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The Drake Equation

Some state that by making what they feel are reasonable assumptions and arguments we can ascertain that if life is possible at all, then the universe is so vast that it should not only be possible, but almost certain that there are large numbers of extraterrestrial civilisations in the Universe. In the early 1960’s Frank Drake sought a way to calculate the probability of finding other intelligent races. He came up with an equation to calculate the possibility of extra terrestrial civilizations; which became known as the ‘Drake Equation’. Drake writes, 'The basic premise behind the equation is that what happened here will happen with a large fraction of the stars as they are created, one after another, in the Milky Way galaxy and other galaxies. People unfamiliar with the accepted pictures of cosmic and biological evolution might think the equation is highly speculative; in fact, it is just the opposite, since the phenomena it assumes to take place in the Universe are only those we are sure have taken place at least once' ('The Drake Equation: A Reappraisal', pp. 115-18, First Contact).

Here is the equation also known as the Green Bank equation:


N = the number of technological civilizations in our galaxy

R* = The rate of formation of suitable stars

F(p) = the fraction of stars having planets.

N(e) = the number of suitable planets per planetary system.

F(l) = the fraction of planets on which life develops

F(i) = the fraction of life that evolves to intelligence beings.

F© = the fraction of intelligent species to develop the means of communication.

L = The length of time such civilizations release detectable signals into space.

Drake and other early extraterrestrial-life enthusiasts, including Carl Sagan, arrived at a value for N between 100,000 and 1,000,000--still only about one technological civilization per million stars in the Milky Way, which astronomers believe contains some 200 billion stars.

Drake equation parameters

Considerable disagreement on the values of most of these parameters exists, but the values used by Drake and his colleagues in 1961 are: R* = 10/year, fp = 0.5, ne = 2, fl = 1, fi = fc = 0.01, and L = 10 years.

The value of R* is the least disputed. fp is more uncertain, but is still much firmer than the values following. Confidence in ne was once higher, but the discovery of numerous gas giants in close orbit with their stars has introduced doubt that life-supporting planets commonly survive the creation of their stellar systems. In addition, most stars in our galaxy are red dwarfs, which have little of the ultraviolet radiation that has contributed to the evolution of life on Earth. Instead they flare violently, mostly in X-rays - a property not conducive to life as we know it (simulations also suggest that these bursts erode planetary atmospheres). The possibility of life on moons of gas giants such as Europa adds further uncertainty to this figure.

What evidence is currently visible to humanity suggests that fl is very high; life on Earth appears to have begun almost immediately after conditions arrived in which it was possible, suggesting that abiogenesis is relatively "easy" once conditions are right. But this evidence is limited in scope, and so this term remains in considerable dispute. One piece of data which would have major impact on this term is the controversy over whether there is evidence of life on Mars. The conclusion that life on Mars developed independently from life on Earth would argue for a high value for this term. In 2002, Charles H. Lineweaver and Tamara M. Davis (at the University of New South Wales and the Australian Centre for Astrobiology) estimated fl as > 0.33 using a statistical argument based on the length of time life took to evolve on Earth.

fi, fc, and L are obviously little more than guesses. fi has been impacted by discoveries that the solar system's orbit is circular in the galaxy, at such a distance that it remains out of the spiral arms for hundreds of millions of years (evading radiation from novae). Also, Earth's very large, unusual moon appears to aid retention of hydrogen by breaking up the crust, inducing a magnetosphere by tidal heating and stirring, and stabilizing the planet's axis of rotation. In addition while it appears that life developed soon after the formation of Earth, the Cambrian explosion in which a large variety of multicellular life forms came into being occurred considerable amounts of time after the formation of Earth, which suggests the possibility that special conditions were necessary for this to occur.

The well-known astronomer Carl Sagan speculated that all of the terms except for the lifetime of a civilization are relatively high, and the determining factor in whether there are large or small numbers of civilizations in the universe is the civilization lifetime, or in other words the ability of technological civilizations to avoid self-destruction. In Sagan's case, the Drake equation has been a strong motivating factor for his interest in environmental issues and his efforts to warn against the dangers of nuclear warfare. A lower bound on L can be estimated from the lifetime of our current civilization from the advent of radio astronomy in 1938 (dated from Grote Reber's parabolic dish radio telescope) to the current date. In 2004, this gives a lower bound on L of 66 years.

In an article in Scientific American, Michael Shermer estimated L as 420 years, based on compiling the durations of sixty historical civilizations. Using twenty-eight civilizations more recent than the Roman Empire he calculates a figure of 304 years for "modern" civilizations. Note, however, that the fall of most of these civilizations did not destroy their technology, and they were succeeded by later civilizations which carried on those technologies, so Shermer's estimates should be regarded as pessimistic.

