The argument about irrational numbers like PI supposedly disproving the simulation hypothesis is intriguing, but ultimately based on misunderstandings about both mathematics and how simulations function. While it’s true that irrational numbers have infinite, non-repeating decimal expansions, this doesn’t mean they can’t be used—or approximated—in computational systems. In fact, we already approximate these numbers in every real-world scientific and engineering application. Physics doesn’t require us to compute PI to infinity; it just needs values precise enough to match the limits of our measurement tools and observational needs.
Even in our most advanced simulations and scientific models, we operate with finite precision. This doesn’t make those models invalid or useless. Simulated environments work by mimicking the necessary aspects of reality at a given scale, not by reproducing every mathematical constant in full. A simulation, by definition, only needs to generate a convincing reality for the observers inside it—it doesn’t have to conform to perfect, Platonic ideals of mathematical purity.
Moreover, modern physics, particularly quantum theory, already suggests that reality might not be continuous at all. Space, time, and energy appear quantized at fundamental levels. If our universe is already discrete in nature, then finite resolution wouldn’t be a limitation of a simulation—it would be a feature that aligns with how our universe actually behaves.
So, the idea that a simulation couldn’t include irrational numbers misunderstands how both physics and simulations work. We’ve never needed infinite precision to describe reality convincingly, and a simulated world wouldn’t either. As for the hope of finding a cosmic watermark in the tail end of PI, it’s a fun thought—but it’s not the kind of evidence that would make or break the simulation argument.