According to the Bible, God’s “chosen people” were the tribe of Israel. In the New Testament this is expanded to include anyone who accepts Jesus as the Messiah. For a long time this has, by extension, been interpreted by many as inferring that humanity is somehow unique. The long-held misconception that the Earth lay at the centre of the universe only served to reinforce this belief. Ever since science was able to firmly establish that the Sun, Moon, planets and stars do not revolve around the Earth, but are, in fact, celestial bodies in their own right, there have been writers who have speculated about the possibility that life could exist elsewhere in the universe.

            Despite the efforts of conspiracy theorists and the SETI (Search for Extra-Terrestrial Intelligence) programme, there has, as yet, been no firm evidence discovered (at least, none that is in the public domain) that proves the existance of even microbial life beyond the Earth. This is despite the fact that current scientific thinking suggests that intelligent life should be reasonably abundant in our galaxy (and, by extension, in every other galaxy).

            There is a famous speculative equation – known as the Drake Equatiom – that is used to find a viable estimate of the number of civilisations in our galaxy that are capable of interstellar communication. It reads:

N = R_* f_p n_e f_l f_i f_c l

where

N = the number of civilisations that are detectable in our galaxy

R_* = the number of stars formed per year

f_p = the fraction of stars with planets

n_e = the number of such planets that lie at the “right” distance from the star

f_l = the probability of life forming on such planets

f_i = the probability of such life attaining intelligence

f_c = the probability that intelligence becomes technologically advanced

l = length of time they transmit detectable signals

            Scientists are reasonably certain about the left-handmost element of this equation and become decreasingly confident as you go towards the right, until the last element is reached, which is usually little more than an educated guess. Despite this uncertainty, there is broad agreement about the results, which suggest that, if all of the intelligent life in the galaxy was evenly spread, then our nearest intelligent neighbours would be between twenty and fifty light years away. Expressed as miles, this seems quite distant: 120 to 300 million million miles. However, on the cosmic scale this really is “on our doorstep”. Mankind has been pumping radio signals into the galaxy for over one hundred years. The earliest of these signals would have passed dozens of intelligent aliens’ planets by now, if they exist and are evenly spread in the galaxy. If they, also, used radio, then we would expect to have picked up their signals by now. So why haven’t we?

            Firstly, the alien civilisations would not be evenly spread. Our galaxy is a “barred spiral”, meaning that the stars are clustered in a characteristic pattern. This takes the form of a “bar” at the centre, from the ends of which “arms” spiral out. There is a greater concentration of stars near the centre of the galaxy and also near the centre of each arm. The Earth is located about a third of the way out from the centre and towards the edge of an arm. Hence, there are considerably fewer stars in our region of space than in most other parts of the galaxy. It is also the case that any alien civilisations would be “randomly” scattered, creating regions with high densities of civilisation and others with low densities. Earth may simply be in a “low density” region.

            Secondly, the search for alien life is concentrating on radio signals (and only selected frequencies). Mankind has been using radio for about a century, but already we are moving on to other methods of communication. It may be that any aliens out there have long-since moved on from radio.

            There is a third possibility. It may be that scientists have simply got it wrong (it would not be the first time!) Recent discoveries are shedding more light on the way that life has evolved on Earth that seem to suggest that it is almost a miracle that we have survived at all. This may mean that the values that are inserted into the “life” equation will have to be re-evaluated.

            It must be realised that we are faced with a huge problem when trying to estimate the prevalence of life in the galaxy – that is, that we only have one model of life on which to base our calculations: that of Earth. It is hoped that what follows will succesfully take this into account, but it should be continually borne in mind that strange and exotic methods for the creation of life (and, ultimately, intelligence) may exist that can never be taken into account (until, of course, we encounter them).

            For our purposes, we will use a modified version of the life equation:

            N = S x Sv x P x L x I x T

            where

            N = the total number of intelligent species in the galaxy

            S = the total number of stars in the galaxy

            Sv = the proportion of stars that are suitable for supporting life

            P = the proportion of stars that have suitable planets

            L = the proportion of suitable planets on which life forms

            I = the proportion of life forms that develop intelligence

            T = the likelihood of such intelligence both surviving and still being extant

            As with the original equation, science is increasingly uncertain as we move from left to right through this equation. However, as we examine each part in detail, we may begin to discover that science is more uncertain that it once thought.

S – The number of stars in our galaxy

            This the one number about which few would argue. Over the past hundred years the figure has been revised many times, but recent scientific advances have now set this number – fairly certainly – at around two billion (2,000,000,000).

Sv – The proportion of stars suitable for supporting life

            Until now, science has largely taken the view that, if a star exists, it almost certainly able to support life if there is a planet of appropriate size and distance. Thus, they have taken the view that this part of the equation should be given a value so close to 1 (i.e. 100%) that it may as well be 1.

            However, this utterly fails to take into consideration a number of factors. The most significant of these is that a large proportion of stars do not exist alone: they come in pairs or groups of three or more. In the majority of such systems, any planets would be totally incapable of supporting life. This is because of a number of factors: the high levels of radiation, the bizarre gravitational fields and the extreme magnetic fields to name but three. Whilst it is conceivable that life in some other form could exist in such environments, it seems that such life would be rare indeed. Hence, we should eliminate all stars that exist in multiple systems. The best estimates suggest that up to 90% of stars exist in such systems.

            There are other factors that affect the viability of a star for supporting life that affect our figures less drastically. For example, a significant number of stars lie in “globular clusters”. These clusters of mostly very old stars are roughly spherical in shape and orbit the centre of the galaxy in highly eccentric ways. What diminishes the stars in these clusters ability to support life is that they are so densely crowded in the cluster. It is probable that the radiation within the cluster would be too high to allow life. It must also be realised that any star in the cluster that explodes as a supernova would saturate the entire cluster with lethal radiation.

