My_House__My_Blue_Planet_Earth

Astronomy Without A Telescope – Bringing The Planetology Home

Article Updated: 24 Dec , 2015

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We keep finding all these exoplanets. Our detection methods still only pick out the bigger ones, but we’re getting better at this all the time. One day in the not-too-distant future it is conceivable that we will find one with a surface gravity in the 1G range – orbiting its star in, what we anthropomorphically call, the Goldilocks zone where water can exist in liquid phase.

So let’s say we find such a planet and then direct all our SETI gear towards it. We start detecting faint morse-code like beeps – inscrutable, but clearly of artificial origin. Knowing us, we’ll send out a probe. Knowing us, there will be a letter campaign demanding that we adhere to the Prime Directive and consequently this deep space probe will include some newly developed cloaking technology, so that it will arrive at the Goldilocks planet invisible and undetectable.

The probe takes quite a while to get there and, in transit, receives indications that the alien civilization is steadily advancing its technology as black and white sitcoms start coming through – and as all that is relayed back to us we are able to begin translating their communications into a range of ‘dialects’.

By the time the probe has arrived and settles into an invisible orbit, it’s apparent a problem is emerging on the planet. Many of its inhabitants have begun expressing concern that their advancing technology is beginning to have planetary effects, with respect to land clearing and atmospheric carbon loading.

From our distant and detached viewpoint we are able to see that anyone on the planet who thinks they live in a stable and unchanging environment just isn’t paying attention. There was a volcano just the other week and their geologists keep finding ancient impact craters which have revised whole ecosystems in their planet’s past.

It becomes apparent that the planet’s inhabitants are too close the issues to be able to make a dispassionate assessment about what’s happening – or what to do about it. They are right that their technological advancement has bumped up the CO2 levels from 280ppm to over 380ppm within only 150 years – and to a level much higher than anything detectable in their ice core data, which goes back half a million years. But that’s about where the definitive data ends.

Credit: Rahstorf. NASA data is from the GISS Surface Temperature Analysis. Hadley Centre data is from the Met Office Hadley Centre, UK.

Advocates for change draw graphs showing temperatures are rising, while conservatives argue this is just cherry-picking data from narrow time periods. After all, a brief rise might be lost in the background noise of a longer monitoring period – and just how reliable is 150 year old data anyway? Other more pragmatic individuals point to the benefits gained from their advanced technology, noting that you have to break a few eggs to make an omelet (or at least the equivalent alien cuisine).

Back on Earth our future selves smile wryly, having seen it all before. As well as interstellar probes and cloaking devices, we have developed a reliable form of Asimovian psychohistory. With this, it’s easy enough to calculate that the statistical probability of a global population adopting a coordinated risk management strategy in the absence of definitive, face-slapping evidence of an approaching calamity is exactly (datum removed to prevent corrupting the timeline).

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25 Responses

  1. Aqua says:

    OF COURSE! Stealth aliens… it all makes sense now… the guy down the street… the mailman… the Comcast guy…my next door neighbor…. the X-37B.

    Actually you bring up a good point. Intelligence breeding benevolence is one thing, due caution another.

  2. I love this. It spurred my imagination for the day

  3. Lawrence B. Crowell says:

    Instead of Asimov I would consider AC Clarke. Suppose we find by various chemical signatures of some terrestrial planet indicating the presence of life. The so called “red edge” at around 500nm is a good sign for photosynthesis. So there may be life there, but this planet is 400 light years away. It is also radio silent, no signature of some ETI phoning out. So sending a probe is a bit problematic, for it will take over 800 years to get a return — a bit like reading the books of Thomas Aquinas for the first time.

    So what might we do? We might decide to send a probe anyway, but the purpose might not be to send data back to us, but to send data to some future ETI there. The probe is highly AI capable and once it inserts itself into the stellar system is puts itself in some sort of stasis where it waits, maybe for many millions of years. It might collect data about this planet and send it back to Earth, it might record this data, but largely its purpose is to wait.

    Then if there come signatures of intelligent radio communications from this planet the probe starts to wake up. It begins to send radio signals to the planet. The ETI in time receive these signals, eventually find it is coming from their local space and send their ET-nauts or a robotic probe to investigate. From there they down load the compendium of human knowledge.

