Chapter 14
Dogmatic Toll Takers: Detour Via the North West Spiral: Triangles and
Squares
2Dogmatic disciples of the mind-over-matter philosophers immediately converted postulations of the original truth evolved by the early geometrists into graphic formula, and, in consequence, participated with the fans of the unselfish-to-death-degree prophets in the bogging-down of man. The scientists dogmatic fans carelessly accepted ‘‘points’’ and ‘‘straight’’ lines as matter-of-fact static realities, without troubling to discover for themselves the inherent principles of relative progression. This satisfied their ‘‘traditional’’ concept of life as non-improvable and changeless except for seasons, a concept then as yet unchallenged by any scientific instrument progression such as man has witnessed in the last century, which progressively breaks down time and space. Their interpretations were made in terms of a ‘‘world’’ not much greater than a day’s walk from the hamlet of the thinker, which ‘‘anyone could see was a flat plane’’; hence they evolved a static geometry with an apparently static material line as its essence.
3 After assuming this quasi-factual line, they next supposed a plane which was representative of a series of touching parallel lines. They admitted, naively, that their plane was theoretical and, therefore, non-sensorially existent. This contradiction, far from bothering them, was easily explained away. To demonstrate the static sensorial world in which they thought they lived, they next imagined a stack of planes, thus demonstrating, in effect, the cube upon which they based a theory of sensorial solid geometry.
4 Partly as a result of their endeavor to justify this rationalization and partially due to pure arithmetical coincidence, the dogmatic philosophic school discovered the principle that the product of units of length multiplied by units of width equaled the sum of square units of the posited linear module of the area of a right angled quadrangular plane. They further multiplied the number of square units of the plane by the height of the cube, as determined by the number of the same linear module units in a third perpendicular line at right angles to the plane, and so arrived at the volume of the three-dimensional cube. Thus far the process happened to coincide with their purely abstract multiplication system.
5 Finding it impossible to discover a fourth perpendicular to the cube, that is, one that would not be coincidental with one of the three lines of perpendicularity already established, and assuming through the coincidence of its occurring in squaring and cubing that it was a constant and requisite property of all dimensional appraisal, they were unable graphically to realize the mathematically indicated fourth dimension—not to mention the infinity of dimensions b eyond the fourth. Consequently, a cult was developed, the subscribers to which pretended a mystical awareness of fourth and infinity dimensions and ‘‘squaring of the circle,’’ et cetera. They overlooked entirely the philosopher’s geo-metry (measurement of an expanding sphere) and used, instead, as a yardstick for the interpretation of the spheroidally and radiantly expanding energy universe, a static, structurally unstable, static line-cube, unstable because it lacked triangular diagonals and was, therefore, collapsible.
6 The fallacy of this dogma is readily apparent. First, a dot was hypothecated, out of which was evolved a supposed line, out of which grew a supposed plane, and out of two non-realities a reality in the form of a cube that was objectively insisted upon as factually truthful, though actually non-existent. If the dogmatists had been logical they would have been compelled to admit that since it had no longevity it did not exist in time, (without time dimension) and
7 consequently not in their own life-time-reality. This compromised cube was satisfactory enough to them, however, because it coincided with their empirical building block of stone which seemed real enough and which was from their viewpoint quite eternal. Non timedimensioning, they, of course, conceived of no relative longevity.
8 The cube thus arrived at by arbitrary inclusions and exclusions, which coincided with the building blocks of their physical world, made it possible for the dogmatists to calculate ‘‘practically’’ in shelter design. The then-current satisfaction of this integration of their geometrical interpretation and every day requirements dismissed from the tradition of academic geometry the true characteristic of the original thought demonstrations of the scientific philosophers.
9 The original dynamic demonstrations allowed of concept extension into coincidence with that concept recognized by modern physicists of an expanding energy universe. The self-satisfied dogmatic exclusion of the time-energy-geometry and confinement of rationalization to a relatively static concept (leading to the building by the populace of temples and cathedrals that required seven to ten generations for completion under the misapprehension that they would stand forever, which misapprehension has underwritten the fallacial economics of collateralized debt) has caused the academic imposition upon new students, throughout 2000 years, of a static concept in their cultivated knowledge which has made it almost impossible for the population now considering itself fairly well educated to comprehend the logical significance of ‘‘relativity’’ implicit in mathematics as re-cited by Einstein and his contemporary physicists.
