The Hidden Reality_ Parallel Universes and the Deep Laws of the Cosmos - Brian Greene [169]
My view on mathematics periodically changes. When I’m in the throes of a mathematical investigation that’s going well, I often feel that the process is one of discovery, not invention. I know of no more exciting experience than watching the disparate pieces of a mathematical puzzle suddenly coalesce into a single coherent picture. When it happens, there’s a feeling that the picture was there all along, like a grand vista hidden by the morning fog. On the other hand, when I more objectively survey mathematics, I’m less convinced. Mathematical knowledge is the literary output of humans conversant in the unusually precise language of mathematics. And as is surely the case with literature produced in one of the world’s natural languages, mathematical literature is the product of human ingenuity and creativity. That’s not to say that other intelligent life-forms wouldn’t come upon the same mathematical results we’ve found; they very well might. But that could easily reflect similarities in our experiences (such as the need to count, the need to trade, the need to survey, and so on) and so would provide minimal evidence that math has a transcendent existence.
A number of years ago, in a public debate on the subject, I said that I could imagine an alien encounter during which, in response to learning of our scientific theories, the aliens remark, “Oh, math. Yeah, we tried that for a while. At first it seemed promising, but ultimately it was a dead end. Here, let us show you how it really works.” But, to continue with my own vacillation, I don’t know how the aliens would actually finish the sentence, and with a broad enough definition of mathematics (e.g., logical deductions following from a set of assumptions), I’m not even sure what kind of answers wouldn’t amount to math.
The Ultimate Multiverse is unequivocal on the issue. All math is real in the sense that all math describes some real universe. Across the multiverse, all math gets its due. A universe governed by Newton’s equations and populated solely by solid billiard balls (with no additional internal structure) is a real universe; an empty universe with 666 spatial dimensions governed by a higher-dimensional version of Einstein’s equations is a universe too. If the aliens happened to be right, there would also be universes whose description would stand outside mathematics. But let’s hold that possibility off to the side. A multiverse realizing all mathematical equations will be enough to keep us occupied; that’s what the Ultimate Multiverse gives us.
Multiverse Rationalization
Where the Ultimate Multiverse differs from the other parallel universe proposals we’ve encountered is in the reasoning that leads to its consideration. The multiverse theories in previous chapters were not dreamed up to solve a problem or answer a question. Some of them do, or at least claim to, but they weren’t developed for that purpose. We’ve seen that some theorists believe the Quantum Multiverse resolves the quantum measurement problem; some believe the Cyclic Multiverse addresses the question of time’s beginning; some believe the Brane Multiverse clarifies why gravity is so much weaker than the other forces; some believe the Landscape Multiverse gives insight into the observed value of dark energy; some believe the Holographic Multiverse explains data emerging from the collision of heavy atomic nuclei. But such applications are secondary. Quantum mechanics was developed to describe the microrealm; inflationary cosmology was developed to make sense of observed properties of the cosmos; string theory was developed to mediate between quantum mechanics and general relativity. The possibility that these theories generate various multiverses is a by-product.
The Ultimate Multiverse, by contrast, carries no explanatory weight apart from its assumption of a multiverse. It achieves precisely one goal: cleaving from our to-do list the project of finding an explanation for why our universe adheres to one set of mathematical laws and not another, and it accomplishes