Extraterrestrial life after the Drake and Seager Equations: the 'Nastrazzurro Equation'! (the what?)

In previous posts I discussed the Drake Equation (DEq) and the Seager Equation (SEq), and promised to expand those by presenting my own version, the Nastrazzurro Equation (NEq). Let's start with a quick refresher of the DEq and SEq. Both provide estimates regarding extraterrestrial life, but in different ways.

Frank Drake aimed to estimate the number of intelligent civilizations. Actually, the DEq was aimed at just one particular subset of alien intelligences, meaning those that we should be able to detect on Earth because the aliens in question live nearby and obligingly send out electromagnetic signals into space in very much the same way that we do. Quite a bit of effort is spent listening to the stars to find out whether anyone out there is actually doing that. Writing my post on the DEq strongly influenced my opinion on the matter: I do not expect this method to produce any exciting news anytime soon. The numbers seem to be against it: electromagnetic signals decrease with the square of the distance, so they become very weak even over short distances; short in the astronomical sense, that is. To detect such signals with our current equipment the strength of the signal would have to be ludicrously strong, making you wonder why anyone would want to do so. You may also wonder how long a civilization will keep on transmitting, which is an important factor in the DEq. Apart from the question how long civilizations last in the first place, there is added problem that sending out electromagnetic signals into all directions at once, as we do, seems a bit silly. If the message is meant for people on your own planet or in your own solar system, surely an advanced civilization can somehow direct the signal to where it should go.

Sarah Seagers' approach is quite different. Her primary aim is not aim to detect signs of intelligence. Instead, she wishes to study the composition of a planet's atmosphere by seeing how that atmosphere changes the light of the planet's star when it shines through it. If the atmosphere alters the star's light in a way that suggests metabolic processes, than life is the easiest way of explaining their presence. In other words, does the atmosphere host a biosphere? Just as people are trying to obtain factual evidence of alien radio signals, there will be factual efforts to seek for biospheres in this way. The 'Transiting Exoplanet Survey Satellite' (TESS) was launched in 2018, and will probably find lots of potential planets to investigate later. That 'later' means scrutiny by the James Webb space telescope, not yet launched. Here is some more information on that telescope from NASA. By the way, NASA asked artists and the general public to produce art for the occasion; one of the results is the poster above (here is a link to the art section). The James Webb telescope will apparently launch in 2021, so we might have an answer to the question 'Is there life out there?' within 10 years. National Geographic has some nice information on the search for extraterrestrial life and the methods to find out, right here.

Astronaut Bowman looking at the monolith. "Oh my god, it's full of stars!"

The current count of exoplanets is about 4000. That is impressive. Not so long ago the presence of planets outside our own solar system was completely hypothetical, and by now we have become accustomed to the idea that the universe is full of planets. I still find it exciting that that hypothesis is now a fact, but finding life -LIFE!- outside Earth would be news of a much larger magnitude. I doubt that life is as ubiquitous as planets are, but learning that there are planets with life should make people think a bit more about life on Earth. Perhaps they will become a bit more respectful of it (they had better). Finding proof of alien life would make me feel like astronaut Bowman in the book 2001, or the film 2010. He looked into the monolith drifting in space and exclaimed: 'Oh my god, it's full of stars!' Perhaps 20 years from now we can look up and say 'Oh my god, it's full of life!'. I guess I'm a romantic at heart...

Anyway, back to the equations: both result in estimates of the number of either civilizations or biospheres that we can detect. And there's the rub: detection! The DEq and SEq aim to obtain factual evidence. And that is precisely the difference with the 'Nastrazzurro Equation' that I propose here. Let me make it clear that I see the NEq as a fanciful thought experiment in science fiction; it is not a competitor of the serious DEq and SEq. If there would be a diminutive of 'Equation', I would use it (it might be 'equationicula', but that sounds as silly as 'equationette').     

