Help Circumvent Obstacles

Many people are unable to solve problems because, quite simply, they do not know how to solve problems. They may not even know what it means to solve problems.

It is important to give people the widest possible exposure to problems and their ways of being solved; and to dramatize the extent to which problems have been and are being solved. But how might this be done? What can be done to radically improve upon the existing situation?

Some individuals will object that there is only so much that can be taught, that students can easily be overwhelmed with too many problems and methods, that if what is presented is too diverse it will lead to overgeneralization, superficiality, and a chaos of the mind.

Yet is there necessarily a limit to the amount that we can be taught? Might not the amount ultimately depend upon the ways in which things are taught or upon our capacity to innovate? Can we speak of overgeneralization without knowing the degree of generality that is intrinsic to nature or that the universe demands of mankind?

Traditional answers to these questions may be corrupted by fallacies and preconceptions. Many are the great questions that have long since been answered - erroneously.

Few problems - if any - are truly elementary. Most can be decomposed intro two or more component problems or sub-problems, which may be analyzable in turn into series, clusters, and networks of problems of lesser and lesser order or of ever greater number, diversity, specialization, or disconnection.

Problems seemingly or truly insoluble at one level may be soluble at some quite different level; or they may require solutions at many levels simultaneously and cooperatively. They may require one to work back and forth between a set of levels sequentially and perhaps improvisatorially.

Problems can likewise be decomposed into elements that would not ordinarily be described as problems. The number of these elements may be finite or virtually infinite. In the latter case there may exist subsets whose discovery and exploitation permits one or more, often subtle and surprising solutions to the problem. But in either case the problem may be solvable via few or many combinations, permutations, or transformations of the elements or subsets of the elements; indeed the problem may have originated from, or be a matter of, the combinations or their kith.

Many problems are in an analogous way presided over or derived from larger or higher-order problems, or systems or series thereof. Their alternative, best, or necessary solution may likewise be vicarious or conjoint, or involve the solving or curtailment of the super-problem or meta-problem.

Many apparent problems are really pseudo-problems: an illusion of a problem produced through ignorance, misunderstanding, one's own designedly constructive or innocent actions, a misrepresentation of the problem or situation, or a simple failure to treat the problem as inconsequential or interchangeable with equivalent or quasi-equivalent problems.

Many problems are in fact but reincarnations of oneself, or unconscious externalizations and anamorphoses of one's internal problems; for being such they can seem all the more real and at once special and specially important (which they may not be). Problems of this sort may require one to investigate and alter oneself.

Problems of a purely relative nature are common. Their appearance, essence, importance, or very existence may depend upon or derive from the appearance, essence, structure, tendencies, complementarities, or effective prejudices of the environment, circumstances, or larger context in which the problems are encountered or which one shares with the problems.

Most of the time problems are understood and solved only in the most superficial, expedient, elementary, formal, and supposititious way; that there are deeper problems and solutions may not even be realized. Possible consequences of this are many: Bad habits form that could be avoided; Collective knowledge becomes less integral, fundamental, and reliable; Revolutionary possibilities are overlooked or discounted; Existence - ways of doing things - become needlessly complex; Problems are mailed to others; Mental skills are left undeveloped; Cowardice becomes institutionalized; Etc.

Ideonomy can take a random or particular problem and reveal the scope, complexity, and profundity - the universal grandeur - of that didactic problem in a fantastic and unforgettable way. Nothing rivals the instructive power of a memorable example.

Problems can be transformed into other problems and other types of problems, and back into themselves. Knowledge of the local and universal transformations of problems - which can be cultivated, systematized, and taught - can aid the classification, analysis, synthesis, and reduction of problems and even enable them to be exploited. No form of knowledge is more powerful than dynamical knowledge of a thing, which affords true mastery.

If one knows about all of the possible transformations of problems, those problems or their equivalents can be recognized whenever and wherever they occur in nature or human experience; and all that one knows about those problems from their occurrence or feasibility in other contexts and domains can potentially be imported and made use of in specific situations.

General types (and causes) of problems include: Excess, redundancy, oversupply, or overproduction; Deficiency, underproduction, lack of redundancy, limitation, or boundaries; Absence of boundaries, constraints, rules, order, control, or government; Blindness, inattention, ignorance, lack of feedback, etc; Stupidity, poor planning, fallacies, etc; Error; Conflict, contradiction, antagonism, opposition, friction, obstacles, or interference; Accidents, surprise, or disaster; Damage, loss, wear, or failure; Instability, change, or deviation; Bad timing; Crisis; Pathology; Contamination; Confusion among things; Overreaction; Disrepair or maladjustment; Isolation; Overburdened condition; Haste; Stagnation; Indecision; Overdependence; Congestion; Undesirable or excessive feedback; Etc.

Recurring types of solutions to problems include: compromise, prevention, mitigation, ignoration or hiding of the problem, approximation, containment, revisualization, restructuring of a situation, etc.

Bring To Light Important Omissions and Neglects

What does not exist? What is it that things are not? What in human history or existence has been omitted or neglected?

What most certainly has been neglected is this very set of negative questions, or attempts to answer these questions in any serious, comprehensive, and systematic way.

