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New Angles on the Drake Equation

The Drake Equation in its various forms has been tormenting us for decades, raising the question of how to adjust variables that range from astronomical (the abundance of terrestrial planets) to biological (the probability of life’s emergence) and even sociological (the average lifetime of a technological civilization). Wildly optimistic estimates of the number of technological civilizations in our galaxy are now giving way to more sober reflection. Now Reginald Smith (Bouchet-Franklin Institute, Rochester NY) offers up a new analysis looking at how likely radio contact is given a civilization’s lifetime, and how widely that civilization’s signals can be clearly received. The key question: What if there is a reasonable horizon for the detection of a signal from an extraterrestrial sender?

Signals and Their Lifetime

This is useful stuff, because contact depends not just upon the density of communicating civilizations (CC) but their average lifetime and the maximum detectable distance for their signals. A CC with a short lifetime is unlikely to be heard unless its neighborhood is crowded with other civilizations. But a longer living CC increases the necessary density — a culture producing a continuous signal over a span of a million years is obviously much more likely to be detected than one producing that signal over a single millennium. And if Fermi’s paradox continues to plague us, Smith would argue that perhaps it shouldn’t. From the paper:

What is most interesting about this analysis is that it demonstrates it can be possible for many CCs in the same galaxy to never contact one another. For example, even assuming the average CC has a lifetime of 1,000 years, ten times longer than Earth has been broadcasting, and has a signal horizon of 1,000 light-years, you need a minimum of over 300 CCs in the galactic neighborhood to reach a minimum density. For example, if there were only 200 CCs in our galactic neighborhood roughly meeting these parameters, probabilistically they will never be aware of each other. This finding can give pause to both those who predict no other CCs or those who predict a high number of CCs in our galactic neighborhood.

A pause for reflection is not a bad idea, given the flexibility of the values in the Drake Equation. Smith continues:

Arguing that the lack of contact signifies the lack of CCs may be tempered with the fact that if there is a signal horizon, even a galaxy replete with life may have relatively isolated CCs in the absence of interstellar travel or extremely power[ful] signals. On the other hand, high estimates of CCs in our galactic neighborhood does not guarantee that there will ever be contact between them, especially reciprocal.

From Radio to Artifact

Hold the density of technological cultures down to a certain level and contact is unlikely. Or is it? Note what this presupposes about the cultures we might expect to exist out there. Smith himself says that the constraints on contact can be circumvented by interstellar travel or automated beacons. And if we are willing to move into the realm of von Neumann probes and other self-replicating technologies, we have to deal with the possibility that a single ETI could blanket the galaxy with its sensors given enough time. Frank Tipler famously estimated the needed span to be about a million years, and argued from that that ETI does not exist.

Let’s assume for the sake of argument that there are no von Neumann probes. If this were the case, given that we believe a sufficiently advanced civilization ought to be able to build them, it seems to suggest that ETI would have universally chosen not to build them because, as Carl Sagan once speculated, such probes would constitute so potent a viral-like menace that no sane species would introduce them. The other possibility, far starker, is that no civilization can survive long enough to reach the stage of technology needed to produce them. For in terms of physics, a self-reproducing von Neumann probe appears to be feasible, assuming we or our hypothetical ETI develop the tools to the needed point without turning them on ourselves.

Statistical Approaches to Drake

I’m wandering far from Smith’s original point, which is to show that variables like short lifetimes or small maximum distances for communications could mask the presence of other technological cultures. We’re left to wrestle with the implications that follow from this. The paper is Smith, “Broadcasting but not receiving: density dependence considerations for SETI signals,” submitted to the International Journal of Astrobiology and available online. Also significant here is Claudio Maccone’s “The Statistical Drake Equation,” which was presented at the 2008 International Astronautical Congress held last year in Glasgow.

Maccone has re-worked the Drake values by taking what had been single value estimates and converting them into statistical form, with intriguing results. And while I don’t want to turn this into a bibliography, I do need to mention Duncan Forgan’s “A Numerical Testbed for Hypotheses of Extraterrestrial Life and Intelligence,” accepted by the International Journal of Astrobiology and available here. Working with statistical treatments of SETI’s key parameters is opening up new insight into their uses. Both the Maccone and Forgan papers have been on the back burner here for longer than I intended, an issue I hope to remedy soon.

Comments on this entry are closed.

  • AlfaCentavra February 3, 2009, 11:32
  • John Hunt February 3, 2009, 14:12

    There’s a lot of assumptions that one has to deal with here. It is often pointed out that radio frequencies may be replaced by a much better method so that there may be a large number of civilizations in communication with each other but we haven’t yet been able to figure out how to get connected. The problem I have with this is that it means that the other civilizations are choosing not to also contact us at our stage of development even though, I believe, they easily could (by radio frequency). Are we to believe that they are choosing to not communicate with us at a time when we are within decades of developing our own self-replicating technology which may pose an existential threat to ourselves? Or, is it more likely that the reason they aren’t communicating with us is that they too stumbled into an existential event of their own making and were never told about it by preceding civilizations who also stumbled into their own existential events? Given that we are within 40 years of being able to produce self-replicating molecules and/or nanomachines I think that the latter scenario needs to be taken seriously.