So what does the somewhat arrogantly named 'Nastrazzurro Equation' actually do? Well, it utterly  and completely ignores any wish for actual evidence. That makes it science fiction. Of course, the whole subject of speculative biology is science fiction, even though I like my science 'well done' rather than 'rare'. I like films with alien intelligences in it, especially if these films also betray human intelligence, which is not a given. My main interest in all this is alien biology as a whole, and I can do without the intelligence. I would probably have preferred 'Avatar' to be a documentary rather than a drama. Actually, there is such a documentary, but it is only four minutes long.

The NEq deals with the question 'How many interesting biologies might there be out there?' At present, I will accept anything as 'interesting', such as a planet with microbial life only, although my interest might become less keen quickly. I would accept with unmoving spongy thingies on the sea floor, spending aeon after aeon doing a spot of quiet filtering. I would love things that jump, move and fly, but for now, any life will do. So: how much life could be out there?

Click to enlarge. Screen shot from this website

Actually, you can use the Drake and Seager equations to answer that question! For instance, take the Drake equation; rather than doing the actual hard work ourselves, let's use the nice program to do the calculations I used before, found here. The image above shows how it works: there are successive boxes in which you can fill in estimates.

• First, choose an overall setting such as "today's optimistic" and proceed. 
• We can leave the first four estimates as they are. 
• The fifth box asks for the percentage chance that life develops intelligence. We do not care about intelligence and we do not want that box to reduce the estimate, so we simply put in 100 (If we were to use a proper equation, this term would be left out). 
• The next box asks about the percentage chance that life can communicate across space, and we do not want that one either, so we set that to 100% too. 
• We then are asked to fill in the length of time that a civilization actually transmits signals. Here, we do have to fill in a number, but it should represent something else: it should be the length of time a planet harbours life. That's a tricky guess, but the number will certainly be much larger than the time a civilization is transmitting. But we can use actual data! Life has already existed on Earth for 3.7 billion years (3.7x10^9 years), and might exist until the conditions for life cease to exist, which might be in 2-3 billion years, according to Wikipedia. So we can put in 6x10^9 years as an estimate. Unfortunately, you will find that the programme does not accept such large numbers, so for now we just leave the setting at 10 million (10^7) instead of 6x10^9 and remember that the result will later have to be multiplied by 600. 
• The last box asks for the number of times a civilisation can redevelop. Here, we will assume that life needs to evolve only once, so we set that to '0' instead of  '3'. 
• Press calculate and get 18,900,000 planets with life in our galaxy, or, say, 1.9x10^7. 

We must not forget that the estimate of duration was 600 times too short, so our estimate becomes 11.4x10^9 planets with life in the galaxy. That is 11,400,000,000 planets. Nice! You will get other results, depending on the starting conditions, but the message is clear. But estimates need to be compared to something, so let's compare them to the number of starts in the galaxy. Here is a post by NASA from someone who tried to find out, and the result is 100 to 400 billion. Let's use a nice average of 250 billion, or 2.5x10^11. Our increasingly wobbly NEq tells us that that one in every 22 planets has life. Wow! 
 

Click to enlarge. From this website

How about the Seager equation? We can hijack that and turn it into a Nastrazzurro Equation too! Let's go for the "original Seager values".

• The first box asks us about the number of 'observable red dwarfs'. We do not care about 'observable', and we will also allow for other types of stars. Again, we need an estimate for the number of stars in a galaxy, and we can take the 250 billion estimate again (2.5x10^11). The highest settings seems to be 500,000, so let's remember that our calculation will be 500,000 times too low. 
• The next box asks for minimal disruptions. Let's leave it at the original 20%. 
• The next box concerns the percentage that can be observed. We wish to ignore that, so put it at 100%.
• Let's leave the estimate for 'rocky planets' as it is, at 15%. 
• Let's set the percentage with life to a low value of 1% as per the original values. 
• The next one is about detectability again, so that becomes 100% for 'omit this box'. 
• We press calculate and get 15,000. 

That's not very much, but we still had to multiply the number by 500,000. So now we get 7.5x10^9 planets with life. That is one in about 33 planets. Still wow!

So this is the result of the official 'Nastrazzarro Equation' for the number of planets in our galaxy with life on it. It is a bit silly but not idiotic. After all, it is merely a simplified form of the Drake and Seager equations. It only contains one factor not present directly in the DEq and SEq and that is the number of stars in the galaxy. Here's an interesting twist: the NEq reduces the number of parameters in the DEq and SEq, and all these factors have a very large uncertainty. So, and I rather like pointing  out this somwewaht cheeky observation, by reducing the number of factors the Nastrazzurro Equation can be said to be more precise than its more serious predecessors. Well, perhaps 'less immensely uncertain' is probably a better term...

A megarusp; click to enlarge; copyright Gert van Dijk

What I like about all this is that The Nastrazzurro Equation suggests that there is room for something like a 'woolly haired shuffler' somewhere in the galaxy; there is room for rusps too, and spidrids, and, well, all of it. Not so bad for a thought experiment in speculative biology, is it?

Equations II: The Seager Equation

Click to enlarge; composite of web photo with painting by Gert van Dijk

The Drake equation, discussed recently on this blog, provides an estimate of how many communicating civilisations there are in our galaxy. It does so by multiplying a series of factors; none of these is rock solid, so some say it is basically guesswork. That is true, but in the absence of hard facts an educated guess is the best evidence there is. The nice thing about the Drake equation is that it in essence falsifiable, meaning that it is, at least in theory, possible to say whether there are such civilizations or not. In theory, that is, because one of the two possibilities is that are no such civilizations, and it is usually much harder to prove the absence of something than its presence. If someone in another solar system one day decides to answer our interstellar call, for instance to ask mankind to please turn the volume down, or to stop pestering them with unwanted phone calls in the middle of dinner, then we will know for certain that there is someone out there. But at present we have not received any signal, which tell us precisely nothing. It is like fishing: as long as you haven't caught any fish, you cannot conclude there aren't any. Only when you've caught one can you say that there are fish (or, more precisely, that there was at least one fish; you may just have exterminated the species).

Habitable zones (from https://www.saraseager.com/)

Sara Seager, an astronomer at MIT, proposed a different approach. If you Google her you will find many entries, among them her own website. Her reasoning rests something much more basic then intelligent being using radio signals: is there a biosphere? Her idea starts with the concept that life requires liquid water, an concept that certainly holds water (sorry for that one). Liquid water requires a planet in the habitable zone at the right distance from its star. What I learned from an overview of the conditions under which you might get liquid water is that there might even be liquid water on runaway planets that are no longer circling a star. Anyway, take a planet, add life, stir and wait, and you might get a biosphere. It is wise to search for stars with a nice quiet long term behaviour, so the stars do not cook their planets halfway down the line. Lifeforms have metabolisms, and spew out interesting gases that provide a 'biosignature' in the atmosphere around an alien planet.

Life on Earth certainly altered the atmosphere. At one point there was a nice community of anaerobic organisms quietly doing their thing, and then some new-fangled intruders called 'plants' starting using a highly polluting process called photosynthesis, with a highly reactive dangerous poison as a by-product: oxygen. Plants may have caused the very first mass extinction. Later on, animals learned to control how to burn stuff slowly with that oxygen, making a dent in the amount of oxygen, but not a large one, so Earth's atmosphere now still consists of 20% oxygen. And that can be measured from afar.

Click to enlarge; principle of spectroscopy on transit signal

Unfortunately, the detection is not easy. The method Seager proposes rests on planets passing exactly through the line of sight from Earth to the planet's star, so they appear to transit the disk of that star. That process works well and has already resulted in the discovery of many exoplanets. The TESS satellite was launched in April of 2018 to find many more. When the planets pass the star, they alter the composition of the star's light, and that change tells you something about the planetary atmosphere. Of course, not all planets happen to pass through that line of sight, so only some are observable this way. There is another problem: many biosignature gases are destroyed by ultraviolet radiation from the star, reducing their amount. These gases will be easier to detect if they are not broken down by UV, which is why Seager proposes looking at M-type stars (red dwarfs), because that live long and put out little UV. The latter job is to be done by the James Webb satellite, to be launched in 2021 (probably).    

Here is the Seager Equation:

N = N* FQ FHZ FO FL FS

* N is the number of planets with detectable biosignature gases
* N* is the number of stars within the sample
* FQ is the fraction of quiet stars
* FHZ is the fraction with rocky planets in the habitable zone
* FO is the fraction of observable systems
* FL is the fraction with life
* FS is the fraction with detectable spectroscopic signatures

If you study the parameters, you will see that several factors have to do with the 'detectability' of a biosphere. That holds for the fractions that concern 'quiet stars', 'observable systems' and detectable 'spectroscopic signatures'. Those fractions decrease the total number appreciably.

Click to enlarge; from: https://informationisbeautiful.net/visualizations/the-drake-equation/

But what is the number? Luckily, there is a very nice website allowing you to play with all the parameters in both the Drake and the Seager Equations, so you can see how they alter the final estimate. The settings shown above are for the "today's optimistic" option. Pressing calculate will give you 750 planets, while  the "Seager original values" only give you 0.45 planets. Running the Drake equation with the original settings results in 10 communicating civilizations in our galaxy. Note that the drake and Seager equations rely of completely different detection techniques, that in part explain the differences.

Does it matter for speculative biology? Well, you could say that speculative biology has to start with astronomy, so yes. In the last of these 'equation' posts, a forthcoming post on the 'Nastrazurro Equation', I will try to apply all this astronomical reasoning to speculative biology in another way. Soon. Probably.

Equations I: Drake's equation

People with an interest in speculative biology will probably know Drake's equation well. It describes how many civilisations in our galaxy are at present broadcasting their existence by emitting electromagnetic radiation into the universe. If you are only interested in the purely biological side of speculative biology, then alien intelligence might not appeal to you very much. Still, it makes sense to think that any biological intelligence will be deeply shaped by the specific biological background, so alien intelligence is a part of speculative biology (probably until that in turn gives rise to machine intelligence; would that reflect its maker too?). I aim to write two or three posts on the biological evolution in our galaxy, starting with Drake's equation.

I do not have that much affinity with speculative intelligence. I once started to evolve an intelligent species on Furaha. The creature was derived from hexapod predatory stock, so its forelimbs were not used for locomotion, as an example of centaurism. Most such 'neopredators' evolved their front limbs into clubs or spears, as can be seen on the Furaha website. These modified front legs lost all their toes in becoming spears or clubs, but the proto-intelligent species belonged to a group of small neopredators that had in fact developed the grasping ability of toes on their front leg. This allowed them to radiate into a number of interesting shapes.

Click to enlarge; copyright Gert van Dijk

This old and rather poorsketch shows this putative proto-intelligent species. It evolved on an isolated island and was supposed to have gone extinct shortly before humans came to Furaha, say only 30,000 years before. There would be some evidence of shaped clay or other things suggesting that the use of purposely shaped objects. at the time of human discovery, the island's ecology was supposed to be devoid of large species and to have remarkably little diversity. The idea was based on the presumed history of Easter Island, as described by Jared Diamond in his book Collapse. The story holds that overpopulation caused the inhabitants of Easter Island to cut down all trees and to destroy their environment, and through that their civilisation. Easter Island, seen in this way, holds a mirror to all of Earth, telling us to stop and think what we are doing. While reading up on Easter Island, I found that  these depressing ideas have later been questioned, and the case of Easter Island has even been labelled as a story of efficient adaptation. The trees are still all gone, so I find this rather depressing as successes go. 

I had tucked these proto-intelligent species away on a remote island where they would provide the Furahan equivalent of Easter Island, providing a lesson without ruining the entire planet. I later felt that I did not need such a heavy-handed approach so I erased the story entirely.

Back to Drake's equation. Below is a text taken directly from Wikipedia. The equation describes the number of civilisations, N, with which communication might be possible. It is assumed to be equal to the mathematical product of the following parameters:

R, the average rate of star formations, in our galaxy,
fp, the fraction of formed stars that have planets,
ne, for stars that have planets, the average number of planets that can potentially support life,
fl, the fraction of those planets that actually develop life,
fi, the fraction of planets bearing life on which intelligent, civilized life, has developed,
fc, the fraction of these civilizations that have developed communications, i.e., technologies that release detectable signs into space, and
L, the length of time over which such civilizations release detectable signals.

