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.