This month we revisit the Drake Equation. Nearly everyone interested in SETI has heard of it, but views of its utility vary widely. To some, it is a useful way to estimate the number of technological civilizations in our galaxy and the chances of detecting an extraterrestrial message. Others view it as a wasted effort, given the huge range of conjectures involved in its components. There is a middle ground to use it to update and assess the reliability of relevant data that we have and the ways to improve upon the uncertainties. It can certainly be an effective tool for stimulating curiosity on this subject. Frank Drake presented the Equation in 1961 at what may have been the first formal SETI conference with the intent to stimulate discussion and evaluate proposed research, not to arrive at a true estimate of the number of intelligent ETs whose signals we could detect by multiplying its components. In its original form, the Drake Equation is:

N = R* x fp x ne x fl x fi x fc x L where:

• N is the number of intelligent civilizations in the Milky Way Galaxy, who, for this exercise, emit radio, light or other transmissions that are detectable from afar.
  
• R* is the rate of star formation per year for the galaxy.
  
• fp is the fraction of those stars with planets.
  
• ne is the average number of planets capable of supporting life (think of e for “earth-like” or “ecologically fit”).
  
• fl is the fraction of those that actually develop life.
  
• fi is the fraction of those where life becomes intelligent.
  
• fc is the fraction of emitting detectable signals into space.
  
• L is the lifetime of a communicating civilization.
  

Multiplying the terms would yield estimates that range from a galaxy teeming with ETIs (extraterrestrial intelligent beings) to us alone. Let’s visit each of these terms. N is usually considered the number of communicating civilizations in just our Milky Way galaxy. Keep in mind that there are hundreds of billions of other galaxies in the visible universe. The factor R* is estimated to be about 1 by some astronomers, based on the current rate of star formation in our entire galaxy. But the rate of star formation was once higher, and dividing the number of stars in the galaxy (200-400 billion) by its estimated age (roughly 10 billion years) would yield an R* closer to 10 per year, the number I will choose to plug in.

fp is one of the more constrained fractions because of recent advances in astronomy. Even a decade ago it was a conjecture, based on the theoretical likelihood that gas and dust left over from the birth of new stars would coalesce into planets. But data is now available. We have detected planets orbiting stars by the wobble in red shift caused by the pull of gravity on a star as a planet orbits it and tugs it towards and away from us during the course of its “year”. We can also directly observe stellar eclipses as the planet passes in front of its home star. This produces a periodic dimming of the of the star light, even though we don’t have telescopes powerful enough to actually see the dark round disc of the planet against the background star. Following ground-based observations, the recently completed Kepler Satellite mission has scored thousands of extra-solar planets. With this data, astronomers now claim that roughly half of stars to have planetary systems, each of which is likely to contain more than one planet. The current champion is the TRAPPIST-1 system, located a mere 39 light years from Earth, with 7 rocky planets in orbit. Keep in mind the limitations of current searches and the selection effects involved. Only two types have stars (relatively low mass M and G class stars) have been more thoroughly searched, so extrapolations to other star types are required. In addition, it’s the large planets and ones orbiting close to their sun that are easiest to spot, since they will cause more gravitational wobble on their star and be more likely to cast a detectable shadow as they cross in front of it. Therefore, many small, “Earth-like” planets have escaped detection. It’s probably safe to plug in the estimate of fp = 0.5.

Estimates of ecologically fit for life, fe, are often said to mean that the planet orbits in the “Goldilocks zone” where it has a surface temperature just right to have liquid water. This is a reasonable prerequisite for life, though alternate scenarios are possible. For example, spacecraft have recently found that Saturn’s moon Enceladus and Jupiter’s moon Europa have liquid oceans beneath icy crusts which might conceivably harbor life, though not likely to be the kind that would broadcast radio or laser signals into the cosmos. Requirements in addition to having the right distance from a star of given luminosity would reduce fe. This list of possible prerequisites for an Earth-like ecology includes: having the right kind of atmosphere to stabilize the surface temperature (avoiding a runaway greenhouse effect that has super-heated Venus), having an atmosphere that is “breathable” for its life-forms, having both open oceans and solid land, possessing a large moon to stabilize the planets rotation, and a few more. I allow these fitness extras to reduce my estimate of fe from nearly 1 to about 0.5.