    Ac Clarke’s monolith was something of this sort. Maybe there is something of this sort lurking in our solar system. An important process in this whole ETI issue is to exploit the prospect that intelligent conscious observers in the universe somehow compare notes. In this way we can test our cherished notions that our understanding of the universe is not anthro-centric, but has some universality to it. If we contact ETI this would be what would be of great interest to test. Conversely we might want to deliver a message as well. If we find bio-planets out there we might begin to consider how we would conduct such an expedition, where maybe many millions of years after we have shuffled off the Darwinian game table our knowledge is transmitted to other form of intelligent life.

    LC

  4. Uncle Fred says:

    As I see it, the scenario as proposed by LC is the more likely one to postulate about. Firstly, we are unlikely to detect any early stage communications as it is my understanding that radio/TV signals degrade into static at around 1-2 light years (please correct me if I am wrong).

    Secondly, the odds of us making contact with a contemporary civilization within our galaxy is pretty low. Lets assume we are primarily interested in looking for life on worlds that have followed a path of development similar to our own. Despite the seemingly endless quantity of stars in the Milky Way, due to many factors (effects of Jovian brother planets, main-sequence metal rich G-class stars, etc, galactic position.) we may realistically be only looking at a few thousand worlds with rich biospheres like our own.

    We may need need to look a hundred light years out or more just to find another Earth.

    Now factor in the odds of one of these planets developing a contemporary civilization. Different biospheres may be at different stages of their development. The Earth is 4.5 Billion years old, life on Earth about 3.5 Billion. In contrast, our civilization is only 10,000 years old. Furthermore,if competitive biology is the norm, the window for meaningful contact may be quite short. My gut instinct tells me that civilizations are overwhelmingly flash-in -the-pan events. We may be the only active civilization at present in our galaxy.

    Lastly, even if there was another civilization, contact may not be realistically possible. An alien civilization may not have any indication that something unusual is occurring on Earth until light reflected off our industrial age atmosphere reaches their planet. A probe would require vast resources to construct and huge timescales before if could return any meaningful information.

    Consider this scenario:

    Earth year: 4000 CE – Alien civilization monitoring all planets with complex biosphere’s in the galaxy detects evidence that Earth’s atmosphere may be undergoing changes consistent with an early industrial civilization.

    Earth Year: 4100 CE – Alien civilization now confirms the presence of a late industrial civilization. Curious, they develop a near light speed probe and send it in our direction.

    Earth Year 5200 CE – Alien probe reaches Earth, collect information.

    Earth year 6300 CE – Alien probe returns to Alien world. It dutifully transmits it’s repository of information about a long dead civilization to …. a long dead civilization.

    Bummer.

  5. @ Uncle Fred
    This may mean that the key role of every civilization is to teach its robots how to communicate.

    So that when two robot probes of two disparate and long dead civilisations meet way out in empty space – at least they can have a meaningful exchange of information (remember STNG s05e25 – The Inner Light).

  6. Spoodle58 says:

    @ Steve
    And I thought I watched to much Star Trek. 🙂

  7. Lawrence B. Crowell says:

    @ Uncle Fred: You are right about our radio transmissions falling off into noise. If one considers radio waves as a radially symmetric flow of photons (particles), then the number of photons N, is constant. They are conserved, but the number of them drops off with the radius. An imaginary sphere enclosing the transmitter has an area A = 4pi r^2, for r the radius of this imaginary sphere. The number of photons per unit area on this sphere is then N/A = N/4pi r^2. So the signal drops off as the reciprocal of the radius squared.

    By extension the electric field line from a charge is also conserved which is why the Coulomb law is a 1/r^2 force. If you understand this argument then you have a basic understanding of Gauss’ law.

    So our radio transmissions should be decreasing in amplitude by a 1/r^2 law, right? Not exactly, the problem is interstellar space is filled with charged particles and ions. A charged particle will oscillated in response to the EM radiation field and absorb these photons. The photons are then re-radiated as other photons with other frequencies. This serves to scramble what ever signal they carry. Any electric or electromagnetic field will then not drop off as 1/r^2 but as exp(-br}/r^2, where 1/b is the Debye length, with a fixed value for zero frequency and increasing in distance for increasing frequency (as a rule of thumb). This is a dispersion relationship which effects some frequencies more than others, which largely attenuates radio frequencies, but not IR or optical frequencies. That exponential term causes field strengths to drop a lot faster, so the source of radio transmissions has to be very powerful for it to be detected across considerable distances. So it is unlikely there are significant signals we are sending beyond maybe a few light years. Those old 1920 radio and 1950-60 TV broadcasts are lost in EM noise.