10 If those long ago embryonic academicians had been more accurately observational, as was the scientist Democritus when promulgating the atomic theory, they would have realized that their dot, if graphed at all, could be but an aggregation of a myriad of primarily spheroidal particles (Democritus’s ‘‘worlds’’). Had they been more earnest and persevering in their research they must have been forced inevitably into a scientific study of the phenomenon of radiation into which the modern scientist has penetrated, by the difficult elimination of their presumptive errors.
11 They would have realized that there is only one dimension or infinity of the one dimension: TIME, or HOW FAR (or more properly ‘‘FAST’’) RADIALLY OUTWARD, IN TIME AND SPACE, INTEGRATED AS RATE FROM THE CENTER OF THE SPHERE. Such a conception would have brought them success in their attempts to graph the implied progressive dimensions of simple mathematics in terms of the perpendicular, for an infinity of perpendiculars (radii) maybe applied to the surface of a sphere without any impingement, one upon the other, and the progression of volumetric increase in the terms of any uniform radial division modulus as II.R3, is identical to the progression of new dimensions of the expanding universe. Moreover, the infinity of radii in a sphere permits graphing their multiplicity in time, together with a coordinate symmetry of unity in the universe by virtue of the directional coincidence of all radii in a sphere. Each radius extends to the outermost boundary (the radiant surface of the sphere) from the only true point (the radial convergence directional center of the sphere) in the shortest ‘‘distance’’ possible, i.e„ in the shortest ‘‘space’’ of time.
12 A sphere is unit, but a line is not because the terminals of a line must represent arbitrary cut-offs. All lines, except when abstractly considered as ‘‘direction,’’ are somewhat curved, and all curved lines must eventually intersect,—no matter how remotely. Not even a graphed spiral is forever possible because the errors in a graphed line constantly dislocate the line and insist upon an ultimate intersecting contact. This, quite simply, is the essential concept in Einstein’s ‘‘curved space.’’ The only possible symbol of unity in plane geometry is the CIRCLE.
13 There is incontestable evidence that those who were central in the mind-over-matter emergence era comprehended the infinity of progression and glimpsed, at least, a truthful system of graphic formula. The evidence is found in the peak reached by symbology, in mathematics, words and decoration. In particular may be cited the evidence that occurs in navigation, in which the angle <, an abstract unit of a whole, abstract because it is the space between the converging lines, is used for measure. The rounded wheel, which at first was solid and later became compression and finally tension spoked, and the ‘‘HALO’’ in decorative art as the unit symbol of the energy or power God ‘‘radiantly’’ expansive above man, is empirical testimony of long existing knowledge of a radiant time dimension. The wheel is centra-mechanical to time-space-relativity evolution and popularization.
14 When starting their academy, the dogmatic mathematical prophets set in motion a retrogression in knowledge of almost twice the duration of the retrogression initiated by the religious disciples. Consequently, only through individual pioneer inventors and a small band of true researchers has there been maintained a body of amplifying knowledge which has, however, been continuously the source of the momentum of industrial growth.
15 The vast majority of ‘‘educated’’ people will have to unlearn almost all that they ‘‘think’’ they know in order to divest themselves of vocabularies so largely embodying words of a static nature: ‘‘basic,’’ ‘‘good,’’ ‘‘bad,’’ ‘‘is,’’ ‘‘distance’’ (as miles), et cetera. (San Francisco 3 minutes from New York telephonically, 20 hours aeronautically, 150 days ambularly; it all depends on relative satisfaction requirements of man.) These static words will have to be dropped from current usage before society can be happily synchronized through comprehension of the phenomenon of the energy-expanding universe.
16 An indication of society’s intuitive awareness of the need of this throw-off of old meanings reveals itself in many ways. For instance, it is to be amusingly witnessed in the quickening shift from one fashion to another in women’s hats and gowns, the fashions of which are predicated on satirical exhumations of forms earlier evolved in earnest pomp and circumstance. These current adornments come under the classification of ‘‘costume’’ and in no way indicate that the wearers today think of themselves alternately as a harem gal and the Empress Josephine. The originals, however, were worn in all seriousness not as fashions but as empirical developments (as various materials became available) of the most alluring feathers-for-female-survival.
17 The failure of the academies founded in the wake of the great Mediterranean scientist-philosophers to recognize ‘‘time’’ as a prime factor of mathematics was primarily due to man’s relatively stationary position in his environment, caused by limited means of transportation. Popularly speaking, man could travel only so far as he could walk. He had little or no communication with the world beyond his hamlet unless he were a bully leader and had a ‘‘horse.’’ Even then travel was highly confined.
