Omnidirectional Halo

Omnidirectional Halo

R. Buckminster Fuller

Doubleday Anchor | New York City

ISBN: 9780000000000

ISBN-10: 0000000000

Updated: 2024-12-16 13:152024-12-16

Copyright ©1963

All rights reserved. No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without permission in writing from the Copyright Holder.

ENCODED IN THE UNITED STATES OF AMERICA

Contents

1 Introduction to Omnidirectional Halo

2 Omnidirectional Halo

List of Figures

List of Figures

List of Tables

List of Tables

Bibliography

Index

Index

Contents

1 Introduction to Omnidirectional Halo

2 Omnidirectional Halo

List of Figures

List of Tables

Bibliography

Index

1  Introduction to Omnidirectional Halo

The useful but infrequently used word epistemology means science of the thought processes. A total epistemological reorientation and, to the best of my knowledge, a unique philosophical reconceptioning, regarding the regenerative constellar logic of the structuring of the universe (both as a new cosmology and as a new cosmogony), seem to have followed gradually upon my hypothetically-initiated querying regarding the possibility of formulating more comprehensive and symmetrical statements regarding dawningly apparent natural laws. I intuited in irrepressible degree that such a potential formulation might be accruing and harvestable in all of our acceleratingly—reconsidered and progressively—integrated world-around, all-history experience as now only diffusely inventoried at the middle decades of the twentieth century.

Out of multi-overlaid experience patternings there sometimes emerges an awareness of what we may call a coincidence pattern—a localized thickening of points. These emergent patterns of frequency congruences and concentrations display a unique configuration-integrity which has up to now been so dilute in any one experience as to be only invisibly common to many differentiated or special experiences, e.g., a pack of one hundred 4-inch by 5-inch file cards each riddled with hundreds of different sized small holes. Each card appears to be chaotically patterned with holes. However, when the cards are stacked with edges aligned three holes in each card are vertically aligned; all others are obscured by blank spaces on one card or another. A triangular pattern relationship of the light coming through three tubes in the stack of cards is now lucidly conceptual. To such persistently emergent, uniquely mutual, coincidence-patterning relationships as the same triangle array of holes in each and every card we may apply the term ‘‘pattern generalization’’ as used in a mathematical sense, in contradistinction to the word ‘‘generalization’’ as used in the literary sense. The latter often means a too-ambitious subject range which consequently permits only superficial considerations of any specific case data.

When the uniquely emergent generalized patternings become describable by us in mentally regenerative conceptual terms, as completely divorced from any one of the specific sensorial conditions of any of the special experiences out of which they emerged, yet apparently, as seen in retrospect to have been persistent in every special case, then we may tentatively assume such unique mutual pattern content to be a generalized conceptual principle, as for instance the conception of tension as opposed to compression independent of textures, smells, colors, sound, or size of any one tension-dominated experience.

It is in just such an epistemological process that we discover that size is not a generalized conceptual principle. Whether referring to the size of an object in respect to other objects or the sizes of any one object’s subdivision, size emerges exclusively as a frequency concept uniquely differentiating-out each ‘‘specialized case.’’ Generalized shape conceptioning is independent of size. A triangle is a triangle independent of size.

When a second order of pattern distillation as a generalized conceptual principle emerges, but this time exclusively from the emergently-induced co-ordinate consideration of a plurality of generalized conceptual principles themselves, each independent of any special case sensoriality, and in such a regeneratively recognizable manner of patterning as to provide a means of mathematical accounting and therefrom a tentative forecasting capability, not only of generalized developments but also of special forward experiences in the terms of specific sensorial conditions, and those calculated forecast conditions materialize, and the forecasting capability is subsequently verified by recurrent experimental demonstrations under controlled generalized conditions, then we may tentatively assume that we have discovered at least a clause of ‘‘natural law.’’ For example, we tentatively assume that radiation is generalized compression and that gravity is generalized tension and that tension and compression are inseparable, precessionally-complementary functions of universal structure.

Newly recognized generalizable principles seem emergent in unprecedentedly accelerating accumulation as reported from the instrumentally extended range, velocity, and exactitude of special case experiences in the most recent moments of history’s scientific venturing. The manywhere local probings have been meticulously organized and reported regarding measurable relationships and rates of changing relationships throughout the vast macrocosmic and exquisite microcosmic angle and frequency universe events both infra and ultra to man’s direct tuneability yet instrumentally tuneable and transformably readable within regeneratively informative tolerance despite inherently limited observational exactitude.

Out of cumulative patterning overlays there emerges what seem to be generalized principles apparently governing all associative and disassociative transformings and their resultant regeneratively persistent hierarchy of constellar configurations. These hierarchies of constellar configurations disclose in turn a hierarchy of dynamically symmetrical constellation phases and their respective maxima-minima, asymmetric and complementary, accommodative transformabilities which are apparently permitted within an omnirational, omnidirectional, omniequi-economic, energy-accounting, co-ordinate system of universe. This omnirational, arithmetical-geometrical accountability is of such sublime simplicity in contrast to the awkward ‘‘mathematics’’ of all known yesterdays as to have occasioned an almost universal incredibility and nonconsideration of its potential significance though it has been in disclosure for one quarter of a century.

This co-ordinate system may be described as an isotropic vector system; that is, a generalized Avogadro system in which the energy conditions and relative quanta ratios are everywhere the same yet multi-differentiable in local patterning aspects, which aspects are interchangeably emergent without altering the comprehensive energy equilibrium or its unitary totality as implicit in the Law of Conservation of Energy by which it is assumed that energy may be neither created nor lost.

The discovered co-ordinate system is apparently governed by generalized laws, some of whose mathematical equatability I have been allowed not only to discern (as far as I know for the first time by anyone) but also to codify and translate into unique structural realizations. This codification governs the total co-ordinate abundance ratios of the unique pattern aspect relationships of uniquely irreducible co-operative function aspects of locally nonsimultaneous events and their equilibrious pattern totality.

Discovery of the primary and corollary laws of constantly co-ordinate relative abundance of pattern function-aspects of totality as an omnirational regularity governing all local patternings of universe as a minimum-maximum family of complexedly complementary yet uniquely identifiable conceptual function patterning relationships followed upon intuitive formulations of the seemingly most comprehensive self-querying question I was capable of propounding to myself regarding possible detectable pattern significances accruing to progressive life experience integrations and overlays.

That most comprehensive question was, ‘‘What do you mean by the word 'universe'?’’ ‘‘If you cannot answer, you had best abandon use of the word 'universe'for it will have no meaning.’’ My intuitively-adopted rules for self-questioning and answering were that the answer must be made exclusively from man’s experience patterns. I learned many years later that the Nobel physicist Percival Bridgeman had identified this same rule adopted by Einstein as ‘‘operational procedure,’’ subsequently a much-abused phrase. My answer (or discard of the word ‘‘universe’’ as a communication tool) was operationally inherent: ‘‘Universe is the aggregate of all consciously apprehended and communicated (to self or relayed to others) experience of man.’’ If my finite answer holds against all specific experience challenges as being comprehensively anticipatory and adequate, the universe is finite, and all its components definable. Each life as we know it is definitive, i.e., consists of a plurality of terminable, ergo definite, experiences, beginning with each awakening and terminating with each surrender to sleep (no man can prove upon awakening that he is the man who he thinks went earlier to sleep, or that aught else which he thinks he recollects is other than a convincing dream). The intermittent beginnings and endings of conscious experience constitute an aggregate of definitive experiences—and the aggregate is therefore finite.

In the recent moments of historical experience, men as scientists adopted the law of conservation of energy: as predicated upon the sum total experience of physicists which recalled no contradiction to this hypothesis. They thus accomplished a finite packaging of all physical behaviors of physical universe as predicated also upon the hypothesis that all physical phenomena are entirely energetic.

