Gaia, Compressed: Pathwise and Compressor-Relative Measures of Regulation in Daisyworld

Daisyworld's biosphere compresses its planet's temperature history — and that compression is measurable on a single trajectory, without an ensemble.

The core idea is simple: a regulating system makes its environment more predictable, and more predictable means shorter to describe. Daisyworld is the classic test case — black daisies warm their patch, white daisies cool theirs, and together they hold planetary temperature near the growth optimum as the star brightens. Previous work measured this regulation statistically, averaging over hundreds of independent simulations. This paper measures it algorithmically, on one realized trajectory at a time, using Lempel-Ziv compression as a proxy for Kolmogorov complexity (roughly: the length of the shortest program that reproduces a string). The key operation is an ablation — run the planet with the biosphere, then run it without, and compare description lengths. Removing the biosphere lengthens the temperature record by 591 ± 109 bits, consistently across 20 trajectories and five different encoders, including an exact prefix-free code where bits are counted directly rather than estimated. The surface-luminosity correlation drops from 0.993 to 0.582 when life is present — the biosphere screens the planet from its star. The paper is careful about what this does and does not license: a difference in computable code lengths is not a bound on the underlying Kolmogorov gap, so no posterior suppression factor is claimed. What it does carry is an exact evidential meaning relative to the code used.

Two further results are built on this foundation. First, a viability-information curve — how much information the biosphere holds about its star as a function of how hard you intervene on it — turns out to be computable pathwise rather than requiring an ensemble. The biosphere sheds most of its ~120 bits of star-tracking at nearly constant viability, then collapses steeply rather than at a sharp threshold. Shannon mutual information and transfer entropy reproduce the shape of this curve (r ≥ 0.93), but the irreducible fraction — the number that is supposed to summarize how much information is causally necessary for survival — comes out as 0.27, 0.47, and ~0 depending on which estimator you use. The paper's conclusion: the curve is the result; the fraction is an estimator artifact.

Second, the paper asks whether the black-white architecture needs to be imposed at all. It doesn't. In an individual-based model where each daisy carries its own heritable albedo on a continuous scale, a single gray population spontaneously splits into a standing black-white polymorphism under fast seasonal forcing — reversibly, from either initial condition, with the transition set by the ratio of forcing period to genetic tracking time. The mechanism is a storage effect: overlapping generations let unfit-but-living individuals persist as standing variation, and once environmental oscillations are large enough, the population mean becomes the worst place to sit. An invasion-fitness analysis locates the branching threshold analytically — selection turns disruptive when RMS temperature excursion exceeds 1/√(2k(1-repl)) — but the model's own truncated growth law kills monomorphic residents before that threshold is reached, hiding rather than eliminating the branching point. A smooth growth law exposes it, and the simulation branches exactly where the formula predicts. The evolved polymorphism compresses its planet's record much as the hand-wired one does. And crucially: it is the architecture — the standing two-mode distribution — that holds information about the star, not the ongoing evolution. Freezing the trait distribution and switching mutation off raises shared information further; evolution's job is to find the architecture, not to perform the tracking.