the simulation argument

Nick Bostrom suggests the fascinating Simulation Argument, which considers whether the universe is a computer simulation, and if not, what the alternatives are.

His version of the argument is rigorous and leads to weak conclusions. That’s what you want if you’re trying to get at the truth. I propose a wifty version, not an argument so much as an exploratory line of reasoning, which (if you care to accept it) suggests strong conclusions. My version is interesting if you want to explore possibilities.

Catchphrase: It’s turtles all the way up!

The reasoning is based on the observation that you cannot tell whether you are living in a deliberate computer simulation or an accidental universe. (Though if you’re into Intelligent Design you may believe you can. Being in a simulation is formally equivalent to “being a thought in God’s mind” for suitable values of God. Calling it a computer simulation brings in less baggage.)

the argument proper

Anyway, here’s my version.

1. How many universes do we have? Answer: One.

2. How many computer simulations do we run? Answer: Zillions.

Therefore: 3. What are the odds that we are currently living in a computer simulation? Answer: Based on the observed statistics, zillions:1.

Why should we think we’re in the single privileged reality?

further consequences

If you buy that, then what is the authorial intent of the universe? Perhaps life did not originate spontaneously.

The same argument applies to the next level up, the reality in which we are information being shuffled around. The most elegant model of the whole meta-situation is that there is no such thing as a real universe; every level is a simulation at a higher level. There is no privileged reality; it’s turtles all the way up.

If we accept that the tree of simulations is rooted infinitely far away, then how is it that we are near the leaves? Because a simulated reality is necessarily simpler than the simulating reality. If there are many simulations at each level, then nearly all the simulations are near the leaves.

If the universe is infinite, apparently we have to assume the Axiom of Choice to draw conclusions. It is entirely possible that a larger universe can run an infinite simulation. Isn’t that interesting?

a trick question

Accept the infinite nesting of simulations for the sake of argument, and suppose that every simulation has an end. Your mission: Calculate the expected lifetime of our universe. Our universe stops if any of the infinitely many universes it is nested within should stop—either because it finished and returned results, or because it hit a bug, or because somebody tripped over the power cord.

What conclusions can we draw about our universe? None! Each universe outward is necessarily more complex than the universe inward. Suppose, for example, that each one has a lifetime 1,000,000 times longer than the lifetime of its nested simulation (making the simulation far longer in relative terms than any simulation humans have run). Even though every universe in the stack, to infinity, has a finite lifetime, most likely none of them will end before our universe does. Calculate the probability if you don’t believe me.

nature of outer universes

Outer universes may be larger than ours in basic ways: They may have more space dimensions; they may have more time dimensions; it may be possible to operate on infinite amounts of data and to build a hypercomputer that can complete infinitely many steps; it may be possible to represent information that can’t be represented in our universe. They may have fundamentally different structures, which words like “dimension” do not describe. What can be computed depends on the laws of physics, and outer universes may have more permissive laws of physics. Therefore, outer universes may have characteristics that we cannot conceive of even in principle, because the concepts are not computable in our universe; any conclusion that we draw about them must be uncertain.

Another way to look at it is that it is easy to construct a simulation from inside which no information about the outer universe is detectable. That is the argument of Descartes’s Demon, the one Descartes made and then wimped out on. The existence of the outer universe makes it clear that there may be rules of our own universe which we cannot figure out—but that’s not news, because it’s true even if there is no outer universe. See also Plato's cave.

other variations

At the heart of the simulation arguments is a counting argument. Start with a set X of worlds, whether real or simulated. The counting argument goes: “There are lots of simulations in X and at most one real world, so if our world is a random sample from X then our world is probably a simulation.” (See also There’s Nothing Special About X.)

The X I propose above is the weakest, “all simulations”. The obvious objection is “but there’s no reason to expect that our world is a random sample from that set. It’s much more complicated than any simulation that we’ve seen.” That’s why I consider it an exploratory line of reasoning, not a conclusion-drawing argument.

The strongest X is “worlds which we can’t distinguish from our own.” But it’s difficult to argue that there are or will be many simulations which we can’t distinguish, because they would have to have a purpose that we can’t see. So that variant is less interesting.

Nick Bostrom’s X is in between, “worlds simulated by post-human civilizations trying to understand their own history.” That variant is airtight but requires extra assumptions, leading to his complicated three-part conclusion.

Many, many other variants are possible with other choices of X. I personally feel that Nick Bostrom’s interesting choice has a rather ad hoc air. I hold out hope for even more interesting choices. I expect that someday we will understand the rise and needs of advanced civilizations, and then we will be able to draw firmer and stronger conclusions.

Original version, June and September 2006.
Updated and added here May 2011. Fixed a typo September 2015.