Stimulate the Advance of Pure and Applied Mathematics

The value of mathematics in itself is limited; its real value lies in its infinite applicability (both to other things and to itself). Ideonomy - the natural sister to mathematics - can enormously accelerate the discovery of that infinite pertinency and utility.

The meaning of mathematical concepts is not finite in the sense that a particular representation can exhaust it. On the contrary, diverse and ever new representations of both old and new concepts in that subject are apparently able to enlarge the meaning of those concepts - and of mathematics as a whole - without limit. And ideonomy is inter alia a science of all possible representations (of all possible things in all all possible ways via all possible means); it even embraces the infinite complexes and series of representations OF representations.

Mathematical concepts in general are representable by other and divergent - indeed by arbitrary - mathematical concepts. Numbers are obviously not necessary - there is "abstract" algebra, for example - but neither are the other notational forms of mathematics. Mathematicians may be shocked, but the truth is that mathematics can be fully translated into words, that no mathematical concept will ultimately prove impervious to verbalization. Moreover, mathematical concepts can be given a form that immediately transcends mathematics and that enlarges them into the still more manifestly universal realm of ideonomy. The guts of mathematical concepts - if descried - would mean little to today's (fundamentally obsolete) mathematicians, and not merely because those guts are infinitely complex and strange.

Mathematics can also be translated - or reconstructed - purely as shapes, shifting imagery, music, logic (sic), games, metaphors, etc. Placed in each of these forms it will acquire greater meaning than when it is 'artificially' limited to a single form or medium. Of course people will have to be trained to appreciate and use mathematics in these new and unexpected embodiments; and we will have to discover how to train them. But these are preeminently tasks for the ideonomist. Partly ideonomy may simply break down the ingrained habits of mind that hold us in their blinding and paralytic grip; the fearful conviction that the interplay of abstract visual patterns, say, could never serve as a vehicle for concepts in the same vocabular, grammatical, and semantic way that the language of words, for example, does normally and with staggering power and ease. Growth of the mind is more than anything growth of the tolerance of the mind (for queer reality).

One of the greatest benefits of ideonomy to mathematics should come from its tendency to relieve the latter of its arbitrary features, notably its idiosyncratic self-restrictions. If one examines almost any area of mathematics it becomes obvious at once that the terms, conditions, assumptions, variations, ranges, topics, operations, and so forth are overly constrained; in fact the constraints abort immensities with their crudity and lack of necessity. Why in the world should the links and nodes of graph theory, for example, be limited to the structures and phenomena producible and treatable by 'dimensionless' edges and vertices? Allow the links and nodes width and volume and a door is opened to a new universe of the imagination. The same opportunity exists for knot theory and helixes. Presently in mathematics extensions and generalizations of these kinds are being tentatively explored, already with remarkable pure and applied results.

Mathematical concepts need not, and very often do not, originate within mathematics itself. In fact, some of the most revolutionary innovations and departures have resulted from physical, technological, and philosophical inquiries - occasionally even in the complete absence of mathematical methods in the usual sense. In part this has to do with the obscurity, intuitiveness, bizarreness, or nonexistence of the foundations of mathematics. Metamathematics is really a subject that transcends or lies outside mathematics; or put otherwise, the mathematical arises from something pre- mathematical, in its purity or primacy of experience and thought. What we call mathematics is merely the simplest, best known, most formalized, most unified and standardized, or momentarily most useful part of mathematics; and extant mathematics is almost certainly an infinitesimal - and least interesting and essential - part of the full world of potential mathematics.

As a result, the development and use of pure and applied ideonomy - with and without a conscious concern for the mathematical possibilities - can lead to breakthroughs in mathematical theory and methods, and even to a rebuilding of the basic structure of mathematics and a reformation of mathematical research. It can propose new problems and suggest new solutions. It can make explicit mathematical ignorance and needs. It can better define the capacities and limits of, the elements of mathematics. It can show how forms of mathematics that have been developed and profitably used in one area of science have been needlessly and sacrificially confined to that area, rather than having been exploited elsewhere or everywhere. It can be used to improve the classification of mathematical concepts. It can awaken a consciousness in mathematics of the larger realm of human values, ideals, and possibilities. It can transform the systematic planning of the future evolution and use of mathematics. It can maximize the interwovenness of mathematics with other fields of inquiry and endeavor. It can clarify the ideonomic meta-structures that invest and constrain mathematics as they do all other subjects. It can assist the automation of pure and applied mathematics, and the explication of their cognitive bases.

Enhance Meaning

We live life little mindful of its meaning, and of the structure, scope, and fundamentality of that meaning. Things are done by rote, custom, imitation, formula, expedience, chance - anything but reason and understanding. People are in a hurry; they are superficial, rigid, ignorant, and uncaring.

Civilization suffers as a consequence. Its spirituality is diminished. Coherence, purpose, and passion are lost. The actual, much less potential, interconnectedness of human beings is never imagined. Tragedy occurs but is never recognized for what it is. Opportunities pass unseen. Risks, costs, and consequences of actions and situations are ignored. What is had is not appreciated or is wrongly appreciated. Things are taught but not their importance; the role of character in the direction of the world goes unmentioned.

Ideonomy can enlarge human meaning by celebrating the manifold and synergistic functions, roles, causes, purposes, values, interests, and possibilities of everything that we know and experience: the reasons for marriage, the functions of good food, the roles of the clergy in the rediscovery of human truths, the causes of play and of social change, the purposes of human acts and actions, the values of social harmony, human diversity, aphorisms, and chance, the interest of recreational games and of cosmological discoveries, and the greater possibilities of thought, art, science, and industry.

Improve the Use and Understanding of Metaphor

What is meant by metaphor, especially by distinction to what is meant by analogy?