            Some stars are also too short-lived. They burn so fast that there simply would not be enough time for life to evolve. Other stars are too variable – they literally flare up and die back down. In fact, all stars seem to be variable to some degree, but our Sun is considered to among the least variable. Had our Sun been just a little more variable then life as we know it would never have been able to evolve on Earth. It seems likely, therefore, that a star that is too variable could not support life.

            With all of these factors taken into consideration, it is probable that only a fraction of a percent of stars are actually suitable for life. If we give some allowance for exotic forms of life that could develop in unusual environments then a reasonable figure for Sv would seem to be around 0.01 (1%).

P – The proportion of stars with suitable planets

            The process of planetary formation is still rather poorly understood, but it is generally believed that stars form from large clouds of dust and gas that gradually coalesce under the force of gravity, until they reach a “critical mass” and ignite as stars. Inevitably, this process has a substantial amount of “left over” material that will usually go on to form larger bodies. Thus, it is generally accepted that almost all stars will have some sort of planetary system. The question, therefore, is whether such planets include one or more that is capable of supporting life.

            Astronomers define a “Goldilocks Zone” around stars, which is the region where conditions are “just right” for supporting life. Any planet closer than this zone would suffer too much radiation, while planets outside this zone would be too cold. Unsurprisingly, this zone is defined based upon our experiences here in the solar system, but are nevertheless based on reasonably sound scientific principles. For example, high radiation or heat are known to cause RNA molecules to break down, so it is not unreasonable to conclude that life as we know it could not survive on a planet too close to its sun. Unusual forms of life have a better chance of survival in the colder regions of a star’s system. For example, a large enough body circling a large gas giant is subject to a lot of gravitational stress that would keep the body warm. There are a number of scenarios in which such a body could harbour life. However, conditions would at the least be harsh and may be so variable as to preclude the long-term survival of all but the most primitive organisms.

            The proportion of life-capable planets outside the Goldilocks zone is likely to be very small, so we will concentrate on those that may lie within that zone. Within our own system, this zone was originally believed to stretch from the orbit of Venus out to that of Mars, with our Earth conveniently and ideally placed between the two. Mars proved to be too small to sustain life – at least over the long term. Today, it’s atmosphere is too thin and its interior has cooled to the extent that there is no volcanic or tectonic activity. However, had Mars been significantly larger, it is possible that it may have been able to harbour life, if the conditions had been right. Venus, on the other hand, is almost identical to Earth in size, but is even less hospitable than Mars because of the “runaway greenhouse effect”. Because Venus is so much closer to the Sun, and therefore much warmer, the atmosphere was unable to retain the lighter molecules, such as water, and is, instead, thick with heavy molecules that act like a blanket, trapping radiation and heating the surface to a temperature that would melt lead. The general consensus, now, is that this effect is probably inevitable for a planet as close as Venus is to the Sun. Therefore, the Goldilocks zone, for our system, is now believed to start somewhat beyond the orbit of Venus and end somewhere close to the orbit of Mars.

            The habitable zone for other stars varies according to the nature of the star. For the cooler (generally redder) stars, this zone begins and ends closer in. For the larger, hotter (generally bluer) stars it is farther out. The size and temperature of the star has little effect on the width of the zone, as cooler stars have gentler radiation, allowing for a wider zone, while larger stars are more energetic, reducing the width of the zone.

            We need to consider, therefore, the likelihood of a planet forming within the habitable zone. Until recently, the only model for comparison was our own system, but in 1995 the first planet beyond our solar system was confirmed and many others have been found since. At the time of writing almost two thousand have been confirmed or strongly suspected. However, these planets have only been found by indirect means: as the planet passes the star, it causes a slight dip in the star’s light-level, a dip that has been likened to a flea passing a car’s headlight a mile away. As yet, we cannot “see” other systems and the majority of the planets found have been gas giants similar to Jupiter. Hence, our knowledge of planetary formation remains speculative. However, using computer models based on the knowledge we do have, there is a reasonable assumption that around half of all stars will have planets form within the Goldilocks zone.

            For our present purpose, we are considering planets that are suitable for life. Location, alone, is not sufficient. We must also consider the nature of the planet. In our solar system there are a variety of bodies: Gas giants, rocky planets, sub-planets, asteroids, comets and other, smaller debris. For a body to be capable of sustaining life it must be large enough to retain an atmosphere, but not so large as to have a crushing gravity. The gas giants are all too large and anything smaller than the rocky planets is too small.

            There are four rocky planets in our system: Mercury, Venus, Earth and Mars. As has already been stated, Mars is too small. It has been unable to retain all but the thinnest of atmospheres and its interior is now too cold. Mercury is even smaller than Mars. Only Venus and Earth are of sufficient size.

            With as yet a limited understanding of planetary formation, there is no certainty as to the proportion of planets that are of the “right” size. Computer models seem to suggest that our solar system is fairly typical, meaning that, of the eight large bodies in our system, two are of appropriate size, giving a proportion of one in four. Given that half of stars have planets in the habitable zone, this suggests that one in eight would have a planet in this zone of suitable size.

            The picture is not so simple, however. The computer models tell us that the Earth – and the other planets – were not always where they are now. When the solar system first formed, Jupiter and Saturn were much closer in and the rocky planets were further out. Over time, Jupiter and Saturn entered into a period of orbital resonance, where, for every “year” on one of them, precisely two “years” passed for the other. Thus, every two “years” their gravity combined to “nudge” the other bodies in the solar system. Over time, this continual “nudging” had a dramatic effect on the solar system. All of the planets were pushed into different orbits, Neptune was turned onto its side, Pluto was sent into a highly eccentric orbit and huge numbers of smaller bodies were sent to the outer reaches of the solar system (more on this later). Jupiter and Saturn were themselves affected, albeit more slowly.

            It is only due to this “coincidence” of Jupiter and Saturn in orbital resonance that the Earth and the other rocky planets are where they are now. It is, as yet, impossible to determine how common such an event is, but it is almost certainly not inevitable in every system. It is also very likely that in many systems such an event would have the opposite effect, pushing smaller bodies outwards rather than in, or into highly eccentric orbits.

