# Drake equation

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The Drake equation is a famous formulation for calculating (or more accurately, guessing) the number of intelligent extraterrestrial civilizations with which we can communicate in our own Milky Way galaxy at a specific moment in time.

## History

Frank Drake formulated the equation at the famous 1961 Green Bank SETI meeting, reportedly just before giving his talk and as little more than something to write up on the board; Carl Sagan later popularised and refined it, adding variables for other vital components of a healthy life and technology supporting system.

## The equation itself

The Drake equation is as follows:

$N=R^{\ast} \times f_p \times n_e \times f_l \times f_i \times f_c \times L$
• N: The number of civilizations with which we might be able to communicate.
• R*: The average rate of star formation in our galaxy.
• fp: The fraction of stars which, after formation, have 1 or more planets.
• ne: The average number of planets that can potentially develop life, per star which has 1 or more planets.
• f: The fraction of planets that actually do develop life.
• fi: The fraction of life-developing planets that actually do develop intelligent life.
• fc: The fraction of civilizations that develop a technology that releases detectable signs of their existence into space.
• L: The length of time such civilizations release detectable signals into space.

While the Drake Equation may look long and scary, it can be seen that it merely starts with the number of stars and then defines the fraction that will take a step in the right direction for life, starting with the number that even have planets for life to form on (we ignore the possibility that contactable life can form or exist on stars) and ending with the probability that they'll develop technology and stick around. Although the Drake equation does not include all possible variables, it is generally accepted as a helpful, though not authoritative, tool for the field of exobiology. Some variables, such as the rate of star formation, are known or can be calculated; others such as the number of planets and the number that can support life are currently unknown, but obtainable. The remaining values are the most controversial and really, anyone's guess is as good as anyone else's with regards to these. Life could be very easy to start, but difficult to get to the "advanced" stage, or it may be inevitable that intelligent species will emerge once life has started — the answer to this is completely unknown. Guessing at these values allows the number of civilisations to be guesstimated, so the numbers do vary wildly depending on how likely an individual thinks each component is. Given the number of stars in the galaxy (and in the entire universe) even very conservative figures for the unknown values give a large number of civilisations that could be contacted.

## Limits of the equation

The equation has one big assumption.

Where the Drake Equation is limited, it is due to it making several assumptions about life and the universe in general.

### Life as we know it

The equation is restricted to life "as we know it", as the factors involved imply that planets for life to evolve on must be Earth-like. This ignores the possibility of far more exotic forms of life, such as life evolving in the atmosphere of gas giants or by thermal vents in otherwise frozen moons, as we have a term for detecting Earth-like planets in habitable zones. This can be made more general by asking "what is the fraction of planets with environments that can form life", but this is more difficult to refine given our present ability to detect exoplanets. The next assumption is that life must evolve on a planet, ignoring the conjecture that life could form out of the super-fast quark reactions inside a neutron star, or sentient gas clouds having emergent thoughts over periods of millions of years.

Therefore, these assumptions are mostly valid for practical purposes, particularly when it comes to actually detecting this life. The exotic forms of life are of interest to science fiction authors, but from a practical point of view there are limitations regarding observation of these civilisations and what relevance they would have to us. Underwater or gaseous life would probably not be able to develop communications technology, and the aforementioned exotic life inside neutron stars would — hypothetically — evolve and die out in a blink of an eye, making detection completely impossible.

### Applying the equation

The Drake Equation is essentially a model for the number of civilisations we can detect, taking in variables that would affect this number and representing it as an equation. The application of the equation is relatively straightforward. Starting with the number of stars (which is around 100-400 billion[1], assume the low end for this illustration), each subsequent term is a fraction that whittles this number down to the final value of N. For example, if one thinks that 50% of stars will have planets, then this leads to 50 billion. If you think that only 10% of these will be capable of supporting life, the number drops to 5 billion. If only a small fraction, 1%, actually do develop life you get 50 million planets with life. The remaining factors are regarding how this life develops and evolves. So if only 10% of life bearing planets develop intelligent life and only 10% of those develop communications technology, then we see 500,000 civilisations. The final factor in a civilisation's longevity is difficult to think about, but it essentially "how many of these civilisations will survive long enough for us to see them now?" 10%? 1%? Even these small figures lead to several hundred, if not several thousand observable civilisations in just our galaxy. Given that there are more galaxies in the universe than there are stars in the galaxy, applying the Drake equation to the whole universe makes life appear very common indeed, even more, the most conservative estimates for each individual term.

### Value of the terms

Each term in the equation is open for lively debate due to the numerous unknowns and the speed at which research is generating data to give more informed values for these terms. As technology and knowledge of the universe increases, the guesses may become more informed and the values applied may be more representative of reality. The first two terms, for example, — the rate of star formation and the number of planets — are two that are becoming clearer with additional research; the discovery of numerous exoplanets in recent years indicates that this could be a very favorable number. Currently, however, the variables are all of a nature that cannot be accurately determined. The number of planets capable of hosting life (at least "as we know it") is unknown, as technology is biased to discovering exoplanets that aren't suitable for life — namely large planets, like gas giants, that orbit very close to their stars. The other terms, involving the formation of life and the development of intelligent life are still questions that are wide open. On the one hand, we haven't observed any signals from intelligent life, indicating that it is rare — but on the other hand (although this is a rather cheeky reasoning) the one planet that we're aware of that has produced life has also produced intelligent life, a success rate of 100% for fi and fc.

