Brendan O’Connor

Symbolic Systems 205, Spring 2005

Systems, Theory and Metaphor

Instructor: Todd Davies

Commentary on Nick Bostrom’s “Are You Living in a Computer Simulation?”

This paper is brilliant. Nick Bostrom presents a clear and thought-provoking analysis of the possibilities of whether we are now living in a computer simulation. He argues that at least one of three propositions is true.

(1) The human species is likely to go extinct before reaching a “post-human” stage, in which massive energy and computational resources make it feasible to run simulations of human societies.

(2) Any posthuman civilization is unlikely to run simulations of their evolutionary history.

(3) We are likely living in a computer simulation.

His reasoning is as follows. First, some form of functionalism or physicalism is true: if you run a very good simulation of the human brain, you’ll get a computational thing that will behave just like a human brain. It can be said to think just as much as any human being thinks. This simulation has to be possible because the real-life human brain runs via the laws of nature and those laws are precisely describable as to permit simulation, given sufficient scientific understanding and computational resources.

Second, there is an assumption about the “post-human” trajectory of human civilization, in which humans progress to harness tremendous amounts of energy. With some back-of-the-envelope calculations about the neural complexity of human brains and the computational power of microprocessors, he calculates that a computer the size of a planet could simulate the lives of millions of human beings, using microprocessor nanotechnology that will already be available in just ten years’ time.

In (1) his assumption of “either progress or extinction” is a bit annoying. I’d amend (1) to include the possibility that the technology/energy-harnessing level of the human species merely fluctuates, stays static, or otherwise does not reach the “post-human” level. Surely Bostrom’s (weird!) beliefs about transhumanism influence his interest in this topic; but amending them out in (1) does not change the overall argument.

He also has an assumption that the only way simulation can happen is through the scenario of advanced humans running simulations of their own history. He does not even consider non-human intelligences running simulations, simulations that arise from non-intelligent actors (an emergent computer, say – is this “simulation”?), simulations run by God, gods, or other supernatural beings, etc. The argument, however, can be amended to accept these scenarios. Replace (1) and (2) with a conjunction of statements of the form

EITHER (1) agent X is unlikely to exist OR (2) agent X will not run human simulations

for example:

“no posthumans” or “posthumans don’t run simulations” AND

“no aliens” or “aliens don’t run simulations” AND

“no gods” or “gods don’t run simulations” AND

“no emergent computation” or “emergent computation doesn’t cause simulation” AND...

So we have to make a conjunction that ranges over all possible agents/things we suspect could run human simulations. At the end of Bostrom’s article, he makes an absurd claim that faced with his three propositions and our ignorance of whether they are true or false, we should weigh them equally. I suspect he said this to shock people into thinking “this guy says there’s a 1/3 chance we’re living in a simulation!” This application of the principle of indifference seems dubious. I’m not sure what adding these conjunctions does to the probability calculation, but I think it shows the realm of analysis is a bit outlandish for any sort of mathematical pretense. What’s your prior belief in the existence of extraterrestrials, indeed?

There are even more troubling uses of probabilities. He draws probabilities as frequentist even fractions where events span over multiple universes and levels of hierarchy of embedded simulations. Consider his stylized reasoning:

DOOM: humanity goes extinct before reaching the posthuman stage

SIM: you are living in a simulation

N: Average number of ancestor-simulations run by a posthuman civilization

H: Average number of individuals that have lived in a civilization before it reaches a posthuman stage

Expected fraction of all observers with human-type experiences that live in simulations:

[1 – P(DOOM)] * N * H

f_sim = ---------------------------------------

([1 – P(DOOM)] * N * H) + H

The experiences of observers in a simulation are indistinguishable from those living in unmediated physical reality. Therefore by a principle of weak indifference:

P(SIM) = f_sim

There is a serious issue here. It is problematic to take sums of persons over multiple simulations and universes. The assumption is that there is a single “real” universe at least somewhat like the one we live in. This may be our universe or it may not. If it is likely for simulation-running posthumans to exist, then it is reasonable to think posthumans occupy the “real” universe, and ours is just a simulation they’re running, or is an embedded simulation thereof.

I’ve often heard the following reasoning: it is very unlikely that you are living the life you live, because only a tiny percentage of the world population was born in the country you were born in (the U.S.). It is much more likely that you were born and live elsewhere. Only by a slim chance are you so lucky/unfortunate to be born as who you are.

That is: P(born_in_us) = f_born_in_us = small.

This reasoning is odd: you can’t calculate the probability of who you were born as. Who you were born as is a pretty important constant in your world. Maybe if souls were lining up in heaven and being distributed to newborns/conceptions through a random process, it might be sensible to talk of that probability. This scenario makes that probability sensical because it grounds the frequencies together in a common universe of the soul-distribution process, and identifies your self as a soul, of which the body/person is a mere property. It is reasonable to calculate probabilities of which property you were assigned.

Bostrom’s P(SIM) = f_sim argument has the same problem. He asks: What universe are you living in? What is the probability of living in a particular universe? The problem is, the fact you live in the universe you live in is an a-priori fact. There’s nothing wrong about reasoning about what your universe might be like, but taking ratios of possible universes is just bizarre.