The Seven Mysteries of Life

by Guy Murchie

  The only reason garnet (dodecahedral) forms are commoner than TKH (tetrakaidekahedral) forms in solid matter evidently is that friction is usually enough to inhibit cells from flowing into easier configurations. Experiments in squeezing masses of dry clay pellets together, for example, result in their coming out as models of nearly perfect garnets yet, after wetting and resqueezing (as might happen to massed fish eggs under tremendous pressures on the ocean floor) some of their rhombic faces begin to lop into pentagons, then hexagons, as corners are blunted to start new facets and the slippery little figures wind up as semi-TKHs in various stages of perfection. Naturally a substance as fluid as soapsuds really does come close to shaping its internal bubbles into perfect tetrakaidekahedra, but anything with the slightest viscosity, such as the colloidal cells of life, tends instead to compromise into a stew of polyhedra with the numbers of their faces ranging from four to more than twenty, a good half of them showing either 13, 14 or 15 sides and an overall face-count averaging close to fourteen. And that may well be the prevailing shape of life everywhere.

  Hexagonal faces are common in such cell masses, but pentagonal ones are more so, probably because hexagons naturally fit together to form a flat plane in two dimensions, while pentagons incline to three dimensional curvature. The microscopic globular animal in the sea called a radiolarian, for instance, is covered by a layer of hundreds of frothlike vesicles all about the same size which, like honey cells, get pressed into hexagons. Inevitably, however, there have to be, and are, a good many pentagons (occasionally a rectangle or triangle) among them for the inviolable geometric reason that, without the pentagons, etc., the animal's mantle could not curve around it and it could not be a radiolarian or even be alive!

  Thus does abstract mathematics hold sway over life's forms, including the form of the colonial creature called a sponge, which begins its skeleton with hundreds of separate crystals, assembling them later into one design or another of prefabricated dwelling, the simplest example of which may be a six-rayed siliceous sponge whose spicules frame a living jackstone, a shape a mathematician might describe as a Cartesian coordinate hub with 90° angles in three dimensions. And if that strikes you as remarkable, let me say that dynamic relationships are virtually unlimited, there being probably as many of them inside a small biocrystal as, say, between a cat and a mouse, a sand dune and the wind, a coral reef and the sea, a city and the earth, a star and the Milky Way ...

  SOCIAL GEOMETRY

  One of the most revealing aspects of living order is the complex and invisible cell structure of territories that stabilize social and political interaction from the pecking hierarchy of any small population of animals to the established boundaries of human empire. The concept of individual distance is critical here and closely analogous to the spacings of subatomic particles inside the atom or to molecular intervals in any crystal lattice. The first person to recognize individual distance as a law of nature, I am told, was Heini Hediger, the Swiss zoologist, who suddenly realized one March morning in 1938 while standing in Zurich's Bellevue Square that the black-headed gulls on the lakeside railing had spaced themselves with remarkable regularity almost exactly a foot apart. Then he noticed that the swallows on a wire were perched only six inches apart, while flamingoes in the zoo kept to a range of nearly two feet, the distance being roughly proportional to the size of the bird. Somewhat as the diameter of the hydrogen atom spans exactly one angstrom while the space between H2O molecules in solid ice is a uniform 2.72 angstroms, each kind of organism has its characteristic distance. Thus a deer may become apprehensive if you approach within 200 yards of him in a field, a mountain sheep about half a mile, an eagle a mile or an alien spaceship 100 miles. Social researchers report that an American man in the street stands on the average about 20 inches away from another man in a conversation, and about 24 inches from a woman. But these distances vary with countries as well as with sex, age and mood. In Cuba, for instance, a man may stand only 13 inches from an educated woman without being unduly suggestive.

