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Home » The Mathematical Equation That Proves We Are Likely Living in a Simulation—And Who Found It
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The Mathematical Equation That Proves We Are Likely Living in a Simulation—And Who Found It

Sam AllcockBy Sam AllcockJuly 29, 2026No Comments4 Mins Read
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The Mathematical Equation That Proves We Are Likely Living in a Simulation
The Mathematical Equation That Proves We Are Likely Living in a Simulation
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In 2003, while working on existential risk and philosophy of mind in his Oxford office, Nick Bostrom released his simulation argument. The article did not immediately make headlines. It was discussed at conferences, distributed in academic philosophy, and developed into a thought exercise used by instructors to liven up epistemology classes. After Elon Musk publicly stated that the likelihood that we are not in a simulation is “one in billions,” the internet discovered it. Suddenly, a thoughtful piece of academic philosophy became one of the most popular existential questions on the internet.

Bostrom’s argument is a trilemma, meaning that at least one of the three options must be true. Either posthuman civilizations continuously lose interest in conducting ancestor simulations, or civilizations consistently go extinct before gaining the technology to run convincing simulations of reality; or we are most likely currently living in a simulation. According to the reasoning, it is statistically likely that any given mind is simulated if simulations are feasible and civilizations typically run a large number of them. This is because the simulated minds will much outweigh the biological ones. The argument doesn’t tell you which of the three alternatives is correct, which is unsettling. It just states that one of them must be.

In 2020, Columbia University astronomer David Kipping, who often looks for exomoons and far-off planetary systems, made the decision to try something that the philosophical literature had not yet done: apply Bayesian statistics to Bostrom’s thesis. Kipping employed Bayesian reasoning, a technique for updating probability estimates in response to new information, to the simulation conundrum by giving the question of whether simulation technology is even feasible at the scale Bostrom envisions a 50/50 prior probability. According to his calculations, there is a 50.2 percent chance that we are in base reality and a 49.8 percent chance that we live in a simulation. A toss of the coin. Almost identical to chance.

The outcome is both intriguing and rather disappointing at the same time. It’s intriguing because applying a serious quantitative approach to a serious philosophical argument results in actual ambiguity rather than rejection. The fact that 49.8 vs 50.2 isn’t actually a revelation—rather, it simply indicates that we don’t know, represented in decimal places—makes it anticlimactic. The sensitivity of the result to earlier assumptions is what Kipping’s approach does capture. The output changes significantly if you give the initial premises even slightly varying weights. The math makes sense. The inputs seem questionable. The majority of the actual intellectual work is done there.

The debate becomes truly complex when it comes to the physics counterarguments. Drawing on Gödel’s incompleteness theorem and its implications for quantum mechanics, some academics contend that non-algorithmic processing—computation that conventional Turing-complete machines are fundamentally incapable of performing—would be necessary for a full reproduction of reality. If that’s correct, simulating the cosmos isn’t that difficult. In theory, no computer that we can currently imagine can simulate it. Others draw attention to the rapidly growing energy and computing costs of modeling nested realities, or simulations inside simulations, which render civilization-scale simulation increasingly unfeasible even with cutting-edge technology.

The fact that different societies have responded to the simulation debate in different ways is something worth considering. For the reasons mentioned above as well as the fact that it does not produce testable predictions like practical physical theories do, physicists typically regard the strongest versions of the hypothesis to be unpersuasive. It is a valid and unanswered inquiry concerning the nature of reality, according to philosophers. People in the tech sector find it strangely appealing, perhaps because it fits with a perspective that views computational systems as the most basic explanation for everything. Depending on who is carrying it, the argument moves in different ways.

The Mathematical Equation That Proves We Are Likely Living in a Simulation
The Mathematical Equation That Proves We Are Likely Living in a Simulation

Both Kipping’s Bayesian model and Bostrom’s trilemma address the age-old query, “What is the nature of the reality we inhabit?” — and apply a sort of logical reasoning that, rather than discounting the uncertainty, makes it apparent. 49.8% is not the correct response. The truth is that our methods for answering the question result in a coin toss, and we truly don’t know. That is not insignificant. It’s not proof either.

Columbia University astronomer Mathematical Equation Oxford Martin School philosopher
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Sam Allcock
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Sam Allcock is a journalist, digital entrepreneur, and media strategist with a passion for purpose-driven storytelling. With over a decade of experience in the media landscape, Sam has built a reputation for creating impactful narratives that bridge the gap between innovation, integrity, and social responsibility. As the founder of multiple digital ventures, Sam understands the power of strategic communication in shaping public discourse. His work explores how technology, entrepreneurship, and ethical leadership intersect to create meaningful change. On Purposed.org.uk, Sam contributes thought-provoking articles that challenge conventional thinking and advocate for a more conscious approach to business and media. Beyond his writing, Sam actively supports initiatives that promote transparency, trust, and long-term value in both corporate and community settings. His insights are grounded in a belief that purpose is not just a trend, but a transformative force in today's world.

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