by Guy Murchie
A familiar example of this is the drunkard who doesn't know whether he is coming or going but who nevertheless staggers onward from somewhere to somewhere. Although no one can say in which direction he will move next, his net rate of progress is significantly predictable, in fact so much so that there is a well-established equation for it: D=dVn. This is a concise way of saying that the number (D) of feet of distance covered by the drunk (measured in one straight line from his starting point) tends to equal the average length (d) of each zig or zag that he staggers times the square root of their number (n). Thus 4 one-foot aimless staggers would net him on the average 2 feet of distance, or 9 staggers 3 feet, 16 staggers 4 feet... etc.
This goes for staggering molecules too - and presumably for stars and galaxies and the sleepless supergalaxies whose motion we have not yet had time to measure. D=d/n is the equation of disorder behind all diffusion and it tells us how fast a drop of ink will diffuse through still water or a puff of smoke in a lazy sky. It also explains why drunkenness (or dopeyness, if you prefer) is an expression of disorder diametrically opposed to the orderliness that means life. If something or somebody has a will to live, you see, it or he must resist diffusion and move from disorder to order, which means avoiding all those easy paths away from the previous position in favor of returning to it or, better, staying with it from the beginning. Basically it connotes sticking around: being stable and solid and working toward some sort of structure, developing something that could be called an organization. The word "sticking" is surely germane here. For stickiness is a key to life - and it says something as to why the Earth sticks together with the aid of gravity and why our bodies stick together with the aid of molecular forces in bone, gristle, colloid and collagen, of why the jellyfish is "icky" and even of why old horses traditionally get hauled off to the glue factory.
CRYSTALLIZATION
Putting it in terms of evolution, when a bunch of milling molecules makes its initial change toward what is generally considered life, the change appears first as an increase in stickiness, a familiar quality of stability, which is the beginning of order or negentropy, which is essential to life. But what form does this vital viscosity take on its way to stability and order? Exactly how do the milling molecules arrange themselves? The answer is: they begin to line up, to sort themselves, to form rows, layers, lattices. In short, they crystallize - for this is what a crystal is in essence: an ordered structure. And this is why the crystal is the basic structure of life, of order, and why ordered solids from rock to wood to muscle to bone to gene are all describable as crystal.
But what, you may wonder, is there about a crystal and its order that gives it this vital potential, this curious lease on life? If a solid is cooler, quieter and more dormant than a liquid or a gas, why isn't it also deader since dormancy and deadness are more or less synonymous? There is probably a relativity factor in this paradox and, I suspect, a dimensional compromise as well between order and movement, with life requiring at the same time enough order to order its movement and enough movement to move its order.
It is not an easy question, for no one seems to know why atoms accept orderly arrangements. I imagine they just fit together better that way and so "feel" more comfortable (therefore more alive) when they are in order, particularly when outside pressure, drought or falling temperature forces them into a dense mass. Come to think of it, a rather apt analogy of crystal order was encountered by a wayward classmate of mine recently when he found himself spending a month in a primitive Spanish jail cell in the company of nine none-too-palatable other characters. For he told me on emerging that by far the "nicest" nights he endured on the floor of the ten-by-eight-foot enclosure were those in which he was able to induce his fellow prisoners to align themselves, as a geometrician would say, parallel rather than transverse.
In some situations, order of this sort actually spells the difference between life and death, demonstrating quite dramatically its Promethean quality - but there are innumerable classes of order and semiorder and, if we are to understand crystals and life, we must learn something about them. Bear in mind: it is not as simple as studying disorder, which generally means examining gases and liquids that have practically no structure or form. Besides, there are many kinds of order not based on wallpaperlike repeating patterns and that, as a result, do not quite qualify as crystalline and so presumably (to the same degree) are unsuitable as building material for life.
When we finally get down to the viable crystal orders with their repeating patterns, the varieties not only seem endless but are literally multiplied further by impurities, by contagious "diseases," by microbubbles, by mixtures of different substances and by the inevitable discontinuities that creep between crystal systems even in a pure, unmixed substance, as the illustration shows. And the biological approach to crystalline complexity is to remind oneself that crystals are now classified into some 1500 "species," each of which has a characteristic form that is only the outside expression of a highly organized internal (almost genetic) arrangement of sextillions of atoms that differ for every element or compound they utter. And the racket and traffic involved are suggested by the recent calculation that a crystal cube one millimeter thick has about 100 quintillion energy "levels" occupied by the valence (loose) electrons of its constituent atoms forming a continuum. Further, when any face of such a crystal is growing at the seemingly gentle rate of two millimeters a day, more than a hundred layers of molecules must be accurately stacked on its surface per second on the average, each layer comprising some ten million precisely regimented atoms. And amid this microblizzard strewing forth a billion orderly atoms a second, is it any wonder that a few (or a few million) miss their proper niches, leaving empty spaces or bubbles, or that foreign particles sneak in among them, either replacing those absent or just squeezing into interstices that hadn't seemed big enough to try for? And, as for the discontinuity areas between two differently oriented crystals of the same material, these boundary zones are now classified as crystalline defects, a curious feature of which is that the layers of atoms involved show signs (by their wavering movements) of being uncertain as to which crystal they belong. Indeed this eerie, almost mental phenomenon apparently occupies one of the inner seams of life where indeterminism is born amid determinism and free will sprouts shyly out of rocklike resignation to fate.