  More complicated is the interrelation when a family or flock lives and communes together, something expressable by the formula of mutual understanding (im) which gives the number of direct communication lines (... telephones, smoke signals, whiffs of perfume ... ) needed between any number (n) of individuals in order that no two of them will be without their unique private channel of interchange. If the number of individuals (n) is three (call them A, B and C), the formula (im) amounts to or or or 3, indicating that three channels of communication are just enough to connect each of the three individuals with both of the others, the channels forming a triangle (im). While the formula is presumably fundamental to everything from crystal structure to multicellular life in general, it may be modified by various factors, like the pecking order in the tribe or the overall hierarchies of evolution, both of which augment crystalline stability in life's intra- and inter-relations.

  A kindred fact came to light in a Harvard project in 1967 known as the "small world problem," which discovered that a chain of only five friends will link any two average individuals in the United States and probably ten friends any two on Earth. One test, for instance, required each of 160 randomly chosen Nebraskans to reach a stockbroker living in Sharon, Massachusetts, by writing a letter to a friend (one close enough to be called by his first name) who seemed to have the best chance of knowing him, asking the friend to write in turn to another friend until the broker was reached. The number of intermediaries in this typical sample varied from two to ten, averaging five and, by simple extrapolation, it should take no more than ten of them on the average to link the whole planet, the number being presumed to decrease as international travel increases. Of course if you count the strange intangibles of acquaintanceship the chain is bound to shorten still more, because familiarity with one's fellow planetary passengers obviously does not depend wholly on personal contact or private communication. An actor and a television commentator might know each other intimately, just from seeing one another on the screen where their manners and opinions have been household fare for years.

  And another factor is life's uncertainty principle, roughly comparable to Heisenberg's Uncertainty Principle inside the atom, and which deals, among other things, with the orbits of one's family. Just where a spouse or children may be at any particular instant when they are out of sight is normally uncertain, except within vague physical and mental limits. You "know" they are within some sort of boundary, such as the town lines, the marital domain, the home lot, the house, a particular room or a bed. But exactly where and when they are in that bed, room, house or other area you seldom know with certainty - nor would it be necessary or natural to know it continuously. Life enjoys some leeway. It is a vital law without which life would not be life. Even a babe in the womb goes through orbits his mother cannot follow... and there are worlds of humming mystery within us all.

  Accidents and mutations, almost always passing unnoticed in the microcosm, like the crystal lesions in plant protein (here shown), barely whisper the inscrutability of life and matter. How long, did we say (page 106), a cell remains a cell? A molecule a molecule? Even Democritos surmised in the fifth century B.C. that "the love and hate of atoms is the cause of unrest in the world" and Shakespeare, who could not know that a man contains 1028 atoms, the earth 1052 and the visible universe 1087 atoms, concluded, "It is as easy to count atoms as to resolve the proposition of a lover."

  THE MUSIC OF WAVES

  The average farmer would probably be surprised, not to mention skeptical, if told there is a precise wave effect resembling music and life in wire fencing: that two lengths of ordinary hexagonal chicken wire laid crosswise, one upon the other, will weave visually together (like intersecting waves) into a mesh of small pentagons. Or that a triangular netting overlaid upon a piece of the same chicken wire will produce a fine lace of trapeziums. Such results are hardly what you'd call expectable, and even less so are the exquisite patterns now known as moire art that are created b
y the juxtaposition of two or more silky fabrics or screens, often with dazzling if not psychedelic effects. The grain of any of the screens may be rectilineal, radial, wavy or of some other crystalline weave, the combination producing its own shimmery wave effect, which is optically analogous to the aural beats in music made by dissonance between notes of slightly different pitch. Or it can come in the form of Lissajous figures or harmonograms, which

  are multiple line patterns drawn by vibrating tuning forks or the precessing orbits of pendulums or wheels that oscillate pens, feathers, beams of light or electrons until they have woven zany, topologic, cyclic, overlapping lattices full of similar unexpected graphic dissonances.

