The Seven Mysteries of Life

by Guy Murchie

  The fact that every individual of us is so fantastically improbable then, so negentropic if you like, is of life's essence as surely as life is the mysterious force that resists entropy and increases order in the worlds. And improbability seems to be the only factor preventing many, if not most, people from having genetic duplicates of themselves here and there among the world's population, something more than theoretically possible, as is demonstrated both by the occasional phenomenon of identical twins (where improbability is naturally circumvented) and by cloning, a similar asexual reproductive process (where improbability is artificially circumvented) and which some prescient researchers say will someday enable anyone of means to keep a deepfrozen identical twin called a clone on hand in a "clone bank" for organ transplants, a rather nightmarish service that conceivably will ultimately include the transplanting of the entire body or mind (two faces of the same coin) through some sort of transference of memory cells, perhaps involving temporarily induced amnesia, hypnotism, astral projection or a form of psychic anesthetic today not even hypothesized. When (or if) such a day comes, the study of death will presumably have become a promising branch of science closely allied to the already growing researches of memory and consciousness with psychologists inducing losses of memory so complete the patient can be mentally reborn with a second mind, later a third, fourth, etc., amounting to a multiple consciousness, not to mention a multimortality and heaven knows what other states of mind that in turn might lead all the way to colonial or group consciousness or even some sort of unprecedented macrocosmic immortality.

  DIMENSIONS

  Unfortunately it is more than possible that a discussion like this will turn less than comprehensible because, when we talk about consciousness, death, time and other dimensions as criteria of life, we are in the same hard-to-visualize field Einstein explored when working out his relativity theory along with its contingent concept that every individual's personal orbit through life is representable as a "world line" framed in the common four-dimensional crystalline coordinates of space-time. And in case you didn't notice it, a prime philosophical deduction from world lines is that, if relativity be true, an independent "I" bounded by birth and death is an absurdity, since, as we will explain in Chapter 17, the field concept now so well established as a foundation for relativity implies continuums in virtually everything, including space-time and most certainly its best-known derivative: life. In my view, furthermore, the key to comprehending space-time is the obvious (to me) fact that space is the relationship between things and other things while time is the relationship between things and themselves. The time relation thus requires some establishment of identity (between things and themselves) seeing as identity is indispensable in temporal continuity. But if identity is of the essence of time, it follows that when a human being gives himself to a cause, letting his individual identity be absorbed in something larger than himself, he is proportionately liberating himself from the field of time. Which tells one something about the relation between mortality and immortality and between life and death, for it presumes that, as one's self is swallowed by universality, to a comparable degree one becomes immortal.

  How this relates to dimensions in the universe is not very apparent, but if you've ever had the feeling P. D. Ouspensky once hinted he'd had, that your 'piece of universe" is not as big as it should be, it just could turn out that one of your dimensions is slipping. Two-dimensional people from Flatland, for example, who have length and breadth but no depth, can see one-dimensional worms and two-dimensional flatfish, and they naturally accept the flat plane they are in as the whole universe, but any evidence of a third dimension that shows up is likely to be regarded as a curious phenomenon in that "universal" plane, something presumably supernatural. Should their world plane be wrapped around a sphere, let us say, so that they dwelt on its surface as humans do on Earth, they would be able to draw circles only as big as a certain size (a great circle like the equator) but no bigger. For no matter how hard they tried, if they were dimensionally confined to the surface, they would be unable to draw a bigger circle because there would be no room for it in their finite world. A virus swimming through the bloodstreams of a flatfish or a tapeworm likewise might be considered to be in a 2-D world (assuming the tapeworm had approximately zero thickness) even though the tapeworm be tied into a knot. For the knot would be a knot only from the 3-D viewpoint of an outside observer (say a 3-D bear) and the virus could swim on through all the tapeworm's convolutions and twists without knowing they existed. If he ever got outside 2-D he would presumably think he were "dying" until he discovered he was being "born."