18 The world was apparently flat. Anyone could see that it was. Each isolated hamlet thought itself egotistically to be ‘‘it’’—the center of the flat universe. Strangers beyond their horizon had best be wary lest they fall off the edge. The evening sky was a decorative panorama oscillating above a flat static stage. Ego ‘‘stood pat.’’ Naturally, in terms of this flat world, men thought that two or more perpendiculars to the earth’s surface (columns or tree trunks) must be parallel. Thus was fabricated the delusion of parallelism. Seeming parallelism (for instance, that between two sun rays [radii] an inch apart upon arrival at ‘‘earth’’) is termed parallax in astronomy. The seemingly parallel columns of the ancients could be capped by lintels, if the span were not too great and if the column height in proportion to girth could support the additional load. So quadrangular openings appeared. Ere long the square became the fundamental architectural (arch) module limited in proportions only of weight and width for stability in a factually non-static universe erroneously treated as static. The lack of panoramic background in early painting is indicative of the confinement of early scrutiny.
19 The ‘‘square’’ illusion, which coincided with the cube module concept, was so seemingly true, real and practical that square-blocked ramparts were erected about the static towns of square blocked buildings inflexibly jointed. This architecture was diagnostic of ‘‘fear’’ of molestation and disrupture, and of an inability to face the facts of a world of time, change, and motion. Even to the present this ‘‘fearful’’ tradition survives for the static realist not only in his architecture but in his economics—he is so proud of being a ‘‘square shooter.’’
20 Fortunately for progress, there have always traveled across the flat scene a few who were fearless. Travail, ‘‘work’’ and ‘‘hardship’’ were part and parcel of travel at that time in contradistinction to luxury-travel-cruises of today. Travel was then as popularly shunned as it is today courted. Then a traveler was a ‘‘nut’’ to undertake such ill-conceived hardship. Weight-and-width-for-stability shelters (obviously grossly inefficient) were incompatible with travel. So, of necessity, the traveler invented portable readily pitchable tents, structurally formed of pure compression members in triangular flexible-jointed stability, covered with pure tension webs. These were directly and unmistakably a manifestation not only of highest scientific mental segregation and reordering of elements, but also, of the longing urge for experience and knowledge, derivable through explorative travel.
21 The triangle, through the ages, has been the symbol of the architecture of motion, first in tents, then in the rigging of sailing ships, thereafter in trestles, and most recently in airplane wings and radio masts. It is found as the primary module in the decorative design of mobile people, as, for instance, the American Indian.
22 In the early days of travel, mobility involved a high mind-overmatter conquest of the elements in the non-environment controlled wilderness. The ingenuity and wisdom of the leaders who empirically evolved light mobile tents, et cetera, was essential to the welfare of tribal followers.
23 If a succeeding true mind-over-matter leader was not to be found in the tribe after the death of a mobile leader, the tribe intuitively dared not to move further than the last locality to which the leader had brought it. This must have occurred time after time throughout ages. (We find reference, for instance, to the ten ‘‘lost tribes’’ of Israel, bereft of their leaders.) Fearful to travel further, such people excused their fear complex by a myth. Superstitiously there evolved wide subscription to legends of a ‘‘promised land,’’ a goal, a destiny, an arbitrary terminal to a line, to which leaders had brought their ‘‘faithful followers.’’ This self-backpatting conceit disguising fear and inferiority to circumstances still characterizes all localized, static people. It is the root of swollen-locus-vanity and ego of the misappropriated and paradoxical self-styling ‘‘conservative.’’ Only pioneers have conserved society. Satisfied with their destination theory the ‘‘statics’’ proceeded to dig in. With new generations the old triangular forms, formerly necessitated by travel, disappeared, and the static square, consistent with a flat earth, automatically appeared. Mobility degenerated into NObility.
