Why We (Probably) Aren’t Living in a Computer Simulation — A New Mathematical Challenge to the Simulation Hypothesis

Why we (probably) aren’t living in a computer simulation

It can sometimes feel as if our lives are being run inside a vast computer program. A team of international mathematicians, however, argues in a recent paper in the Journal of Holography Applications in Physics that the simulation hypothesis is not merely unlikely but, in their view, impossible.

From ancient skepticism to modern computation

Questions about whether perceived reality is the ultimate reality are ancient: Indian mystics, Greek philosophers, Chinese thinkers and Mesoamerican traditions all asked variations of this question. In the 20th and 21st centuries, the rise of digital computation reframed the idea as a scientific possibility: could an advanced computer simulate conscious beings and whole universes?

The authors' argument: mathematics, Gödel, and non-algorithmic foundations

Mir Faizal and colleagues begin from developments in quantum gravity suggesting that space and time may not be fundamental but instead emerge from an underlying mathematical structure — a kind of abstract, information-based "Platonic" realm. They argue that a complete theory of reality must reach into that deeper mathematical substrate.

Their central claim invokes Gödel's incompleteness theorem (1931), which shows that in any sufficiently powerful formal system there are true statements that cannot be proved within that system. The authors use this principle to argue that no purely algorithmic or computational framework can capture every true fact about such a foundational mathematical reality.

"Therefore, no physically complete and consistent theory of everything can be derived from computation alone," Faizal says. "A non-algorithmic understanding — something beyond computation — is required."

If the deepest layer of reality truly requires non-algorithmic elements, the authors contend, then even the most powerful conceivable computer could not simulate it, because any simulation must operate by algorithms and programmable rules.

Responses and counterarguments

Not all researchers accept this conclusion. Melvin Vopson (University of Portsmouth) and colleague Javier Moreno argue that Faizal's team commits a category error by assuming a simulator must use the same computational resources available inside the simulated world. A higher-order simulator might operate with different physics, additional dimensions, or resources not constrained by our constants such as the speed of light.

Vopson notes alternative perspectives: the universe might itself be a computation without being a nested simulation, or the host of a simulation could implement non-algorithmic processes that do not map directly onto our internal mathematics.

What this means — and what remains unsettled

Faizal and co-author Lawrence Krauss present a provocative case that Gödelian limits place fundamental constraints on purely computational accounts of reality. Their argument highlights deep philosophical and mathematical issues at the interface of physics, information theory and metaphysics.

However, critics emphasize that conclusions about external simulators cannot be established solely from the rules we observe inside the universe. Whether Gödel-style incompleteness prevents any form of simulation, or only limits simulations built from our own algorithmic frameworks, remains contested.

Bottom line: This paper advances a rigorous, mathematically flavored objection to the simulation hypothesis, but it does not settle the debate. The question of whether reality can be simulated depends on subtle assumptions about what computation and simulation would mean at levels beyond our current physics.