            The computer models seem to suggest that rocky planets rarely form within the habitable zone and only a fortuitous cosmic coincidence can push them into that zone. However, allowance must be made for the fact that science has only an imperfect understanding of planetary formation. If the computer models are completely wrong, then, at best, one in eight stars have a rocky planet of sufficient size within the habitable zone (P = 0.125). On the other hand, it may be that the positioning of a rocky planet in the habitable zone is a very rare event indeed (P = near zero). For the time being, let us assume a reasonable compromise between these two extremes and set P, the probability of a suitable planet forming in the habitable zone, at 0.01 (1%).

L – The proportion of suitable planets on which life forms

            The most difficult aspect of this part of the equation is finding a suitable definition of “life”. Scientists and philosophers have struggled with this question for centuries, but it is essential to find some sort of answer if we are to determine the likelihood of intelligent life in the universe.

            For our purposes, we are not, at this point, concerned with whether an organism develops into something more complex (that is considered in the next section), but it must, surely, be capable of development. Thus, for our purposes here, “life” is considered to be any entity that is able to reproduce itself and has the capacity for development into a more complex entity. Our main consideration, therefore, is whether a planet harbours conditions that allow for such an entity to exist.

            Life as we know it is often described as “carbon-based”, because all such life contains three elements: carbon, oxygen and hydrogen. It is a well-known principle of chemistry that these three combine readily in an almost infinite variety of forms and, especially, into the larger, more complex molecules that are the basis of life. It has been speculated that other elements than carbon (especially silicon) could be combined with hydrogen and oxygen to form sufficiently complex molecules to produce life. Whilst other, even more exotic, combinations may be possible, it is important to consider that only a limited number of elements are abundantly available in the universe.

            When the universe began the only elements present were the two lightest: hydrogen and helium. As these condensed to form stars, the nuclear reactions in these stars began to combine the hydrogen and helium atoms to form heavier elements, such as carbon, silicon and oxygen. However, the heaviest element that can be formed in this way is iron. The only way that elements heavier than this can form is in the death-throes of stars, when the massive explosions can force the elements to fuse together. Thus, while hydrogen and helium are extremely common in the universe, the lighter elements up to iron are also relatively common and the heavier ones are very rare. It is, therefore, reasonable to assume that any life would be based upon these lightest elements. The only certain combination that produces life is carbon, hydrogen and oxygen. The only other speculated combination that uses the lightest elements replaces carbon with silicon.

            Thus, for a planet to produce life it would need a sufficient quantity of oxygen, hydrogen and carbon or silicon, readily available where it is needed. It is the question of availability that is most important here. The way that planets form tends to cause the heavier elements to concentrate in the core, while the lighter elements rise to the surface. Hence, both carbon and silicon tend to be readily available on the surface of any rocky planet.

            The real question lies with the availability of hydrogen and oxygen. Both are common elements, so are present in large quantities when a planet forms. The first issue, therefore, is whether the planet is able to retain its supply of these elements. When a star first ignites, it sends a powerful shockwave out into space. Any lighter elements, such as hydrogen and oxygen, are carried away by this shockwave to the outer reaches of the system. This same shockwave would also have the effect of “scouring” any young planet of its atmosphere if it is close enough – and any planet within the Goldilocks zone would certainly be close enough. Therefore, if any planet is to harbour life, it must retain a sufficient quantity of hydrogen and oxygen (and other gases) within its body to replenish its atmosphere.

            It is assumed that any planet would still be very young at the time its star ignites. Such a planet would still be extremely hot and many chemical reactions would be taking place that are now seen only rarely on Earth. Such reactions would release large quantities of hydrogen and oxygen. However, the vast majority of these elements would be locked into molecules that are of little use to any potential life. It is generally believed that water is an essential ingredient of life. In the early years of a planet water would boil off, often ejected into space, or combined with other gases to form other, even more toxic compounds. This, it would seem, is the most likely fate of such a planet: to be shrouded in a toxic mix of acids. So, why isn’t Earth like that?

            Once again, we have the fortuitous orbital resonance of Jupiter and Saturn to thank. It will come as no surprise that the bodies most affected by this were the smallest and lightest. Among the smallest and lightest in our solar system are the comets, which are mostly composed of ice and dust. When Jupiter and Saturn began to affect these, many were sent into highly eccentric orbits, while the rest were flung out to the farthest reaches of our system. Over the following millenia, those in eccentric orbits inevitably came into contact with other bodies in the system. It is now believed that a large proportion of the free water on Earth arrived as a result of these comets impacting us in a period known as the “late heavy bombardment”.

            It is likely that any planet that is nudged into the Goldilocks zone in the way that Earth was would also undergo a similar bombardment, as the same process is involved in both incidents. There are also a number of other ways in which water might be delivered to a planet. However, planets that form in the Goldilocks zone by other means are far less likely to receive a sufficient supply of water.

            So, any planet is almost certain to have a sufficiency of carbon or silicon, but it is far less certain that there will be enough water, and hence hydrogen and oxygen. Any figure we put on this is rather speculative, but it seems likely that the chances of such a planet having all of the necessary ingredients for life is unlikely to be better than one in ten (L = 0.1).

            Having the basic ingredients is only the first step in producing life. Those ingredients must be combined, with other elements, in the right conditions for life to appear. The “other elements” are not an issue, here, as almost all elements are likely to be present and there is an almost infinite variety of combinations that could, potentially, create life.

            Experimentation has shown that, given the same “chemical soup” as existed on the early Earth, the application of a jolt of electricity (e.g. lightning) will cause the creation of RNA, the basic building-block of DNA. It has also been discovered that many of the components of that “chemical soup”, such as amino acids, exist freely in space. It is not hard to see how such chemicals would arrive on Earth. Hence, a planet with sufficient water is extremely likely to harbour the conditions for creating RNA. In fact, it is so likely as to be considered more or less certain. With no information to the contrary, we must assume that this is equally true for forms of life not based on carbon.

