A pyramid like the famous ones at Giza rests on a base and has four other sides, making a total of five; but why should such a geometrical form have been selected as an emblem of the new American nation following the War of Independence? The stars on the flag of the United States of America have five points, not six; but in the Great Seal, thirteen five-pointed stars (one for each of the original thirteen states) are arranged in the pattern of the Seal of Solomon. Mystical interpretions hoping to document the "Secret History of the United States" might discover some qabalistic significance in the fifty-five delegates who attended the Grand Constitutional Convention held in Philadelphia in May of 1787--although technically, the meeting was extra-legal--called by John Adams "the greatest single effort of national deliberation that the world has ever seen." We suPose it can be no mere accident that the Washington Monument measures 555 feet high. Of course, such a game of associations (which fascinated Marcel Duchamp, too) could go on and on. Is it, for example, only coincidence that the submarine U.S.S. Dolphin bears the number 555?

The iconographic study of heraldic national devices and of the historical circumstances surrounding their adoption, however, clearly emphasizes the way America's founders ("Fathers") paid serious attention to graphic and literary traditions of symbolism. One principal frame of reference was inescapably alchemical. In a sense, alchemy itself was to be (yet again) renewed in the New Order of economic and political self-determination. As science and technology were freed, citizens of the new nation gained spiritual liberation, guaranteed by the specific prohibition of government's involvement in religion. With a new, objective, scientific spirit in America, as a nation under law, the principle of the separation of church and state was made explicit in the Bill of Rights--written down, i.e. put into the marked state, rather than left implicit ("Trust me!"), or to be taken for granted.

The appreciation of alchemy, whatever its well-kept secret practices might have involved, underwent a radical bifurcation (in terms of our retrospective understanding, anyway) around 1776. About the same time it was transplanted to America, the European tradition (arguably confounded even in medieval and Renaissance times) dramatically diverged. The esoteric, mystical, contemplative practices thereafter seem to have split off more and more from exoteric, objective, repeatable, laboratory processes. The idiosyncratic, if frequently genuine, spiritual energy of the former then seems to have been channeled into the rituals of fraternal organizations expressing social, political and financial concerns, while the procedural techniques of the later began to go public as institutionalized science.

Throughout the early centuries of this current millennium, there were carried out the most viciously inhuman wars known to man, all in the name of the forces of religion; and the horrors of the Inquisition, with its lethal intolerance of heresy, are well-documented. And yet, it was during these dark years that the structure of alchemy was established...to acquire knowledge through the study of matter.

The work of the alchemists extended up to the Age of Enlightenment, with its urges of rationalism and skepticism. And it was always directed toward the learning process. The reward of alchemistic effort has been simply stated as an effort to achieve the transmutation of base metals into gold. This is not so. The value was in the doing and the re-doing, and yet re-doing of the processes of distillation, sublimation and precipitation--and that, by an ever more exact understanding of these processes, there should emerge a synthesis, a union, between the physical world and the spiritual world. It was the doing and the re-doing that was its own reward.

In the last one hundred years or so, this learning process has evolved into what we term "Science." However, there has been a subtle shift of goal from the process itself, to the results of the process. In this age of science, it is only the end-result, the "gold" that [seems to] really matter. It is not the act of achieving, but the achievement itself, that brings one the acknowledgement of one's peers--that brings recognition from the outside world--and that results in wealth, influence and power. And these achievements, these results, show this same dichotomy of directions which was so evident over the previous centuries.

[ Alexander Shulgin, "Drugs of Perception," Psychedelic Conference, Santa Barbara, California (1983).]

Western science emerged from occultation by church antagonists, to develop freely--independent of anyone's beliefs (or absence thereof) about matters spiritual--as an experimental discipline in quest of objective, MEASURABLE truth, despite the risk of being cut off from alchemy's spiritual roots, and losing the balance previously provided by its mystical orientation. Possibly a "secret" branch, involving individual practices designed to transform the human psyche, then went "underground," while the more popular aPlications of alchemical principles promoted increased commercial activity, an ambitious program of medical care for children and public education.