Yet negative things are not necessarily inferior in importance to positive ones, and in many respects both are profoundly complementary to one another.

Attempts to define what is nonexistent often lead to the discovery of things whose existence was neither known nor suspected and that may not even have been imagined. And on the other hand, research that seeks to discover, map, and understand the existence of things frequently reveals the surprising or unsurprising absence, invalidity, or partiality of various things, of a related or different nature.

Yet if things--even nonexistent things--are not deliberately sought they may never be found or they may only be found belatedly.

The things that are missing or neglected may be essential to human reason or purpose, or to the plenitude of the universe: some piece of a theory, some corollary of a postulate, some proper element of human nature or of civilization, some variation within a musical composition without which its statement of an aesthetic idea will remain incomplete or disturbingly self-ignorant, some residual physical particle needed to complete and vindicate a group-theoretic scheme, some link in a lengthy mathematical proof, some exception to a rule or relationship, etc.

A surprise may be that the set of things that are nonexistent is larger than the set of existent things; in which case it may actually be more important. Then again, an important discovery may be made that there is nothing that is nonexistent, either because other things are fundamentally impossible or meaningless, or because all possible things have a surprisingly great tendency to exist, or factually coexist for some surprising or unknown reason.

The existence, discovery, or achievement of things characteristically blinds one to the entire realm of the nonexistent; and what is worse, it blinds one to the fact of one's blindness, or even to the knowledge of what it would be mean to be sighted.

We have discovered vitamins, organic substances a small quantity of which is essential to the nutrition--to the survival or health--of certain species of organisms, although as nutrients they contribute neither energy nor building units. Yet attention to this class of indispensable nutrients has probably diverted science from the parallel discovery, investigation, and exploitation of a class of analogous but not strictly--or at all--essential nutrients: e.g. organic substances merely contributory to the vitality of the species, or key to a subpopulation within the species, or part of various substituent groups or groups of substituents collectively encompassing masked nutritional needs.

Years of research and tremendous ingenuity may go into the development of a sealant for the cylindric parts of a rocket, yet the possible effects of frigid weather upon that sealant may be overlooked, and this omission or neglect may eventually lead to a disaster.

For decades ever more powerful serial computers may be developed, but single-minded concentration upon the evolution of such computers, and spectacular accomplishments ensuant upon their use, may perpetuate and solidify ignorance of alternative, non-serial (massively parallel) architectures for computers and of the unique powers and possibilities they might have.

Historically the tree of science has shown a tragic tendency to rashly branch and grow in only one direction, to the neglect--or without any apparent awareness--of complementary or synergistic alternatives, and science has needlessly wasted much time in backtracking and rebalancing itself. Moreover, many great imbalances have probably gone uncorrected to the present day and done incalculable harm.

We think of human reason as pure and general, and yet it is quite likely that the neurological evolution of animals has ultimately equipped Homo sapiens with a brain that is very specialized and idiosyncratic, and for which many forms of logic--needed to understand different facets of nature--are difficult or impossible. This chance and conceivably grotesque brain of ours, moreover, may preclude the future emergence of dimensions of human behavior and character that are of the utmost importance to the perfection of civilization. Yet it might be necessary for one to possess such dimensions to fully appreciate their importance.

Ideonomy permits one to know many things indirectly that cannot be known directly or in conventional ways. It enables one's knowledge of what one knows to be transformed into knowledge about what one does not know. It allows knowledge to be amplified in a variety of ways. Through it one can acquire vital prior knowledge about the fundamental possibilities for knowledge.

Possible separate and combined reasons for the nonexistence of things include: mutual exclusion, past extinction, abortion, chance, lack of preparation, untimeliness, inadequate resources, lack of a proper environment or regime, enemies or antagonistic conditions, excluded paths or directions or irreversible evolution, illusory nonexistence (mere hiddenness), lack of a trigger or of a 'seed' or beginning, contradictoriness, past transmutation, virtual nonexistence within a limited frame of reference, self- destructiveness, oversight, etc.

Some recurring questions when treating omissions and neglects are: What else was neglected--or was anything else neglected? If the thing was formerly neglected, should it be neglected now or in the future? Should something else be (or have been) neglected instead? What were all of the costs and risks of the omission or neglect? What good is associated with the neglect? What kind, or kinds, of neglect did the neglect represent? What causes a neglect? What are all of the effects or corollaries of a neglect? What are the least and most important things that have been neglected? What can and should be learned from the study of a neglect? What is and is not known about a neglect? Can a neglect or omission be corrected, and what are all methods and means for repairing same? What are all ways and dimensions by which to quantify a neglect? What is the best way to define or describe a neglect? How is a given neglect similar to or different from other neglects?

Among the things that may not exist (or occur) are: beginnings of the universe, earlier universes or things preceding the universe, ends of the universe (in time or space), other universes, other biological or intelligent life--or other technological civilizations--in the universe, divinities, universal purposes or 'meanings for existence', the fundamental flow of time (which could be an illusion), fundamental physical forces (beyond the four known), exotic physical particles (such as magnetic monopoles, subquarks, or mere gravitons), a transuranic "island of stability", a supreme universal physical force, absolute laws of nature--or ways around those universal laws that have been postulated, etc.

