The New Ambidextrous, M Gardner

Tags: animal, bilateral symmetry, environment, sensory organs, vertebrate eye, earth creatures, spherical symmetry, Thomas Carlyle, planes of symmetry, Honeysuckle, Oh my darling, fearful symmetry, Frank Baum, John Dough and the Cherub, animals, Bindweed, the Honeysuckle, fragrant Honeysuckle
Content: THE NEW AMBI DEXTROUS UNIVERSE SYMMETRY and ASYMMETRY from MIRROR REFLECTIONS to SUPERSTRINGS THIRD Revised Edition MARTIN GARDNER Dover Publications, INC MINEOLA, NEW YORK
C. H Plants and animals Among the billions of k axies scattered through space, each containing billions of sta reasonable to suppose that circling around many of these stars be planets, and that on some of these planets there must be l spectacle!" exclaimEd Thomas Carlyle, as he considered the that the universe might contain planets by the millions. " inhabited, what a scope for pain and folly; and if they be not what a waste of space!" At the moment, no one really knows whether life in any for throughout the universe, confined to our own galaxy, or conf solar system. We do not even know if there is some primitive on Venus or Mars, the two planets nearest the earth, thou cases it seems extremely unlikely. Assuming that forms of life have evolved on other planets, forms be wildly unlike anything that even science-fiction w imagined? Or will they possess certain features in common with know it? It is all sheer speculation, of course, but with respe tions of symmetry we can make some educated guesses. On the started out with spherical symmetry, then branched off in 53
4 Chapter 7 irections: the plant world with symmetry similar to that of a cone, and he animal world with bilateral symmetry. There are good reasons to hink that evolution on any planet, if it occurs at all, would tend to follow similar pattern. Primitive one-celled life, floating in a sea and constantly tumbling bout, would naturally assume a spherical form with planes ofsymmetry n all directions. But once a living form anchors itself to the bottom of a a or to the land, a permanent up-down axis is created. The rooted end any plant is obviously distinguishable from the upper end. There is othing, however, in the sea or air to distinguish between the ends of a ont-back axis or a left-right one. It is for this reason that plant forms, or the most part, have a rough, overall symmetry similar to that of a one: no horizontal plane of symmetry, but an infinity of vertical planes. tree, for example, obviously has a top and bottom, but one is hard put distinguish the front from the back of a tree, or its right from its left. Most flower blossoms have, in a rough way, a conical type of symmetry. uits sometimes have spherical symmetry (if you ignore the spot where ey attach to a branch): oranges, cantaloupes, coconuts, and so on. A ylindrical-type symmetry (an infinity of planes of symmetry passing rough one axis, and one plane perpendicular to that axis and bisecting is exhibited by such fruits as grapes and watermelons. Familiar fruits ith conical symmetry are the apple and pear. (Biologists use the term dial symmetry for symmetry of both cylindrical and conical types.) The nana furnishes an example of bilateral symmetry. Owing to its curvare and its pointed end, it is possible to cut a banana into mirror-image lves by only one plane of symmetry. Are there examples of asymmetry (total absence of planes of symetry) in the plant world? Yes, and the most striking examples are the ants that display helices in some part of their structure. As we learned an earlier chapter, the helix cannot be superposed on its mirror image. therefore has two distinct forms: the right-handed helix, which correonds to a wood screw that turns clockwise as it enters wood; and the ft-handed helix, which is the mirror image of a right-handed one. elices abound in the plant world, not only in stalks, stems, and tendrils t also in the structure of myriads of seeds, flowers, cones, and leaves, as ell as in