  Now there is ponderable evidence that the world beyond our present mortal life on Earth is far greater than what we can know here. I mean greater in dimension and, from the earthly view, it probably should be considered infinite. For if we are limited here-now to the familiar three dimensions of space and the one of time, which together construct our finite 4-D world line, the fifth dimension looming up after death might be a line perpendicular to and intersecting all world lines - I mean a line passing through some moment of all life, an encompassing orbit of vital eternity, a symmetric circuit of infinite simultaneity simplifiable in mathematical notation to NOWinfinite. The sixth dimension could be an evolutionary spiral composed of all such 5-D orbits, amounting to the totality of all the events that happen on all world lines, the unending expanse of which weaves the texture of a world surface. The seventh could be an evolutionary lattice crystal made of these 6-D woven expanses in the form of endlessly layered surfaces that together compose a world volume. The eighth could be a sequence of world volumes, the ninth a succession of world sequences, and so on...

  The new mathematical concept of fractals adds the complication of fractional dimensions: partway between whole numbers, produced by curves or surfaces that wiggle enough to partially fill the gap between one dimension and the next. And Ouspensky speculated that there must be negative dimensions also - that is, immeasurable ones such as the lengths and breadths of streets in cities that are but dots on a map. And equally plausible negative dimensions come to mind like those of seeds harboring potential massive trees and forests (ultimately planets), of galaxies so distant they are but sizeless points of light in the black sky, of atoms enclosing mystic worlds too tiny to measure. The curvature of space is parcel of this of course, not to mention the curvature of time or higher dimensions, and it raises such questions as to whether the space-time in the known universe curves positively like a ball or negatively like a saddle. Although the preponderance of evidence so far points to negative curvature, this may be illusory because of the nearer, more visible, space flowing continuously through the waist of the hourglass of time, a saddlelike region; while the more distant space progressively yields to positive spherical curvature in every direction beyond our powers of detection.

  Some physicists have tried out mass-energy and temperature as dimensions, I am told, also wavelength-frequency, spin and presumably some of the less-known attributes of subatomic particles. And there always seem to be hypothetical entities in the offing, like the new tachyons that "travel faster than light" and conceivably could compose the "bodies" of intelligent "beings" with whom, fortunately or unfortunately, no one has yet figured out a way to communicate. This all seems pretty fantastic, but is not out of line with the way many hypotheses have established themselves. The fact that temperature is the rate of molecular motion, which is a quotient of space / time, evidently denies temperature a separate dimensional status. And the same with frequency and spin. But it is hard to know what other aspect of matter may yet turn out to qualify as a dimension, if any.

  There seems to me a significant and perhaps dimensional analogy between space-time, mass-energy and particle-wave, the first member of each pair being quite concrete as compared to the second one, which is so obviously abstract. On page 324 I pointed out the dimensional difference between a concrete body at any moment and its abstract essence over a period of time,
and on page 446 a dimensional compromise between order and movement. Later (page 491) I will try to show how the classic paradox of free will vs. fate may be resolved by dimensional perspective.

  And could it be that life itself is a dimension? Life seems to be an aspect of everything (both concrete and abstract) and in some ways remarkably independent of space-time, not to mention mass-energy, particle-wave or even body-mind. Dreams and thoughts certainly overleap the accepted spacial and temporal dimensions of mass and materiality and who can say where or when or to what extent life may exist outside our familiar physical span of a few score years? Should I deny then that whatever the factor is, if any, that distinguishes life from nonlife, its nature just might be dimensional?

  MATHEMATICS

  As dimensions are magnitudes measured in numbers, they naturally and logically lead us to the venerable science of numbers known as mathematics, which is also called the language of abstraction because it is made up not of words but of symbols of quantity. Mathematics indeed is the only language based on pure logic which can therefore be understood equally well by trained people in every country.