    The idea of communicating with other ETI requires some “out of the box” thinking. The Voyager spacecrafts have the germ of the idea I present above. Of course these craft will be tiny dead motes in interstellar space and are not likely to be picked up by any ETI. They are a case of messages in a bottle, but where it is very unlikely the bottle will be washed up on any shore so the message can be read. Yet we are now able to detect planets and the Kepler probe is maybe the first of those able to find terrestrial planets with spectral features signifying the presence of life. So we might in the future send probes there with the idea of transmitting information to this planet if EM transmission signals start to radiate sometime in the far future. We might then end up transmitting our presence and knowledge to some ETI 50 million years in the future, long after we have gone the way of T rex. There might be something of this form within our own solar system, maybe sent by some ETI many millions of years ago.

    This requires some interesting engineering to get some artifact capable of functioning for that long period of time. Yet that is important. A dead Voyager that comes within even a fraction of a light year from some ETI bearing planet is not likely to be picked up. If such a dead probe from some ETI is passing within .01 light years from the sun right now we are not going to detect it. The probe needs to transmit some beacon upon detecting the presence of EM signals from the biologically active planet. That way the ETI are alerted to its presence. We might indeed consider doing this within our own solar system, for after Homo sapiens is long gone and fossilized there might evolve some other form of intelligent life here on Earth.

    As for how to communicate, I think the Golay codes from sporadic groups or Goppa codes form elliptic and projective varieties are possibly the universal encryption/decryption system. These mathematical structures are I think the quantum information “rules” for quantum gravity, black hole information and the universe.

    LC

  8. Lawrence B. Crowell says:

    Interesting comparison with STNG – The Inner Light, I had to look this up to remember what this epsiode was. This was one of the better episodes. So thiese involved “Bracewell probes.” According to the Wiki-P entry these are related to von Neumann probes. In some sense they would have to be in order to maintain functionality over very long periods of time.

    LC

  9. Torbjorn Larsson OM says:

    What we will actively do when respectively if we observe biospheres and ETI is an open question, there is no forcing constraints on those possibilities. Likely we will do nothing respectively attempt communication FWIW, which is much cheaper than sending probes.

    The observation of biospheres is much more exciting in the perspective that it can help answer such things as how life got started. I can’t wait for some statistics on biospheres! … but I have too. Darn.

    Some reflections on raised proposals:

    – “cloaking technology”. I got the impression that there is or will be a “no go” prediction, as phase detection will detect any “bending around” of light. Through projection (projecting the background in front) would be feasible for far away objects through a narrow angle though.

    – “a brief rise might be lost in the background noise of a longer monitoring period” That science denialism argument breaks down in the case of a predictive theory as here. In fact, “Detection and attribution of climate change: a regional perspective”, Stott et al, WIREs 2010, claims there are now models that predict the GW rise with 95 % certainty.

    [I played around with approximating the diverging signal + noise vs noise distributions and a probit diagram to see how fast they diverge. (Probit diagram, as it is approximatively to go out on a tail of a properly weighted normal distribution: this is multifactor noise and ~ 5 % weak forcing.)

    Rate is given by time lapsed since IPCC -07 report, which update from 2001, and estimated “80 % certainty” overall. Using the model then 60 % certainty would give even faster rate.

    I get that 3 sigma certainty will happen in about 10 years. Likely sooner, as these are accelerating changes. I give even odds that next IPCC -14 can claim regular testing beyond reasonable doubt.]

    – “psychohistory”. Enough said. 😀

    But really, risk adversity is balanced on ROI. Even if there is evidence of future costs and human suffering, some will believe it isn’t worth the cost and the moral adversity taken. I doubt evidence and its value has anything to do with it.

    Besides, while I don’t argue for this precisely because of the evidence for human suffering (and the financial cost), the ecology will likely benefit from it in the end. Every extinction event since the large Permian-Triassic one has resulted in increased diversity. There is, IIRC, a recent paper claiming that diversity after extinction events is regained in less than 1 My.

    So its no skin off either our future technologies’ (excluding agriculture and medicine, perhaps), population’s or biosphere’s noses.

    – “The so called “red edge” at around 500nm is a good sign for photosynthesis.”

    I’m not sure it is. These, admittedly old, papers claim that minerals will overlap the detection and that plants (like lichen) can show a sloping edge. The first paper notes that “if an extrasolar planet reflectance edge is detected care must be taken with its interpretation.”

    Also, it is predicted on plants needing cooling for synthesis. Lichens and others seem to disagree somewhat. It is more likely a plant detector for moderate temperature Earth analogs.

    Even so, water and clouds show up IR reflecting, so it is AFAIU an iffy detection proposal at best.

  10. Torbjorn Larsson OM says:

    Ops, that is “water ice and clouds shows up IR reflecting”.

    While I’m at it and before IVAN3MAN gets wind of this:
    “there is no forcing constraints” – there are no forcing constraints
    “I got the impression” – I get the impression

    “Using the then model” – Using the then models
    “Its no skin” – It’s no skin

  11. Aqua says:

    Imagine the ET probe’s crew’s astonishment at sensing a similarly cloaked vessel also on orbit. Then quite suddenly, the Probe and crew wink out of existence…

  12. Lawrence B. Crowell says:

    Learning that alien biospheres exist would be a huge scientific coup. Maybe if one is close enough we could send a robotic probe there to get a close up look at this alien biology.

    There is nothing which forces us to send a Bracewell type of probe to such a solar system which waits out enormous stretches of time to contact possible future ETI. Such a proposal would be expensive and is not the sort of thing tea bagger types are eager to fund.

    At the end of it all we might wonder if all our observations of the universe, study and theoretical understandings are just howling at the moon. Maybe if we are fortunate enough we might in 50 years get the hailing from some alien Bracewell probe which gives a live replay of “2001 A Space Odyssey.” We might compare our theoretical understanding and mathematics with those of these aliens. It can only work if there is some universal mathematical encryption code that both we and these ETI for the far past understand. We may then reciprocate in kind and send very deep space probes of a similar nature to very distant stars with bio-planets. Of course we could be just plain lazy and do nothing, which would be more likely the case if there is no such thing hiding out in our solar system about to announce its presence.

    LC

  13. Duncan Ivry says:

    @ Steve Nerlich

    My compliments to you on this article (without any irony or sarcasm on my side). You promote a politico-scientifical agenda disguised as a short story in the literary tradition of projecting our own real or supposed problems onto a society existing far away in space or time. I appreciate this, and it is far better than what somebody tried here on Universe Today some time ago.

  14. Jlazor says:

    I doubt that an alien civilization would face a problem identical to the one we are having. The chemistry of life on other planets is probably so different from ours that their problems will also be different. Even in an oxygen atmosphere a sudden increase of CO2 may have no effect on the biosphere.

    Instead of sending probes to other solar systems, It may be easier to build large telescopes that take advantage of the gravitation lensing of the host star. Considering we can already determine the composition of extra-solar planet atmospheres, an advanced alien civilization could possibly have enough telescopic resolution to map the earth. Considering the Earth has hosted life for at least 3 billion years, if there is advanced ET out there, they have probably known about the Earth for a long time. I think this increases the probability of a probe watching us from our own solar system. Perhaps news of human civilization is on its way to the host star right now, or maybe civilizations are “flash in the pan”, and none are around to watch. The most valuable information ET or a probe could give us is; their interpretation of the fundamental laws of nature, and the location of known planets with life in the galaxy. If they would be motivated to provide with that information is another issue, I think a “hands off” policy is most likely.

    So if advanced alien civilizations exist, they are probably watching us from a distance. And if they are, how tragic it would be for them to watch us trash our only home, before they could even send a message to us.

  15. Torbjorn Larsson OM says:

    not the sort of thing tea bagger types are eager to fund.

    Sorry, I’m not familiar with that brand of politics (IIRC US terms correctly). My point, which I believe you acknowledge here, is that probes are expensive. That will work against them under any politics or economics if there are alternatives.

    At the end of it all we might wonder if all our observations of the universe, study and theoretical understandings are just howling at the moon.

    I think that is too pessimistic. The reason we, as I believe, don’t know enough to answer Fermi’s question with something approaching a testable theory (outside perhaps of the closest stellar neighborhood) is that we haven’t tried to mount the effort to colonize space.

    If we do, we would know more about the feasibility of long lived societies of technological civilizations. (Since we would form such a loose knitted group inside the solar system.) We would also start to colonize nearby star systems as the societies would expand through the Oort cloud and beyond.

    I keep remembering one of the comic xkcd’s graph of the universe, where the logarithmic distance (but not the gravitational energy effort) makes the largest jump for the Moon. When we have colonized that, exponential population and technological progress should make everything else a piece of cake. 🙂

  16. Torbjorn Larsson OM says:

    Note on my last comment: Of course when colonies expand beyond the solar system they will no longer be loosely knitted, as distances would prohibit sensible economics. They would be colonizing ships, literary if inhabiting asteroids, sailing to distant harbors.

  17. @Duncan Ivry
    Thanks for your kind comment. I enjoy geeking out on the alien space probe issue too – but you put your finger on a key theme of the article.

    @Jlazor
    Not sure you could use a host star to visualise its planet by gravitational lensing – I think you need more focal length.

  18. Lawrence B. Crowell says:

    You basically need a better lens, or more gravity, for such a short focal length. The effective Lorentz contractions are not enough to get much serious lensing action.

    The problem with the theme of the article is that is about as probable as our sending Bracewell probes and the like. The one book in the Bible which does say a lot about the human condition is Ecclesiastes. Essentially the problems we face today are the same as they ever were, but we do manage to magnify them and make them more complicated. “There is nothing new under the sun” Ecclesiastes. In some sense it is sort of true or en francaise “Plus ca change, plus ce l’meme chose.”

    LC

  19. Uncle Fred says:

    @LC

    Interesting idea about Bracewell Probes. I like this idea as it seems to offer the most probable chance of comparing our knowledge with a present or future civilization. I imagine such a machine would need to be artificially sentient, so as to maximize the potential of 2-way communication. I would be particularly interested if such a sentience was programed to look for common knowledge (i.e. some variant of math/physics).

    However, I am unsure any Bracewell type probe would make it a priority to share its knowledge with us. Moreover, this posting reminded me of such Prime Directive styled episodes as Voyager’s “Friendship One.” In that episode the database of a deep space probe shared nuclear and antimatter tech with a pre-warp civilization. As the story goes, the technology set in motion a chain of unintended events that threw that civilization back into the stone age. Perhaps we have to consider what a not so rosy 2001 Odyssey encounter may bring for the lesser civilization.

    Lets speculate for a moment:

    Would a Bracewell probe somewhere around our Solar system be that surprising? I don’t think it’s a great stretch of the imagination to assume that an Alien civilization is/was aware that Earth has a complex biosphere. As it stands now, we are not that far off from detecting other similarly sized planets. We would surely read the atmospheres for signs of the same chemical imbalances that have graced our planet. Surely the evidence of Earth’s biosphere has had the time to travel across the galaxy (correct me if I am wrong). Earth may very well be a target of interest and be under observation.

    So lets assume some alien culture is using Bracewell probes to collect and transmit information. What steps could we take to test this hypothesis? If we were to look for such a device(s) in our local space, where would we look? What would be the best locations in the Solar System to observe the Earth, yet remain hidden? What kind of obstacles are we aware of in physics that could be used to conceal such contraptions? carefully arranged sequences of meta-materials designed to fool all manner of wavelengths simultaneously? How would we counter such technologies and force a detection or a response?

  20. Duncan Ivry says:

    @ Lawrence B. Crowell

    An interesting quote: “There is nothing new under the sun”. As far as I can see remarkably many comments on the web show the attitude expressed in this statement (by the way, I don’t say, you are sharing this attitude). If I compare our modern human world — differentiated societies, advanced sciences, sophisticated technologies, resourceful arts — with the human world, say, 2.000, 5.000, and 10.000 years ago, then I see many — really many — things being completely new.

    I don’t want to insult anybody, but it would be ridiculous saying — as just two examples –, that the theory of relativity and quantum mechanics are only some kind of repetitions or rearrangements of ideas which have already been there. I know, there are indeed some “problems we face today” that “are the same as they ever were”. But talking about “the human condition”, even the so called “old greeks” — at least cultural forefathers of the western culture — handled *some* aspects of the human condition substantially different than it is done today in Europe and Northern America. When I look at the old Grecian tragedies, I would even say terribly different.

  21. Lawrence B. Crowell says:

    I believe it was Albert Einstein who said something life, “Everything has changed except man himself.” That is the main point of “nothing is new under the sun.”

