Motive ". . . don't we know that all of this is a prelude to the song itself . . . the song itself that dialectic sings . . ." Plato, Republic, 531c-532a Objective. On Earth, the human race -- the race to achieve humanity before accumulating contraventory consequences foreclose forever on the very possibility of that achievement -- is now a race against time. Upon the outcome depends the future of all life on Earth, and more. Most human beings alive today do not know this explicitly, but only implicitly, subconsciously. A chance still remains for humanity to awaken, to rally its forces, and to acquit itself in the trial to which it now summons itself. Humankind is the only immanent hope for the regeneration of Earth's biosphere, of its capacity for further existence. Realized humanity can avert the otherwise inevitable abortion of this planet, if it will. It can tame the self-destructive tendencies inherent in Earth's co-biosis, its "mutual way of living", its total bio-geo-physis. The process of "natural selection", at this locus, now converges to a 'meta-Darwinian' planetary selection test, a test of the fitness for further evolution of the planet entire, the total life-system of Earth, led by humankind. This is a test, not of technological fitness alone, but of the ethical fitness to survive of planetized humanity, whose concerted and omni-symbiotic action will be required to save itself and its world. Earth's blind-running fitness for biosocial evolution and beyond is temporary and self-terminating. Unless this planet evolves a moral/technological species able to act intentionally to extend that fitness, then this 'living planet' will fail of its test and die. See the other planets that share Earth's sun: corpses, corpses -- every one! Soon, either Earth must join them in death, or [re]turn them to life. James Gleick, in his 1987 Chaos: Making a New Science, called the attention of Terran humanity to the fundamental self-enfetterment now paralyzing its moral/technological progress, The Nonlinearity Barrier. He also described the enormous undertow of this biosphere's doom attractor, which humanity must overcome, or to which it and its biosphere must soon succumb. He describes the potential planetary destiny we of the Foundation know as The White Death: "Climatologists who use global computer models to simulate the long-term [and highly nonlinear -- F.E.D.] behavior of the earth's atmosphere and oceans have known for several years that their models allow at least one dramatically different equilibrium. During the entire geological past, this alternative climate has never existed, but it could be an equally valid solution to the system of equations governing [NB: "system of equations" is here 'reifically' and fetishistically posited as a pseudo-'subject'/pseudo-agent/pseudo-actor/pseudo-cause -- F.E.D.] the earth. It is what climatologists call the White Earth climate: an earth whose continents are covered by snow and whose oceans are covered by ice. A glaciated earth would reflect seventy percent of the incoming solar radiation and so would stay extremely cold... Computer models have such a strong tendency to fall into the White Earth equilibrium that climatologists find themselves wondering why it has never come about..."1. Whether or not it has happened before on Earth, could it be about to come about [again]? Climatologist H. Lamb noted, in 1982:"...The cooling of the general run of European summers since 1953...has had another consequence which marks out the change of climatic tendency since the middle of the century...on Baffin Island in northeast Canada, in the central part of which 70 percent of the highland region seems to have been covered by 'permanent' ice and snow between two hundred and four hundred years ago and where this had been reduced to 2 percent by 1960, the 'permanent' snow beds have been increasing again since and incipient new glaciers have been found."2 Geophysicist R. G. Johnson noted, in the July 8, 1997 edition of EOS, the Transactions of the American Geophysical Union: "When the last ice age began 120,000 years ago...the insolation at all latitudes was nearly the same as today...That today's climate may be close to the threshold for new glaciation may indeed be the case. Large plateau areas of Baffin Island are now covered with semi-permanent snow fields that expanded during the historic Little Ice Age 150-350 years ago when cool summers and extremely severe winters were frequent in northern Europe...Canadian glacial nucleation areas are now perilously close to the threshold for new ice sheet growth, as indicated by the historic expansion of snow fields on Baffin Island...Initiation of new ice sheet growth is of great concern because the strong positive feedback of enhanced albedo and heavier cloud cover... might lock in the ice age growth mode despite CO2 warming."3 Viscoplastic circumferential ["horizontal"] transmission of radial ["vertical"] shear stress, rising locally at the edges of increasing loads of far-Northern land ice -- on Baffin Island and elsewhere -- may also hold clues to the causation of the marked recent resurgence in seismic and volcanic activity at the lower-Northern and equatorial latitudes, as exemplified by the Mt. St. Helens eruption, et sequelae, possibly including sub-oceanic lava flows that may amplify "El Ni–o" phenomena. H. H. Lamb: "There have been some studies...which seem to indicate greatly enhanced volcanic output during various main stages of the last major ice age...it is possible that changes of stress on the Earth's crust, when enormous masses of water from the oceans were converted to ice on land, produced waves of volcanic activity...there may well have been a reaction -- a ["positive"-- F.E.D.] 