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How do we know we’re not living in a computer simulation? Is it even possible to tell? For what it’s worth, researchers have drawn from various scientific frameworks to reject this hypothetical hypothetical reality—and a team of mathematicians now says they’ve taken the argument a step further.
In a Journal of Holography Applications in Physics study published earlier this year, researchers demonstrated that, assuming the universe runs purely on mathematics and physics, it would be impossible for any algorithm to simulate reality as we know it. This is because the universe exists “on a type of understanding that exists beyond the reach of any algorithm,” the researchers explained in a statement.
“Drawing on mathematical theorems related to incompleteness and indefinability, we demonstrate that a fully consistent and complete description of reality cannot be achieved through computation alone,” Mir Faizal, a physicist at the University of British Columbia in Canada, added in the statement.
The model builds on several mathematical theorems, including Gödel’s incompleteness theorem. This idea, announced by the eponymous scholar in 1931, very simply states that no set of axioms, or algorithm, can perfectly prove every true fact about numbers.
For instance, an algorithm would have trouble parsing the statement “This true statement is not provable.” If the statement were provable, it’d be false and illogical. If it weren’t provable, then it’s true, but how would the algorithm compute an answer?
This might sound like a pointless exercise, but it highlights a key aspect of mathematical endeavors—or, in this case, computation—that it’s bound to whatever mathematicians set as their starting assumptions. This is evident in the history of physics, the researchers explained, as humanity has transitioned from Newtonian physics to Einstein’s general relativity and now to quantum mechanics and beyond.
In the context of the universe, this suggests that there will always be a deeper layer of reality, an “information-based foundation” that cannot be fully described by computation alone, according to the paper. An obvious example of this is that human mathematicians can easily grasp “Gödelian” truths, like the statement “This true statement is not provable,” whereas computers cannot.
“Any simulation is inherently algorithmic—it must follow programmed rules,” Faizal said. “But since the fundamental level of reality is based on non-algorithmic understanding, the universe cannot be, and could never be, a simulation.”
On the other hand, the researchers’ calculations suggest that we may never arrive at a “theory of everything”—at least not one that operates algorithmically. The so-called theory of everything—a holy grail among physicists—works beyond computation, according to the researchers. If a complete, consistent understanding of reality were to lie outside the realm of formal rules, it would be illogical to believe that they could even exist, the researchers noted.
The paper offers fascinating food for thought while subtly expressing appreciation for the natural complexity of the universe. Then again, humans have a tendency to anthropomorphize most things. While I have no qualms against Gödel’s theorem, can it definitively prove something to be impossible—if that something potentially lies beyond the capacities of the human brain?
I am not sure. But I might be nitpicking. I’ll have to ask my simulation operator.
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