the helical arrangement of leaves around a stalk. (Helical uctures are also found in the world of animals, as Chapter 8 shows. For cartoonist's view, see Figure 25.) It is in the climbing and twining plants that the helix can be seen in its ost regular form. The majority of twining plants, as they coil upward ound sticks, trees, or other plants, coil in right-handed helices, but ere are thousands of varieties that coil the opposite way. Some species ve both left- and right-handed varieties, but usually a species has its wn handedness, which never varies. The honeysuckle, for example, ways twines in a left-handed helix. The bindweed family (of which the
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Figure 25 Screw threads might be a status symbol among earth bu permission of Johnny Hart and Creators Syndicate, Inc.) morning glory is a well-known species) always twines in a ri helix. When two plants of the same handedness twine around the result is a fairly orderly production of interwound helice same type; when plants of opposite handedness coil around they produce a hopeless tangle. The mixed-up violent left-rig of the bindweed and honeysuckle, for example, has long English poets. "The blue bindweed," wrote Ben Jonson in 1 Vision of Delight, "doth itself enfold with honeysuckle." Sha Act 4, Scene 1, of A Midsummer-Night's Dream, has Queen scribe her intended embrace of Bottom the weaver (whose t transformed by Puck into the head of an ass) by saying: "Ste I will wind thee in my arms. . . . So doth the woodbin honeysuckle gently entwist In Shakespeare's day the bindweed was sometimes calle bine. Later woodbine became used exclusively as another term suckle, a fact that has confused dozens of easily confused S commentators. Some of them have even reduced the passage by supposing that the beautiful Queen Titania, "sometime of was speaking of herself and Bottom as entwined like honey honeysuckle. Awareness of the opposite handedness of bin honeysuckle heightens, of course, the meaning of Titania's metaphor. More recently, a charming song about the love of the bi the honeysuckle has been written by Michael Flanders, a London poet and entertainer, and set to music by his frie Swann. On a visit to the natural history museum in K Flanders had been struck by an exhibit dealing with the left handed habits of climbing plants. The result was his song "M (You can hear it sung by Flanders and Swann on the Angel r
Chapter 7 eir engaging two-man revue, At the Drop of a Hat.) With Flanders's rmission, I quote the lyrics in full: MISALLIANCE The fragrant Honeysuckle spirals clockwise to the sun And many other creepers do the same. But some climb counterclockwise, the Bindweed does, for one, Or Convolvulus, to give her proper name. Rooted on either side a door, one of each species grew, And raced towards the window-ledge above. Each corkscrewed to the lintel in the only way it knew, Where they stopped, touched tendrils, smiled, and fell in love. Said the right-handed Honeysuckle To the left-handed Bindweed: "Oh let us get married If our parents don't mind, we'd Be loving and inseparable, Inextricably entwined, we'd Live happily ever after," Said the Honeysuckle tO the Bindweed. To the Honeysuckle's parents it came as a shock. "The Bindweeds," they cried, "are inferior stock. They're uncultivated, of breeding bereft. We twine to the right, and they twine to the left!" Said the counterclockwise Bindweed To the clockwise Honeysuckle: "We'd better start saving, Many a mickle maks a muckle,1 Then run away for a honeymoon And hope that our luck'll Take a turn for the better," Said the Bindweed to the Honeysuckle. A bee who was passing remarked to them then: "I've said it before, and I'll say it again, Consider your offshoots, f offshoots there be. They'll never receive any blessing from me." Poor little sucker, how will it learn When it is climbing, which way to turn. Right--left--what a disgrace! Or it may go straight up and fall flat on its face!
