Home > Clement's Game, Fermi Problems, Worldbuilding, Your Turn > Your Turn, Round 2-3: A Problem: The Drake Equation In This Setting

Your Turn, Round 2-3: A Problem: The Drake Equation In This Setting


Frank Drake’s formula for estimating the number of intelligent civilizations in the universe that could be located by SETI efforts has some limitations.  But it does provide a convenient framework for thinking about the real search for extraterrestrial intelligence.  And it can also be used to see the implications for the Fermi Problems setting of having two intelligent species within 15 parsecs of Earth.

The equation: Number of civilizations in the galaxy N = (number of stars)*(number of planets per star)*(fraction of planets where life evolves)*(fraction of biospheres where intelligence evolves)*(how long intelligence lasts)/(age of the universe)

There are some modifications here from the usual form of the equation.  As I mentioned earlier, the usual definition of ‘intelligent’ for SETI is ‘having built a radio transmitter or other beacon readily detectable over interstellar distances’.  Here I’m using a more comprehensive definition, which includes humans anytime since behavioral modernity has been around.  And any one occurrence of intelligence lasts a long time.  As a starting point, call it 1 million years.

Several of the numbers in the equation are known.  The universe is 13.77 ± 0.06 billion years old, although I can round that to 10 billion for this because it takes a while for nucleosynthesis to work up to building enough non-hydrogen and non-helium material to make planets.  There are ~300 billion stars in the galaxy – although there could be somewhat more depending on how we count brown dwarfs.  The Kepler Mission and micro-lensing surveys show that there at least as many planets as there are stars.  Again, the accounting here is difficult: the surveys are generally not sensitive to planets smaller than the Earth (to say nothing of asteroids – although they should be massively down-weighted compared to larger objects).  Call the number of planets per star 3, to make the order-of-magnitude calculation easier.

So: In the Fermi Problems setting, N = 10^8 * (fraction of planets with life) * (fraction of biospheres that evolve intelligence).  There are ~1900 stars in ~1400 stellar systems within 15 parsecs of Earth right now.  If civilizations are uniformly distributed, which they may not be, for there to be two civilizations extant in that volume, there must be one civilization per ~700 stellar systems on average.  I can make it 1 per 1000 stars without straining the odds.  But N = 10^8 is 1 civilization per 3000 stars.  This poses a problem.

What Should I Do?

There are five different variables I can adjust in the setting.  The fraction of planets with life can’t be greater than one, and based on the evidence of our solar system it is most likely far less than 0.1.  I could say that biospheres evolve intelligence many times, making that fraction greater than 1. Counting the apes, the dolphins, the elephants, the canines, the cats, the parrots, the corvids, and some of the cephalopods as separate evolutions of intelligence on Earth gives 8, but we are obviously by far the most extensive of the lot.  It is pretty much impossible to get the product of those two fractions above 1, so I am left with three possible changes:

1. Intelligence lasts a long time.  I have had the ursians be trapped at the bottom of a hole in high-tech social stasis for hundreds of thousands of years.  Can I make it several million instead, to push the number up to 10^7 years?  This starts to get problematic for the neari, who can spread across 15 parsecs in that time even with limited technology; and technological stasis does not apply for them.  I don’t think I can push the lifetime up much further than that without the setting breaking.

2. There are more ‘planets’ per star.  In addition to terrestrials and gas giants, I count large satellites like Europa and Titan and some appropriately-down-weighted number of asteroids.  But, like the lifetime number, this can only go up so much.  Maybe we count 15 places in the solar system rather than 8, but most of those are less appealing for biologically interesting chemistry.

This leaves the last option, which is the easiest in scientific terms, but much harder in terms of plot:

3. Move the neari and the ursians further away from each other and from Earth.  Putting them each 150 pc away rather than 15 gives 1000 times as many stars.  Then, with civilizations lasting a million years and 3 planets per star, (fraction of planets with life)*(fraction of life with intelligence) need only be 0.001 or so.  In this version of the setting, one out of every 30 stars will have a biosphere near it somewhere – there will be strange microbes all over the place, and the nearest macroscopic ET organisms will be something like 30 lightyears away.  And in places with fossil records, there will be ruins/remains of billion-years-dead cultures; far far more of those than the extant cultures.

If I do increase the distances so much, then there is no way for a neari comet boat to travel to Big Bear and find the ursians.  And the timeline will need to be extended; with things involving humans and either group of aliens happening thousands of years in the future rather than only 500 years from now.

So, shall I change the setting to avoid the improbability of having not just two, but three civilizations so close together?  The price is much less of characters meeting aliens in person, much longer time lags when talking to aliens remotely, and much more far-future exoplanet geobiology and archaeology.  It seems that’s what the universe is like.

