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More about Operation Iago

Operation Iago (The Confederated Worlds, Book 2) has been out four weeks now. If you haven’t picked it up yet, its focus is an exciting story about a likable character struggling to grow as both a leader and a man. But one of the joys of reading science fiction is the chance to explore strange new worlds. And Arden certainly is a strange one… Read the rest of this entry

The Fermi Paradox and the Drake Equation – From the Origin of Life to the Cusp of Intelligence (f_i, part 1)

Uncertainty in calculating the Drake Equation has led us to a broad range, with N = [0.84-16.03] * f_i * f_c * L. Despite the uncertainty, we concluded that relatively high values of f_i (the fraction of life-bearing worlds that give rise to intelligence), f_c (the fraction of intelligent species that develop technology detectable across interstellar distances), and L (the lifespan of that high-technology phase of that species’ civilization) would lead to scores, if not hundreds or even thousands, of intelligent species producing detectable signals in the Milky Way galaxy right now.

The radio silence we observe from other intelligent life suggests at least one of f_i, f_c, or L is very low. Today we’ll examine part of f_i, from the origins of life to the cusp of intelligence, from self-replication to genus Homo.

Here are some factors tending to lower f_i:

* It took roughly 4 billion years to go from the formation of Earth to something we would recognize as an animal or plant. (Assumption: only animals or plants can evolve intelligence). If Earth is normal, then we know from the maximum stellar lifespan data that all O, B, A, and the largest and hottest F type stars cannot live long enough. That knocks out about two-thirds of all stellar systems. So f_i is instantly no greater than 0.33.

* Intelligent life requires a lot of energy. (More on this in the next post). Assuming that free oxygen is required for life to generate enough energy, oxygenic photosynthesis has to evolve. (If it doesn’t, all the free oxygen in an atmosphere would rapidly react with carbon, iron, etc. It’s that high reactivity that makes free oxygen so potent in energy generation). If Earth is normal, oxygenic photosynthesis will evolve on any life-bearing planet. The first tranche of free oxygen liberated by photosynthesis will be consumed by metals in a planet’s oceans and surface. (That’s where most of Earth’s commercially relevant iron ore deposits are from). The second tranche of free oxygen will be consumed by gases in the planet’s atmosphere. If Earth is normal, then methane will be one of those gases. Methane would, in effect, burn, yielding carbon dioxide and water.

Methane is a greenhouse gas far more potent than carbon dioxide and water. What happens if most of the methane in a planet’s atmosphere is lost? In Earth’s case, the planet froze over for up to 400 million years. It was only continued volcanic activity, spewing more methane and other greenhouse gases into the atmosphere, that allowed Earth to heat up again enough for the global ice cover to at least partially melt.

Without unglaciated land to colonize, intelligence wouldn’t have appeared on Earth. (Even if dolphins and whales are intelligent, they are mammals adapted to return from land to the sea). So with little or no volcanic activity, a planet after the evolution of oxygenic photosynthesis could freeze over and remain frozen for billions of years, i.e., until its primary star leaves the main sequence. On average, planets smaller than Earth would be more likely to have cold cores and little or no volcanic activity. Let’s say a third of all planets would be too small to have significant volcanic activity, and thus, couldn’t recover from a freeze over. That drops f_i to 0.22.

* “Without photosynthesis, no free oxygen; without free oxygen, no intelligence” also means that intelligent life could not evolve in an atmosphere without sunlight, because photosynthesis would never arise. Good-bye, intelligent Europans, in your ocean encased by 15 miles of ice. If about a third of all planets on which life arises are moons of gas giants, f_i is now 0.15.

* It’s easy to assume there is an inevitability to evolution. (We’ll talk more about this in the next post). But to get to the cusp of intelligence, life on Earth went through a lot of contingent events. The evolution of photosynthesis. The symbiosis of the first eukaryotic cells. The evolution of sex. The evolution of multicellularity. The formation of the ozone layer, to make land habitable against excessive UV. The emergence of animals. Delay any one of these–at least from photosynthesis to multicellularity–on a planet, and you increase the chances of its primary star running out the main sequence clock.

Why assume any of those could be delayed? Why not? There’s no purpose to evolution: it’s simply the blind pursuit of local optima. In light of that, we’ll lower f_i by another two-thirds, to 0.05.

* One last point. Sporadic waves of mass extinction are a good thing, at least as far as we’re concerned, because they cleared the way for the species that gave rise to us. It may be that Jupiter’s size is in a sweet spot to propel the optimal number of large, dinosaur-killing impacts our way. A smaller gas giant would send too many impacts our way, thus interrupting the rise of the successors; one much larger than Jupiter would not send enough. Even if Earth is normal, there are reasons (hot Jupiters, super Jupiters) to conclude Jupiter is not. So f_i ratchets down again, to the arbitary value of 0.02.

We’re now at N, the number of detectable civilizations in the galaxy, at [0.02-0.32] * f_c * L. And that’s assuming intelligence is inevitable when sufficiently complex multicellular life on land has arisen. Is it inevitable? Find out in the next post.

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.

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.

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.

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.