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†This wasn’t the result of a mysterious mathematical coincidence. Instead, in a precise mathematical sense, strings are highly symmetric shapes, and it was this symmetry that wiped away the inconsistencies. See note 4 for details.

*The first revolution was the 1984 results of John Schwarz and Michael Green, which launched the modern version of the subject.

*If you’re being careful, you’ll note that a slice of bread is really three-dimensional (width and height on the slice’s surface, but also depth from the slice’s thickness), but don’t let that trouble you. The thickness of the bread will remind us that our slices are visual stand-ins for large three-branes.

*You could still ask whether the entire higher-dimensional spatial expanse can move, but however interesting to contemplate, it’s not relevant to the discussion here.

*For readers familiar with the puzzle of time’s arrow, note that I am assuming, in keeping with observations, that entropy decreases toward the past. See The Fabric of the Cosmos, Chapter 6, for a detailed discussion.

CHAPTER 6

New Thinking About an Old Constant

The Landscape Multiverse

The difference between 0 and . might not seem like much. And by any familiar measure it’s not. Yet there’s growing suspicion that this tiny difference may be responsible for a radical shift in how we envision the landscape of reality.

The tiny number printed above was first measured in 1998 by two teams of astronomers making meticulous observations of exploding stars in distant galaxies. Since then, the work of many has corroborated the teams’ result. What is the number, and why such a fuss? Evidence is mounting that it’s what I referred to earlier as the entry on the third line of the general relativity tax form: Einstein’s cosmological constant, which specifies the amount of invisible dark energy permeating the fabric of space.

As the result continues to hold up under intense scrutiny, physicists are becoming increasingly confident that decades of previous observations and theoretical deductions, which had convinced the vast majority of researchers that the cosmological constant was 0, have been overthrown. Theorists scurried to figure out where they’d gone wrong. But not all had. Years earlier, a contentious line of thought had suggested that a nonzero cosmological constant might one day be found. The key supposition? We’re living in one of many universes. Many universes.

The Return of the Cosmological Constant

Remember that the cosmological constant, if it exists, fills space with a uniform invisible energy—dark energy—whose iconic feature would be its repulsive gravitational force. Einstein latched on to the idea in 1917, invoking the cosmological constant’s antigravity to balance the otherwise attractive gravitational pull of the universe’s ordinary matter, and thus allow for a cosmos that neither expanded nor contracted.*

Many have reported that upon learning of Hubble’s 1929 observations, which established that space is expanding, Einstein called the cosmological constant his “greatest blunder.” George Gamow recounted a conversation in which Einstein is purported to have said this, but given Gamow’s penchant for playful hyperbole, some have questioned the accuracy of the story.1 What’s certain is that Einstein dropped the cosmological constant from his equations when the observations showed that his belief in a static universe was misguided, noting years later that had “Hubble’s expansion been discovered at the time of the creation of the general theory of relativity, the cosmological constant would never have been introduced.”2 But hindsight is not always 20–20; it can sometimes blur earlier clarity. In 1917, in a letter he wrote to the physicist Willem de Sitter, Einstein expressed a more nuanced perspective:

In any case, one thing stands. The general theory of relativity allows the inclusion of the cosmological constant in the field equations. One day, our actual knowledge of the composition of the fixed star sky, the apparent motions of