  But how mathematics originated remains a mystery. One version has it that two cavemen got to quarreling over a woman, but, being friends, decided to try to settle the issue by peaceful contest rather than just belaboring each other with clubs. Then, after agreeing that the one who could think of the highest number could have her, one said, "You go first." The other retorted, "No, you go." Finally, after deep thought, one of them said, "Three." The other scratched his head a long time but eventually gave up. So the one who had thought of three became our ancestor and taught all his many children to count. As the millenniums passed, however, people thought of new numbers with which to count higher and, little by little, discovered ways to compare one thing with another through measurement and eventually by counting the numbers of standard units. "Things are numbers," taught Pythagoras. And in his later years he added, "There are also numbers beyond things." Thus mathematics advanced into abstraction and took a major stride forward when the Hindus introduced the zero. At first this seemed nothing but witchcraft, and it provoked fierce opposition throughout Europe when the Moors started promoting it in ninth-century Spain. Then slowly it took hold after a learned Arab explained that "the zero is not nothing. It is more than nothing, for it is something that has to be there in order to show that nothing is there. Also, like magic, it turns 1 into 10 because, of no value itself, it gives value to others."

  Negative numbers like - 2 or - 7 logically followed the zero which, serving as a mirror, reflected them as images of the positive numbers. Next came irrational numbers like pi, the circumference of a circle divided by its diameter, ten decimals of which give the circumference of Earth to the fraction of an inch, thirty decimals the circumference of the known universe to a precision imperceptible to any microscope, yet whose decimals, for no known reason, go on and on - apparently forever. Then, like a revelation, appeared impossible numbers like V-1 which, meaningless in itself, mystically led to the discovery that three-dimensional space could be combined with time into the four dimensions of general relativity.

  And when the distances discovered by astronomers became too big to visualize, mathematics helped mankind see the relation between actual and possible worlds by providing a quicker, simpler way of saying difficult things, such as I /r2 for Newton's law of gravitation or E=mc2 for Einstein's equation of the atom. Even an extreme comparison like that between the masses of the observable universe and, of the unobservable electron became easy when you could list the former as 1055 grams and the latter as 10-27 grams. Or if you wanted to know, say, how thick a piece of fine tissue paper would become if you could fold it over upon itself fifty times, a straightforward exponential calculation would tell you that anything one thousandth of an inch thick folded double 50 times (if that were possible) would become 17 million miles thick, or fat enough to reach to the moon and back 35 times! The secret of this calculation of course is that 50 doublings multiplies to the fiftieth power of 2, which happens to be 1,125,899,906,842,624. And if you just harness the power into modern notation as 250, it is almost mystically simple without being any less powerful.

  Mathematics is obviously a vast, as well as mysterious, science - and keeps on telling us such things as that four colors are enough to color any flat map unambiguously, though a map on the surface of a doughnut takes seven; that 33+43+53=63 which, represented as a cube 6 inches on each edge, contains exactly the same number (216) of square inches on its surface as of cubic inches inside it; that a skillful high jumper lets his center of gravity pass just under the bar abstractly while his body, bit by bit, goes over it; and that, if n represents any number, the sum of the first n odd numbers is always n2. But, logical as mathematics is, it can't solve everything, for it contains both unsolvable problems and undecidable propositions - like, for instance, the sentence: "This sentence is not true," which cannot logically be either true or false since, if true, it confesses its falseness and, if false, its confession is true.

  Also confirmations of a hypothesis sometimes, instead of supporting it, will paradoxically disprove it. Like, for example, when three cards are marked (on their faces) 1, 2 and 3, then shuffled and laid face down on a table to demonstrate the hypothesis that no card will be found in the same order as its number. For if the first card turned over is the 2 and the second the 1, the hypothesis has been confirmed in detail so far - and yet the revealed certainty (by elimination) that the third card must be the 3 has totally disproved it.