Plants and An Said the right-hand thread Honeysuckle To the left-hand thread Bindweed: "It seems that against us all fate has combined. Oh my darling, oh my darling, Oh my darling Columbine, Thou art lost and gone forever, We shall never intertwine." Together they found them the very next day. They had pulled u their roots and just shrivelled away, Deprived of that freedom for which we must fight, To veer to the left, or to veer to the right! In this book I have adopted the convention of calling a handed if it corresponds to the helical thread of a common w Flanders adopts the opposite convention of calling such a handed because, when you look at it from either end, you see toward you in an anticlockwise direction. This confusion of t runs through all the literature on climbing plants. In addition to coiling around things in a helix of a certain h twining plants also have stems that twist in the same way Sometimes two or more stems of the same plant will twine ropelike fashion. The bignonia, for example, tends to form tr that twist to the right; the honeysuckle tends to form double twist to the left. At times the trunks of beeches, chestnuts trees exhibit a violent twisting of the bark into helical patte the twist may be either to the right or left regardless of the Sessile animals (animals attached to something and unab about on their own power), such as the sea anemones, usu conical type of radial symmetry like that of most plants. Slo moving animals, such as the echinoderms (starfishes, sea cuc other species) and jellyfish, likewise have conical symmetry mals float about in the sea or lie on the bottom where food approach them with equal probability from all sides. Howeve a species evolved strong powers of locomotion it was inev features would develop that would distinguish the animal's fr back. In the sea, for example, the ability to move about rapid of food gave an animal a great competitive advantage over slow-moving forms. A mouth is obviously more efficient on t of a fish than on its back end; the fish can swim directly towa gobble it up before some other animal gets it. This single fe the mouth, is sufficient to distinguish the front end from the biologists like to say, the cephalic from the caudal part) of a features, such as eyes, also are clearly more efficient on th
8 Chapter 7 ear the mouth, than at the back. A fish wants to see where it is going, ot where it has been. In short, the mere fact of swimming through ater brought about a situation in which it was inevitable that forces of volution would devise features that would distinguish one end of a sea nimal from the other. At the same time that locomotion was leading to distinctions between ont and back, the force of gravity was causing similar differences etween an animal's top and bottom, or, to use the biologist's terms gain, the dorsal and ventral. (When an animal such as man stands pright, then of course his dorsal and ventral sides correspond to back nd front, and his cephalic and caudal ends become top and bottom, but this section we are confining our attention to sea life.) What about ght and left? A moment's reflection and you will realize that there is othing in the sea's watery environment to make a distinction between ght and left significant. A swimming fish encounters a marked differce between forward and backward because one is the direction it goes, e other is the direction it comes from. The fish also encounters a arked difference between up and down. If it swims up, it reaches the rface of the sea. If it swims down, it reaches the ocean floor. But what fference does it encounter if it turns left or right? None. If it turns left, finds the sea, and the things in it, exactly like the sea that it finds if it rns right. There are no forces, like the force of gravity, that operate orizontally in one direction only. It is for these reasons that various atures--fins, eyes, and so on--tended to develop equally on left and ght sides. Had there been a great advantage for a swimming fish to see ly to the right and not to the left, no doubt fish would have developed ly a single eye on the right. But there is no such advantage. It is easy to nderstand why a single plane of symmetry remained, dividing fish laterally into mirror-image right and left sides. When the reptiles crawled out on the land and evolved into birds and ammals, there was nothing in their new environment to call for a ange in bilateral symmetry. Up and down now became an even onger influence on an animal's structure, because appendages were eded for locomotion across the ground. Feet are of little value atched to the back of an animal and sticking up in the air! Of course the fference between front and back continued to be important. There are some amusing exceptions to this in ancient mythology and odern fantasy. The amphisbaena (in Greek it means "go both ways") as a fabled Greek snake with a head at each end. It crawled both ways. ere is how Pope described it in his Dunciad: Thus Amphisbaena (I have read) At either end assails; None knows which leads, or which is led, For both Heads are but Tails.