    The point of a Bracewell probe is to communicate one way. If a bio-planet is detected around a star a Bracewell probe is set to wait out the long stretches of time until it detects radio transmissions from the bio-planet. This might take tens of millions of years, so this probe requires some design capable to enduring those time frames. That is not an easy job. Spacecraft last at most a few decades. Then once the AI systems on board begin to detect radio transmissions of sufficient sophistication it announces its presence. It then begins to transmit information in some form of universal code, say the quantum error correction code M_{24} or a Goppa code based on elliptic curves or projective/algebraic varieties. The point would then be to communicate our knowledge to whatever ETI there might come into existence around this planet. I estimate there might be several thousand bio-planets in our galaxy, and we could end up detecting half of these. It is highly unlikely any of them has ETI coincident with our being here.

    I increasingly suspect that intelligent life that is technologically capable is not very long lasting. Evolution selects for organisms which are optimal energy exploiters, and I suspect that in the case of intelligent life this leads to the sort of eco-spasm morass we see unfolding around us. Of course I can’t know that is a general rule, but there is no evidence for ETI super-technology activity anywhere in the universe, such as Dyson spheres etc, and clearly there has been no major ETI activity on Earth. Yet maybe there is a Bracewell probe sent by some long gone ETI lurking in the solar system, or nearby space, and it might announce its presence in a fashion similar to the lunar scene in “2001 A Space Odyssey.” We would then download its data and compare notes.

    LC

  22. Duncan Ivry says:

    @ Lawrence B. Crowell

    I think that intelligent life will be very long lasting, because that’s what “intelligence” is about, especially solving problems and learning from experience. I’m optimistic.

    “Evolution selects for organisms which are optimal energy exploiters …”
    If you mean biological evolution, then your statement isn’t implied by the usual definition, and, as far as I can see, it’s no observable fact, and above that, it’s not necessary for evolution to work successfully.

    A minor point: “Man” *has* changed, e.g. most Europeans have a relatively new gene which enables them to drink cow’s milk, whereas most people from China can’t. Banal but true.

  23. Uncle Fred says:

    Just a quick factual corection:

    “A minor point: “Man” *has* changed, e.g. most Europeans have a relatively new gene which enables them to drink cow’s milk, whereas most people from China can’t. Banal but true.”

    This is an old European wives-tale. I lived with a number of Chinese during my University years (both Northern and Southern Han Chinese students) and they all were perfectly capable of drinking milk. Eating dairy products is just not something mainstream in Chinese culture.

  24. Duncan Ivry says:

    Uncle Fred: “I lived with a number of Chinese during my University years … and they all were perfectly capable of drinking milk.”

    How could it be different: somebody knows somebody 😉 Through my work, I also know some Chinese capable of drinking milk. But this is not the point, and a small number of counter examples says nothing against a statement about *most* people.

    But if you don’t like my example, there are other genetic differences between certain human groups, and genetic changes which occured in relative recent times, especially with respect to the immune system. What I got from my readings is, that homo sapiens *did* change in rather recent times, that the human immune system did evolve and continues to evolve, and that the human immune system and pathogens coevolve. E.g. some retroviral human pathogens, including HIV, crossed into human population only recently.

    There are geographically restricted patterns of selection in humans. Signatures of positive selection were found in population exposed to malaria. Several alleles common in West Africans but rare in other ethnic groups are associated with protection from severe malaria. A certain allele has been selected in Europe. It confers resistance against HIV-1 but was selected not against HIV, which has arisen as a human pathogen only recently, but against some other infections such as bubonic plague or smallpox.

    But, as I said, a minor point.

  25. Lawrence B. Crowell says:

    To be optimistic let me assume we humans manage to get our affairs in order to survive as a technological species for another 1000 years. This will mean that our footprint on the timeline as a technological species is about two millionths of the time complex life has existed here. That is a very small fraction. Now if there are say a few thousand stars in the galaxy we can use that to estimate the probability for the occurrence of an ETI now. As a simple model I will use Poisson statistics which is

    P(n;L) = L^ne^{-L}/n!,

    for n the number of occurrences of an event, and L the expected occurrence of an event in a given interval. We use n = 1, the known number of outcomes (ourselves). The L is then the above fraction on the timeline L = 2e{-6}. we have

    P(1,L) ~ 2e^{-6}, exp(L) ~= 1

    For n = 2, assuming there exist another ETIs in our galaxy now gives us

    P(1,L) ~ (2e^{-6})^2/2! = 2e^{-12}

    And you can continue on with this and find that the probability rapidly falls down. You can play with other timeline “footprints.”

    Given that we human beings are on course to drive half the species on this planet into extinction this century, which amounts to a K-T level extinction on its own, suggests that our tenure on this planet may not be that long.

    LC

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