Despite the wild unknowns, even the most conservative estimate produces a high likelihood of another technological society inside our galaxy, given the number of stars. Low estimates put the number of detectable civilisations in our own galaxy as many thousands, but these would be spread so thinly that active communication and interaction would be difficult, if not impossible.[2]

With the terms regarding the development of life being almost entirely conjectural, possibly the most interesting factor is "L", the time a civilization might spend indicating its presence. This can be inferred by looking not at the stars, but ourselves; the longer that mankind succeeds in not annihilating itself and continuing to broadcast detectable signals, the longer we can guess other civilizations will do the same. Current developments in communications technology have led to this component of the Drake equation being the most hotly contested.

### Reliance on waste communication

Highly advanced civilisations are likely to just "disappear" as the observable waste they generate is reduced to zero. This is taken into account in the final part of the Drake equation which is the "longevity" of a civilisation. Originally this factor was thought to represent the amount of time it took for a civilisation to destroy itself — rendering itself unobservable due to extinction — but recent developments in Earth's communication technology has led to the disappearance of broadcast signals.

Another factor is the Inverse-square law where the intensity is inversely proportional to the square of the distance from the source. The SETI Institute’s Seth Shostak has previously pointed out that we couldn’t even detect our radio signals with our current equipment at the nearest star, Proxima Centauri, 4.2 light-years away.[4] Worse, "Because of this inverse square law, all of our terrestrial radio signals become indistinguishable from background noise at around a few light-years from earth. For a civilization only a couple hundred light-years away, trying to listen to our broadcasts would be like trying to detect the small ripple from a pebble dropped in the pacific ocean off the coast of California – from Japan."[5]

However, more specialized (and powerful) systems such as airport radar and cold war military radars would be detectable 50 to hundreds of light years away. But that is simply the ability to detect such signals, any sign of intelligence in those signals degrades faster; the 70-meter Evpatoria radio antenna in the Crimea could send a signal that would be detectable 648 light-years...but would loose any coherent message within 20 light years.[6]

If we accept the Drake equation (or a modified version) as true, then the Fermi paradox results. The paradox is the apparent contradiction between high estimates of the probability of the existence of extraterrestrial civilizations and the lack of evidence for, or contact with, such civilizations. The paradox takes its name from physicist Enrico Fermi, who put it forward in informal discussions during the 1950s.

A succinct paraphrase might be where is everybody? As far as we can tell from our limited data set (we only have one documented case of the emergence of intelligence and civilization), intelligent life in the universe should be relatively common. The Fermi paradox is an open question, an invitation to ponder what particular assumption we are making that has led there to be no apparent evidence for extraterrestrial intelligence.

Given even conservative estimates for the components of the Drake equation, it is still possible to arrive at very large figures for the number of intelligent civilisations in the galaxy, hence the reasons that many scientists consider exobiology a reasonably respectable subject to ponder rather than outright quackery. However, there is still no empirical evidence for extraterrestrial life or intelligence. Essentially, either one or more components of the Drake equation has a value far lower than even our most conservative estimates, or there is one factor missing. In more recent years, the focus has been on the final component of the Drake equation: that of the longevity of civilisations and their ability to be observed.

There are several possible resolutions to the Fermi paradox based on looking at components of the Drake equation and figuring out the plausibility of each, indicating what is and what is not particularly likely:

### It is rare for life to evolve

It's hard to evaluate the plausibility of this until we know more about the origin of life. But, speaking from the Copernican principle, there isn't anything about the physical or chemical composition of the Earth or the solar system that suggests extreme rarity. Even if only one in a billion star systems have earthlike planets in them, that's still hundreds of billions of potential sources for life that we could recognise as such.

It is possible there's something about the Earth that has made it easier for life to arise. The formation of the Moon seems to have left a somewhat higher concentration of heavier elements, which might have helped. Or the presence of such a large moon may have helped stabilize the planet's rotation and/or reduced the incidence of asteroid impacts, either of which would improve the planet's habitability.

### It is rare for intelligence to evolve

Again, going by what we know about Earth, and assuming in general that the Earth isn't in any sort of cosmically privileged position, this proposed rarity is hard to account for, but impossible to decide either way until we have more evidence. In general, the more closely we examine them, the more we find intriguing evidence of cleverness in many animals. Given the millions of potential years for an evolutionary timescale, it's not unreasonable to posit that wherever life evolves, something intelligent must pop up sooner or later.

### It's rare for intelligent beings to reach a sufficient level of technology to communicate their presence

In the case of Earth, our radio transmissions have made us visible to anyone who may have been interested in the past several decades — but the switch to wired internet, directional satellites and short-range microwave transceivers for mobile phones is quickly diminishing this. Another possibility is that alien civilizations develop means for communication that are as efficient as ours or more but far less detectable. However — as with the SETI program — species could always deliberately advertise themselves. Even if most species don't, statistically speaking we should be able to come across signals from those that do.

