Rare Earth Hypothesis - Rare Earth Equation

Rare Earth Equation

The following discussion is adapted from Cramer. The Rare Earth equation is Ward and Brownlee's riposte to the Drake equation. It calculates, the number of Earth-like planets in the Milky Way having complex life forms, as:

where:

• N* is the number of stars in the Milky Way. This number is not well-estimated, because the Milky Way's mass is not well estimated. Moreover, there is little information about the number of very small stars. N* is at least 100 billion, and may be as high as 500 billion, if there are many low visibility stars.
• is the average number of planets in a star's habitable zone. This zone is fairly narrow, because constrained by the requirement that the average planetary temperature be consistent with water remaining liquid throughout the time required for complex life to evolve. Thus = 1 is a likely upper bound.

We assume . The Rare Earth hypothesis can then be viewed as asserting that the product of the other nine Rare Earth equation factors listed below, which are all fractions, is no greater than 10−10 and could plausibly be as small as 10−12. In the latter case, could be as small as 0 or 1. Ward and Brownlee do not actually calculate the value of, because the numerical values of quite a few of the factors below can only be conjectured. They cannot be estimated simply because we have but one data point: the Earth, a rocky planet orbiting a G2 star in a quiet suburb of a large barred spiral galaxy, and the home of the only intelligent species we know, namely ourselves.

• is the fraction of stars in the galactic habitable zone (Ward, Brownlee, and Gonzalez estimate this factor as 0.1).
• is the fraction of stars in the Milky Way with planets.
• is the fraction of planets that are rocky ("metallic") rather than gaseous.
• is the fraction of habitable planets where microbial life arises. Ward and Brownlee believe this fraction is unlikely to be small.
• is the fraction of planets where complex life evolves. For 80% of the time since microbial life first appeared on the Earth, there was only bacterial life. Hence Ward and Brownlee argue that this fraction may be very small.
• is the fraction of the total lifespan of a planet during which complex life is present. Complex life cannot endure indefinitely, because the energy put out by the sort of star that allows complex life to emerge gradually rises, and the central star eventually becomes a red giant, engulfing all planets in the planetary habitable zone. Also, given enough time, a catastrophic extinction of all complex life becomes ever more likely.
• is the fraction of habitable planets with a large moon. If the giant impact theory of the Moon's origin is correct, this fraction is small.
• is the fraction of planetary systems with large Jovian planets. This fraction could be large.
• is the fraction of planets with a sufficiently low number of extinction events. Ward and Brownlee argue that the low number of such events the Earth has experienced since the Cambrian explosion may be unusual, in which case this fraction would be small.

The Rare Earth equation, unlike the Drake equation, does not factor the probability that complex life evolves into intelligent life that discovers technology (Ward and Brownlee are not evolutionary biologists). Barrow and Tipler review the consensus among such biologists that the evolutionary path from primitive Cambrian chordates, e.g. Pikaia to Homo sapiens, was a highly improbable event. For example, the large brains of humans have marked adaptive disadvantages, requiring as they do an expensive metabolism, a long gestation period, and a childhood lasting more than 25% of the average total life span. Other improbable features of humans include:

• Being the only extant bipedal land (non-avian) vertebrate. Combined with an unusual eye–hand coordination, this permits dextrous manipulations of the physical environment with the hands;
• A vocal apparatus far more expressive than that of any other mammal, enabling speech. Speech makes it possible for humans to interact cooperatively, to share knowledge, and to acquire a culture;
• The capability of formulating abstractions to a degree permitting the invention of mathematics, and the discovery of science and technology. Only recently did humans acquire anything like their current scientific and technological sophistication.