A metaphor is a statement: that uses conventional means to say something unconventional; whose truth is not literal or exact, but rather substitutional, indirect, and allusive; whose power to command attention, and to inform, may not be immediately obvious; whose meaning may be inordinately diffuse and multidimensional; whose validity may be unusually uncertain, because the statement is a high gamble justified by the great payoff should it turn out to be true; whose importance may be that of a half- truth, or of a flawed truth momentarily communicable in no other way, or in no other way with such economy or fractional power; whose ambition may be greater than its actual capacity; whose value lies in its expedient ability to move the mind in a proper or intelligent direction, without itself necessarily being true or having any lasting value; whose merit may lie in its tendency to be associated with the truth, without actually being the truth; that operates on some unorthodox level of meaning; etc.

Of course in good part the difference between metaphor and analogy is purely definitional, or a matter of the senses that one would care to assign to the words or that may have been assigned by those who have used the words, individually or in combination, in the past.

An important point that should be stressed in connection with both terms is that they relate together to a far larger range of complex and distinctive concepts than has ever before been made explicit, and that this medley of concepts has always been the cause of much confusion, vagueness, and error. There is an urgent need for the many different recognized and merely implicit possibilities to be prized apart, distinguished, defined, and re-related in a comprehensive, organized, and prescient whole. Otherwise systematic thought in this area will remain impossible and even meaningless.

The most obvious, albeit trivial, difference between an analogy and a metaphor is that the first often involves a direct comparison between two simultaneously present things.

A metaphor may be more abstract, an analogy more concrete. A metaphor may not involve a simile of extant things, but rather a figurative use of language to illuminate a real thing by a fictional thing or a mere concept. Sometimes a metaphor differs from an analogy in that it asks one to imagine that the whole of a thing, or even the whole of one's ideas about or ways of treating a thing, can be applied to understanding another thing; whereas with an analogy that which is to actually be assimilated may be more limited or specific.

If a metaphor is sometimes a higher-level analogy, one could speak of it as an analogy between or among analogies; whereas a simple analogy is merely a likeness of things.

The purpose of a metaphor may be, not to actually indicate an analogy, but rather a difference between two things, or some other--even more complex--relationship or pattern.

For Aristotle, metaphoric thinking was of the essence of genius or the highest form of thought.

It is easy to appreciate why rigid adherence to the conventional meanings of words and concepts, and strict avoidance of unconventional and more daring modes of thought, would hobble the free play, and ultimately limit the scope, of intelligence. The world is just too big for such condensation, and the language we use for its description is far too idiosyncratic and approximate. Moreover, the invariant use of terms cannot help being inconsistent with the true energy of the human mind.

If nature approximates to something infinitely complex, then the meaning of words-and of concepts themselves-must constantly change and evolve; or to put it another way, new and greater opportunities for the use of words and concepts must be brought into being each time they are employed.

Words and concepts may have an infinite hierarchy of higher and lower meanings and relationships--a hierarchy fundamentally irreducible to any finite and final interpretation. The exploration of this hierarchy may be necessarily metaphorical.

The treatment of metaphor to date has remained prescientific for many reasons: it has eschewed any effort to be systematic and comprehensive, and to identify and classify the types of metaphor that operate or might operate in every area or in connection with every possible concept and mental endeavor; it has disdained to distinguish between what is extraneous and what is fundamental in metaphors; it has failed to identify laws controlling the genesis, analysis, and use of metaphors; it has made no attempt to develop methods, tools, and materials for generating metaphors en masse; it has made no effort to describe specific metaphors exactly and completely, or as natural phenomena; it has failed to fit metaphor into a general theory of cognition; it has never rigorously explored the possible combinations, permutations, and transformations of metaphors, or the meta-structures and idea spaces they define or in which they operate or reside; it has never canvassed the many reasons why the use--or study--of metaphors is or might be important; it has never explored the limits--or the full possibilities--of metaphorical thinking; it has never undertaken any systematic criticism of the contemporary and historical use and study of metaphor; it has left unplanned the future scientific investigation of metaphor; it has made no effort to perfect the teaching--or the literature upon--metaphor; it has avoided quantifying metaphors; it has not tried to decompose metaphors into their parts, elements, and dimensions; it has seldom conducted scientific experiments upon the nature of metaphor; etc.

Various questions need to be asked and answered about metaphor, including: How complex--and simple--have metaphors been (e.g. in the works of Shakespeare)? Do metaphors often do as much damage as they do good (e.g. because of their tendency to inflame the ambiguity of a situation, or to seem to relate things that in fact are disparate or unrelated)? To what covert degree is supposedly nonmetaphorical language itself metaphorical or equivalent to metaphor? To what relative extent do metaphors say genuinely new things, or merely recall the mind's attention to old meanings or to things that it already knows? How do metaphors contribute to the appreciation of other metaphors? Is metaphorical reasoning special or is it really just another form of reasoning or an old and ordinary form of reasoning disguised? Might metaphorical reasoning be inherently incapable of being made systematic? Is the power of metaphor more aesthetic than rational? What have been the most important and productive metaphors historically, and what specific benefits resulted from them? What metaphorical alternatives are there for given metaphors? What metaphors are underdeveloped and how might they be perfected? What are all of the types of risks and costs of metaphors? How have given metaphors changed and evolved over time? What types and senses of metaphor should be distinguished by being given new names (and what should those names be)? What metaphors, speculatively, should be invented for particular things? What are the totality of metaphors that would be applicable to the treatment of a particular, random thing?