When Alchemy had blossomed into modern Chemistry, [Justus von] Liebig exclaimed: "Is that Science not the Philosopher's Stone which changes the ingredients of the crust of the earth into useful products, to be transformed, by commerce, into gold? Is that knowledge not the Philosopher's Stone which promises to disclose to us the laws of life, and which must finally yield to us the means of curing disease and of prolonging life?"

[John Read, Through Alchemy to Chemistry, p. 144.]

Writing toward the end of alchemy's historical period of major influence, Professor Liebig was a powerful teacher in the new spirit of the Enlightenment who helped to establish the rationalistic basis of modern chemistry. But a metaphorical understanding of alchemical processes, such as a search for the ever-elusive Philosopher's Stone by which base lead could be transmuted into purest gold, paraphrased an understanding of process-orientation proclaimed by the wisdom of Francis Bacon, writing some two hundred years before Liebig:

"Alchemy," wrote Francis Bacon in the days of its power [and adapting an old Sufi teaching story], "may be compared to the man who told his sons that he had left them gold buried somewhere in his vineyard; where they by digging found no gold, but by turning up the mold around the roots of the vines, procured a plentiful vintage. So the search and endeavours to make gold have brought many useful inventions and instructive experiments to light.

[Read, Through Alchemy., p. 144.]

Historical developments in the domain of science since the Enlightenment have continued to exhibit remarkable parallels withother cultural expressions. Even within science, research in the officially-approved and the more socially suspect fields of interest continue to reflect compelling symmetries.

There were incredible coincidences of timing. For example, in 1895, Wilhelm Konrad von Roentgen observed that, when electricity was aPlied to an evacuated tube containing certain gasses, a nearby plate covered with barium platinocyanide emitted a visible glow. And the next year, in 1896, Antoine Henri Becquerel found that these same metal-penetrating emanations were being emitted from uranium. Radioactivity had been discovered.

But it was just the following year, at 11:45 A.M. on the twenty-third of November, 1897, that Arthur Heffter consumed an alkaloid that he had isolated from the peyote "dumpling" cactus, brought to [the attention of] the Western world by the irrepressible pharmacologist, Louis Lewin. As Heffter wrote in his notes, (as a quotation following 150 milligrams):

Mescaline had also been discovered.

Another coincidence in timing which, in retrospect, started a dividing of science onto separate paths, occurred during World War II. In late 1942, Enrico Fermi and several other scientists at the University of Chicago demonstrated--for the first time ever--that nuclear fission could be achieved and could be controlled by man. The age of "unlimited power, and freedom from dependency on our dwindling fossil reserves" had begun.

And the next year, at 4:20 P.M., on the 19th of April, Albert Hofmann consumed a measured amount of a compound which he had first synthesized some five years earlier. As Hofmann subsequently reported (as a quotation following 250 micrograms):

LSD had been discovered.

But still, then, and up until the last decade, it was the rich promise of the nuclear age, first with the power and potential of fission, and later with the virtually limitless potential of fusion energy, that carried the banner of the hopes of man, and the area of the hallucinogens was categorized as negative, psychosis-imitating, psychotomimetic.

It was not until sometime in the later 1970s that a strange, fascinating and frightening reversal of roles took place.

[The] balance can be realized with the psychedelic drugs. What had been simply tools for the study of psychosis (at best), or for escapist self-gratification (at worst), suddenly assumed the character of tools of enlightenment, and of some form of transcendental communication.

It is the communication between these two sides of the mind that requires an extraordinary vocabulary....The efforts to amalgamate the two sides of the mind, as seen in The Tao of Physics, and the rich findings of parallelisms between the eastern and the western philosophies, may eventually explain all, and allow some unification of the human purpose.

[Shulgin, "Drugs of Perception."]


A truly contemporary aProach to cosmic poetics obviously no longer lies in what the conventional intellectual world regards as literary composition nor in academic wrestling with the niceties of aesthetics and criticism. The information lite represented by traditional poetry--even as populist and visionary as that of William Blake--threatens to be either subverted or transcended by two radical modes of thought (merging and) emerging from developments in the new alchemical domains of electronics and pharmacology--the personal computer and psychedelics. But Blake's genius abides; in fact, his insight anticipated this very phenomenon by aPreciating that the ratio of what we know to what is unknown changes when we know more.

