Hearing an alien civilization may be easier than exchanging replies

Counting civilizations is not enough to determine whether they could communicate. Their distances, active periods and signal travel times also matter. In an arXiv preprint, Kohji Tsumura models these ingredients together, asking when isolated contacts could become an extensive network. The work concerns hypothetical populations, not evidence that extraterrestrial civilizations exist.

Several meanings of contact

Tsumura distinguishes four communication relations. Listening means one civilization receives another’s transmission during its active lifetime. Audibility means reception occurs in at least one direction. Mutual listening requires both civilizations to hear each other, although their transmissions need not be responses to anything received.

Relaying adds another possibility: an intermediate civilization forwards a message to a recipient beyond the original sender’s range. Such a route must respect timing at every step. An intermediate civilization cannot forward information before receiving it or after its transmitting period ends.

A completed reply is more restrictive still. Both participants might hear independently emitted signals, yet a response triggered by reception could return too late. In the common-lifetime model, completing a reply requires a separation shorter than half the distance light travels during one communicative lifetime.

Modelling civilizations through time

The model represents civilizations as randomly appearing events in a two-dimensional Galactic disc. Each transmits and listens for the same finite duration. Appearances occur at a constant average rate, all civilizations share a detection range, and transmissions spread equally in every direction. Every recipient is assumed able to retransmit a received message.

Two lengths are kept separate: the maximum detection range and the distance light travels during a civilization’s communicative lifetime. Their ratio, called chi, measures observational reach relative to longevity. A large ratio means signals can be detected across distances whose travel times are long compared with that lifetime.

Another quantity, contactability, is the average number of currently active civilizations inside the detection radius. Tsumura derives average contact counts mathematically, then uses repeated random simulations to estimate when extensive connected networks emerge. This transition is called percolation: contacts link into a component that remains a substantial fraction of the population as the simulated system grows.

For relayed messages, the simulations track earliest possible arrival times. Tsumura also reports comparisons with previously studied percolation problems to check the numerical methods.

More listening does not guarantee conversation

The mathematical analysis gives a simple result: averaged over civilization appearances, the number of other civilizations heard across a full communicative lifetime is twice the contactability. At fixed contactability, this count does not depend on chi. The result also survives a distribution of lifetimes when detection range is common.

This lifetime count differs from the number detectable at one instant. It includes both signals already arriving when a civilization begins listening and signals that arrive later. It is not a forecast for any particular observer.

Network formation changes too. When detection range is much shorter than the lifetime light-travel distance, Tsumura estimates a listening threshold of 1.32 ± 0.01, compared with 4.51 in the earlier contemporaneous model. The lower threshold means an extensive network can arise at lower contactability within these idealized calculations.

Relaying requires roughly 10 percent higher contactability than listening across the range studied. Mutual listening becomes substantially harder as chi increases. Greater observational reach can therefore support one-way reception without providing enough time for reciprocal exchanges.

What Galactic silence can—and cannot—say

Tsumura compares the thresholds with a reference upper bound of 2.75 on contactability near the Sun. Crucially, this assumes an ideal survey detecting every transmitter within range. It is not a constraint established by actual SETI coverage.

Under that benchmark, a civilization could hear at most 5.5 others on average over its lifetime. Yet the average number of partners satisfying the completed-reply condition falls below one around chi equal to one.

In the paper’s structured Galactic disc, replacing the earlier threshold with the small-chi spacetime threshold shifts a locally estimated connectivity frontier outward by 3.2 kiloparsecs. This is a model comparison, not a mapped boundary of an observed network.

The limitations are substantial. Real populations need not share lifetimes or detection ranges, transmit continuously in all directions, or forward every message. Short detection ranges also require three-dimensional geometry rather than a thin disc. Numerical thresholds retain finite-size and finite-duration uncertainties. Meeting a local threshold does not establish that the Sun belongs to a Galaxy-wide network.

Tsumura’s conclusion is therefore conditional: our lack of detection can be compatible with some connected model populations. The study does not resolve the Fermi paradox, but clarifies why hearing a signal, exchanging replies and belonging to a communication network are different questions.