an open invitation to be foundation for quantum mechanics plus pregeometry.”

Still, Wheeler was lost. “Not seeing a dramatic clear path ahead,” he wrote. “Now have concluded just have to push in through the undergrowth. ‘Traveler, there are no paths. Paths are made by walking.' ”

The calculus of propositions gave the rules for relating two-valued, true/false binary propositions without any reference to the
meaning
of the propositions. Inherent meaning was irrelevant; all that mattered were the relationships, which held true regardless of the truth or falsity of the individual propositions. If
p
implies
q
and
q
is false then
p
is false—a rule that holds regardless of whether or not my pants are in fact on fire. In that Wheeler saw a glimpse of structure without structure, form without content, the something from nothingness to which he hoped ∂∂ ≡ 0 would lead.

“A certain uniqueness, naturalness, and beauty must characterize the real equations,” he wrote, “and above all, simplicity. What is the simplest mathematics one knows? … There is nothing simpler than the + -, true-false, yes-no, up-down choice. As subsequent thought and analysis has revealed, there are many structures that can be built upon this binary element, but every one of them that has been looked into possesses some arbitrary element or number or structure with the sole exception of the calculus of propositions. It would seem to have the desired element of uniqueness and simplicity, and this in a satisfying and even truly striking way. Logic is too important to be left to the logicians.”

Wheeler wasn't ready to give up on Gödel. After having been spurned at the cocktail party, Wheeler brought some of his students in to see Gödel at Princeton to ask him again about the connection between undecidability and quantum mechanics. Gödel threw them out of his office. So Wheeler tried another tactic. Glued into the journal I found a letter he had written to Gödel in December 1973. Apparently Wheeler thought that Gödel might be more likely to answer the question if it was multiple choice. The letter read: