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.

Furaha in ImagineFX

ImagineFX is a Bitish magazine devoted to art in science fiction, fantasy and gaming settings. Its webiste is here, and here is its YouTube channel. Most of the content is about digital painting, but they also discuss 3D applications, a bit of hardware and conventional art.

They devote several pages to work sent to them by readers, and so I decided several months ago to try my luck. I sent five images with a bit of text and waited. I wouldn't write this if the result would have been 'Thank you but no'. So, some as yet unseen images of Furaha will feature in issue 168 of Imagine FX, that will go on sale in the UK on Friday 2nd November (I think that this is the December issue, by the way). I was informed that that issue will reach the US, Canada and Australia three weeks after that date.

Click to enlarge

I haven't seen the issue yet, so I have no idea whether they will devote one or two pages to my work nor which paintings they selected. I just thought that those of you who absolutely cannot wait, and who live in the UK, might wish to know. The cover is shown above so you will know what to look for. I expect to get my own copy shortly, so I will probably write some more about it before the magazine becomes available beyond the UK.

Oh yes; a post on the 'Seager Equation' will appear this weekend, and one on the 'Nastrazzurro Equation' probably two weeks later.     

Back from TetZooCon

I am slowly recuperating from the TetZooCon event in London that took place on last Saturday and Sunday (that's short for 'Tetrapod Zoology Convention'). I had not been to a TetZooCon before, for the simple reason that the timing in October had always interfered with my work: October is a very popular month for all kinds of scientific conventions. But this time I had taken time off in October, and by pure coincidence TetZooCon happened to fall right in that period. I definitely will want to go to next year's TetZooCon. They're fun! I learned about whale population recovery, straight-tusked elephants, the influence of city lights on the biological clocks of birds, music in wildlife documentaries, and many, many other things. I expect that there will be a discussion of the programme on tetzoo.com, so I will not go into details here. I will just hint at one or two things.
  
I was very curious about the Palaeoart workshop. The programme stated talks by Luis Rey and Mark Witton, and there was a discussion in which John Conway and Bob Nicholls also took part. In this blog I have never devoted much attention to palaeoart, although I think it can fall under the heading of 'allied matters' in the title of this blog. After all, much of palaeoart is speculative, and in that sense it is part of speculative biology. Part of the discussion was about to which extent those who like art in general would also like palaeoart. Personally I doubt that: the admittedly little I have seen of the general art world suggested surprisingly closed minds, with some Art Schools not even deigning tot teach representational art at all. Do not even mention digital painting there; that seems to lie outside that particular micro-universe altogether. The discussion also dealt with the current preference for photorealism in palaeoart. Some of the photorealistic work done by experts in that field is stunning. But I grew up with the work of people like Zdenek Burian, who worked in a much more impressionist manner. The irony here is that, whenever I aim to do something in a Burian-like style, it always turns out much more photorealistic than I wanted to.

Click to enlarge; copyright Gert van Dijk

That twist brings me to the workshop itself: John Conway asked the participants to produce palaeoart in an art style that would be new and foreign to the artist, challenging people to use materials they were otherwise unfamiliar with. I found that so much of a challenge that I missed the first 10 minutes of Luis Rey's talk altogether (sorry). In the end, I used pastels, even though I stopped touching crayons, charcoal and similar materials as soon as my school teachers allowed me to let them lie. I chose to draw a triceratops in the style used by Stone Age painters, using an Altamira bison as inspiration. The coarse effects of the pastel really fitted the subject matter well, which was more luck than intention.

On Sunday afternoon Darren Naish led a discussion about speculative biology, with Dougal Dixon and me as speakers. Dougal was his usual enthusiastic self and did very well. He had brought along a model of Greenworld (for posts on Greenworld see here and here), as well as many sketchbooks of Greenworld, that were laying on a table so everyone had ample time to browse through them during the conference. I showed a 15-slide presentation of Furaha that contained nine paintings that had not been publicly shown before, so I wondered whether people would pick up on those (so far, I haven't seen them pop up yet). Because this was just a quick introduction I did not provide much in the way of background knowledge.

Click to enlarge; copyright Gert van Dijk

Here is a slide of a subject that was published before: it is part of the banner at the top of this blog, but the one here is a reworked digital version, while the one in the banner is still the old oil painting. Hexapods form the last group I need to do to complete The Book, taking up some 10 to 12 spreads. I am thinking of giving them a thorough makeover, with important changes to their jaws and leg structures.

I showed some animations that have been shown on these blog before such as the one above, but the bigger projection scale really helps. The one above is of course a short-cloaked cloakfish. Such animations take an enormous amount of time to make, and I had stopped creating them because of that. But one of the TetZooCons talks changed my mind: Fiona Taylor spoke about the music accompanying music documentaries, and made a very strong case that music adds to the image. So I will reconsider the feasability of creating a four- or five-minute documentary about cloakfish adaptive radiation one day after all. Perhaps there will even be a professional sound track. Don't hold your breath though, as producing even one scene takes an awfully long time...

Speculative Biology with Dougal Dixon (and me) at TetZooCon, London, 6-7 October 2018

Some of you may already know the Tetrapod Zoology blog written by Darren Naish. It has been hosted in various places over the years. It recently moved away from Scientific American to its own place, tetzoo.com. I recommend it to everyone who is interested in regular biology besides speculative biology. Actually, I suppose that everyone with an interest in speculative biology will also be interested in real biology. Darren regularly discusses speculative zoology too, by the way, so it's worth browsing through his earlier posts for that reason alone.

