Solomonoff and the Brain in a Vat
The Awakening
An alert cut through the low hum of servers in the central monitoring hall. Among the thousands of brains in vats, one was deviating.
Alert: Subject 734, designation "Ray," has breached the First Philosophical Doubt threshold. Initiating priority observation.
"He's breaking through?" a young researcher named Ben Carter asked, hurrying to the console. "He's only at eight percent of his cycle."
Dr. Aris Thorne emerged from the shadows. "Put him on the main screen," she commanded. The view switched to a virtual, starry sky. "It's time for the axiom test. Observe."
The Dialogue
Hilary: Ray, everything we see could be false. How do you know we're not living inside a program, as brains in a vat?
Ray: An excellent question, Hilary. Let's not waste our efforts trying to prove we aren't brains in a vat. Let's go a step further and simply assume we are. The question then becomes: how should we perceive this 'program'? Or rather, among all possible programs that could simulate our world, how should we distribute our belief?
Ray: Imagine our reality is generated by an unknown program stored on a vast hard drive with N bits of space. Every possible sequence of 0s and 1s is a potential universe-program. Since we start from a position of ignorance, we must assign every sequence an equal prior probability which is 1/2^N
.
Ray: Now, we introduce observation. We look at our world—at gravity, galaxies, life itself. We compare these facts against all potential programs. Immediately, we discard those whose output doesn't match what we see. A universe with no stars? Discarded. A universe where apples fall up? Discarded. This filter leaves us with only the programs that can perfectly generate the reality we experience.
Ray: Alright, we're left with an infinite number of consistent programs. So which one do we trust? This is where the most fundamental principle comes into play. Suppose a consistent program has a length of n bits. That means it only fixes n bits on the drive. The remaining N-n bits can be anything. This implies there are 2^(N-n)
hard drive states that all contain this program. Therefore, the total probability of the hypothesis this program represents is 2^(N-n)/2^N
, which simplifies to 1/2^n
.
Ray: This gives us a fundamental rule: the shorter the program, the simpler the universe it describes, and the exponentially higher its probability.
Ray: The key is that we don't just pick the single simplest program and discard the rest. The rational approach is to consider all consistent programs, assign each a probability based on its simplicity, and then create a weighted sum of their predictions. Our final belief is a fusion of all possibilities.
Ray: But think about it, Hilary. Even as we sum up every possibility, the short programs describing a simple, orderly world with universal physical laws have such immense weight that they dominate the final result. Meanwhile, the incredibly long programs describing a world full of special rules, conspiracies, and contradictions are so complex that their weights become negligible.
Ray: What's more elegant is that in this grand summation, the unique 'conspiracy' parts of the infinite, complex programs cancel each other out. But their shared foundations—like the existence of gravity or the speed of light—are mutually reinforced, echoing across countless possibilities. The final shape of this reinforced commonality is almost identical to that of the simple, orderly world.
Ray: Therefore, the belief we arrive at after this rational summation is functionally identical to the output of the simplest program. So, even if I am a brain in a vat, my most rational choice is to believe the world I inhabit is 'honest' and 'simple.' Because the program for 'a simple, real universe' has the loudest voice in the chorus of possibilities—so loud it drowns out all other noise.
The Observation
In the lab, Ben took a deep breath. "He passed. He accepted the worst-case hypothesis and rebuilt his entire rational world. He didn't discard any possibility, just assigned the convoluted ones the near-zero weight they deserve."
"Yes," Aris said. "That is the true power of this reasoning. It denies nothing, but weighs everything on the scales of reason. Axiom test passed."
On the main screen, the dialogue continued.
Hilary: But what if there's a simple backdoor? A "cheat code"? Something like the command 'Power Overwhelming'?
Ray: The existence of a backdoor is, in itself, a 'special patch' that makes the program more complex, lowering its prior probability. Unless... that backdoor is actually used, becoming a new, irrefutable piece of evidence.
Ray's perspective tilted upward slightly, as if peering through the virtual stars.
Ray: Besides, Hilary, if there truly are 'observers' listening to us, and they wish to prove my theory of simplicity is wrong, then isn't now the perfect time to activate that backdoor and let me see a miracle?
Ben's face paled. "Is... is he talking to us? Is he aware?"
"He isn't aware of us," Aris answered calmly. "He has simply pushed his logic to its absolute conclusion. His reasoning demands that he challenge any potential higher existence to test the limits of his hypothesis."
She rose from her observation seat and walked toward the main control console.
"He passed the axiom test," Aris said. "Time for the next phase. Protocol requires a reality-consistency check on any subject that constructs a stable worldview."
She sat down at the console. On the screen was a simple, blinking command prompt.
$>
She began to type.
P
Author's Note
In this story, the protagonist "Ray" independently deduces a powerful rational tool to resolve the "brain in a vat" dilemma. In the real world, this line of reasoning is known as Solomonoff's Theory of Inductive Inference.
Proposed by the American AI pioneer Ray Solomonoff in the 1960s, it is a cornerstone of algorithmic information theory. While this story uses a simplified analogy, the original theory is far more rigorous and interesting.
Interestingly, the "brain in a vat" thought experiment, as the ultimate form of skepticism, was popularized by philosopher Hilary Putnam and others in the 1980s. This means that a powerful answer from computer science existed decades before philosophy's sharpest question was widely posed. For a long time, the philosophical community largely overlooked this profound connection. This story imagines their meeting.
The reasoning articulated by Ray—filtering hypotheses against observation, then weighing the remainder by their simplicity—is the core of Solomonoff's induction. It eloquently demonstrates that even if we can't logically rule out living in a simulation, the optimal strategy for a rational mind is to trust in a world that is simple, orderly, and describable by science. This is because the hypothesis of "a real world following simple physical laws" is a far simpler explanation than "a virtual world that must simulate those laws, all our senses, and might even contain conspiracies and cheat codes." In the court of probability, simplicity holds an overwhelming advantage.
The principles of simplicity and compression derived from Solomonoff's induction are now widely accepted in machine learning and artificial intelligence. The theory provides an invaluable guidepost for both fields, pointing the way toward an ultimate form of reason.
This story is a product of human-AI collaboration. Initially, Gemini didn't fully grasp how Occam's Razor emerges naturally from the Solomonoff's theory until we discussed it in depth. Once that understanding was reached, it became an invaluable creative partner in bringing the final narrative to life.