Gaia, Compressed: An Algorithmic Reading of Exo-Daisy World

Life on a planet makes its temperature history shorter to describe — and that compression is measurable on a single trajectory.

The core idea is simple: a biosphere that regulates its planet's temperature is, by definition, removing unpredictable structure from that temperature record. A bare planet tracks its star closely — when the star brightens, the surface heats, and the two signals are nearly identical. A planet with daisies doesn't: the biosphere absorbs the star's variation and converts it into shifts in daisy composition, leaving the surface temperature comparatively flat and boring. "Boring" has a precise meaning here — it compresses better. The paper measures this directly using Lempel-Ziv compression (the same family of algorithms behind gzip), treating the temperature history as a string of symbols and asking: does ablating the biosphere make that string longer to encode? The answer is yes, by 591 ± 109 bits, on every one of 20 independent trajectories, under every encoding tested including an exact prefix-free encoder whose output bits are literally counted and verified by round-trip decoding.

The paper is careful about what this number does and doesn't mean. It is not an estimate of the Kolmogorov complexity gap the Algorithmic Regulator Theorem is stated on — a difference of computable code lengths doesn't bound a difference of incomputable complexities. What it does carry is an exact coding-mass interpretation: the regulated temperature record receives 2^2036 times the probability mass under the code's induced distribution compared to the ablated record. The paper also shows that the biosphere screens its planet from its star in a more direct sense: the surface-luminosity correlation drops from 0.993 (bare planet) to 0.582 (with daisies), and this screening is confirmed to be causal — nulling the daisies' albedo effect while keeping them alive and sensing destroys regulation just as completely as removing them entirely.

Two further results extend the picture. First, a viability-information curve is constructed pathwise (on single trajectories, not ensembles): as the biosphere's ability to distinguish which species the environment favors is gradually scrambled, it sheds most of its ~120 bits of star-tracking information at nearly constant viability, then collapses steeply once little remains. The qualitative shape — shed information cheaply, then collapse — is reproduced by Shannon mutual information and transfer entropy on the same trajectories (correlation r ≥ 0.93), but the "irreducible fraction" η disagrees badly across estimators (0.27, 0.47, and ≈0), so the paper correctly identifies the curve as the result and η as an estimator-specific summary not to be over-interpreted. Second, the black-and-white daisy architecture need not be assumed: starting from a population with a single continuous heritable albedo gene, fast seasonal forcing spontaneously splits it into a standing black-white polymorphism. An invasion-fitness analysis shows why — overlapping generations create a storage effect that makes environmental variance disruptive rather than stabilizing, once the temperature excursion exceeds a threshold set by generational turnover. The model's own growth law happens to kill monomorphic residents before that threshold is reachable, concealing rather than eliminating the branching point; a smoother growth law exposes it cleanly.