'feedback effect' -- of the dust veils in the atmosphere leading to sharper cooling of the climate at the Earth's surface."4 The parade of prodigious Pleistocene glaciations, whose miles-deep Juggernauts Of Ice shaved bald vast stretches of Earth's biosphere, never truly ended. It merely paused, again, some 10,000++ years ago. It has paused repeatedly, every ~100,000 years, since the Pleistocene began, some 2 million years ago. That most recent pause opened the current interglacial. This interglacial has been humanity's window of opportunity for the development of ethical and technological civilization, for noospheric evolution, and for the partial regeneration of Earth's biosphere from the ravages of these reiterated Ages Of Ice. If Earth's humanity allows the current interglacial to end, that window will close -- this time, forever. Earth will become a Planet Of Ice, the final cadaver in a solar system of planetary cadavers. Earth has entered the closing period of its current interglacial, an interglacial already highly extended -- and extenuated -- relative to all of the previous Pleistocene pauses, due to some so far unintentional but ecologically beneficial consequences of human socio-technological evolution. Hypothesis A. The "Law" Of The Tendency Of Ecological Primary Productivity To Decline? The burgeoning oceanic and continental physis of Earth's ascendant photosynthetic biosphere removed vast masses of carbon dioxide from its once predominantly "carbonic" atmosphere. Much of this carbonic matter accumulated under water, in vast fresh water tropical swamps and bogs as well as in marine sediments, and later deep in Earth's continental crusts and ocean-bottom strata in the forms of anaerobically decaying animal, plant, and protiste corpses. Those corpses transformed into the peat and coal, and, to some extent, also into the petroleum, natural gas, etc., that later became the fossil fuels of human industry. Climatic cooling ensued, due to this massive CO2 depletion, as well as to the self-depletion of spontaneously radioactively self-decaying elements within Earth's lithosphere, and to other self-induced, blind-running, and cumulative secular processes. Earth's self-cooling at length self-bifurcated its climate. Earth became vulnerable, in a new way, to aperiodic, and tendentially 'self-perpetualizing', global glaciations. Such glaciations were triggered, in part, by the low-points of insolation of the various [Milankovitch] irregularities in Earth's orbital path with respect to its sun. These low points had hitherto oscillated Earth's CO2-saturated atmosphere between the temperature regimes "warm" and "slightly less warm". But biospheric CO2 depletion at length allowed the threshold of self-accelerating land ice accumulation to be crossed. Gigantic glacial Jaws Of White, poised repeatedly, from the start of the Pleistocene onward, on the verge of closing irrevocably over the waning equatorial enclave of Earth's once-global rainforest. This Maw of massive biomass massacre was the self-reflexive action, the self-caused mirror reflux, of that great mantle of Green, the self-expanding photosynthetic biosphere, which earlier engulfed the planet's oceanic and continental surfaces. Some might entitle this hypothesis "The "Law" Of The Tendency Of The Rate Of Photosynthesis To Fall" as a consequence of the tendency of that rate to accelerate to high levels early on, leading to massive anaerobic, anoxic decay of dead biomass, and to progressive, cumulative depletion of atmospheric CO2 as a consequence, a 'self-braking' and 'self-breaking' of the global acceleration of 'phyto-synthesis', and thus of most global formation and accumulation of biomass, metaphytic and metazoic alike. This Terran biosphere is thus a self-bifurcating meta-system, a self-developing sequence, or 'macro-ecological succession', of qualitatively distinct biospheres, of qualitatively distinct dynamical systems. This meta-system is a 'meta-continuity', bridging the "singular", catastrophic, qualitative abysses of discontinuity that separate each biospheric predecessor system from its successor system. E.g., the "Chemosynthetic" / prokaryotic archaea / bacterial-Biosphere branched off to the eukaryotic, 'Phytosynthetic'/Photosynthetic Biosphere. Each successor biosphere connects to the next by a 'meta-continuous' discontinuity, a 'meta-finite' "singularity", a 'self-bifurcation' bridge, a "meta-system transition" [cf. Turchin]. The self-activity of the present macro-ecosystem, the Photosynthetic biosphere itself, and not of any external controller, shifted the value of its own atmospheric CO2 concentration control parameter across a critical, bifurcation threshold. This parametric 'self-shift' induced a "phase transition" not only in the state trajectory of that system, but in its state-space/control-space, or 'meta-space', itself, in the dimensionality and dimensional content of that space, describing a qualitative, 'ontological' change in dynamics or "laws" of motion. This "change of laws" was caused, mediately, by that system itself. This self-causation was mediated through or transmitted via the biosphere's climatic environment. The resulting "phase transition" in climate moved the biosphere from its former 'global rainforest' regime to one of 'equatorial jungle/desert/temperate