Help Explore and Exploit the Omniverse

The dictionary defines "omniverse" as a universe that is spatiotemporally four-dimensional. The word could be used to refer to the totality of spacetime--to all that is, has been, or will be. In ideonomy the Omniverse-- capitalized--is the universe of all real things and real possibilities.

The Ideocosm, on the other hand, is the universe of all possible things and ideas. This is conceived of as having a universal, unique, and necessary structure that can be systematically and progressively explored, mapped, and exploited. It is supposed to have its own laws, phenomena, and even forces.

However, ideonomy is a science, not a school of philosophy, and for this reason it itself takes no stand on many deep philosophical questions in connection with the interrelations of the Omniverse and Ideocosm that remain troublesome and unanswered: the question, for example, as to whether the Omniverse and Ideocosm are identical. Of course ideonomy can, and no doubt eventually will, make an important and special contribution to the effort to clarify and resolve these supreme problems.

Clues as to the possible interrelationship of the Omniverse and Ideocosm may be gotten from mathematics, a science that is very similar to ideonomy and in certain respects is synonymous. The universe that is represented by all of the known and as yet undiscovered elements of mathematics has, it has been remarked, a profound unity and self-connectedness. Moreover, it appears to have a queer isomorphism to the physical universe, and to exercise either a partial or absolute power over the latter. The logic of mathematics, that is, seems a cousin--perhaps a twin--to physical logic. Mathematical ideas ideas rooted in mathematics--transcend mathematics.

The stuff of the Ideocosm--its laws, phenomena, relationships, and processes--would appear, at this early stage in the development of ideonomy, to exercise an analogous power over physical reality.

Perhaps the patterns that define reality are simply the common property of mathematics, ideonomy, and physics.

There are a variety of ways in which ideonomy can enable the exploration of the Omniverse and Ideocosm.

It could begin anywhere--or with any topic, problem, or concept--and search for things of an analogous or related nature that must coexist. It could then define the class or classes represented thereby, or to which the things in question simultaneously belong. It might then seek a few higher and lower taxons that in some sense contain or are contained in that class or those classes. Using these taxons as 'seeds', it could then define their range, structure, and raisons d'etre more precisely-. Perhaps it would seek the principles, relationships, or patterns that generate these taxons. In any case, it would attempt to identify, based on the foregoing, the general taxological scheme--with all of its many levels, elements, meanings, and extensions--that pertained to the situation.

Transformations of this scheme into other taxological schemes able to classify other kinds of things in more or less analogous ways might be found. These classificatory schemes could then be adapted so that they would also be able to function as schemes defining what should or must coexist as or in connection with the new things. Further adaptations might reveal things that must coexist within the framework, or in terms of the joint requirements, of all or many of the different schemes simultaneously.

Many things would have to coexist simply because they are unexpectedly tautologous.

The evolving enterprise could also require, or be made to require, simple existence--not just the more demanding coexistence--of things.

This hints at an all-important principle: that the development of of such an ideonomic structure or system can and should be deliberately 'pushed' in many different directions, or forced to take on desired properties, to achieve certain goals, and to undergo maximal or optimal growth and evolution. Bases for exponential progress of the whole, for example, are especially important.

Such a structure or apparatus requiring in a progressive way the existence of more and more things might only naturally point to the existence of things of every greater diversity or range of properties; or in other words, come to require things related to more and more of the world as we know it.

The enterprise here envisioned would not only explore a finite part of the Omniverse, but provide infinitely reusable machinery for the further exploration of the Omniverse in all future times. Moreover, it would inevitably enable the creation of other and more powerful ideonomic machinery for the same purpose but on a larger and more diverse scale.

Furthermore, in the course of time the ideonomic machinery developed for the investigation of the Omniverse would continually increase in efficiency, flexibility, intelligibility, automation, etc.

And of course comparable machinery could be developed for the systematic exploration of the Ideocosm.

Suggest Opportunities

The feasibility, importance, and appropriateness of things vary profoundly as a function of time or in various situations and circumstances.

Opportunities arise that did not previously exist, that are better than others, that can only coexist or that inevitably coexist, that derive from earlier--or permit subsequent--opportunities, that are incompatible or antagonistic, that are similar or equivalent, that are different or opposite, that are orthogonal, that are related or connected on lower or higher levels, that pertain to entire systems or infinite chains or networks of opportunities, that are part of exponential series of increasingly numerous, diverse, large, or better opportunities; that are two-edged opportunities for both or either good or bad things to happen; that if overlooked--or not exploited or appropriated--by one's self or by one thing, are liable to be used by some competitive or inimical party, thing, phenomenon, or tendency; that are essential or decisive for the development, course, or transformation of a thing; that do not always exist or that are rare, unique, or supreme; that will not persist or that are literally instantaneous; etc.