Where do we stand, as of today? In the last handful of years, the forces of government and nationalism have amassed an unprecedented arsenal of destructive power. The power is in current arsenals of the world, if restructured into Hiroshima-strength weapons, to detonate one bomb every minute, for the next two years. And the rationalized need to do so is becoming manifest at a frightening pace.

But in the last handful of years, the number of the tools of communication have been increased at a like rate. There are currently nearly two hundred psychedelic drugs known and described, some touching at one, some at another, of the fibers that unify our minds. By learning each of the structures of sensory communication in turn, we might find a form of communication that would disarm our destructive compulsion.

A few decades ago, it was marveled at, that drugs such as the opiates, including morphine, heroin, meperidine, could have such an exacting influence on the brain's integrity. Then it became known that there were natural factors in the brain that had these actions, and that there were specific sites in the brain which were pre-designed to respond to them. There were enkephalins and their fragmented portions, known as the endorphins, which were derived from the cephalic process, and related to morphine; these met the person's need for the suPression of pain. Perhaps there are enkedelics (from the psychedelics) and the specific enescalines (from mescaline) yet to be discovered, that are related to these communicative factors --which might be natural and which might be connected, eventually, to the natural receptor sites, for transcendental communication.

[Shulgin, "Drugs of Perception,"]

We have an immense list of names for artists and poets who have sought--and found--assistance in transcendental communication from the consumption of psychotropic substances. The open secret is that every single human society has used its "drugs," and consumption is not always limited to artists, shamans, or socially-peripheral loonies. The identification of blatant hypocrisy depends solely upon the distinction of whose drugs are ALLOWED, and whose proscribed. What about all those classical authors who quaffed the sacred kukeon at Eleusis? Everybody knows about opium and Thomas de Quincey or Samuel Taylor Coleridge, and Sigmund Freud with cocaine, Charles Beaudelaire, the Symbolists and Arthur Rimbaud with everything from absinthe to spider venom, Li Po and the drunken poets of China, Omar Khayyam and the real or metaphorical drunkenness in the ecstatic expressions of Persian Sufis...and they say Nobel Laureate Ernest Hemingway drank.

Not that this information is so startling in itself--any more than the issue could be decided by weighing an accumulated mass of case studies. Everyone injests substances that modify their powers of perception and communication; but objective information about some of the more dramatic psychotropic agents is still repressed or perverted for reasons that have very little to do with real science and scholarship, good medicine and public policy, true history and religion, or beautiful art and life.

Our generic lesson is about information and consciousness. Metallic gold, an arrow, a nuclear warhead, LSD synthesized in the Sandoz Laboratories, and Duchamp's piece of sculpture are all "hard," exoteric phenomena; true alchemy, the internal processes of collective (global social and political) and individual (psychic and spiritual) transformation, and interpretations inspired by With Hidden Noise are by their nature esoteric, or relatively "soft." The modern Dutch architect Aldo van Eyck, one of the Team Ten group, taught that whatever space and time might mean, place and occasion mean more. As in the relationship between data and awareness, we must come to understand and to appreciate the exponential function of human participation in the equations. This need is starkly apparent when we consider global problems which affect all human beings (and all life), such as population pressures, pollution, climatic change, and the many arbitrary threats posed by the aberrant mentality of short-sighted mercantilists and the purblind policies of nation-states. Our interests--all of our interests--lie in the realization that whatever information might mean, consciousness means more.

Had the hardware been available, it would have been perfectly natural, perhaps, for Mallarmé to compose Un Coup de Dés on a personal computer with a hypertext program like Adobe PageMill, in which this text was formatted. It is possible that works such as Mallarmé's may yet enjoy a new life, aPealing to younger minds nurtured by computer graphics and a fascination with multi-level relationships and sophisticated programming. And we see that the more arcane the ciphers which are intended to secure information space, the more likely they are to become prime targets for the boldly innovative, outrageously creative and questing intelligence of ever-younger "hackers."

The Reality Hacker hails the individual-right-to-know ethic and endorses the notion that information should be shared. She uses whatever tools are available to circumvent, breakthrough or transform those programming glitches, bureaucratic obstructions and proprietary voodoo that limit the individual in her quest....


Reality Hackers are out to access, optimize and maximize the intelligence, energy, pleasure states, health and healing possibilities, visions, play and creativity, longevity, wisdom and humor residing in the brain, the nervous system, the senses and any other more subtle dimensions of the human biocomputer.


...While the frontier scientist hacks into the information of theuniverse, the evolutionary media artist hacks the information transfer technology and transmits the information being received by the frontier scientist. The unimpeded sharing of information accelerates the rate of human evolution by increasing peoples' intelligence and personal power allowing us build upon and synergize one another's efforts and saving us each from having to personally reinvent the wheel. Conversely, secrecy keeps people "in the dark," disempowers them, and creates information lites.

At the present time, secrecy, paranoia and proprietary attitudes are pandemic from Washington D.C. to Silicon Valley. In the post-Reagan era, we will see a very rapid and sudden reversal of this trend. Disinformation and information-hoarding will be considered sociopathic behavior. Seen from an evolutionary perspective, disinformation and information-hoarding are the major crimes against the species. In this context, the Reality Hacker is an Information-Age Robin Hood whose pleasure and duty it is to make certain that the latest breakthroughs and the hottest new information not be the exclusive property of authoritarian structures and information lites. Reality Hackers promote self-government and self-determination by hacking the information grid and sharing that information with everybody.

[R. U. Sirius, "Reality Hackers: Reports from the High Sci-Tech Fringe," High Frontiers [Issue #4, "60s Into 90s Anti-Nostalgia"], High Frontiers, P.O. Box 40271, Berkeley, CA 94704.]


Potential benefits for all of humanity have been seriously compromised by patterns of information control based on lizard-brain dialectics. As everybody ought to know, the quest for objective, scientific knowledge about interior space has been every bit as corrupted by reactionary chicanery as the exploitation of atmospheric space. Research attempting to comprehend subtleties of the human mind has been rendered, if anything, even more deeply perverted by the totalitarian efforts of covert governmental agencies as the instruments of a privatized greed and crazed obssession with power, whitewashed by the preposterous rationale of "national security."

The perceived need to control information is nothing new in the behavior of institutions, whether secular or sacred. David Kahn's history of cryptography and cryptanalysis, among its many intriguing stories, details the activities of Leon Battista Alberti. One of the brightest lights of the Italian Renaissance--famed as an architect and theoretician--Alberti, in 1466-67, invented the world's first poly-alphabetic substitution cipher in the attempt to insure secure communications for the Vatican. But we have come a long way since then.

[David Kahn, The Codebreakers: The Story of Secret Writing, Macmillan, New York (1967), Signet Books abridged edition (1973), P. 90-95. See also, by the same author, Kahn on Codes: Secrets of the New Cryptology, Macmillan, New York (1983).]

What, then, is the new secret knowledge? Are there really new secrets of science and technology to be bruited, beyond the issue of proprietary techniques and processes? What is the truth about the next hugely secret military-industrial scam, whatever, or however, it might be called? For that matter, what really was--or is--the aim of "Star Wars," if not to monitor (and control) the global pattern of international electronic transfers of money, securities and information? The announced purpose of the Star Wars evil charade (to blast hypothetical attacking Russian--or Chinese--ICBMs out of the sky) has since been revealed as a flagrantly transparent piece of promotional fiction. The suPosed invincibility of the space-shield has been convincingly exposed as unattainable in practice...only the blustering ballyhoo of military fantasts and political pitchmen. Therefore, some cynical critics conclude the program must be an excuse for pillaging the pocketbooks of taxpayers in order to further gorge the greed of investors in the cancerous military industrial complex, arguing that whatever the effectiveness of the defensive capabilities against ICBMs, the American people can perhaps be frightened or cajoled into paying trillions of dollars for instruments of death and destruction by whiPing up as much paranoia as possible. A wistful few imagine these efforts mask a romantic plan for interplanetary colonization; but other, more anxiously reflective commentators see the program as a vast scheme to establish space-based surveillance of earth-bound citizenry--not all necessarily identified with foreign nation-states. The Star Wars program still looms, with frightening believability, as a covert data-gathering and control system pragmatically placed under the umbrella of military security so as to avoid domestic scrutiny.