deciduous forest/tundra/standing glacier', with the signature oscillating long Ice Ages followed by short interglacials characteristic of Pleistocene/Recent times. This previous 'self-induced transition' has itself lately begun to 'self-transition', to 'self-bifurcate', once again. Global emergence of human agricultural, then industrial, practices -- including the partial conversion of forests into cultivated fields, and the combustion of peat, coal, and later other fossil fuels -- partially replenished atmospheric CO2, diverting the would-be next 'Big Ice Age' into the short-lived "Little Ice Age", postponing the close of this interglacial, and the return of global glaciation, until now. By burning fossil fuels, Terran humanity has, in part, merely restored to Earth's atmosphere some of the CO2 that was depleted from it by pre-human nature, by some of the consequences of accelerated natural photosynthesis during preceding geological eras. But such unconscious consequences of human action no longer suffice to avert what the Milankovitch Effect and accumulated consequences of pre-human ecological evolution all impend: resumption of Ice Age eco-suicide. The greatest ecological hazard to Earth's biosphere flows not from humanity, but from the internal dynamics of this planet's and its solar system's pre-human and extra-human 'endolithic', lithospheric /hydrospheric/- atmospheric / biospheric system itself, as well as from the exolithic residuum, the leftovers of planetary-system formation itself. Climatogenic actions of Terran humanity have - inadvertently - ameliorated the 'endolithic', climatic threat so far, by returning to the atmosphere a small part of the CO2 that was depleted in the action of the pre-human photosynthetic biosphere upon itself, with the massive self-devastating and self-denuding self-consequences for that biosphere that we have noted above. The CO2 that human industry has added [back] to the atmosphere is, for this biosphere, not a "pollutant" as some are wont to say. It is a vital nutrient required to sustain green plants, this biosphere's photosynthetic primary producers, upon whose productivity virtually all Terran biological life depends. It is a basic atmospheric and oceanic biospheric resource that has been depleted, and in dire scarcity relative to the concentrations needed to fulfill the potential productivity of those primary producers. And this dire scarcity is a consequence of the activity of the biosphere itself, lodged long before the emergence of humankind. Relative to the context of today's Terran biosphere, carbon dioxide is a primary resource in short supply. As a consequence, the primary productivity of this balding biosphere has been in severe depression ever since the beginning of the Pleistocene at least -- due to this shortage of CO2. Increase in ambient atmospheric carbon dioxide levels is a key to this biosphere's regeneration. Not just a few species, but all species, are endangered due to this CO2 shortage. Not just a little bit of bio-diversity, here or there, but all Terran bio-diversity -- any surface bio-diversity whatever -- is at risk. All this is at risk due to the shortage of CO2, as well as to all of the other trends of depletion and accumulation, metered and controlled by the control parameters of this biosphere's next 'self-bifurcation', which result from the many extra-human, nature-induced, not humanity-induced, trends that converge to a final Age Of Ice, and to a biocidal, sterilized planetary surface -- unless Terran humanity mobilizes and intervenes technologically. Hypothesis B. The Greater versus the Lessor Threat. Temporary climatic "over-warming" could possibly become a short-term issue. Catastrophic Ice Age cooling is by far the deadlier long-term threat. While it might take eons before mile-deep ice could again engulf the Northern Hemisphere, temperate zone agriculture would be brought to its knees by less than a decade of successive winters like those of the Little Ice Age, or like those of much more recent record-setting cold seasons -- viz. 2000-2001, 1993-4, 1990-1, 1989-90, 1988-9, 1987-88, 1984-5, 1983-4, 1981-2, 1977-8, and 1976-77 - with global famine resulting. Do not be decoyed! Drought and desertification, dry-heat "heat waves" over dry land, are not the sign of "Global Warming", but of its opposite! The signal of net over-warming is the opposite of drought - moistness; return of rainforest-like raininess; pervasive re-moisturization, incipient re-tropicalization in the Northern temperate zone; a succession of wet, rainy, humid, iceless summers and winters. Despite local exceptions due to the nonlinear complexity of Earth's climato-dynamic system, rising wetness, not drought, is the global companion of general warming. Drought and desertification are, au contraire, perennially, the preludes to Ice; symptoms of the secular cooling trend of ocean surface waters, which, because rate of water evaporation rises with water surface temperature, entails reduced evaporation; hence reduced precipitation; translating into drying; hence "heat waves" over land. Self-denudation, 'the balding of the biosphere', is almost as much a feature of the prelude and 'foremath' of each Ice Age, due to drought and desertification wrought by general oceanic surface cooling and consequent reduced H2O evaporation, as it is of the main course and aftermath of each Ice Age, due to the Razor of Ice. Hypothesis C. _The Principle of The Planetary Selection Test. __If the emergent sentient and self-sentient species