No, we do NOT live in a simulation—Math disproves Matrix theory once and for all

The idea that reality—the universe, our world, and everything we perceive—is a simulation has fascinated philosophers and scientists for millennia, but new findings suggest that the theory, despite its immense popularity, is not just flawed but mathematically impossible.

The new study, by researchers at the University of British Columbia's Okanagan campus, not just debunked the theory that we live inside an advanced civilization's supercomputer, but also proved something far more profound: that the universe is built on a type of understanding that cannot possibly be modelled by any algorithm, however advanced it may be.

While the findings may seem mind-bending, we'll try our best to explain what the researchers found.

While interest in the simulation hypothesis has ebbed and flowed over the years, the idea gained a solid following after the release of The Matrix, and subsequent scholarly work, most notably Oxford philosopher Nick Bostrom's 2003 paper, 'Are You Living in a Computer Simulation?'.

Even renowned astrophysicist and science popularizer Neil deGrasse Tyson has occasionally thrown his weight behind the idea, saying that with enough computational power, it would be possible to create a simulated universe.

The most recent and notable proponent of the simulation hypothesis was none other than Tesla and SpaceX CEO Elon Musk, who, in 2018, said in a Joe Rogan podcast: "If you assume any rate of improvement at all, [video] games will eventually be indistinguishable from reality. We’re most likely in a simulation."

Turns out, all of them were wrong.

No matter how advanced, all computer simulations are built on algorithms, which are essentially like recipes: step-by-step computational rules that create an end-product (like code in a video game, for instance).

So, for a computer to be able to simulate the entire universe—including its most fundamental laws—it would need a complete and consistent set of programmed rules for everything.

This, however, is not mathematically possible, as the researchers found.

To demonstrate the same, they drew on one of the most interesting facets of reality as we understand it.

Today, quantum mechanics has transformed our understanding again, and the cutting-edge theory of quantum gravity suggests that even space and time, long deemed to be the pillars of physics, aren't fundamental either.

Rather, space and time themselves emerge from something far deeper—pure information, which exists in what physicists call the Platonic realm, a mathematical foundation that is more "real" than the physical universe we inhabit.

However, the study demonstrated that fundamental mathematical limits prove that a complete description of reality requires a deeper, non-algorithmic understanding.

To that end, the researchers drew on one of the most powerful theorems in modern mathematics—Gödel's Incompleteness Theorem—which proves that any formal system of rules (including say the theoretical code of a perfect simulation) will always contain true statements that cannot be proved or derived within the rules of that system.

These true statements that cannot be derived or proved within the rules of a formal system are what scientists call "non-algorithmic" truths, truths that are "grasped" (understood) rather than "computed" (calculated).

To demonstrate, let's take a formal system like the English language. Assume that one of the system's rules or one of its axioms is that every declarative sentence must be either true or false.

Now consider the following statement: "This sentence is false".

If one assumes the above statement to be true, then what it says must be correct, which leads to the conclusion that the statement is false (a contradiction).

Conversely, if one assumes the above statement to be false, then what it says must be incorrect, which leads to the conclusion that the statement is true (a contradiction again).

The vicious loop that this sentence forces you into—it must be true if it is false, and it must be false if it is true—is a demonstration of the limits of the system.

In other words, the statement ("This sentence is false") exists perfectly within the system: it is written using the symbols of the English language and is grammatically sound. However, when the system attempts to use its internal rule and tries to assign a value (true/false) to the statement, it fails repeatedly.

The actual truth about the statement—that it is a paradox that is undecidable—falls outside the rules of the system, which allows only true or false.

Our small thought experiment on Gödel's Incompleteness Theorem is what the researches demonstrated at more fundamental, mathematical level.

They found that the deep structure of the universe—the so-called Platonic realm of fundamental information from which space and time emerge—is built on a type of understanding that cannot be merely computed, but has to be grasped.

Reality, at its core, is not merely the product of a set of computations, but includes "non algorithmic" truths that have to be understood, not calculated.

Commenting on the findings of the study, Dr Faizal, Adjunct Professor with UBC Okanagan's Irving K Barber Faculty of Science and a lead author of the study said: "It has been suggested that the universe could be simulated. If such a simulation were possible, the simulated universe could itself give rise to life, which in turn might create its own simulation. This recursive possibility makes it seem highly unlikely that our universe is the original one, rather than a simulation nested within another simulation."

"This idea was once thought to lie beyond the reach of scientific inquiry. However, our recent research has demonstrated that it can, in fact, be scientifically addressed," he asserted.

Dr Faizal went on to describe his team's core findings: "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."

"It requires non-algorithmic understanding, which by definition is beyond algorithmic computation and therefore cannot be simulated. Hence, this universe cannot be a simulation," he explained.

The study, titled ‘Consequences of Undecidability in Physics on the Theory of Everything’, demonstrated that it can indeed be tested using science.

Further, it demonstrates that the holy grail of physics, that is, a Theory of Everything—a single set of equations that describes all physical phenomena—can never be purely computational; it will require non-algorithmic understanding.

The full published study can be accessed in the Journal of Holography Applications in Physics.