Monday, 1 April 2019

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?


Sigmund Nastrazzurro said...

PS. I guess I should explain my long absence. I will shortly!

Anonymous said...

this may seem off-topic, but do you have any animations of a hexapod gait in a six-legged creature with longer, more slender legs? the example on the furaha site, the marshwallow, is stout and short-legged like a hippopotamus, and while the gait patterns we see there are definitely interesting-looking i'd love to see how those would work on a skinnier, deer-like hexapod.

Sigmund Nastrazzurro said...

Anonymous: I used to have those animations, but they were done a long time a in a language calles BBC Basic, and I only rabnsered one or tow to windows. But hexapod gaits are a main reason for the long delay. I wish to redesigns them completely, and that is not strightforward. I aim to discusss that in more detail in the next post.

Anonymous said...

Found this gif of a galloping hexapod from jayrockin in tumblr. It seems that the front and hind legs move simultaneously while the middle legs, spaced wider apart, swing outside the other legs and oppose them in movement, creating a smooth run with the legs not hitting each other.

That said, I wonder how this would apply to an eight-legged creature such as the Thoats? Would it basically double up the middle legs? Would the fourth pair also be widely spaced to avoid hitting the third?

Sigmund Nastrazzurro said...

Anonymous: It is a nice animation. I think I would call it a 'bound' rather than a 'gallop', but words for tetrapodal gaits need not be b-very useful for hexapod gaits. I have also use the idea of offsetting legs to avoid them bumping into one another. Hexapods use it, and so do rusps.
For thoats that would be a bit more difficult but not impossible: you could have the second or thoird pair of legs be the widest one, and the ones in front or back use a narrower track the further they are ways from the wides pair. An alternative is alternating track widt: the first and third pair use a narrow track, and the second and fourth a wide one. Again, that's what some rusps do.
Another way, and this is nothing new since you can see dogs usning it, is to skew the body a bit, so it is held at an agle to the direction of movement. Anatomically you can then have all legs in line, but funtionally they would be staggered. Some thoats might prefer left angling, others right angling...

Anonymous said...

a fine delving into the mathematics of alien life, with the Seager and Nastrazzurro Equations both giving so much new food for thought to us all. super work on all of that, and on whats to come.
-anthony docimo

Sigmund Nastrazzurro said...

Anthony: thank you!

Petr said...

This was a fun read! I really like this sort of musings. I a firm believer in abundant Life somewhere out there as well.

I'll be here to read your next post about gaits! It was your analyses of various aspects of animal biomechanics that got me interested in this blog, so it's definitely going to be a fun read for me.

P.S. How is the book comic along? <3

Unknown said...

Petr: thank you! The book is coming along slower than before because of unexpected but good events made me spend my hours other than expected. I should be able to pick up speed again in a few months, and then I will also increase the blogging frequency. I think I have your email. I can explainmmore later when I aam back home again (I'm abroad now).


Anonymous said...

congratulations on the good things in your life

Sigmund Nastrazzurro said...

Anthony: Thank you; much appreciated!

Petr said...

Hello Gert!

No pressure, just asking to let you know I'm still excited for it, no matter when it comes! :)

Roelien said...

Hi Petr! I listened (thanks). Gert