Researchers have observed that Musk is correct if you assume propositions 1 and 2 of the trilemma are false. Meaning, the probability we are living in a simulation is close to one. For a better understanding of Bostrom’s simulation hypothesis, researchers decided to fall back upon Bayesian reasoning. This kind of analysis utilizes Bayes’ theorem, name in honour of Thomas Bayes, an English statistician and minister from the 1700s. Bayesian analysis enables one to estimate the probability or odds of an event occurring, referred to as the “posterior” probability, by initially making assumptions about the thing or object being evaluated. Allocating a “prior” probability to it. 

Researchers started by converting the trilemma into a dilemma. Propositions one and two were subjected to collapse and made into a single statement, as in both cases, the hypothesis is that there are no simulations, at all, in the universe – as far as humanity is concerned. Therefore, when converted into a dilemma, a physical hypothesis, (there exist nil simulations) goes up against the simulation theory (there exist base reality(ies) and there exist simulations as well.) 

What’s done here is that a probability is assigned to each of these notions. We just make the assumption of the principle of indifference, which is the standing assumption when we don’t have any information that shifts our inclinations and opinions either way. Therefore each possibility of the dilemma gets assigned a fraction of 1/2 , not much unlike if we were flipping a coin to decide a bet. 

The next phase of the evaluation needed contemplation about “parous” realities – realities which can produce other, disparate realities, and “nulliparous realities” or those that are incapable of generating offspring realities. If the physical hypothesis were true, and there were no simulations, then the probability of a nulliparous reality would be 100%. Even within the scope of the simulation hypothesis, a majority of the simulated realities would be nulliparous. This is due to the fact that simulations, in turn, generate additional simulations, the computational firepower available to each successor generation reduces to the extent where the dominating percentage of realities will be ones that do not possess the computational resources required to further simulate other ‘child’ realities that have the capacity to host sentient, conscious entities. 

Put all of these factors into a Bayesian formula, and we have the solution, the posterior odds that we are dwelling in a base reality, or a real reality is nearly exactly the same as us being inside of a computer simulation. The odds, however, are a bit swayed in favour of base reality, by just a tad. 

These odds would be altered considerably if humanity developed a simulation with sentient beings dwelling in it, as such an event would alter the probability that we had prior allocated to the physical hypothesis. (i.e., there are no simulations.) You can remove that hypothesis without thinking about it. That leaves us with just simulation. The second we develop that tech, it alters the odds from 50-50 in favour of we are real to almost definitely we are unreal, going by these observations. The day we prove this conclusively, if we do, will be a strange day indeed – humanity would be at a crossroads with regards to what to make of their existential states. 

There are upsides to the current research in the field. With the data that we have at present, Musk is incorrect with regards to the astronomical odds he assigns to us living in a base reality, or a real reality. Bostrom concludes with the outcome – with a few stipulations to boot. “This does not contradict the simulation hypothesis, which only asserts something with regards to the disjunction,” the notion that one of the three former propositions of the initial trilemma is true”, he stated. 

Bostrom, however, takes umbrage to researcher’s choice to allocate equivalent prior odds to the physical and simulation theories at the beginning of the research. “The invocation of the principle of indifference here is rather shaky” he states. “One could equally well invoke it over my original three alternatives, which would subsequently provide them with one-thirds odds each.” “Or an individual could carve up the possibility space in some other fashion and obtain any outcome that one desires to achieve.” 

These quips hold validity as there is no solid evidence to strongly stand behind one proposition or the other. We’re talking in terms of the dilemma here. Our scenario would be altered if we can find conclusive proof of the simulation, we apparently live in. How can we detect glitches in the matrix? 

Researchers of computational mathematics at the California Institute of Technology has pondered on this perplexing matter. “If the simulation contains limitless computational capabilities, there is no possibility of us observing that we are living in a simulation, that is finding evidence – as this unfathomable computer to end all computers could put out whatever code you want, whatever reality you want, to the nth degree of realism.”, researchers state. Let’s go back to the observation regarding video gaming, several of which are reliant on intelligent coding to reduce the resources needed to develop a digital universe. 