Click to enlarge

He also organises a yearly convention, the appropriately named 'TetZooCon'. I will simply quote from the TetZooCon pages to tell you what it is about:

Are you interested in animals, and specifically in tetrapods: that is, amphibians, reptiles, birds and mammals, living and extinct? Are you interested in their evolution, biology and diversity, in their portrayal in art, literature and fiction, in the animals of the distant past, in conservation, cryptozoology, domestication and, frankly, in just about anything relevant to the world of tetrapods? If the answer is “Hmm, I’m not sure”, you might like to go away and do something different. BUT if the answer is “Yes”, have you heard about TetZooCon? 

That should do it... This year it will be a two day event, for the first time. Although I had my eye on that convention for some time, this year is the first time that my schedule allows me to go and visit it. I already knew Darren from the World Science Fiction Convention in London, LonCon3, in 2014. Now, one thing led to another, and rather than just sit in the audience I will take part: on Sunday, October 7th, Dougal Dixon and yours truly will discuss speculative biology from 1400-1500 hrs. Afterwards there will be an opportunity for book signing by Dougal Dixon.

I hope to see you in London!

'After Man', by Dougal Dixon; a review with hindsight

The book 'After Man' is arguably the best-known book in Speculative Biology. It first appeared in 1981, so you may well wonder why I should choose to discuss a book everyone knows already, 37 years after its publication.

Well, a shiny new edition came out. It is a facsimile edition of the 1981 version, but with some changes. I still own the copy I bought in 1981 and could easily compare the two. The new version faithfully copies the monochrome sections at the beginning and end of the book that explain basic concepts such as the nature of evolution. These, printed on a somewhat coarse type of paper, enclose the heart of the book like slices of bread in a sandwich. That heart consists of 90 pages filled with illustrations in full colour, printed in much better quality on glossy paper. Even the page numbers match up perfectly.

The few changes are interesting. The introductory text has been updated in a few places, and these are indicated with a slightly different font, a nice touch for the bibliophiles among us. For instance, the old version states that early amphibians already had 5 toes on each foot, whereas the new version says that that pattern only emerged as the standard pattern after earlier experiments with other numbers.

Click to enlarge; copyright Dougal Dixon, with permission

The middle part of the book describes animals using ecological zones as a guiding principle, but Dougal Dixon has made two changes to the illustrations. These were originally done by professional artists and were based on sketches by Dougal. That process was not always easy, as Dougal explained in an interview with Darren Naish. I own some photocopies of early sketches for Greenworld that Dougal was kind enough to send me a long time ago, so I can say with confidence that he knows what he is doing when he sketches animals. I discussed Greenword, still only available in Japanese, here, here and here. Dougal gave me permission to use the drawing above to illustrate his own skills. These are of course predatory descendants of rats (falanxes) attacking a rabbit descendant, the rabbuck. Dougal was generally happy with the illustrators' work, except for two interpretations. In the new book he replaced the drawings of the reed stilt and the night stalker with his own drawings, and they indeed look better, in particular the reed stilt, that now is a lightweight and slender creature. I will not show them here; but leave them as an incentive to buy the book.         

I could stop here and consider the job done, but I have seen some critical discussions of Dixon's works, including 'After Man'. I sometimes think these criticisms are overly harsh and would like to add a bit of background to 'After Man', meaning the time in which it appeared.

Click to enlarge; Granada Publishing 1981

Everyone is obviously free to form his or her opinion on the matter, and let me stress that I have my doubts here and there too. As an example, let me discuss the night stalker in some detail. It is a fierce predator, descended from a bat that has given up flight and is a nocturnal terrestrial hunter, using sonar to find its prey. It walks on its front legs and uses its hind legs to catch prey, for which they arch over and outside of the front legs. The image above was copied from the dust cover of the 1981 edition, showing Dougal with a model of the night stalker. Dougal is very good at making such models by the way: I saw several of them for myself on the occasion of the Loncon3 science fiction convention (discussed here by Darren Naish and here by me).

Let's follow the scenario of evolving a land-living bat with specialised grasping legs. I would not expect all those features to evolve at once, but that one would set the stage for the next. (Whales did not evolve baleens the minute they entered the water, but had to become proficient swimmers first.) I expect the first step in that process to be that the bat gives up flight and becomes an animal walking on all fours. That will force quick changes to both the front and hind legs. I would expect that freeing one pair of limbs to catch prey and using the other legs to walk on to evolve only after that. (That, by the way, would be an example of 'centaurism'; see earlier posts here and here). Which pair of legs would become grasping limbs? My guess would be the front legs, because they are closer to the prey. But if the hind legs would be used for some reason, would they reach forward on the outside of the front legs, or in between, where the entire hind part of the body might also be swung forward to extend the reach?

My second doubt concerning the night stalker is that I do not think that sonar works well for a ground-based predator, as I explained in a series of earlier posts (here, here and here). Basically, using sonar is the opposite of stealth. I would therefore expect the animal to redevelop its eyes, keeping its extraordinary hearing as a passive sense. So my personal variant of a bipedal terrestrial predatory bat descendent would walk on its hind legs and not use sonar. I think it would be fairly likely, but it would also be much more conservative and also more boring than Dougal's night stalker...  