Some computations of the Drake equation, given different assumptions:

R* = 10/year, fp = 0.5, ne = 2, fl = 1, fi = fc = 0.01, and L = 50 years N = 10 × 0.5 × 2 × 1 × 0.01 × 0.01 × 50 = 0.05

Alternatively, making some more optimistic assumptions, and assuming that 10% of civilisations become willing and able to communicate, and then spread through their local star systems for 100,000 years (a very short period in geologic time):

R* = 20/year, fp = 0.1, ne = 0.5, fl = 1, fi = 0.5, fc = 0.1, and L = 100,000 years N = 20 × 0.1 × 0.5 × 1 × 0.5 × 0.1 × 100000 = 5000

The remarkable thing about the Drake equation is that by plugging in apparently fairly plausible values for each of the parameters above, the resultant expectant value of N is generally often >> 1. However, this conflicts with the currently observed value of N = 1, namely ourselves. This conflict is often called the Fermi paradox. However those people who adhere to the premise of the Fermi Paradox believe that, due to a lack of evidence to the contrary, in all probability, humans (as a technologically advanced species) are effectively alone in at least our part of the Milky Way Galaxy. They further say that since we cannot yet determine the variables of the Drake Equation with any real confidence, we cannot determine the numbers of extraterrestrial civilizations based solely on this equation. We must therefore, they argue, rely on data collection - which is only now beginning to be collected in a significant manner. Only then can we even begin to presume what the values of each of the variables in the Drake equation are, they say.



1. Crop Circles.

One of the earliest reports was in Lyon in 815AD, and a late 16th Century woodcut depicts the devil mowing a field into patterns. They began to appear in significant numbers in the fields of southern England in the mid-1970s. Early circles were quite simple, and simply appeared, overnight, in fields of wheat, rape, oat, and barley. The crops are flattened, the stalks bent but not broken.

As the crop circle phenomenon gained momentum, formations have also been reported in Australia, South Africa, China, Russia, and many other countries, frequently in close proximity to ancient sacred sites. For the thousands reported every year, the vast majority go completely undetected. Most of the complex formations occur in the United Kingdom and they are also more likely to be detected because of the country's smaller land mass.

Over the last 25 years, the formations have evolved from simple, relatively small circles to huge designs with multiple circles, elaborate pictograms, and shapes that invoke complex non-linear mathematical principles. Since the early 1990s, however, the phenomenon has grabbed world attention, as the formations evolved into enormous, increasingly mathematically complex and perfectly executed shapes appearing in fields, often near the sacred sites of Wiltshire.

The largest to date, a perfectly formed spiral formation 244 metres in diameter, composed of 409 circles covering almost the entire field, appeared overnight on a rainy night at Milk Hill in Wiltshire Aug. 12, 2001.

The movie Signs, starring Mel Gibson, while universally scorned by serious crop circle researchers, nevertheless renewed interest in crop circles after years of the phenomenon being dismissed in the media as a sophisticated hoax, following the announcement of two elderly landscape painters named Doug Bower and Dave Chorley who confessed in 1991 that they had been making crop circles in English grain fields since the 1970s after reading about the Tully, Australia Saucer Nest of 1966. The truth is that they were both unable to draw a decent crop circle in daytime and to remember the exact location of their exploits.

Plasma Vortex
Various researches were conducted in this phenomenon and a number of observations have also been made over the years that finally seem to indicate that there are particular characteristics that "genuine" (or non-mandmade) formations appear to exhibit.

Research has been conducted over a ten year period with samples and thorough laboratory testing carried out by the biophysicist Dr. Levengood, Nancy Talbott, and John Burks -- the BLT Research Team, and a small army of volunteers worldwide. Their findings include from samples taken within the crop formations in contrast to the control samples taken from outside the circles.

Levengood studied biophysics at the University of Michigan in the late 1960s and holds several patents on his inventions to increase seed growth and vigor. He has studied biochemical and biophysical changes in crop formation seeds and plants for over a decade.

He has found out that the plants from more than 95% of the sampled events revealed either single or multiple anomalous and readily apparent structural alterations at the macroscopic level. In general, these consisted of significant enlargements of the cell walls, expulsion cavities in the nodes of the plant stalks, significantly extended node lengths, and changes to the soil composition (ie. vastly higher level of magnetite concentration) Significant changes in seed germination and development were also found. Affected plants also have characteristics suggesting the involvement of transient high temperatures. Not one of these clearly anomalous plant alterations had been mentioned – much less explained – by the proponents of the croppies theory, nor can they be accounted for by the supposed methods employed to create crop formations through claims made by the circle makers.

Levengood thinks what is creating the crop circle is a complex energy system that he describes as a "spinning plasma vortex" of ions with microwave frequencies that rapidly heat water in plants, causing them to collapse to the ground with stems not cracked or broken. Further, the microwave frequencies can heat up water in the plant's growth nodes which burst out, creating small holes that have often been found in extraordinary crop patterns. Those complex energies can also affect the seeds.

