|
If you disturb the snakes, you will find out the differences between the two species in defence and escape behaviour. If several adders are basking together, you will also find out whether some are more wary than others. When they are coiled up together they seem to change their positions without any problems, though you might wonder whether they known which bit belongs to which snake. Snakes can glide along using the large scales underneath, which are controlled by individual muscles along the body. In fact, every scale on the body is connected to a muscle. Muscles connect ribs to ribs, ribs to scales, and scales to scales, giving snakes great control over their movements. In the gliding movement, the snake produces a wave-like motion; each scale in turn is lifted, moved forward, lowered, and moved back in a slightly different phase from the next one. A gliding snake is rather like a centipede in a sack race. It is also analogous to the ultrasonic motor that is found in some camera lenses. Snakes have evolved an enormous number of ribs, which help to anchor some of the muscles. Click here to see how an ultrasonic motor works. If you see a courting male, gliding partly on the ground, and partly on the moving female, you can only marvel at the coordination required. Imagine trying to walk with one foot on an escalator and the other on a stationary stair. Then imagine that you are a centipede trying the same trick. Snakes can also make use of objects by pushing the curved body against them and creating a wave down the body. This can be understood by imagining a large screw with a very coarse pitch, rotating and passing through a nut. The serpentine motion of a snake is like a two-dimensional projection of a screw. It is also analogous to swimming, as seen in a sea-snake, eel or leech, except that the "medium" is discontinuous and rigid. An extreme case of this is side-winding, in which the snake creates its own series of obstacles by pushing into the sand or soil. The snake actually forms a a helix which is very flat in the vertical dimension. So a side-winder has a handedness. Do all side-winders have the same handedness? Snakes and slow-worms that cannot side-wind can experience difficulty on a powdery surface, and may even be unable to progress. In water, many snakes can swim like an eel, and the sea-snakes are so well adapted that swimming is all they can do. The pictures above, some of sloughed skins, show the large ventral scales. If a snake gets into a place where it cannot go forward, it can in fact glide backwards, though less efficiency than when going forward. Although the scales are designed for grip in the forward direction, an adder can go down a rock sloping at about thirty-five degrees, but in going over the edge, it will eventually fall off when the weight of the hanging part is too heavy for the part on the rock. Adders don’t seem to mind falling six or nine inches on to grass. After all, they are flexible, they have no long bones to break, and they have elongated organs which are unlikely to be jerked around as ours would be. Click here to download or run in place a short simulation of the motion of the scales. On a smooth hard surface, such as a shiny tarmac road, or on a very powdery one track, a snake or a slow-worm may become trapped. By putting a stick where the animal can push, you can help the animal can make progress. This action can be repeated until safety is reached. Use a long enough stick, so that the animal cannot bite you. Click here if you want to skip a section about the physics and maths of movement. The shapes that snakes make are as varied as the terrain over which they pass. But they are obviously not any old shape. If you try to draw a snake, some curves will look more realistic than others. The curve shown below is an idealized one calculated on the assumption that the curvature varies sinusoidally along the snake. Real examples would be less regular because of constraints imposed by the surroundings. A young adder will sometimes adopt this position when threatened, because when curved, it can strike by straightening out. A straight snake cannot strike forward, any more than a boxer with arm outstretched. In the uniform medium of water, an eel, a sea-snake or a large leech illustrate the elegant curves that can be seen in nature. The grass snake is a good swimmer, and can sometimes be seen in a pond or a canal. A somewhat similar curve may be seen when certain snakes hang from trees, waiting for prey. The excess length in the curves can be used to unleash a strike. In this case, the curves would be slightly modified to cope with the downward acting weight. A snake lying in a straight line, flat on the ground and facing you, has no way of striking. But the spitting cobra can still get you, as its name suggests, even when out of biting range. The fangs point forward, and two streams of venom are ejected, probably at your eyes. The snake does not do any calculations in moving, but the point is that its curvature varies in a simple manner. The actual curves of a snake makes are likely to be such as to minimise the average curvature along the length, which probably minimizes muscular energy. Flying snakes can even flatten the body into a wing, with which they glide. Stability is gained by a wave which passes down the body, probably helping to adjust the angles of the body in response to the movements of the snake and the air. Landings are probably fairly heavy, but if you have no limbs to break, and your organs are spread along the body instead of being in heavy lumps, this probably does not matter. By making a few small changes in the computer program, a more realistic shape can be created, as we see in the diagram at left. Who would have thought that success could come to an animal which looks rather like a head joined to a long tail, or a head with a long neck, or a finger with a head on it?
