Brandon Carter pointed out that we shouldn’t take the Copernican principle—the fact that we are nothing special in the cosmos—too far. He reminded astronomers that humans are the ones who make observations of the universe; consequently, they should not be too surprised to discover that the properties of the cosmos are consistent with human existence. For instance, we could not discover that our universe contains no carbon, since we are carbon-based life-forms. Initially, most researchers took Carter’s anthropic reasoning to be nothing more than a trivially obvious statement. Over the past couple of decades, however, the anthropic principle has gained some popularity. Today quite a few leading theorists accept the fact that in the context of a multiverse, anthropic reasoning can lead to a natural explanation for the otherwise perplexing value of the cosmological constant. To recapitulate the argument, if lambda were much larger (as some probabilistic considerations seem to require), then the cosmic acceleration would have overwhelmed gravity before galaxies had a chance to form. The fact that we find ourselves here in the Milky Way galaxy necessarily biases our observations to low values of the cosmological constant in our universe.

But how reasonable is the assumption that some physical constants are “accidental”? A historical example can help clarify the concept. In 1597 the great German astronomer Johannes Kepler published a treatise known as Mysterium Cosmographicum (The Cosmic Mystery). In this book, Kepler thought that he had found the solution to two bewildering cosmic enigmas: Why were there precisely six planets in the solar system (only six were known at this time) and what determined the sizes of the planetary orbits? Even in Kepler’s time, his answers to these riddles were borderline crazy. He constructed a model for the solar system by embedding the five regular solids known as the Platonic solids (tetrahedron, cube, octahedron, dodecahedron, and icosahedron) inside each other. Together with an outer sphere corresponding to the fixed stars, the solids determined precisely six spacings, which to Kepler “explained” the number of the planets. By choosing a particular order for which solid to embed in which, Kepler was able to achieve approximately the correct relative sizes for the orbits in the solar system. However, the main problem with Kepler’s model was not in its geometrical details—after all, Kepler used the mathematics that he knew to explain existing observations. The key failure was that Kepler did not realize that neither the number of planets nor the sizes of their orbits were fundamental quantities—ones that can be explained from first principles. While the laws of physics indeed govern the general process of planet formation from a protoplanetary disk of gas and dust, the particular environment of any young stellar object determines the end result.

We now know that there are billions of extrasolar planets in the Milky Way, and each planetary system is different in terms of its members and orbital properties. Both the number of the planets and the dimensions of their circuits are accidental, as is, for instance, the precise shape of any individual snowflake.

There is one particular quantity in the solar system that has been crucial for our existence: the distance between the Earth and the Sun. The Earth is in the Sun’s habitable zone—the narrow circumstellar band that allows for liquid water to exist on the planet’s surface. At much closer distances, water evaporates, and at much larger ones, it freezes. Water was essential for life to emerge on Earth, since molecules could combine easily in the young Earth’s “soup” and could form long chains while being sheltered from harmful ultraviolet radiation. Kepler was obsessed with the idea of finding a first-principles explanation to the Earth-Sun distance, but this obsession was misguided. There was nothing to prevent the Earth (in principle) from forming at a different distance. But had that distance been significantly larger or smaller, there would have been no Kepler to wonder about it. Among the billions of solar systems in the Milky Way galaxy, many probably do not harbor life, since they don’t have the right planet in the habitable zone around the host star. Even though the laws of physics did determine the orbit of the Earth, there is no deeper explanation for its radius other than the fact that had it been very different, we wouldn’t be here.

This brings us to the last necessary ingredient of anthropic reasoning: For the explanation of the value of the cosmological constant in terms of an accidental quantity in a multiverse to hold any water, there must be a multiverse. Is there? We don’t know, but that has never stopped smart physicists from speculating. What we do know is that in one theoretical scenario known as “eternal inflation,” the dramatic stretching of space-time can produce an infinite and everlasting multiverse. This multiverse is supposed to continually generate inflating regions, which evolve into separate “pocket universes.” The big bang from which our own “pocket universe” came into existence is just one event in a much grander scheme of an exponentially expanding substratum. Some versions of “string theory” (now sometimes called “M-theory”) also allow for a huge variety of universes (more than 10⁵⁰⁰!), each potentially characterized by different values of physical constants. If this speculative scenario is correct, then what we have traditionally called “the universe” could indeed be just one piece of space-time in a vast cosmic landscape.