Some of the things for which "ocean" is a metaphor, or for which it could serve as a metaphor, include: peace, Heaven, mother, woman, God, adventure, the irrational, wisdom, flux, destiny, human knowledge or wisdom, the hypothetical Collective Unconscious of mankind, the bios, civilization, eternity, our planet, the unconscious mind, life, illusion, entropy, the Eros, the atmosphere, the cosmos, the Dirac quantum vacuum, the blood system, intercellular space, the creative imagination, infinity, the electron bath in which molecular matter is immersed, the cytoplasm, the prairie, the semifluid contents of the stomach, dreaming, etc. (Some of these things could in turn serve as metaphors of the sea, although the general relationship is not strictly symmetric, by any means.)

Things that, more or less speculatively, may one day turn out to have been metaphors include: fundamental particle, time, causality, IQ, soul, God, universe, truth, objective reality, number, mathematical equality, the Big Bang, speed of light, life (biological), love, infinity, nothingness, randomness, physical law, and mathematical point.

And that, again, means that it may be demonstrated that they are or were: invalid, misleading, trivial, half-truths, oversimplifications, relative, inelegant, superficial or metaphenomenal, meaningless, opposites of the truth, symbolic of something else, purely definitional, or the like.

Among other things, ideonomy can be used to: Show how everything is a metaphor for everything else; Clarify the psychological and cognitive forces that have given rise to, or that condition, particular metaphors; Exhaustively compare one metaphor with another; Predict the relationships among different metaphors; Illustrate the ways in which the meaning of metaphors varies with context; Make precise the boundaries between different metaphors; Etc.

Develop Methodologies

Methodologies are groups, systems, or combinations of methods, of a like or unlike nature. Or more generally, methodology refers to a body of methods, procedures, working concepts, rules, and postulates employed by a science, art, or discipline; or to the processes, techniques, or approaches employed in the solution of a problem or in doing something.

Up until now the development of a methodology has been more of an art than a science, and has usually occurred via the historical and often hodgepodge accretion of different methods or through borrowing from other fields or circumstances. The novel promise of ideonomy is to rationalize, systematize, and perfect the creation of methodologies in every area. The process should be made more direct, painless, and insightful, and methodological standards will presumably be elevated universally.

And of course ideonomy itself is a universal methodology.

Since the development of methodologies would essentially mean synthesizing in various ways the many different things that are being discussed here generally, comments on this topic are almost unnecessary.

Of course methodologies can have many purposes and values: They can permit recourse to alternative methods when one method has become dull through overuse; They can enable one to examine in advance a menu of optional methods and to select the best method or set of methods for a given case or one's own needs, ends, means, style, or expertise; They can help one to plan and manage the use of methods; They can facilitate appropriate adjustments, adaptations, specializations, and generalizations of methods in diverse situations; They can enable great numbers of methods to be made use of simultaneously and harmoniously in complex programs of research and endeavor; They can facilitate the teaching and learning of the many methods pertinent to a given area; They can enable a more universal, standardized, and objective comparison and evaluation of different methods, procedures, tactics, concepts, etc-and of what results from their use; They can facilitate the long-term evolution of a subject or undertaking; They can increase flexibility and preparation for contingencies; They can heighten the style and intelligence of an endeavor; Etc.

Random examples of situations in which methodologies normally exist or would be apposite include: Chemical engineering laboratories, Diplomatic corps, Defensive planning for possible world wars, Management of an economy by the national government, Coaching of a football team, Psychological counseling services, Institutes (or think tanks) researching public policy, Governmental agencies protecting the environment, Etc.

Ideonomy can discover and dramatize how equivalent and contrasting methodologies have worked in different fields or in the treatment of disparate problems. It can analyze the virtues and vices of different methodologies, and their powers for achieving different things in different ways. it can depict the costs and requirements for developing and using various methodologies. It can describe efficient and inefficient ways of using and managing them. It can show how to perfect their ideonomic character. It can render covert methodologies explicit, or help to formalize and codify them.


Help Model Things

Healthy science seems to combine several key and complementary activities: philosophizing, theorizing, modeling, experimenting, practical application, and criticizing.

Models enable one to: Rediscover reality; Test predictions, corollaries, and assumptions; Simplify and rectify one's calculations; Uncover limits and boundaries; Gradually adapt theory to reality; Extend theory; Explore complex and nonlinear relationships; Demonstrate one's ideas to others; Justify further pursuit and funding of one's work; Visualize better what one means; Interconnect what one is doing with what is already known elsewhere; Notice omissions and defects-or increase the organic wholeness-of theory; Think in a more practical way; Compare different theories, hypotheses, and assumptions; Establish proportional relationships; Economize (by freeing one from the cost and trouble of real-world experiments or full-scale constructions); Directly and fully manipulate the phenomenon that interests one; Examine a more extreme or complete version of a thing, phenomenon, or process than exists or is accessible to one-or subject something to extremes, conditions, or events unknown, rare, or poorly observable in nature; Experiment upon a thing without destroying the original; Re-create what no longer exists; Explore what is nonexistent, impractical, or impossible; Examine directly alternatives to a thing; Observe a thing in isolation from other things; Repeat an experiment endlessly and exactly; Explore dynamics, processes, and mechanisms; Examine the very origin and history-or the ultimate fate-of a thing; View a thing partially-or with certain of its features abstracted or others 'frozen' or disconnected; Examine a thing outside of time and unhurriedly; Expedite an experiment-or accelerate a phenomenon; Experiment upon the same phenomenon or event in endlessly many ways; Investigate a thing in a perfect, archetypal, or ideal form; Experience a prototype of a thing that one is planning to construct; Etc.

Models may variously be: mathematical, statistical, verbal, imaginary, graphical, analogue (say in which a selected process is used to represent some other process), scaled, logical, etc.