of a planetary biosphere is either (1) eliminated, by external and/or internal action, or (2) deranged, acting in a self destructive manner either directly upon itself, or indirectly, through destructive commissions and omissions with respect to the rest of the planetary eco-system, or both, then the entire planetary-surface biosphere perishes, due to that eco-system's own internal, blind-running, cumulative self-abortive tendencies, due to the commissions and omissions of its human[oid] species, or due to both. Such an eco-system fails to graduate to the stage of planetary reproduction [multi-planetary ecosphere expansion via bio-regeneration of nearby biotically-deceased planetary surfaces]. In sum, if a human species emergent within a given planetary biosphere fails to achieve the moral and technological fitness to survive, then the entire development aborts, delivering-up a stillborn planet. The humanity to which Earth's biosphere has given rise is the only hope to overcome this as well as other mortal hazards - mostly self-hazards to which the blind-running biosphere exposes itself. The fruition of this hope demands from humankind more than the unintentional amelioration of global cooling by partial CO2 replenishment, or other unconscious ecological contributions. The era of "accidental" advantages, of unnoticed beneficial by-products of humanity's gestation, is about over. Terran [meta-]evolution, if to be sustained, must become deliberate and self-responsible. The only available deliberative agency from within the ecosphere of Earth is Earth's human species. Terran humanity has, unconsciously, saved the biosphere from the biosphere itself so far. Humanity needs now to consciously save [the rest of] this nšo-biosphere, to thereby save itself [as part]. The Earth is not a final stable home in space, or an eternal mothering womb, which Terran humanity can forever relax back upon, or lapse back into, or husband best by doing as little as possible to "disturb" its "perfect balance", its static "equilibrium". There is no such static equilibrium for Earth's biosphere. One hears a lot these days about "permanence" and "sustainability". But, in this pure-noun-less, noun/verb cosmos made of nothing but [self-]conversion processes -- nothing but depletion/accumulation processes -- nothing in nature is "permanent" or "sustainable". The Terran biosphere as presently constituted, from long before the appearance of Terra's proto-human[oid] species, is not "sustainable" much longer, is doomed, unless Terran humanity intervenes technologically. The Earth is a self-dynamizing and ultimately ecologically self-de-stabilizing, dis-equilibrium system whose biosocial fitness will derail itself if Terran humanity fails to play its part by successfully taking the helm. Terra is Terran humanity's window in time, a window of opportunity, to meta-evolve and transcend, or to perish. 'Terra-Reforming' -- the production of an enduring post-glacial epoch on Earth by Terran humanity -- requires this humanity's theoretical and practical technological mastery of highly nonlinear, non-equilibrium behaviors of matter-energy, including those of the non-neutral, electro-magneto-self-active plasma phase of matter. This mastery begins with the harnessing of plasma power in the form of nuclear fusion energy. Hypothesis D. The Fusion Barrier and The Nonlinearity Barrier. __Nuclear fusion technology can provide power resources sufficiently-low in economic-cost and sufficiently high in energy-density to enable Terran humanity to bifurcate the Terran atmosphere/lithosphere/biosphere away from its Ice Age attractor. The advanced fuel-cycles of fusion machines designed to advantageously utilize 'closed-form knowledge' of the nonlinear dynamics of the 'self-confining', 'self-fusioning' meta-states of plasmas can provide a non-radioactivating form of high-energy-density nuclear energy. This new energy source can both (1) end the unintended evolution of atmospheric CO2 concentration, by obviating the burning of fossil fuels as the main available means of energizing Terran human social reproduction, and (2) afford Terran humanity better means to accomplish the crucial benefit that this unintended evolution of CO2 has so far unconsciously accomplished -- the averting of a return to Ice Age eco-suicide on Earth. The latter would also avert the eventual catastrophic social-reproductive collapse that will otherwise attend the ultimate depletion of fossil fuels in the long-run, and, in the short run, the social-reproductive collapse ["global economic depression"] that would result from the draconian cost-prohibition of industrial use of fossil fuels for which the "global warming" lobby is pressing, along with the global and poly-genocidal 're-Nazification' which that collapse would engender. The recent pull-back from the precipice of global thermonuclear warfare is a hopeful sign of the moral potential of Terran humanity to survive the planetary selection test that is now looming. However, the steep global decline of nuclear physics -- in the United States of America, the Republic of Russia, and elsewhere -- is also ominous6, given the urgency of the breakthrough to plasma technology if this potential is to be actualized. The most advanced extant conceptual and linguistic expressions of the "laws", or "habits", of Nature, as presently known to Terran humanity, take the form -- almost without exception5 -- of nonlinear partial integrodifferential equations. The general and "closed-form", "analytical" solution of these equations has eluded Terran human science, and has been evaded by that science, so far, ever since their first formulation on Earth, some 333 years ago. The unknowns to be solved for in these so far unsolved equations are not single numbers, as in the more familiar algebraic equations. They are entire functions. These so far unfathomed functions encode rich repositories of presently inaccessible knowledge. Within the limits of their homeomorphisms, these functions reconstruct the past histories of the [meta-]states of every portion of physical space constituted or "occupied" by the physical bodies of the natural [meta-]systems that their equations partially describe. These missing functions -- these formulae that remain unformulated by Terran humanity to date -- also predict the probable futures of those [meta-]states, for all possible initial conditions. The equations that these function-formulae solve are called "nonlinear" because, in them, the unknowns, the unfathomed functions, appear with their values, or their derivatives, operating upon themselves, and/or upon one another. This signifies the dynamical or time-like interaction and self-interaction of the underlying actualities that these functions mime. Linear integro-differential equations, the kind that have been easily solved by Terran mathematicians for so long, are characterized, in contrast, by function-unknowns which occur singly, without interaction, operating neither upon self nor upon other unknown / to-be-solved-for functions. Such linearizations are also massively omissive in their mimesis of the actual phenomena of nature, producing predictions which err egregiously both quantitatively and qualitatively. For the past 333 years human knowledge and industry have been partially paralyzed by perennial failure to "solve" general nonlinear equations, that is, to attain the means by which the vast knowledge-potential that these equations encode can be explicitly extracted and practically applied. Key instances of this incapacity include the Newton gravity-equations for more than two gravitating bodies, the Einstein universal gravity field equations of General Relativity, the Navier-Stokes equations of electro-neutral liquid/gaseous hydrodynamics, and the Boltzmann-Vlasov equation for electro-dynamically non-neutral, 'magneto-hydro-dynamical' plasmas. This is The Nonlinearity Barrier. It blocks the progress of theoretical knowledge and of engineering praxis around this humanity's entire horizon with "the unknown" - the horizon with its own present unknowing and yet-to-be-known. Our key objective is to call your attention to certain ideas that might aid you in breaching this barrier. We hope thereby to help encourage a new mood on the part of key contributors to the scientific culture of contemporary Terran civilization, a mood which courageously and confidently targets The Nonlinearity Breakthrough as its central next objective. This Breakthrough means 'closed-form' solution of general nonlinear total and partial integro-differential equations, through a radical deepening of the realm of known "non-elementary" transcendental functions / operations, with all the burgeoning conceptual advances -- and the new, praxical, engineering opportunities -- that this will unveil. Another objective is to exemplify, in a rich conceptual context, the 'dialectical operations' mode of cognition, and to "capture" its operatorial essence in a rule-based ideographic language-system -- an arithmetic -- of the simplest kind that we have been able to fashion. Indeed, one of the central objectives of Dialectical Ideography is to make explicit a rules-system -- inescapably 'homeomorphically defectious' though it must be -- for the praxis of dialectical thinking/modeling, to the extent that it will 'become heritable'. By 'becoming heritable' we mean that dialectical reason rises from being the isolated, episodic attainment, mainly by rediscovery and reinvention-from-scratch, of those rarest human geniuses -- of intellectual/philosophical/scientific/spiritual heroes such as Heraclitus, Zeno, Socrates, Plato, Hegel, Marx, Chardin, etc. -- to being a teachable/learnable/diffusible and cumulatively-advancing, socio-culturally expandedly-reproducible, cumulating species-asset and skill-of-consciousness. We mean that it thereby enter the 'Phenome' or 'Memenome' of Terran humanity, as a crucial "acquired characteristic", a continually-renewed intergenerational inheritance. We do not attribute to ourselves the genius of the dialectical adepts named above. As their students, we have endeavored to locate, mapped into their texts, the patterns of their thought, and their visions as to those of the workings of the world, and we have attempted to encode and codify those patterns in the 'meta-arithmetical', 'meta-algorithmic' rules-systems of Dialectical Ideography. The technical foundation of this immanent critique of "Natural" arithmetic grew out of the discovery that there is a 'Contra-Boolean' arithmetic of 'onto-logic' which arises from a hitherto unnoticed, 'strong' contrary of Boole's "fundamental law of [formal-logical] thought", taken as an axiom of Boolean logical arithmetic. The resulting "non-standard" arithmetic of [onto-]logic also turned out to be, equally, a concrete instantiation of the "non-standard models" of "Natural Numbers" arithmetic. The 'constructibility' of such "non-standard natural numbers" had been known, however "non-constructively", ever since the advent of the Lšwenheim-Skolem theorem, and of