  Waves and the oscillations that generate them are of course among the most universal of phenomena and are familiar today in tides, winds, weather, rivers, ocean currents, magnetic lines of force, earthquakes, sound, radiation belts in space, sunspots, meteor showers, galactic gyrations, mass migrations of fish, birds, insects, microbes, mammals, man, etc. But two centuries ago almost nothing definite was known about the dynamics of waves and their oscillations, nor was it until just before the French Revolution that an imaginative German scientist and musician named Ernst Chiadni discovered that, if he covered a metal plate with sand and vibrated it with his violin bow, the sand would be rapidly shaken away from most of the plate, disposing itself as if by magic in a pattern of nodal axes along which the plate was almost motionless.

  Out of this rather Pythagorean and almost mystical revelation has gradually emerged the science of cymatics (from the Greek kyma, wave) in which modern researchers use piezoelectric crystal oscillators (page 452) to vibrate various powders, liquids, gases and blazing plasmas at thousands of cycles per second to see (and hear) how they will react. In effect it unleashes a new brand of molecular excitement that sews sand into lace and weaves honey into tapestries, the texture becoming finer as the pitch rises. It induces cream or iron filings to dance, regiments liquid waves into quavering "roof tiles," impregnates a film of glycerine with a fishbone spine, crimps flame or smoke into mackerel ribs and honeycombs soap bubbles into hexagonal prisms that literally "breathe." Music is made visible by it, notably with the aid of a sensitive diaphragm covered with a film of liquid that ripples with all the fleeting cross-currents and subtle complexities stirred by the sound of anything from a ditty to a symphony. And even though the beautiful melodies of Bach or Rachmaninoff here flow far too fast for the unprepared eye, they may be shot "dead" in their crystalline time tracks by a camera and mounted, as you see, in full photographic fidelity for leisurely yore-phase analysis.

  Probably the most interesting of all examples of vibrational sculpture is the virtually cosmic behavior of club moss spores strewn upon an oscillating plate, for these fine grains of powder quickly congregate into round clods that grow, rotate and orbit around each other like stars in a globular cluster, the size of each body varying in ratio to the intensity of the vibration, each crescendo a frenzy of love drawing more of them together, each decrescendo a quenching liberation. And a definite quality of life arises in this "otherworld" landscape with each pulsating pollen "organism" repeatedly oozing forth a probing linger, then creeping after it like an ameba, whereupon, by acting at the same time inherent in the universe and coherent in itself, it emerges as a tiny piece of world.

  The vibration that means life does not necessarily come from outside, however, for any temperature above absolute zero keeps molecules in perpetual motion and the H2O molecule in solid ice changes its position in its crystal lattice a million times a second. This of course is the inorganic brand of vibrant life that throbs through every snowflake that spirals down the sky - and, at still faster rhythms, every dancing drop of rain, every bolt of lightning. A drop of emulsion diffusing into ink without outside interference, for example, shows a natural to-and-fro movement like a flag waving, a whistle being blown or smoke tumbling from a chimney. It spurts and yaws and folds into unpredictable wispy patterns that are a mystic example of the emerging truth that turbulence naturally promotes life in the sense that it liquefies and sensitizes a medium to modulate the forces and rhythms that act on it: light and sound waves, mechanical motion, chemical and radiational influences of every sort. And most of the forms we have been discussing, whether created by artificial or natural vibrations, or holograms or fluid models that simulate fields of force, bear such close resemblances to crystal and other quantized structures common in rocks, plants and animals that one can't help realizing there is a fundamental law at work here ordering the textures and shapes and life of everything in the universe.

  CHAPTER 18

  Fourth Mystery: The Polarity Principle

  * * *

  BETWEEN THE CREST AND THE TROUGH of a typical wave, including many of the kinds we've been talking about. there is a certain up-down polarity like the north-south polarity of Earth. This is one of the simpler geometric examples of a little-known but universal relationship that, in many ways, is the most paradoxical and provocative of the Seven Mysteries of Life. It is the subject of this chapter.