Recurring and general causes of opportunities include: coincidences or combinations of things, drift of circumstances, anomalous events, deliberate or spontaneous removal of obstacles, inversions or reversals of situations, emergence of new things, maturation or evolution of things or consummation of plans, triggers, precedents or anlages, chaos, settled conditions, attainment or crossing of thresholds, forks in the road, search for or discovery of opportunities, intersections of paths or convergences, errors, interruptions, collapse of the status quo, mathematical singularities, arrival at a step or point in a sequence, abatement of an antagonist or of opposition, other opportunities, beneficial forces; sudden knowledge, insight, or disillusionment; appearance or acquisition of new methods, means, or resources; disappearances of other things or the abandonment or creation of niches, oscillations of things or cyclic events, gaining of control over things, synergisms or 'resonances'; regeneration, repair, or correction; external help or guidance, usefully 'analogous' situations or factors, reorientations or redirections, changes in the environment, changes of location, trains or chains of events, adjustments or adaptations, surprises, conflicts or other problems, etc.

The possible range, diversity, and extremity of opportunities needs to be speculated upon systematically. For example, might there be opportunities for: Chemical reactions to change in mid-course or initially take very different courses; Our universe to have taken disparate courses in the beginning; Reinforcement and conditioning of brain states, animal behavior, or even alternative ontogeneses of plants; Sudden establishment of a lasting world peace; Unrecognized types of interstitial businesses; Geochemical cycles to become "chaotic"; Telephone systems to fail in thousands of different ways; Any wrestler to defeat any wrestler in any wrestling match; Etc?

More generally, there are constant and pervasive opportunities for: Being heard (paid attention to); Catalysis or triggering of things; Closing deals; Making points; Escape; Error or failure; Accidents; Catastrophe; Testing, checking, or verifying things or performing experiments; Business enterprise; Seizing control; Theft; Taking rest; Putting plans into effect; Correcting problems; Effecting repairs; Deceiving people; Giving or getting misimpressions; Explaining things; Saving money; Finishing tasks; Changing one's mind; Aborting or reversing actions or processes; Making announcements; Altering, rearranging, or redirecting things; Innovation, starting, or introducing things; Learning or finding things out; Making observations or noticing things; Acquiring things; Thinking about something; Losing things; Doing harm or destruction; Occurrence of problems; Repeating something; Getting rid of things; Getting behind (slippage); Catching up; Asking questions; Misunderstandings; Things failing out of adjustment; Occurrence of chaos; Comparing one or more things; Improving, advancing, or benefiting things; Replacing, substituting, or exchanging things; Leakage; Enjoyment; Using things; Gaining insight into things; Conflict; Movement; Occurrence of things; Negation or invalidation of things; Emergence of new species; Synthesis or unification; Transitions or transformation; Emergence or development of things; Cooperation; Interaction; Reactions or responses; Interference or disturbance; Etc.

Opportunities may cause or have as their effect, consequence, or postcedent: No change (the status quo ante); Competition; Innovation; Conflict; Learning; Interadjustment; Self-adjustment; Assimilation; Growth; Improvement or evolution; Movement or relocation; Transformation; Counteractions or suppression; Other opportunities; Continued survival; Negotiation or exchange; Ecological adaptation or revolution; Flight; Complacency; Neglect of the opportunities; Struggle, stress, strain, or failure; Cogitation, debate, or experimentation; Generalization or specialization of the opportunities; Actions that secure or reinforce the opportunities; Changing of priorities or rescheduling of things; Reinforcement or amplification of an existent thing or situation; Reorganization or redistribution of resources; Separation or division; Oscillations; Extension, formation of connections, or integration; Disequilibrium; Energetic behavior; illusion; Differentiation or dedifferentiation (relaxation); Costs, wastes, or risks; 'Winners and losers'; Freedom from constraints or liberation; Restratification; Changes of role, function, use, value, meaning, goal, or mechanism; Etc.

Possible descriptive or other properties or dimensions of opportunities include: age or recency, probability, reliability, availability, simplicity or complexity, genericness or specificity, breadth, depth, clarity or obscurity, amplifiability, interest, importance, stability, variability, competitiveness, optimality or imperfection, controllability and manipulability, multiplicity of significance, rarity or frequency, analogizability or uniqueness, essentiality, persistence, priority, exploitability, purity, proximity, imminence, magnitude, number, fungibility, investigability, range and diversity, reducibility and separability, etc.


Point To the Ways In Which Opposites Meet and Merge

When things of an opposite or seemingly antithetical nature meet, intersect, unite, mimic one another, or exhibit interdependence, complementarity, or synergism, this is termed antisyzygy or an example of antisyzygy.

The inevitability, ubiquity, endless recurrence, fundamentality, universality, infinite diversity, essentiality, and complexity of antisyzygies--throughout nature and in every dimension of our lives--makes the subject one of the most profound and important in all of ideonomy.

The relevant questions are: What are all known and possible opposites to all known and possible phenomena, concepts, entities, quantities, terms, principles, processes, etc? What are all of the known and possible ways, senses, and degrees in which all such opposites 'meet'? What are all of the known and possible effects, corollaries, importances, and implications of antisyzygies? What are all of the ways in which, and reasons for which, opposites do not meet? What are all known and possible direct and indirect causes, mechanisms, and geneses of antisyzygies? What are the laws and principles of antisyzygies? How can antisyzygies be usefully exploited? How do different antisyzygies interact, cooperate, and conflict? What are all possible levels, dimensions, and meta-structures of antisyzygies? How can all antisyzygies be classified in terms of one another, and what are their analogies, differences, and complete relationships? What are all of the properties, forms of behavior, and transformations of antisyzygies? What do we know and what do we not know--or what must we learn and what might we discover--about antisyzygies? What practical and fundamental problems are associated with antisyzygies?