the Gšdel completeness and incompleteness theorems, analyzed in terms of their joint implications for the four "first-order" Peano axioms of the "Natural Numbers". These non-standard "Natural"/logical numbers satisfy those axioms no less than do the standard "Natural Numbers", even though those axioms were intentioned to characterize the standard "Naturals" alone. Moreover, these non-standard numbers, when their rules-system is 'enacted' in the mind of a human subject, are seen also to display a marked, multi-characteristic homeomorphism to key characteristics of the categorial-progression thought-praxis of systematic dialectic, and of the 'onto-dynamical' and 'meta-finite' singularity-dynamics of dialectical processes of external/objective nature, i.e., of recorded pre-human / extra-human natural agents/proto-subjects, or 'subject-verb-object eventities', all centering on a 'meta-fractal', generalized ÇaufhebenÈ process of determinate auto-negation. This arithmetic was found to function like a 'dynamized' version of what is recorded about the sketchily-recorded Çarithmoi eidetikoiÈ, the dialectical 'arithmetic of_____(' of Plato. This, new, 'arithmetic', this -- therefore dialectical -- ideography, was thus seen to develop the neglected sides of both the 'intra-duality' of logic and the 'intra-duality' of "Natural" arithmetic. Furthermore, it was found to do so in the form of a 'meta-arithmetic' whose 'meta-number' concepts and whose 'meta-numeral' symbols ÇaufhebenÈ-incorporate/negate existing, standard arithmetics, number concepts, and numerals. And this initial, ÇarchŽÈ meta-arithmetic issues forth from itself, when a human subject 'enacts' its rules-system, a systematic succession of increasingly complex, increasingly "concrete", descriptively-rich /-capable categories of meta-arithmetic; ideographic languages for 'quanto-qualitative' modeling of the empirical phenomenologies of nature, including human-nature. This progression of meta-arithmetics at first approaches, then surpasses the descriptive potential of the models -- the systems of ordinary integro-differential equations -- of Standard Dynamical Systems Theory. Moreover, the ÇarchŽÈ meta-arithmetic itself can model the dialectic of its own progression of meta-arithmetics. And it arrives, in the process, at a 'meta-finite' resolution of the zero-division "singularity" problem that besets especially the nonlinear varieties of these equations-system-models, resolving their "infinite residuals" [infinitely-wrong predictions] at their moments of singularity into meaningful, semantically/empirically correct, ['meta'-]finite predicted values at these 'meta-evolutionary' moments of 'onto-dynamasis', of state-space-/control-space-expanding, "laws-of-motion"-changing, new-dimensions-erecting quanto-qualitative mutation and "meta-system transition". The primary purpose of this section is to make motives manifest. Our motives for sending this text into your hands. Motives that might recommend themselves to you to consider it, and to act upon it - to critique, to correct, to apply, to modify, and to further develop its concepts in your own work. We also hold that the alarm being sounded regarding "global warming" is a decoy. A second purpose of this introduction is to urge your inquiry -- if you have not so inquired already -- into what motives might propel a certain subset and 'subsect' of your fellow species-mates to deploy such a decoy. Vast and urgent discoveries attend that inquiry6. Desiderata. A number of lines of development converged in the discovery and design of the Q, U, and __ ideographic languages and rules-systems. Several of these might have been, even singly, sufficient to guide the entire discovery, though they were not so in our cases. These 'ideo-genealogies' also disclose the desiderata of our quest. We denote by Q -- singly underscored Q -- the "set" or "space" of ' "pure", non-additive, unquantifiable 'unit-interval-confined', ontic qualifiers' or 'purely-qualitative meta-numbers' basing the dialectical ideography set forth herein [note that Q ( Q, the "Rational Numbers"; indeed, Q Q]. We denote by Q -- doubly underscored Q; Q underscored again -- the total syntactico-semantic rules-system of that ideography. Likewise, U denotes the space of 'quantifiable ontic qualifiers' or 'ontologically qualified quantifiers' of the 'full-multiplicity', 'quanto-qualitative ontological universe-of-discourse, multi-population meta-distribution arithmetic', and U denotes its rules-system, while __ denotes the space of 'quantifiable metrical and ontological qualifiers' or 'metrically and ontically qualified quantifiers' of the 'quanto-qualitative metrico-ontological arithmetic', and __ denotes its rules-system. One goal of our quest is to construct a Q-based ideographic or "mathematical" model of the emergence of Q itself. Pursuant thereto, it may thus be helpful to set forth, by 'retro-intro-spection', or 'memoric reconstruction' of the inner conceptual path that we have trod, a summary of the factual historical material of our own ideative genealogy or discovery-history with respect to Q. This is, at least in part, in that part known to us, the data, the psycho-historical material with which such a model should contend, and for which it should account. Some of these thought-lineages are summarized below, in the terms of the key features we desire for the theory that we seek. The quest which resulted in, among other developments, this essay, and which continues, aims at an ideographic, algorithmic, 