504.00 Special Case

504.01 Experience is always special case.
504.011 Events: Energy events and structures are always special case (see Sec. 1075).
504.02 The human brain apprehends and stores each sense-reported bit of information regarding each special-case experience. Only special-case experiences are recallable from the memory bank.
504.03 There is in Universe a vast order. It never forsakes. I throw a coin in the air, and it returns and hits the floor every time. Nature is never at a loss about what to do about anything. Nature never vacillates in her decisions. The rolling oceans cover three- quarters of Earth. Along the beaches, the surf is continually pounding on the shore. No two successive local surf poundings have ever been the same nor will they ever be the same. They typify the infinitude of individualism of every special-case event in the Universe.
504.04 Weightless, abstract human mind reviews and from time to time discovers mathematically reliable and abstractly statable interrelationships existing between and amongst, but not "in" or "of," any of the special-case experience components of the relationship. When a long-term record of testing proves the relationship to persist without exception, it is rated as a scientifically generalized principle. Whenever human mind discovers a generalized principle to exist amongst the special-case experience sets, the discovery event itself becomes a new special-case experience to be stored in the brain bank and recalled when appropriate. Amongst a plurality of brain-stored, newly understood experiences, mind has, from time to time, discovered greater and more significant understandings, which in their turn as discoveries, which are "experiences," constitute further very special-case experiences to be stored in the recallable and reconsiderable brain bank's wealth of special-case experiences.
504.10 Truth as Special Case Realizations
504.11 We may say that thinking about the truth alters truth, but only to the extent of defining it. We may always clarify and redefine the truth by making it more comprehensively considerate and more incisively exquisite. Truth alters truth only by refining the definition. The substance of the sensing and instrumental control of the physical means of communication is always refinable and tends toward the ephemeralization of doing ever more with ever less, but you can never get to the exact, most economical statement of the truth, for the very communication will have ephemeralized to pure metaphysics. Truths are like generalized principles: interaccommodative and nonintercontradictory. Truths are special case realizations of the generalized principles; by these very aspects are they discovered to be truths.
504.12 The experience of life inevitably brings inspirational glimpsing of the cosmic orderly vectors, all of which point convergingly to the absolute. The synergetic integral of all truths__being absolute__is incomprehensible to temporality.
504.13 Truth is special case. Truths tend to articulate generalized principles. All the cosmic generalized principles are omniembracing. Truth, like gravity, is nonlinear; it is omniembracing. Of all the creatures on our planet only humans have demonstrated the ability to discover progressive truths.
504.14 As humans are physically situate halfway between the largest and smallest known bio-organisms, they are also halfway between the astro-largest and nuclear-smallest physical phenomena; humans thus find themselves between an absolute, omnidirectional, equilibrious, dimensionless, metaphysical core contained within a spheric twilight zone of macro-almost-true and themselves containing a spheric twilight zone of micro-almost-true. As humans are in the middle of the cosmic scheme metaphysically, truth itself is an unreachable, omnidirectional, cosmic center. The truth is zero eternal. Temporality=tempo-reality=time-reality. In temporality you cannot reach the truth. You cannot be exact because truth is zero. Absolute truth is an omnizerophase condition. The metaphysical comprehension passes through, expandingly and contractively, but fails ever to remain at the zero core of equilibrious truth.
504.15 As we reduce the tolerance for error, we begin to get near the eternal, which is what we call the truth. But we will never quite get there. The inexhaustibly attractive and truthfully inspired thoughts of human minds ever approach an evolutionary refinement while constantly intertransforming as a precessional consequence of progressively experienced complexes of omniinteraccommodative, intercomplementary transactional events; the process results in ever-closer proximity to perfect equilibrium of all intertransformative forces, but it never attains such equilibrium.
504.16 Truth may be dealt with only as relative relationships of interactions of dynamic principles. Degrees of accuracy are refinements that in no way affect the fundamental reliability of the directional or angular sense toward centralized truths. Truth is a relationship; it is a direction rather than an attainment. The search for truth is a yielding to the integrity of the intellect, revealing information and nuances that are ever more impressive, more delicate, and more exciting.
504.17 Truth is the progressive diminution of residual error. The generalizations are eternal. The more accurately we state the truth, the less frequently it becomes necessary to modify our statement of it. We have to change what we say less and less. Eventually it works back to the eternality of No Change.