            It is not known with certainty what factors were involved in causing RNA to combine to form DNA. Many theories exist about the conditions required. It is possible that most or all of these are actually true. In other words, so long as there is sufficient RNA available, there are a large range of conditions which would allow its combination. It is equally possible that there is only a single, very specific instance where such a combination is permissible. The growing consensus, such as it is, is that, if RNA is present in sufficient quantities, then the formation of DNA will almost always happen eventually. In the absence of better information, we will, for the purpose of this calculation, assume this to be true.

            There are, however, quite a number of “ifs” and “maybes” in the above: a planet may not be in a part of space where the ingredients of the “chemical soup” are abundant; it may have a neighbouring planet of such size (planets up to ten times the size of Jupiter appear to be quite common) that it “gobbles up” too many of the comets to allow enough free water on the rocky neighbour; a planet may have an eccentric orbit that creates temperature extremes too great for RNA to survive. There are a number of other ways in which a planet may not be able to create or support RNA. It seems reasonable, therefore, to assume that, at best, a planet that otherwise has an abundance of the right ingredients, nevertheless only creates life about half of the time (it is likely to be far less than this). Therefore, we can set L, the probability of life forming on a suitable planet, at 0.05 (5%).

I – The proportion of life forms that develop intelligence

            The previous section considers only the potential for creating life that may develop intelligence. This section must consider a vast number of factors to determine the likelihood that these primitive organisms could reach a point in their development where they are capable of interstellar communication.

            On the basis of our only working model (Earth), one significant criterion required for the development of intelligence is time. Ignoring speculations about “ancient civilisations”, life on Earth only developed the intelligence necessary for interstellar communication sometime in the last two hundred thousand years (the technology is far more recent, but it is believed that the earliest forms of homo sapiens were of similar intelligence to ourselves. If they had had the technology they could have used it.) The Earth formed around five and a half billion years ago, but was initially somewhat inhospitable. The first life on Earth probably formed around four billion years ago.

            The fact that it took life around four billion years to develop technology on Earth does not mean we can assume so long a time is required in all cases. There have been events in Earth’s past that may have extended the time required here (we will come to these shortly). However, the Earth took one and a half billion years to cool and settle into a condition that was conducive to life; a similar time frame is probably required in all cases.

            Once life appeared, it began the slow process of transforming the planet. Initially, Earth had little free oxygen and the earliest life forms processed other chemicals in order to survive. It was this process that gradually transformed the Earth, as one of the “waste” products of these early life forms was oxygen. Whilst it is conceivable that life could have evolved without free oxygen, there is good reason to believe that it would have been limited in its ability to evolve. Organisms that utilise carbon dioxide, for example, metabolise their energy slowly and are thus unlikely to evolve beyond plants. It also seems likely that, once a sufficiency of carbon dioxide-consuming organisms have developed, a “tipping point” is reached, where the levels of free oxygen will begin to rise and the available carbon dioxide reduces. Once this happens, oxygen-consuming organisms will develop. As these metabolise far faster, they are more “aggressive” and rapidly develop. On Earth, this process appears to have taken about one and a half billion years.

            At some point, more complex organisms may develop. On Earth this happened a little over half a billion years ago and development from that time has been relatively swift.

            At a minimum, a planet needs over a billion years to cool sufficiently to allow life to form, another billion years for that life to “terraform” the planet to conditions suited to more aggressive life-forms and then a further half a billion years for these life-forms to evolve intelligence. At a minimum, a planet must be at least two and a half billion years old to harbour intelligent life.

            The process of evolution may, of course, take longer than this, as it has on Earth. There is no reason not to assume that it requires considerably longer than the time it has taken here in some instances. However, not all planets will get the required time. Our Sun is about half-way through its “life”. In about four billion years it will begin the process that will lead eventually to its “death”. At that time its output will be some 10% higher than it is today; it will begin to expand, rapidly engulfing the planet Mercury and eventually also Venus, Earth and Mars. Eventually, the internal fires will start to grow cooler. The outer layers of the Sun will be blown off, leaving behind a slowly cooling red dwarf.

            The life-cycle of our Sun is similar to the majority of stars. However, the larger a star is, the shorter its life-span. Our Sun is described as a “yellow dwarf”, because of its colour and relatively small size. Some stars are so massive that they complete their life-cycle in less than the two and a half billion years required by life. Many others complete it in a shorter time than our Sun.

            Thus, we can eliminate those planets which are not old enough and which orbit stars with too short a life-cycle. A reasonable approximation of this would be about a quarter of them (I = 0.75).

            One factor was not fully considered earlier, in the development of life, as it has greater relevance here. That is, relative stability.

            For most of its history, the Earth has enjoyed a fairly stable orbit. Once it had reached its current position, it soon settled down into an orbit that is close to circular and close to the plane of the solar system (an imaginary, huge circle that extends outwards from the Sun’s equator) and with an axis of rotation tilted at around twenty three degrees from the perpendicular, without too much variation. This relative stability has given the inhabitants of Earth an environment that has never reached extremes so great as to wipe out life. But the source of this stability has been, possibly, the single greatest slice of luck that life on Earth has been dealt: the Moon.

            As satellites go, the Moon is huge compared to its primary (in this case, Earth). Although there are larger satellites than the Moon in the solar system, they all orbit planets that are hundreds of times larger than Earth. Had the Moon been orbiting Mars, we would probably have described it as a “double planet” system. The best computer modelling suggests that the natural formation of double-planets is so rare that they as well be considered impossible. So, how did the Earth-Moon system form?