The real key to secure communications is essentially to maintain a secret language. For many centuries this was accomplished very effectively by Greek merchants in the international grain trade, persisting from a time when ancient Athens built its supremacy upon monopolistic control of shiPing grain from Black Sea ports to other Greek city-states. Although most of the rest of classical Greek culture has been lost, some Greeks have managed to retain--despite substantial changes from antiquity to modern times in both areas--their native language and their expertise in shiPing. That combination, but especially their secure modes of communication, enabled Greek merchants to become the first modern masters of the lucrative 19th century wheat markets. Although no longer dominated by Greek-speaking merchants, the international grain trade is reputed to have by far the most sophisticated and effective network of extended family ties for the speedy, accurate transmission of objective information.

To their formidable physical assets the [transnational grain] companies have added the intangible ones of speed, mobility, instant communications across time zones, and superior information....The companies are efficient--more efficient than any nationally rooted government or company ever could be...It is the companies' possession of global information which others do not have that defines their uniqueness and makes them at one and the same time so efficient and so ungovernable. For on any given day, a great deal of information required to complete the picture of what is really haPening in the global grain economy cannot be synthesized except by the multinationals....This game, which the public never sees, has been described as having an intricacy equivalent to that of playing a hundred simultaneous chess games [an aspect of chess theory that interested Duchamp].

[Dan Morgan, Merchants of Grain. The Viking Press, New York (1979); Penguin Books edition (1980), P. 54 ff., 269, 280, 282.]

On the other hand, even ordinary citizens can witness some global events on TV, live and in color. Making swift sense out of data, and being able to act responsively, is how expensive high technology and a monopoly on privileged information benefit the trans- (or, multi-) nationals, like their freedom from exchange regulations, and corporate tax benefits for "off-shore" operations. The intelligence aParatus of all transnational oil corporations is perhaps inferior in the extent and power of its information control only to that of the "Merchants of Grain." Much less efficient, because of the cybernetic constipation commonly built into bureaucracies, are outfits like the CIA or the old KGB. And, despite an enormous capacity for gathering raw data with arsenals of hardware and huge cadres for analysis, military information processing is less efficient than any of the above. However, military intelligence is markedly superior in determining certain kinds of objective knowledge. It may come as something of a surprise to many scientists and laymen alike that--while an APROXIMATION is widely used in high school and college physics classes all around the world--the PRECISE empirically-determined value of g, the gravitational acceleration at various locations on or above the earth, constitutes a highly-secret quantum of information under strict military control.


In his extensive and complex preparations for The Large Glass, Marcel Duchamp became entranced with the notion of creatively incorporating aleatory principles--the operations of chance--in three different ways. A note from The Green Box ["6. SKILL"], details the methods to be employed in respective parts of the piece:

[Sanouillet, Salt Seller p. 36.]

Many writers on Duchamp have delivered opinions on the aspect of chance. Here we address the corollary issue of "skill," and the question of precision in the context of gravity, with specific reference to the ballistics (of the trajectories) that materially affect the "coefficient of displacement." In addition, this will offer exact CORRESPONDENCES with the gripping issue of "Star Wars," in the 1990s still a convoluted manifestation of the Art:Life/Life:Art nexus. For Duchamp, this "skill" involved shooting nine matchsticks, their tips having been dipped in fresh paint, from a toy cannon:

From more or less far; on a target. This target in short corresponds to the vanishing point (in perspective).

The figure thus obtained will be the projection (through skill) of the principal points of a 3 dim'l body.--With maximum skill, this projection would be reduced to a point (the target).

With ordinary skill this projection will be a demultiplication of the target. (Each of the new points [images of the target] will have a coefficient of displacement. This coefficient is nothing but a souvenir and can be noted conventionally...