Some of the reasons why, or ways in which, opposites meet include: Coessentially or essentially they may be the same; They may differ only by a trivial enantiomorphism or the equivalent; They may be complementary or co- necessary (e.g. as contrasts); They may be 'dialectically' interlacing, contrapuntal, intersecting, or oscillatory; They may be cut across by orthogonal dimensions; They may be ambiguous, or not be fundamental or real; They may be more complex than they would be if they were, say, 1- dimensionally bipolar or antithetical; They may be continuously or partially intergraded; They themselves may not be the maximal or true extremes or antitheses; They may be coinfinite and hence subject to the many paradoxes of infinity; They may be equivalent, identical, or nonexistent from the standpoint of infinite complexity (or the Greek apeiron); They may have an infinity of different related and unrelated senses; They may co-occur or associate; They may be convergent; Etc.

Illustrative examples of opposites that meet include: Laughing and crying (one may cry because one is so happy; or laugh because crying or sadness seems so ridiculous or disaster so total; or be at once happy and sad owing to a janus-faced event, such as the marital loss of one's daughter); Giving and receiving (giving brings joy-the joy of giving; giving may have selfish motives; and giving involves or maintains reciprocity and equilibrium); Honesty and mendacity (as with an honest liar, dishonest or misleading candor, or the dishonest honest man--so honest as to approach dishonesty); Problem and opportunity (all problems are also opportunities--to learn, enjoy life, gain advantages over the lax, or find out about oneself; and all opportunities, in turn, create or involve many problems); Poverty and riches (wealth can impoverish, poverty can amplify the meaning and joy of tiny things); Perfection and imperfection (perfection bares imperfection and gives rise to new problems and flaws; imperfection creates and reveals possibilities for perfection); Etc.

Reveal Underlying Order

By "order" here, is not simply meant pattern, sequence, form, law, manifold, control, relationships, or the like, but something more fundamental that is hard to define, either to other persons or to oneself. Although a more satisfying definition will have to remain a problem for the future, a partial characterization of order is possible now, or at least there are things that can be said that will point the reader's mind in the right direction.

Order, then, might be understood to represent an especially, or perhaps maximally, fundamental level, type, or sense of structure; or whatever kinds or concepts of structure are most apt to transcend place, time, detail, variation, discoveries of new phenomena, substitutions of one class of phenomenon for another, movement from one science or subject to another, or even changes of perspective or logic. In a crude sense, order refers to the actual or possible arrangements of things in nature or the mind. It might also be said to designate the generic or specific structure of any physical or abstract space; or the essence of any spatial, temporal, or semantic manifold. It signifies the interrelation of the deepest categories of reality, and the derivation of lesser order therefrom.

The basic problem in defining order is that it is so fundamental that all the terms that we are compelled to rely upon in an effort to define it are necessarily less fundamental, and the opportunistic employment of such gross means warps and cheapens the reality. A somewhat similar difficulty is encountered in quantum physics, in the attempt to use quantum entities or terms to characterize themselves.

A sense of the supreme importance of order may be gotten from the fact that mathematics has been defined as the science of order (as has ideonomy itself, for that matter).

Clarifying the nature, kinds, and processes of order can clarify all else, indirectly or directly, because in a sense everything else depends upon order and simply expresses its manifold possibilities.

If science benefits from research into its foundations, and order represents the foundations of all foundations, then the scientific investigation of order cannot help but improve science.

If the topic of order has hitherto been neglected, however, that could only have been because of the special difficulty of the subject. Or possibly the blame must be shared by the fanatical specialization of science, since the subject of order, being the most universal, demands for its advancement an opposite cast of mind, or a willingness to think in the most generalized terms.

No doubt the pathetic cleavage between the mathematician and the scientist has also frustrated progress in understanding and exploiting order.

Order either stands or operates at the crossroads of the mind and physical or external reality. Research, discoveries, and possibilities in the three complementary fields of neurology, noology, and artificial intelligence have therefore a deep interest to the student of order, as also must the profound contribution that ideonomy can make to the furtherance of those subjects.

There is a chance that reality is infinitely complex, and if it is infinitely complex, then the study of order is infinitely important, for order must be the source of that complexity, as well as the key to its mental simplification. Power, both cognitive and practical, springs from mastery of order.

Order might be described as the language of nature. It is a language that should be progressively deciphered and taught to the newest and youngest minds. Arguably it should be taught before all other subjects, given its purity, elementariness, universality, and fertility, and the relative superficiality of all else. If other subjects and things are taught first they will permanently blind, prejudice, and cruden the mind, whereas if the mind awakens to a clear vision of order itself it will commence life with a stupendous advantage.

The objective of ideonomy is to gradually identify all species, genera, and taxons of order, to classify them into a pyramid of levels, and to interrelate them as a continuum at once infinitely complex and infinitely simple and specific; or negatively expressed, it is to avoid any illusorily truncated treatment of these things.

Up until now, the scientist and mathematician have almost always been content merely to discriminate different classes of order, and have rarely made the additional effort to link and synthesize them, qua complementary, synergistic, and coessential aspects of the same, or some greater, reality.

