Our species will have a longevity between 205,100 and 8 million years and we will not colonize the galaxy. These were some of the many conclusions that J. Richard Gott III drew in his article ” Implications of the Copernicus principle for our future .”

Although they may seem strange, these estimates are not at all extraordinary if we look at them through the eyes of the Copernicus principle, which teaches us that it is a mistake to assume that we occupy a privileged position in the Universe.

Our little planet, orbiting a fairly ordinary star in a normal galaxy, is little special. A proper use of this notion allows to estimate easily and with great precision the duration of different events, in particular of our own species.

The central idea is very simple. Suppose that the event we are observing has a finite duration, defined by a time interval determined by two times, t (initial) and t (final) , of which the latter is unknown.

If the observation is carried out at a time t (now) that does not play any special role, we can assume that this time will occupy a random place in said interval. Therefore, the fraction of the time elapsed since the start of the event, r = (t (now) – t (initial)) / (t (final) – t (initial)), will be a number uniformly distributed between 0 and 1.

The probability that r is between 0.025 and 0.975 is 0.975-0.025 = 0.95, that is, we have a 95% probability that 0.025 <r <0.975. Manipulating the expression a bit, we get:

Using this argument, known as delta t, we can estimate the duration of many events whose total duration is unknown a priori, as long as the moment in which we carry out the observation of the event has nothing special.

For example, I visited the Segovia aqueduct for the first time in 1973, when 1856 years had passed since its construction.

Taking into account that my visit was totally anodyne (I was one of thousands of visitors in any given year of the 20th century), applying the Copernicus principle I could have estimated that the aqueduct would remain standing for 47.58 years <t (future ) <72384 years. With 95% confidence, I was going to be able to enjoy the view of the aqueduct until 2020 at least, as it has been.

What about the duration of our species? If we assume that we are at any given moment in the history of Homo sapiens , which has been roaming the Earth’s surface for about 200,000 years, the delta t argument predicts that we will continue to exist between 5,100 years and 7.8 x 106 years plus.

This allows us to affirm that there will continue to be humans on Earth for at least 5000 years, which is nothing more than the period elapsed since the reign of the Yellow Emperor Huang in ancient China until today; but not for more than ten million years in the future, which in cosmic or geological terms is a sigh, “sic gloria transit mundi.”

Our civilization must take extraordinary care of its actions in the immediate future if we are to guarantee our survival. With a little more work, the delta t argument can be applied to estimate the total population of a species.

If we chronologically order all the individuals in a list and again our place in the list is nondescript, we can estimate the maximum number of individuals of that species using again the estimate N (future) <39 N (past) , where N (past) is the total number of humans that have existed so far and N (future)is the total number of humans that will be born from this moment on. In our case, it is obtained that the total number of humans that we can expect to exist will be between 1.8 billion and 2.7 billion.

This result imposes strong restrictions on the evolution of the human population and only scenarios where the human population expands rapidly and suddenly becomes extinct or, after a period of rapid growth, declines and stabilizes at a few hundred thousand million, are compatible with it. individuals who would inhabit an extremely impoverished planet for the next four million years. Of course we will not expand exponentially until we colonize the Galaxy.

The predictive power of Gott’s argument has been questioned . It cannot be used lightly. For example, it cannot be used whenever we can suspect that the basic hypothesis is not true, that is, when the moment of observation is special.

And it can be argued, for example, that the present moment is so because we know the argument delta t and its implications, which allows us to act and modify the circumstances that define our observations.

Despite this, Gott’s arguments indicate something very significant that affects other evidence: our civilization must take extraordinary care with its actions in the immediate future if we want to guarantee our survival.

Alberto Ibort is Professor of Applied Mathematics at the Carlos III University of Madrid and a member of the ICMAT

Café y Teoremas is a section dedicated to mathematics and the environment in which they are created, coordinated by the Institute of Mathematical Sciences (ICMAT), in which researchers and members of the center describe the latest advances in this discipline, share points of encounter between mathematics and other social and cultural expressions and remember those who marked its development and knew how to transform coffee into theorems.

The name evokes the definition of the Hungarian mathematician Alfred Rényi: “A mathematician is a machine that transforms coffee into theorems.”