### Intelligent beings are vulnerable to (self)-destruction

Intelligence typically evolves prior to the psychological traits that are necessary to use that intelligence sanely. Humans have conceived of nuclear, radiological, chemical, and biological weapons of mass destruction, yet have not progressed very much psychologically since the age of killing each other with rocks and spears. Maybe the period during which an intelligence can survive without being destroyed, either by itself or some kind of natural catastrophe, is too small to allow contact.

### The evidence is already there, but we can't detect it

The possibilities range from a government conspiracy to withhold contact to messages/media that are quite literally too "alien" for us to perceive. (e.g. Our own era of pumping out vast quantities of easily-decoded AM audio and video may only run about a hundred years, as broadcasting shifts to digital encoding with the frequency spectrum of white noise if you don't know what's encoded in it.). Other include they did not broadcast in the frequencies where we're looking for them, not broadcasted at all, but instead sent highly focused (and far less expensive in energetic terms but much harder to detect) transmissions wherever they wanted, and more especulatively that their methods were indetectable by us (lasers and even other methods such as neutrinos or things as wormholes (assuming those things existed at all, that is))

### We're just not interesting enough to contact

We probably shouldn't write this one off — the more we explore the cosmos, the more human pretensions to uniqueness and importance we tend to have punctured. But — if extraterrestrial intelligence is everywhere, the more likely it is that one aspect of it will contact us — even if it's a rogue or a renegade. Alternatively, if intelligence is an extreme rarity, it makes all the more sense to try and contact someone else. Of course, there is the possibility that we are being shepherded carefully by some advanced undetectable intelligence, but if that's the case it isn't clear how we should be modifying our behavior or that we should stop looking for anyone else.

### Maybe we're just early to the party

It took about half of the estimated habitable time frame of Earth for humans to evolve. On a universal scale, we're estimated to be relatively early in the possible time frame of the universe (The Earth being 4.54 billion years old in a universe that is "only" 13.75 ± 0.11 billion years old.). It's entirely possible that we're one of the first intelligences to evolve, and, thus, everyone else that exists are simply in currently non-intersecting light cones. An explanation for this might be that the younger universe was smaller and more crowded, and that gamma-ray bursts frequently sterilized otherwise habitable planets.[7][8]

### Humans evolved from a uniquely social species

Other intelligent species might not have the same motivation to communicate as humans do, or have a natural system of communication that obviates the need for radio technology. Or frequently leapfrogged past broadcast technology for other reasons.

### Great Filter

The Great Filter describes the possible unlikelihood of advanced civilized life (beyond our questionable own) being prevalent in our galaxy and in the universe at large. It is a prime contender as a resolution to Fermi's Paradox which asks why we get no radio signals from interstellar civilizations even though many seem likely to exist according to some estimates. Most of the optimistic hopes for a thriving universe rely on the Drake Equation which yields very positive estimates. The Great Filter might be seen as the pessimistic antithesis of the Drake Equation.

Formulated by Robin Hanson, the initial premise of the Great Filter can be inadequately summarized by the following bullet points:

• Life will naturally advance, via significant "steps", to the point where interstellar travel and galactic colonization is inevitable.
• In the context of our civilization, any one step might be in the past, such as the Precambrian explosion or development of big brains and hands.
• There may also be future hurdles — "steps" we are yet to encounter — to technological advances that need to be overcome without effecting a civilization's own annihilation (I'm looking at you Earth — Sincerely, The Universe).
• For any sufficiently advanced civilization, and fuel efficiency be damned, such civilizations will have developed the grunt to propel themselves at near light speed.
• Such a civilization will, therefore, colonize a galaxy at near light speed and, if not by themselves at first, by use of drones to prepare the way.

The conclusions are outlined in the following lazy bullet points:

• Our radio antennas don't even hear a peep from alien Carl Sagans let alone there ever having been a (fortuitous) blitzkrieg on Capitol Hill by a mammoth trash can lid. This suggests that galactic colonization has never happened (though the anthropomorphic assumption that a totally alien life form's communications technology would proceed along lines basically equivalent to our own is a leap unto itself.)
• Extraterrestrial civilizations may possibly have made it as far as we have in terms of technology but never made it any further which is bad news for us. Their technology develops to our point but they inevitably screw themselves back to the stone age or worse.
• Extraterrestrial civilizations may never have even arisen due to failure in achieving one of the various "steps" required from simple unicellular life to galactic colonists and we are the lucky ones… so far (see previous point). This is closely related to the "rare Earth" hypothesis.
• Even if the evil alien drones missed our bountiful solar system, there should be plenty of spectroscopic evidence of stellar scale industrial activity that is necessary for interstellar colonization. (This would currently be somewhat difficult to pick up, present or not, due to the ways in which exoplanets are detected, but coming technology like the ATLAST telescope should make it possible to observe those planets more directly.)

Naturally, like the Drake Equation, the entire concept relies on nested assumptions.