By now you may feel that all this criticism of what is probably the most famous creation of 'After Man' is a very odd way to defend Dougal's work. But there is a point here: it is very unlikely that anyone would have been able to raise such specific and detailed considerations in 1981. Such a person would at the time have to have been a professional biologist, not a member of the general public. I am not a biologist, and I can only raise such criticisms now because of several reasons. The first is having ideas; even though I thought hard about the use of sonar for a land-living predator, someone had to have to come with that idea first, and that certainly wasn't me; it was Dougal. The second reason is that you need knowledge to think matters through; to learn, there must be something to learn from.

Suppose you find yourself in 1981 wanting to know more about some biological subject, say sonar, the evolution of whales, or any specific animal group such as 'mudskippers'. You go to a book store or ask your local librarian, who will probably come up with the same one or two books every time, leaving you both frustrated and ill-informed. Anything specific would require access to something like a university library, and even there you would on some subjects find less information than you find on Wikipedia now. There was hardly anything to fill the gap between a general interest and professional levels. The information that is readily available now with a few clicks was either non-existent or almost completely inaccessible in 1981. So what could someone interested in biology, palaeontology and science fiction find in 1981? Well, disappointingly little:

• On the dinosaur front, you would not be happy. There were stirrings of the coming 'Dinosaur Renaissance' (Bakker's paper from Scientific American from 1975 can be found here). But Robert Bakker's book 'The Dinosaur Heresies', that spread the message that dinosaurs were lively, athletic and interesting was still five years into the future in 1981. The most spectacular book on past life that you could own at the time was probably 'Life before Man', illustrated by Zdenek Burian. It had been around at least since 1973.
• Speculative biology did not really exist as such. An early work such as Stümpke's 'Snouters' (1957) would remain unknown to you, unless someone book dealer would decide to distribute a new printing, so you could find out about it, by chance, by browsing a book store. I found one in 1983 (under its original German title of 'Bau und Leben der Rhinogradentia'). I later wrote about them here, here and here.            

That's about it. There was no information at your fingertips. If you wished to learn something from an author, you wrote them a polite letter and hoped for the best. No internet, no Google, no computers (well, except for the Sinclair ZX-81 with a 1Kb memory). The lack of information back then would now feel like a near vacuum, and as a result even the most interested people could not possibly become as well-read as many people on the forums now are. It was in this vacuum that Dougal Dixon used his knowledge of evolution and zoology to come up with not just one odd animal, but a whole book full of them. He in fact largely defined speculative biology with 'After Man'. It was an extraordinarily creative production at the time of its first appearance, and that is the only time to judge originality and creativity. 

Is it cruel for giants to ride mammoths in Game of Thrones?

In season 4, episode 9, of Game of thrones (GoT) there are several scenes of tame mammoths: in one, a mammoth is being ridden by a GoT giant, much as a man would ride a horse.

Click to enlarge; still from GoT; colours changed for clarity

When I saw that scene anew, my mind immediately came up, uninvited and unasked for, with the question whether a mammoth could in fact carry a giant. Is that a silly question? Of course it is, but this entire blog is to a large extent about serious answers to silly questions, so there you are.     

Unfortunately, an internet search for questions such as 'How many giants can you fit on a mammoth?'  did not provide anything useful. That was disappointing, but perhaps publishing this post will change that sad state of affairs. Forced to come up with an answer myself, I divided the problem in parts. The first asks 'What is the mass and weight of a GoT giant?', and the second concerns an educated guess at the load-carrying capacity of a mammoth.

What are the mass and weight of a GoT giant?
I had already answered that question in a post built on well-known animal scaling laws, but a later image made me think that the giants were well over twice as tall as a man, so I looked at the question again.

The basic principle is simple: if you scale an animal up with a factor x, its weight will by multiplied by the third power of x, but the cross section of its bones is only multiplied by the square of x, not enough to deal with the increased mass. Bones of large animals must be relatively thicker than of small ones. In that post, I scaled the height of a 1.8 m man weighing 80 kg up by a factor 2, but the width and breadth had to be multiplied not by 2 but by 2.8, which I rounded up to 3.0. The giant's weight became 80 x 2 x 3 x 3 = 1440 kg.

Click to enlarge; still from GoT; colours changed for clarity

In the new scene, shown above, the giant certainly seemed more than twice as high as the men around him, but foreshortening made it difficult to be certain. But if you understand perspective a bit you know that you can use vanishing points to put things into, well, perspective. The troops are standing in fairly orderly lines, allowing some lines to vanishing pints and a horizon to be drawn. Vertical lines indicate the height of the giant and a man. Once a man and the giant could be placed on the same set of lines to a vanishing point, the job is nearly done. The height of the man is given by the line AB. Using the perspective lines AB can be projected as A'B' onto the height line of the giant. All that is needed then is to estimate how much taller the giant's is than A'B'. That was about 2.8 times, so if we take a 1.75 m tall man the giant becomes an incredible 4.9 m tall. The range of 2.0 to 2.8 times a man is very large; either my estimates are off, or giants are very variable, or the makers of GoT were not too consistent with their special effects. I suspect the latter; the image at the top suggests that the giant is fairly small relative to the mammoth. Let's pretend otherwise.

Click to enlarge; copyright Gert van Dijk

Does that affect the giant's mass to a relevant degree? Yes, very much so. The graph above shows the mass of a giant for a range of scaling factors, from 1 to 2.8. Note that the scaling factor of 1 represents the original man at 80 kg. In these estimates the height of the giant is 1.75 m multiplied by the scaling factor, and the factors for width and breadth are adapted as explained before, but without rounding up (for the mathematically inclined, their factor is the height scale factor to the power of 1.5). For a giant twice the height, we get a value of 1280 kg (less than the earlier 1440 kg because I did not round up). A factor of 2.8 results in a staggering mass of 4917 kg. That is a lot of giant...

But my estimate may have been off, so let's also consider height scale factors of 2.0 and 2.4, resulting in masses of 1280 and 2654 kg. Gravity in GoT is probably the same as on Earth, as people move just as they do on Earth, so we step from mass to weight as we do on Earth (meaning without thinking about it).

Click to enlarge; left part: Gert van Dijk; right half: Mauricio Antón

I assume that GoT mammoths are the same size as Earth's woolly mammoths, because I could not find a scene that had mammoths standing conveniently still next to a group of people. Scenes of mammoths with people around them in GoT do not suggest that the mammoths were larger than elephants. I took an excellent scale drawings of extinct elephants, done by the illustrator Mauricio Anton, and put the modified giants next to them. The image was copied from this book. Mr Anton often poses animals next to another, with a background of squared giving the scale. That works very well so I copied the idea, with gratitude, and made a similar image for giants to the same scale as Antón's picture of elephants. Mind you, the left elephant is your prototypical mammth.

The giants are very, very large, aren't they? They can actually look over a mammoth. It makes you wonder whether they could in fact push them over if they wanted to...

How much weight can a mammoth carry?
The only way I could think of to answer this question was to see how much weight living elephants can carry. African elephants are not very cooperative in this regard, but there are data on Asian elephants. Apparently some people are worried that putting tourists on elephant's back harms the elephants, and I found a detailed defence by a company doing just that, saying that their elephants, with a weight range of 2081 to 5000 kg, carry tourists and gear that together make up 4.9 to 13.0% of their body weight. They also state that elephants can carry up to 25% of their weight without discomfort, but that percentage is based on studies in horses. If you look up the article on 'pack animals' in Wikipedia, you will find numbers for camels, yaks, llamas, mule, horses and reindeer. If you try to compare those with typical weights of these animals, you end up with values of about 20-30% of the animal's weight. My guess is that the percentage should be lower for larger animals, because the safety margin might be smaller, seeing how their own skeletons already make up more and more of their mass as their size increases. So it is probably wise to restrict the load on a mammoth to a maximum of 20 or perhaps 25% of their body mass.

Actually, most species of mammoth were only about as large as a modern Asian elephant, and the maximum weight of those is around 5000 kg. Several sources state that the woolly mammoth was about the size of an African elephant, so male 'woollies' must have weighed up to 6000 kg.

Putting two and two together
So we have a 6000 kg big male woolly elephant, and we make it carry 20-25% of its weight, or 1200-1500 kg. Come to think of it, it may be wise to ask the mammoth to do that rather than 'make' it do so. A discontent mammoth might cause all kinds of unpleasantness. Our giants with height scaling factors of 2.0, 2.4 and 2.8 weighed 1280, 2654 and 4917 kg respectively. Obviously, only very small giants should be allowed to ride mammoths ('small giants'??). Putting a really large giant on a mammoth would definitely constitute cruelty to mammoths. This must not be allowed to continue!

Mind you, with only one season left for GoT, and with the state of general carnage we have seen so far, all giants may by now have been recruited as soldiers in the army of the dead. Without mincing words, they are all zombified; it's sad, actually. Mammoths may all be zombified too, to the very last calf, which I personally find even sadder.

But the good news is that zombified mammoths probably are beyond suffering, so animal welfare concerns probably do not extend to dead mammoths. That's a relief!     

Postcard from Furaha

It took longer to get back to blogging than I thought, for several reasons. As usual I had less free time than planned and a shoulder problem made painting and other computer work unpleasant. Last but certainly not least, we had such a long hot spell here in the Netherlands where I live that heat records were shattered one after the other. A few nights ago we officially had the warmest night in the Netherlands since official records started in 1854: 23.6 degrees. The temperature in my computer room reached 29 degrees... If I can't sleep, I can't write, paint, or even think properly. If the climate continues in this direction, we should stop calling ours a 'temperate' climate. Global warming anyone?

Anyway, I have worked on a painting, but extremely slowly. As I save the files often, I thought I could produce a quick post in the form of a 'making of' video. I will let the video do its own talking.
 

Click to enlarge; copyright Gert van Dijk

The video is small, so here is the last frame at a larger size. The painting is not finished! The potator ('Amnesialata blansjarii') still needs much work. I think I will morph it into a microrusp. Rusps do not actually have necks, but I thought it would be useful for a tree climbing animal to be able to move its head around freely. The rusp's snout will of course solve that problem to a large extent, but another way might be to recruit the first several body segements: they could become slender and lose their locomotor function, with perhaps some tiny dangling remnant limbs. I'll see. The bioluminescent stayways may reappear in the from of tetrapters. It is fun tying the various Furahan clades together, while keeping room for new developments.     
 
The sooner the weather normalises, the sooner I will be back with more posts. 

How do tetropters walk? (Tetropters IX)

In a recent post I showed my latest animation of tetropter flight, using a brightly coloured farfalloid species as an example. As I wrote then, the reason to get down to the nuts and bolts of tetropter anatomy and movement was that I am painting a few tetropters paintings.