By embracing all the energetic phenomena of total experience, the scientists secured a synergetic advantage for all energy accounting and prospecting. ‘‘Synergy’’ means ‘‘behavior of whole systems unpredicted by the behavior of any of its components or by any subarray of its components.’’ Corollary to synergy is the law of the whole system. Systems are definite as they return upon themselves in a plurality of directions, ergo have concave inwardness and convex outwardness, ergo inherently subdivide universe into mutually exclusive definitive macro and micro entities. The law of whole system states that, given the sum of whole system pattern conception its component behaviors may be differentially discovered and predictably described as required by the already evidenced behavior functions implicit in the apriori-definitive experience and conceptioning of any given experience-verified system. Thus by the law of whole system as corollary of synergy, the component behaviors of systems may be predictably differentiated as primary and secondary componential subdivisions of whole system and then progressively isolated and locally reconsidered for further dichotomy.

Adopting synergetic advantage, science hypothesized that the physical portion of universe is energetic and finite. Under this hypothesis Einstein wrote his equation of physical universe as E = MC^2. This said that the total of local system energy is the product of all concentric local systems of energy’s self-interfered, shunt-holding patterns (M for mass) as multiplied by the entirely noninterfered local omnidirectional velocity of surface growth of an omnidirectional, outward-bound spherical wave of radiant energy (in terms of second power of radial wave module frequency growth rate).

In Einstein’s formula mass constitutes all the patterns of precessionally self-interfered and concentrically shunted, ergo locally articulated and locally and periodically regenerative holding patterns of energy. This is also to say that M equals all the locally complex, concentric, self-associative, unique holding patterns of all energy, and C^2 equals all the eccentrically disassociative individual patternings of all energy (C being the radial or linear speed of radiant energy, which is approximately 186,000 mps).

But physical science lacked the experience which might have persuaded it to hypothesize what all universe is. Physical science therefore restricted its comprehensive accounting strategy to the special case of definitive isolations within the physical portion of universe. This left the remainder of all experiences, no matter how earnestly and meticulously reconsidered, outside the definitive portion of comprehended experiences of universe, i.e., the physicists said all that is not physically encompassed as E = MC^2 is metaphysical.

However, by my definition of universe, all that was relegated to metaphysical nebulosity is now embraced by finite universe along with the physically energetic wherefore all the hitherto ‘‘inexact sciences’’ may become rigorously defined, enjoying equatable treatability at optimum degree of determinability.

I have found a general law of total synergetical structuring, which we may call ‘‘The Scenario Principle.’’ This principle discloses that ‘‘universe’’ of total man experience may not be simultaneously recollected and reconsidered, but may be subdivided into a plurality of locally tuneable event foci or ‘‘points’’ of which a minimum of four positive and four negative points are required as a ‘‘considerable set’’; that is, as a first finite subdivision of finite universe. (This fourness coincides with basic quanta strategy.) All experience is reduced to nonsimultaneously ‘‘considerable sets’’ and holds irrelevant to consideration all those experiences which are either too large and therefore too infrequent, or too minuscule and therefore too frequent, to be tuneably consider able as pertaining to the residual constellation of approximately congruent recollections of experiences. A ‘‘considerable set’’ inherently subdivides all the rest of irrelevant experiences of universe into macro-cosmic and micro-cosmic sets immediately outside or immediately within the considered set of experience foci.

There are two inherent twilight zones of "tantalizingly almost relevant recollections" spontaneously fed back in contiguous frequency bands—the macro-twilight and the micro-twilight.

It is a corollary of this first subdivision of universe that a considerable set is a locally definitive system of universe returning upon its considerabilty in all circumferential directions and therefore has an inherent withinness and withoutness, which two latter differentiable functions inherently subdivide all universe into the two unique extremes of macro and micro frequencies.

The ‘‘Principle of Design Co-Variables’’ says that local structure is a set of frequency associable (spontaneously tuneable) recollectable experience relationships, having a regenerative constellar patterning as the precessional resultants of concentrically shunted periodic self-interferences, or coincidences of its systematic plurality of definitive vectorial frequency, wave length and angle interrelationships.

The precessionally regenerative concentricity of structure is antientropic, and evolutes toward optimally economic local compressibility and symmetry. (See The Dymaxion world of Buckminster Fuller, by Marks and Fuller, for Fuller’s Law of omnioptimally economic, omnitriangulated-point-system, symmetry relationships and relative abundance of frequency modulated multiplicative subdivision of unitary local systems; i.e., M(mass) means: All the universe’s self-interfering complexes having concentrically self-precessing, local-focal-holding patterns resulting in locally regenerative constellar associabilities as positive-outside-in structures. C^2 (radiation) means: All the universe’s nonselfinterfering complexes having eccentrically inter-precessing, omnidirectionally diffusing patterns resulting in comprehensively degenerative negative limits of dissociabilities as negative (inside-out) de-structures.

In the chapters on Energetic-Synergetic Geometry I identify second powering with the point population of any one radiant (eccentric) or gravitational (concentric) wave systems circumferential arrays of any given radius stated in terms of frequency of modular subdivisions of the circumferential arrays radially read systems' concentricity layering; third powering with the total point population of all the successive wave layers of the system; fourth powering with the interpointal domain volumes; fifth and sixth powering as products of multiplication by frequency doublings and treblings, etc. The Doppler effect or wave reception frequency-modulation caused by motions of the observer and the observed are concentric wave system fourth and fifth powering accelerations.

The Doppler effect is usually conceived of as an approximately ‘‘linear’’ experience. ‘‘You,’’ the observer, stand beside a railway track (which is a ‘‘linear’’ model); a swift train approaches with whistle valve held open (at constant frequency pitch as heard ‘‘on board’’ by the engineer ‘‘blowing’’ the whistle). The whistle sound comes to you at approximately 700 mph, but the train is speeding toward you at 100 mph. The train’s motion reduces the interval between the successive wave emissions, which in effect decreases the wave length which gives it ‘‘higher’’ pitch as heard at your remote and ‘‘approached’’ hearing position. After the train goes by, the train runs away from each successive wave emission, thus increasing the interval between wave ‘‘crests’’ and therefore lengthening the waves, which apparently ‘‘lowers’’ the pitch as you hear it but not as others elsewhere may hear it. This is pure observational ‘‘relativity.’’ But the real picture of the Doppler effect is not linear; it is omnidirectional.

Figure 1.1: Omnidoppler Effect

The Doppler effect may also be explained in omnidirectional, experience-patterning conceptionality which is more informative than the familiar linear conceptioning of the railroad train and ‘‘you, at the crossing.’’ ‘‘You were flying in an air transport which exploded, and because of the sudden change in pressure differential between your in‘ards and your out‘ards at high altitude you personally have just been ‘‘exploded’’ into many separate parts receding from one another at high velocity. A series of secondary explosions follows from somewhere in the center of the galaxy of exploding debris, as one item after another of the late airplane’s explosive cargo is reached by progressive local conflagration-heat concentrations. The sound waves of the successive explosions speed after your receding parts amongst which are your two ear diaphragms as yet ‘‘stringily’’ interconnected with your exploding brain cells, which ‘‘hear’’ the explosion’s sound waves first at low pitch. But as your parts explode from one another at a decelerating rate because of air friction, etc., the waves of remote explosion sounds ‘‘shorten’’ and pitches go ‘‘up.’’ Now consider many separate, nonsimultaneous, secondary explosions of your various exploding parts all of varying intensities of energetic content and in varying degrees of remoteness and realize that the decelerations and accelerations of Doppler effects will render some of the explosive reverberations infra and some ultra to your tuning range limits of hearing, so that the sum total of heard events provides very different total conceptioning as heard from various points in the whole galaxy of exploding events whose separate components would tend to new grouping concentrations.

The Halo discovered in the next chapter is that of an omnidirectional, complex, high-frequency, Doppler-effected hypothetical-zone experience in an omnidirectional universal maelstrom of nonsimultaneous near and far explosions and their interaccelerating and refractive wave frequency patternings. Several of these fundamental concepts are also repeated several times in Halo, being reintroduced in various complex associations each of which provides unique discoveries.

In order to generate a spontaneous comprehension of the significance of the thoughts expressed in ‘‘Halo,’’ which now follows, the latter essay will open with a swiftly marshalled digest of the epistemological concepts of this introduction.