The ideonomist, per contra, is interested in working out, not just all the types of order, but the system of all their combinations, permutations, transformations, and equivalences. What, for example, are all of the ways in which one type of order can combine with itself, or with any and all other types of order? How can all types of order be derived from any single type of order?

The different types of order can be mapped into a common space. Such mapping can reveal their redundancy and irredundancy, clustering and overlapping, differential generality, dimensions and dimensionality, interconnectivity, behavior, completeness and incompleteness, boundaries, metastructures, homology, interoperation, oppositeness and antisyzygies, etc.

Among the questions about order that ideonomy can help us to address are: What causes particular types of order to exist in particular cases or situations? What contradictions and conflicts exist among different types of order? How ordered are things? Why are types of order absent at times? What are the immediate and long-term consequences of given types of order? What finite and infinite groups of order are there? What methods and means are there for determining the existence of types of order? What is essential and extraneous to forms of order? How does order grade off into things that are not actually order but that are related or analogous to it? What means and ways are there for representing different types of order? What illusions, fallacies, and errors pertain to different types of order? What are the extremes of, and in connection with, all forms of order? How knowledgeable and ignorant are we about order? Is order relative or absolute? What are the dynamics or temporal patterns associated with types of order? What are the potential uses of various forms of order, and what are the functions and roles of order in nature and civilization? What methods can be devised for investigating order, and what is it that is important for us to find out about it? What rules and principles are there for working with forms of order? What are the costs and penalties of various forms of order?

Ideonomy could help one espy underlying order in such things as: Brain waves (the EEG), Neural networks (no general theory of which exists at present), Patterns of human behavior, Genetic control or evolution of the phenotype, Statistical data sets, Music, Surface waves of the sun, So-called elementary particles, Patterns of clouds in Earth's atmosphere, Economic fluctuations, Cosmic structure and dynamics, Esoteric patterns in number theory, Idea-maps created via MDS (multidimensional scaling), The visual structure of scenes, Etc.

There are probably many things that are not perceivable, conceivable, or doable in the absence of knowledge of relevant order.

Things can appear completely different when reseen from the perspective of an alternative form of order.

The content, relationships, and meanings of things or sensory experiences may be much more diverse than can be imagined when one relies upon the logic of a narrow form or spectrum of order.

New types of order, or greater knowledge of order, can permit one to do things far more efficiently, appropriately, confidently, systematically, thoroughly, flexibly, authentically, etc.

Much of what seems to be random, amorphous, accidental, chaotic, indeterminate, meaningless, inconsistent, directionless, illogical, complex, or the like may turn out to be quite the contrary when it viewed in an appropriately ordered way.

There can be many different types-of-types of order, or at least different schematizations of order.

Thus one type-of-type of order might include: recurrence, identity, concinnity, continuity, isochrony, etc.

Whereas in another type-of-type, or scheme, of order there might be such natural, named, or convenient types of order as: automorphistic, holomorphic, holonomic, meromorphic, symplectic, renormalizational, etc. (Many of the latter correspond to mathematical groups.)

Scientific revolutions have often been a direct or indirect result of the discovery of a new type of order, extension or generalization of an old form of order, or working out of the theory of some type of order. Certainly any of the latter things will often trigger major and minor revolutions in science, technology, and society.

Yet ideonomy has the potential to bring about deliberate and mass discovery of new types of order, or to drastically accelerate human exploration, discovery, and utilization of new or all possible types and schemes of order.

The remarkable thing about the discovery of some fundamentally new class of order is that it can simultaneously entrain breakthroughs almost everywhere in science. Today we are witnessing such transdisciplinary rashes of discoveries in connection with chaotic, fractal, cellular-automaton, spin- glass, and other types of order,

Explicate Origin

By origin is meant the start of a thing: the fact, how, why, or possibilities of any beginning. In the vocabulary of ideonomy, origins are not synonymous with geneses, histories, causes, or emergents.

But even in this restricted sense, origins are a primary concern of every science and of practically every area of scholarship.

Ideonomy is a universal science that is at once capable of facilitating inquiry into the origins of things as diverse as: A biont, Great religions, A lightning bolt, Albert Einstein's relativity concepts (in his childhood development), Animal trails (in the forest; in time, in space, or starting species), Aristotelian two-valued logic (the process of logical or dichotomic affirmation and negation; in evolution, human history, or psychogenesis), Brain waves, Gambling (in the history of civilization), Cancer, Matter (baryons and leptons), the Mississippi River, Mathematics (say the concept of number), Or one's marriage.

Where in a symphony can one theme properly be said to originate from another? From what did all that we term the universe itself originate? When in life did the most rudimentary form of one's self originate; what was the moment before and after which one existed?

Among the systematic ways in which ideonomy will be able to clarify origin are: By reducing origins to general or universal taxons; By encouraging analogies between seemingly unrelated origins and types of origins of seemingly unrelated things; By highlighting the differences among origins; By defining the finite ways in which, alone, things can originate; By distinguishing the different stages and degrees of origins; By demonstrating how things cooriginate; By proving the necessity for things to originate in certain ways; By describing the relationships, environments, and circumstances associated with origins; By enlarging the meaning of origin; By bounding, limiting, and qualifying origin; By rigorously illustrating how combinations of elements can originate different or like things; By revealing characteristic convergences and divergences of things; By identifying paradoxes connected with origins; By revealing the true complexity and simplicity of origination, Etc.