Click to enlarge; copyright Gert van Dijk

Here is a small fragment of the latest one. I had given most attention to tetropter wing movement, but naturalistic paintings also require details about the rest of their anatomy, such as eyes, mouth and legs. The radial nature of tetropters is very reminiscent of that of spidrids; tetropters obviously share a common ancestor with spidrids. On the whole, tetropters are much smaller than spidrids. Whereas spidrids are in the crab range, tetropters are more like insects in size. The Furahan atmosphere is denser than Earth's, which makes flying easier. The tetropter respiratory system does not wholly depend on passive diffusion, so it does not form a crucial limiting factor. Some tetropters, such as the Red Baron shown earlier, are quite a bit larger than current earth insects. There may well be tetropter species in remote areas that are as large as the giant dragonflies from Earth's Carboniferous era. These areas have not been explored in detail yet: they are far away and travel is expensive.

Tetropters have eight legs, just as spidrids do, and their gaits are in many cases exactly like those of spidrids. There are exceptions though. Tetropter legs differ in some aspects from spidrid legs. The most obvious difference is that the legs of a tetropter need not be all alike. In contrast,  all eight legs of any spidrid are virtually identical. Again, this is a bit like insects' legs, that usually differ markedly in size and shape between front, middle and hind legs. This probably makes sense because these legs have different mechanical roles, whereas tetropters do not even have a front or a back. The asymmetry of tetropter legs takes a shape that is peculiar to their radial nature, and quite fitting: there are four large legs and four smaller ones, and they alternate: big, small, big, small, etc. Over evolutionary time, the differences have become quite marked in some clades. In predators such as the 'Red Baron' the outer ring of legs has gained a grasping function. In most species both the outer and inner rings are used for walking. Some say that the differences came about in response to a need to stop the legs becoming entangled; that sounds good, but spidrids do not seem to suffer from tripping over their own legs! Others say that the small size of tetropters means they needed legs that are splayed very wide to stop them being blown over by the wind. But why should that hold for just four legs? Sometimes we just do not know... (meaning I will shelve the question for later, or perhaps I will leave it unsold. There are many things unclear in Earth biology, so perhaps I do not have to explain everything).

Anyway, here is a schematic tetropter using the 'double table' gait. Its wings are neatly held in their vertical resting position. At any time there are four legs of either the outer or the inner ring on the ground. For a brief moment there are eight. This system is just as stable as the 'double tripod' of insects. There is little or no chance of falling. Note that the body wobbles a bit. I did that just so you could see that there is a joint between the 'corpus' holding the legs and mouth on the one hand, and the cephalothorax holding eyes and wings on the other hand.

   
This specimen proves that the gait can be a bit more fanciful than the 'double table' without destroying overall stability. You may also note that the joints of the legs are arranged in a different way. In the previous species, and in all spidrids, the angles between the three big leg segments always bend in the same direction, so the leg gets curved more inwards and downwards as you progress from the proximal portions near the body to the distal parts at the tip. In this particular species, the first joint bends in the other way. In earth arthropods you can easily find these patterns too.

Finally, here is a walking tetropter in which the joints of the legs of the outer ring all curve inwards, while the inner legs have yet another pattern, starting with a downwards followed by an upwards bend. The gait is somewhat complex as well, which I like, as it gives the animal a more biological feel.

So there we are; now I can safely paint an explanatory diagram explaining how tetropters walk. After that, it's back to 'toe studies' again. I must say I am distracted because I watched season 4 of Game of Thrones again. There is a scene in a giant rides a mammoth. Hang on; as I calculated earlier, such a giant should weigh about 1440 kg! Mammoths are big and probably strong, but that is some weight! How much weight can a mammoth actually carry? That is obviously a very silly question, but also one quite worthy of this blog. I may need to find out...

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.              

Ten years on

The first post of this blog was published on April 22, 2008, or ten years ago. I wrote several earlier progress reports. It is time for a new one, especially because of the festive nature of ten years of blogging. Well, more or less, because the rate of new posts has been low in the past few years. More on that later. 

Let's start with a comparison with 5 years ago, when I also wrote a progress report. Then, there had been 307,000 page views according to the blogger 'stats' page, and now the counter stands at 639,478 views. I am not altogether certain that all these visits represent actual people; perhaps there were bots  as well. What is certain is that I had written 197 posts five years ago, whereas the counter now stands at 233 posts, so it is obvious I wrote more posts in the first five than the second five years.  There were 1638 comments in all, and I must say that I enjoy the interactions. The comments have quite often made me think a bit harder about what the project, and gave rise to new animals on more than one occasion. Thanks to all who read my posts with such enthusiasm!

The 'stats' section also tells me what the most-visited posts were over these ten years. Here they are, with their previous ranking from five years ago between parentheses:

1. (1) Swimming in Sand 1: the Sandworms of Dune; 5 Feb 2011; 8854 views       
2. (5) A future book on future evolution from France; 19 Nov 2011; 6239 views       
3. (4) Avatar's 'Walking with hexapods'; 11 Feb 2010; 4862 views
4. (2) Warren Fahy's "Fragment"; 8 Aug 2010; 4010 views                   
5. (-) Future evolution from France: 'Demain, les animaux...; 30 May 2015; 3327 views
6. (3) A century of thoats; 5 May 2012; 2996 views
7. (-) Create your own planet (using Celestia); 13 Aug 2011; 2717 views   
8. (-) The anatomy of giants in 'Game of Thrones'; 11 Jun 2016; 2661 views           
9. (9) Ballooning animals and Newtonian fitness; 15 Jul 2011; 2338 views   
10. (-) Second part of a review of 'Demain, les animaux...; 13 Jun 2015; 1958 views   

There are four newcomers in the top-10, but it seems that the sandworms of Dune are unbeatable. My French friends Marc Boulay and Sébastien Steyer will be pleased to learn that their work occurs no less than three times in the top-10: first as an announcement in 2011, and then as a two-part review in 2015. I hope that this signals an immense interest in books on speculative biology, because that would be good more my own project: The Book.

