Three Roads To Quantum Gravity

KNOTS, LINKS AND KINKS
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knotted with one another. So the relationships among the
loops could change dynamically. I had thought about intersecting
loops, but I had never wondered about how loops
could knot or link.
I went inside and called Louis Crane. I asked him whether
mathematicians knew anything about how loops might knot
and link. He said, yes, there is a whole ®eld devoted to the
subject, called knot theory. He reminded me that I had had
dinner a few times in Chicago with one of its leading thinkers,
Louis Kauffman. So the last step was to rid the theory of any
dependence on where the loops were in space. This would
reduce our theory to the study of knots, links and kinks, as
James Hartle, one of the leading American relativists, teasingly
began to call it shortly afterwards. But this was not so
easy, and we were not able to take this step for over a year. We
tried very hard, with Louis and others, but we could not do it.
The workshop at Santa Barbara had closed with a conference
at which our new results were ®rst presented. There I
had met a young Italian scientist, Carlo Rovelli, who had just
been awarded his Ph.D. We didn't talk much, but shortly after
he wrote to ask if he could come to visit us at Yale. He arrived
that October, and took a room in Louis Crane's apartment. The
®rst day he was there I explained to him that there was
nothing to do, because we were completely stuck. The work
had looked promising, but Louis and I had found the last step
to be impossible. I told Carlo he was welcome to stay, but
perhaps given the sad state of the subject he might prefer to go
back to Italy. There was an awkward moment. Then, looking
for something to talk about, I asked him if he liked to sail. He
replied that he was an avid sailor, so we abandoned science
for the day and went straight to the harbour where the Yale
sailing team kept its boats, and took out a sailing dinghy. We
spent the rest of the afternoon talking about our girlfriends.
I didn't see Carlo the next day. The day after that he
appeared at the door to my of®ce and said, `I've found the
answer to all the problems.' His idea was to make one more
reformulation of the theory, so that the basic variables were
nothing but the loops. The problem was that the theory up till
then depended both on the loops and on the ®eld ¯owing