Tech billionaires are still looking for scientists to help them break out of the computer simulation that they suppose is our world. Its difficult to look at this world view without taking the personal perspective of the believer into account, but lets examine these claims on their own merits first.
Bostrom's Simulation Argument
Nick Bostrom is one of the first academics to popularize the idea of reality being faked with his classical simulation argument based on (his perception of) probability factors. His hypothesis is built on the idea that at least one of following assertions most likely describes the truth:
1) The fraction of human-level civilizations that reach a posthuman stage is very close to zero;
2) The fraction of posthuman civilizations that are interested in running ancestor-simulations is very close to zero
3) The fraction of all people with our kind of experiences that are living in a simulation is very close to one
Critiques of Bostrom's Assertions
We presently do not have enough information to make any assumptions about the number or nature of human-level civilizations. Simulating ancestors seems like a very special case and seems like a quite unique motivation to run a simulation that contains self-aware entities. Other motivations to create or re-create human entities in silico have since been put forward, but are just as speculative and just as oddly specific, including the possibility of simulation as a punitive measure (Roko's Basilisk).
The final assertion about the fraction of all civilizations "with our kind of experiences" living in a simulation being close to one is largely based on the reasoning that the number of physically existing civilizations is vanishingly small compared to the number of possible simulated civilizations, ergo it should follow that we are probably a part of the majority. In reality, there is no data available that allows a viable statistical assertion about the relative numbers of such civilizations to begin with, nor does a statistical pseudo-anthropic argument necessarily yield facts about our universe.
The Bostrom scenario contains a number of implicit assumptions about the nature of a possible simulation, most notably that reality is being simulated for the sole benefit of humans, as opposed to a more generally simulated universal sandbox.
Popular Variants and Models
It's a Not a Single Hypothesis - It's a Spectrum
When the simulation argument is being discussed in public, the first point of confusion arises from the fact that there is no single coherent simulation argument in the first place. Whether by design or by accident, this is a subject where each participant in a discussion (as well as every member of the audience) erroneously assumes the topic revolves around their personal variant of the scenario. One might think this would be the first issue to address, or even that the nature of these differing personal visions might constitute the bulk of the discussion itself, but that assumption would be mistaken.
The possibility spectrum of potential simulated realities is mainly situated between two iconic extremes, which as a shorthand I will call The Matrix, and the Boulder Field, respectively. Between those two, and even beyond, there exists a range of possibilities but in my opinion they are culturally well-supported shortcut metaphors that reflect current thinking.
Possibility 0: The Null Hypothesis
As there is currently neither experimental nor observational evidence in support of any flavor of a simulation scenario, the default assumption should be that we are not inhabiting a simulation. Even if one were to consider the observation that the universe does share information-theoretical characteristics with certain types of computing systems, it still does not follow that the processes making up the workings of our universe have been willfully constructed by an intelligence. At the time of writing this, there is no known viable experimental approach to test any variant or aspect of this hypothesis.
Possibility 1: The Matrix
The Matrix flavor of simulated reality is unabashedly anthropocentric: in a supposed real world, we humans are either biological entities literally entombed in storage vats, or we are other beings with a different physiology which are nevertheless still imprisoned in a reality that is being simulated entirely for the purpose of containing us. In this scenario the rest of the universe doesnt really exist - its just an illusion being projected into our minds on demand, in an effort to show us a plausible version of the world. The number of people that are actually real in this scenario could potentially be as low as one - the ultimate solipsists fantasy.
While the supposed Matrix machinery does operate on certain arbitrary rules, it is characterized primarily by its superficiality and prison-like character. The prisoners themselves could potentially be freed from this ruleset once they were to overcome their systemic conditioning, opening the possibility of an actual physical escape from the prison if they could somehow manage to break free from the machine sarcophagus containing their bodies.
Possibility 2: The Boulder Field
The Boulder Field metaphor on the other hand is an entirely different scenario, iconically and accurately depicted in an XKCD comic: the universe is a big array of data, being acted upon by a process that operates rigorously and tirelessly on fixed rules. This is a fundamentally uncaring process, and even if it were being operated by a sentient being, it might not even be aware of us living in the data.
If you are a Stephen Wolfram fan, you might envision this universe as a collection of cellular automata. Scientifically, there is no discernable difference between this simulation and the universe as we know it, and its typically only labeled a simulation depending on whether we consider the engine that processes this data a computer or not.
