If the probability of life arising is too low, then it hardly has time to appear.
Humanity's cosmic loneliness may turn out to be a natural statistical law of the Universe: a new mathematical model has shown that the probability of multiple intelligent civilizations arising is extremely low.
In 1933, Konstantin Tsiolkovsky, in his essay "Planets Are Inhabited by Living Beings," reflected on the universal mechanisms of the emergence of life and the reasons why humanity is still alone. He concluded that due to the countless number of worlds (the observable Universe is estimated to contain about two trillion galaxies, and the number of planets is around 22 sextillion), the habitability of some of them is statistically inevitable. The absence of registered signals from extraterrestrial civilizations or their visits was explained by the primitive level of development of human civilization.
These reflections largely anticipated the famous question "Where is everybody?" posed by Italian physicist Enrico Fermi in 1950, which led to the emergence of the eponymous paradox or "great silence paradox" — one of the main mysteries of modern astrobiology, inspiring numerous attempts to quantitatively describe the probability of extraterrestrial civilizations existing.
Mathematician Antal Veres from the Hungarian University of Agriculture and Life Sciences proposed his own solution to the paradox. In an article published in the journal Acta Astronautica, he presented a mathematical model based on a narrow range of probabilities, where the emergence of at least one intelligent civilization is statistically inevitable, while the emergence of two or more is unlikely. This range was termed the "zone of loneliness" by the scientist.
Since life in the model is considered a random event, its emergence in potentially habitable worlds depends on the history of the planets, conditions on their surfaces, and a specified "level of complexity" — an abstract scale that combines biological and technological characteristics: simple life forms, if they exist, are likely widespread. At the same time, for hypothetical civilizations whose level of development significantly exceeds that of Earth, the probability of loneliness increases (depending on the level of complexity).
Applying the model to various scenarios, including the most optimistic and pessimistic, Veres found that the results support the so-called Rare Earth hypothesis. This hypothesis states that complex life forms require a chain of extremely rare events, and the probability that humanity in its current form is the only intelligent civilization in the Universe is 29.1%.
However, if life arises easily and everywhere, then loneliness becomes virtually impossible. This means that the cosmos must be populated by numerous civilizations. If, however, the probability of life emerging is too low, then it hardly has time to appear: in such cases, the "zone of loneliness" disappears, and the Universe becomes truly empty.
Veres's work resonates with the central ideas of astrobiology: it can be viewed as a statistical analogue of the Great Filter hypothesis — one of the possible solutions to the Fermi paradox proposed by British economist Robert Hanson in 1996. According to this hypothesis, the path to intelligent life is limited by numerous "filters" — barriers that prevent its emergence and development. The new model describes the same effect, showing that the most likely scenario is the existence of only one civilization that has passed through all stages of evolutionary complexity.
Veres's scale is also conceptually close to the Kardashev scale (1964), where civilizations are classified by their level of energy use: the higher it is, the rarer representatives of such types are found in the expanses of the Universe. Finally, the new model can be seen as a probabilistic development of Frank Drake's ideas, who introduced the eponymous equation in 1961 to estimate the average number of intelligent civilizations in the Universe. The only difference is that Veres clearly defined the maximum range where the existence of only one of them is most likely.
The results of the new study neither refute nor confirm the existence of other civilizations but combine classical hypotheses into a single statistical scheme, presenting the Fermi paradox as a natural consequence of probability theory. If the mathematician's conclusions are correct, then the "great silence" does not mean that there is no one else in the cosmos besides us — perhaps we simply live in a statistically lonely Universe.
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