The Hidden Reality_ Parallel Universes and the Deep Laws of the Cosmos - Brian Greene [170]
That’s my view, but not everyone agrees. There’s a philosophical perspective (coming from the structural realist school of thought) that suggests physicists may have fallen prey to a false dichotomy between mathematics and physics. It’s common for theoretical physicists to speak of mathematics providing a quantitative language for describing physical reality; I’ve done so on most every page of this book. But maybe, this perspective suggests, math is more than just a description of reality. Maybe math is reality.
It’s a peculiar idea. We are not used to thinking of solid reality as being constructed from intangible mathematics. The simulated universes of the previous section provide a concrete and enlightening way to think about it. Consider that most celebrated of knee-jerk reactions, in which Samuel Johnson responded to Bishop Berkeley’s claim that matter is a figment of the mind’s conjuring by kicking a large stone. Imagine, however, that unbeknownst to Dr. Johnson, his kick happened within a hypothetical, high-fidelity computer simulation. In that simulated world, Dr. Johnson’s experience of the stone would be just as convincing as in the historical version. Yet, the computer simulation is nothing but a chain of mathematical manipulations that take the computer’s state at one moment—a complex arrangement of bits—and, according to specified mathematical rules, evolve those bits through subsequent arrangements.
Which means that were you to intently study the mathematical transformations the computer carried out during Dr. Johnson’s demonstration, you’d see, right there in the math, the kick and the rebound of his foot, as well as the thought and the famous articulation “I refute it thus.” Hook the computer to a monitor (or some futuristic interface), and you would see that the mathematically choreographed dancing bits yield Dr. Johnson and his kick. But don’t let the simulation’s bells and whistles—the computer’s hardware, the fancy interface, and so on—obscure the essential fact: underneath the hood, there’d be nothing but math. Change the mathematical rules, and the dancing bits would tap out a different reality.
Now, why stop there? I put Dr. Johnson in a simulation only because that context provides an instructive bridge between mathematics and Dr. Johnson’s reality. But the deeper point of this perspective is that the computer simulation is an inessential intermediate step, a mere mental stepping-stone between the experience of a tangible world and the abstraction of mathematical equations. The mathematics itself—through the relationships it creates, the connections it establishes, and the transformations it embodies—contains Dr. Johnson, both his actions and his thoughts. You don’t need the computer. You don’t need the dancing bits. Dr. Johnson is in the mathematics.8
And once you take on board the idea that mathematics itself can, through its inherent structure, embody any and all aspects of reality—sentient minds, heavy rocks, vigorous kicks, stubbed toes—you’re led to envision that our reality is nothing but math. In this way of thinking, everything you’re aware of—the sensation of holding this book, the thoughts you’re now having, the plans you’re making for dinner—is the experience of mathematics. Reality is how math feels.
To be sure, this perspective requires a conceptual leap not everyone will be persuaded to take; personally, it’s a leap I’ve not taken. But for those who do, the worldview sees math as not just “out there,” but as the only thing that’s “out there.” A body of mathematics, be it Newton’s equations, those of Einstein, or any others, doesn’t become real when physical entities arise that instantiate it. Mathematics—all mathematics—already is real; it doesn’t require instantiation. Different collections of mathematical equations are different universes. The Ultimate Multiverse