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six of which were compactified around the loops, making them somewhat exotic mathematical objects. The space they vibrated in had been quantized by twenty-first-century theorists, into loop patterns called spin networks, in which lines of force in the finest grain of the gravitational field acted somewhat like the lines of magnetic force around a magnet, allowing the strings to vibrate only in certain harmonics. These supersymmetrical strings, vibrating harmonically in ten-dimensional spin networks, accounted very elegantly and plausibly for the various forces and particles as perceived at the subatomic level, all the bosons and fermions, and their gravitational effects as well. The fully elaborated theory therefore claimed to mesh successfully quantum mechanics with gravity, which had been the problem in physical theory for over two centuries.

All very well; indeed, exciting. But the problem, for Sax and many other skeptics, came with the difficulty of confirming any of this beautiful math by experiment, a difficulty caused by the very, very, very small sizes of the loops and spaces being theorized. These were all in the 10-33 centimeter range, the so-called Planck length, and this length was so much smaller than subatomic particles that it was hard to imagine. A typical atomic nucleus was about 10-13 centimeter in diameter, or one millionth of a billionth of a centimeter. First Sax had tried very hard to contemplate that distance for a while; hopeless, but one had to try, one had to hold that hopelessly inconceivable smallness in the mind for a moment. And then remember that in string theory they were talking about a distance twenty magnitudes smaller still— about objects one thousandth of one billionth of one billionth the size of an atomic nucleus! Sax struggled for ratio; a string, then, was to the size of an atom, as an atom was to the size of . . . the solar system. A ratio which rationality itself could scarcely comprehend.

Worse yet, it was too small to detect experimentally. This to Sax was the crux of the problem. Physicists had been managing experiments in accelerators at energy levels on the order of one hundred GeV, or one hundred times the mass energy of a proton. From these experiments they had worked up, with great effort, over many years, the so-called revised standard model of particle physics. The revised standard model explained a lot, it was really an amazing achievement, and it made predictions that could be proved or disproved by lab experiment or cosmological observations, predictions that were so varied and had been so well fulfilled that physicists could speak with confidence about much of what had gone on in the history of the universe since the Big Bang, going as far back as the first millionth of a second of time.

String theorists, however, wanted to make a fantastic leap beyond the revised standard model, to the Planck distance which was the smallest realm possible, the minimum quantum movement, which could not be decreased without contradicting the Pauli exclusion principle. It made sense, in a way, to think about that minimum size of things; but actually seeing events at this scale would take experimental energy levels of at least 1019 GeV, and they could not create those. No accelerator would ever come close. The heart of a supernova would be more like it. No. A great divide, like a vast chasm or desert, separated them from the Planck realm. It was a level of reality fated to remain unknown to them in any physical sense.

Or so skeptics maintained. But those interested in the theory had never been dissuaded from studying it. They searched for indirect confirmation of the theory at the subatomic level, which from this perspective now seemed gigantic, and from cosmology. Anomalies in phenomena that the revised standard could not explain, might be explained by predictions made by string theory about the Planck realm. These predictions had been few, however, and the predicted phenomena very difficult to see. No real clinchers had been found. But as the decades passed, a few string enthusiasts