N = R   fp  ne  fl   fi  fc  L

I confess that I always had trouble understanding why this product represents the number of civilizations that are transmitting signals now. In an interview posted here Frank Drake said he started with the rate of new stars being produced because the equation was based on a continuous production of new planetary systems. As a result, the number of detectable civilizations is proportional to the rate of star formation. That makes sense, but still... Say that 10 stars are formed in the galaxy over one year. The equation ends with the average number of years that a civilisation actually transmit signals, say 300. The product would be 3000, modified by the other parameters. This suggests that the equation results in the total number of 'transmission years' resulting from one year's batch of new stars, and I do not quite understand why that would equal the number of civilisations that are transmitting right now. It seems more logical to start such an equation with the total number of stars in the galaxy and to modify that number. In fact, there are equations out there that do just that, and I found that there are several variants that are also called "Drake's equation".

Regardless of the different versions of Drake's equation, the message is clear enough: any estimate of the number of transmitting civilizations depends on a fairly large number of parameters, most of which rely more on guesses than on facts. The Wikipedia paper discusses that nicely, stating that N can vary from less than one to over 15 million. Drake himself arrived at about 20 civilizations in our galaxy. The more there are, the more you have to wonder why we never heard from them, which is of course well-known as Fermi's paradox. Here is a very thorough and entertaining book discussing 75 possible solutions to Fermi's paradox.    

Something like 20 civilizations distributed over one galaxy is not much. The average distance between such civilizations would be enormous, giving us little chance of hearing them. Note that Drake's equation is about how many civilizations are out there, not about our chances are of detecting them. Any considerations on actually detecting them must take the size of the galaxy into consideration. I could not resist playing with these ideas a bit.

Click to enlarge; copyright Gert van Dijk

The figure above shows a solar system containing a transmitting civilization. This civilisation started transmitting at some point in time, here just 30 years ago. From that moment on the signal travelled into space with the speed of light. For every year of time it obviously travels over a distance of one lightyear. After just 10 years the civilisation stopped transmitting. Perhaps the inhabitants found more efficient ways to contact people on their own planet than wasting energy by blasting a signal in all directions. Perhaps they went the Easter Island way, by cutting down all their trees, by nuking themselves to oblivion, by using creative biological weapons, or perhaps their successors, machine intelligences, decided they did not want pets. Whatever happened, a shell of transmissions with a thickness of 10 lightyears is still expanding outwards at the speed of light. The signal strength will decrease quickly, as it is governed by the square of the distance (see here for an explanation, on sound rather than electromagnetic radiuation, but the principle is the same). I tried to find information about how far the type of unfocused signals earth sends out might be received with current equipment; here is one source saying that 21 light years is optimistic, which is not much at all. Another source, from a senior SETI astronomer, states that detecting Earth from 'a few hundred light years' require an antenna the size of Chicago. That's impractically large...

Here is a simple model of a galaxy with most stars in the middle. The image spans 1,500,000 lightyears horizontally and vertically. Over a span of 100,000 years, civilizations evolve and transmit for a while, in this case for any duration between 0 and 5000 years (as longer as all of human history). The thickness of the expanding rings show the duration the civilisation was transmitting. I assumed their signal could just still be detected at a distance of 25,000 lightyears, requiring fantastically sensitive devices. The brightness of the colour indicates signal strength: at 25,000 lightyears it fades to nothing. Note that signals can only be detected in the coloured rings themselves, not in their blank interiors. The result is clear: the total area of the galaxy that lies in a ring is very small, and those are the only areas where transmissions can be picked up.

 
Here it the same scheme, but with a shorter duration of transmission and a smaller distance over which a signal can be detected. There are thin small shells here and there, but you have to look carefully or you will miss them altogether. This is still a very optimistic vision, I think. If there are just 20 transmitting civilisations that require a ridiculously large antenna to be heard seems to mean that it's not surprising we haven't heard anything yet. But there is Seager's equation:  looks at the problem in another way, so that's one I will have a look at in later post.