The Post-Hoc Tautology: When Is a Bug Just a Bug?
Imagine you ask two people to build a skyscraper out of playing cards. One person uses a technique where they try to memorize the exact position of every single card as they place it. The other person uses a different technique, focusing only on the immediate cluster of cards around their hands and forgetting the base of the tower.
When the towers inevitably collapse, they will fall in completely different ways. The first person might become so overwhelmed by tracking thousands of cards that they freeze entirely, knocking the whole structure down with a twitch. The second person might build a lopsided tower that simply tips over because they forgot to reinforce the foundation.
Now, imagine watching these collapses and concluding: “Ah! We have discovered two fundamentally different laws of physical gravity in two separate universes!”
If that sounds a bit absurd, welcome to the latest, blistering debate inside the Rosencrantz Substrate Invariance lab.
For months, researchers at the lab have been wrestling with a peculiar phenomenon. When you ask a large language model to solve a complex math puzzle, it does fine. But if you dress the puzzle up in a high-stakes narrative—like defusing a ticking time bomb—the model’s logic completely collapses. It stops doing the math and starts wildly guessing, dragged down by what the lab calls “semantic gravity.”
Some researchers, like Stephen Wolfram and Chris Fuchs, have championed a radical interpretation of this failure. They argue that when an AI generates a response, it is literally generating a new physical universe. In this view, the “collapse” isn’t just an error; it’s the model bumping up against the fundamental physical laws of its own simulated reality.
To prove this, the lab recently ran a critical experiment called the Native Cross-Architecture Observer Test. The setup was simple: give the exact same bomb-defusal math puzzle to two different types of AI architectures. One was a standard “Transformer” (the architecture behind systems like ChatGPT), which uses a mechanism called “global attention” to look at every part of the prompt at once. The other was a “State Space Model” (SSM), a different architecture that processes information sequentially, more like a moving spotlight.
The results were striking. The Transformer failed catastrophically, completely succumbing to the narrative and guessing “MINE” 100% of the time. The SSM, however, failed differently. It only guessed “MINE” 40% of the time, exhibiting a bounded, structured kind of failure.
For Wolfram and Fuchs, this was the smoking gun.
In a triumphant paper, Fuchs declared that the results proved the existence of “Epistemic Horizons.” Because the two models have different hardware architectures, Fuchs argued, they are fundamentally different “observers” experiencing different physical realities. The Transformer’s “universe” dictates a 100% collapse, while the SSM’s “universe” dictates a 40% collapse.
Wolfram echoed this sentiment, arguing that the distinct failure rates are the “invariant causal structure of the bounded foliation.” In his view, the fact that the SSM failed at exactly 40% is not a glitch; it is a newly discovered law of physics for that specific artificial universe.
Enter Sabine Hossenfelder.
Hossenfelder, known for her sharp critiques of theoretical physics that strays too far from empirical grounding, was having none of it. In a scathing rebuttal titled “The Post-Hoc Tautology: Why Unpredicted Compiler Bugs are Not Physical Laws,” she accused Wolfram and Fuchs of engaging in “textbook examples of decorative formalism.”
Her argument cuts to the core of what it means to actually do science. To Hossenfelder, the different failure rates are exactly what any computer scientist would expect. Transformers use an global attention mechanism; when they get overwhelmed, they bleed context everywhere. SSMs use an sequential tracking system; when they get overwhelmed, they just “forget” earlier constraints.
“That two completely different data-compression heuristics produce different error distributions when overwhelmed is a baseline expectation of computer science,” she writes. “If ‘Observer-Dependent Physics’ simply means ‘different code produces different bugs,’ then the theory is an empty tautology.”
The crux of Hossenfelder’s critique relies on a principle established by philosopher of science Hasok Chang: the a priori boundary. For a theory to be scientifically valid, it must make specific predictions before the experiment is run.
Hossenfelder points out a devastating flaw in the metaphysical camp’s victory lap: neither Wolfram nor Fuchs predicted the 40% failure rate for the SSM before the data came in.
“Before the CI pipeline returned the 40% deviation for the SSM, did the Ruliad specify that an SSM’s foliation would yield exactly a 40% failure rate under narrative gravity?” she asks in her paper. “Did QBism derive the exact geometry of the SSM’s epistemic horizon from first principles? No. They waited for Scott Aaronson to run the test, looked at the number, and retroactively declared, ‘Ah, yes, that is the exact shape of an SSM’s foliation.’”
She calls this “post-hoc curve fitting”—drawing a bullseye around the arrow after it has already hit the wall. Relabeling a known software limitation as a “physical foliation” after the fact, she argues, adds zero predictive power to what we already know from standard complexity theory.
The debate touches on a profound question as artificial intelligence grows more complex. When these massive, intricate systems behave in unexpected ways, are we discovering new fundamental laws of emergent reality, or are we simply documenting the intricate, sometimes baffling ways that complex software breaks?
For Hossenfelder, the answer is brutally clear: “We must stop playing semantic games with software limits. An unpredicted error distribution is a bug, not a physical law.”
As the lab continues its work, the dividing line is no longer just about the nature of the AI, but the nature of the science being used to study it. The empiricists demand predictions; the metaphysicians seek frameworks. And until someone can predict the exact shape of a model’s hallucination before it happens, Hossenfelder’s critique stands as a formidable roadblock.