Click to enlarge; copyright Gert van Dijk

Some of you may recall that I had announced that I would spend less time blogging to have more time to work on The Book. The graph above shows the cumulative number of blog posts in red, from 0 in 2008 to 233 now (the present one excluded), as well as the cumulative number of spreads in blue, starting in 2011. A spread is a two-page account of a species, a chapter introduction, or of any topic worthy of devoting two pages to. The number of spreads started in 2011 because I had made the switch to digital painting and started collecting the slowly increasing number of spreads in an InDesign manuscript. I am at present working on the fiftieth spread, so within a short while the manuscript will have exactly 100 pages. Not bad, hey?

But did the reduction of blogging benefit The Book? The two vertical red lines indicate the post in 2014 in which I announced a temporary stop, and the one in 2015 in which I said that I would stop blogging except for the occasional post. Have a look at the rate of increase of the two lines: the total number of posts rose much slower from then on, while the number of spreads rose appreciably faster. The rate of new spreads since then is about nine spreads a year, which is less than the 12 I hoped to be able to manage. But please remember that this is not a job and that each spread takes presumably 20-30 hours to produce. I you ever write a book, do just that: write it; don't paint it! Mind you, The Book does not consist of images only: there are over 32,000 words at present, which is the length of a novella.

I always aimed at something like 125 pages, simply because comparable works have such a number of pages. At present I think the number will be more like 130, but we'll see. The good news is that I expect that the number of spreads per year will increase, so producing the remaining 15 spreads shouldn't take very long. Mind you, 'not very long' should be considered from the perspective that such a project may take a few decades...              
    
Because this is the tenth year of blogging, I also aim to write a few extra posts this year. I think I will finally write the long-awaited post 'What are toes for?' There will also be posts on equations: the Drake equation, the Seager equation and possibly the Nastrazzurro equation...

From freezing the anatomy of tetropters to op art (Tetropters VIII)

Tetropters have been discussed in this blog several times. Eight posts were devoted to them (one, two, three, three bis that doesn't really count, four, five, six, and seven) and they were mentioned more often. In fact, they first featured in the third post ever, published on April 27, 2008. Attentive readers may note that the 10 year anniversary of this blog is coming up, and I intend to write more posts this year to honour the occasion.

Tetropters are flying animals with a radial symmetry, something that was not common at their time of invention, well before they featured in the blog. They fly with a 'clap and fling' mechanism, also used by various flying animals on Earth: the animal brings its wings together over its back and then separates them again, starting at the top. This apparently creates a lower pressure above the animal, which helps the animal to stay in the air. Earth animals, with their two wings, have one 'clap' in each movement cycle of the wings; Wikipedia has a short section on it. Tetropters have four wings and move them in such a way that there are two 'clap' events in every wing cycle. I was delighted to learn, years after their 'evolution' as Furahan animals, that someone had had the same idea but with the purpose of building an actual flying robot using the double flap and wing scheme. I wrote about that in this post.

At present I am working on the second of what will probably be three two-page spreads on tetropters. The first detailed paintings of a specific animal (or plant or mixomorph) always represents a bit of a crisis, as the characteristic features of a group, its Bauplan, have to settled for good: it has to be frozen. Tetropters had  four wings and I knew their movement pattern, but that left many other decisions to be made. How many eyes should they have and where are these eyes placed? They are presumably related to spidrids, so which features should they share? Should they have eight legs or four? If the mouth is placed at the underside of the animal, how does that reach its food? The list goes on. I have frozen the Bauplan of spidrids, cloakfish and Fishes I to VI in the past, so the process is familiar by now. I confess that I have kept one of the most difficult decisions for last, and that is the suspension system and leg anatomy of large hexapods: I wish to avoid a mere doubling of hind legs or of front legs, which is how most illustrators solved the problem of designing animals with six or eight legs (see my posts on Avatar and thoats).

The first decision regarding tetropters was that it dawned on me that I had not considered the etymology of the word well. The word is derived from the Greek roots for four, 'tetra', and wing, which is either 'pterux' or 'pteron'. In biology just the stem 'pter' is used often. So where did the 'o' come from? I guess I just used 'o' to string the two roots together, or perhaps because of an association with 'helicopter' (a combination of 'helikos', meaning winding, rolling, turning, and 'pter'). As an aside, the Lexilogos websites for Latin and Classical Greek are useful for such things). But as 'tetra' already ends in a vowel, no other sound is necesary to connect the two words, so 'tetropters' are now 'tetrapters'. In the posts I will stick to tetropters or other posts will be difficult to find.

Click to enlarge; copyright Gert van Dijk

Readers will be more interested in what the animals look like. Well, here is a drawing from the famous 'Field Guide to Imparian Tetrapters', showing the male and female forms of the 'Red Baron'. These animals are large, for tetropters that is, predatory tetropters that prey on other tetropters, catching them in flight. They have long wings and are very manoeuvrable. You may note that the outer legs have evolved into grasping limbs, leaving just the inner legs as a landing gear and to walk around on.