  Perhaps the most abstractly beautiful revelation in the history of mathematics came in the Pythagorean discovery of the ideal and elegant five regular convex solids: the tetrahedron, cube, octahedron, dodecahedron and icosahedron, all known ever since to be harmonically related in concentric order, the simple 4-faced tetrahedron in the center, the cube with 6 faces and 8 corners next to its reciprocal octahedron with 8 faces and 6 corners, followed by the dodecahedron with 12 faces and 20 corners next to its reciprocal icosahedron with 20 faces and 12 corners - all five complying with the mystic rule that the numbers of their faces plus their corners equals the number of their edges plus 2.

  Neither Pythagoras nor Plato, who adopted these famous figures after him, nor Kepler, who looked for them in the heavens, had any idea that they might be alive or actually living on Earth. Yet recently in fact all five of them have been found alive among the crystalline plankton in the sea, rather gaily betas sled yet minding their own business in benign indifference as to whether Pythagoras, Plato or mankind ever existed. The tetrahedron, somewhat rounded as if from internal pressure, is embodied in a protozoan called Callimitra agnesae, the cube is Lithocubus geometricus, the octahedron Circoporus octahedrus, the dodecahedron Circorrhegma dodecahedrus and the icosahedron Circogonia icosahedrus.

  Of course these living Platonic solids express an extraordinary synergy between abstract geometry and life, as do the patterns of leaves and florets in trees and flowers in relation to the Fibonacci series of numbers (page 58), but most wonderful of all is the fact that these various synergies are part of one abstract whole that amounts to far more than all of them individually added together. There is also a particularly mystic and irrational number or ratio known to mathematicians and architects as the Golden Section and sometimes represented by the Greek letter Φ, which could, for aught I know, signify Tree or Topology or Tao. Certainly it is one of the world's magically beautiful relations that directly affiliates protozoa and trees with geometry. Heaven only knows where it ends, or if.

  I might define Φ by saying that it is the ratio between two incommensurable quantities of which the lesser is to the greater as the greater is to the sum of them both. Or, taking a specific example, Φ is the length of the diagonal of a regular pentagon or of the radius of a regular decagon expressed in units equal to any side of either of these equal-sided figures. Such units of course could extend any distance: an inch, a mile, an angstrom, a light year. It makes n
o difference, for Φ always comes out 1.61803 ... which is the length of the diagonal or the radius in whatever units we use Φ, in other words, is the ratio between two lengths (expressed in numbers) in the same way that pi or 3.14159 ... is the ratio between the diameter and circumference of a circle. Like pi, Φ is an irrational number because it discriminates distances that lack a common denominator. And so there is no known end to its decimal places and therefore no way it can be expressed exactly, a discovery credited, by the way, to Pythagoras himself and which shocked science in the sixth century B.C. Neither does it help much to turn trigonometrical and say that Φ=2 cos pi/5. Better, if you have the philosophy: just to realize that this Golden Section is exemplified in a rectangle whose width (I) times Φ equals its length (1.61803...). This sublime figure (despite its irrationality) remained sacred to the Pythagoreans, who first drew it out in rows of dots after probably gleaning its approximate proportions from Egyptian priests. There is no doubt that they knew how to erect a square Φ2 on the rectangle's longer side Φ so that the two figures combined would create a new and larger rectangle of exactly the same proportions as the original. Such a square was one form of the Greek gnomon, which Hero of Alexandria later generalized as "any figure which, added to any other figure, creates a resultant similar to the original."

  Gnomons of course apply to triangles among everything else and any triangle may be divided so that one section is a gnomon to the rest, But the point here is that almost any shape of figure, including solid ones in three dimensions, can be built up, gnomon upon gnomon. And this, I take it, is the prime geometric and genetic secret of the chambered nautilus (whose chambers are gnomons) and of many sensitively balanced spiral shells and horns, and it's the key to the self-congruence that enables them to grow year after year without appreciably shifting their centers of gravity.