2  Omnidirectional Halo

Synergy means behavior of integral aggregate systems unpredicted by behaviors of any of their components or subassemblies of their components. Chrome-nickel-steel has a higher tensile, or integrally self-cohering, strength than the sum of the separate tensile strengths of its alloyed elements. Synergetic behaviors are commonplace throughout chemistry and biochemistry but so unfamiliar to man’s visible spectrum range events that the word synergy, though the equal in age of its companion word en-ergy, is popularly unfamiliar.

The lack of popular and academic familiarity with the word synergy, which in the English language alone denotes the behavior of whole systems unpredicted by behavior of their components, means that man in his everyday social world has not been in need of this word, which in turn tells us that he lacks this fundamental conception in his conscious thinking processes. He ascribes all behaviors unpredicted by his statistical probabilities to ‘‘luck’’ or miracle. This particular gap in man’s everyday fundamental thinking and common sense accounts for many fallacies in his spontaneous reflexing and contemporary behavior. Ignorant of the regenerative significance of synergy, man is vulnerable to de-generative feed-back consequences in his comprehensive determinations.

Universe is the comprehensive integral-aggregate system embracing all the separate integral, aggregate systems of all men’s consciously apprehended and communicated experiences. The total of experiences is integrally synergetic. Universe is the comprehensive a priori synergetic integral. Universe continually operates incomprehensive, co-ordinate patternings which are transcendental to the sensorially minuscule apprehension and mental comprehension and prediction capabilities of mankind, consciously and inherently preoccupied as he is only with special local and nonsimultaneous pattern considerations.

Encyclopedias and dictionaries inventory man’s progressively invented words for communicable identification of all his evolving experience cognitions. Dictionary is a collective concept. Universe is the ultimate collective concept—i.e., the collection of all intelligible, inherently separate evolutionary event aspects which latter apparently occur exclusively and only through differentiating considerations which progressively isolate the components of whole and inclusive sets, super-sets, and sub-sets of generalized conceptioning in retrospectively abstracted principles of relationships. The generalized comprehensive principles of interrelationships progressively discovered as governing our subsidiary generalized principles are embraced by our finition of universe.

The word con-sider-ation comes from sidus, the Latin for star, the focal point of an as yet nondifferentiated concentration of events—ergo, con-sider-able, or con-stellar patterning, means an exploratory grouping of ‘‘stars’’ or complex idea entities that seem to man’s limited tuneability to stand out together.

Neither the set of all-experiences nor the set of all-the-words which describe them nor the set of all the generalized conceptual principles harvested from the total of experiences are either instantly or simultaneously reviewable. ‘‘What was that man’s name?’’ Our answering service may take five seconds, five minutes, five hours, five days, or five generations to reply. Our conscious orderly reconsideration of our variable lag experiences discloses subconsciously co-ordinated regularities of feed-back rates governing the recall phenomena.

All experiences are finitely furnished with differentiated cognitions, recognitions and comprehensions. The finite furniture consists of widely-ranging degrees of comprehensive constellar complexities. A wide range of time investment magnitudes must be assigned to the respective considerations of the multitude of different constellar, experience-pattern comprehensions. We cannot read simultaneously all the words in the dictionary; yet the dictionary is a finite collection of finite word entities each in turn consisting of collections of finite letter symbol entities.

Universe is finite because it is the sum total of finitely furnished experiences. The comprehensive set of all-experiences synergetically constituting universe discloses an astronomically numbered variety of sub-set event-frequency rates and their respective rates of conceptual tuneability comprehension. It takes entirely different lengths of time to remember or ‘‘look up’’ different names or past event facts. Universe, like the dictionary, though integral is ipso facto nonsimultaneously recollectable and, therefore, as with the set of all the words of the dictionary, is nonsimultaneously considerable and therefore is also nonsimultaneously reviewable, ergo is synergetically incomprehensible, yet progressively revealing.

The age-long fallacial propensity which has frustrated adult man’s adequate conceptioning of universe is that of spontaneously assuming that universe must consist of a simultaneously unit conceptuality—ergo, of simultaneous geometry or shape, i.e., a simultaneous structure. What is the shape of the universe? What are its boundaries? These are unitary, simultaneous static questions. They have no logical answer for universe though finite is a nonsimultaneous structure. Children know this better than their parents through innate conceptioning as yet unspoiled by erroneous logic. They remember the juggler putting a simultaneous array in the sky with nonsimultaneous tosses. The childhood representational pictures depict their dynamically arrayed concept of the ‘‘whole world’’ inventory, of mentally juggled arrays of nonsimultaneously occurring experiences agglomerated without any intended geometrical interrelationships. In all lands the children’s spontaneous pictures contain ‘‘the’’ house, trees, birds, dogs, flowers, grass, clouds, stars, the sun and the moon. The parents say, ‘‘Darling, a nice picture, but we don’t have both the moon and the sun at the same time.’’ The parents are wrong both the sun and moon coexist at all times whether temporarily covisible or not. The parents' rationale has been damaged so that it can only consider and associate those items which are simultaneously grouped in unitarily static array. Yet in equal illogic the parents keep on attempting to see the universe of nonsimultaneity in unitary, static and simultaneous geometrical array as a ‘‘thing’’—a very big ‘‘thing’’—the biggest ‘‘thing.’’

It is in evidence that universe, as the co-ordinate integral of allexperience is finite yet nonsimultaneously recollectable—ergo, unitarily unpatternable-ergo, conceptually unthinkable—ergo, undefinable. This is to say undefinable does not mean infinite or un-finite. It means that-definability-de-finite is a sub-set of finite—ergo, pattern definition is a subdivision of finite-yet-unitarily undefinable universe. The definable conception is therefore the first thinkable sub-set functioning of universe.

There are metaphysical yet cogent early words emergent from the limbo of prehistory’s quasi-logical accounting continuities which show that intellect has long been aware of the DEfunction. For instance, DI-Vine, DI-, DE- (of Di-chotomy—cell division—regenerate through bi-multiplication). The concept of a DEVINING DEITY, i.e. the defining deity, the great intellectual capability of differentiating discernment, probably originated in the same conceptual logic as did DI-VIDE out of DI-VISION to see the whole as functionally differentiable yet only locally and progressively conceptual. In the differential calculus this becomes the delta—Δ δ D—of fundamental differentiation.

Differentiable function x in respect to y. Functions do not occur exclusively of one another. Functions occur only as inherently co-operative and accommodatively varying sub-aspects of synergetically transforming wholes. MULTIPLICATION accomplished only by DIVISION. Universe expanding through progressively differentiating considerations.

Definable thought patterning deals only progressively (by re scanning) with the local event foci of experienced patternings of universe. Definable thought though constituting systematic consideration and orderly reconsideration, which returns omnidirectionally upon itself in local conceptual relationships in only a subdivision of finite, which is universe, which is inherently inconceivable unitarily.

Inconceivability does not mean infinite anymore than does invisible. Finite is unique to universe because it means complete, but not terminal. The locally definable entity is not complete, for it does not exist by itself. All experiments show that local entities are inherently both entropic and antientropic, i.e., all local systems are always intimately linked with the rest of universe by measurable import and export pattern transactions. Definable entities are uniquely functioning components of universe. Universe is the minimum as well as the maximum closed system of omni-interacting, precessionally transforming, complementary transactions of synergetic regeneration. Local perpetual motion systems are impossible, since universe is the minimum regenerative set of perpetually intercomplementary transformative functioning.

Systematic conceptioning and recollected conceptioning, both universal and local, which progressively traces, relates, and compares nonsimultaneously observable locally functioning entities is self-disciplined. The self-discovered capability to communicate to others by the recollectable and pictured word-tool developed a co-ordinate memory of all men.

Generalized systematic conceptuality’s omni-directional relationships are only angularly configured and are independent of size or dimension. No man has ever ‘‘seen’’ outside himself. His brain is a multi-frequency (four sensory ranges) scanning (TV) integrator, continually operating in co-ordination with a multitude of memory (kinescope taped) TV scanners. The whole array of new and memory TVs is frequency monitored by an angular and frequency modulated pattern commonality scoring and score-predicting conceptual co-ordination capability. The TV co-ordinating conceptual capability includes a score-guessing and score-guess testing faculty, as well as a strategic-tests contriving-pattern considerator, all of which conceptual pattern ing proclivities are self-started and regenerated by synergetical intellection.

