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Geometric Simulation Theory and Verification Spaces

Extrapolating our science and technology in an exponential fashion into the future leads to a couple of fascinating prospects, for example the rise of artificial superintelligence, or the possibility to create very precise simulations of whole worlds. Both of these topics were explored in detail by the philosopher Nick Bostrom, famous for his book “Superintelligence” and the proposal of the simulation hypothesis.

What do superintelligences want?

Let’s take these proposals seriously here. What would superintelligences do? Well, what kind of motivations for doing something would they have? Even if we assumed that they had boringly simple utility functions, they would still display some common characteristics, for example striving for increasing their capability to fulfill their own purpose. Knowing more about the world usually increases one’s chances to reach one’s goals, among a wide variety of different goals. Therefore, it is reasonable to expect that curiosity is a kind of convergent motivational pattern that appears in nearly all incarnations of higher intelligence. Rational agents want to be successful in achieving their goals. With learning more about the world as instrumental goal for their primary goals, they also want to be successful in doing exactly that.

Superintelligences will do science

Science does precisely that: It makes people more successful at creating more fitting models for reality. Superintelligences will at least be supremely scientific (unless they happen to come up with something better than science). Now what kind of scientific tools would a superintelligence have? Well, it would be able to create very detailed simulations of about anything. And that includes whole worlds – given sufficient resources for running such a simulation, of course.

Simulations as scientific tools, giving rise to verification spaces

Simulations can be created to test scientific hypotheses. The events in those simulated worlds can strengthen or weaken a hypothesis. This gives rise to a geometry of hypothesis verification consisting of points that are simulated worlds which strengthen the hypothesis, and a complementary space of points that are worlds which weaken the hypothesis. For each scientific hypothesis you get what I call its verification space. It is very hard to compute verification spaces, because the points they consist of are full-fledged space-times. Since worlds can differ in an astronomical number of ways, the dimensionality of verification spaces is astronomical, too.

Astronomic integer overflow

Add to this the fact that there is an astronomical number of hypothesis you can propose and examine, and you get a potential number of simulated worlds that is astronomical times astronomical. Even a civilization consisting of superintelligences possessing astronomical resources will simply not be able to compute all verification spaces. Yet, it may be necessary to start brute force attacks on truth by approximately computing verification spaces in order to solve the hardest and most important scientific questions there are.

You are likely an entry in a matrix

Some of those questions pertain to sentient beings. Often to humans in particular, even though they might be out of fashion in a distant future. To answer those questions, it is reasonable for a superintelligence to compute verification spaces consisting of simulated worlds containing human populations. This may make it seem relatively likely that we find ourselves in some of those simulated worlds that are computed in order to compute a verification space.

So what?

How is that insight relevant to anything? If our world is a means to answer a scientific question, and we have no clue as to what that question might be, we aren’t much wiser than before. Of course, we could speculate about the nature of the question that is the potential reason for our existence, but that would drift too far into the realm of religion, rather than science of even philosophy.

Strange new horizons

Nevertheless, it opens up strange new possibilities. Besides “regular” worlds one can imagine “irregular” simulated worlds in which the simulators interfere with the simulation in quite interesting worlds in order to provide some additional variation that is not easily reachable by letting regular simulations go through their evolution “naturally” with the simulators taking a backseat. Direct interference of the simulators can give rise to apparently “supernatural” phenomena, or phenomena that seem to be rather unlikely in a “regular” world, such as aliens, or time travelers. Therefore, it should surprise us less, if we indeed are confronted with such phenomena. Indeed, it seems reasonable to update one’s subjective probability that one lives in a simulated universe, if one encounters such unlikely phenomena.

The world is just a stage

On the other hand, perhaps this world is just a game created by superintelligences, though that doesn’t mean that there won’t be any connection to the purpose of computing verification spaces. Science and play may be merged in strange ways in our distant future.


Nice clarity of exposition here. Thanks.

I do always get to the point with this topic, though, where I ask whether these thoughts have any impact on anything I should do, or think. My answer is always, no. And further, I have decided that spending much time thinking in this way (beyond the original thought process, which I agree has much force) is counter-productive - to my aims, at least - in that one implication is that life is, truly and deeply, pointless (unless I subsume myself into joy at serving the unknowable purpose of the imagined simulation).

Pointlessness has been shown to have a debilitating effect on the happiness and effectiveness of humans. So (again, after the initial, hopefully honest and thoughtful, foray into the subject) I tend to avoid subjects which converge on pointlessness.

I saw an interview with Elon Musk where he said that he and his brother had spent so much time discussing this subject that it was now a banned topic.