The importance of origins or of their study includes: Their value in defining things; Classificatory power; The utility of precising the temporal range of things; Identification of lineages and affiliations; Exclusion of confusable and erroneous origins; Enablement of predictions; Confirmation of theories and hypotheses; Specification of the substantial nature of things; Indexing of the quantity (population, frequency, probability, dominance, etc) of things; Mapping things into a general framework; Etc.

What is all that we know, or do not know, about the origin of a single, random thing?

With what priority should the origin of different things be inquired into?

What origins are interdependent and independent?

What is the relative contribution of chance and law to different origins and types of origins?

What are the chained, hierarchic, and reticular relationships among different origins?

The generic causes of origins of things are, for example: Maturation of an underlying productive process; Temporary or permanent disappearance or inhibition of whatever has been preventing something from originating; Development of a need or requirement for the thing; Conjunction of 'mutually' necessary factors or events; Simultaneous origin of something else; Transformation from one regime or epoch to another; Transformation of a thing into a new thing; Simple recognition of the preexistence of a thing (producing a virtual origin); Attainment of some relative criterion for a thing's existence or origin (representing another instance of virtual origin); Etc.

Exploit Paradoxes

Discovery, explanation, application, generalization, and transcendence of paradox accounts for a great deal of human progress. Anything that can contribute to the process can help advance civilization.

The reasons for this are many: Paradox checks arrogance; Paradox can reveal and index unsuspected underlying complexity; Paradox may also indicate the possibility of some peculiar simplification in a difficult situation; Many paradoxes spring from antisyzygies (meetings of opposites in the greater nature of things); Paradoxes can afford at least partial freedom to escape from rigid laws, limitations of situations, and supposed absolutes; Confronting paradox can lead to a reformation of one's mind or a greater wisdom; Paradox is often associated with the emergence of novel categories of things; Etc.

There are many general forms of paradox that occur over and over again: Augmentation leading to diminution, Self-annihilating existence, Self- generation, Equivalence or meeting of opposites, Self-contradiction, Self- divergence, Self-avoidance, Ignorance or incapacity produced by knowledge, Bad associated with or engendering good, Good associated with or engendering bad, Simultaneous existence of a thing at many levels (of space, time, etc), Disproportionate importance of seemingly insignificant things, Coexistence of contrafactuals, Fundamental immeasurability or indeterminacy, Self- containment, Nonlinearities, Etc.

Paradox is defined in five ways by Webster's III: A tenet or proposition contrary to received opinion; A statement or sentiment that is seemingly contradictory or opposed to common sense and yet perhaps true in fact; A statement that is actually self-contradictory and hence false even though its true character is not immediately apparent; An argument that apparently derives self-contradictory conclusions by valid deduction from acceptable premises; and Something (as a human being, phenomenon, state of affairs, or action) with seemingly contradictory qualities or phases.

Hence orthodoxy can be challenged and often errs, what seems obvious and entirely logical may be wrong, a valid proposition may invalidate itself on another, higher, or lower conceptual level, a proposition may be covertly self-inconsistent, and an entity may transcend in its complexity any conventional harmony of its elements.

Conventional concepts and words are in their simplicity and familiarity chronically confused with the different, stranger, and greater things and realities to which they lamely point, which gives rise to discoveries that are much of what we mean by paradox.

The awkwardness of reason is another parent of paradox. Reason looses itself in its own complexity and forgets the truncation of its analysis that is perpetually necessary. Logic has a life of its own: an organic evolution and a continuity of curious idiosyncrasies, prejudices, and errors; its recursive essence is forever overlooked. As reason adapts to receive truth it distorts it.

Clarify Pathology

The tentative view of the ideonomist is that 'disease' (or what it prefers to refer to, generically, as pathosis) is fundamentally an altogether universal phenomenon that completely transcends biology, organisms, or the realm of life, a phenomenon whose infinite analogical diversity is exemplified by, in, or through all entities, relationships, processes, and systems in all sciences and subjects.

By pathosis is meant an abnormal state or condition that develops progressively, is complex, specific, and characteristic, has a certain autonomy, has a transformative effect, mimics some of the properties of biological organisms (say by seeming to propagate or adapt), and/or the like.

Already diseases of the psyche and a society are recognized, and the term is applied to some phenomena in technology (in materials, computer, and food science, for example). What is termed pathological in mathematics is not unrelated to this generalized concept of disease.

Often what are otherwise normal or characteristic behaviors, laws, or properties become so extreme that we say they are pathological. In special regimes or circumstances what is otherwise normal becomes pathological. Pathology can arise suddenly and seemingly spontaneously from random or very subtle causes.

Pathological behavior may result when the burden upon things is too great, or when too much is asked of them.

Other generic causes of pathosis include: aging, decay, obsolescence, misuse, conflict, self-interference, isolation, excessive feedback (either positive or negative), overcomplexity, overspecialization, hurry, over- connectedness, inflexibility, indeterminacy, mimicry or self-mimicry, resonant coupling, oscillation, "chaotic" behavior, excessive threshold dependence, pluralism, resource shortages, inconsistent 'programs', growth, etc.

