Model A · 1965
Daley–Kendall
Both parties fall silent. The caller and the informed village it reached become stiflers.
spreaders −2
01The Paradox
The galaxy looks crowded.
It sounds empty.
Sun-like stars with planets appear to be abundant in the Milky Way, and the chemistry that life requires is common throughout the Universe. It is therefore quite plausible that life — including intelligent, technically capable life — exists elsewhere in the Galaxy, and that some of it has learned to communicate across interstellar distances.
So why have we neither met nor heard from anyone? That is the essence of Fermi's Paradox. Dozens of solutions have been proposed: they are rare, they are far, they destroy themselves, they are hiding, they do not communicate. This paper proposes a different kind of answer — one that requires no catastrophe, no rarity, and no deliberate silence.
What if the network exists, is busy, and works exactly as advertised — and the message simply never reaches everybody? Mathematically, that is not a malfunction. It is the expected outcome.
02The Model
A galaxy of villages
with one telephone each.
The classical rumour models imagine n0 + 1 villages, far apart, connected only by a primitive wired telephone system. Each village has one telephone, and only one conversation can happen at a time. One village learns a piece of news and starts calling the others at random. Every agent is in exactly one of three states.
-
Ignorant
Has not heard the news. Waiting, without knowing it is waiting.
-
Spreader
Knows, and is actively calling others — the only agents doing any work.
-
Stifler
Knows, but has stopped calling. Assumes everyone else already knows.
The rule that kills the rumour
A spreader dials a village at random. If that village is ignorant, it learns the news and may begin calling too. But if the village already knows, the caller concludes the news has gone around, gives up, and becomes a stifler.
Spreaders therefore consume themselves. The process always halts — not because everyone has been reached, but because nobody is left willing to dial. Whoever has not been called by then never will be.
Model B · 1973
Maki–Thompson
Only the caller falls silent. The village it reached carries on spreading, unaffected.
spreaders −1
In both cases the classical literature reports the same stubborn residue: about one fifth of all villages are still ignorant when the process ends — 0.203 for Daley–Kendall, and 0.238 (later argued to also be 0.203) for Maki–Thompson.
03Two New Dials
Villages become civilizations.
Telephones become radio.
The fit is uncomfortably good. Vast distances prevent casual contact, much as they did between the villages; electromagnetic waves stand in for the wire; and a capable but uncontacted civilization may well behave like an explorative villager — building the means to search once it learns there is something to search for. Three assumptions carry the translation:
- Agents can contact others, or acquire the skill to, once contacted themselves.
- Agents survive and remain able to communicate until the simulation ends.
- The timescale is long enough to cover the whole communication process.
What this paper adds
The classical models assume every agent is equally eager and gives up after a single wasted call. Real civilizations would not be so uniform. Two parameters were added to the agent-based model to relax exactly those assumptions.
Parameter 1 · eagerness
Conversion probability Pc
The probability that a civilization, once reached, actually takes up the search and starts calling others. When it does not, nothing changes at all — the call leaves no mark, and that world stays among the uncontacted. Read the other way, Pc is the share of genuinely curious civilizations in the Galaxy.
default 100% — reproduces the classical models
Parameter 2 · persistency
Stop criterion Sc
A spreader gives up when it reaches a world already inside the network — but only once it has been searching for at least Sc rounds. Below that threshold the disappointment is shrugged off. Sc is how long a civilization stays committed before one wasted call is allowed to end its search.
default 1 — reproduces the classical models
The model was written in NetLogo 6.1.1 and published openly on Modeling Commons, so that any reader can change the dials and watch the consequences.
04Watch It Run
One thousand worlds.
Watch how many stay dark.
Below is the published algorithm, running live in your browser. One world learns the news and starts calling. Cyan lines are calls that landed, slate lines are calls nobody took up, ember lines are calls that reached a world already inside the network. Cyan points are still searching, ember points have given up — and everything still slate-grey at the end never joined at all.
