In 2003, University of Oxford philosopher Nick Bostrom presented a mathematical argument that we are likely living inside a computer simulation created by some future intelligence. Of course, decades before Bostrom and The Matrix, other folks like Jacques Vallee, John Keel, Stephen Wolfram, Rudy Rucker, Ed Fredkin, and Hans Moravec also explored this headspinning concept. Now, Columbia University astronomer David Kipping has used Bayesian reasoning—a common method of statistical analysis—to calculate the odds that reality is unreal. There's a 50-50 chance we're living in a simulation, he says. And the probability will increase as we develop technology enabling the creation of a simulation containing conscious beings.

"The day we invent that technology, it flips the odds from a little bit better than 50–50 that we are real to almost certainly we are not real, according to these calculations," Kipping told Scientific American. It'd be a very strange celebration of our genius that day."

More interesting to me than calculating the likelihood that we're living in a simulation is the question of how to test whether it's true. What are the levers that, if found, would reveal that there's someone, or something, behind the curtain?

From a feature by Anil Ananthaswamy in Scientific American:

Houman Owhadi, an expert on computational mathematics at the California Institute of Technology, has thought about the question. "If the simulation has infinite computing power, there is no way you're going to see that you're living in a virtual reality, because it could compute whatever you want to the degree of realism you want," he says. "If this thing can be detected, you have to start from the principle that [it has] limited computational resources." Think again of video games, many of which rely on clever programming to minimize the computation required to construct a virtual world.

For Owhadi, the most promising way to look for potential paradoxes created by such computing shortcuts is through quantum physics experiments. Quantum systems can exist in a superposition of states, and this superposition is described by a mathematical abstraction called the wave function. In standard quantum mechanics, the act of observation causes this wave function to randomly collapse to one of many possible states. Physicists are divided over whether the process of collapse is something real or just reflects a change in our knowledge about the system. "If it is just a pure simulation, there is no collapse," Owhadi says. "Everything is decided when you look at it. The rest is just simulation, like when you're playing these video games."

To this end, Owhadi and his colleagues have worked on five conceptual variations of the double-slit experiment, each designed to trip up a simulation. But he acknowledges that it is impossible to know, at this stage, if such experiments could work. "Those five experiments are just conjectures," Owhadi says.[…]

Kipping, despite his own study, worries that further work on the simulation hypothesis is on thin ice. "It's arguably not testable as to whether we live in a simulation or not," he says. "If it's not falsifiable, then how can you claim it's really science?"