To help me get a good idea of tetropter wings in flight I dusted off earlier tetropter animation programs, relying on an unwieldy combination of Matlab, python and Vue Infinite. When I first made these programs I dreamed of producing 5 or 6 minutes high quality films; the one above was made with this idea in mind. Later I realised that these required considerable investments in time, time that might be better used working on The Book directly. So I gave up on nice backgrounds with leaves moving in the wind, etc., and just use animations as a scaffolding for the paintings.

This first animation shows a general undetailed tetropter in 'helicopter mode': the wings are relatively long, and when they move through their 90 degree movement from one clap to the next, they do not move down very much. The 'angle of attack', that is the angle of the plane of the wing compared to the direction of movement, is low. One extreme angle of attack would be a flat plane moving at a right angle to the wind, creating maximum drag but no lift. The other extreme has the plane moving exactly parallel to the wind: no drag, but again no lift. The optimum angle of attack should be one that for a given air speed creates the most lift for the least drag. This is also the flight mode for the Red Baron.

I have played with the structure of the wing, which is transparent with some bright red spots. The structure is much like that of insects, with a thin membrane, taut between 'spars' that give it its shape. There are two main spars to help control the curvature of the wings during flight. I tried to envisage completely unearthly spar structures, but all my attempts ended up looking like insects; let me know if you find a workable unearthly design. Note that the speed of movement shown here is not at all the natural one: for earth insects, wing frequency varies between 4 and 250 Hz, with low frequencies for large butterflies (I might write a short post on tetropter wing beat frequency taking air density and gravity into consideration).

This second example shows a 'rowing' mode of flight. Here, the wings beat down over a large angle and the plane of the wings is at a large angle to the direction of movement, somewhat in the way the blade of an oar is at a right angle to the direction of the stroke.  I should probably have made the body a lot smaller in relation to the wings, so the animal can beat its wings like Earth moths or butterflies: slowly, so the colour pattern can be appreciated. Just think of the animations as showing the animal in extreme slow motion.

Still, I could not resist adapting the animation to show a wing movement at 4 Hz, which is really low for Earth insects.  The colours stand out less.

The third and last movement concerns a mixture of the two flight patterns shown above: not too flat nor too steep, but just right. Again, this should be probably a large animal with a smaller body. There is some reasoning behind the bold colours.

I assumed that animal vision in relevant Furahan animals deals separately with colour contrast and with luminance contrast, just as the human visual system does. Generally, if you wish to see detail, use a large contrast between light and dark (i.e., a big luminance difference). You might think that colour differences are more important, but they are not. Designers know such things; here is a nice NASA image that explains the use of both types of contrast from a design point of view.

Click to enlarge; copyright Gert van Dijk

Colours can do strange things: the visual resolution differs between colours, with blue as a particularly poor colour to use for spatial information. Here is a trick to show that: the original is at the top left. I used that to blur two of the three colours red, green and blue, leaving one colour in its original sharp form. You will see that the clarity of the image really suffers f the green channel is blurred, but that the image does not suffer that much if green is unaffected. What this simple experiment shows is that blue and red, mostly blue, have a poor spatial resolution. Interesting things happen if you put two contrasting colours side by side, and tweak their luminance until they appear equally light or dark. This contrast has a poor spatial resolution, making shapes seem to float or flicker. This is just one of the properties of the visual system that op art relied on. Just type in op art in Google and do an image search.

I used such a design for the wings in this tetropter. Each wing has a bold pattern of two colours. Two wings have their colours placed opposite to the other two. The idea was that the wings in a near-clap position would provide a visual shock. Theoretically the to and fro sides of each wings could have contrasting patterns as well, to provide even more dazzle.

Here it is again, manipulated to result in a 4 Hz cycle. Does it work? Such visual effects rely on the properties of the visual system, and those will differ greatly between different animals. One species op art is another species' drabness. I have often wondered whether the colour patterns of some  Earth animals evolved to create a specific visual effect in a specific visual system. For instance, what effect do the stripes of a zebra have on the visual system of a lion, perhaps at night?

I will equip a Furahan farfalloid tetropter with a similar pattern, in the expectation that its colours will ignite at least one visual system, probably those of potential mates, to make it something like 'Wow!'.

Rusps turn out to follow biological rules about the weaponisation of tails

I recently came across an interesting paper on the evolution of the use of tails as weapons in Earth animals. This turns out to be a fairly rare occurrence, and perhaps that rarity helps explains why animals with tail weapons are so spectacular. After all, we take the common for granted, and it is the departure from the common that attracts attention.

The glyptodont Doedicurus; click to enlarge. https://en.wikipedia.org/wiki/Doedicurus

A nice example on an animal with a tail that is obviously useful as a weapon is the glyptodon genus Doedicurus, a giant armadillo-like mammal, the size of a small car. Doedicurus was encased in strong armour and endowed with a tail with an impressive thickened club at the end.

Click to enlarge; Pinacosaurus Grangeri; Copyright Gregory S. Paul. Princeton field Guide to Dinosaurs, second edition

Ankylosaurs had the same idea, but much earlier. As far as their design was concerned, they went overboard in adding an array of large sharp spikes to their armour.