The conceptual process is never static. Thinking does not consist of the insertion of invented images into an otherwise empty vacuum-tube chamber called brain. Thinking is the self disciplined process of preoccupied consideration of special-case sets of feed-back answers selected out of the multitude of high frequency alternating transceiver brain traffic. This traffic consists of omniexperience processed answers to present or past questions, formulated either by the conscious or subconscious co-ordinating initiative of the individual or possibly by the individual overlapping generation of group memory.

Because of the varying depths of storage of past experiences, some answers come back swiftly, some slowly. The recollectability rates are unpredictable. The returning-answers traffic is heterogeneous. Many answers come to questions we have for gotten that we have asked. Conceptually systematic tuning of questions and feed-back answers, comparatively considered in the brain, results in temporary, tuneably valved exclusion of all other incoming signals traffic. Discreet tuning admits consideration only of those recollections which are clearly relevant to the omnidirectional rounding out of systematic comprehension of the special case set of events intuitively selected for momentary focal consideration. Thinking consists then of a self-disciplined deferment of conscious consideration of any incoming information traffic other than that which is lucidly relevant to the experience intuited quest for comprehension of the significance of the emergent pattern under immediate priority of consideration.

The thinking process results in varying degrees of lucidity of the arrayed residue of focal event patterns uniquely consequent to the disciplined deferment of irrelevancies. Thinking is a putting-aside, rather than a putting-in discipline, e.g., putting aside the tall grasses in order to isolate the trail into informative viewability. Thinking is FM-frequency modulation-for it results in tuning-out of irrelevancies as a result of definitive resolution of the exclusively tuned-in or accepted feed-back messages' pattern differentiatability. As the exploring navigator picks his channel between the look-out detected rocks, the intellect picks its way between irrelevancies of feed-back messages. And as the navigator realizes secondarily that the channel winds between two sets of rocks, the rocks to starboard and the rocks to port, intellect also discovers secondarily that all the irrelevancies of feed-back information have inadvertently fallen into two main classes, as follows.

1.

The class of all the finitely-furnished experience events which are too large and too infrequent to have considerable frequency significance in-tuneability in respect to the modular magnitude ranges under consideration.

2.

The class of all the finitely-furnished experience events too minuscule of wave module and of too high frequency to in any way be significantly tuneable into the considered spectrum range.

Each class has its twilight zone of almost (or tantalizingly almost) relevancy which, if we were to accelerate our consideration rate, might attain considerability within the tactical limits of assignable capital-life-time intuitively budgetable to such consideration. Between the twilight zones of almost-too-large and almost-too-small to be relevantly considerable lies a zone of lucidly tuneable relevancy of the experienced event recollections.

Because of the incessant wheeling about of humans first in the womb, then in the baby carriage, then on foot, in the auto and ship and plane roundabout a spinning earth in a spinning solar system within an involuting-evoluting, spirally spinning galaxy, totally inventoried experiences are inherently omnidirectional when considered as the sum of observational orientations. Universe (as all-experience) is inherently omnidirectional in its observational orientations-ergo, the temporary putting-aside of the two classes of irrelevancies requires an omnidirectional put ting aside which differentiates as an outwardly dismissed macrocosmic disposition of the too-large and too-infrequent conceptual informations and an inwardly dismissed residue set of all the too minuscule and too frequent events-ergo, the lucidly tuned in, residually considerable set of event-foci lies within a spherical zone between the thus separated twilight zones of almost-considerable minuscules and bigs, respectively. As a consequence, the residual set of tuned-in experience event-foci are caught in a spherical zone trap of feed-back recollected considerability appropriate to systematic reviewing and possible definition.

Out of nonsimultaneously conceptual, yet finite, universe has emerged a definitively conceptual geometry, not a geometry invented by the conceiver but an a priori geometry discovered by the re-considerer as a residual relevancy constellation.

We thus discover that systematic recollection and thought-out definition lies within a geometrically conformed zone which in herently subdivides the universe into distinctly separate microcosm and macrocosm, which two are, however, only meagerly isolated from one another by a local constellation of considerable relationships. No matter how meager the network of zonal relationships of the residually considered star set of holding-pattern relevancy, the latter shuntingly impedes in some degree the velocity of omnidirectional universal information traffic, forced by geometrical surroundment to pass through the zonal constellation. If a squadron of boats enters a river’s mouth and passes upstream and anchors, their presence and the friction of their hulls will mildly retard or choke the river’s flow. Thus do the constellation of considered events mildly choke the otherwise unimpeded universal and geodesically-inter-routed communication traffic which they have separated into the two (micro-macro) realms. As Heisenberg shows in his principle of ultimate indeterminism the physical act of measurement always alters the behavior of the measured phenomenon. In the same way we show here that the thinking process inherently alters the fundamental patterning of universal thought-about interrelationships.

Figure 2.1:  Linear Tetrahedron (A) A linear tetrahedron has six relationships. (B) Four unique frequencies (sizes) of entities, or particles, comprise the tetrahedron.

We thus discover that thought and its tuneably differentiating local definitions constitute the first subdivisions of finite universe. Ergo finite universe is something greater than any definable local system’s zone of constellar, geometrical lucidity which zone is itself secondarily definable by its disparity of concavity of withinness and convexity of withoutness.

In a con-sideration four is the minimum number of stars having an inherent arrangement of within-ness and without-ness. Therefore we discover next that the minimum conceptually considerablegeneralized-experiences-set, affording macro-micro separation of universe, is a set of four local event-foci. These four stars have an inherent sixness of interrelationships. This four-foci, six-relationship set is definable as the tetrahedron. This minimum fourness of relevant-frequency, ergo thinkable ‘‘stars’’ coincides with quantum mathematics' requirement of four unique quanta numbers per each uniquely considerable ‘‘particle, ’’ quanta are inherently tetrahedronal.

In the prime dichotomy of universe into a thinkable tetrahedronal zone between unconsiderable irrelevancies, which in turn requires a secondary zonal separation into macro-micro momentarily unthinkable cosmoses, it becomes evident that the tetrahedronal zone itself introduces a tertiary dichotomy—into the two inherent twilight zones of almost considerable bigness and almost considerable littleness, respectively.

We find a fourth-stage dichotomy of universe when we consider that the big and little twilights each respectively are again also comprised of two tetrahedra as minimal requirement, one as the concave inward tetrahedron and the other as the convex outward tetrahedron.

Figure 2.2:  Pattern of Thought. Thinking is frequency modulation-tuning out finite irrelevancies into two main classes: micro-macro, which leaves residual defined system as lucidly relevant.

We next, fifthly, discover that the positive-negative (convex concave) tetrahedra constitute only the minimum functional dichotomy of finite universe, resulting in a minimum portion of the universe disposed in the microcosm and a maximum portion of universe assigned to the macrocosm. Among geometrical systems a tetrahedron encloses the minimum volume with the most surface and a sphere the most volume with the least surface. An approximately spherical polyhedronal zonal dichotomy of finite universe by a spherical array of considered relevancies provides the minimum portion of sum totally finite universe assigned to the macrocosm and the maximum relative portion of finite universe assignable to the microcosm.

Figure 2.3:  Pattern of Thought—Phase 2. De-finite equals finite minus outwardness and inwardness.

We may say that the minimum zonally defined withinness conformation is tetrahedronal and the minimum zonally defined withoutness is spherical. Therefore, the most extensive lucidly conceptual and definable recollected-experience zone range lies between a tetrahedronal ‘‘withinness’’ twilight and a spherical ‘‘withoutness’’ twilight, beyond which are the nontuneable (1) outwardness and (2) inwardness—the subtracted Euler’s twoness from nonconceptual finiteness which permits conceptual definiteness or definition of cognition.

Because the permitted conceptuality involves a unit expenditure from universe of a de-finite twoness, unit conceptuality must have a finite twoness penditure value, ergo prime conceptual unity acquires an inherent value of two. Unity is inherently plural. Unity is always divisible as twoness, or fourness, or sixness, of inherent minimum relationships. The alternate relative proportions of finite universe’s micro-macro magnitude limits of definitive dichotomy as tetrahedronal minimum or spherical maximum introduce an inherently alternative propensity of universal finite accountability whose alternative eccentric-concentric reciprocity of omnidifferential-lag-rate compensations inherently propagate and regenerate preferably considered universal evolution accomplished by omnidirectionally expansive-contractive wave propagating oscillations.

