The Limits of Resolution

My own suspicion is that the universe is not only queerer than we suppose, but queerer than we can suppose…I suspect that there are more things in heaven and earth than are dreamed of, or can be dreamed of, in any philosophy.  –  J.B.S. Haldane, “Possible Worlds” (1927)

If you’re anything like me, you were already tired of the “We’re living in a simulation” nonsense before it even got as widespread as it is now.  The idea that what we perceive as reality might not actually be real goes back at least to Plato’s cave and the Hindu concept that the universe is the dream of Brahma, but for the genesis of its current popularity we must turn from the sublime to the ridiculous, namely the movie The Matrix (which stole both its name and its central concept from a 1976 episode of Doctor Who and many of its details from the works of Philip K. Dick, most notably Ubik, but does justice to neither).  This currently-popular version of the philosophical exercise postulates a creation with the grandeur and inescapability of what we might call the “primordial simulation” models (wherein the “simulation” is either the natural state of the universe or was created by an eternal demiurge far beyond the comprehension of any being within the simulation), yet residing within some physical realm at least resembling the “simulated” universe in which we are imagined to exist.  Expressed more succinctly, the modern “simulation” fantasy as typically conceived imagines a simulacrum of a universe created by some finite being or beings for some definable purpose and existing within some physical instrumentality.  And such a model is, due to those arbitrary limitations, pure claptrap.

The problem with this version of the idea lies in the very concept of a “simulation” as a thing that requires a “simulator”, rather than recognizing it a state intrinsic to the mathematical structure of the cosmos itself (a la Plato) or else as a product of a form of existence as far beyond our comprehension as the totality of the universe is beyond any given individual who might ponder their state of existence (as in Hindu cosmology).  But the Matrix-style simulation fans aren’t imagining an open-ended, intrinsically unknowable system; quite the opposite.  Instead, they postulate a very complex but still finite formal system, resident within something like a supercomputer (albeit an immense and very advanced one).  However, no formal system can adequately describe itself*, which means it also cannot adequately model itself; any simulation of this sort must therefore be of dramatically smaller scope and lower resolution than the world in which its simulating mechanism resides, just as no fictional world or electronic simulation within our world can ever be as large or complex as our world.  If our universe were truly a finite simulation within a knowable, physical system, there would be some point, probably but not necessarily on the scale of the infinitesimal, that we would be able to perceive the limits of granularity.  Sooner or later, our instruments would reach a point at which the resolution of our universe was no longer sufficient to allow us to subdivide structures into still-smaller parts, and given that our theoretical models already extend down to phenomena smaller than a billionth the size of the smallest particles we can detect, which are themselves far tinier than the electrons whose movements define the contents of our own computers, I think it’s safe to say that isn’t likely to happen.

*If you’ve never studied Kurt Gödel’s incompleteness theorem, here’s a very accessible book which might help you to understand both its narrow implications for mathematical modeling of phenomena and its philosophical implications for the universe as a whole.