  On first venturing into space, I used to feel I was way up here looking way down there upon the world. But now I've come to know that, in a bigger, truer perspective, up and down are only provincial illusions of local planetary life - illusions that, I was surprised to discover, were well understood by at least a few philosophers several millenniums ago. For wasn't it Herakleitos of Ephesos who said, in the fifth century B.C., that "the way up and the way down are one and the same"? And wasn't it he who later generalized the concept by adding, "It is sickness that makes health pleasant ... weariness precedes rest, hunger brings on plenty and evil leads to good"?

  Probably by now you have an inkling of the underlying pattern lurking behind such contradictions - or at least you suspect there must be a principle of some sort to account for the paradoxes that keep turning up in life. You are right. Let's call it the Polarity Principle. Evidence of it is virtually everywhere. When you open a window in winter you not only let in the cold but, in that one act, you also let out the heat. When the blacksmith hammers the anvil, the anvil also hammers the blacksmith. It's Newton's famous law of action and reaction. Then there are such inspired responses as the oyster's healing an ugly wound by turning it into a beautiful pearl. And, seeming to the contrary, all kinds of lovely creations serve the most deadly of purposes: the graceful leopard prowling, the orb spider spinning, the owl swooping silently in the dark, the snake stalking a frog, the barracuda herding a school of mackerel, the dragonfly overtaking a mosquito ...

  All creatures are affected more or less by others, and many are literally nibbled by the enemy, their fur or feathers often as not ragged from the struggle of life. Even the most handsome buck may have a piece of antler missing, a split hoof, a louse in his tail and a worm in his heart. After all, where would you go if you were a heartworm?

  PREDATION

  Here we are back to a subject touched on at the beginning of this book, and again in Chapter 13: predation. It is the interaction between predator and prey - a problem few philosophers seem to want to discuss and virtually none has seriously tried to resolve. I call it a problem because the idea of killing seems unacceptable to most law-abiding, life-loving people, and the question arises: is it important to the world for so many animals to kill and eat each other? Is a meal really more precious than a life? Is the traditional concept of animals "red in tooth and claw," battling each other to the death under the natural law of "survival of the fittest," true? And, if so, does man have to be a participant in it today or in the future?

  First let me say that the interaction (including predatory interaction) between all creatures is so pervasive that it surely includes man. And it must continue to do so for the foreseeable future, despite such evasions as the reported sale of rubber "worms" to squeamish human anglers, who may not have even considered whether fishing is harder on the fish than on the worms. I know there are idealists who rate predation as bad because all c
reatures are "brothers" and it's wrong to kill your brother - a doctrine that, if carried to its logical extreme, would make a cannibal out of everyone who eats lunch. And many such people persuade themselves to become vegetarians, presumably because cattle behave more brotherly than carrots.

  Practically speaking, of course, man, like all large animals and almost all small ones, can survive only by killing, be it directly or indirectly. I can imagine a fanatic who might try to get along by eating only vitamin pills and milk or perhaps animals or vegetables that had died naturally, but his wouldn't be much of a life even if he survived. Almost everyone, in choosing food, condones the killing of fresh vegetables if not animals, and even a vulture implicitly approves the predation that provides his meat, to say nothing of the slaughter of vegetation that nourished the prey or the prey's prey beforehand.

  What I am saying is that killing per se is not evil, for it is woven into the very fabric of the planet. "All flesh is grass," and inevitably everyone who really lives has to choose at some point among the interacting traffic around him. Even if he never hunts or farms, in effect he must take sides somehow in the competition between animals, vegetables, minerals, man, disease, weather, fire, flood, earthquake ... or else he might one day find himself living precariously in an overgrown jungle or swamp that is about to be consumed by plague, war, insects, fungus, poison, drought or some other influence beyond his control. But man has long been a hunter and it isn't reasonable to suppose he got into the business or its offshoots (herding and farming) just by accident. There is every evidence that hunting (including vegetable hunting) has been his main occupation as long as he has existed, and the excitement and challenge of the animal hunt has been important, perhaps vital, to the development of his mind, his speech and much of his early culture.