Many such causes may conspire to produce a pathosis.

Remaking pathology into a theoretical and transdisciplinary science is vital in our increasingly complex, abstract, and integrated world.

Confronting pathology will afford us a chance to remove many of the infirmities of nature and civilization that hitherto we have had to take for granted.

Also, the truly pathological or "bad" character of pathoses is relative, and as science and technology become more sophisticated it will be possible to find virtues in and exploit ever more, and ever more diverse, pathoses.

Moreover, ideonomy has led to the conjecture that in biology both "good" and bad diseases may exist, with the former being as common and important as the latter.

To the extent that bad pathosis is universal, 'good pathosis' may play an equally general, but even less recognized, role in nature.

Some purely fanciful examples of pathoses in various fields are: Supernova epidemics in galaxies (though actually astronomers have often proposed the operation of such contagions), Terrestrial epochs of catastrophic volcanism (say of idiopathic character), Rashes of propagative defects in crystals, 'Conspiracies' of message errors in the brain's interneuronal traffic, Self- destructive cycles of the universe (if it is oscillatory) or self-destructive universes (if there are many cosmoses), Sudden and inexplicable transformation of good weather or climate into bad, "Chaotic" oscillations of the stock market or world economy, Contradictions (or simple indeterminacies) in a noble ethic degenerating it to sordor in the course of time, Debilitating changes of a language occurring historically in a multiplicative cascade, Purely chemical 'infections' destroying the taste of wine or some other stored food, Etc.

Abiotic pathoses are such an unexplored territory that it is exceedingly hard to even imagine the possibilities.

But with respect to universal pathoses ideonomy can systematically work out the generic: causes, mechanisms, effects, types, components, properties, indications, interactions, rules, abilities, hierarchies, sequences, solutions (or 'therapies'), questions, problems, theories, implications, etc.

By aiding the treatment of pathoses, ideonomy should have the effect of gradually raising levels of: efficiency, excellence, economy, health, longevity, conservation, safety, stability, power, capacity, precision, control, evolution, simulation, etc.

Biological and abiotic pathology will progressively clarify one another.

Deeper, broader, analogous, and divergent causes and effects of pathology will be recognized thanks to ideonomic research.

Many medical diseases are probably related, identical, or virtually identical after a simple ideonomic transformation; and many others, on the other hand, are probably divisible into various separate and unrelated diseases. Many such diseases probably have simple mathematical or physical causes and solutions that are abundantly illustrated in inanimate nature and that can only be obscured by a narrowly or essentially biological approach. A single disease thought to have a few forms may in fact have a thousand different forms and manifestations or be distinct in all of its occurrences. A few powerful laws may give rise to virtually all diseases.

These questions and matters are the sort that ideonomy is designed to illuminate.

Ideonomy can clarify the basic dimensions of all pathology, including those suggested by such questions as: What are the slowest, most persistent, or longest-lived, and the fastest, most ephemeral, or most fragile, of all pathoses? What pathoses are rarest or the most ubiquitous? What are the most hidden pathoses? Are pathoses of finite or infinite diversity? Are pathoses linked or independent? What, spatially or massively, are the smallest, and what are the largest, pathoses? What are the simplest and most complex pathoses? What are the most extreme pathoses? What basic categories of pathosis can be imagined but do not exist in nature?


Help One Discern Patterns

There are countless senses, types, and examples of pattern: Style or law of behavior; Typical or apparent course of development; Internal, external, comparative, or reciprocal structure; Configuration, distribution, or grouping; Cluster of traits, acts, properties, elements, or tendencies; Habit, tendency, or history; Systematic quality; Analogical character; Quiddity; Holistic character; Higher-level , abstract, or final pattern; Etc.

The ideonomist is especially interested in patterns that represent meta- phenomena, archetypal phenomena, and phenomena nearly of the status of entities but that are not quite entities. Meta-phenomena are higher-order phenomena or phenomenon-like patterns-of-patterns. Archetypal phenomena are that quasi-finite set of physical or mental phenomena that are, or that are treated as being, the most universal, fundamental, important, characteristic, necessary, explanatory, simple, regular, multiform, etc, or to which all other known or discoverable phenomena can in some sense be reduced. Some phenomena naturally approximate to entities without quite being entities; their resemblance to entities being due to their imperfect: individuality, persisting and characteristic effects, organizing and self-organizing tendencies, qualitative distinctness, meaningfulness, e/vc.

Recognizing patterns is important because they can indicate things': forms, laws, histories, courses, activities, relationships, causes, effects, origins, destinations, present status, quantitative properties, differences, internal content or structure, mechanisms, methods, problems, needs, values, 'languages', forces, etc.

Patterns are present all the time, everywhere, and in everything, but often they are overlooked because of their subtlety or because the mind is ignorant of the language that is necessary for perceiving or even imagining them. The density and diversity of natural patterns may even be infinite.

Ideonomy may be the ultimate key to making sense of this ocean of patterns, for it is essentially a qualitative universe defined by and defining an infinite interweaving of ideas. Patterns lead to other patterns because there are lawful transformations of ideas.