The Fermi Paradox and the Drake Equation – Fraction of Planets Where Life Arises

This has been the toughest post in the series to write, because the question of how life arose is the most open. A look at the linked article will show a lot of different conjectures. Which one(s) explain how life actually arose on Earth and/or would arise on other planets are still unknown.


Let’s make some guesses about the upper and lower limits on f_l.

The upper limit is, of course, 1. In other words, it might be the case that life arises on every planet where the ingredients are present for a sufficient length of time (estimating from the early Earth, life needs 500-750 million years). This fits with the mediocrity principle, that there’s nothing special about Earth, and so since life arose here, it would arise anywhere.

Even so, let’s bear in mind Clarke’s comment that “the universe is stranger than we can suppose,” and step back from the max. For our purposes, we’ll say the upper limit on f_l is 0.95.

The lower limit depends on which conjecture for the origin of life you subscribe to.

Does the origin of life require sunlight and tidal pools? Then a large moon (for a terrestrial planet) or a large primary (like Jupiter for Europa) would be very important, if not mandatory. (The sun drives only about half of Earth’s tides). For a terrestrial planet to have a large moon probably requires an impact with a [planetary-embryo-sized] body at a particular speed and angle to form that large moon. Though impacts are common in young stellar systems, large moons are not. (See Venus).

Does the origin of life require a step of nucleic acid solutions absorbing UV radiation? Then stars that generate little UV (e.g., the highly numerous stellar class M) are less likely to meet that requirement.

Does the origin of life require deep sea hydrothermal vents? Those vents would be driven by hot planetary cores, which generally would result from the heat of planetary formation and/or radioactive materials. The upshot: small planets (cooling too quickly) or planets around metal-poor stars (not radioactive enough) are unlikely to support life. However, note the moons of gas giants have a third route to core heating—tidal forces from the gas giant and other moons. (That’s the source of Io’s volcanoes and whatever liquid ocean might exist under Europa’s ice.)

(Aside: The further we go in this series, the more I conclude the moons of gas giants would be the most common homeworlds for life).

What, then, is the lower limit for f_l? Who knows. Out of intellectual laziness, we’ll say the lower limit is 0.05 and be done.

Plugging into the Drake equation, we get:

N_upper = 16.03 * f_i * f_c * L

N_lower = 0.84 * f_i * f_c * L

We’re close enough to end of the series to see that, even at the lower limit, if the values of f_i, f_c, and L are relatively high (the first two > 0.90, the last > 100 years), then scores of intelligent civilizations are sending out signals of their existence at all times. If we go closer to the upper limit, and bump up L to 1000 years, then the number of intelligent civilizations is north of 10,000.

Is the explanation for the Fermi Paradox simply that we’re oblivious to their signals? Or is one or more of f_i, f_c, and L very close to 0? My answer is coming up.

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The Fermi Paradox and the Drake Equation – Planets Potentially Supporting Life

As we discussed in the series so far (1 2 3), the Drake Equation gives an estimate of the number of civilizations in our galaxy with which communication might be possible, N. After entering the first two values, we have:

N = 5.625 * n_e * f_l * f_i * f_c * L

Today, we’ll talk about the third term, n_e = the average number of planets potentially supporting life per star that has planets.

(Credit: NASA / Jenny Mottar)

What does a planet need to potentially support life? Three things:

Elements capable of forming a wide variety of chemical bonds
A solvent for those elements
An energy source to drive otherwise unfavorable bonds formations

On Earth, those requirements are primarily met by:

Carbon, hydrogen, oxygen, nitrogen, sulfur, and traces of other elements

Let’s be carbon- and water-chauvinists and assume we need the same elements and solvents to potentially support life off-Earth. After all, while silicon can form the same number of bonds as carbon, silicon is about 900-fold more prevalent in Earth’s crust, yet life is built with carbon. As for water, it has a huge advantage over other plausible solvents for biochemistry: its solid form is less dense than its liquid.

Regarding an energy source, though, sunlight isn’t the only game in town. Geothermal energy can support life, and all planets have molten cores early in their existence.