Among the things that have been modeled are: the universe (its start, present, and future), epidemics, pathogenesis, human thought, the psyche, social interaction, business cycles, nuclear war and its climatic aftermath, chemical reactions, biochemical cycles, ecological relations and interactions, events in the life of stars, galactic encounters, hurricanes, elementary particle interactions, nuclear reactor malfunctions, baseball games, earthquake genesis, computer architectures and programs, bridges, the spread and decay of civilizations, mathematical equations themselves, brain processes, fires, tree morphogenesis, and manufacturing processes.

There are infinities of parameters by which to alternatively represent simulated phenomena, and infinities of ways in which to represent those parameters and their values. In addition, there are infinities of alternative phenomena that one might wish to represent, and infinities of aspects thereof. Presumably the possible purposes, values, and human aspects of representations likewise encompass infinities.

The power of computers to model phenomena is increasing exponentially. As models are created they are stored for future use. Models lead to other models that are more sophisticated and complex. Models combine to generate compound and different models. Models of models and modeling itself evolve. Audiovisual technology relevant to modeling improves. Software, mathematical techniques, the form of scientific theory in general, logic, artificial intelligence, cognitive science, aesthetics, data storage and retrieval techniques - all of these things evolve in their ability to help man model and simulate things.

Although human knowledge is already mountainous, it continues to grow and differentiate explosively. It is this knowledge that can be used in the models we make. We need these models to reduce this knowledge to simpler, more essential, more powerful, and more useful forms. Yet the use of the models will itself give rise, both directly and indirectly, to more knowledge.

The infinite kaleidoscope of modeling possibilities presents an extraordinary challenge: to turn the present chaotic practice of modeling into an organized, fundamental, and universal science, under the tutelage
or within the framework of ideonomy.

Among the things that need to be discovered are: What are all of the canonical ways of representing things? What are all of the ways of mapping things--both quantitatively and qualitatively--onto, into, and via all things? What are all of the relevant needs, idiosyncrasies, and possibilities of human neurology and psychology? What are all ways of presenting data to the brain in sensory space and time, or via sensorimotor interaction and evolution? How much can be communicated, known, and done at once? What is the maximal possible multiplexing of symbols, sensa, languages, percepts, thoughts, memories, and human purposes? Is the human mind capable of infinite, or only of finite and modest, abstraction? What meta-structures (hierarchies, series, networks, vergences, cycles, rings, trees, etc.) can serve models, and what are the optimal ways in which they can serve modeling? In what infinities of ways can models--and the things they model, within those models--be combined, permuted, and transformed? What are the most powerful--and optimal--models of things we can create? The most realistic, elegant, energetic, complex, fundamental, informative, ingenious, clear or comprehensible, multilevel, encompassing, multidisciplinary, beautiful, exciting, etc? What is the capacity of the individual human mind and of mankind as a whole to be educated and trained to understand, appreciate, use, and create ever more diverse, specialized, generalized, abstract, and 'intelligent' models of things, ideas, and processes? What are all of the possible and best--or simply specialized--ways of combining, permuting, and transforming all familiar and possible sensa and percepts; and what are all the laws, paradoxes, interactions, paths, structures, systems, traces, spaces, manifolds, taxa, "groups", "categories", mathematics, matrices, contingent possibilities, etc. thereof? What are all of the symbols, grammars, notational operators and forms, codes, ideographs, textures, shapes, color schemes, graphs, 'choreographies', etc that can be invented, discovered, and organized to serve models and modeling? What are the best and most important phenomena, laws, processes, things, concepts, relationships, experiences, events, etc. to model?

Some of the most important GENERIC aspects and elements of things to model are: morphogeneses, analogies, differences, opposites and antisyzygies, paths, flows, order taxons, stories, motions, patterns, complexities, scales and ranges, bads, goods, commonalities, contents, functions, changes, conflicts, ambiguities, opportunities, problems and solutions, disequilibria and equilibria, symmetries and asymmetries, probabilities, games, perspectives, illusions, chains of consequences, and interdependences (apart from those things that were mentioned earlier).

The development and use of models on the scale imagined here should lead to the improvement and diversification of human intelligence, perception, learning, creativity, and work; the probable degree in which it should do this, and the maximal degree in which it might do this, are, however, uncertain.

Lessen Mortmain Or the Stifling Effect of Habit, Tradition, and Orthodoxy

What already exists, what already is known, gets in the way of everything that would come after. This is a staggering problem. But because we identify with what we have, and can hardly see a thing that is not already familiar or a relatively trivial variation upon the old, we have almost no ability to recognize the problem or the harm that is done. The status quo looks just fine.

A prime cause of the problem lies in the hierarchical nature of our knowledge: the questionability of what we know is relative, and varies over an astronomical scale. Relative to certain things, some things are - or appear to be - virtually certain. But what if the simplest and seemingly most absolute and unquestionable things actually themselves have problems, albeit perhaps ones of - or regarded as of - a vastly less urgent or tractable nature? The result is apt to be that over the long term the subtler puzzles and imperfections are completely forgotten and the humility that ought to be associated with an awareness of them is lost. And that is exactly what has happened! We have lost sight of the fundamentally infinite and irreducible complexity of reality, or of the ground of reality above which all that we 'think and know and perceive' shimmers like some cosmic mirage.

How, then, to disengage ourselves from our grand (or petty) illusions and our microscopic appreciation of the Creation? How to dig deeper into the real nature of things and the limitless possibilities that knowledge obscures and achievement, ironically, asphyxiates?

One way would be to develop means that would re-enable, or perhaps permit for the first time, the free play of ideas and the progressive self- liberation of the human mind and spirit.

Ideonomy promises to provide such means. By getting at the (relatively) fundamental combinatorial elements that can generate or approximate the possibilities of existence in their systematic totality, ideonomy can give us a range of experiences that manifestly transcend the accidental and irrelevant restrictions of present-day life and of civilization's current intellectual norms, and that takes us far closer to the processual or dynamic essence of being.