Now we get to speculate about life. Many scientists claim that life formed “soon after” the Earth solidified, and its surface cooled from an original molten state resulting from its birth pangs of rocky collisions and supercharged volcanism roughly 4 billion years ago. “Soon” in this case means a few hundred million years. If so, the advent of life might be thought of as “easy” and fl is near 1. But there is more to this issue. If one seeks an evidence based-value of fl, the geological proof of the earliest life is uncertain. Rocks that are reliably dated by radioactive decay still don’t contain the kinds of recognizable fossils of that we come to expect from far later life forms. It has been argued that regular microscopic features in rocks more than 3.8 billion years old were formed by bacteria-like organisms in that era, but non-living mineral process could also account for them, and the debate is on. More generally accepted evidence of life does appear in the geological record about 3.5 billion years ago.

Another way to estimate fl considers the chemistry and biology of the origin of life. This process is far from solved. Landmark experiments have shown in the lab that organic molecules, including amino acids and nucleic acids (the eventual building blocks of proteins and RNA and DNA), can form from simple precursors like carbon dioxide, ammonia, water and other inorganic molecules. Such building blocks of life have now been observed in interstellar clouds, meteorites and comets. However, to create the first living cells required a confluence of molecules fighting entropy to extract energy from sunlight (or alternative sources of heat) to sustain their molecular engines and build molecular structures. Plus, at some point, these linked chemical reactions and “proto-cells” had to find a way to reproduce and encode the instructions for building future generations. This seems like a hard task. But given time, space, and many opportunities to try, we know it has happened at least once. Thus, some contend that life will form wherever it can and fl = 1, while others argue that it is very unlikely and represents a bottleneck in the Drake Equation. Choosing odds from an example of one is a hazardous exercise. Indeed, this conundrum supports the scientific value of searching for even primitive life forms beneath the surface of Mars or in the oceans that underlie the ice layers on the moons of Jupiter and Saturn. If we found that life arose on two or three different planets or moons in our solar system, I would revise my guesstimate of fl to 1. But for this exercise, I will choose a conservative value of fl = 0.1, rather lower than the current popular choice.

Personally, I like the odds of the next two components in the equation, fi and fc , that planetary life begets intelligent species, and that they eventually communicate into space. Once life has gotten going, Darwinian evolution seems likely to set in. It’s called natural selection because it really is. It’s survival of the fittest. The best functioning varieties that produce the most viable descendants win out in the game of life. Of course, that’s an over-simplification of modern evolutionary theory, but the kernel of truth is there. Evolutionists use the term “adaptive” to refer to a trait that offers a Darwinian advantage in surviving numbers of the like and in the ability to morph into new species. Evolution is unpredictable and choosing a value of fi approaches guesswork. (One sobering thought is that life on Earth remained microbe-only for nearly 3 billion years before multicellular animals arose.) I think however, that intelligence is powerfully adaptive. So, I am willing to be optimistic and guess 0.5 for fi. Perhaps this is an over-estimate, given the possibility of planet-scale catastrophes such as the asteroid collision that killed off the dinosaurs and many other species 65 million years ago, which was only one of several mass-extinction events that we know of in Earth’s history.

Next, what are the odds that intelligent species communicate with other planets? It’s not fc = 1. Dolphins are certainly intelligent, but they are unlikely to build powerful radio transmitters and point them skyward. I set fc = 0.5, hoping that half the planets that have evolved intelligent species sport at least one life-form that signals outward either intentionally or inadvertently.