'quanto-qualitative' computational language consistent with the following hypotheses, referenced below as 'working convictions': a. The Dialectics / Nonlinearity / Self-Reflexivity Link. Working Conviction: There awaits worldwide [¶re-]discovery a dialectical logic that will be: (i.) a valuable supplementary organon, likely, among other benefits, to: (ii.) hold keys to a The Nonlinearity Breakthrough, and which will be found to be: (iii.) one kind of contrary or negation of the statical/Parmenidean and anti-genealogical presuppositions of classical formal and 'ideographic' ("symbolic") logic and set-theory / totality-theory. The latter conjecture led us to the study of contraries of Boole's "fundamental law of thought", which he stated as x_ _ x. Those contraries include x_ _ x, x_ _ x, and, lastly, x_ x, which asserts that x_, the 'self-reflexion' of x _ x_, is neither greater than, nor equal to, nor less than x, but, on the contrary, differs from x non-quantitatively, i.e., qualitatively. b. The Nonlinearity / Set-Theoretical Paradoxes Link: Dialectics as Logos/Logy/Logic of 'Self-Reflexive' /'Self-Refluxive Functions'. Working Conviction: Our sought-after dialectical logic is a 'logic of self-reflexiveness', a logic of 'self-reflexive action', of 'self-activity', or of 'self-change', deeply related to both integrodifferential nonlinearity and singularity and to the standard "reflexivity" paradoxes", i.e., the 'truth-value-self-oscillatory', "self-contradictory" propositions of formal-logic and set-theory, as well as to 'non-standard paradoxes' such as that of the 'set of all sets'. It is a logic of 'self-iterative multi-ontic cumula', of '¶self-recursive processes', of the form Ex_ _ x____ _ x_[x_] _ x__ or x_ _ x___ vs. that of fixed-point 'allo- iterations', Ex_ _ x____ _ Fx_ or x_ _ F_x_, wherein F x_. c. Self-Action Yields 'Quanto-Qualitative' Meta-Finite Growth. Working Conviction: Internal "self-reflection" in human thought-processes, and external, causal 'self-reflexion' of natural systems generally, is typically 'onto-productive'; is productive not only of quantitative but of ontic, ontological, qualitative change. By 'self-reflexion' we mean 'self-reflexive action', 'self-reflux' or "feedback"; 'back-feed', 'back-flow', or "blow-back"; 'return flow of the action of self from self back to self'; the "self-interaction", "self-action", or "self-activity" of self-induced quanto-qualitative change. We model this as action from state-space, to and through control-space, back to state-space, which "singularly" and topologically transforms the entire, unitary state/control meta-space. We hold that such self activity is typically 'expandedly self reproductive'. I.e., it may yield an ontic, quanto-qualitative "surplus", "gain" or 'meta-fractal, meta-gnomonic increment'. 'Other-interaction', interaction with other 'selves', other 'subjects' or 'agents' of natural history; other contributors to time; other portions of the 'non-self' or 'other-than-self', may do so also. Such "gain" is typically not simply a quantitative increment within the same ontological qualit(y)(ies) that prevailed before interaction. Such gain typically also includes a qualitative, ontological increment; qualitative gain, "innovation", "novelty", "surprise"; an ontological and topological "unprecedentedness". Such self-action produces 'elevation'; 'change of direction', 'gain/change of [ontic and/or metrical] dimension(s)', 'transcendence', or "qualitative change". d. Self-Operation of 'Operators' as Ideographic Representation of 'Onto-Genic' and 'Onto-Generative' 'Self-Reflexion'/'Self-Refluxion'. Working Conviction: Such 'self-reflexion' & 'self-refluxion' can be fruitfully represented in "symbols", that is, in symbols of the kind known as "ideograms" -- ideographically, or "mathematically" -- via 'generalized self-multiplications', as 'self-operation', that is, via self-application of operations in the form of operators; via sequential 'self-product[-ion]s' of 'meta-number' or 'meta-scalar' values; in sum, via continual self-escalations of a recurrently "2nd degree" or "quadratic" nonlinearity. Connected conviction: such representations hold some of the keys to the "closed-form" solution of the still-unsolved nonlinear "total" and "partial" integro-differential equations, through expanding the humanly-recognized and humanly-recognizable realm of "elementary transcendental functions" [cf. G. N. Watson] to include, especially, more of the nonlinear, i.e., non-commutative / non-distributive -- or 'non-homogeneous / non-superposable' -- 'meta-numbers', "functions", "operations", or "transformations". e. The Parmenidean Roots of The Nonlinearity Barrier. Working Conviction: The statical ontology -- the longstanding and implicit Parmenidean presumptions of prevailing Terran academic and scientific sub-cultures -- is one of the keys to the reaction against the conceptual phenomena of these "[self-]reflexive" or "self-referential" paradoxes, as to the connected apparent "unsolvability" of general nonlinear equations. Those "paradoxes" -- truth-value-self-changing, truth-value-self-toggling, 'truth-value-self-oscillating' propositional functions -- inhere in, and can be formally derived within the "intuitive", unguarded axiomatics of these formal systems. Those paradoxes constitute a self-refutation, a reductio ad absurdum self-denial, of these formal systems' own tacit denial of the possibility of self-changingness among their formal, logical and set-theoretical conceptual objects. The paradoxes