24 The Jews are a seeming exception. They were and still are an involuntarily wandering people, their symbol being superimposed equilateral triangles ($). It is known as the ‘‘seal of Solomon’s highest wisdom.’’ (King Solomon designed his throne upon wheels.) Involuntarily do the Jews wander. Bereft of unified leadership, they long and try continuously to settle down, but their hereditary development of high survival ingenuity as an originally cast out and forced to travel minority, non-submissive to temporal rulers, that very same survival ingenuity (that eschews and evades the majorityadopted ‘‘ethics’’ of materialistic societies compounded with an ingenuity to effect permanent settlement), renders them too disruptive a force for staticizing societies and inevitably they are cast out once more. Their casting out has, throughout history, coincided with the impending decline and fall of the society which cast them out. Oddly and sadly the ‘‘outcast’’ complex inclines them perversely to excel in the very pursuits to which they were originally and still orthodoxly most spiritually opposed, to-wit, the exploitation of social essentials. It may be said, then, that the cause of their proverbial ‘‘wailing’’ is paradoxically their linkage to survival, their contribution to mankind’s welfaring and environmental conquest being the preservation of those arts and proclivities which may be kept alive only through economics of intermittent emergency mobilization.
25 The history of static, bogged-down, leader-bereft hordes is fraught with the saying, ‘‘This is the place to which HE brought us. It is good enough for us. We shall let well enough alone.’’
26 ‘‘Letting well enough alone’’ has precluded exploration of physical phenomena other than in terms of surfaces, superficialities and superstitions. Of necessity such inadequate explanations have had to be maintained by ‘‘ethics’’ and ‘‘hands off’’ laws, which initiate a progression of divestment of attained knowledge ultimately shrinking demonstrations of intelligence to zero.
27 There is quite possibly a scientific truth to be evolved from the fact that motion, particularly rhythmic motion, is highly provocative of thought objectification. Certainly travel provides perspective, broad angles, and accelerated progressions potential of clarification of the experience trend. Most authors will testify that thoughts come to them in profusion as they speed clickety-dicking over the country in a transcontinental train, and in even greater profusion in droning flight. It is the writers experience—noted because we are all our own best laboratories—that he unconsciously paces the room while objectifying thought in dictation, punctuating by sitting down and becoming aware for the first time of the pacing that has occurred.
28 It is to be noted that historically the mobile tribes were primarily present in the areas northerly to, or altitudinous above, the isotherm of mean low temperature of 32° R, along which isotherm the large majority of the world’s people dwell. In Eurasia ‘‘invading hordes’’ came from the area north of this isotherm. In America, the cubical pueblo dwellers lived south of, and the triangularly tented mobile Indians roamed north of this isotherm, though all were genetically at least partly Indian. The most southerly were pure Inca and Mayan Indian. The border-line and northerly Indians were cross bred with Mongolians who had coursed over Bering Strait and down through Alaska.
29 In testament of this history, the static or square architectural habits are found mainly along and to the south of the popular isotherm. Very far north the simple hemispherical igloo is witness of an innate sense of the radiant universe amongst northerly people. The hemispherical, conical, cylindrical, and hexagonal hut forms may be widely found in all semi-nomadic ‘‘light traveling’’ primitives: African or Indonesian. They were primary dynamic-sense forms.
30 Populations originally existing in warm climes but which dared to penetrate colder realms or higher altitudes have been abetted further in their progressive ‘‘thinking ability’’ by the abatement of the myriad of parasitical infections with which they were originally afflicted in warmer regions and which still persist rampantly in populations south of this isotherm. This ‘‘delousing’’ of the cold climate pioneers yielded a relative physical calmness which, compounded with the hibernation necessitated by a cold climate, has favored carrying through mental concentration into effective thought. The science of mathematics and the central philosophies have come from the high places and from relatively cold climes. Currently, as an end result, almost the complete body of what is classifiable as ‘‘industrial society’’ is found, in America and to a considerable degree in Eurasia, to be wholly north of the isotherm of 32° mean low temperature. (See chart.) The ‘‘outs’’ of the great progression of man’s events and mindover-matter emergence from stale-mated settling down are always clockwise around east to west and spiralling up toward the North Pole. This spiral tends toward an integrating of the world populace by the industrial people of North America and North Eurasia over the Arctic. Canadian Airways are now carrying 40% of the world’s air freight, their eight main airlines being north and south, not east and west, with more terminals in the Arctic circle than over the U. S. Border. In the summer of 1937 the Canadian Government sent 50 geological expeditions ‘‘into the north’’ to roll back the map of Canada.
31 The long sought ‘‘north west’’ passage dreamed of by early explorers is coming true by air as it spirals ever north west finally to leap back and forth directly over the Pole. Russia’s scientific colonization of the Arctic and pioneering of the North Pole air route, compounded with the Canadian activity, promises integration by 1942, punctuated meanwhile with certain political integrations and developments. This north west spiral is directly instrumented by mind-over-mattering, and the latter’s current extensions, aeronautics and radio, are central to its graduation to industrial magnitude.