Old habits of mind that deny the possibility of there being anything other or more than what we see, are taught, and believe can be dissolved away by exposure to the full participatory complexity of existence, to the mechanisms that everywhere give rise to the illusions of simplicity and uniqueness, to the paths untrodden that lead everywhere (save to where we have already been), to the interdependences both of ideas and of facts that are the sources of our complacency, to the ideonomic meta-structures against which any given vision of the world is as nothing, to the linguistic codifications of nature that at once give civilization its power and its stupidity, etc.

Ideonomy can help to combat habit, tradition, and orthodoxy in many ordinary ways.

Multivariate analysis, multidimensional scaling, and other statistical techniques can be incorporated into computer programs that will reveal, and both quantitatively and qualitatively describe, the many different and important idiosyncrasies of one's mind and mental habits, and of the ways in which one uses--by contrast to how other people use--concepts and words to say and perceive things and to create ideas. By making one aware of the fact and particulars of one's mental structure and processes--in both an absolute and comparative sense--these programs and methods will give people the ability to criticize, reshape, and transcend their rational and irrational habits.

Ideonomy can document the historical origins, course, and fate of transient intellectual traditions. The mesmeric effect, poverty, and cost of these traditions can be dramatized. A synopsis of these things can be included in the academic curriculum, but the larger results of such research can be made available to curious individuals working in different fields so that those individuals can clarify the nature of their own investigations within the framework of their own knowledge and ideas.

Ideonomy can comprehensively survey contemporary and historical theories, doctrines, hypotheses, investigations, and attitudes of a heterodox nature, and place these beside what orthodoxy has espoused. The true variation of beliefs, and range of thought, can be made better known in this way, and tolerance, freethinking, and imagination encouraged. The length, complexity, profundity, bitterness, and human comedy of these disputes will be instructive, and will surprise many persons who would have thought the resolution of the nature of things to be a simpler and more inevitable process than it was, or than it could ever be.

Even long-accepted doctrines often continue to have deep problems associated with them. They may have theoretical or methodological inconsistencies or contradictions, arbitrary and dubious features, unproven or disproven corollaries, limitations of scope, etc, that should be better known, or most closely attended to, than they are. Often such blemishes are never made explicit, or are hidden away in the secret lore of a discipline rather than being made known at once to those who are first learning the field at the time when they are forming what will be their most basic and enduring images of it.


Identify Needs

Examples of questions about specific needs that ideonomy could help to ask and answer are: What does an ordinary violin need to equal the instrumental excellence of a Stradivarius? What nonessential dietary needs does man have that have not yet been noted? What generic needs does a molecule have, for it to taste like a pineapple (that is, properties that encompass all actual alternative bases for pineapple flavor in their descriptive or causal universality)? What are all of the needs and criteria that an artificial (prosthetic) blood must meet to be successful (as a perfect substitute)? What conditions are needed to maximize the probability that life will begin on a lifeless planet? What initial properties must a 'universe' have to develop along the lines of our own? What needs of civilization have not yet been met - or realized to exist? What events are necessary for an elementary particle to decay in a certain direction? What is necessary for a symphony to be great, in the historical sense? What conditions must be fulfilled before magma deep within the earth will progress to the surface and erupt as a volcano?

Universal genera of things that may be needed include: knowledge, acts, proof, examples, models, theories, exceptions, generalizations, predictions, justifications, goals, precedents, instruments, efforts, etc; physical materials, energy, opportunity, conditions, circumstances, catalysts, sequences of events, thresholds, perturbations, constancies, connections, interactions or cooperations, controls, contingencies, limits, conflicts, beginnings, paths, differences, similarities, capacities, changes or transformations, combinations, groups of things, varieties, isolations, simplicities, adjustments, adaptations, competition, etc.

More specifically, there may be a need for something to: be present or absent, behave in a certain way, have a certain age, have had a certain history or be mature in some way, be guided over a certain course, be subject to a set of constraints, affect or interact with itself in some way, occur at a unique location or instant, be repaired or have its errors corrected, etc.

Possible generic effects of (absolute or unmet) needs include: drift, striving, stress, competition, malformation or misdirected development, underdevelopment or overdevelopment, aborted development, lack of strength or stability, cannibalism, self-consumption, retrogression, misbehavior or constricted behavior, underactivity or overactivity, impoverished appearance, inefficiency or waste, impaired evolution (as opposed to development), continuing growth, etc.

Different types or aspects of needs include: Ongoing, temporary, or periodic; Absolute, relative, or conditional; Synchronous or asynchronous (including sequential); Interdependent or independent; Progressive, regressive, or invariant; Quantitative or qualitative; Good, bad, or neutral; Generic or specific; Higher or lower; Partial or complete; Central or peripheral; 'Primary or secondary'; Intrinsic or extrinsic; Simple or complex; Etc.

Recurring questions in treating needs are: What will happen if a certain need is met? What will happen if a need is not met? What will happen if a need is only partially met? Is a need met, met fully, or met properly? How is a need met? Can a need be met in unconventional ways? What caused a need, or how did it originate or develop? Is the need growing or is it static? Is the need essential or can it be ignored? What other needs might the thing have? In what order should different needs be met? What tradeoffs are there between different needs? How can I discover what the needs of a thing are? How can I experiment upon the properties of various needs and upon their relationships to the thing that possesses them? How is one need similar to or different from another? How do the needs of a thing intergrade with other aspects of the thing, of a decreasingly or increasingly related or analogous nature? Might I be mistaking certain needs for certain other needs? Are there sub-needs or super-needs that are related to given needs? What systems of needs might there be? Apart from how it can be met, how can a need be controlled or altered? What do I not know, or do I need to know, about a need, and how can I find it out? What are the structure, elements, and laws of a need? What concepts underlie a need and how should the need be defined? Is a need real or merely apparent? How do the needs of one thing resemble or differ from the needs of other kinds of things? What are all of the consequences, corollaries, and implications of a need? What is the full extent of what is known about a particular need?

