Why the World Is Simple: Regularity, Compression, and the Grounds of Induction

Simplicity isn't just a good idea — it's the only way anything like you could exist.

The paper's central move is an inversion. Most treatments of Occam's razor ask: "why should we prefer simple models?" and then offer various justifications — Bayesian model comparison, information theory, generalization bounds. This paper argues that framing gets the logic backwards. The right question is: "why does the world have to be simple?" And the answer is that it doesn't have to be — except that if it weren't, you wouldn't be here to ask.

The argument runs through five distinct legs, each answering a question the previous one raises. Bayesian inference (the "decisional" leg) requires a concentrated prior to produce actionable beliefs — a diffuse prior over an astronomical hypothesis space leaves you paralyzed. But concentrated on what? Solomonoff induction (the "predictive" leg) says: shorter programs, with out-of-sample error bounded by the Kolmogorov complexity of the true environment. But why does that work here? The No-Free-Lunch theorems say no learner beats any other when averaged over all possible environments uniformly — so the predictive argument only lands if the world is already biased toward low-complexity outputs. That bias is "Axiom 1," the world-is-simple axiom, and it's the load-bearing assumption of the whole structure. Then: Kolmogorov complexity is uncomputable, so no agent can actually run Solomonoff induction — the driver must take the form of a finite portfolio of provisional models, refined by experience (the "constitutive" leg). Finally, agents in a resource-constrained environment who fail to compress simply dissipate — compression isn't a strategy you can opt out of, it's a survival filter (the "persistence" leg).

The key insight is that the persistence leg is the only one that doesn't assume the world is simple — it implies it. If you exist as a persistent, compressive agent, then by the Good Algorithmic Regulator Theorem, your environment must admit short generative descriptions at the scale you operate on. Worlds where that fails don't contain agents to notice. This is a transcendental argument in the Kantian sense: not "the world happens to be simple" but "the world must be simple relative to us, because we are the kind of thing that can only exist in such a world." The paper formalizes this as Proposition 4.

The paper also does useful housekeeping: it shows that the Bayesian Occam factor (MacKay) and Solomonoff/MDL are genuinely different arguments that come apart when the hypothesis class is misspecified — which is almost always. A worked example with a binary sequence demonstrates that Bayesian model comparison can prefer the more flexible wrong model, while MDL correctly identifies the short alternating-pattern description that neither parametric model contains. Practitioners who cite MacKay to justify predictive claims are quietly smuggling in Solomonoff. Friston's free-energy principle is recovered as one particular bounded-rational implementation of this scheme — useful, but it silently assumes Axiom 1 rather than deriving it.