    There is also the issue of statistical probability. Just because 200 CCs may not become aware of each other at this point in time doesn’t mean that, over a billion years, statistically, some two might be lucky enough to happen to be near each other. Once two civilizations start communicating the equation can be significantly changed. For example, when one civilization winks out of existence (or stops communicating), the other civilization may have a good idea why that happened and may choose to avoid that situation.

    Then there’s the concern about Von Neumann probes mutating and getting out of control. But it should be possible to construct self-replicating systems which don’t have the ability to mutate. For example, a Freitas-style Daedalus variant could have multiply redundant blueprint information – rare errors would stand out from all of the other correct blueprint versions. Also, such craft could be programmed to stop replicating after a certain number of replications.

  • David February 3, 2009, 15:07

    A bit off target, but the first transiting Super-Earth may have been found by CoROT


  • Adam February 3, 2009, 17:48

    Hi All

    David beat me to it. It’s hopefully not as dense as the figures imply – a mass of 0.035 Jupiters and a radius of 0.13 Jupiters means a density over 21!!! Slightly less extreme is if we use the low and high end of M, R respectively – just over 7, which means it’s mostly iron alloy. If it really was ~20+ might that imply a stripped core that hasn’t relaxed to uncompressed density? Or something really, really weird?

  • David February 3, 2009, 22:40


    Good point about the density. I am inclined to agree with you that the density implies it is mostly Iron. Mercury has a density of around 6, so I can easily see that the exoplanet with its much greater mass could via compression have a higher density than Mercury.
    Mercury though is thought to have lost most of its less dense Mantle material in a collision so one wonders if the same is true here. Perhaps we have here not a Super-Earth, but a Super-Mercury.

  • Adam February 4, 2009, 7:08

    BTW the estimate on CC density is akin to the “infected volume” that life-bearing planets might spread life to via panspermia with meteorites or ETI space-junk as vectors. The usual estimate for viability timescale of semi-protected bacterial spores is assumed to be 1 myr, with a spreading speed of 15-30 km/s – low enough to allow survivable capture into other systems, but not too low. A range of 50-100 lightyears is then indicated. Assuming roughly random relative speeds between stars of ~ 15 km/s this implies the Sun could capture life from another star in a skinny toroidal or heliacal volume around the Galaxy. For it to happen once in 4.5 billion years there must be less than ~4,000 systems with life presently.

    Problem is, if Life here is akin to Life there, then how do we tell if it has invaded us recently or not? And would we even notice if it was truly alien, because bacteria so readily trade genetic material back-and-forth? Pretty rapidly any newcomers that survived would be “related” to terrestrial life thanks to horizontal gene-transfer.

    I don’t think we have a sufficient grip on the potentials of contact via electromagnetic signalling to really say we aren’t presently being hailed and we’re too dense, slow, narrowly focussed to notice. Perhaps we can safely say that nothing obvious is being sent our way, but then why would ETIs be obvious?

  • James M. Essig February 5, 2009, 8:48

    Hi Folks;

    It is interesting to also consider the possibility that certian bodily extraterrestrial lifeforms, whether or not they are intellegent and/or technological, might inhabit higher dimensional spacetime and/or parallel dimensional space time. Any such beings need not be “supernatural” or “God Like” from an ontological perspective and might have all of the physical vunerabilities that we have, at least relatively so. As a result, the consideration of the existence of the possible existence of such beings is well within the realm of normal scientific exobiology paradigms.

    If higher dimensional space is quantizied at the Planck Distance Scale or simmilar scale, and I think by symmetry , that if our 4-D Einstienian space is, there is no reason why higher D space time should not also be, then for flat Euclidean higher D space, say of 10 dimensions and cubic edge length of say 1,000 Lightyears or 10 EXP 16 meters, the hyper 10 -D volume would include an matrix of [(10 EXP 16)(10 EXP 35)] EXP (D-3) =[(10 EXP 16)(10 EXP 35)] EXP (10-3) =[(10 EXP 16)(10 EXP 35)] EXP 7 three dimensional cubes, each cube being 1,000 lightyears on edge, stacked in a matrix like pattern assumming no space between the cubes.

    If higher dimensional space is populated by mattergy distributions, even though it may and I feel probably is quantized at the Planck distance scale, that is a huge amount of territory to consider. Note however, if any UTI exist in such a cube, they might be completely un-aware of our presence, it might likely be the case that we will have to search for our kindred space alien friends the conventional way, and that is out among the stars in 4-D Einstienian space time. But our universe, even just the visible portion of it is huge, with perhaps 10 EXP 11 galaxies, so I remains hopeful in that in the comming centuries, millenia, if not eons, we will meet ETI.



  • synthesis February 5, 2009, 21:02

    A point to consider in future improvements of
    this modelling is not only ‘interstellar panspermia’ but very fundamentally ‘Interstellar Colonization’:

    The intelligence timescale is calculated in the model by stochastic process: life does evolve on a planet by evolution stages that are randomly sampled. The resetting events (catastrophic life destroying events) are placed uniformly throughout each of the stages. If Nresets > Nstages, then any
    given stage may suffer several reset events. The model compute that if a reset occurs and if that reset results in annihilation, life is exterminated, and the process ends; otherwise the evolutive process decreases.