            Originally, the Earth formed on its own, as did the Moon. It is probable that the Moon formed at the same distance as the Earth from the Sun, but at a location about a third of the way along its orbit. This location, known as a “LaGrange Point” is usually stable, and it is probable that the Moon could have stayed there to this day. However, tidal forces from Jupiter gradually pulled it out of this stable orbit and it was set on a collision course with Earth. The nature of that collision was the next great slice of fortune for Earth. The Moon struck a glancing blow, heavily damaging both bodies without completely shattering them. This allowed the Earth to retain huge amounts of material blasted out by the collision (and possibly increasing its mass somewhat), but also allowed the Moon to retain sufficient mass to become the body it is today. Further, the mass of the Moon then settled into an orbit that was at the closest possible distance. This point is crucial to the development of life on Earth. If the Moon had been any closer, it would have spiralled back into the Earth, forming a single, larger body. If it had been any further out, it would have rapidly spiralled away from the Earth.

            So, it is a matter of great fortune that we have the Moon, but why is this so important? It all comes down to tides.

            Because of its great size and proximity, the Moon exerts a significant gravitational pull on the Earth. The side closest to the Moon is pulled outwards, forming a bulge on the surface that travels around the Earth as it spins. The most obvious evidence of this is the tides of the oceans, but this tidal pull is also exerted on the more solid parts of the Earth and this played a crucial role in the development of life.

            The tidal pull of the Moon acts like a “brake” on the Earth – a slight drag that is causing it to slow down. This effect is tiny, but cumulative. We are used to a twenty-four hour day, but the drag of the Moon has been lengthening days ever since it formed. Originally, the Earth was spinning so quickly that a single day passed in less than six hours. We can only speculate on the effect this would have had on the development of life had the Moon not been there to slow it down. As Newton famously said, every action has an equal and opposite reaction. While the Earth has been spinning ever-slower, the Moon has been revolving around the Earth ever faster. Again, this effect is tiny, but cumulative. As anyone who has sat on a roundabout in a playground can attest, as things rotate faster, the more it is pushed away from the centre of rotation. As the Moon has got faster, it has slowly been moving away from the Earth. This means that, in the distant past, it was much closer to the Earth and, therefore, its gravitational (tidal) influence was far greater.

            When a planet forms, its heaviest elements tend to sink towards the centre. This includes the majority of the trace heavy elements, such as uranium and gold, but also, significantly, the heaviest of the abundant elements, especially iron. During any planet’s early years, the centre retains heat that was generated during its formation. To begin with, this heat is sufficient to keep elements such as iron in a molten state, but over time this heat is slowly dissipated into space. Unless more heat is introduced, the planet will eventually cool to the point that its centre solidifies. This is what has happened, for example, on Mars. Despite having the largest volcano in the solar system (Olympus Mons), Mars has been cold for so long that this volcano has not erupted for billions of years.

            Clearly, the size of a planet will dictate how long it takes to cool, but there are other factors that can keep a planet hot for longer. The presence of the heaviest elements is a major factor, as these are usually radioactive and the radioactive decay may continue for billions of years introducing significant amounts of heat. The other major factor is tidal forces. Whenever any body is subjected to tidal forces, energy is introduced into that body, which generates heat. Jupiter’s moon, Io, is tiny, but is so close to Jupiter that the tidal forces have kept its interior hot until now, and are likely to keep it hot for as long as both exist.

            Despite its great distance, the huge gravitational pull of the Sun exerts a tidal influence on all of the planets in the solar system, extending the “life” of their interior fires. But on the early Earth the greatest tidal influence was the Moon. Had the oceans existed soon after the Moon formed, they would have had daily tides measured in hundreds of metres. This same influence was felt throughout the Earth. This increased both the heat and motion of the Earth’s interior. It seems likely that this had a significant effect on plate tectonics and it is probable that, without the Moon, the Earth would not have such large continents. This also resulted, significantly, in greater and more prolonged volcanic activity. This released huge quantities of gases into the atmosphere. Crucially, it also brought huge quantities of heavier elements from the interior to the surface, especially iron.

            About a billion years after the Earth and Moon had collided, the Earth had cooled sufficiently that a relatively stable crust had formed, but it would have been a very different world to the one we see today. Volcanic activity was far more prevalent and the atmosphere would have been thick with toxic gases. There was no free oxygen, the vast majority of it locked up in carbon dioxide. Around this time, water was finally able to condense to form shallow seas. This was the first, crucial step in the formation of life. In these seas the material for the “chemical soup” of life was able to gather, with a huge supply of atmospheric carbon dioxide available to fuel its development. However, the mere presence of these ingredients, it seems, would not have been enough for life to form. The “soup” needed to be stirred. Once again, the Moon’s tidal forces play an important role. Although by this time the Moon had moved away somewhat, it was still far closer than today. The shallow seas were violently pulled by its gravity, agitating the ingredients of our chemical soup more than sufficiently for the formation of RNA and, hence, presumably, DNA.

            In order to develop and reproduce, life needs fuel. For the first life on Earth the only readily available source was carbon dioxide. Unfortunately for this life, its own “waste” product was oxygen, which, in large enough quantities, would have proven toxic to that life. With no means of removing the oxygen from the atmosphere, life would eventually have suffocated under its own waste. Fortunately, the actions of the Moon once again came to the rescue. Its tidal forces continued to drag huge quantities of iron from the Earth’s interior (along with, incidentally, an abundant supply of other material, including the carbon dioxide that life needed to survive). Iron is a fairly reactive substance that combines readily with oxygen to form rust. The large quantities of iron (and some other elements) formed an oxygen “sink” that kept the planet habitable for early life for a long time.

            By the time the oxygen sinks had been used up, the Moon was even further away (although still close by modern standards) and its ability to drag more iron from the interior was much more limited. Oxygen levels began to rise about two and a half billion years ago. As this happened, life that was able to metabolise the free oxygen also developed. Interestingly, the carbon dioxide-breathing life forms were also able to flourish.

            The question that arises from this is whether the tidal effects of the Moon facilitated the flourishing of life, by allowing time for evolution to work, or did it retard the development of oxygen-consuming life?