Ignorant
1000
100.0%
Spreaders
0
0.0%
Stiflers
0
0.0%
Ported directly from the published NetLogo source; at its defaults it reproduces the paper's Table 1 to within sampling noise. 1000 agents, one run — single runs scatter around the mean, which is what §06 reports.
05The Published Model
The real thing,
exactly as published.
The NetLogo model behind the paper is hosted openly on Modeling Commons and runs in the frame below — the same code, the same controls, the same plots that produced the published figures. Press the play button to load it.
- Start here — leave Pc at 100% and Sc at 1 to reproduce the classical models.
- Then — drop Pc to 25% and watch the ignorant population refuse to fall.
- Then — push Sc to 10 and see persistence very nearly close the gap.
Model hosted by Modeling Commons, a service of Northwestern University's Center for Connected Learning and Computer-Based Modeling. If the frame does not load, open it in a new tab.
06Results
Eagerness and stubbornness
decide who gets found.
Forty runs of 2000 agents were performed for every combination of the two new parameters. Each cell below is a mean final ignorance ratio with its standard deviation — the fraction of civilizations still uncontacted when every spreader has given up. Dimmer means better connected; brighter means more of the Galaxy left in the dark.
Table 1 · mean ± s.d. · 40 runs · 2000 agents
| Sc ╱ Pc | 25% | 50% | 75% | 100% |
|---|
uncontacted share · 0 → 0.7
Ignorance never quite reaches zero
Under classical settings — every civilization eager, everyone giving up after one wasted call — a fifth of the Galaxy is left uncontacted. That residue is the model's whole point.
Persistence beats eagerness
Raising the stop criterion collapses ignorance far faster than raising eagerness does. A stubborn minority reaches more worlds than an enthusiastic but easily discouraged majority.
The two models converge
Daley–Kendall always leaves more worlds ignorant than Maki–Thompson — but at Sc = 10 the gap nearly vanishes, as the passive agent's silence stops mattering.
A note on the literature
The published values for these models have long disagreed. Daley and Kendall reported 0.203; Maki and Thompson reported 0.238, which Watson (1987) and Belen & Pearce (2004) argued was a typographic error that should also read 0.203. These runs found 0.203 under original Maki–Thompson settings — supporting that correction — but 0.266 under original Daley–Kendall settings, noticeably higher than the canonical figure.
07Conclusion
Today, we sometimes learn from the news that thousands of people still live in uncontacted tribes, completely away from our modern civilization — even in our hyper-connected world.
We mount no expeditions to find them. We assume the lines are already drawn. If civilizations behave the same way — limiting their searches once they have joined the Galactic Club — then a dense, working, galaxy-wide communication network still guarantees nobody that they will be found.
A new entry for the master list of solutions
“They do not communicate.”
“They do not establish new contacts anymore.”
Stated limitations. Rumour spread models ignore the travel time of news and therefore take no account of distance, and they raise a simultaneity problem for civilizations at different stages of development. They offer a basic insight, not a map.
08Cite & Access
Cite this work
Uyar T, Özel ME (2020). Agent-based modelling of interstellar contacts using rumour spread models. International Journal of Astrobiology 19(6), 423–429. https://doi.org/10.1017/S1473550420000191
BibTeX
@article{Uyar2020Fermi,
author = {Uyar, Tevfik and {\"O}zel, Mehmet Emin},
title = {Agent-based modelling of interstellar contacts using rumour spread models},
journal = {International Journal of Astrobiology},
year = {2020},
volume = {19},
number = {6},
pages = {423--429},
doi = {10.1017/S1473550420000191},
url = {https://doi.org/10.1017/S1473550420000191}
}
Authors
Tevfik Uyar
Istanbul Kültür University
Faculty of Economics and Administrative Sciences
İstanbul, Turkey
Corresponding author
[email protected]Mehmet Emin Özel
Çukurova University
UZAYMER Space Research Center
Adana, Turkey