505.00 Pattern

505.01 When we speak of pattern integrities, we refer to generalized patterns of conceptuality gleaned sensorially from a plurality of special-case pattern experiences that have been proven experimentally to be existent always, without exception, in every special case within the required class of experiences.
505.02 Special-case events may appear to be both continuous and "linear" __but only as locally and momentarily experienced. For all experimental observations of at first seemingly "continuous" and "straight-line" experiences (subjective) or of experimental experiences (objective), when projected or prolonged, are always discovered to have been short increments of larger multidirectionally peregrinating, curvilinear, wave actions of discontinuous events (stars) in Milky Way__like, stepping-stone, "linear" arrays.
505.03 All experiences are omnidirectionally oriented. Omnidirectional experiences resolve themselves scientifically into discrete angle and frequency patterns. That is life! Relationships are local to pattern. Patterns are comprehensive to relationships.
505.04 In a comprehensive view of nature, the physical world is seen as a patterning of patternings whose constituent functions are fields of force, each of which compenetrates and influences other localized fields of force.
505.05 Action and interaction of events are accompanied by relative omnidirectional displacements and accommodations of other events. In considering a total inventory of the relative abundance of different patterns, it becomes apparent that patterns are reciprocal.
505.06 The artist frequently conceives of a unique pattern in his imagination before the scientist finds it objectively in nature.
505.10 Euler: Minimum Aspects of Pattern
505.101 Euler said that we are dealing in pattern. Mathematics is pattern, and there are irreducible aspects of pattern. That is, the patterns represent events. A line is a unique kind of pattern. If I have two lines, where the two lines cross is distinctly different from where the two lines do not cross. Euler called this the vertex, the convergence. He saw this as absolute pattern uniqueness. (See Sec. 523.)
505.11 Euler showed that all optical experiences that we can pattern or form are composed exclusively of three patterning elements: lines, vertexes, and areas__or trajectories, crossings, and openings, as they are known in synergetics. These incontrovertible minimum aspects of pattern are all that is necessary to analyze and inventory all parts of all optically apprehended patterns as well as of all whole patterns. And Euler disclosed three algebraic formulae characterizing the constant relative- abundance relationships of these three fundamental topological elements in all patterns.
505.12 All happening patterns consist of experience recalls. The recallable ingredients of experiences consist inherently of paired-event quanta of six-vectored positive and negative actions, reactions, and resultants.
505.20 Pattern Integrity
505.201 A pattern has an integrity independent of the medium by virtue of which you have received the information that it exists. Each of the chemical elements is a pattern integrity. Each individual is a pattern integrity. The pattern integrity of the human individual is evolutionary and not static.
505.21 Each of the chemical elements is a uniquely complex pattern of energy event interrelatednesses which interact inter-interferingly to continually relocalize the involved quantity of energy. These self-interference patterns of atomic element components are in many ways similar to the family of knots that are tied with rope by sailors to produce various local behaviors, all of which, however, result in further contraction of the knot as the two ends of the rope immediately outside the knot are pulled away from one another by forces external to the knot__and thus all the attractive forces of Universe operating upon the atoms may result precessionally in keeping the atomic knots pulled together. (See Sec.506.14.)
505.30 Waves
505.301 When we drop a stone into water, we see a wave emanate outwardly in a plane. We agree that it is not water but that we are seeing a wave in pure principle. It is not simultaneous: therefore to conceptualize we are using our memory and afterimage. We can never have static waves; they have nothing to do with statics. We see a wave operative in time and in pure principle. If we initiate wave-propagating energy action at one point, a complete omnidirectional wave develops.
505.31 When a stone is dropped into a tank of water, the stone does not penetrate the water molecules. The molecules are jostled; they "accommodate" the stone and in the process jostle their neighboring molecules, which, in turn, jostle their own outwardly surrounding water molecule neighbors. Thus waves of relayed jostling are propagated. Each relayed wave, although a composite of locally forwarded actions, provides a synergetic continuity scenario of those actions. The consequence is a pattern of events that has an integrity of its own, independent of the local displacement accommodations (which are innocent with respect to the overall synergetic pattern).
505.32 The same stone dropped successively in pools of water, milk, or gasoline will generate the same wave patterns. Yet the waves are essences neither of milk nor of water nor of gasoline. The waves are distinct and measurable pattern integrities in their own right, visibly growing and traveling outwardly as each locally involved molecule of the liquids develops a narrow vertical ellipse circuitry returning to where it started, unless a powerful wind operating parallel to and above the liquid blows the top molecules free as bubbles to tumble down the wave side like water on a hillside. (See Sec. 1005.14.)
505.33 Individuals regenerate their own sound and air displacement waves and ripples in the physical environment just as stones create waves and ripples in the different liquids into which they are thrown. They also propagate metaphysical wave patterns that develop local pattern displacements in the human affairs cosmos. They also propagate both conscious and unconscious electromagnetic waves. The wave is as abstract as the concept of an angle. Waves are weightless patterns.
505.34 The room we sit in is permeated by thousands of weightless waves, each of unique character. You can tune in hundreds of wide-frequency-range radios within your room, and each can bring in a different program from a different part of the world because the individual, weightless waves flow through trees and house walls. That extraordinary world of weightless, invisible waves is governed by mathematical laws, not by the opinions of men. The magnificent orderliness of that ever individually and uniquely patterning weightless wave Universe is not of man's contriving. The infinite variety of evolutionary complexities, inherent to the orderliness of complementary principles operative in Universe, is of unending synergetic uniqueness.
505.40 Wave or Particle