Plants and A Iii recent fantasy for children there is Duo, the twoheaded Frank Baum's John Dough and the Cherub; and the Pushmi Hugh Lofting's Dr. Dohttle books. Both animals had a head a As for left and right, the situation on land or in the air re symmetric as in the sea. An animal in the jungle or a bird in th its environment on the left pretty much like its environment o It is easy to understand why the bodies of land and air animal the bilateral symmetry they had previously acquired in the se Coxeter, in his beautiful book Introduction to Geometry (Wi reminds us that it may have been this bilateral symmetry th Blake described in those familiar lines: Tyger! Tyger! burning bright In the forests of the night, What immortal hand or eye Dare frame thy fearful symmetry? In view of the overall symmetry of the earth and the fo upon it, it is hard to conceive of circumstances in the future alter this fundamental type of symmetry in the bodies of an slightest loss of bilateral symmetry, such as the loss of a right have immediate negative value for the survival of any animal could sneak up unobserved on the right. (See Figure 26.) We are now in a position to understand why, if there are another planet, capable of moving through its seas, throug sphere, or over its land, it is likely that they, too, will hav symmetry. On another planet, as on earth, the same factors ate to produce such symmetry. Gravity would provide a f difference between up and down. Locomotion would crea mental difference between front and back. The lack of any f asymmetry in the environment would allow the left-right s bodies to remain unaltered. Can we go further than this? Can we expect more detailed of extraterrestrial life with life as we know it? Yes, we can. In seas of another planet, regardless of their chemical comp hard to imagine a simpler form of locomotion for evolutio than the motion achieved by waving tails and fins. That evol find this type of propulsion is supported by the fact that e earth it has developed independently. Fish developed tail-a pulsion. Then fish evolved into amphibious forms that cra the land and became reptiles. The reptiles developed into ma when some of the mammals returned to the sea -- those tha became whales and seals, for example--their legs evolve flippers and their tail into a finlike instrument for prop steering.
0 Chapter 7 "Oh, yeah? If you're alone, then whose eye Is that?" uuriree2d6mTohreesfelecxriebaitluitrye,soarjpupsetgarretaotehravvuelneveroalbvieldityr?ad(iFarlolymsyBmemyoetnrdictehyeeFs.aHr aSviedethbeyy y Larson, Andrews & McMeel, 1983.) Similarly, it is hard to imagine a simpler mode of flying through the than by means of wings. Again, even on earth there has been indepennt, parallel development of wings. The reptiles evolved wings and ame airborne. So did the insects. Some mammals, like the flying irrel, developed wings for gliding. The bat, another mammal, develd excellent wings. A species of fish, leaping out of the water to escape ture, developed rudimentary gliding wings. Even man, when he ds an airplane, builds it with "wings" on a pattern that resembles a d in flight. On land, is there a simpler method by which an animal can move ut other than by means of jointed appendages? The legs of a dog are much different in mechanical working from the legs of a housefly, ough they had a completely independent evolution. Of course the el also is a simple machine for moving along the ground, but there good reasons why it would be difficult for a wheel to evolve. For one
Plants and A thing, it needs to be supported by an axle; either the whe detached from the axle and free to turn on it, or the axle itse and therefore be detached from the body. Then there i problem of finding a way for the body to rotate a wheel. The are great, though I suppose not insurmountable. L. Frank Bau of Oz invented a race of men called the Wheelers who had fou dog, each terminating in a small wheel instead of a foot. In Th of Oz he invented the Ork, a bird with a propeller on the end on some planet nature found a way of inventing the wheel, w there animals resembling bicycles and cars, fish resembling and birds resembling airplanes, although the prospects unlikely. Although no known animal uses a wheel for propelling itse ground or through the air, there are bacteria that move thro by actually rotating flagella like propellers. (See "How Bacte by Howard C. Berg, in Scientfic American, August 1975, p There may be rotary devices inside cells for unwinding twiste DNA. (See Scientf1c American, February 1967, page 37.) Som animals propel themselves through water by rotating their e Nor must we overlook the dung beetle, the sacred scarab of transports little balls of dung by rolling them across the gro Sensory Organs such as eyes, ears, and noses also have ab kind of inevitability if life evolves any type of advanced intel ity. Electromagnetic waves are ideal for giving a brain an accu of the outside world. Pressure waves transmitted by molecu additional valuable clues to the environment and are picked The spread of actual molecules