Figure 2.4:  Pattern of Thought—Phase 3. Concave means concentrate; convex means diffuse.

Frequency of modular subdivision of vectorial lines are ratioed to cyclic increments of time realizing the accomplished velocity. Unity is the full circle sweep around an axis. Angles are fractions of cyclic unity. Frequency means a discreet plurality of cycles within a given greater cyclic increment. Angle means a fraction of one cycle. Angle is therefore sub-cyclic-unity, while frequency is plural unity. Angle is less than finite cyclic unity. Frequency is greater than finite cyclic unity. All physical realizations have relative-size, i.e., dimensionality. The phenomenon size consists of frequency modulated linear (i.e. vectorial) dimension. Angular phenomena being sub-finite cyclic unity, or zero frequency, may be independent of size. Generalized angular or tri-angular or tetrahedronal conceptioning may be independent of size.

The three angles of one face of a triangle always add up to 180° as a phenomenon independent of the relative dimensional size of the triangles. 180° is one-half definitive cyclic unity. Every triangle has two faces-its obverse and reverse. Unity is two. So we note that the angles of both faces of a triangle add up to 360° . The sum of the external angles of two triangles’ obverse and reverse faces is 720° . The sum of the external angles of a tetrahedron is 720° . The sum of two triangles’ external angles is equivalent to one tetrahedron.

The relative size of a triangle is a secondary, observer induced consideration and depends upon the frequency modulated edge increments of the triangle as ratioed to some other physical experience entity.

Angles of tetrahedra always add up to 720° independent of size. The angles of a cube always add up to 2160° independent of the cube’s size. A tetrahedron is definite yet independent of size. All angularly modulated definite geometrical systems or figures are independent of size.

Relationships which have definite integrity and independence of size are conceptual principles of abstract thought independent of physical realization. The difference between the sum of all the angles around all the vertices of any system and the total number of the vertices times 360° (as angular unity) is 720° which equals two unities. The sum of the angles of a tetrahedron always equals 720°. The tetrahedron may be identified as the 720° differential between any definite local geometrical system (Greek solid) and finite universe.

Table 2.1: Angular Topology Independent of Size.

A line has two vertices with angles around each of its vertexial ends equal to 0°. The sum of these angles is 0°. The sum of the vertices (2) times unity (360°) is 720°. The remainder of 0° from 720° is 720° or two unities, or one tetrahedron, Q.E.D.

A triangle has three vertices. The sum of the externally viewed angles around each is 120° of which 60° is on the obverse side of each vertex of the triangle; for a triangle, like a line, if it exists, is an isolatable system always having its positive and negative aspects. The angles of ob- and re-verse triangles add up to 360°. The triangle is three vertices times 360deg = 1080deg which minus 360° ( sum of triangles' angles) = 720° Q.E.D.

Two triangles' external angles make one convex tetrahedron or 720°. The coincident concave tetrahedron’s angles add up to 720°. The positive and negative tetrahedra always coexist +720deg −720deg = 0deg.

Four vertices equal one positive tetrahedron therefore, one positive conceptual convex tetrahedron is +720° and the difference between it and finite universe is one-negative nonconceptual concave tetrahedron. Neither the positive nor the negative tetrahedron may occur without the other.

A zero tetrahedron is vector equilibrium, is universe.

Experience is inherently discontinuous and islanded and each special experience represents a complex of generalized principles operative in special or limited size (i.e., dimension, i.e., frequency) modulated realization.

Brower’s mathematical theorem states that if any number of points on a plane are stirred around an x amount on cessation of the stirring, one of the points may be shown to have been the center point of the stirring-and never to have moved in relation to the others. In order to be ‘‘stirred,’’ these points must have multi-dimensionality and the cluster of stirred points must have obverse and reverse sides. Therefore, the obverse-reverse sides must each have visible points that were the centers of the stirring and, short though the distance between the obverse-reverse sur face neutral center points, the short line between the obverse reverse visible central points' obverse-reverse poles constitutes a neutral axis of the system of points and isolates two points for axial functioning in every layer of both polar zones of every point system swarm. Pauli’s exclusion principle verifies that each of the stirred points in Brower’s theorem and the point which did not move have their inherently separate counter part points which discloses both the neutral axis formed by the two points that do not move and the obverse and reverse sets of moving points. Thus, we discover that even a ‘‘points’’ angular topological difference between its definiteness and finiteness is 720°.

Table 2.2:  Tetrahedronal Mensuration applied to Well-Known Polyhedra. We discover that the sum of the angles around all vertices of all solids is evenly divisible by the sum of the angles of a tetrahedron. The volumes of all solids may be expressed in tetrahedra.

There is no phenomenon ‘‘solid matter’’; therefore there may not be a ‘‘solid’’ sphere, nor a ‘‘solid’’ surface sphere. All spheres consist of a high frequency constellation of event-points, all of which are approximately equidistant from one central event ‘‘point.’’ All the points in the surface of a sphere may be interconnected. If most economically interconnected, they will subdivide the surface of the sphere into an omnitriangulated spherical web matrix. As the frequency of triangular subdivision of a spherical constellation of omnitriangulated points approaches subvisibility the difference between the sums of the angles around all the vertex points and the numbers of vertices when multiplied by 360° remains constantly 720° which is the sum of the angles of two times unity (of 360°). The sum of the angles of a tetrahedron, regular or irregular, is always 720°, just as the sum of the angles of a planar triangle is always 180°. We may state two laws which say: (1) the sum of the surface angles of any polyhedron equals V n multiplied by 360° minus one tetrahedron; (2) the sum of the angles of any polyhedron (including a sphere) is always evenly divisible by one tetrahedron. We may also say that: Where unity (1) equals 360°, 180° equals one-half unity (1 ⁄ 2) and that 720° equals two times unity (2); therefore, we may identify a triangle as one-half unity and a tetrahedron as two unities (1 ⁄ 2), (2).

Table 2.3: Tetrahedronal Mensuration applied to Spheres.

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The calculus assumes that a plane is infinitesimally congruent with the surface of a sphere at the point of the plane’s tangency of the sphere. The calculus and the spherical trigonometry therefore also assumes that the sums of the angles around any point of any sphere are always 360°. The demonstration thus far made discloses that the sums of the angles around all the vertices of a sphere will always be 720° or one tetrahedron less than the sum of the vertices times 360°, ergo, one basic assumption of the calculus is invalid.

In review, this chapter shows that the phenomenon ‘‘infinity’’ of the calculus is inherently finite. Universe equals the aggregate of men’s consciously apprehended and communicated experiences. By my definition, universe is nonsimultaneous but finite because all experiences begin and end and being terminal are finite; ergo, universe as the sum of finites is finite. The first subdivision of nonsimultaneous universe is effected by a local system which divides the universe into three finite parts: the portion of universe outside, the portion of the universe inside, and the system. We find local spherical systems of universe are definite rather than infinite as presupposed by the calculus' erroneous assumption of 360 degreeness of surface plane azimuth around every point on a sphere. Nonsimultaneous universe is finite but conceptually undefinable; local systems are definable. We discover that universe is finite and a local system is definite and the definite local system plus one tetrahedron (or two unities) equal finite universe. The difference between universe and any local system is always one tetrahedron. Every local system may be subdivided into whole tetrahedra.

If we combine, first, the fact of Van’t Hoff’s discovery that all the organic chemical compounds are structurally cohered in the terms of the tetrahedra’s four vertexes and, secondly, the fact of Linus Pauling’s X-ray diffraction implemented discovery that all the metallic elements thus far experimentally analyzed combine in nonvertexially interlinked tetrahedronal structures and, thirdly, the facts which I have disclosed in this and the preceding pages we may well conclude that it is reasonable to adopt the working assumption that: all of the definable structuring of universe is tetrahedronally co-ordinate in rational number increments of the tetrahedron.

Finite minus de-finite means two tetrahedra minus one tetrahedron. Finite universe equals four cyclic unities. Each tetrahedron equals two; therefore, finite (4) minus conceptual definite (2) equals two, which constitutes one negative invisible tetrahedron.

