Despite the small matter of lack of evidence, most astrophysicists and cosmologists today are persuaded that extra-terrestrial intelligent life must exist.

The logic behind the assumption seems compelling. There are billions of galaxies in the universe, each containing billions of stars, around a proportion of which orbit billions of planets. Given the vastness of those numbers, it would be statistically perverse to suggest that intelligent life evolved only once in the entire system.

But what, however, if the startlingly improbable is nevertheless the truth? What if Homo sapiens is, in fact, the only species ever in the entire history of the universe to invent radio, build an X-ray observatory, and send a ship into space?

What if – the existence of exoplanets coated in blue-green slime notwithstanding – we are utterly on our own?

That’s the contention of physicists Anders Sandberg, Eric Drexler and Toby Ord, all of the Future of Humanity Institute at Oxford University in the UK. In a paper lodged on the pre-print server Arxiv, and thus still awaiting peer review, the trio model what happens when two touchstones of astrobiology – the Fermi Paradox and the Drake Equation – are combined and subjected to mathematical rigour.

The results, it must be said, aren’t good, at least for people hopeful that somewhere, out there, at least one alien civilisation is bubbling along.

Existing calculations for the probability of extra-terrestrial intelligent life, they report, rest on uncertainties and assumptions that lead to outcomes containing margins for error spanning “multiple orders of magnitude”.

Constraining these, as much as possible, by factoring in models of plausible chemical and genetic mechanisms, results, they conclude, in the finding “that there is a substantial probability that we are alone”.

The Fermi Paradox is named after physicist Enrico Fermi, who noted in 1950 that there are so many stars, just in the Milky Way, that given the age of the universe even a small probability that intelligent life has evolved would mean that their existence should be plain to humanity by now.

Yet, he continued, in terms of evidence, we have squat, which, given the probability of intelligent life emerging, is odd. Hence the paradox. “Where are they?” he asked.

The Drake Equation, formulated by American astronomer Frank Drake in 1961, attempts to place an analytical framework around Fermi’s contention, by estimating the number of intelligent civilisations that exist in the universe, regardless of the fact that we can’t see them.

Drake’s work can be expressed thus: N = R ∗ f p ∗ n e ∗ f l ∗ f i ∗ f c ∗ L

In the equation, N represents the number of civilisations within the Milky Way capable of emitting detectable electromagnetic signals. The number is determined by the other factors in the model, which express the rate of suitable star formation, the fraction of those stars with exoplanets, the number of those planets suitable for life and the number on which life actually appears.

That total is then further reduced by adding in other refinements – the number of life-bearing planets on which intelligence emerges, the number of those that produce technology capable of emitting signals into space, and the number of those that actually go ahead and do so.

It’s all very impressive, but “sciencey” rather than scientific. Sandberg, Drexler and Ord gleefully quote US astronomer Jill Tarter, who described the Drake Equation as “a wonderful way to organise our ignorance”.

The problem with the way the equation is usually wielded, the researchers argue, is that the parameters assigned to most of the various elements represent simply best guesses – and those guesses, furthermore, are heavily influenced by whether the person making them is optimistic or pessimistic about the chances of intelligent life existing. The result, they note, often involves well-estimated astronomical numbers multiplied by ad hoc figures.

They quote another US astronomer, Steven J. Dick: “Perhaps never in the history of science has an equation been devised yielding values differing by eight orders of magnitude … each scientist seems to bring his own prejudices and assumptions to the problem.”

Dick, they note, was being nice. Many outcomes from Drake Equation calculations yield probabilities that range over hundreds of orders of magnitude.

In a not altogether unrelated sidebar, the researchers acknowledge a recent calculation by Swedish-American cosmologist Max Tegmark, estimating the chances of intelligent civilisations arising in the universe.

Tegmark assumes there is no reason two intelligent civilisations should be any particular distance from each other, and then argues that – given the Milky Way is a minuscule fraction of the observable universe, which is itself only a tiny part of the universe beyond what we can see – it is unlikely that two intelligent civilisations would arise in the same observable universe. Thus, to all intents and purposes, we are very probably alone.

Sandberg, Drexler and Ord use a different approach in their modelling, incorporating current scientific uncertainties that produce values for different parts of the equation ranging over tens and hundreds of orders of magnitude. Some of these concern critical questions regarding the emergence of life from non-living material – a process known as abiogenesis – and the subsequent likelihoods of early RNA-like life evolving into more adaptive DNA-like life.

Then there is the essential matter of that primitive DNA-like life undergoing the sort of evolutionary symbiotic development that occurred on Earth, when a relationship between two different types of simple organisms resulted in the complex “eukaryotic” cells that constitute every species on the planet more complicated than bacteria.

The results are depressing enough to send a thousand science-fiction writers into catatonic shock. The Fermi Paradox, they find, dissolves.

“When we take account of realistic uncertainty, replacing point estimates by probability distributions that reflect current scientific understanding, we find no reason to be highly confident that the galaxy (or observable universe) contains other civilizations,” they conclude.

“When we update this prior in light of the Fermi observation, we find a substantial probability that we are alone in our galaxy, and perhaps even in our observable universe.

“‘Where are they?’ — probably extremely far away, and quite possibly beyond the cosmological horizon and forever unreachable.”