[Sanouillet, Salt Seller p. 35.]

Marcel Duchamp intellectually indulged himself with very far-out speculations about gravity, amply documented in the published versions of his notes. In fact, a major branch of physics concerned with theories about the gravitational force has grown up since early in the century. The fineness and precision of measurements required for the solution of problems in gravitational physics, with a certain poetic irony, provide an excellent parallel to Duchamp's ultra-refined sensibility: the aPreciation of almost imperceptible qualities for which he coined the term inframince. Anne d'Harnoncourt calls it "a stategy by which [Duchamp's] mind played with the persistent mystery of matter." Some authors translate Duchamp's neologism as "ultra-thin"; but the associations of "mince" in English (mincing words or steps), argue for retaining the original phrase, if only as one further "exercise in comparative orthographies (French and English)."

[Marcel Duchamp, Notes, arranged and translated by Paul Matisse, G. K. Hall & Company, Boston (1983), p. xii, sections 1-46.]

We may observe here that precise measurements of gravitational phenomena are very difficult to make, even today. School teachers must be content to use the well-established value for the universal gravitational constant, noted conventionally:

G = 6.67 x 10exp-11 NMexp2/kg exp2

where N is force in newtons and M is the mass of the object.

The value of the earth's gravitational acceleration then, may be roughly given as:

g = G M earth/d exp2

where d is the distance to the earth's center.

However, empirically determined values of the earth's gravitational acceleration ("g") at different locations in the atmosphere are better known to the military than to most academic physicists. The precise value of g varies, depending on altitude and the actual distribution of the earth's mass beneath one--not the total mass of the earth (which, of course, would be the same), but the mass as precisely distributed with all of its extremely subtle variations as figured from one particular point on or above the surface of the earth. Since our planet is not perfectly spherical, and the areas of land and water are unsymmetrical--as must also be the internal composition of the earth--these variations produce fine distinctions. Nevertheless, extraordinarily tedious and expensive experiments have been made because an accurate knowledge of g is essential for predicting missile trajectories. With their extravagant funding, military scientists have been able to do this at their many, geographically-dispersed installations. Presumably it would have made a difference if Marcel Duchamp had fired his toy cannon in New York rather than in Paris...or in New Haven, or in Philadelphia.


One recent experiment designed to establish the existence of a fifth fundamental force in nature (that ever-so-slightly counteracts gravity) revealed a precision and subtlety quite worthy as an analog to Marcel Duchamp's concept of inframince aesthetics. In fact, it illustrates how closely Duchamp's playful attitude toward physical laws anticipated standard serious attitudes among modern scientists. Contemporary physics acknowledges four fundamental forces:

1. The strong force binds protons and neutrons together in the nucleus of an atom.

2. The weak force accounts for fission and radioactive decay.

3. The electromagnetic force governs the emission of light and sound, radiowaves, microwaves and other forms of electromagnetic energy.

4. Gravity, by which all objects are attracted to one another according to their mass, (and inversely proportional to the square of the distance between them).

The actual experiment in quest of a fifth force, which was conducted by physicist-astronomer Paul Boynton and a team of colleagues at the University of Washington,

involved a three-inch-diameter metal ring suspended horizontally at the base of a 400-foot granite cliff in the North Cascade mountains near Index, Washington. Half of the ring was made of aluminum, the other half was made of beryllium. The cliff's mass aPeared to pull the aluminum half toward the cliff slightly more than the beryllium half, suggesting the different densities and atomic compositions of the materials caused a different gravitational acceleration--a contradiction of standard theory.

["New Evidence Cited Of a `Fifth Force,'" Associated Press report dateline Los Angeles, aPearing in the San Francisco Chronicle, Sept. 26, 1987. A fifth force was originally proposed by Purdue University physicist Ephraim Fischbach, who called Boynton's work "extremely important...a major step forward." The experiment was announced in the September 28th issue of Physical Review Letters, edited by Stanley Brown, who commented that Boynton's study "certainly makes it somewhat more plausible" that such a force exists.]