THE MYSTIC INNER LIFE OF CRYSTALS
We might even go far enough lo surmise that the atoms and molecules busily growing a crystal must at times make a choice of sorts as to where they will lodge or relodge themselves. Certainly there are competing magnetic and other attractions between atom and atom which normally induce an approaching molecule to seek out the snuggest berth on a growing crystal, not just on a flat plane where it would be attached on one side but in the trough between two surfaces where it can be latched two ways or, better, in an inside corner between three walls or, still better, in a rare nook boxed in from four or five directions.
If there is almost no place at all for each molecule to go, the entropy is rated very low, while if there is but one remaining place for it (as in a perfect crystal at absolute zero degrees) the entropy drops to zero, which, in effect, renders the negentropy maximal and the potentiality of life unlimited. You will see, therefore, that each molecule's yen for coziness is vital and it serves as the guiding force that regulates crystal growth to a degree approaching the mystical and, depending on the shapes of the atoms and molecules, continuously directs it in assembling the wonderful structures of Earth and life.
Of course it took centuries for man to realize all this even after crystallography became an exact science in 1782. That was when the Abbé Hauy, a geometry professor at the Museum of Natural History in Paris, demonstrated that the regular angles of any known crystal can be mathematically explained simply by assuming it to be a congregation of uncountable, tiny, invisible "bricks" all made in the same shape. Hauy evidently made his basic discovery by one of those seeming accidents which so often create the i
ndividual waves that, by joining a thousand others, form the advancing tide of knowledge.
While admiring a mineral collection in a friend's house, he inadvertently dropped a calcite crystal, which smashed into hundreds of pieces on the floor. Then, in sweeping up the fragments, the apologetic Abbé suddenly realized that every chunk and crumb of this crystal was similarly shaped with six faces all in the precise form of a 60° - 120° rhombohedron. (im) Excitedly he returned to his laboratory and began a series of experiments in fracturing crystals, which soon taught him that any crystal's beauty is purely geometric and derives directly from its natural materialization of abstract planes and angles, a revelation that led straight as an axis to his Law of Rational Intercepts. And, continuing from this noted law during the next century, a whole dynasty of crystallographers recognized and explained the four divisions of symmetry through which
The point, the line, the surface and the sphere In seed, stem, leaf and fruit appear.
Of course these same four symmetries also correspond roughly to the four classic kingdoms of mineral, vegetable, animal and man. From which crystallographers, using the new tools of modern science, sorted and defined crystals according to the angles of their axes of symmetry into the six systems called cubic, tetragonal, orthorhombic, monoclinic, triclinic and hexagonal, which use just 14 lattice patterns in assembling exactly 32 classes of symmetry into the aforementioned 1500 crystal species now known to man.
CRYSTAL DISCONTINUITY AS SEED OF LIFE
In their search for life in all this seemingly frozen abstraction, the crystallographers eventually settled on the spiral crystal as the probable ancestor or cousin of the helical molecules that compose all protein and genes. They also deduced the spiral must have originated as a lattice discontinuity or imperfection in an otherwise smooth crystal, which would make it not only a kind of crystal mutation (some call it a disease) but the place where unexpected surfaces act to stimulate and accelerate growth. This supports the concept that irregularity or asymmetry is a key to life. And the discontinuity I have most in mind is called the screw dislocation because it is centered on an axis in such a way that the molecules stacked sequentially, around it are induced to build a screwlike body, enclosing themselves like cambium cells girdling the stalk of a flower, patiently assembling their curved lattice, layer upon layer, as the growth plateaus sweep around and around and upward in the manner of a spiral staircase.
A few crystals, however, including certain plant proteins, are so programmed that they grow square and hexagonal spirals and seem to be trying to reconcile the diverging mineral and vegetable kingdoms. Others, like hydroquinine, have evolved a double interlocking shape with twin-brotherly or schizoid crystals, both of whose members overlap in the same space at the same time without really becoming part of each other. Still others naturally grow in only two dimensions, fanning out into thin flakes such as mica. And certain very simple ones grow primarily in one dimension, ultimately sprouting into silky whiskers such as asbestos. There are even a few so lax in organization that they do not grow in any definite dimension. These are glass, which is structurally just a stiff liquid, not crystal at all.