            At present, we do not know with any certainty. The first carbon dioxide-consuming organisms were extremely simple and may not have been able to adapt to an oxygen-rich atmosphere. It is likely, therefore, that the release of oxygen needed to be delayed for some time to allow more complex forms to develop. Equally, the development of oxygen-consuming life seems to have been an evolution from the carbon dioxide-consuming forms, rather than a separate development. This, also, would have required time for the earlier life forms to develop sufficiently that they could adapt.

            On Earth, there was a period of about one and a half billion years without free oxygen in the atmosphere. Without the Moon it is likely that this would have been far shorter, perhaps just a few hundred million years. On the one hand, it is possible that so short a time would not have allowed the early life time to evolve to the point where adaptation to the oxygen was possible. On the other hand, life is tenacious and pervasive. Some argue that adaptation would have not only been possible, but virtually inevitable.

            So, the Moon was created by an act of great fortune. Its tidal action has helped to keep the Earth warm and may even have been the necessary “agitator” in the “chemical soup” from which life formed. It may have helped retard the production of oxygen long enough for life to be able to cope with that oxygen, or it may have held back the development of oxygen-consuming life for up to a billion years. But how has it helped to maintain the stability of planet Earth?

            The axis of the Earth is tilted by about twenty-three degrees relative to its plane of motion around the Sun. This means that, during the summer months in the northern hemisphere, the north pole is tilted by twenty-three degrees towards the Sun. During the winter months, the south pole is tilted towards the Sun. When the north pole is tilted towards the Sun, the northern hemisphere receives much more radiation and the reverse is true when the south pole is tilted that way. It is this tilt that gives us our seasons.

            Over long periods, the gravitational influence of the other planets can pull at the Earth, pushing it more or less “upright”, changing the tilt and, therefore, the seasons. Computer modelling of this effect shows that it can be very pronounced over long periods of time, reducing the tilt to zero or even pushing it to around ninety degrees, so that the Earth would, in effect, be on its side. It should be fairly obvious that such drastic changes in the tilt of the Earth would have dramatic and devastating effects on the seasons. It has been calculated that, if the Earth were to tip onto or nearly onto, its side, the severe changes in temperature experienced across the globe would be so great that most of the Earth would alternate between being colder than the arctic and hotter than Death Valley. Clearly, this would not be conducive to life. In fact, there is no known organism that could adapt fast enough to the extremes that we would experience.

            Given that life has survived and flourished on Earth, it is obvious that such extremes of tilt have not happened. This, once again, is due to the Moon. Because of its relatively great size and gravitational influence, the Moon acts as a stabilizer on the Earth, preventing the tilt from becoming too great. It does not keep it completely stable and the Earth’s tilt has varied by several degrees over time, but this modest change has never been sufficient to threaten the continued existance of life.

            Having a relatively, and unusually, large satellite has helped keep the Earth stable and it is fairly certain that life here would not have survived without it. However, this does not mean we can assume that such a large satellite is a prerequisite for stabilising other planets. As stated earlier, the reason that the Earth is subject to such a huge potential tilt is the gravitational pull of the other planets. Another planet may exist where the other planets in the system are too small, too distant or too few to have so drastic an effect. It is also possible that other planetary configurations would actualy help to stabilise a planet’s tilt. It is also true that the Earth was given its tilt by the collision with the Moon in the first place. Although the other planets would, nevertheless, have had a dramatic effect on the Earth, it is probable that such an effect would not have been quite so devastating.

            Planetary dynamics are extremely complex and there are many potential scenarios in which one planet may be sufficiently stable as to allow the continued existance and development of life. Nevertheless, in the majority of instances it is likely that, over time, most planets would not be sufficiently stable. If the presence of a large satellite was a prerequisite for the sustenance of life, then it should be clear from the above that life is an extremely rare event. We cannot, at this time, say with any certainty what the full extent of the Moon’s influence has been on life and we do not have any other models on which to base any assumptions. We can only say that the Moon has played a crucial role here, but, by extension, we can surmise that unusual circumstances may well be required for both the formation of life and its continued preservation, let alone for its development into intelligent forms. It is very likely that considerably fewer than one percent of all otherwise suitable planets are found in circumstances that are both unusual and conducive. However, for the purposes of our calculation, we assume the most optimistic of figures and say that one in ten of planets have unusual circumstances such as a large satellite. Taking the ages of the stars into consideration, we now have I = 0.75 x 0.1 = 0.075 (0.75%).

            At the start of this section it was stated that a planet must be relatively stable. For Earth, the Moon has helped to maintain a relatively stable orbital tilt. The question of whether a planet has a stable orbit (i.e. close to the plane of the stellar system and close to circular and maintaining this over sufficient time) is covered in the earlier section – “P – The proportion of stars with suitable planets” – as a planet with an unstable orbit would not be suitable. The remaining aspect of stability that must be addressed is the long-term climate of the planet. Once again, we will look first at the only available working model.

            Temperatures on Earth are generally within a sixty degree range, from less than minus twenty at the poles to over forty in the hottest deserts. For any one place on Earth, the temperature variation is usually about half of this value, with the winters being at most about thirty degrees colder than the summers, albeit that greater variation can occur occasionally. Over the course of modern history (the issue of human-induced climate change is being ignored here) the average global temperature has changed little, the extremes of human experience being at most about five degrees either side of current temperatures. Whilst climate scientists will, rightly, tell us that even a one degree change would have a dramatic impact on modern life, taken in the context of the geologic age of Earth a five degree change is negligible. It might impact greatly on modern living, but it would certainly not impact on life itself. Humanity, and the vast majority of other life on Earth, would easily cope with a change of this size.

            Planet Earth has not always been so benign. There have been periods in its history when the temperature has varied from the current average by considerably more than five degrees. There have been times when the Earth has been so warm that tropical forests have grown close to the poles and other times when it has been so cold that ice sheets have almost completely covered its surface. Despite these extremes, life has survived and thrived, albeit with occasional setbacks. There have been several “mass extinctions”, when climate change or other events have impacted so greatly on the environment that a significant proportion of life has been destroyed. However, such upheavals have usually been a two-edged sword, and it is for this reason that a planet must be relatively, rather than wholly, stable.