The importance of ideonomic research into needs includes: Future recognition of needs may as a result be made more immediate, automatic, efficient, and comprehensive; Knowledge of given needs, or of other matters related to needs, can be used to predict the existence and nature of undiscovered needs-even in very different domains; Future needs can be anticipated and met in advance; Ways can be discovered or developed for meeting a multitude of needs at once, with the same means or measures and hence more economically; The world's scope, wealth, and scale can be augmented by retiring and answering needs en masse; Unsuspected needs must be the source of many unexplained problems; The essence or real importance or promise of many things may not be realizable or recognizable until many or all obstructive and inhibitory needs are met; Needs of things, generally, are apt to be far more diverse, complex, and subtle than has hitherto been assumed; Many needs may be answerable in surprisingly simple ways; Many needs can probably be obviated; Knowledge of needs is required if many other divisions of ideonomy, or ideonomy as a whole, are to function effectively or fully; Etc.

What progress was made historically in answering genera and species of needs? How were the needs discovered, explored, and met? What benefits accrued? Were the needs met only partially? What needs are growing larger, more urgent, or more dangerous at the present time? What needs reinforce other needs? What myths, fictions, fallacies, and illusions exist regarding needs? What mathematical relationships and patterns are characteristic of needs in general? What are the most extreme or anomalous types of needs? What theories might be developed to explain certain classes or sets of needs?


Depict Networks

The networks that things, events, and ideas are, contain, are contained in, are controlled by, or may otherwise involve or interact with, represent a vast, fascinating, and yet poorly studied subject and a major interest of ideonomy. The network is one of the most fundamental and universal genera of structure - or meta-structures - found in nature. Networks must be explicitly or implicitly present in any description of reality.

Networks might loosely be defined as self-connected and anastomosed multiply-branched patterns or systems. Yet the definition is neither comprehensive nor exclusive in any absolute way - if only because the universe is too complex, subtle, and paradoxical to dignify any humanly conceived or conceivable absolute, or to conform to the artificial simplicities and umbrageous metaphors of human language.

Illustrative known networks include: Gel microstructure; Electrical circuits and electronic microchips; Road networks; Body's circulatory system; Networks of human associations; Telephonic networks; Intracellular cytoskeleton; Microstructure of the Dirac quantum-mechanical vacuum; Networks of ecological interactions and relationships; Computational networks in massively parallel computers or in neural nets; Neuropile of the cerebral cortex; Crystal lattices; Networks of economic transactions and industrial flows; Clay microstructure; Crosshatched earthquake fault systems; Cave labyrinths; Mazes; Joint systems; Haptic and visual textures; Networks of strings of hyperclusters of galaxies, or the like; Braided river channels, say on a deltaic plain or in an estuary; Interconnected and interwoven biochemical pathways; Textile fabrics; Tessellations (tile patterns); Arrays of convection cells; Honeycomb; Protein molecule (anastomosed via bonds, fields, or systems of motions); Porous microstructure of topsoils or aquifers; Cellular networks represented by tissues; Interference patterns; Foam; Certain mathematical groups and matrices; Semantic networks in artificial intelligence; Explicit or implicit networks of cross references in a dictionary or encyclopedia; Mental structure and interactions; Polygonal crack systems of patterned ground; Obscure dynamical networks represented by (or at least known to be present in) turbulence; Etc.

Possible effects, values, or uses of networks include: They can model or explicitly define and show the complex interrelations and interactions of multitudinous things, concepts, processes, and domains; They can provide an instant overview of the whole of something; They can facilitate the dispersed or central coordination, control, and government of an entire subject or thing; They can serve the flow and interflow throughout a thing of energy, information, matter, resources, effects, products, events, agents, adjustments, ideas, innovations, etc; They enable the simultaneous, synchronous, and synergistic combination of a maximal number of different-- related or unrelated--things; They maximize the possible or coactive redundant or irredundant--and homogeneous or heterogeneous--paths that things are able to take between or among things; They can maximize the descriptive or existential dimensionality of the relationships between or among things; They can assist the teaching, planning, construction, or further evolution of a thing; They can facilitate the quick, efficient, and repeated growth and contraction of a system or of a thing qua system; They can facilitate the interactions or define the interrelations of a thing with itself; They permit the multiplexing of flows and interflows--or the minimization of their mutual interference and confusion, and the maximization of their separation and concentration; They enable the simultaneous comparison of a maximal number of things; They enable a single thing to control or communicate with many or all things, or many or all things to control or communicate with a single thing; They can facilitate the maximally fast transformation or reorientation of a thing; They can minimize the path between arbitrary pairs or sets of things; They can simultaneously define all of the possibilities of things inter se; They can help with the treatment of maximally complex things; etc.

General or possible elements, properties, or dimensions of networks include: Nodes, centers, intersections, points, vertices, joints, poles, knots, singularities, etc; Links, edges, lines, paths, intervals, branches, etc; Reflections, refractions, diffractions, etc; Convergences, divergences, decussations, vergences, radiations, trees, etc; Domains, neighborhoods, faces, holes, etc; Loops and cycles; Transmissions, traffic, flows, signals, noise, messages, etc; Combinations, permutations, transformations, inversions, rotations, oscillations, translations, etc; Maxima, minima, and optima; Linearities, nonlinearities, functions, operands, operators, dimensions, manifolds, symmetries and asymmetries, transitivities and intransitivities, sources and sinks, sequences and trajectories, subgraphs, gates, occupants, games, weightings, probabilities, obstacles, partitions, rules, etc.

