But what they have proven has implications far beyond the Matrix movies and the scientists who have proposed that science fiction scenario as an actual possibility. It also asserts the impossibility of finding a “theory of everything,” suggests the limits of AI, raises questions about the validity of computer simulations, and gives us a glimpse of a so-called “Platonic realm” that underlies all reality.
The fundamental nature of reality operates in a way that can never be replicated by pure computation. . . .
Co-author Dr Francesco Marino, of the Italian National Institute of Optics, told Daily Mail: ‘We have shown that a fully algorithmic description of the Universe is impossible.
‘Any simulation, by definition, runs on a set of programmed rules or algorithms that determine how things behave step by step.
‘A simulated world could only mimic the algorithmic parts of reality, but would always fail to include those deeper, non-algorithmic truths.’
Here is an overview of how these researchers proved that:
The researchers use several mathematical theorems to show that you can’t just use computation to get a complete and consistent description of the world.
To put that simply, even if you knew everything there was to know about this world of pure information, there would still be things about the universe you couldn’t work out.
This might seem very strange, but it is actually something that mathematicians have suggested for a very long time.
All the way back in the 1930s, a mathematician named Kurt Gödel proved that there were statements about numbers that we knew were true but could never prove.
It isn’t that we haven’t found these proofs yet or that we just haven’t been trying hard enough; rather, it is mathematically impossible to prove some true facts about the world.
The researchers say the fact that there are these ‘Gödelian truths’ is proof that a full description of the universe requires something called ‘non-algorithmic understanding’. . . .
Dr Faizal says: ‘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.’
Let’s turn to a physics site, Phys.org, where Patty Wellborn has written her take on the findings in Mathematical proof debunks the idea that the universe is a computer simulation. She gives some critical background that indicates a radical shift in worldview that is now accepted by scientists:
The research hinges on a fascinating property of reality itself. Modern physics has moved far beyond Newton’s tangible “stuff” bouncing around in space. Einstein’s theory of relativity replaced Newtonian mechanics. Quantum mechanics transformed our understanding again. Today’s cutting-edge theory—quantum gravity—suggests that even space and time aren’t fundamental. They emerge from something deeper: pure information.
This information exists in what physicists call a Platonic realm—a mathematical foundation more real than the physical universe we experience. It’s from this realm that space and time themselves emerge.
A Platonic realm? Why not call this what Augustine did: the mind of God?
This foundation of existence cannot be fully described by mathematics.
“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,” Dr. Faizal explains. “It requires non-algorithmic understanding, which by definition is beyond algorithmic computation and therefore cannot be simulated. Hence, this universe cannot be a simulation.”
More importantly, this insight shoots down what physicists have long been searching for: a theory of everything.
Co-author Dr. Lawrence M. Krauss says this research has profound implications. “The fundamental laws of physics cannot be contained within space and time, because they generate them. It has long been hoped, however, that a truly fundamental theory of everything could eventually describe all physical phenomena through computations grounded in these laws. Yet we have demonstrated that this is not possible. A complete and consistent description of reality requires something deeper—a form of understanding known as non-algorithmic understanding.”
It also raises questions about computer simulations in general:
The team’s conclusion is clear and marks an important scientific achievement, says Dr. Faizal.
“Any simulation is inherently algorithmic—it must follow programmed rules,” he says. “But since the fundamental level of reality is based on non-algorithmic understanding, the universe cannot be, and could never be, a simulation.”
Right, the universe can’t be a simulation. But I would think this would also at least raise questions about computer simulations in general, which have become a staple of much of today’s scientific research, using computer modeling–inputting data and applying algorithms–to extrapolate conclusions (as in predictions about climate change).
And if there are limits to what algorithms can do, that surely means that the capabilities of AI, which is entirely based on algorithms, are also limited. It is already being recognized that much about the human mind–such as intuition, imagination, emotional perception, consciousness, conscience, and creativity–is non-computational.
The superpowers hyped for AI–that it will make new scientific discoveries, that it will attain human-like consciousness, that it will become greater than the human mind, to the point of becoming super-intelligent and omniscient–would seem to be as impossible as the universe being a computer simulation.
FUN FACT: Kurt Gödel, who is considered one of the greatest logicians since Aristotle, described his religion as that of a “baptized Lutheran.” Though he didn’t go to church, he read the Bible every Sunday, was a theist who believed in a personal God, offered a proof of God’s existence, and defended the immortality of the soul.
Photo: Kurt Gödel colorized by Photocolorization – Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=70778920
Source: The Limits of Algorithms
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