The most robust way to identify possible paradoxes and contradictions developed by such computational shortcuts is via quantum physics and experiments. Quantum systems can exist in a superposition of states, and their superposition is detailed by a mathematical abstraction referred to as the wave function. In conventional quantum mechanics, the action of observing causes this wave function to arbitrarily collapse to a potential state. Researchers are currently split with regards to if the process of collapse is something tangible and actual, or is just indicative of an alteration in our knowledge with regards to the system. “If it is just a hardcore simulation, there is no collapse.” “Everything is determined only when you choose to look at it, or perceive it. The remainder is just a simulation, like when you’re gaming on your computer or console.” 

With this conclusion at hand, researchers have developed five theoretical variants of the double-slit experiment, each developed to catch a simulation in the act. But he does specify that it is not possible to be aware, at this juncture, if these experiments would prove valid, or reap any tangible results. “At this point, we’re dealing in conjectures.”, researchers state. 

Researchers at the University of Maryland, College Park, have also accommodated the notion that a simulation with limited computational infrastructure could show itself. Current research concentrates on strong interactions, or the strong nuclear force – just one of the four forces inherent to nature. These equations detailing these strong interactions, which hold together quarks to produce protons and neutrons, are so complicated that cannot be solved with analysis. To comprehend these strong interactions, researchers are compelled to do numerical simulations. And in contrast to any presumed supercivilization containing no holds barred computational capabilities, they must be reliant on shortcuts to render these simulations feasible at a computational level – typically by taking into account spacetime to be discrete, instead of continuous. The most progressive outcome scientists have coaxed from this approach as of yet is the simulation of a single nucleus of helium that consists of a couple of protons and neutrons. 

“Naturally, you begin to question, if you simulated an atomic nucleus today, probably in 10 years, we could be capable of doing a bigger nucleus, maybe in a couple of decades, or three, we could achieve the capability of doing a molecule. In half a century, it’s up for grabs that we might be doing the size of a few inches of physical matter. Perhaps, in a century, we can do the brain.” 

Researchers opine that conventional computing will very soon reach a wall, within the next couple of decades, we will observe the limitations of our conventional simulations of physical systems.” Therefore, researchers are turning their focus towards quantum computing, which is reliant on superpositions and other quantum techniques to render tractability to particular computing issues that would not be possible through conventional approaches. “If quantum computing actually materializes, in the sense that it’s a big scale, reliable computational options for humanity, then we’re going to wind up in a totally different age of simulation.”, researchers state. They are then at the juncture of pondering about how to carry out their simulations of strong interaction physics and atomic nuclei if they simply had quantum computers that were up to the task.  

These aspects, cumulatively, have caused researchers to make speculations with regards to the simulation theory. If we are dwelling in a simulation, then the individual or group simulating is also exercising its discretion over spacetime to limit the usage of computation fireworks (going by the assumption, that it is utilizing the same techniques as our researchers for that simulation.) Signatures of discrete spacetime could possible be observed in the direction high-energy cosmic rays come from: they’d possess a direction of preference in the skies as the breaking of the apparently called rotational symmetry.  

Telescopic equipment have not made any observations with regards to deviations from that rotational invariance, yet. And even if something like this were to be observed, it would not consist of undisputable proof that we exist in a simulated reality, the base reality, or the real reality by itself could possess such attributes. 

Researchers however, worry that subsequent research into the simulation theory is in murky waters. “It’s debatably not testable if we are dwelling in a simulation or not.”, they state. “The hallmark of a true theory is that it can be disproven. If that’s not the case how can we call this actual science?” 

For these researchers, there is a more apparent solution, Occam’s Razor. According to it, without the presence of other evidence, the simplest explanation of phenomena is likeliest to be accurate.” The simulation theory is very detailed, assuming realities upon realities, in addition to simulated beings that cannot discern that they are dwelling in a simulation. “As it is much too complicated, and a detailed model to begin with, going by Occam’s Razor, it really shouldn’t be given much credence, in comparison to the more spontaneous explanation. 

Believers, including Musk, and the Matrix, hold onto a bizarre kind of hope. It’s arguable that computational advances will never stop, and with the speed at which technology is progressing and the accuracy with which predictions are being made, it will be a strange day indeed, when we conclusively prove that we are in fact, unreal. 

What our keepers will make of our little discovery, it remains to be seen. 

References 

https://www.scientificamerican.com/article/do-we-live-in-a-simulation-chances-are-about-50-50/