            Around two and a half billion years ago, the first oxygen-consuming life forms appeared on Earth. These evolved, as did their carbon dioxide-consuming cousins, into a number of forms, all of which were still relatively simple. Then, evolution appears to have stalled. Nothing more complex appeared until almost two billion years later, at a time known as the “Cambrian Explosion”, when the ancestors of almost all modern life appeared in just a few hundred million years. The event that caused this sudden “kick-start” of the evolutionary process has been nicknamed “Snowball Earth”.

            There are a number of cyclic events that have an effect on the Earth’s climate. The slight changes in the Earth’s tilt has already been mentioned. The direction of this tilt also changes over time. Anyone who has observed a child’s spinning top will have seen how the axis of the top slowly spins, in addition to the spinning of the top around that axis. The same is happening with the Earth, albeit on a much longer scale. The Earth’s axis rotates, relative to the “fixed” background of stars, once every twenty-three thousand years. Although this does not affect the total radiation that strikes the planet, it does affect where that radiation hits. If the direction of tilt causes areas with a lot of ice to receive more radiation, then a higher percentage of that radiation is reflected back into space. On the other hand, if more ocean receives the radiation, then far more is absorbed.

            The Earth’s orbit is not a perfect circle. It is, in fact, more properly called an ellipse and, over long periods of time, the gravitational pull of other planets can cause this ellipse to stretch and contract, meaning that the Earth travels further away or closer in to the Sun.

            The Sun, also, is a variable star: its output is not completely constant. There is an eleven year cycle of sunspot activity, during which the Sun becomes more active. It also undergoes long-term variations. Neither of these causes a huge change in the Sun’s output, but a small change in the Sun can have a significant effect on Earth.

            All of the above are cyclic events; that is, they occur in regular, predictable intervals. Occasionally, these events occur in combination, sometimes cancelling out each other’s effects and sometimes reinforcing them. If enough of these cycles occur together, their cumulative effect can have a very dramatic effect on Earth’s climate. Over the last few million years, for example, there has been a regular cycle of cooling and warming that has resulted in an ice age occuring approximately every hundred thousand years. The length and severity of these ice ages has varied because of the variations in the numerous cycles that can affect Earth’s climate.

            There are other, unpredictable, factors that can also affect the climate. If the solar system passes through a cloud of dust and gas, the amount of energy from the Sun may be severely reduced. Nearby supernovae can flood the region with radiation. If one of these were to occur at the wrong point in the normal cycle of climate change, it can greatly exacerbate the effects of that cycle.

            It is not known which, if any, such external event occurred almost a billion years ago, but something certainly did affect the Earth’s climate to a catastrophic extent. At that time the Earth entered an ice age, but it grew so cold that the ice did not stop in the usual place. Instead, it continued growing until virtually all of the Earth’s surface was covered. Although it may seem that a particularly severe series of coincidences might have been required for this to happen, in truth, this is not the case. Ice is one of nature’s most reflective substances. The more ice there is on the Earth, the more of the Sun’s energy gets reflected back into space, reducing the temperature of the Earth still further. It has been calculated that there is a “tipping point”, beyond which the normal warming cycle cannot recover the surface from the ice. Once this tipping point is passed, the continued growth of ice is inevitable until unusual circumstances allow the planet to warm again. Earth’s tipping point is only a little beyond the normal maximum extent of ice during the colder ice ages, so it would require only a small additional reduction in temperature for “Snowball Earth” to have happened.

            Snowball Earth continued for many millions of years. It is not known with certainty how it finally escaped from the grip of the ice, but the favoured theory is that volcanic activity was able to create gaps in the ice and spew gases and dust into the atmosphere, eventually creating a greenhouse effect (once again the Moon gave us a helping hand!) Life had clung on during this period in only a limited number of places. The ice may not have quite fully covered the Earth, allowing small pockets of open ocean or land by the equator. Other forms of life may have clung on near the volcanic vents, while some others may simply have been dormant.

            Conditions were clearly very harsh. What little life existed was forced to adapt and it would seem that this is what created the greater variety of life forms that became known as the “Cambrian Explosion” during the millions of years after Earth again thawed out.

            Complex life has only existed on Earth since that thaw. It has been subject to numerous catastrophic events in the half a billion years that it has existed. A principle of evolution is that, the more complex an organism, the more specific it is to its environment. The catastrophes that have struck Earth have often killed off huge numbers of creatures who have been unable to adapt. Equally, more complex life is faster, smarter and more aware of its surroundings. It has been able to move away from its limited environment and occupy other, more comfortable surroundings, where it often has had to adapt itself over and over again.

            It should be clear now that a planet must have a reasonable degree of stability to allow life to survive, but it must not be too stable, or life is not given the stimulus to adapt and evolve. The fossil records show at least two occasions when life on Earth was almost completely wiped out and about a dozen where a significant percentage of life and/or species were destroyed. Had any of the events that precipitated these “extinction events” been a little more severe then life may have been wiped out completely. On the other hand, had these events not occurred then other forms of life may not have had the “space” to expand into and evolve into the more intelligent forms we see today. The obvious instance of this is the last great extinction event, about sixty-five million years ago, when a huge asteroid impact wiped out the dinosaurs, allowing the small mammals to eventually grow and take their place.

            We cannot be certain that the dinosaurs, or the giant reptiles that preceded them, could not have eventually developed intelligence. However, given the millions of years in which they could have done so, there is no evidence that it did occur. Our best estimates of the capacity of these creatures suggests that their brains were exceptionally tiny, mostly because there was little need for anything larger. They had enough capacity to acquire food and to reproduce and no need for anything further. The only creatures at that time that had a “surplus” brain capacity were small. Possibly these creatures needed to be smarter to avoid being eaten; perhaps they needed more intelligence to find their food. However, they would never have evolved beyond this stage without the extinction event, because the reptiles and dinosaurs were so dominant.