So far, my personal tally for all of the Drake factors is 0.0625. We now come to L. By our definition of a technological (transmitting) civilization, we have been around for about 100 years. How sanguine are you about the future of homo sapiens? Or for that matter, do you foresee the evolution of a more stable intelligent life form on Earth? Part-cyborg/part human? Or just a triumphant computer with self-repairing capability? And are you more pessimistic and presume that a technological civilization becomes inherently unstable once it invents weapons of mass destruction and the means to ruin the ecology of its home planet? Do you favor L = 500 years, or 5,000, or 5 million, or 5 billion? Do you bump this up by allowing repeated episodes of development of technological civilizations on a planet following an Armageddon? The range of uncertainty of L swamps that of all the other factors in the Drake Equation. This is perhaps the greatest value of the exercise. I personally can’t come up with a more precise conjecture than between 500 and 5 million years.

So, all of the above considered, my current guess for N ranges from 31 to 310,000. In other words, our closest neighbors might be well across the Galaxy from us or amongst the nearest stars. That’s not very predictive and awfully dependent on one’s mood and the news of the day.

For further consideration, a number of extensions have been suggested to revise the original Drake Equation. Might not even a rare super-advanced civilization spread throughout the galaxy and show up in many places (perhaps humanoid, with slightly different masks on their faces, a la Star Trek)? On the other hand, what if ET does not want to bother to communicate to other planets? And if it does, would we be able to comprehend anything a vastly advanced intelligence would try to say to us? Yes, we heard from someone, but the message seems like pure gibberish, or resembles how your cat perceives your learned conversations. This could be a serious issue. The odds dictate that the ETIs we hear from will be extremely advanced compared to us. We have been capable of interstellar signaling for about 100 years, counting from the first radio and TV shows through the advent of radio telescopes and powerful laser bursts. Stars like the sun last for about 10 billion years (some far longer and some far shorter, which might have insufficient time to evolve technological life). So, the bell-shaped curve of probability indicates that it is far more likely that we receive a message from an ET who will be billions of years farther along in its trajectory of evolution than us. The odds of hearing from someone a more comfortable few hundred years ahead of us are minuscule, and those more primitive than us are unable to send radio signals. Will we understand these hyper-advanced beings? Will they bother to make themselves understood to primitive Earthlings? (I presume that the burden of having comprehensible conversation should fall on the more advanced creatures. In the otherwise wonderful science fiction movie Arrival, I was puzzled that it was left up to Amy Adams to figure out the language of the visiting cloud creatures, rather than the other way around.)

The Drake Equation was formulated to estimate the number of ETI civilizations out there. Just learning that we are not alone will be mind-blowing enough, but why not tack on the odds that we will understand a message from them? And what about the odds that while someone decodes a message, much of humanity will ignore it or not believe it? After all, there is still a Flat Earth Society. The science fiction writer Arthur C. Clark famously said that any sufficiently advanced technology will be indistinguishable from magic. Others have extended this axiom to state that any sufficiently advanced extraterrestrial will be indistinguishable from God.

Let’s close this current discussion with a reminder that the Drake Equation is not a vehicle for precise predictions and budget planning. Have useful and enjoyable discussions about it. Don’t try to get overly-predictive based on a “solution” of the Drake Equation. Admit that we can’t really figure the odds. It has been said that the Drake Equation was never meant to be solved. It’s value lies in the thought-provoking question marks. After all, no one is asking congress to devote a sizable percentage of the national budget to SETI, nor even a large percentage of the NASA budget. But it shouldn’t be 0%. The pay-off is much too great to devote zero effort to the search. And we certainly have not exhausted the search. If N = 100,000 it means that we should search more than 3 million stars at multiple wave lengths to have a solid chance of making contact. To paraphrase Carl Sagan, our chances clearly improve if we actively seek out a signal, rather than merely “waiting for the flying saucer to land in Harvard Square”.

If N = 100,000 it means that we should search more than 3 million stars at multiple wave lengths to have a solid chance of making contact.

Does anyone know how close Seti@Home is to having searched 3 million stars?

Tom

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A proud member of the OFA (Old Farts Association).

That's a great question. I'd love to know the answer to this too.

( I did some back of the envelope math that is very likely wrong but... to the best of my abilities after spending no more than 5 minutes on this and I came up with a number as low as 100,000 stars. But again, my abilities aren't great so that may as well be a guess. Edit: In fact you may treat this as my "guess how many jellybeans are in the jar" answer. I could easily be exponentially wrong as cubed light years are involved in the equation...)