Reviewing again, this halo conceptioning discloses the minute yet finitely discrete inaccuracy of the fundamental assumption upon which the calculus was built; to wit, that for an infinitesimal moment a line is congruent with the circle to which it is tangent and that a plane is congruent to the sphere to which it is tangent. Calculus had assumed 360° around every point on a sphere. The sum of a sphere’s angles was said to be infinite. The Halo concept and its angularly generated topology proves that there are always 720° or two times unity of 360° less than the calculus assumption of 360° times every point in every ‘‘spherical’’ system. This 720° equals the sum of the angles of a tetrahedron. We can state that the number of vertices of any system (including a ‘‘sphere’’ which must, geodesically, in universal energy conservation, be a polyhedron of N vertices) minus two times 360° equals the sum of the angles around all the vertices of the system. Two times 360° which was the amount subtracted, equals 720°, which is the angular description of the tetrahedron. The spherical error of calculus is one discrete tetrahedron. We have to take angular ‘‘tucks’’ in the nonconceptual finity (the calculus infinity) to make a local definite system (the calculus finity). The ‘‘tucks’’ add up to 720°, i.e., one tetrahedron. The difference between conceptual de-finity and non-conceptual finity is one non conceptual finite tetrahedrin.

In the general theory of variables it has been recognized that the set of all the variables may be divided into two classes—(1) the class of all the inclusive variables within a given system and

Table 2.4:  Topological Hierarchies. Copyright 1959 by R. Buckminster Fuller. Reprinted by Permission of Mr. Fuller.

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(2) the class of all those operative exclusive of the system. It has been further recognized that the variables outside the system may affect the system from outside. In varying degrees specific levels of sub-classes of these ‘‘background’’ or outside variables are identified as parameters. This background ‘‘inside and outside’’ concept is a two dimensional or flat-projection concept.

Our omnioriented Halo concept converts the parameter consideration to conceptual four dimensionality and discloses a set of parameters inside as well as outside the zone of lucidly considered system stars. And the parameters are at minimum four fold: [1] the convex twilight zone of inward relevancy, [2] the concave twilight zone of outward relevancy, [3] the stark nonconceptual irrelevancy inward, and [4] the stark nonconceptual irrelevancy outward. Parameter [1] is a tetrahedron. Parameter [2] is a tetrahedron. Parameter [3] plus parameter [4] comprise an invisible tetrahedron.

The considered relevancy within the zone of lucidity consists of one more tetrahedron. For each ‘‘considered tetrahedron’’ there are three parameteric tetrahedra. We discover that our omni-halo epistemological accounting consists of rational tetra hedronal quantation.

When we missed the moon in our first attempt to shoot a rocket to it, the tetrahedronal tuck in universe may have represented that discrete error. It was directly relatable to our lack of awareness of the disparity of the calculus. This disparity is corollary to the same mathematical disparity that was physically discovered in atomic behavior, which brought its discoverer’s the 1957 Nobel prize and which discovery invalidated ‘‘physics'’’ long held ‘‘law of conservation of parity’’ which held the obverse and reverse to be identical, ergo, redundant. A further corollary to the tetrahedronal disparity of systems invalidates the functioning significance of the transcendental irrational constant Pi. The comprehension of this mild error and implementation of the mathematical strategy of nature’s co-ordinate system which I have disclosed and named Energetic/Synergetic Geometry may greatly improve the extra-terrestrial undertakings whose effectiveness has not been frustrated so much by inadequate energy supply as by inadequacy of fundamental mathematical conceptioning and its resultant technical incapability. Our computer instrumentation is phenomenally good, but our problem stating and question asking have been inadequate.

In the inherently subjective language of physical transformation of an omni-interaltering and accelerating universe there are only two fundamental kinds of observable transformational changes, i.e., angular, or sub-unity alterations, and linear, or plural unity (frequency modulated) accelerations. These subjectively viewed transformations of universe are also objectively and locally controllable by man through designed angle and frequency modulations.

In the Energetic/Synergetic Geometry’s isotropic, vectorially triangulated, omnidirectional matrix initiations the angular and linear accelerations are rational and uniformly modulated, whereas in the xyz co-ordinate analysis of the calculus only the linear is analyzable and the angular resultants are usually irrationally expressed.

Substituting the word tetrahedron for the number 2 completes my long attempt to convert all the residual heretofore unidentifiable integers of topology into geometrical conceptability. By the omnidirectional star-studded Halo reasoning the development of a conceptual tetrahedron automatically charges a negative yet invisible tetrahedron into the nonsimultaneous, nonconceptual finite universe, comprehensive to the local definite conceptual system.

This discovery that all the differences between de-finite conceptual systems and finite, yet nonconceptual total universe seems to provide a fundamental means of identifying the physical phenomena entropy. Entropy no longer means inherent escape of energy from any local system or decrease of local order or increase to disorder. Entropy now means the invisible extraction from any local definitive system of the negative conceptual entity, i.e., one negative tetrahedron deposited into universe balance of energy conservation permitting the local extraction of any visible orderly conceptual system. Entropy is not random; it is always one negative tetrahedron. It may have a wide variety of relative size (frequency) dimensions. A tetrahedron is 720° and is an angular constancy independent of size. It is finite. It can account finitely for any discrete rate of energy loss.

Table 2.5:  Dymaxion Energetic Geometry. Copyright 1950 by R. Buckminster Fuller . Reprinted by permission of Mr. Fuller.

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In résumé: By our systematic accounting of angularly definable concave-convex local systems we discover that the sum of the angles around each of every local system’s geodesically inter related vertices is always two vertexial unities less than universal nondefined finite totality. We call this discovery the law of finite universe conservation. Therefore, mathematically speaking, all defined conceptioning always equals finite universe minus two. The indefinable quality of finite universe-inscrutability is exactly accountable as two.

This is a subtractive 2—not a divisive 2, which latter occurs as the second derivative stage of systematic zonal differentiation into the fundamentally positive and negative yet disparate and inseparable aspect characteristics of concavity and convexity.

The finiteness of universe is thus finitely proven by comprehensive geometrical system topological accounting. We have, therefore, a comprehensive universal synergetic accounting advantage in respect to all systematic experience considerations both physical and metaphysical.

The first synergetic accounting advantage of known man history derived from the two-millennium-old discovery of the invariant sum (180°) of the angles of the obverse face of any plane linear bound triangle. The second major synergetical advantage accrued to Newton’s inverse ratio law of gravity as a comprehensive astronomical accounting system. The third major synergetical accounting advantage was derived one hundred years ago from Euler’s topological discovery that the numbers of vertices of polyhedra plus the number of their faces always equalled the sum of the number of the polyhedra’s edges plus the number two.

The fourth major synergetical accounting advantage accrued a half century ago to the physicists'hypotheses of the law of conservation of energy which held that energy had shown experimentally that it could be neither created nor destroyed. From this assumption, which threw all scientific and nonscientific considerations, other than the energetically physical, into the then seemingly indeterminate realm of metaphysical, came the successive wave-quanta accounting theory and subsequent fission and successful nuclear components discovery and inventorying. Fifthly, Willard Gibbs'phase rule in a formula similar to Euler’s in which the degrees of freedom are in effect the vectorial edges brought synergetic advantages to chemical strategy. Sixthly, the same synergetic accounting advantage is now extended by our law of non-simultaneous finite universe pattern conservation to embrace definitive consideration of any and all experiences, physical or metaphysical. The latter strategically equatable accounting advantage derives from a corollary of synergy which shows that systematic accounting of the behavior of whole aggregates may disclose discretely predictable angle and frequency magnitudes required of some unknown components in respect to certain known component behaviors of the total and known synergetic aggregate. Therefore, the definitive identification permitted by the law of finite universe conservation may implement conscious synergetic definition strategies with incisive prediction effectiveness, possibly of epoch initiating magnitude. We inaugurate exploration with our theorem of omniuniverse tetrahedronal structuring. Whereas Van’t Hoff showed that all in organic chemical structuring is tetrahedronally configured in vertexial linkage and Pauling’s X-ray diffraction analyzes show omnitetrahedronal configuration interlinkages of gravitational centers of compounded atoms in all metals analyzed our omnitetrahedronal structuring as a triple bonded linear tetrahedronal array may coincide with the DNA helix, and the tetra’s four unique quanta corners may explain DNA’s dichotomy transferred T,A; G,C patterning control of all biological species reproductions.