Possible genera of network relationships and/or of things connected in and as a network include: choices, decisions, possibilities, alternatives, probabilities, facts, evidence, ideas, dependences, independences, interdependences, relevances, importances, applications, origins, destinations, flows, motions, interests, corollaries, hypotheses, needs, causes, effects, consequences, products, adaptations, sequences, series, degrees of freedom, aspects, structures, examples, taxons, definitions, analogies, equivalences, measures, times, places, components, antagonism, synergism, events, topics, systems, phenomena, differences, conditions, qualifications, changes and transformations, tactics, questions, answers, generalizations, specializations, means, numbers, mathematical relations, problems, niches, assumptions, bads, goods, combinations, complexities, simplicities, conservations, nonconservations or losses, correlations, extensions, discoveries, individuals, groups, laws, levels, mechanisms, opportunities, functions, etc.

Questions about networks that ideonomy can help to ask or answer include: What is a network--as opposed to those classes of things that resemble or differ from networks? Has does or could a network start, develop, evolve, regress, or vanish? How do networks facilitate their own development? How do networks govern or interact with themselves? What are the most complex--and the simplest--actual or possible networks? What networks coexist? How do different networks ignore, interact with, cooperate with, interfere with, govern, compete with or oppose, alter, and give rise to one another? What is the incidence--and the full range and diversity--of networks of every possible and actual type? Are there both finite and infinite networks? How many different networks do particular or random things--phenomena, realms, processes, concepts, etc.--involve? Are networks absolute or relative; or what perspectives may they depend on or belong to? How multiplexed are networks, internally and mutually? What are all of the signs of the existence, nature, effect, or importance of a network? How could or should networks be studied or otherwise treated? What undiscovered uses might networks have? What networks do not yet exist but ought to be created? What are the most important networks to study, in connection with different fields, phenomena, and problems? What methods, means, and materials could facilitate the universal study of networks? What are the most difficult problems, questions, or aspects of or connected with networks? How do those things that traverse networks actually traverse them; what routes do they take, what governs their travels, and what experiences do they have along the way-or changes do they undergo? What is the relative extent-and the integral anatomy-of our knowledge and ignorance of networks and network phenomena? What research has and has not hitherto been-explicitly or implicitlyconducted upon networks? How should all networks be classed in terms of all other networks? What are all known or as yet undiscovered concepts that are relevant to the consideration, investigation, or use of networks? What universal laws of networks need to be, and can be, developed; and how might such laws function or be used?

Illustrative unknown or speculative networks include: The infinite--and perhaps infinitely strange--network of interrelationships and interdependences that must exist within the total structure of mathematics; Hereditary and evolutionary networks belonging to lateral gene flows across the bios; Networks of relationships and interactions--within or even beyond our universe--of various exotic physical entities that have been hypothesized (incl. tachyons, negative mass, advanced potentials, dark matter, cosmic strings, etc); Whatever networks might arise from or be associated with Carl Jung's concept of synchronicity ("an acausal connecting principle" hypothesized to lie behind the most extraordinary coincidences of life and the cosmos); Panhuman and all-historical networks of linguistic, folkloric, musical, or other cultural interaction, diffusion, or coevolution; Various heterodox flows of information or control that could be theorized to occur within the human body or among its distant and manifold parts (e.g. flows of extreme velocity, flux, power, efficiency, or complexity); Etc.

What are all of the relationships of networks to other meta-structures and of those other meta-structures to networks? For example, what networks of hierarchies--and hierarchies of networks--exist or are possible; and what properties, dimensions, paradoxes, forms of behavior, powers, and opportunities pertain to them? Similar questions deserve to be asked about: Networks of trees and trees of networks; Series of networks and networks of series; Etc.

The potential size and intricacy of some networks may be suggested by the example of the human mind. The mental structure of the brain could conceivably represent a network whose full description would require roughly the number of bits of information that would be contained in 10 exp. 14 sets of the Encyclopaedia Britannica.


Suggest Higher Niveaus

Ideonomy can suggest one or more--or infinitely many--higher levels or plateaus of existence, achievement, or transformation--past, present, or future--in an evolutionary progression.

More generally, in connection with such niveaus it can suggest or assist with the treatment of: minima, maxima, and optima; conditions, circumstances, properties, laws, cycles, contingencies, perturbations, thresholds, transitions, transformations, emergents, relaxations, continuities, discontinuities, causes, forces, effects, origins and ends, resources, opportunities, losses and gains, states, configurations, stochastic and deterministic processes, illusions, paradoxes; flows, courses, and paths; convergences, divergences, and vergences; games, processes, and events; ranges, hierarchies, generalizations, elements, relations, analogies, differences, types and taxons, sets, defects, perfections, unknowns, needs, fundamentals, interferences and cooperations, predictions, theories, transvaluations, principles, strategies, goals, interests, appearances, questions and answers, economics, inversions, interdependences, opposites, manifolds, reciprocities, symmetries and asymmetries, etc.

By chance or necessity, the past evolution of life on Earth has arguably passed through a series of niveaus, which makes it likely that it will exhibit a future sequence of niveaus as well. Ideonomy could help biologists to define or speculate upon the latter possibilities, and this could benefit their science in many ways. For example, simulations of future biological niveaus could clarify historical niveaus.

Those who exist at a given niveau often suffer from illusions of its specialness, finality, or even eternality. Momentarily a multitude of things may all converge to a single state or in a common direction, making subsequent divergence seem highly improbable. Diverse phenomena often have a tendency to relax, stall, or reverse synchronously--owing to such things as the rich and queer interconnectedness of the world's phenomena, exponential multiplications and propagations of effects, superabundance of natural symmetries and asymmetries, competitive forces in the cosmic background, etc.--which again can give rise to an illusion of an irreversible law. Thus we in the present may be blinded by the present to possibilities for social change and evolution in quite other directions than those with which alone we are familiar.