from a substance is detected is not impossible that there may be advanced cultures of nonterrestrials in which smell and taste not only are the dom but also provide the primary means of communication betwe uals. Only in recent years have biologists discovered how mu tion, in terrestrial animal species, is transmitted efficiently transfer of substances now called pheromones. See Edward nose-opening report in his article "Pheromones" in Scientfic May 1963. Since light, sound, and molecules certainly exist on othe seems likely that evolution would invent senses to exploit the ena as a means of achieving greater control over the circum life. Here on earth, for instance, the eye has had no fewer quite independent, parallel developments: the eyes of vert mals, the eyes of insects, and the eyes of various mollusks. T for example, has a remarkably good eye -- in fact, in some r superior to our own. It has eyelids, cornea, iris, lens, retina -- human eye--yet it evolved entirely independently of the e
Chapter 7 e vertebrate eye! It is hard to find a more astonishing instance of how olution, operating along two disconnected lines of development, maned to invent two complicated instruments that have essentially the me function and structure. There are good reasons for eyes and other sensory organs to form a nd of face. In the first place, there is an advantage in having eyes, ears, d nose close to the mouth, where they are useful in the search for food. here is an equally great advantage in having them close to the brain. It kes time for a nerve impulse to get from the organs to the brain; the icker it gets there, the quicker an animal can react in catching food or oiding danger. Even the brain itself, needed to evaluate and interpret nsory data, accomplishes its thinking by electrical networks: a kind of niature electronic computer of great complexity. Nerve filaments that rry electrical impulses may be essential for the brains of advanced ing creatures. If life on another planet reaches the intelligence level of man on earth, seems probable that it would have at least a few humanoid features. ere are obvious advantages in having fingers at the ends of arms. For otection, the valuable brain would need to be heavily encased and as from the ground as possible, where it would be best shielded from the ocks of moving about. Sensory organs, close to the brain and in front, ould create something like a face. "Senator" Clarke Crandall, a Chigo entertainer, had a funny routine about the advantages of having nsory organs at other spots on the body. An eye on the tip of a finger, example, would make it possible to see a parade by holding up a hand d looking over the heads of everybody. Ears under the armpits would kept warm in cold weather. A mouth on top of the head would allow a an to put a sandwich under his hat and eat it on the way to work. It is sy to see why evolution has avoided such arrangements. An eye on the ger would be too vulnerable to injury, too far from the brain. Armpit rs would not be very efficient for hearing unless you kept your arms rpetually raised. A mouth on the head would expose the brain to ury, make it difficult to see what one was eating, and so on. Of course so many chance factors are involved and environments of nets are so varied that one would not expect to find on another planet y form of life that was a close replica of any species on earth. No one pected to find an elephant or a giraffe on Mars. On the other hand, en life may not be so wildly different from earth forms as one is mpted to think. The BEMs of science fiction (BEM is an acronym med by the initials of Bug-Eyed Monster), unlike any earthly animal t nevertheless recognizable as animals, may prove to be not far from e truth after all. It is hard, in fact, to imagine how extraterrestrial atures could differ from earth creatures to any greater degree than th creatures differ from each other. The octopus, the platypus, the rnbill, the ostrich, the snake -- if one had never seen or heard of these
Plants and A animals, their structure would seem as bizarre and improbabl any animal we are likely to find on another planet or a large have a fine specimen of a miniature BEM in the anableps, a sm Central American carp that has four eyes! Well, not really eyes, like monstrous bubbles, are divided into upper and lowe an opaque band. Each eye has a single lens, but there are lower corneas and irises. The little fish (it is about 8 inches l with the opaque band exactly at water level, so that its two up can see above water while its two lower "eyes" see under w next chapter we will learn something about the asymmetric this curious creature. Animals as weird as the anableps, no doubt much weirder, roam the seas, land, and skies of alien planets, but they are n be so unearthly that we do not recognize them as animals. Th for this recognition, more fundamental than any other asp forms, is likely to be the bilateral symmetry of their bodies. NOTE 1. A Scottish phrase meaning "many a little makes a lot

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