Interesante articulo Richard, lo ultimo que haces referencia es indudablemente cierto ¿ que tanto creemos o no sobre los ET ?

Interesante articulo Richard, lo ultimo que haces referencia es indudablemente cierto ¿ que tanto creemos o no sobre los ET ?

Interesting article Richard, the last thing you are referring to is undoubtedly true, how much do we believe or not about ET?

I think a valid extension of the Drake equation would be a second time factor. An advanced, communicative civilization could evolve, develop and die out before the sun condensed. Adding one you could say it showed how many communicative intelligences exist today.

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Wave upon wave of demented avengers march cheerfully out of obscurity into the dream.

you got it !!

Dolphins are certainly intelligent, but they are unlikely to build powerful radio transmitters and point them skyward.

This is an essential point, in my opinion. We humans tend to assume that our life form be the self-evident summit of evolution. We shouldn't forget, however, that the dinosaurs existed for several hundred million years and if there hadn't been this big asteroid bouncing down, they might still continue to prevail our planet without ever emitting radio waves. Despite they were highly evolved creatures, they couldn't have been detected by our techniques. Life restarted almost at zero after this mass extinction event and brought new forms of life into existence and coincidentially, the fittest of them is emitting radio waves for about 100 years now. After the next mass extinction, which might be immediately impending, another well-developed life form my prevail, perhaps even a technical one, which however does not use to use electromagnetic waves for communication but is based completely on glass fibres. Yes, highly developed, but not detectable from lightyears away.

Nonetheless, I think we shouldn't miss the - unlikely - event that signals from a civilisation similar to ours might hit our antennae if this should occur anyway. That's why I support SETI@home.

The concept and the ideas of intelligent beings being found in the galaxy is next to zero. The reason why is that we had intelligent beings here on earth other than human beings, a couple of swim in the ocean, the Whales and the Dauphins. Some live on the land, the elephant and the great apes. The only one of those animals mentioned above that have been actually communicated with is the great ape through sign language, that we taught her.

Another factor that would affect the Drake formula, and that is the social life of the intelligent being. If he is warlike, and develops technologies as we did, only 40 years after learning how to fly, he may have destroyed himself in a nuclear war, or poisoned his planet with poison gases, during a war.

I base my assumptions on my studies of biology, on history of our own world, and on reading science fiction by great writers, Isaac Asimov, Arthur C Clarke, and Ben Bova.

I grew up on a farm and watch the behavior of animals both wild and tame, the honey bee has its own language, we have figured out what it's little dance stands for. The aunt also has a language, it drops chemicals and pheromones to tell the other ants in the colony, what is going on. They hardly even have a brain, yet they have a language.

So think about it, all animals have their own language, but we have only been able to communicate with one great ape, because we taught it our sign language. Maybe it was more intelligent than we are, we still don't know it's language.

M L A

It would not be possible to communicate with an ape in terms of speech as their vocal biology differs from ours. Sign language is communication.

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Wave upon wave of demented avengers march cheerfully out of obscurity into the dream.

Soy novato en todo seti@home, me encanta haber encontrado un sitio donde se hable sobre estos asuntos y donde mi computador sirva para descubrir una Inteligencia extraterrestre.
Especialmente, Mis más sincero agradecimiento a el autor de "The Drake Equation: Revisiting a Classic Tool to Estimate the Odds of Contact", puesto que repasa,con seguridad conceptos que te abren los ojos.

Se me ocurre que, , entrando de lleno en el terreno de S&F, que a mi modo de ver es magnifica, hablando sobre la trilogÍa de Cixin Liu,

EL recuerdo del pasado de la tierra

galardonada en el año 2015 con el premio HUGO, en ella se manifiestan algunos de estos conceptos y donde se especulan cuestiones fillosoficas sobre lo que ocurre al emitir ondas de radio al espacio.

lo recomiendo encarecidamente.