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  1. michaelbusch
    2013/01/02 at 6:33 pm

    After this, I’ll be taking a break from posting for a while. Don’t worry. Rachel has some ideas to keep you all entertained.

  2. 2013/01/02 at 9:54 pm

    In general, my solution to these kinds of things is to distribute the extra factor you need over as many variables as possible. Here’s how I would handle this particular problem:

    By my math, your new scenario implies that (fraction of planets with life) = 0.015-0.03 (3 planets per star with every tenth or twentieth solar system containing a biosphere). Since you postulate life in a vacuum and in the atmosphere of a gas giant, life appears to be common, and I think you can safely multiply that by 10.

    If we also set (fraction of life with intelligence) = 1 and count double the number of “planets”, then the product of your last two variables needs to be 6-12 to have 1 extant civilization per 700 stars. Let’s say 10 for convenience.

    Letting the time scale be proportional to the length scale, you need only multiply both scales by 10^(1/4) ~ 1.8 to take care of this. If you don’t want that extra factor of 10 in (fraction of planets with life), then you need to multiply both scales by 100^(1/4) ~ 3.2.

    • michaelbusch
      2013/01/03 at 12:09 am

      The fraction of planets with life cannot be made higher than 0.1, and ideally should be much less than that. Otherwise, we would expect there to be life on another planet in the solar system – which there does not appear to be, barring microbes hiding under the ice at Europa. Hence my 0.01 number.

      I also don’t think we can put (fraction of life with intelligence) anywhere close to 1. After all, life on Earth was happily microbial for nearly three billion years. Unless we argue that once some critical conditions are met, intelligence will arise repeatedly and persistently in a biosphere – sufficiently often to offset the 80% or more of places with only microbiota – the number is going to be a lot less than 1. Hence a value of 0.1.

      And, again, a million years seems like the most I can justify without the neari either going extinct or working their way up from making a bag full of steam to building fusion-powered starships and spreading at 10% the speed of light. So I’m reluctant to increase the lifetime by a factor of several – that would make it as long as we’ve been distinct from the chimps. Thus the factor of 10 in distance (1000^(1/3)).

      But even increasing the distance by a factor of three would kill the neari comet boats. There are only so many large comets, and they can only impart so much momentum to them. I am forced to have the ursians and the neari not be in the same place unless the neari have much better toys, losing the whole stone-age starship appeal.

  3. 2013/01/03 at 5:14 pm

    I guess it depends on what you want to do with this setting and how much you care about the narrative you outlined. If it’s important enough, you can afford to strain the laws of probability by invoking the Rule of Cool, or to bend the rules of your setting, e.g. adding microbes on Mars/Europa/Jupiter/etc., increasing (fraction of life with intelligence), making the stone-age technology better, and so on. I admit that all of these are compromises, but as a fellow writer, I think that they are worth considering if you choose to take the setting further (I’d read it).

    • michaelbusch
      2013/01/03 at 7:05 pm

      I could move the neari and ursians further from Earth, but still keep them close to each other.

      With N = 100,000, such a situation has a ~0.065% chance of happening for any given civilization and will be happening many tens of times in the galaxy at any given time. Humans, neari, and ursians would just happen to be some of the lucky ones. That’s as compared to a one-in-a-two-million chance of having two other active civilizations within 15 pc of you given that N, which would not happen for anyone in the galaxy more often than once per 15 million years. I can live with humanity being part of the many one-in-a-thousand cases; it would bother me for us to be part of a single one-in-several-million one.

      However, given that the humans are now traveling over 150 pc/490 lightyears to get to Ursa, I would then need to move things further into the future – 2900 CE or so for their arrival. The humans will also have spent many generations en route, rather than only the older members of the crew that left the solar system dying before they got to Big Bear, and will no longer have direct family ties to anyone back home. Fortunately, I can handwave some lack of additional technological advancement by that information not yet having caught up to the Ursa-bound ship. But the human characters that meet the neari and ursians in person and their culture will be different than I had thought.

      I’ll have to think about this some. As I said, I’ll be taking a break from post-writing for a while, but I may eventually get around to revising portions of the rush-job I did for Nanowrimo. Thanks again for your interest and for catching the ursians’ ability to make some electronics!

      • michaelbusch
        2013/09/16 at 8:53 am

        Note to myself:

        I have now moved Big Bear to HIP 66461, a G5 star near the boundary between Ursa Majoris and Draco. That lets me keep Druk in Draco and so justify the naming convention while having the distance from Earth be reasonable.

        The Inquest took 300 subjective years to make the crossing.

  1. 2013/05/25 at 12:35 am
  2. 2015/11/22 at 8:27 am

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