A trial balance reconsideration and interconsideration of the significance accruing to the inherent order of consciously permitted cognitions thus far inventoried as derived from our epistemological premise that universe is the aggregate of consciously observed and communicated experiences discloses an orderly succession of derivative dichotomies and synergetic surprises accruing to the grand operational review of derivative patterns.

First, we recognize that intellect took the measure of definitive energy universe because Einstein as intellect wrote E = MC^2 And we recognize the inherent irreversibility of that definitive capability because the concept of energy defining intellect is unthinkable. The defining of finite universe is a function of intellect synergetically manifest in universe. Subsequent to Einstein’s intellect’s definition of energy universe in two conceptual functions M and C^2 his definitive physical realm hypothesis of universe was proven valid by fission. With fission came empirical validation of Einstein’s theretofore hypothetical equation as now energetically definitive. Because the difference between definite and finite universe is definitively two, it follows that the difference between the physical portion of universe and total universe is definitive two. Whereas all metaphysical phenomena were shuntingly disposed by the Einsteinian physicists into a then supposedly infinite universe’s ephemeralization; it now comes as a surprise result of our finite-universe hypotheses that the metaphysical is as strictly definitive as the physical. Ergo the definite physical portion of universe plus the metaphysical or nondefinitive portion of universe together equal total finite universe and the metaphysical must therefore equal a nondefinitive but finite twoness.

The metaphysical which is now also contained within the comprehensive finiteness of universe is greater by two in its comprehensive magnitude than the physical portion of universe which lies inherently within the micro-macro metaphysical. And as the metaphysical embraces intellection, we may say that the nonsimultaneous all-knowledge (omniscience, or wisdom) gained by all men out of all-experience (universe) is comprehensive by a discreet margin of two to all-energy (omnipotence) whose measure omniscience took. Omniscience is greater than omnipotence and the difference is two. Omnipotence plus two equals omniscience. META = 2.

Intellections are cumulative pattern apprehensions and are synergetically integrative as wisdom and wisdom initiates new mathematical hypotheses. Mathematics implements man’s calculation within minutes regarding energy actions requiring eons of time. Man’s intellect masters energy’s fastest behaviors. Energy light years are calculated in intellect in seconds. Omniscience is evidently of comprehensively transcendental alacrity to the speed of light whose relatively slow articulations in universe are readily anticipated by intellectually initiated and disciplined computation of mind.

There is a question-asking-possibility that omniscience may be transcendental in velocity to the definitive physical speed of energy omnipotence. The synergetic anticipatory capabilities of intellect (in respect to conceptual formulations of evolutionary transforming potentials of universe and the anticipatory stratagems evolved by intellect to test such hypotheses) imply the possibility of a velocity transcendence of omniscient functioning over omnipotence functioning which could mean an intellectually regenerated evolutionary extension of universe in generalized synergetical integrity. Intellect’s comprehensive anticipatory objectivities indicates a speed of functioning transcendental to physical events. Intellect may be ‘‘creating’’ finitely extending and re-fining universe as it asks each next good question.

List of Figures

1.1 Omnidoppler Effect

2.1 Linear Tetrahedron (A) A linear tetrahedron has six relationships. (B) Four unique frequencies (sizes) of entities, or particles, comprise the tetrahedron.

2.2 Pattern of Thought. Thinking is frequency modulation-tuning out finite irrelevancies into two main classes: micro-macro, which leaves residual defined system as lucidly relevant.

2.3 Pattern of Thought—Phase 2. De-finite equals finite minus outwardness and inwardness.

2.4 Pattern of Thought—Phase 3. Concave means concentrate; convex means diffuse.

List of Tables

2.1 Angular Topology Independent of Size.

2.2 Tetrahedronal Mensuration applied to Well-Known Polyhedra. We discover that the sum of the angles around all vertices of all solids is evenly divisible by the sum of the angles of a tetrahedron. The volumes of all solids may be expressed in tetrahedra.

2.3 Tetrahedronal Mensuration applied to Spheres.

2.4 Topological Hierarchies. Copyright 1959 by R. Buckminster Fuller. Reprinted by Permission of Mr. Fuller.

2.5 Dymaxion Energetic Geometry. Copyright 1950 by R. Buckminster Fuller . Reprinted by permission of Mr. Fuller.

Bibliography

[MF60]

Robert W. Marks and R. Buckminster Fuller. The Dymaxion world of Buckminster Fuller. Garden City, N.Y.: Anchor Books, 1960. ISBN: 0385018045.

Index

Accounting.

See Economic accounting

Anticipatory design science, 22

Anti-entropy, 101--102 See also Entropy

Areas. See Topology

Astronauts: all humans as, 56

Atomic energy, 129.

See also Energy Automation: of human biological processes, 54; and loss of jobs, 124

Automobiles: ownership of, 134

Bank wealth, 89

Behavioral sciences: in educational process, 26

Brain: as coordinating switchboard, 25; difference between mind and, 101; imitated by computer, 118

British Empire and the great pirates, 37--38

Categoryitis, 31

Children: as comprehensivists, 25--26 Circle. See Great circle Comprehension: defined, 77 Comprehensivity of Great Pirates, 34--35; Great Pirates abandoning their, 50--51; man forced to reestablish, 53

Computers: provide new impersonal problem solutions, 45; as superspecialist, 53; strategy combined with general systems theory and synergetics, 93--94; as imitation of human brain, 118; beginning of, 122; resolving ideological

dogmas, 138

Craftsmen: early specialized, 29; tools of, 122; in the industrial economy, 123

Cross-breeding: of world man, 131

Cybernetics: defined, 95

Darwin, Charles: theory of animate evolution, 47

Da Vinci, Leonardo, 35--36

Democracy, 92--93

Design: capability of early world men, 28--29; of spaceship Earth’s internal support systems, 59--60; of universal evolution, 111--112; revolution in, 134

Design science: anticipatory, governing yesterday’s naval mastery, 22

Divide and conquer: grand strategy of, 39

E = MC^2, 69, 96. See also Energy

Economic accounting: by great pirates, 94--95; synergy in, 103; need for realistic, 112

Educational task: to allow physical and metaphysical success, 130

Einstein, Albert: formula E = MC^2, 45, 69, 96; definition of physical universe, 70; reassess universe, 97

Electromagnetic spectrum: great pirates’ first use of, 43--44; effecting human evolution, 110 Energy: impounding of sun’s radiant, 58, 59, 93; generalized law of, 73; savings as fossil fuels, 94, 129; in synergetics, 95; finite, 96; harnessing of, 129; atomic exploitation of, 129

Entropy: energy systems eventually run down, 46; assumed universe subject to, 96; wealth as antientropy, 101

Environment: early society inability to cope with, 26; evolution synergeticaily produced, 103--104; changes in physical, 110

Euler, Leonhard, 81

Evolution: success of human dependent on mastering metaphysical, 46; design and patterns in, 49, 54, 111--112; man’s feeling about, 53--54; inexorable, 55; our present position in, 65--66; effected by electromagnetic spectrum, 110; comprehending phases of, 127

Experiences: to extract generalized principles, 62; is finite, 70

Exploitation: of atomic energy, 129; of fossil fuels, 129. See also Energy

Extinction, 48

Failures: humanity’s, 24--25 Fellowships, 125

Forecasting, 22

Fossil fuel: energy savings account, 94, 128; expending of, 129. See also Energy

Generalized principles: minds discovering, 21; extracted from human experience, 61--62; first was leverage, 63; surviving with, 118; inventively employed only through mind, 127

Genera! systems theory: as tool of high intellectual advantage, 67, 70--71; combined with computer strategy and synergetics, 95

Geodesic lines, 76

GI Bill, 115

Gold: demand system inadequate, 88--98; used by Great Pirates for trading, 90

Grand strategy: divide and conquer, 39; organizing our, 65.

