"Are You Living in a Computer Simulation?" (by Nick Bostrom) is a fascinating article, which Gayle Dean brought to my attention. It is a bit bizarre to read right now, as my last few months have been spent programming simple simulations, so I'm well immersed in the notion of simulations.
Nick Bostrom's article reminds me of several things:
- The supposition that there is a universe outside of the universe.
- The Matrix and the Animatrix (which feature this, more or less).
- Streams of consciousness while tripping in high school.
I was impressed by the attention to estimates at orders of magnitude. Since I know a little bit about computer science and their implications for simulations, I wish the author had brought up the analysis of algorithms. Computational power is of secondary importance to the efficiency of the algorithms being executed on those computers. His omission of the analysis of complexity, I believe, invalidates his estimates, not by a few orders of magnitude but potentially by as many orders of magnitude as his total estimate size (e.g., ~10^50 orders of magnitude).
I think the author, Nick Bostrom, missed one more significant facts that could be true:
- Substrate-independence is costly.
- Searching the space of possible simulations to find a valid simulation is prohibitively costly.
- The argument is a non-falsifiable hypothesis.
- The transhumans must possess relatively omnipotent processing power and relatively limited creativity.
- Even if true, the ethical impact to inhabitants of the simulation is negligible.
Substrate-independence is costly. The overhead required to engineer equivalent consciousness through virtual means of what could have been implemented directly via physical means is inefficient. For the quality of consciousness being striven for, optimizing the architecture of the substrate is of primary practical interest. For example, computers often operate on substrate-independence. Virtual machines construct computer architectures that only exist when the lower-level code is in operation. But these have an overhead, and can never compete with the run-time efficiency of their physical counterparts if the physical counterparts have equivalent processing power.
The implications of chaos theory on a simulation were not stated by the author. Weather simulators fail to provide even a good two-week forecast, let alone a thousand year forecast, because the level of granularity being simulated is not equal to the physical level. Even simulating events on the neural level leaves out the atomic events which comprise the neural level. Butterfly effects could arise which make the simulation substantially divergent.
A serious problem that the transhuman simulators will have is finding the actual starting conditions of the simulation. Without being precise, the simulation would not carry out according to history. Minute differences in starting conditions could mean the difference between life on Earth or not. Even if actually simulating an already correct model of humanity's universe were feasible, finding the right starting condition could imply executing the simulation several times until a good match was found. This match would be for the complexity of the simulation (say 10^50 per second), over the number of seconds needed to be simulated (say over a 1 million years, or about 10^14). That multiplies to 10^64. The proper configuration must be found, which would be a search of all possible universes, with each universe having a size of 10^64. That could be a search of 10^64 of 10^64, or 10^128. Now the problem is that we are above the number of molecule-seconds in the span of the universe. Even if a planet could perform 10^50 operations per second, it would take 10^50 planets 10^28 seconds (or longer than the expected life of the universe) to run the correct simulation at the level of human perception.
There is an oversight on the complexity of the algorithm required to simulation human perception. The lower bound could theoretically be 0, but practically, since data is rapidly changing on the scale of seconds, it wouldn't be less than the size of the data per second. But that's just the lower bound. The usual high estimates (not upper bounds) for computer simulations are exponential relationship to the size of the data. That could mean for example that the simulation of 10^50 bits of data requires 10^(10^50) computations. 10^(10^50) is not a number followed by 50 zeroes. It is a number followed by 10^50 zeroes!
Therefore, the universe in which this simulation occurs must be much much larger than the universe that we perceive. Thus, it would not be ancestors being simulated, but a much universe in this hyper universe.
Simulating the universe to a level of granularity that we experience requires a universe with googols upon googols of more processing space, processing power, and processing ingenuity than our universe. In essence, it supposes (from the point of view of the simulants) omniscience and omnipotence.
(There's a sardonic implication. There would need to be googols upon googols of spare time on their hands and very little creativity on the part of the simulation architects. Out of all the things they could come up with given omnipotence and omniscience, flaccid sacs of protoplasm were the height of their accomplishment? :)
Scientifically, there's a vacuous extravagance. This hypothesis provides no new predictions that can be measured from within the simulation. It complicates all reasoning about the simulation. So the hypothesis is a disadvantage to anyone who believes it. Anyone is better off ignoring the extra layer of abstraction.
Although Nick Bostrom supposes no ethical cost to the simulation, actually there is a vast question on ethics. The above computational estimates suppose costs that are higher than the known universe could have. The costs are beyond substantial. The ethical calculus to be performed is two-fold: If these resources are spent on the simulation, what is the ethical result. If the resources are not spent on the simulation, what is the most ethical alternative? Assuming that the simulation itself had no particular ethical harm to its inhabitants, the question becomes what good is the simulation. It would have to be sufficiently better than any other use of from 10^128 bits to 10^(10^50) bits of computation. It's hard for me to believe that such quantities, which may amount to the computational power of a googol human universes, would be best served in ancestor-simulation without there being a universe in which there is much more such processing power. So much so that this was negligible.
On morality, and the threat of punishment, some probability of punishment would have to be taken into account. Nick took into account one hypothetical probability of experience being in a simulation and at the subject of the simulators. But there is a cost for monitoring the simulation and assessing its inhabitants' behavior. If there are some ten billion (10,000,000,000) ethically-monitored inhabitants then the raw probability for individual assessment would either be low, or the analysis performed would be relatively cheap to perform. If it is not cheap to perform, and is an accurate assessment of moral behavior, through a complicated ethical or moral calculus, then the probability of it being performed would expected to be low given the number of agents available for review. It might be highest for agents whose decisions were creating the largest ethical difference, such as persons in power. But auditing these persons would not be as simple as forking their simulation data. The analysis itself would likely require an exponential asymptotic order of processing power compared to the data being analyzed, which makes auditing more expensive than running the simulation by many many more orders of magnitude.
Such omnipotent beings who were going to simulate a phenomenological universe of humanity would either have to give up precision, in which case there's little reason to suppose that the simulation bears relation to the original experience, or the omnipotent beings would have wasted significant resources; resources so significant as to be relatively infinite from our vantage point. A waste on such scale seems hard to account for as form of Intelligent Design, which this simulation argument is a variant of. It would at best be unintelligent or aimless, and infinitely more likely not to be a simulation at all but to be the real thing.