Living organisms on Earth are characterized by three necessary features: a set of internal instructions encoded in DNA (software), a suite of proteins and associated macromolecules providing a boundary and internal structure (hardware), and a flux of energy. In addition, they replicate themselves through reproduction, a process that renders evolutionary change inevitable in a resource-limited world. Temperature has a profound effect on all of these features, and yet life is sufficiently adaptable to be found almost everywhere water is liquid. The thermal limits to survival are well documented for many types of organisms, but the thermal limits to completion of the life cycle are much more difficult to establish, especially for organisms that inhabit thermally variable environments. Current data suggest that the thermal limits to completion of the life cycle differ between the three major domains of life, bacteria, archaea and eukaryotes. At the very highest temperatures only archaea are found with the current high-temperature limit for growth being 122 °C. Bacteria can grow up to 100 °C, but no eukaryote appears to be able to complete its life cycle above ∼60 °C and most not above 40 °C. The lower thermal limit for growth in bacteria, archaea, unicellular eukaryotes where ice is present appears to be set by vitrification of the cell interior, and lies at ∼−20 °C. Lichens appear to be able to grow down to ∼−10 °C. Higher plants and invertebrates living at high latitudes can survive down to ∼−70 °C, but the lower limit for completion of the life cycle in multicellular organisms appears to be ∼−2 °C.

Interstellar radar is a potential intermediate step between passive observation of exoplanets and interstellar exploratory missions. Compared with passive observation, it has the traditional advantages of radar astronomy. It can measure surface characteristics, determine spin rates and axes, provide extremely accurate ranges, construct maps of planets, distinguish liquid from solid surfaces, find rings and moons, and penetrate clouds. It can do this even for planets close to the parent star. Compared with interstellar travel or probes, it also offers significant advantages. The technology required to build such a radar already exists, radar can return results within a human lifetime, and a single facility can investigate thousands of planetary systems. The cost, although too high for current implementation, is within the reach of Earth's economy.

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.

Gale crater formed from an impact on Mars ∼3.6 billion years ago. It hosts a central mound nearly 100 km wide and ∼5 km high, consisting of layered rocks with a variety of textures and spectral properties. The oldest exposed layers contain variably hydrated sulphates and smectite clay minerals, implying an aqueous origin, whereas the younger layers higher on the mound are covered by a mantle of dust. Fluvial channels carved into the crater walls and the lower mound indicate that surface liquids were present during and after deposition of the mound material. Numerous hypotheses have been advocated for the origin of some or all minerals and layers in the mound, ranging from deep lakes to playas to mostly dry dune fields to airfall dust or ash subjected to only minor alteration driven by snowmelt. The complexity of the mound suggests that multiple depositional and diagenetic processes are represented in the materials exposed today. Beginning in August 2012, the Mars Science Laboratory rover Curiosity will explore Gale crater by ascending the mound's northwestern flank, providing unprecedented new detail on the evolution of environmental conditions and habitability over many millions of years during which the mound strata accumulated.