See also Strategy

Great circle: defined, 76

Great Pirates: as sea mastering people, 34; feared bright people, 35; use of logistics by, 37; and British Empire, 37--38; use of local strong man as king by, 39; tutoring of bright specialists by, 40; in world competition, 41, 43; becoming extinct, 44, 50; rules of accounting still used, 45

Gross national product: estimate for 1970, 108--109

Growth: physical and metaphysical, 61

‘‘Have-nots’’ struggle with ‘‘haves’’ produces war, 87

‘‘Haves’’: struggle with ‘‘have-nots’’ produces war, 87

Heisenberg, Werner: principle of indeterminism, 72

Human beings, as astronauts, 56; will be free, 111; employing real wealth, 124; characteristics in Mexico, 132. See also Man

Humanity: exists in poverty, 23--24; on Earth’s surface, 27; extinction of, 49; place in evolution of, 66; function of, in universe, 83--84; and standard of living of, 102--103

Ideologies: political, 48; resolving dangerous dogmas of, 138

Indeterminism: Heisenberg’s principle of, 72

India: population problems in, 113 Industrialization: demonstration of world, 104

Industry: tooling of, 22, 116, 122, 133; production increased by world wars, 116; craftsmen in the economy, 123. See also Tools

Information: multiplies wealth, 104--105 Initiative, 45

Intellect: as humans’ supreme faculty, 60--61; frees man of special case superstition, 63; use of as man’s function in universe, 99

International Monetary Fund: 1967 deliberations of, 88

Invention, 134

Inventory: of variables in problem solving, 67--68

Jobs: loss of in automation, 124

King: as great pirate’s local strong man, 39, 40

Law of conservation of energy: defined, 98. See also Energy

Learning: always increases, 99; man’s past, 131; industrial retooling revolution, 133

Lesser circle: defined, 76

Leverage: first generalized principle, 63. See also Generalized principles

Life: as synergetic, 79--80; hypothetical development of support systems in, 107--108

Lincoln, Abraham, 45--46

Lines, 81. See also Topology

Machine: spaceship Earth as, 59--60 Macrocosm: as universe outside the system, 70

Malthus, Thomas, 47

Man: utterly helpless as newborn, 61;

as adaptable organism, 118--119.

See also Human beings

Mass production: and mass consumption, 123

Mathematics: improved by advent of zero, 36. See also Topology

Metals: not destroyed in war, 117 Metaphysical: initiative confused between religion and politics, 45; masters the physical, 46; experiences not included in physical universe, 68; defies ‘‘closed systems’’ analysis, 69; in synergetics, 95; need for, in educational task, 130

Mexico: human characteristics in, 132 Michelangelo, 35--36

Microcosm: universe inside the system, 70

Mind: comprehends general principles, 24, 127, 128; difference between brain and, 101; fellowships of, 125

Money: as bank wealth, 89.

See also Wealth

Moon gravity: as income wealth, 94 More-with-less: and generalized principles of, 63

Myth: of wealth as money, 114;

of population explosion, 136 Natural laws: and Great Pirates, 34.

See also Generalized principles Navies: and Great Pirates, 38 Negatives: yesterday’s, realized, 24 North America: early crossbreeding men in, 131

Photosynthesis: impounds sun’s energy, 59

Pirates. See Great Pirates

Planck, Max, 97

Planners: more comprehensive than other professions, 67

Points. See Topology

Politicians: local, asked to make world work, 51.

See also Ideologies

Pollution: as survival problem, 85 ‘‘Poluto’’: as new name for planet, 85 Population: problems in India, 113;

explosion in as myth, 136 Poverty: humanity existing in, 23--24 Principles. See Generalized principles Problem solving: by yesterday’s

contrivings, 21

Resources: of Earth unevenly distributed, 29; no longer integratable, 52; unique materials made ‘‘on order,’’ 106

Revolution: design and invention, 134

Safety factor: in man’s evolution, 111--112

Schools: beginning of, 41.

See also Specialization; Strategy Second law of thermodynamics, 46 Senses: Great Pirates relying on, 43 Ships: logistics for production and maintenance, 37. See also Vessels

Slavery: of specialist expert, 41; human, 107

Sovereignties: claim on humans in, 37--38; categoryitis in, 31

Spaceship Earth: present condition of, 121

Specialist: computer as super, 53 Specialization: society operates on theory of, 25; early leaders who developed, 26, 30, 33; intellectual beginning of schools, 41--42; specialist as slave, 41; over causing extinction, 48, 49; scientific, applied toward weaponry, 52--53

Speed of light: discovery of, 97 Spending: regarding energy is obsolete, 98

Spoken word: as first industrial tool, 122

Strategy: secret and anticipatory, of Great Pirates, 35; comprehensive of naval war colleges, 37

Structures: industrial tool enclosing, 116--117

Students: comprehend elimination of war, 134

Sun: radiation as income wealth, 58, 94. See also Energy

Survival: physical and metaphysical, 61; potentials increased by intellect, 63

Sword: powerful men of, 26.

See also Great Pirates

Synergetics. See Synergy

Synergy: defined, 78, 95; defines universal evolution, 79; combined with computer strategy and general systems theory, 95; wealth develops interest through, 102; in economic accounting, 103; in humanity escaping from local identity, 106

System: universe as biggest, 68; thought is, 72; first subdivision of universe, 71, 83;

variables in evolution, 83

Technologies: as substitute after war, 117

Telford, Thomas: as Great Pirates’ specialist, 37

Thinking: long-distance future of, 22; in terms of whole, 67; as a system, 72; dismissal of irrelevancy in, 76--77; tackling problems with, 83; humans free to, 126.

See also Intellect; Mind

Time: as relative, 135

Tools: industrial, 116; externalizations of integral functions, 117; craft and industrial extinctions, 122; spoken word, 122

Topology: mathematics of comprehension, 77; discovered by Euler, 81; patterns of lines, points and areas, 80--81. See also Geodesic lines; Great circle; Lesser circle

Underlying order in randomness, 74--75 Universe: as biggest system, 68, 96; physical defined by scientists, 68--69, 70, 72, 97; subdivision, 71; generalized law of energy conservation in, 73; defined by synergy, 79; humanity’s function in, 83, 112

Van Allen belts, 58

Variables: inventorying of and

problem solving in, 67

Vectorial geometry: mathematics

of comprehension, 75--80

Vessels: use of, in venturing, 28

War: beginning of the great class, 47--48, 87; as age-old lethal formula of ignorant men, 52; as taking priority over real problems, 87; students comprehend elimination of, 134

Water: desalinization of, as problem solution, 85--86. Pollution

Wealth: generated by integrating resources, 29; as a safety factor, 61; defined, 88, 93; irreversible in evolutionary processes, 91; society’s real, 91, 94,124; income is sun radiation and moon gravity, 94; as anti-entropy, 101; can only increase, 101,105; common, of humanity, 105; of the U.S., 108; of know-how produced by GI Bill. 115

Weaponry: scientific specialization applied toward, 52

Wholes: thinking in terms of, 67; systems in synergy, 78. See also Systems

World: and first seafarers, 28; sea ventures thought in terms of, 30; asking local politicians to make it work, 51; defined, 104, 119; veterans returning from World War II, 115; increase industrial production in, 115--116; cross-breeding in, 131-132

Table of Contents

Contents

Introduction to Omnidirectional Halo

Omnidirectional Halo

List of Figures

List of Tables

Bibliography

Index

Omnidoppler Effect

Linear Tetrahedron (A) A linear tetrahedron has six relationships. (B) Four unique frequencies (size

Pattern of Thought. Thinking is frequency modulation-tuning out finite irrelevancies into two main c

Pattern of Thought—Phase 2. De-finite equals finite minus outwardness and inwardness.

Pattern of Thought—Phase 3. Concave means concentrate; convex means diffuse.

Angular Topology Independent of Size.

Tetrahedronal Mensuration applied to Well-Known Polyhedra. We discover that the sum of the angles ar

Tetrahedronal Mensuration applied to Spheres.

Topological Hierarchies. Copyright 1959 by R. Buckminster Fuller. Reprinted by Permission of Mr. Ful

Dymaxion Energetic Geometry. Copyright 1950 by R. Buckminster Fuller . Reprinted by permission of Mr