Is Reality a Computation?

As usual, it depends on how you look at it. (But no.)

The assertion “Reality is a computer!” is not uncommon. Under a sufficiently broad definition of “computer” the answer can be yes.¹ But I think such a broad definition devalues the notion of computing, and that under a useful definition of computing, the answer is definitely no.

It all depends on what you consider a computation.² I started exploring this in the last post in this series, Computation vs Evaluation. In computer science, a computation is something that can be implemented with a Turing Machine. More simply, a computation involves processing numbers according to some algorithm.³ The old phrase “number crunching” is an apt stand-in for “computation” as defined by CS.

Some define computation more casually as any process behind physical change. So, for example, they might view the formation of a watershed in a landscape as the rain, the terrain, and gravity all “computing” the evolving watershed over time.

More to the point, this view also supports a view that neural processes in the brain are computations. I’ve long thought this conflation is driven by the need those who support computationalism have to see the brain as a computer.⁴ Again, depending on what’s actually meant by “the brain is a computer”, accepting this view forces one to accept other analog systems (such as watersheds) as equally computational.

In fact, there are two levels at which we might consider the brain a computer. Firstly (and the point of this post), that all reality is a computation, so brains are, too. Secondly, that the brain’s architecture makes it a computer (the neurons, synapses, and connections). I wrote about the latter view in Brains Are Nothing Like Computers and Brains Are Not Algorithmic.

I think common sense got a little lost here. Computation is number crunching. No number crunching, no computation. Full stop.⁵

Where Is the Computing?

Let’s consider some basic levels of reality and see what’s going on.

Quantum Level (the most basic level): Fairly simple interaction rules and a small set of objects (less than two dozen quantum particles). It wouldn’t be unreasonable to consider quantum interactions computations, and many do. Indeed, our current quantum theory is a mathematics without a well understood physical meaning. Perhaps reality is just a dance of numbers at this level, yet we seem to live in a reality of matter. And despite its quantum nature, reality at this level is still very much analog.⁶

Atomic Level (made of quantum objects): More objects (118 elements). Chemistry has complex (quantum!) interactions. In theory, chemistry is deterministic, but quantum effects and probability play a role. In fact, atoms can only be fully understood as quantum objects. If reality is computed at this level, the computation is necessarily probabilistic.

Molecular Level (made of atomic objects): All the compounds. Many objects and complex rules. Materials Science. But physics seems more determined, more mechanical at this level. Reality takes on a clockwork aspect.

Object Level (made of molecular objects): Explosion of objects and rules. Classical physics and many other sciences. The Mechanical Domain. In theory, fully deterministic but in practice probably not.

Biological Level (made of molecular objects): Even more possible objects. With biology comes birth, growth, and death. And movement. And brains navigating their biological units through reality. Brains might be the one non-deterministic thing reality has stumbled on.

Human Level (made of biological objects): Infinite Diversity in Infinite Combinations. Domain of psychology, sociology, art, literature, politics, religion, and much else. Consciousness. Free will appears to be in play.

Note that in all cases, there is no dualism, no Digital Divide.⁷ In all cases, there are physical objects interacting (evaluating reality) according to physical rules. Some may see “computation” at these levels, especially the first, but I cannot.

Do We Live in a Virtual Reality?

No, almost certainly not. In my view, even considering reality as a computation is incorrect, let alone considering it a computer simulation.

Back in 2003, Nick Bostrom proposed the simulation hypothesis that, in part, argues:

Any entities with our general set of experiences are almost certainly living in a simulation. ~Wikipedia

(Emphasis mine.) There is more to the argument, but the popular view has focused on the possibility asserted above. In particular, the “almost certainly” aspect.

Bostrom’s idea assumes virtual realities are easy, even trivial, to create and run. Recently, I touched on the memory requirements for simulating a human brain.⁸ Imagine simulating eight billion of them. And a universe for them to exist within (and bodies as well). Also, factor in the energy and materials necessary for the compute resources in such a large simulation.

Representing a single particle in a simulation requires multiple numbers, the actual number and approach depending on whether we’re simulating classical or quantum physics. For the former, each particle needs six numbers, three for position (x, y, and z) along with three numbers for momentum (px, py, and pz). Quantum particles also have properties such as charge and spin, and quantum math requires complex numbers, which immediately doubles the numbers the computer must keep track of.

Each number requires some number of bits inside the computer. How many depends on the precision we need for computation. If we assume 128 bits for each number (probably not enough), a single classical particle requires 768 bits. For quantum particles, at least double that (if not more).

The point is that each particle we simulate (current estimates place the total number of particles in the universe at about 10⁸⁰) requires a much larger space to contain than the original particle. So, a simulation of physical reality is necessarily much (much) larger than reality itself.

The question, then, is how a simulation of a universe can fit within a universe.

Simulating even a crude universe seems to imply the planet-sized computers from science fiction. Even those may not be sufficient. Again, how to store all the information for a universe inside a universe?

Or course, we’ve only explored a tiny fraction of our universe, so it’s possible the simulation is of just our part. The rest might be a sort of virtual backdrop, but that backdrop still requires massive computation to simulate the universe we see through our various telescopes.⁹ There is no real way around the expense and material required regardless of technology.

Moral questions aside, what would motivate such an expensive undertaking? What would they hope to gain? What answers could such a sim provide that the minds capable of creating one couldn’t answer themselves? Why bother?

So, no, I think the simulation hypothesis is “almost certainly” false on several counts. Further, I think belief in it is yet another indicator of how badly modern culture — and worse, even science — has become detached from physical reality.

And in this, our civilization, and the way we think, has become decadent. (Characterized by or reflecting a state of moral or cultural decline. Luxuriously self-indulgent.) That is a theme I’ll be exploring down the road.

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This more or less concludes my series on computationalism. See the My Best Guess newsletter for other posts.

Until next time…

1. Or at least approaches it.

2. The answer to almost every computer science question begins with, “It depends on what you mean…”

3. Set of steps defining how to process the numbers.

4. When, in fact, the brain is nothing like a computer.

5. IMO, obviously.

6. So, if reality is a computer, it’s a massively parallel analog one, not a digital one. See Analog vs Digital.

7. See Digital Emulation.

8. At least 12 petabytes for a static model of one brain. See Digital Simulation.

9. If the simulation is local, then SETI will never find anything. (Of course, I don’t believe SETI will ever find anything regardless.)