The overwhelming tendency of biological evolution could be toward specialization confined to a plateau or within certain limits; the course of life on Earth since its (relatively) indeterminate beginning may therefore mask vastly greater--and altogether strange--evolutionary possibilities. Life created in the laboratory, and perhaps patterned on no life known to us now, might give access to transcendent biological niveaus.

It may be possible to advance physical phenomena to higher niveaus by drastically increasing either the disconnection or the integration of the (so-called) elementary constituents of those phenomena--at extremely high or low pressures, temperatures, energies, etc.


It is possible that man's spectacular transanimalian intelligence represents nothing more than the modest ascent from one mental plateau to another that resulted from a few intrinsically minor changes in the brain, and that vastly higher intellectual niveaus are attainable through additional minor but appropriate neural alterations.

Ideonomy could lead to the discernment of possible higher niveaus of such diverse things as: Genomes (which might be given far more powerful, efficient, and adaptive self-regulatory systems); Foods (whose taste components - not designed by nature with the human palate in mind - could suddenly be adapted en masse, so as to perfect mankind's gustatory existence); Diseases (such as might one day result from revolutionary pathogens--caused by naturally or artificially punctuated evolutionary equilibria or by biological engineering); Languages (which through sets of scientifically guided rule changes might be capable of a much higher level of functioning--or of much greater precision, scope, suggestiveness, etc); Earth's interior (which might be capable of evolving into 'higher' geophysical regimes-or of becoming geophysically more active, more complex, "chaotic", radically different, or the like); Mathematics (which might one day admit of an enormous--pure or applied--simplification); Chemistry (which in the future might, for example, come to be based almost entirely upon the chemical reactions and states of minimally stable molecular species); Etc.

Treat Obscurity and Ambiguity

Things may be said to be "obscure" if their appearance, form, type, basis, nature, content, relations, nature, basis, essence, behavior, implications, boundary, worth, interest, existence, or the like are not readily, fully, or at all understood. "Ambiguity" can refer to duality, multiplicity, diffuseness, inconstancy, or indeterminacy of meaning, significance, reference, nature, state, course, potential, form, etc (whether real or supposed).

Distance in time or space, ignorance, obscurantism, interferences or perturbations of things, obstructions to or distortions of perception, inattention or disinterest, poor conceptualization, complexity, the inherent difficulty of things, inconsistencies, meagerness of acquaintance, unresolved issues, and indeed ambiguities: can all cause, or be the cause, of obscurity.

Things that can cause or contribute to ambiguity are: Incompleteness of development, formation, evolution, transformation, reaction, or adaptation; Chaotic state; Multistage existence; Polymorphism or pluripotentiality; General or universal character; Unfamiliarity of type, or defect in schemes of classification; Ambitendency; Mimicry or natural analogy to other things; Conflicting forces or circumstances; Divergent perspectives, representations, or uses; Inexact or undefined boundaries, or failure to exclude alternatives or to distinguish other things; Indecision; Design, or multiplicity of function; Obscurity; Etc. (also see the above definition of ambiguity).

Among the reasons why ideonomy can help with the treatment of obscurity and ambiguity are: Their types can be categorized, classified, described, and systematized-and they recur over and over again in characteristic ways; Their types and instances can be treated and resolved--and much more efficiently--en masse; They may depend upon or be a function of--or invite treatment by--other divisions of ideonomy; Ideonomy can be used to develop and perfect methods, principles, concepts, and procedures for the treatment of anything whatsoever; Ideonomy enables things to be conceived of and expressed in much more subtle, complex, and rigorous ways; The long-term effect of ideonomy should be to maximize the logical, combinatorial, and spatiotemporal integration of all forms, methods, and themes of research (both scientific and cultural); Obscurity and ambiguity are often superficial--much of the difficulty in treating them derives from the scarcity of starts in treating them or of clues as to how to begin, and is not intrinsic or proportionate to the real task, which may be elementary--and ideonomy can catalyze, as well as motivate, the solution to almost any problem; Etc.

Among the many things that are or can be ambiguous or obscure are: The sky's aspect or changes in the weather; The good and evil of public charity; Facial expressions of one's spouse; Newspaper headlines; Facts or statistical data; Musical chords and themes; The overall course of biological evolution; Cosmogonic 'initial conditions'; Life's meaning and purpose (actual or so-called); Beauty--as of a painting or person; State of the economy; One's feelings or inclinations; Success or tragedy; Proofs; Humor; Trade routes of vanished civilizations; Social trends or civilization's grand course; Course of a battle; Causes of a marine algal bloom; Outcome of experiment designed to test the Einstein-Rosen-Podolsky paradox (or for nonlocal effects of one distant quantum particle on another); Etc.

The costs and other effects of ambiguity and obscurity can be many: Understanding and teaching things may be made far more difficult; Generalizations may be or seem more hazardous or dubious; Corollaries and implications that would otherwise be automatic may be precluded; Research that is in a hurry--which is most research--is liable to rush off to other matters; Evaluating the value of research or endeavor, either in advance or retrospect, may be much harder; An otherwise masterful proof may be rendered worthless; Every step in an endeavor--even the most trivial--may be entangled in difficulties; Mysticism and charlatanry may thrive in the murk; Attempts to automate the treatment of a problem that require flawless computer programming at every point in a sequence or network may be futile; Intolerable need for safeguards, redundancy, and compensations may be created; Mischievous illusions of novelty, complexity, difficulty, profundity, etc may be engendered--or useful and desirable illusions of a similar kind, say whose value derives from their suggestiveness or their ability to stimulate or guide the mind; Defective communication and unilateral or bilateral ignorance of same; Unavoidable reduction of the simplicity, fundamentality, and universality of statements or information; Etc.