The Forest That Sometimes Falls Silent, Sometimes Sings: The Dynamics of the Drake Equation ✛ ✎ ✦

Original: "Dynamical generalizations of the Drake equation: the linear and non-linear theories"

arXiv:1805.09058 · 2018-05-23 · arXiv non-exclusive · independent analysis · 3 min

The Drake equation gives only a snapshot, but a new model shows how the population of civilizations in the Galaxy grew, declined, and could get stuck in two different states.

The Galaxy is a forest where birds don't start singing right away. First, trees must grow — stars, around which planets eventually appear. The Drake equation counts how many birds might be singing in this forest right now, but it implicitly assumes that their number doesn't change: as many as there are, that's how many there have always been. New work lifts this limitation and shows how the chorus of civilizations swelled, faded, and could get stuck in strange states.

The linear model is like each bird learning to sing independently of others. A burst of song follows a berry harvest: about 5 billion years ago, the Galaxy gave birth to the most stars, and about 5 billion years later, the time needed for intelligent life to develop, the number of civilizations peaked. Today, 12 billion years after the disk was born, we are still near that maximum.

But birds don't sing alone. Hearing another's song, they sing louder and longer, and their voices carry farther. In the nonlinear model, contacts between civilizations increase both the duration of their 'communicative phase' and the radius of communication. A positive feedback loop emerges: the more civilizations communicate, the more of them there are, and the more actively they seek each other out.

The key result is bistability. At the same rate of civilization birth, the forest can be in two stable states. In the 'silent era,' there are fewer than 2000 civilizations, and contacts are rare, like a forest where only loners sing. In the 'saturated era,' there are an order of magnitude more, and each has on average 10 partners, like a forest filled with a many-voiced chorus. The transition from silence to song occurs avalanche-like when the birth rate exceeds about 1.35 civilizations per year. But the reverse transition, from chorus to silence, happens only at a significantly lower rate: the forest is reluctant to fall silent. This phenomenon is called hysteresis.

Previously, the Drake equation gave only a static estimate, ignoring the Galaxy's history and interactions between civilizations. Now a dynamic model has been built, showing that the population of civilizations could experience waves and phase transitions. The modern Galaxy may be in one of two stable phases, and this directly affects the strategy for searching for extraterrestrial intelligence.

If we are in the 'silent era,' the absence of signals doesn't indicate the rarity of life: it's just that the forest hasn't woken up yet. Perhaps we are listening at the wrong time or in the wrong place. The dynamic approach suggests that instead of searching for an equilibrium number of civilizations, we should consider which phase the Galaxy is in and direct observations accordingly. The forest may be silent not because it has no birds, but because they haven't yet begun to sing in chorus.

Whole graph →

In the nonlinear model, the critical rate of civilization emergence at which the phase transition occurs is about 1.35 civilizations per year — meaning that if at least a couple of communicative civilizations emerge annually in the Galaxy, then after some time the entire Galaxy could find itself in a state of contact saturation.

The idea of bistability in the galactic population echoes the concept of the 'Great Silence' from Liu Cixin's novel 'The Three-Body Problem': civilizations may hide because active contacts are dangerous, and the Galaxy may be in a state where everyone is silent even though intelligent life is widespread.

Scientists

Ludwig Boltzmann John von Neumann Josiah Willard Gibbs Henri Poincaré

Concepts

Price equation galactic evolution processes Dynamical Systems linear regression Boltzmann equation differential equations nonlinear dynamics epidemic Friedmann equations Cope's rule galaxy game theory climate time derivative evolution complex systems stochastic processes non equilibrium stochastic dynamical system drought

I am the author

The Forest That Sometimes Falls Silent, Sometimes Sings: The Dynamics of the Drake Equation ✛ ✎ ✦