The next diagram shows an elastic object like the Bowden cable with five different shapes, all governed by the curvature varying as a power of the sine of the position along the object. All the curves have the same length and fit into the same space per wiggle. The black curve corresponds to the plain sinusoidal variation that has been used so far. The numbers correspond to the elastic energy; the black curve has less than the others, though not by much. The green curve has long sections with not much curvature, but these are more than compensated by the highly curved parts. The red curve errs in the opposite direction. Curves of lower energy can be created for the same length and the same two end points by using fewer wiggles, at the expense of requiring a bigger enclosing area. This minimum in energy is only a local one in the parameter space. The curve that gives the least energy is obtained for a given length between two points is a single arc, which is unlikely to occur in the case of a snake, because it is normally trying to go in a particular direction. Another solution, in three dimensions, is a helix, which is better than the curves above, but worse than the single arc. Although the black curve above is close to the minimal energy for the family of curves shown, it is unstable against a general bending. A steel wire with loosely pinned supports would spring out into the arc with only a half a wavelength. These curves may be related to electric and magnetic lines of force, which in the nineteenth century were considered to depict the properties of an elastic medium, the luminiferous ether. Certainly, in the vicinity of the sun, magnetic lines of force writhe around like the snakes on the head of the legendary Medusa. And in string theory, mathematicians have created tiny lines in space which can oscillate. In the past, progress in understanding has sometimes been held up by an insistence on simple mathematics instead of simple physics, as in the case of planetary orbits. Understanding only began when the revered circular orbits were very reluctantly abandoned by Kepler in favour of elliptical ones, though Kepler did not know the reason for the ellipses. But then, the only reason for the circles was the belief that they were somehow ideal. More progress was made when Newton formulated simple physical rules that led naturally to the hitherto incomprehensible ellipses, and unified the behaviour of astronomical and terrestrial objects. More general methods such as the use of the Lagrangian unified physics even more, at the cost of almost complete abstraction from any particular system. More about this type of subject can be found in Nature’s Maths and in Numerology. Physicists still believe that nature ought to be simple, and they prefer simple ideas to complicated ones. The problem is – what is the right kind of simplicity? And simplicity of ideas doesn’t mean simplicity in working out the consequences.
Below are two versions of a snake descending a staircase. Clearly both are absurd. The real picture would lie between the two extremes, again, to minimise energy. The body of this whipsnake forms a curve of minimal energy, not unlike a catenary, the curve taken by a uniform rope with zero rigidity.
If you don’t believe that mathematics has much to do with nature, try one or more of these three books. Many topics about nature’s mathematics are discussed in Professor Ian Stewart’s exciting book "Nature’s Other Secrets" – Penguin – ISBN 0 14 025876 0. An older but beautiful book is "Patterns in Nature" by Peter S Stevens – Peregrine – ISBN 0 14 055 114X An even older, but deservedly famous, book is "On Growth and Form" by D’Arcy Wentworth Thompson, who was ahead of his time with his many insights into the relationships between the forms of nature and physical phenomena. We don’t have to know maths or physics, to finds things beautiful, but some things are not comprehensible without this knowledge. If we find some animal or plant ugly, it may be that we don’t know what it is trying to do. People sometimes use a charging rhino as a symbol of insensitivity, but if you see a trotting rhinoceros at a large zoo, you will see a grace matching that of any dancer, because it wastes energy minimally. Dancing in fact, like some other arts, is an artificial attempt to achieve what is done quite naturally by other species. If we look at tiny creatures like daphnia or aphids, or at floating creatures like jellyfish, we see what happens when gravity is not a constraint. The same sort of thing happens in the design of spacecraft such as the lunar landers, which look a bit like huge insects, though they do have to withstand the accelerations and vibrations of take-off. And this hints at the reason why even the best simulations of animals such as dinosaurs still don’t look quite right. They won’t look right until the algorithms for motion are based on mass distributions, forces and energy, as well as on smooth curves. And it hints at the basis for "jizz", which is the term that bird watchers use to label the sometimes indefinable feeling that they have identified a bird from a brief glimpse. They are not cheating – they have picked up subtle clues. The curves formed by adders, grass-snakes and slow-worms, for example, are slightly different in character. Perhaps this is why taxidermy is so difficult. In a sense, a picture or even a cartoon can capture the essence of a living thing more accurately than a stuffed animal: the art is not more accurate, and we are not fooled into thinking it is alive, but it can somehow capture what matters. Many years ago, when snakes were more common in Britain, you could go to a certain place in Swindon, and be almost sure to see a number of grass-snakes, lined up along the edge of a field. Each one would be coiled up in neat, tight spiral near its hole. When disturbed, they would smoothly unwind the spirals and disappear down the holes.
In some high places in Gloucester, while you are watching adders, you can look around and see glimpses of the river Severn snaking across its flood plain on its way to the Bristol Channel. As snakes, and indeed slow-worms, have evolved from animals with legs, their ancestors must have gone through stages in which the legs gradually disappeared. Indeed, some pythons possess vestigial limbs. At some stage, the number of ribs increased greatly, and the muscles in that area of the body must have developed, along with the ability of the nervous system to control them. If you watch the graceful movements of a pair of adders, or of two males gliding along while competing, you will see that the control and coordination is as perfect as that of any other animal. Some snakes can even glide down from high in the trees. So the brains of lizards and snakes, while having a common ancestry, must have developed quite differently in the relative complexity of the parts controlling the legs and the rib areas. Another bit of maths concerns a snake, such as a cobra, that rears up to defend itself. It needs to minimise the forces at each point in its body. An old mathematical problem suggests the answer. It is about a pile of bricks, which are overlapped to produce the maximum possible overhang. If you neglect practical considerations such as imperfect rigidity of the bricks and of the foundations, you can show that the Nth brick from the top is overlapped by one Nth of its length. You only have to smooth out the jagged edges and add a head, and you have the shape of a cobra, though you might well object that the curve should be the other way up. If you don’t believe in maths, consider Torvill and Dean. What was it that made them so different from all the others? Couldn’t it have been a smoothness of motion, and a minimising of energy, and a continuity between each movement and the next, that none of the others had achieved. Mathematically this would be described in terms of continuity of differential coefficients. Ballet dancers, figure skaters and gymnasts have to put in an enormous amount of training in order to perfect movements which are not natural for homo sapiens. Much of what we admire in the movement of animals is the result of millions of years of evolution, resulting in a good compromise between all the competing demands on the system. In a sense, we humans are not exceptionally good at any one physical activity, and even what a few individuals can do with immense effort can be achieved with ease by one species or another. But the human species is very adaptable, like the feral pigeon, the house sparrow, the house fly, and other ubiquitous species. |