Fig. 505.41
505.41 One of the things we have to make clear for society is the intellectual dilemma of the Max Planck-descended scientists: the way they do their problems, they can have either a wave or a particle but not both simultaneously. Heisenberg has the same dilemma. They make the error of thinking of a wave as a physical continuity rather than as a metaphysical, weightless pattern integrity, experimentally detectable only by virtue of the medium of the locally displaced, frequency tuned, physical phenomenon__a principle operating utterly independent of any physical medium. (See Secs. 973.30 and 1009.36.)

505.50 Abstract vs Energetic

[505.50-505.83 Pattern Scenario]

505.51 The science of pattern is mathematical. As the fundamental communications system of all the sciences mathematics is both the most comprehensive and the most abstract of the sciences. Experimentally discovered mathematical relationships permit generalized statements of such laws as are found to be governing all science, and all sciences must use mathematics. Nonexperimentally disclosed mathematical relationships can be imaginatively evolved, however, but they may or may not have identity with physical Universe behavior. It is for instance mathematically feasible to explore a hypothetical Universe theoretically devoid of any one of the family of mathematical operations, such as, for instance, a Universe in which there is only multiplication and no division, or an exclusively two-dimensional Universe.
505.52 Employing only mathematics in the analysis of physically verifiable data (which always includes all the known physically relevant variables) can provide information to humans within minutes regarding cosmic events that in themselves take years to transpire, even though they occur at the speed of light.
505.53 Synergetics conceptualizes in generalized principles, in contradistinction to special-case empirics. We may logically hypothesize either (a) that mathematics is entirely physical, or (b) that the physical is in reality pure abstract principle. You can play the game either way: both are valid, but not simultaneously. There are certainly not two absolutely separate and independently operating Universes: the abstract Universe of the mathematician and the energetic Universe of the physiochemist.
505.60 Minimum-Limit Case
505.61 You cannot have a line that is less than a line, or a fix that is less than a fix, or a virgin that is less than a virgin. Nature comes to minimum-limit case with all her points in order to feel very comfortable. But the resolution is not linear or planar: it is omnidirectional; it is hierarchical in ascending or descending hierarchies.
505.62 You grow or decrease. You get better or worse. In parallelism things do not converge. Science is not getting the right answers because scientists do not think divergently and convergently. If you are in parallel, you can never get to any conclusion whatsoever. Waves require hierarchies. (See Sec.260.20.)
505.63 Only means are parallel: means are the averages of the limits. Dealing in probability calculus scientists can deal only with averages of limits; wherefore they explore and speculate only in terms of parallels. Min-max limits are inherently omnidirectional- inherently divergently expansive toward max-limits and convergently contractive toward min-limits. There are no experimentally demonstrable, absolute-maximum limits. Only the minimum limit is demonstrably absolute__even when it looks like a point.
505.64 All the characteristics of a system are absolute because each of its components is the minimum-limit case of its conceptual category, for all conceptuality-as Euler discovered and proved-consists at minimum of points, areas, and lines.
505.65 An area is a nothingness. A plurality of areas are views of nothingness through separate frames. A point is a somethingness. A line is a relationship between two somethingnesses. An enlarged, apparently single somethingness may prove to be resolvable into a plurality of somethingnesses between which the lines of interrelationship fence off the nothingness into a plurality of separately viewable nothingnesses. Points are unresolvable, untunable somethingnesses occurring in the twilight zone between visible and supravisible experience. (See Secs. 262.02 and 264.01)
