Nick Bostrom's 'Simulation Argument'
This initiates a discussion on Oxford philosopher Nick Bostrom's 2003 publication 'Are we living in a computer simulation?' (Link)

Going by the just the title alone, "Are you living in a simulation?", is there any way for participants in the simulation to test it? Plato's Cave analogy seems to suggest that there isn't.

Examining the three candidate propositions on their individual merits, some immediate objections arise. The transition into a 'post-human' condition is going to be as ill-defined as the transition from 'primitivism' to 'civilization', rendering a species-wide narrative with fixed one-shot epochs quite untenable. Our predictions second-guessing the priorities of post-human societies can at most be taken only as seriously as predictions about our society from futurologists 50 years ago can be.

Coming now to the paper itself...

(1) The sheer increase in the quantity of computing power may not guarantee that we realize a non-biological simulation of consciousness. We can't say at this point whether it is only a computing power deficit that stands in the way of simulating subjective states; or even if certain architectures even with existing computing power can be sufficient for enabling subjective states to emerge and to simulate consciousness.

(2) Why would the post-human race necessarily create more simulated ancestors than the actual number of lived ancestors? Perhaps the super-intelligent post-humans evolve an experimental design where their purposes will be served with data from very few simulations!

(3) Does the paper address what maybe called the 'infinite progress' argument? That is, if we humans are most likely to be simulations of post-humans, aren't they too most likely to be simulations of post-post-humans and so forth? Would this eventually require a computer exceeding the 'energy budget of the universe' to orchestrate this nested complexity?

A note on the prior probability assignments of Bostrom's argument can be found here.
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Daniel Dennett talks about something similar in his book consciousness explained
Suppose evil scientists removed your brain from your body while you slept, and set it up in a life-support system in a vat. Suppose they then set out to trick you into believing that you were not just a brain in a vat, but still up and about, engaging in a normally embodied round of activities in the real world.

Also copying from facebook, via Priyabrata Mahapatro
Refutations of the Simulation Argument
Fabien Besnard,
5th September 2004
By examining the logical consistency of Nick Bostrom’s simulation
argument, we find that its conclusions are not fully compatible with
its premises, a weak form of the liar’s paradox. We also claim that a
flaw in the simulation argument is to be found in the misuse of finite
probability theory.
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Notwithstanding Besnard's criticisms (which are substantial), there is a fatal flaw in the argument in that Bostrom carelessly discards information about the distribution of individuals between real and simulated worlds when constructing his formula for the fraction of simulated individuals (upon which the argument and trilemma rests). It is all well and good if there are very large numbers of simulations, but this may be countered if the average number of individuals per simulation is much less than the average number of individuals per real civilization. This might come about if other, unknown, real civilizations are vast in comparison to the simulated civilizations, or, in a similar way, if very large numbers of simulations exist, but of comparatively very few people each (say each simulation is of only something like a decade long). In these ways all 3 propositions of the trilemma may be simultaneously false.

Bostrom noted this and responded in a 2011 article, A Patch for the Simulation Argument, providing 2 separate patches that he believes to be sufficient to repair the argument. Ironically, the first patch is simply to assume that the above can't happen by fixing the ratio of the average population per simulated civilization to the average population per real civilization at about 1. I'm not entirely sure why Bostrom thinks that disregarding the logical possibility outlined above, simply because it doesn't agree with his conclusions is the proper response, but needless to say it is not sufficient to patch the simulation argument. His second patch, in contrast, does fix the flaw outlined above, but it does this by changing the reference class so that when calculating the fraction of simulated individuals, only those that are born with the same "computer age birth rank" are included (by this he means, if we indexed all individuals by their birth order since the computer chip was first invented or some other technological invention). This step can be seen to be pathological in its choice of reference class by considering that it discards individuals who might be exactly like me except for their birth rank, but includes those who are in no way like me except for their birth rank. An arbitrary redefinition of the reference class, precisely to obtain his prior conclusion, is not a sufficient patch for this flaw. For it to be sufficient he would have to justify this choice of reference class over any other and not only does he make no attempt to do so (excluding the justification that it produces his previous conclusion), but I don't see that such a justification is possible.
Cambridge physicist David Tong suggests there maybe a criterion to tell apart a real universe from a simulated one. A tl;dr version of his argument : (i) A condition for computer simulation, is that quantities should allow discretization. (ii) The Standard Model does not seem to lend itself to computer simulation. (iii) Our universe, described by the Standard Model, is not a computer simulation

In this SciAm article (unfortunately behind a paywall), Prof. Tong explores the implications of 40 years of unsuccessful efforts to simulate the Standard Model on a computer. Quoting from the print version of the article:

Quote:To perform such a simulation, one must first take equations expressed in terms of continuous quantities and find a discrete formulation that is compatible with the bits of information in which computers trade. Despite decades of effort, no one has succeeded in doing that. It remains one of the most important, yet rarely mentioned open problems in theoretical physics.

Physicists have developed a discretized version of quantum fields called lattice field theory. It replaces spacetime with a set of points. Computers evaluate quantitites at these points to approximate a continuous field.
Quantum field theories come in many conceivable varieties, each with different possible types of fermions, and people can now formulate nearly every one on a lattice. There is just a single class of quantum field theory that people do not know how to put on a lattice. Unfortunately, that class includes the Standard Model. We can handle all kinds of hypothetical fermions but not the ones that actually exist.
The difficulty is placing chiral fermions on the lattice maybe telling us something important: that the laws of physics are not, at heart, discrete. We are not living inside a computer simulation.

Prof. Tong's article does not deal with the Simulation Argument except in the cursory mention at the end, and the case it makes is for embracing a fundamentally analog view of reality. The implications lattice gauge theory may have on how the Simulation Argument is viewed, is the topic of this article by Dr. Steven Novella:
Are we living in a simulated universe?

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