Levengood. W.C. 1994. Anatomical anomalies in crop formation plants. - Physiol. Plant. 92: 356-363.
“The affected plants have components which suggest the involvement of rapid air movement, ionization, electric fields and transient high temperatures combined with an oxidizing atmosphere. One naturally occurring and organized force incorporating each of these features is an ion plasma vortex, one very high energy example being a lightning discharge.

Atmospheric-associated plasma formations may plausibly originate in regions where there are clear indications of energy exchange between the ionosphere (60-100 km) and electrical storms in the upper atmosphere (Franz et al. 1990). Currently under consideration are ion plasma vortices which form in unstable regions and act as heat and angular momentum transporters. In fluid dynamics, gases, including air, are considered as having liquid properties (Prandtl and Tietjens 1957). In such a scheme the descent of a vortex through a liquid produces unstable secondary products which form complex, symmetrical patterns such as circles, rings, triangles, double lines and ovals with tubes or 'paths' extending from them (Levenoood 1958). In its descent to the crop surface the shaping of these features of vortex instability would be guided by variations in the Earth's magnetic field (Rossi and Jastrow 1961). At the crop surface the heat, ionization, associated electric fields and angular momentum would be transferred to the living plants. Taken as a whole, ionized air plasmas are electrically neutral, although internally, charge separation takes place and they can have high concentrations of positive ions and free electrons (Lehnert 1961), which in contact with plant tissue might produce transient heating and account for a number of the plant transformations.
The Electro-magnetic Field Theory
According to Dr Colin Andrews, who has studied crop circles for 17 years, about 20% are caused by eddie currents in the earth's magnetic field - a mysterious shift in the electro-magnetic field creates a current that flattens the crops in its path.

That could probably explain the numerous reports of electronic equipment failing in crop circles and compasses spinning out of control in and over the crop circles (even when flying over in aircraft).

The UFO Theory
Crop circle formation is similar to alleged UFO landing site reports where a circular swirling pattern is formed in grass, the grass remains unharmed, and is in inaccessible locations for vehicles.

Channelers and ufologists pretend that crop circles are not symbols intended as a 'message to man.' These deliberately created pictographs are signposts, or reference marks produced by aliens moving in space and time (back and forth/in and out), who are monitoring the course of event trajectories. The pictographs serve primarily as reference markings and for 'event line' orientation and are deliberately embedded in a short-lived, perishable medium so that man's attention would not be attracted to specific locations.

Production of the circles occurs via two primary mechanisms:

Macroscale: external area effects; heat and overpressure
Microscale: internal plant stem effects; pressure changes and cellular damage.
Ultrasonics are produced as gasses escape the plant stem. The concominent drop in turgor pressure within the stem causes the plant to bend over. there is a gentle 'swish swish' sound as this effect is induced, en masse.

Some craft halt in the vicinity of the circles for what appears to be communications checks. On occasion, craft temporarily stop and conduct exploratory probing/testing in the vicinity of the circles.

It must be added that circles have given rise historically to various beliefs connected with the supernatural. for instance, the circles inspired the idea of the 'elves' green rings. The Nazca lines and, most noteworthy, Navajo sand paintings, were ideas born of attempts to copy the 'marks of the Gods', so as to evoke a visitation or response.

The Whirlwind Theory
The official government explanation is that whirlwinds, created by heat thermals, are the true cause of the crop circle anomaly. But whirlwinds or Mini-tornadoes are not static, they travel around and it is very unlikely that they would create such intricate and symmetrical patterns.

Natural Music
Hawkins observed that the circle patterns embodied geometric theorems that expressed specific relationships among the areas of the various circles, triangles, and other shapes. These patterns displayed "exact numerical relationships" (i.e., diatonic ratios) similar to those found in a scale of musical notes. For example, if a circle within a formation is 90 degrees and another is 80 degrees, the ratio is 9/8 which is the same ratio between the notes C and D, C being the eighth note of the diatonic scale and D being the ninth. These are the same ratios that are found in popular music, or in playing the white notes on the piano.

According to Stephen J. Smith, a paranormal investigator and amateur composer, these ratios are not the result of chance "because the numbers have to be very precise in order to be a diatonic ratio. This is why music sounds like music instead of noise, because it is built on precise ratios."

To derive music from the crop circles, Smith used a fractal music-generating computer program. He entered photographs of the formations into the computer, which ëreadí the photographs and generated music from the photos, using the crop circle scales to play it back.

Curiously, not all crop circles embody diatonic rations in their formations. Hence, some do not have musical qualities. Possibly, Smith says, the real circles have diatonic ratios, and the faked ones do not. Further, diatonic ratios may be only a part of the overall geometry of the formations.