The question then becomes, on average, how many planets per star have carbon, water, and sunlight or geothermal energy? Answer: probably several. In the early years of our solar system, Venus, Earth, Mars, and probably Europa had all three requirements for life. It’s also possible Mercury, Io, and Ganymede did as well. Is our solar system typical? Tough to say, until we know a lot more about extrasolar planets.

Based on all that, we’ll write on the back of our envelope a value for n_e of 3. With n_e = 3, our current value for the Drake equation is:

N = 16.875 * f_l * f_i * f_c * L

So far, we’ve given values to the terms that are favorable to a hypothesis of a galaxy full of high-technology alien civilizations. We’ll see if the fractions of planets that develop life (f_l), particularly intelligent life (f_i), and particularly high-technology civilizations (f_c), will further support that hypothesis in future posts.

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Gene Wolfe, science fiction grand master


As reported elsewhere, Gene Wolfe, author of the Fifth Head of Cerebus, the four-volume Book of the New Sun, and numerous other works of complex, erudite science fiction and fantasy, was named this year’s recipient of the Damon Knight Memorial Grand Master Award by SFWA. This is seriously cool news for a number of reasons:

1. A knowledgeable and sophisticated observer of science fiction predicted this about a year ago.

2. I live within a mile of his childhood home. Honest, he grew up in Houston. It’s possible he walked or biked by my house en route to the drugstore where he read pulp sf mags on the racks.

3. To other sf writers, he represents an aspirational archetype. The nearest metaphor is what an old *nix beard, full of command-line- and regex-fu, represents to a computer geek. Wolfe’s vocabulary is immense, and even better, not flashy. He doesn’t call Severian’s cloak “fuligin” because it has three syllables to the one of “black,” but because it’s darker than black and has connotations of sootiness, which metaphorically fits Severian’s starting position as an apprentice torturer. Wolfe is very adept at not explaining his sf props, and instead, providing enough context for the reader to figure them out. (E.g., the arquebusers and destriers.) And Wolfe is the master of using unreliable narration: the first and third novellas in Fifth Head of Cerebus, Severian throughout the New Sun books, head-injured Latro in the Soldier of the Mist series. Again, he doesn’t wield these as tricks, but to enrich the story–consider Severian’s eidetic memory, his response to the note regarding “Master Gurloes and the other masters” early in Claw of the Conciliator, and what that says about Severian that he never puts into his own words.

In sum, a well deserved recognition of the man Neil Gaiman called “our greatest living writer.”

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The Fermi Paradox and the Drake Equation – Stars with Planets

As we discussed in the series so far (1 2), the Drake Equation gives an estimate of the number of civilizations in our galaxy with which communication might be possible, N, as:


N = 6.25 * f_p * n_e * f_l * f_i * f_c * L

Today, we’ll talk about the second term, f_p = the fraction of stars that have planets.

From,, and, we know that essentially all young stars have an accretion disk of gas. When the disk cools, the gas forms dust grains of rock and ices (small, volatile compounds: carbon dioxide, water, methane, nitrogen, etc.). The dust grains may agglomerate into planetesimals. Some of the planetesimals may then form planetary embryos, in a chaotic system that will tend to form terrestrial planets, similar in size and composition to Venus or Earth.

Gas giants complicate the above process. Although they can only form in the outer parts of a protoplanetary disk, they can migrate toward their parent star, which would disrupt the orbits of smaller bodies and could prevent formation of terrestrial planets. Gas giants can also eject smaller bodies from the stellar system by gravitational interaction.

Yet either way, a stellar system would probably form with terrestrial planets, gas giants, or both. Therefore, we’ll assume 90% of star systems will make it to that point, or f_p = 0.9

But how many planets could potentially support life? We’ll get to that next time.

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The Fermi Paradox and the Drake Equation – Star Formation

As we discussed in the last post, the Drake Equation gives an estimate of the number of civilizations in our galaxy with which communication might be possible, N, as:

N = R * f_p * n_e * f_l * f_i * f_c * L

Today, we’ll talk about the first term, R = the average rate of star formation per year in our galaxy.