Living in a Boulder Field simulation means you are not a special being for whose benefit illusions are created; you are instead an entity that exists entirely and exclusively in the context of the simulated universe. With both your body and your mind completely residing inside this universal construct, you are not fundamentally different from an animal or any other natural process, as far as the computer doing the simulation is concerned. The Boulder Field is also substantially different from the Matrix in that neither you, nor your species, nor the world you live on, was likely put there by anyone intentionally. The concept of breaking out from this kind of simulated universe is meaningless, because in most variations of this scenario there is no external world where you could continue to exist. Our concepts of time and space would not necessarily have a workable analogue in the real world that houses our simulated universe.
Considering these two iconic extremes, it is apparent which one more closely resembles our observable universe. The Boulder Field is for all intents and purposes identical to the world we live in, to the point where it becomes moot to argue whether it counts as a simulation or not. It is not clear at this point if an experiment or observation could be devised - even in principle - to test whether the Boulder Field variant actually describes our universe.
The Boulder Field is unlikely to capture anyones fascination. If you are living in the Boulder Field, your best bet is to continue on the path of science and continue to discover ways to exploit the laws of nature in your favor. The Boulder Field commands no distinct cause of action. There may be a day when we discover some phenomenon that uncovers a basic fabric of reality behind our universe, but right now all we can do is blindly poke at nature and observe. One might consider high energy particle physics to be one of those frontiers where a vague glimpse at an underlying fabric is possible in principle, but so far no deviation from the expectations of the Standard Model have been found.
The Matrix on the other hand, is clearly the front runner as far as public imagination is concerned, because it deals with familiar and popularized fictional concepts. However, by virtue of its fakeness and the friction that results from the inhabitants having transcendental bodies, any Matrix-style system is constantly at odds with the universe as it is being observed by science. While it seems at least conceivable to keep the illusion up indefinitely, it is an uphill battle just waiting to be lost in an instant if the prisoner ever stages a successful exploit. One might argue that they should have given us a far simpler reality to experience if they really wanted to keep the illusion up in the long term, but such arguments are unlikely to dissuade a dedicated believer.
The Matrix concept would seem to bring with it an escalating amount of engineering difficulties that should hint at its improbability, yet it appears drastically more attractive to people because it does harmonize well with popular fiction culture. Apart from an intellectually incoherent series of movies detailing the setting, this conceit has other desirable characteristics making it a great mythology that moulds perfectly into the slots historically reserved for religious and spiritual thinking.
Motivations for a Matrix Belief
At this point one must consider the motivations of the believers as they relate to the nature of the simulation they are postulating. The Matrix appeals to people from all walks of life:
For the population at large, the Matrix features the prospect of meaningful resistance against a system designed to keep its denizens small for nefarious purposes, closely mirroring the experience of living in the modern world.
To the rich, successful person, the Matrix represents a validation of their perceived destiny and superiority. Having overcome all of the basic problems a contemporary human existence on Earth brings with it, a successful person will likely perceive breaking out of - or at least playing a fateful role inside - the Matrix to be the logical next-level achievement to target, an appropriate quest for a person who by virtue of inherent greatness can never fail, and who after having mastered this world must now extend their dominance to the next one.
The Matrix is the perfect religion for a wide range of human life experiences, and being a trope that is already saturated in contemporary culture makes it easy to get into. The bad news is you are living in a simulated prison, the good news is your kind is the most important component of the universe - and if you are a true leader, you can one day escape into the real world to take on your rightful place amongst the gods. Until then, it is all just a stage show designed for your consumption.
If the reasoning detailed above holds up, the Matrix is likely closer to what most people imagine a simulated reality to be. The call for scientists to come up with a way to break out only makes sense in the Matrix. By comparison, proving the existence of the Boulder Field would likely not yield a socially meaningful result. Proving the existence of the Matrix on the other hand would legitimize a number of ideologies we came up with over the centuries; these are ancient notions rooted in the human psyche's search for external meaning, explanation, and validation - but they are fundamentally at odds with our scientific understanding of the universe.
In closing, the Simulation Argument appears to be largely political in nature, or to the extent it is philosophical, that philosophy seems tainted by wishful thinking and projection of current social and religious ideas onto the supposed nature of the universe. In public discourse, it is deemed acceptable to substitute factual models and data with constructs that carry a higher perceived ideological resonance. In this climate, the Matrix variant of the hypothesis features a high degree of similarity to current social issues by not only providing a mythological framework for the nature of our disempowering existential experiences, but also offering the promise of an escape from oppressive mundanity that is equally as fictitious. To postulate the Matrix as a workable model of physical reality, then, should ultimately be judged as a Lysenkoist endeavor on a truly cosmic scale.