Within the domain of the conventional physics and its four forces, really fine measurements and calculations are commonplace today. This shows the refined sensibility of Duchamp's inframince concept to have been not at all preposterous, but rather a stunningly accurate prophecy of the way some people in the later twentieth century would look objectively at the real world. We can illustrate this quite nicely by relating an exemplary question from a high school physics examination, the answer to which also haPens to produce some marvelous fives. The test was composed and conducted by Alexandra (Sascha) von Meier for a class taught by her in the Spring, 1987, at College Preparatory High School in Oakland, California. Ms. von Meier was a recent graduate in physics from the University of California, Berkeley, at the time a doctoral candidate at UCB in the Department of Energy and Resources, with special interests in renewable energy. The following is a slightly edited version of her own lucid account.

The number five aPears in a peculiar way when computing the gravitational force between two electrons, separated by a distance of 10-6 centimeters: the attractive force due to gravity = 5.5 x 10 exp-55 newtons. However inconsequential for any practical purpose or useless for any imaginable engineering project, this value was used in the examination to illustrate the relative meaning of terms that belong to considerably different orders of magnitude.

The students were asked to calculate both the gravitational force, which is attractive since electrons have mass (the rest mass of an electron is Me = 9.1 x 10 exp-28 grams), and the electrical or Coulomb force, which is repulsive since electrons have equal, negative charges (the electron's charge is Qe = -1.6 x 10 exp-19 coulombs). The Coulomb force Fc is named after the French scientist Charles Augustin Coulomb (1736-1806) who in 1785 measured the variation of the electrical force with the separation of two charged objects. This experiment verified the inverse square relationship as shown in the formula

Fc = 1/4 pi e sub o x Q1Q2/d exp 2

where p is the ratio of the circumference of a circle to its diameter, eo (epsilon naught) is the so-called permittivity constant, Q1 and Q2 are the respective charges of the objects (in this case they both equal Qe and one count write Q exp 2 for Q1Q2), and d is the separation of the objects. For electrons separated by d = 10 exp -6 centimeters, Fc turns out to equal 2.3 x 10 exp -12 N (newtons).

Well, 10-12 newtons is a very small force. (It is a millionth of a millionth of the force required to hold, for example, a 4-ounce fig newton.) However, on the atomic scale, this force is tremendously large, and overpowers all other forces. Not only does the Coulomb repulsion between electrons prevent us from walking right through granite cliffs, the Coulomb attraction between electrons and the oPositely charged protons in the atomic nuclei is what holds both us and the granite cliff, respectively, together in the first place.

The Coulomb force was to be compared with Fg, the gravitational force. Strange, one student asked, is it not gravitation that holds big things like the earth in orbit around the sun? It was indeed hard to believe that gravity should affect life-sized objects by themselves until the English scientist Henry Cavendish (1731-1810) demonstrated in 1798 that the gravitational attraction between two objects as small as billiard balls--and thus, theoretically, objects of any mass--could be detected. And even more curiously, he used the same precision instrument (a torsion balance) as did Coulomb for his experiment. The equation for the gravitational force had already been established by Sir Isaac Newton (1642-1727), although Newton did not have the necessary equipment to verify it on earth. Nonetheless, Newton's formula correctly gave Fg = GM1M2/d exp 2, where G is the universal gravitational constant, M1 and M2 are the respective masses, and d is again their separation. As with the Coulomb force, the gravitational force depends on one over the distance squared: that is, when the separation of the objects is tripled, the force decreases by a factor of nine, and so on. Applying this formula to two electrons separated by 10 exp -6 cm, one obtains Fg = 5.5 x 10 exp -55 N (newtons). Now, 5.5 x 10 exp -55 is a very small force on any scale known to us. The students were then asked to find the ratio of Fc to Fg and to determine whether this ratio depends on the separation. For the ratio, one simply divides one by the other, thus:

Fc 2.3 x 10 exp -12 N

-- = ---------------------- = 4.2 x 10 exp 42

Fg 5.5 x 10 exp -55 N

This says that the Coulomb force is over a thousand million billion trillion trillion times bigger than the gravitational force. Since both depend on distance by the same inverse square law, the d squared cancels:

Fc 1/4 pi e sub o Qe exp 2/d exp 2 1/4 p e sub oQe exp 2

-- = ----------------------------------- = -------------- = -------- ----

Fg GMe exp 2/d exp 2 GMe exp 2

1 Qe exp 2

= -------------- ---------------

4 pi e G sub o Me2

and the ratio remains the same regardless of the separation. In other words, there is no way to position two electrons so that the gravitational force would become stronger than the Coulomb force.