Caveat: I’m an amateur (hopefully in the best sense of the word), with a day job, a family, and a writing career. These estimates are chock-full of back-of-the-envelope-calculations (BOTEC) and rules of thumb. I’ll show my work, and professional astronomers are welcome to comment.

Average rate of star formation

More accurately, we’re interested in the rate of star formation a few billion years ago, on the assumption other intelligent life would only evolve billions of years after its home stellar system formed, just like us. I’ll assume the rate of star formation has been constant over that time frame. I’ll also assume the number of stars in our galaxy is in equilibrium–the number that form each year is equal to the number that die each year. (“leave the main sequence,” to be more technical).

One more assumption: I will ignore class L, T, and Y red and brown dwarf stars, on the assumption they have such low luminosity, any planets they might have would receive insufficient sunlight for life to arise.

From our equilibrium assumption, if we estimate the number of stars dying each year, we have an estimate for how many formed per year in the time frame of interest. Next question: approximately how many stars die each year?

Answer: approximately the number of stars of each spectral classification in the galaxy divided by the main sequence lifespan for that spectral type.  (Number of stars from here * 100 billion stars in our galaxy, main sequence lifespan for a typical star of that classification estimated from here):

spectral type Number in galaxy max lifespan (yrs) number at max lifespan
O 30000 5000000 0.006
B 130000000 50000000 2.6
A 600000000 1000000000 0.6
F 3000000000 2000000000 1.5
G 7600000000 10000000000 0.76
K 12100000000 30000000000 0.4033333333
M 76450000000 200000000000 0.3822

Summing up and rounding a bit, we get R = 6.25.

One down, six to go. Till next time.

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John Cooper Fitch, 1917-2012

John Cooper Fitch died yesterday. I had never heard of Mr. Fitch either–he was a race driver most active in the 1950s–but you probably see his work every time you travel the freeway:

Fitch barrier

He invented the system of sand-filled plastic barrels you see at bridge pillars and the end of jersey barriers facing oncoming traffic at off-ramps. I drive by two of these every day on my way to work and had never really noticed them before today. In the 40+ years since their introduction on North American freeways, they’ve saved roughly 17,000 lives.

Mr. Fitch was inspired to work on traffic safety measures at the Le Mans endurance race in 1955, after a horrific accident killed his teammate and about 80 spectators. But the absolute best part of the story about Mr. Fitch’s invention is this:

The horror of the crash motivated Mr. Fitch to develop safety barriers, including one for the walls of racetracks to deflect a car and soften its impact. For the highway barrier, he began with liquor crates, filling them with different amounts of sand and then crashing into them himself at speeds of up to 70 m.p.h. to figure out what worked best.

HT: Steve Sailer


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The Fermi Paradox and the Drake Equation – Intro

Enrico Fermi was various kinds of brilliant. His estimate of the yield of the Trinity nuclear test by measuring the displacement of confetti by the shock wave is surprisingly accurate. In science fiction circles, of course, he is best known for the Fermi Paradox. The Fermi Paradox, for those unfamiliar with it, can be stated as: if the Earth is typical, the universe should be full of intelligent life. Why do we have no evidence of it? Or, as Fermi himself more succinctly put it, “Where are they?”

Consider: it seems plausible that humankind could develop interstellar travel within a thousand years. That’s a tiny sliver of the age of the galaxy. Even if interstellar travel were very slow, say 1% of the speed of light, it would only take about 10 million years for our descendants to permeate the Milky Way galaxy. Since the Milky Way is about 13 billion years old, there has been ample time for aliens to have evolved intelligence, developed star travel, and reached Earth. And not just once–hundreds of times over. And even if interstellar travel is essentially impossible, the galaxy’s radio frequencies could be full of messages. Radio signals bearing I Love Lucy and The Honeymooners are now 60 light years away from us and still going.