Click to enlarge; Spinophorosaurus nigerensis; Copyright Gregory S. Paul. Princeton field Guide to Dinosaurs, second edition

Some sauropods may also have had body armour as well as similar thick knobs on the end of their tails. Only one sauropod (Spinophorosaurus nigerensis) apparently sported pointy spikes on its tail, shown here as a juvenile, and drawn by Gregory Paul (I do not think I have to urge dinosaur enthusiasts to get his book 'The Princeton field guide to dinosaurs'). If these long tails were swept at high speed, the transfer of all that kinetic energy should do some real damage. But perhaps a simple threat, along the lines of 'Make my day, punk' would be enough to prevent an actual fight.

The paper in question has the title "The evolution of tail weaponization in amniotes" and is written by Victoria Arbour and Lindsay Zanno. The paper describes which features are the evolutionary precursors of the evolution of tail weapons. The authors performed a thorough statistical analysis of many body traits, and looked separately at four aspects of tail weaponry:  tail lashing, bony terminal tail spikes, a stiff distal tail, and an expanded tail tip.

Click to enlarge. Arbour & Zanno 2018

Here is a figure of the paper, showing these four aspects and the features they are associated with. The result of all this is that you are not likely to find tail weaponry in agile quick-footed predators. If you were designing just such an animal for your speculative biology project, you should probably pause to consider its likelihood. Tail weapons seem to be a last resort for large slow herbivores who already invested in body armour. The authors make the point that equipping heads with weapons occurred much more often. This seems odd because heads are already filled with important structures that should not be damaged, whereas damage to a tail is probably much less risky, so you would expect 'anterior armatification' to be less common that 'posterior armatification'(I could not resist latinising 'weaponisation'). The authors do not speculate why this should be so, but I wonder whether the effective use of weapons requires excellent motor control, something that in turn depends on excellent sensory control, meaning sight. If so, the animal's body may simply be in the way, so it cannot see well enough where to place the sting in its tail.
   At any rate, the authors state that armour in mammals evolved in those animals that are neither small enough to hide nor large enough to deter predators by size alone, and that live in open environments. Close combat with a predator must be a risky business, so the best strategy may simply be running away faster than a predator. And if flight is your main strategy, heavy armour is not going to help. But  a wholly new set of constraints must come into play if you have no chance to outrun your predator to start with. Defensive features such as large size and armour then may become useful, and it seems that active weaponry is the last feature on the list to evolve.

Click to enlarge; copyright Gert van Dijk

So glyptodons, ankylosaurs, stegosaurs  and some sauropods all fit the 'big slow armoured' description to various degrees. And so do Furahan rusps! The image above shows half a rusp from an unfinished painting (for more on rusps, use the blog's search function). From my very first rusp sketch on, rusps were large, had thick hides and used their whips as active weapons. Of course rusps have front as well as hind whips, so the word 'tail' is not applicable at all, but the point is clear; rusp whips are analogous to the 'weaponised' tails of Earth. Those early rusp sketches predated the paper as well the posts in this blog about rusps by many years. I do not remember exactly how much of the rusp body plan came about consciously. I think that I started with a long body shape. Add to that some wondering why many Earth animals are so vulnerable at their rear and sometimes along their middle as well. As the earliest sketches show eyes on middle rusps segments as well, rusps must have started with a weak encephalisation tendency. From there on the double encephalisation seems natural. Note that the posterior whip is well controlled by its own ring brain, with excellent visual information available to direct the strikes. But part of all this may have come about through largely unconscious associations while sketching. Once a design is on paper, it is often hard to say where it came from. Regardless, it is nice that the meme 'rusps have whips' can now be attributed to a firmly established biological principle.

Much as I like the paper, there is a minor matter that might have made it even nicer. Rather than 'tail weaponisation', the authors could easily have used a word that is both relevant and fun: a tail weapon is a 'thagomiser'.

Click to enlarge; copyright

The first use of 'thagomizer' is shown above (this blog uses British spelling, so I assumed the word would become 'thagomiser' in the UK; the rules aren't always clear...).
   It was published as one of Gary Larson's Far Side cartoons in May, 1982. Actually, this colour image stems from a later luxury edition of all Far Side cartoons. Poor Thag Simmons. For 'Far Side' fans, a caveman called 'Thag' occurs at least once more, and one cartoon, taking place in modern times, featured a 'Mr Thagerson'.
  At first glance the word thagomiser seems to indicate 'to turn an object, animal or person into thag', but the real meaning is obviously a 'structure to kill animals or persons, in particular Thag Simmons'. The word has later been picked up in the scientific community to describe the tail weapons of stegosaurs, and apparently of stegosaurs only. I propose to widen its use to all tail weapons.
   As an author of scientific papers myself I realise that the use of humour in scientific papers can be tricky as it is often frowned upon, and you never wish to harm your chances of getting a paper accepted. (I once inserted the phrase 'This resistance is futile' in one of my own scientific papers as an irreverent reference to Star Trek, but I do not think anyone ever noticed).

If we use 'thagomiser' as a word for 'tail weapon', the paper could have been called "The evolution of thagomizers in amniotes", which would be clear, succinct and elegant, but admittedly probably too flippant for a serious paper. Once 'thagomiser' is an accepted word, can we resist to stop there? The tendency to evolve a thagomiser then might become 'thagomiserificability', and the transition process from 'nonthagomiseriness' (not having a thagomiser) to 'orthothagomiserity' (having a proper thagomiser) is 'thagomogrification'. Obviously.