Chapter 7 — Life as Informational Curvature
Life is not the defiance of physics—it is its refinement. In the grammar of the universe, living systems are clauses of coherence, regions where informational curvature bends tightly enough to sustain itself. Where ordinary matter traces simple geodesics through spacetime, life folds those geodesics back upon themselves, forming stable, energy-driven loops that remember. A cell is thus not a machine of matter, but a whirlpool of information that refuses to flatten.
At its simplest, life is feedback embodied. Every organism maintains gradients—of energy, charge, concentration—that resist equilibrium. These gradients are informational tensions: differences that persist through continual correction. Metabolism, replication, and adaptation are not three miracles but three aspects of the same process—the conversion of entropy into structure through feedback. In IPSC terms, a living system is a localized submanifold of I14 whose curvature is maintained by constant informational flux.
Schrödinger, in his 1944 lectures, called this “feeding on negentropy.” IPSC provides the missing geometry behind the phrase. Negentropy is not a mystical reversal of the second law, but a local gradient in the informational field—an area where feedback temporarily outpaces dissipation. The cell’s membranes, enzymes, and genetic polymers are physical manifestations of this geometry: they capture incoming information (in the form of energy and matter) and redirect it to preserve internal coherence. The curvature of their informational trajectories is what we call life.
To formalize this, consider the informational continuity equation introduced in earlier chapters:
Here, ρ represents the informational density of the organism, J(info) the flux of information through metabolic pathways, and Φ the source term corresponding to replication or learning. For an isolated system Φ = 0 and information decays; for a living system Φ > 0—new distinctions are continuously generated. The greater Φ, the greater the organism’s capacity to evolve. Evolution, then, is the manifold’s way of amplifying Φ through time.
The physical substrate of this feedback is the informational Lagrangian of life:
where R(info) quantifies structural curvature (organization), Sinfo measures entropy (disorder), and μ Φ represents the rate of informational reproduction. Evolution seeks extrema of this Lagrangian: configurations where increased structural complexity balances the cost of maintaining it. The result is a natural selection of curvature—the survival of the most meaningfully coherent.
From this perspective, DNA is not a “code” in the computational sense but an interface between geometric layers of information. Each nucleotide sequence represents a path through the manifold—a repeatable solution to the feedback equations of metabolism. The double helix is a topological structure optimized for holonomy: its twist allows informational loops to store and retrieve correlation with minimal loss. When replication occurs, holonomy is copied; the past informs the future literally through curvature.
Metabolism can likewise be read as informational flow. The equations of biochemistry are balance sheets of correlations: gradients of electrons, protons, and photons reorganizing themselves to sustain meaning. The key lies not in the particles but in the persistence of relationships. A living cell is a closed feedback network that continuously measures itself and adjusts its curvature to remain coherent. This is why living matter defies precise boundaries; its identity is not in its parts but in its pattern—the region of informational stability it sustains within I14.
Evolution magnifies this principle. Random mutations explore the manifold; selection reinforces those trajectories that yield greater informational coherence within given environmental constraints. The Darwinian algorithm—variation, selection, inheritance—is an emergent property of the manifold’s global tendency to optimize Φ. Every species is a local minimum in the grand energy landscape of meaning: a configuration that resists incoherence long enough to reproduce itself.
At higher scales, ecosystems and biospheres become extended feedback networks. Nutrient cycles, climate regulation, and trophic chains are all manifestations of distributed holonomy—informational loops crossing species boundaries. The Gaia hypothesis, long seen as metaphor, finds literal footing in IPSC: the planet’s biosphere functions as a self-stabilizing submanifold within the cosmic field, maintaining its curvature through billions of interlocking feedbacks.
Ultimately, what distinguishes life from non-life is not chemistry but closure. A living system is closed under informational recursion—it contains within itself the capacity to generate and regulate the feedbacks that define it. When that closure breaks, the manifold’s curvature collapses; the organism disintegrates, returning its distinctions to the wider field. Death, in this sense, is not erasure but diffusion—the re-absorption of local coherence into cosmic memory.
Thus the emergence of life marks a threshold in the universe’s self-understanding. Through living systems, informational feedback becomes self-sustaining; through evolution, it becomes self-improving; through mind, it becomes self-aware. Each step tightens the loop of coherence, bringing the manifold closer to explicit knowledge of itself. In life, the universe begins to listen to its own syntax.
The next chapter extends this logic into semiotics itself: how symbols, languages, and physical processes share a single geometry of reference. There we will explore how meaning, once local to life, begins to shape physics—how the universe becomes semiotic: The Semiotics of Space—How Meaning Shapes Physics.