            We can say with reasonable certainty that occasional “disasters” are good for stimulating evolution, so long as they are not so severe as to wipe out life altogether. In this, the position of a planet within the “Goldilocks zone” is crucial. If the Earth had been where Mars is now, then it would have completely iced over at every glaciation and would almost certainly have never recovered from the “snowball” phase. Equally, Earth could not have been too much closer to the Sun. At times in the past, the average temperature has risen to over forty degrees in the temperate zones, meaning peaks of over fifty degrees. It is known that RNA begins to break down at a little over seventy degrees. If the Earth had been much closer to the Sun, the temperature could easily have risen beyond this point, destroying life.

            There are a huge number of variables that affect a planet’s continued stability, making any estimate of the number that have the “right amount” of stability somewhat subjective. However, the evidence from Earth suggests that the “right amount” lies in a fairly narrow range. For the purpose of the present calculation, we shall assume an optimistic 20% of planets lie within that range.

            Taking all of the above into consideration we arrive at a value of I = 0.75 x 0.1 x 0.2 = 0.015 (1.5%).

T - the likelihood of such intelligence both surviving and still being extant

            Assuming all of the conditions are right, an intelligent species will develop. This will take at least two and a half billion years, and may take almost as long as the life-span of the parent star. There is no guarantee that such life forms will go on to develop technology. An obvious example is that of an aquatic species, that may be intelligent, but lacks suitable limbs. Lack of suitable limbs may not preclude technology, but would certainly retard its development. However, it appears that humans were using tools long before they had evolved sufficient intelligence to develop technologies. The implication is that any sufficiently intelligent species is likely to develop the use of tools and the use of technology is simply an extension of that. For this reason, we shall assume that the vast majority of intelligent species will develop technology.

            The question of survival arises from the fact that our own species remains so close to self-annhialation. With technology comes great power. Humans could all-too-easily wipe themselves off the planet. However, we have not done so as yet, which gives hope that other species could also show restraint.

            It is probably a safe assumption that at least 90% of species that have sufficient intelligence would go on to develop the right technologies and also not manage to destroy themselves. The only remaining question, therefore, is whether they have the right technology and whether they are using that technology right now.

            It is likely that the vast majority of species will take longer than the two-and-a-half billion years minimum determined earlier – in the section “I – The proportion of life forms that develop intelligence” – to evolve enough intelligence to use technology. A reasonable estimate would suggest that about half of the species that will eventually develop such intelligence are still on the evolutionary ladder.

            One prerequisite for the development of technology is the necessary resources. On Earth, huge quantities of iron, in particular, but also other heavy elements, were drawn out from the interior by the tidal pull of the Moon. It is certainly conceivable that many planets which have life, do not also have a sufficient quantity of minerals and metals to allow technology to develop. If iron were as rare as gold on Earth, the iron age would never have taken place and technological developments on Earth that we now take for granted would likely not have occurred for many thousands of years yet, if at all. We need only look at those parts of the world that are deficient in minerals and metals to see the effect that this has on development.

            Assuming a species has the intelligence and resources necessary, it is fairly certain that they would develop radio technology in a fairly short time, just as humans have done. On the other hand, they may also develop better technologies fairly quickly, as humans appear to be doing. However, any such species, if they are as interested in the prospect of contacting alien species as humans are, would also be well aware that radio is among the first technologies that such species would develop. It is quite possible that such species would continue to broadcast, or at least monitor, radio signals long after such technology has become redundant. However, such issues are a matter of speculation only, at this time. For the present calculation, we need only concern ourselves with those species that are capable of using radio right now, not whether they are actually broadcasting.

            Considering the requirement of resources, the likelihood of having risen far enough up the evolutionary ladder and the possibility that some species may not be able (or willing) to develop technology, a reasonable for T would be about 0.1 (10%).

The Result

            We can now put these figures into our equation:

            N = S x Sv x P x L x I x T

                = 2,000,000,000 x 0.01  x 0.01 x 0.05 x 0.015 x 0.1

                = 15 intelligent, technologically advanced civilisations in our galaxy

            The major caveat to this figure is that we have only really considered life as we know it. However, carbon-based life utilises chemical reactions that are far more vigorous than those of other forms, such as silicon-based life. This does not preclude such life forms appearing, but they would have a much more difficult evolutionary processes than those utilising carbon.

            On the other hand, the figures used above should all be considered somewhat “generous”, in that the highest possible (and still reasonable, given the available information) value has been used, not simply out of optimism, but also to try to make some allowance for those circumstances that cannot be foreseen from our limited perspective. Less optimistic (some may say “more realistic”) values give a considerably lower number. In fact, the least optimistic numbers suggest that life on Earth is probably unique in the universe, let alone in our galaxy.

            Today, most religious leaders, in the light of discoveries about the universe, concede that the view that humanity is unique is probably flawed. At the opposite extreme, scientists continue to use the life equation to suggest that intelligent, technologically advanced life is abundant in the galaxy. Whilst, clearly, the values used in the life equation must, generally, be considered subjective, it is also clearly in the interests of science to use the most optimistic values, as there are so many programmes whose funding would be threatened if governments were not being convinced of the likelihood of finding life.

            However, it is hoped that the above demonstrates that the figures used by science – which have changed little since the life equation was first devised – should now be considered wildly optimistic. Recent discoveries have shown that life on Earth has been extremely fortunate and this good fortune must, surely, be taken into consideration. Science need not deceive us any more. The most optimistic figures used above still give around fifteen technologically advanced civilisations in our galaxy. Whilst this would mean that they are thinly-spread, the search for them will, eventually, be fruitful.

            On the other hand, if life on Earth really has been so lucky, it is very possible that the church – albeit for the wrong reasons – was right in the first place and humanity really is unique in the universe.