Ante todo quiero pedir disculpas por expresarme en español, más o menos leo el idioma inglés, lo hago así, porque mis expresiones son mas ricas, Podéis traducirme.

While I will always donate my spare computer time to SETI@home. Recently I began to wonder, considering the vastness of space. When we receive an "intelligent signal" and try to respond, will anyone at the source remember that a signal was sent? Or even be alive? Consider the Voyager spacecraft that left the solar system. IF it is ever found by another race, will anyone be here? if so will anyone remember what the voyagers were meant to do? Perhaps I'm off the subject somewhat but that is what my first thoughts were after reading the first part of the post.

Just to play God's advocate for a moment. Since in the major branches of monotheism God Gave us free will. What makes anyone think he or she would have put all of his or her faith in one race of beings? That's like pputting all of the eggs in one basket!

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Those who fail to remember the past are DOOMED to repeat it!

Dolphins are certainly intelligent, but they are unlikely to build powerful radio transmitters and point them skyward.

This is an essential point, in my opinion. We humans tend to assume that our life form be the self-evident summit of evolution. We shouldn't forget, however, that the dinosaurs existed for several hundred million years and if there hadn't been this big asteroid bouncing down, they might still continue to prevail our planet without ever emitting radio waves. Despite they were highly evolved creatures, they couldn't have been detected by our techniques. Life restarted almost at zero after this mass extinction event and brought new forms of life into existence and coincidentially, the fittest of them is emitting radio waves for about 100 years now. After the next mass extinction, which might be immediately impending, another well-developed life form my prevail, perhaps even a technical one, which however does not use to use electromagnetic waves for communication but is based completely on glass fibres. Yes, highly developed, but not detectable from lightyears away...

There are low odds for anything if you want them to be. But the Drake Equation, given very, very conservative numbers, is telling us that there are HUNDREDS OF MILLIONS of intelligent creatures in the universe. True, they may not all speak English and look just like us and have exactly 2 ears (maybe they are just dolphins or birds or fish), but I would argue that out of the HUNDREDS OF MILLIONS of civilizations, there have to be say 1% that we can detect if given enough time. 1% of 200million is 2 million civilizations we should be able to detect. But the universe is immensely vast. Even if we should only be able to detect 1000 civilizations, we have to look in just the right place and at the right time. If there is another civilization 50 light years away and pumping signals into space and we detect them, it's going to take us (at best) 50 years to send a message back to them and pray they hear the signal and reply. Just like your local radio station, once the radio wave passes you, that's it. You can't go back 10 minutes and listen to the song again. If that civilization 50 or 1000 light years away spits out a signal and it passes Earth, it's gone and we never would have known.

The Drake Equation does not give us a number we CAN DETECT...it gives us a number of intelligent civilizations that should be out there.

I often think about the fact that us humans have only been around for 100,000 years and have only been pumping radio waves into the universe for 100+ years, had electricity for 100+ years, and developed equipment to detect (hopefully) other civilizations for 50+ years. For the sake of speed and typing, I am going to refer to any intelligent civilization in the universe that is similar to us at the year 2019 as Others...What if there were Others on Mars (or name your planet in our galaxy) 50,000 years ago but got wiped out by an asteroid? What if there are Others somewhere out there that we could detect with our equipment, but, right now, they are living in the year 1800 or 1902?...we would miss them. What if the Others are currently in the year 2389 and no longer use radio waves or similar technology we can detect? And of course, what if they are purposely being silent and/or blocking our detection techniques?

There are countless examples of why we are and/or may be missing the Others. Not to mention we've been searching for less than 50 years, our equipment becomes better and more sensitive every 10 years, and we have searched a minuscule portion of the universe.

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If we ever do contact ET and exchange info or they visit us face to face, that rather puts an end to religion as we know it. Why? Because they aren't supposed to exist. What then? Collapse of civilization and governments, rioting on the streets, half the world killing the other half.?

Why? Part of religion is "faith in the unseen/unknowable". Faith doesn't change for many people, even if facts do.

I agree there might be consequences to discovering scientific proof of ETI. I am hopeful that the refusal to believe scientists/media will be enough to protect the majority of humans from immediate panic. After a while, we can have a "low boil" panic :(

Tom

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A proud member of the OFA (Old Farts Association).