505.70 Topology of Minimum Awareness
505.71 Awareness seems to be the one minimal word best expressing the experience of life. Awareness is inherently plural, for it consists of the individual system that becomes aware and the first minimum otherness of which it is aware: such otherness may be integrally internal or externally separate of the observing system. We say, "No otherness: no awareness" (Sec. 905.02). A philosopher may question that statement, saying, "No, you are wrong because awareness can be exclusively of self." But we reply by recapitulating the inherent minimum topology of awareness: __ minimum self and minimum otherness are both systems, each having both insideness and outsideness;
__ one part of a system cannot exist without the other;
__ an experienceable point is substantial; -all substance has insideness and outsideness;
__ all substances are divisible into minimum substances;
__ each minimum substance is always a whole system; and
__ each system always has insideness and outsideness and four minimum-system- defining events, all of which events are inherently nonsimultaneous and only overlappingly co-occurring.
505.72 Ergo, the minimum cognition employs the information-sensing, remembering, and recognizing circuitry of the organic substance's minimum self-sensing awareness, which could only be at a minimum one as a system of four minimum-event components, being aware of its own integral system's otherness-defining components. Ergo, experientially, no otherness: no awareness. Q.E.D.
505.73 All minimum otherness or all minimum-observer self are both plural unity with mutual interawareness. Interawareness means one system aware of another system or the outsideness of a system aware of its system's insideness.
505.74 The observer and the observed constitute two points differentiated against an area of nothingness with an inherent interrelationship line of awareness running between the two points. (See Sec. 264.01.) Thus there is a minimum set of four awareness aspects of life:
  1. the observer;
  2. the observed;
  3. the line of interrelationship; and
  4. the background nothingness against which the somethingness is observed.
505.80 Background Nothingness
505.81 When we draw a spherical triangle on the Earth's surface (Fig. 812.03), it demonstrates an aspect of geometry apparently not recognized by Euler. The spherical triangle also demonstrates self and otherness. The spherical triangle is the first awareness: there is an inherent twoness in the triangle's insideness and outsideness; and the axis of the two poles constitutes the two points of self and otherness. The background nothingness of these two points represents an area not contained by a line. Euler apparently did not realize that there could be an area not contained by a line.
505.82 From Euler we know that the number of locally identified minimum entities called points plus the number of separate areas equals the number of lines plus the number two. In minimum awareness we have two identified entities which, being local points, must have directional fixedness against a background of nothingness. Ergo, in minimum awareness two points plus one area of nothingness have one inherent line of most economical interrelationship between the two points. These two points plus one area equal the number of lines-in this case "one" plus Euler's abstractly accommodative two. (The line of interrelationship is another aspect of the prime vector. See Sec. 540.10.)
505.83 The Euler "plus one" abstractly accommodates two in the minimum awareness model:
points + area = lines + 2
2 + 1 = 1 + 2
3 = 3
Three of two kinds = three of two other kinds = six of four kinds = the six vector-edge relationships existing between the four different event-point fixes. Points are subdifferentiable systems-i.e., microsystems of events too close to be resolved from one another. Areas are supradifferentiable systems-i.e., macrosystems of event points too far apart to resolve. The nothingness area is unbounded by any visible closed line. Nothingness is the part of the system unencompassed by the observer. (See Sec. 1052.350.)

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Copyright © 1997 Estate of R. Buckminster Fuller