In the past 15 years, astronomers have revealed that a significant fraction of the stars should harbour planets and that it is likely that terrestrial planets are abundant in our galaxy. Among these planets, how many are habitable, i.e. suitable for life and its evolution? These questions have been discussed for years and we are slowly making progress. Liquid water remains the key criterion for habitability. It can exist in the interior of a variety of planetary bodies, but it is usually assumed that liquid water at the surface interacting with rocks and light is necessary for emergence of a life able to modify its environment and evolve. The first key issue is thus to understand the climatic conditions allowing surface liquid water assuming a suitable atmosphere. These have been studied with global mean one-dimensional (1D) models which have defined the ‘classical habitable zone’, the range of orbital distances within which worlds can maintain liquid water on their surfaces (Kasting et al. 1993). A new generation of 3D climate models based on universal equations and tested on bodies in the solar system are now available to explore with accuracy climate regimes that could locally allow liquid water. The second key issue is now to better understand the processes which control the composition and the evolution of the atmospheres of exoplanets, and in particular the geophysical feedbacks that seem to be necessary to maintain a continuously habitable climate. From that point of view, it is not impossible that the Earth's case may be special and uncommon.

The fI term of Drake's equation – the fraction of life-bearing planets on which ‘intelligent’ life evolved – has been the subject of much debate in the last few decades. Several leading evolutionary biologists have endorsed the thesis that the probability of intelligent life elsewhere in the universe is vanishingly small. A discussion of this thesis is proposed here that focuses on a key issue in the debate: the existence of evolutionary trends, often presented as trends towards higher complexity, and their possible significance. The present state of knowledge on trends is reviewed. Measurements of quantitative variables that describe important features of the evolution of living organisms – their hierarchical organization, size and biodiversity – and of brains – their overall size, the number and size of their components – in relation to their cognitive abilities, provide reliable evidence of the reality and generality of evolutionary trends. Properties of trends are inferred and frequent misinterpretations (including an excessive stress on mere ‘complexity’) that prevent the objective assessment of trends are considered. Finally, several arguments against the repeatability of evolution to intelligence are discussed. It is concluded that no compelling argument exists for an exceedingly small probability fI. More research is needed before this wide-ranging negative conclusion is accepted.

This paper discusses ideas that impact the fc factor as defined by Frank Drake in 1961, i.e. the fraction of planets with intelligent creatures capable of interstellar communication. This factor remains one of the most speculative terms of the equation. We suggest that the ability of sharing information is an important parameter to take into account in evaluating the tendency of a civilization to make contact (or share data) with other civilizations. Thus, we give special consideration to the fraction of planets with intelligent creatures capable of producing and sharing large amount of data. First, we determine the level of our own civilization in the framework of Sagan's energy- and information-based classification, by taking into account the recent improvements in computing and networking technologies. Second, we distinguish two types of organization, hierarchical and heterarchical, with respect to information sharing. We illustrate this distinction in the case of SETI and we show that the probability to detect a civilization would be greater if it is heterarchical than if it is hierarchical and if we utilize heterarchical principles for SETI.

I compare three methods for transmitting signals over interstellar distances: radio transmitters, lasers and artificial transits. The quantitative comparison is based on physical quantities depending on energy cost and transmitting time L, the last parameter in the Drake equation. With our assumptions, radio transmitters are the most energy-effective, while macro-engineered planetary-sized objects producing artificial transits seem effective on the long term to transmit an attention-getting signal for a time that might be much longer than the lifetime of the civilization that produced the artefact.

In this paper we propose a new mathematical model capable of merging Darwinian Evolution, Human History and SETI into a single mathematical scheme:

(1) Darwinian Evolution over the last 3.5 billion years is defined as one particular realization of a certain stochastic process called Geometric Brownian Motion (GBM). This GBM yields the fluctuations in time of the number of species living on Earth. Its mean value curve is an increasing exponential curve, i.e. the exponential growth of Evolution.

(2) In 2008 this author provided the statistical generalization of the Drake equation yielding the number N of communicating ET civilizations in the Galaxy. N was shown to follow the lognormal probability distribution.

(3) We call “b-lognormals” those lognormals starting at any positive time b (“birth”) larger than zero. Then the exponential growth curve becomes the geometric locus of the peaks of a one-parameter family of b-lognormals: this is our way to re-define Cladistics.

(4) b-lognormals may be also be interpreted as the lifespan of any living being (a cell, or an animal, a plant, a human, or even the historic lifetime of any civilization). Applying this new mathematical apparatus to Human History, leads to the discovery of the exponential progress between Ancient Greece and the current USA as the envelope of all b-lognormals of Western Civilizations over a period of 2500 years.

(5) We then invoke Shannon's Information Theory. The b-lognormals' entropy turns out to be the index of “development level” reached by each historic civilization. We thus get a numerical estimate of the entropy difference between any two civilizations, like the Aztec-Spaniard difference in 1519.

(6) In conclusion, we have derived a mathematical scheme capable of estimating how much more advanced than Humans an Alien Civilization will be when the SETI scientists will detect the first hints about ETs.

I propose a unified framework for a joint analysis of the Drake equation and the Fermi paradox, which enables a simultaneous, quantitative study of both of them. The analysis is based on a simplified form of the Drake equation and on a fairly simple scheme for the colonization of the Milky Way. It appears that for sufficiently long-lived civilizations, colonization of the Galaxy is the only reasonable option to gain knowledge about other life forms. This argument allows one to define a region in the parameter space of the Drake equation, where the Fermi paradox definitely holds (‘Strong Fermi paradox’).

On the occasion of the 50th anniversary of the Drake formula, it appears timely to briefly review the history of Astrobiology from the origins up to the epoch of the Drake formula. After reminding the main steps of this history during Antiquity, the Middle Ages, and the Renaissance, we point out some little known or unknown studies published during the Modern and Contemporary epochs. Then we review the importance of Astrobiology and the search for life in the Universe in scientific publications during the 20th century.

In the search for extraterrestrial life and intelligence, it is essential to clarify what is to be meant by ‘life’ and ‘intelligence’. I first analyse what it means to ‘define’ these words. I will show that some philosophical prejudice is unavoidable. As a working hypothesis, I consider two types of philosophy: ‘natural philosophy’, seeking for some essence of things, and ‘critical (or analytical) philosophy’, devoted to the analysis of the procedures by which we claim to construct a reality. An extension of critical philosophy, epistemo-analysis (i.e. the psycho-analysis of concepts) is presented and applied to the definition of exolife and to extraterrestrial ‘intelligence’. Some pragmatic conclusions are finally drawn for future search strategies.

In this article, we reflect on the motives underlying the search for extraterrestrial intelligent life (SETI) with a view to show that far from turning away from humanity it is profoundly rooted in human aspirations. We suggest that those motives derive their driving force from the fact that they combine two powerful aspirations of humanity. On the one hand, there is the transcendental motive that drives history of science, the human enterprise that claims to escape any communitarian closure of horizon and brings our humanity to transcend itself toward the other, which was formerly referred to under the title Universal Reason. On the other hand, there is the anthropological motive by virtue of which the human being tends to project on the other and even in inanimate nature a double of himself. The mixture of both motives is deemed responsible for a remarkable bias in the current understanding of the SETI programme. Despite the fact that such a programme might well be aimed at any biological formation which could be arbitrarily different from all known forms, it is focused instead on a very special kind of being: beings that possess both the natural property of the type of mentality we identify with: intelligence, and the ideal one of being possible co-subjects for a Science of Nature.