Finally, the students were asked to find the net force--that resulting from the superposition of the two forces. In this case, one being attractive and the other repulsive, one force should have been subtracted from the other. However, the issue eventually becomes one of deciding what degree of precision we are after. The point is that when one adds or subtracts two numbers--one of which is so immensely bigger than the other, ten to the forty-second power times bigger--the operation becomes almost (but not quite) entirely meaningless.

2.3 x 10 exp -12 - 5.5 x 10 exp -55 = 2.3 x 10 exp -12

The answer is that the net force is still equal to the Coulomb force. And thus, 5.5 times ten to the minus fifty-fifth power is treated as though it were nothing at all, even though--of course--this is not strictly the case. Just so, the Himalayas are still rising, wrinkled by the massive force of plate tectonics. Very soon the precise geographer will be able to declare that, whether or not a flake of snow blows away from the top of Mount Everest--which the natives call Chomolungma, The Goddess Mother of Mountains--or if another snowflake should come to light on its apex, that particular mountain is still 5.5 miles high. We may catapult this illustration of inframince qualities by noting the reports when Edmund Hillary (the New Zealand beekeeper, later knighted for HIS part in that amazing effort of teamwork) and Tenzing Norgay (the Sherpa who received--what was it, a nod?--from the British press and the Crown) first set foot atop Mount "Everest":


Tremendous news for the Queen HILLARY DOES IT

Glorious Coronation Day news! Everest--Everest the unconquerable --has been conquered. And conquered by men of British blood and breed....Queen Elizabeth the Second, resting on the eve of her crowning, was immediately told...the brightest jewel of courage and endurance had been added to the crown of British endeavour.

[News Chronicle, London (June 2, 1953), front page. Reproduced in Ronald Faux, Everest: Goddess of the Wind, Chambers, Edinburg (1978), p. 47; with similar "conquest" reports in other British newspapers.]

At precisely 11:32 a.m. on May 29, 1953, they were not THAT much closer to the sun than any of the rest of us residing nearer to sea level. When Chomolungma's elevation is one day 5.5555 miles high, it still won't make much difference in the ninety-odd million miles from Earth to our nearest star and ultimate source of virtually all our life-sustaining energy. More importantly, study of "renewable resources," which all ultimately derive their energy from the sun, demands a revival of the teachings once considered most sacred wisdom. Yet, in order to understand the periodicities and (aParent) movements of the Sun, five equations should suffice for calculating objective problems of relative location such as need to be known for actual implementa-tion of inherently sensible solar energy installations:

1. Declination--determines the calendar day, the "season" of the year for all locations world-wide; the angle of the Earth's "tilt" (with respect to the sun) between plus and minus 23 1/2 degrees, toward or away from the Sun.

2. Length of the day, given the day of the year and the latitude.

3. Zenith angle--measures the position of the Sun (or of any other heavenly body) from a point directly overhead.

4. Azimuth--projects the Sun's position on the plane of the horizon;the angle measured in a clockwise direction (toward the West).

5. Angle of incidence of the Sun with a collector surface, non-trivial for solar tracking and focussing with mirrors or lenses.

As a modern practical matter, this formerly treasured and guarded super secret information must be bruited about in the curriculum if engineering and science students are to develop a sound intuitive grasp of solar energy's theory and practice. For, in reporting one summer solstice event, the British press could but timidly write:

among the few things that can be said with any reliability about its origins is that Stonehenge was a building of religious significance, and that this was probably connected with the sun.

[London Independent, in the San Francisco Examiner (June 21, 1992).]