    If we permit strictly darwinian “Dawkins’Intelligent Designers” (interstellar interveners) in the eons of life’s evolution on colonizated targets then this stochastic ‘designer events’ must be included in Forgan’s model(s): any
    given evolutionary stage may ‘suffer’ several ‘designer’ events and the model must compute that if a novel design is seeded and if that design results in life (intelligence)’s improvement then the target planet’s evolutionary path is changed for the better; otherwise the evolutive process in it is left to extremaly slow (classical) local darwinian stages.

  • Eadwacer February 7, 2009, 12:43

    Keep in mind the difference between ‘communication’ and ‘signal detection’. For many years, the brightest signals from Earth were the missile detection radars that the US and USSR used. Even plain old TV signals are detectable long after they’ve lost any content. So it might be that there are civilizations that are not interested in communicating with us, but that still use EM transmissions.

    If they’re there, their signals should be detectable.

  • James M. Essig February 7, 2009, 16:31

    Hi Eadwacer;

    Good points.

    Also note that the relatively low power transmissions from our most distant space probes where still deciperable even after the probes had reached a distance of over 6 billion miles from Earth or over 0.001 lightyears. No doubt the transmissions, if I am not mistaken were made in burst mode, but even so, with such a small power source, these transmissions would have still had a very low at source power output.

    A high gain, high fidelity, burst mode transmission made from high gain transmitters such as those on the scale of the phased array nuclear missile launch detection RADARs used by the U.S. and Russia should be able to broadcast high gain signals, and perhaps high gain communications all over the Milky Way.

    With the WOW! signal and some of the other interesting events, perhaps we may have run accross just such an ETI transmission without definately knowing its true source. I am interested in what the SETI folks will come up with in the comming decades. I am 47 years old and still in good health, and so if I am lucky, I may have four more decades, possible another five or six or more if medical anttiaging related science pans out. I hope the SETI folks find something during this time interval.



  • Ronald February 8, 2009, 6:00


    I share your interest (and your age), but maybe I am a bit less ambitious: I would already be very (VERY) happy with the detection of an earthlike planet that clearly shows the spectroscopic biosignature of life, any life. Now, that would be the day, a historic day.

  • James M. Essig February 8, 2009, 13:32

    Hi Ronald;

    Thanks for sharing your perspective.

    I would also be VERY happy if we discovered a signature of an extrasolar biosphere containing planet. I like to mention when the subject of the U.S. program for the planned returning of humans to the moon by 2020,is realized, I will throw one Heck of a Cookout Party. If we discover an extrasolar biosphere, that will be yet another occasion to throw a large outdoor grill party. With the rate of scientific, technological, and observational progress within the fields of astronomy, astronautics, and hopefully exobiology, I am beginning to think that I will need to develop better outdoor cooking skills and associated recipies. As I often lik to say, “Let the fun begin!”.



  • george scaglione February 9, 2009, 13:07

    john hunt,i have gone over the postings above and cannot get over what a good point you made.who is to say that aliens do not communicate in some way we have not yet figured out! we assume “radio” but….why??? funny i was just saying to people in the last few days how there are without doubt alot of cool things that we do not yet know much (if anything at all about.) ! good work john and i hope i hear from you again soon. :) your friend george

  • ljk September 17, 2009, 12:37

    September 16, 2009

    A New “Drake” Equation for Potential of Life

    Written by Nancy Atkinson

    The famed Drake equation estimates the number of technologically advanced civilizations that might exist in our Galaxy. But is there a way to mathematically quantify a habitat’s potential for hosting life?

    “At present, there is no easy way of directly comparing the suitability of different environments as a habitat for life” said Dr. Axel Hagermann, who is proposing a method to find a “habitability index” at the European Planetary Science Congress.

    “The classical definition of a habitable environment,” said Hagermann, “is one that has the presence of a solvent, for example water, availability of the raw materials for life, clement conditions and some kind of energy source, so we tend to define a place as ‘habitable’ if it falls into the area where these criteria overlap on a Venn diagram.

    “This is fine for specific instances, but it gives us no quantifiable way of comparing exactly how habitable one environment is in comparison with another, which I think is very important.”

    Hagermann and colleague Charles Cockell have the ambitious aim of developing a single, normalized indicator of habitability, mathematically describing all the variables of each of the four habitability criteria. Initially, they are focusing on describing all the qualities of an energy source that may help or hinder the development of life.

    Full article here:


  • ljk February 24, 2010, 1:13

    Drake wants off-world listening post for alien messages

    New Scientist Space Feb. 18, 2010


    SETI founder Frank Drake wants to take the search for aliens about 82 billion kilometers away from Earth,where electromagnetic signals fromplanets orbiting distant stars would be focused by the gravitational lensing effect of our sun, making them, in theory, more easily detected. Gravitational lenses could also be used to increase the range…