To help estimate the number of alien civilizations that might be detectable by radio, Frank Drake defined the Drake Equation:

N = R * f_p * n_e * f_l * f_i * f_c * L


N = the number of civilizations in our galaxy with which communication might be possible;


R = the average rate of star formation per year in our galaxy
f_p = the fraction of those stars that have planets
n_e = the average number of planets that can potentially support life per star that has planets
f_l = the fraction of the above that actually go on to develop life at some point
f_i = the fraction of the above that actually go on to develop intelligent life
f_c = the fraction of civilizations that develop a technology that releases detectable signs of their existence into space
L = the length of time for which such civilizations release detectable signals into space

Although directed to interstellar signals, the general logic of the Drake Equation applies to interstellar travel. Substitute f_c with a new term, f_s, the fraction of civilizations that develop interstellar travel.

Either way, if N is close to zero as observation suggests, at least one of the factors in the Drake Equation is close to zero. In future posts, we’ll discuss which one(s), with reasons why. Stay tuned.

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Con report: Apollocon 2012

Last weekend I spent Saturday at Apollocon, Houston’s leading sf/f convention. As usual, it was held at the Doubletree near IAH, so my three-year-old son had an exciting moment when a jumbo jet went loud and low overhead on takeoff. A fine hotel, free cookies on checkin, and passable service for drinks and meals in the bar.

In addition to spending time with old friends and sampling some excellent Scotches, I attended two memorable presentations.

The first, by astronaut Stan Love, was about the engineering difficulties faced in planning a manned mission to Mars. The velocity change required to get to Mars and back (~48,000 mph) isn’t much greater than that achieved by the Apollo moon landings (~42,000 mph), which sounds feasible, but… given that chemical rockets today are about as good as they are likely to get, the only way to get to and from Mars is by using transfer orbits, which only work when leaving a planet during particular launch windows. A manned Mars mission would take 32 months and require schlepping 100 tons of crew, capsule, air, water, food, spare parts, etc. out and back. If we assume the same payload/fuel ratio as the Apollo moon missions, we would need roughly the mass of an aircraft carrier on the launch pad. This is well beyond feasible, at least today.

The second, by NASA scientist Paul Abell, discussed near Earth asteroids. Since a meteor impact killed the dinosaurs, the need to understand and track these objects is acute. Over 9000 are known, with more constantly being discovered. The ongoing discoveries are mostly of small ones, less than 100 meters in diameter, which doesn’t sound bad–but the Tunguska event, which leveled a thousand square miles of forest, was probably caused by a 50-meter object bursting at high altitude. For asteroid detection and deflection, it doesn’t help that some have very low albedos, and are thus difficult to see; and others are rubble piles (literally, collections of rocks held together by mutual gravity) which can’t be moved to a different, Earth-avoiding orbit by strapping a rocket onto it.

Finally, in one of those moments that only happens when conversing with other people who share your passions, while talking with Amy Sisson and Delilah Mitchell Peeler, for the first time I really realized a common thread in a lot of the work of Octavia Butler. In a lot of her stories, the notionally more powerful character (e.g., Doro in Wild Seed, Rufus in Kindred) turns out to be dependent on a less powerful one (e.g., Anyanwu and Dana, respectively). An interesting thought about Butler’s work and human relationships in general.

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First World Problems

I understand the dismissive sentiment behind the phrase “first world problems.” If you can read this blog post, there are a huge number of ways in which you are more fortunate than most people who have ever lived. Even kings, popes, and emperors of centuries past would envy you. The death of your child is a highly unlikely tragedy, instead of a coin flip. You probably have so much food in your society that even your poor can be fat. You probably work in relative safety and comfort, at a career you chose. And you can share words, pictures, and videos with audience of billions around the world.

Consider your good fortune in the context of history: in the great scheme of things, Ink and toner cost too much and Why can’t they line up check perforations with the fold of a letter? are nothing to get exercised over.

But… barring bad luck and poor planning, most people who will ever live, starting now, will be much more prosperous than you and I. In other words, for most of human history yet to come, the only problems will be first world problems. Thanks to the power of first mover advantages, and the indefinite lifespan of knowledge in search engine server caches, the  attitudes and skillsets we apply to our problems are setting the first best practices for generations to come. So when we approach our problems of saving up for Disney World vacations and getting our Linux machines to send print jobs wirelessly, we are building a jumping-off point for the billions of people who will come after us to solve their problems. That’s a deep power, but thing is, we’re already wielding it. We might as well get good at it.

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