"You are entitled to your own opinion but not to your own facts." Patrick Moynihan …………………… Facts can never be claimed by one. One's own facts should be universal, if they are just that - "facts"!

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our solar system is approx. 4 billion years old how they date this is still a mystery to me as they cannot date rocks on earth yet they can on the moon which has seen solar flares for millions of years also how the moon was formed does not make sence to me because it was created a hell of a lot closer to slow the earth down from a 6 hour day to a 24 hour day yet the mass of the moon didn't fall back to earth via gravity also the back of the moon is thicker than the side we see you would think that the thicker side due to mass would be drawn to face the earth.. I think that the universe is even older because all we can see is what the hubble deep field shows us yet it cannot show us the infra red spectrum..so all this means is that the universe is even older than people think and they are to stupid and proud to admit that they are wrong if einstien can admit it why can't modern day scientists do the same

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The Drake equation has been around since 1960, and since then many of the unknowns are now better understood, but that does not make the final answer any more real than one from back in the early days. Whilst we know more, we are finding we also know less in many ways, especially on the topic of the emergence and life and where life may actually arise.

For example, the Drake equation does not take into account Exo-moons, the fact that a planet the size of Earth could easily be a satellite of a Gas giant world, and for all we know, planet sized moons could be as common as major planets, look at our own solar system, Io, Europa, Callisto, Ganymede, Titan and Triton would all be classed as planets if they simply orbited the Sun, and there is an outside chance that life could exist in sub-surface oceans on several of these bodies.

Then we get to another issue, which recently I have been trying to factor into the Drake equation, the age of the galaxy, the rate of star deaths and the size of the galaxy. Playing with some figures based on the Kepler results and trying various parameters, we could have 1 (Humanity) or 10,600 technically advanced societies alive at this moment in time, but when you then take into account the size of the Galaxy, it's volume, you end up with one such society in a space of around 340 light years across, That is a staggering piece of real estate and encompasses some 320,000 stellar systems - and that is the best case scenario. Now it is possible that several of these societies could reside in a space area of space and not be evenly spread out, but even so, we are looking at distances of perhaps hundreds of light years between societies.

I find this rather disappointing, I personally believe that the galaxy, and thus the universe, is teaming with life, and that where environmental conditions allow for complex chemical reactions to occur over hundreds of millions of years, nature will find a way and life will evolve - I suspect that only a very small percentage of life bearing worlds will through up technically advanced societies capable of investigating the Universe and thus potential communication, but even so, I know in my heart they are out there, and that the Drake equation, whilst not pointless, is unhelpful until we are able to pin down more of it's parameters with better data and we have more examples of life, in any form, to better understand it's evolution.

I personally advocate better investigations into Venus, Mars and the major moons of the solar system - we may find nothing, but we may just find the holly grail too..

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Richard M Lawn wrote:

In the otherwise wonderful science fiction movie Arrival, I was puzzled that it was left up to Amy Adams to figure out the language of the visiting cloud creatures, rather than the other way around.

Well that was the whole point of the film, wasn't it? Both sides learned the others' written language because they weren't physically capable of reproducing each others' sounds. The heptapods' language turned out to be their gift to us in exchange for a favour they'd need a few thousand years in the future. Learning it changed Amy Adams's character's perception of time and enabled her to save the immediate situation. It's a sci-fi conceit based on language theory, not a technical error in a documentary about how aliens would communicate from the other side of the galaxy.

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NG

But the Drake Equation, given very, very conservative numbers, is telling us that there are HUNDREDS OF MILLIONS of intelligent creatures in the universe.

This seemingly large number is less than one intelligent species per thousand galaxies, there being over a hundred billion of those. My pessimistic numbers resulted in one or two civilizations per galaxy. I think that intelligent life is exceedingly rare; plenty of bacteria out there, and very few civilizations. But given that they are likely to be far older than ours, I still think it's worthwhile to look for them. A very small chance is always larger than zero. :^)

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