Still others, showing unmistakable signs of life as we saw (page 387), branch into microscopic trees with twigs, foliage and "fruit" resembling berries, plums and apples. Some have also been known to get sick, overweight, neurotic or maybe just spoiled from pampering. And, not surprisingly, they can be treated and cured of illness, put on a diet, or have their wounds healed with new growth. They can also do all sorts of human things like sleep, travel, sweat, blush, glow, sing, even (like lodestones) fall in "love." In which connection I might point out that crystals have actually been seen to attach themselves to each other as if mating and, perhaps consequentially, to produce a family, occasionally including twins, triplets and other multiple births.
CRYSTAL ENERGY
One doesn't usually think of famines as a problem for minerals, but nourishment is as vital to them as to any organisms, and if a crystal is underfed, particularly during its embryonic development, it will almost surely grow up scrawny and open like a skeleton with its substance concentrated on its edges. And if growing conditions get so bad it stops growing altogether, it may even shift into reverse and become smaller, literally ungrowing like an evaporating snowflake or the tadpole who ungrows his tail to transform himself into a frog (page 155), which amounts to self-digestion, a localized dying process that, in a mineral, is called etching. From the viewpoint of minerals, moreover, as I suggested earlier, this kind of dissolution is really more of a reincarnation or reawakening than a dying, since crystallization is essentially a cooling, settling-down and going-to-sleep process in which structure is formed by atoms expending energy and radiating heat as they compose themselves like a bear getting ready to hibernate. The crystal's energy leaks away most easily from its edges and easiest of all from its outer corners and protruding points, in the same way electrons leak off the sharp tips of lightning rods into the sky (to disarm the static potential for lightning), which explains why snowflakes, like cities, bones and other crystals, tend to grow fastest along their branches and twigs while their life is more abstract, negentropic and empyreal than that of secular, entropic rain. In some sense snow indeed serves as a symbolic being in rain's seasonal afterlife so analogous to that of the ethereal butterfly whose generations alternate with those of the cloddish caterpillar. Thus we see the mirrored paradox of life: on the one hand crystal slumber, cool and orderly as the clock that has run down and stopped, latent with complexities, fluid potentialities and disembodied dreams; and on the other hand volatile action, warm and free as a prairie fire, kinetic with restless ferment, simple, corporeal and seething with turbulent creativity.
PIEZO, THE CRYSTAL OF LIFE
The sort of crystal that reconciles this paradox of life best of all is the rather extraordinary type called piezo, with something like a very simple nervous system that makes it generate an electric current whenever it is distorted by mechanical pressure. The verb "to press" in Greek is piezin so it was only logical to name this kind of vital response the piezoelectric effect. It occurs because distorting a crystal means moving its atoms in relation to one another and, since some of them are ions carrying extra electrons, this kind of distortion amounts to a flow of electrons which, by definition, collectively add up to an electric current. Putting it another way, as the illustration shows, when a
piezoelectric crystal unit is not distorted, its centers of positive and negative electric charge coincide, and there is no flow of current. But the instant the same unit is squeezed into a different shape, the charge centers are pushed apart and the current flows as long as the centers keep moving. Furthermore, because the phenomenon is relative, it works reciprocally, so that, when an outside electric current is applied, the charge centers move and the crystal contracts or, if connected to an alternating current, it alternately contracts and expands. In which case of course it becomes an oscillator and can regulate frequencies in all sorts of electronic equipment.
Among the better types of crystals for piezoelectricity are salt (because it is full of ions), quartz, tourmaline and barium titanate, the last of which has become important in radio and TV microphones (where early this century it learned to sing), transmitters, submarine sonar systems, ultrasonic tools and cleaning devices. Then in 1954 two Japanese scientists named Fukada and Yasuda discovered that bones are piezoelectric and documented their report with evidence that the shear stress of collagen fibers, slipping past one another in a bone's crystal layers, generates electricity, presumably by bending or twisting the cross-linked atoms. American biophysicists, taking up the investigation from there, soon demonstrated that bones really are shaped by mechanical forces as D'Arcy Thompson divined half a century ago (page 16) and mostly with very definite help through the medium of electricity. When a growing thigh bone, for example, is bowed by external force, its convex side becomes charged positively and its concave side negatively, with the r
ather miraculous result that positive calcium ions steadily migrate from the convex to the concave surface, straightening and strengthening the bone. Indeed should the strain on the bone be removed, as during a period of weightlessness in space, the electric charges rapidly fade away, halting the migration of calcium ions and allowing them to be resorbed into the bone. In sum, it now appears almost certain that piezoelectricity is a common attribute of tissues, working unobtrusively not only in much of the mineral kingdom but in virtually all of the vegetable and animal kingdoms. And accumulating evidence strongly hints that senses in every kingdom operate more or less piezoelectrically, probably including the still undeveloped ones.
Since any stable structure is in essence crystalline by the very definition of a crystal as a latticed form that "wants" to maintain itself, we find crystallinity a quite universal principle, extending at least from the molecule to the supergalaxy and very probably beyond in both directions. The hemoglobin molecule, for instance, may be described as a crystalline organism whose main body contains four sections, each centered in an iron atom capable of grabbing and holding an oxygen molecule.