constitute a self-denial of these systems' own Parmenidean presumptions, of their implicit 'Parmenidean Postulate' denying the very possibility of the phenomenon of self-change, both as internal, mental, logical, conceptual phenomenon, and as 'external', 'exo-mental' phenomenon. Per this 'Parmenidean Postulate', mathematical-/mental -object existence implies mental object stasis; mental-object motionlessness. The attempt to consistently and formally construct a mental model of the early-Platonic doctrine of an undergirding realm of "pure", statical, timeless, motionless, immutable, 'linear-equilibrium', fixed-point-like idea-objects fails, and -- even formal-logically -- must fail. It fails even by its own, immanent standards of formal, deductive logic and proof. Via the paradoxes, the unstated assumption of Parmenidean staticity deduces to its own negation, through a reductio ad absurdum derivation of the paradoxes as counter-examples, negating its assertion that all mathematical idea-objects must be 'mentally motionless'. This logical non-excludability, short of massively counter-intuitive contraption, of inherently self-dynamical "reflexivity" or essence-ial self-changingness, was first formally faced in the forms of those semantically rather empty, gainlessly oscillatory formal paradoxes. But reflexivity also manifests in the semantically more fruitful forms of the Gšdel Incompleteness Theorems, plus of other, seminal, and cumulatively self-changing conceptual objects which we will explore in the sequel. Both the "statical" Gšdel Incompleteness Theorems, with their 'Gšdelian Meta-Dynamic', and the latter, intrinsically 'self-dynamical', 'self-cumulative' conceptual objects, find one of their several possible alternative convergences in Q and U, as we shall shortly see. The most central and essential exemplar of the latter for this immanent critique is "The Set Of All Sets". One of the early inspirations of this effort, herein termed the 'Heraclitean-Chardinian Product' of Sets, and its close relative, 'The Power-Set Evolute Product of Sets', helped make sense of that otherwise "paradoxical" 'Set Of All Sets', which should be the founding object of [extensional] set-theory, as the set-theoretical definition of the concept of "Set" itself. The latter product rule 'semantifies' The Set Of All Sets as a self-changing, self-developing, self-superseding, self-regenerating mental eventity; a conceptual 'cumulum'; a never-repeating meta-process; an ideational process-object. The former product rule, applied iteratively and recursively to a set with the "empty set" as its initial content [with "no" initial content], generates the Whole Numbers, W, in the von Neumann/Zermelo/Fraenkel manner. These Set Products are alsonon-distributive, non-commutative, and non-associative over "set addition" ["union"]. "Non-superposition", N(x __y) ( N(x) _ N(y), and "non-homogeneity", cN(x) ( N(cx), define an "operator" N as a Nonlinear one. These clues, among others, lead to our working conviction that the 'meta-arithmetic'/'meta-algebra'/'meta-analysis' of The Nonlinearity Breakthrough must be, in general, non-commutative and non-distributive at least, if not non-associative as well; must include a generally "nonlinear arithmetic" and "nonlinear algebra". The realm of such non-commutative, non-distributive algebras is virtually unexplored in the modern mathematics mainstream. Most variants of Q explored herein exhibit non-commutative, non-distributive, and non-associative 'multiplication' among their 'meta-scalars'. They are thoroughly non-linear operatorial meta-arithmetics. Indeed, their ideographic expressions of The ÇAufhebenÈ Principle all imply non-commutativity, non-distributivity, and non-associativity of their ÇaufhebenÈ product-rules. f. Goal: A Non-Reductionist Ideography of the 'Quanto-Qualitative Self-Dynamics' of Natural (Including 'Human-Nature-al') 'Meta-Systems'. Working Conviction: The evolution of our cosmos displays an historical sequence of qualitative, ontological changes, not just quantitative ones, that should be represented as such ideographically, in our mathematical models of that history, for greater empirical, experiential accuracy and for greater explanatory power. The actual cosmological ontology is an expanding one, that should be modeled via a self-expanding ontological possibility-space undergirding the 'actuality-space' or 'population-space' of observed frequencies/populations/proportions/"probabilities" or densities of individual [ev]entities. In the Q and U ideographies, as interpreted herein, later-emerging ontos do not "reduce" to earlier-emergent ontos. Rather, each later-emergent, 'meta-stable' onto spontaneously self-constructs from earlier-emergent ontos. g. The 'Evolute', 'Cumulative', and 'Irrepeatable' Character of 'The Energy-Time/Space-Matter Cumulum'. Working Conviction: Meta-evolutionary change is crucially 'evolute', i.e., 'cumulative', rather than merely 'convolute', i.e., 'erasive'. The application of the terms 'evolute' and 'convolute' herein appropriates their usage in descriptions of the spiral outer shells of certain tide-pool meta-biota. In a "convolute" spiral shell, succeeding whorls hide preceding whorls from view. In an "evolute" spiral shell, preceding and succeeding whorls are concurrently visible. The 'evoluteness' of evolution in this sense thus means that successful prior self-reflexive or non-hybrid/'self-hybrid' product[ion]s as well as hybrid/cross product[ion]s are typically conserved and carried forward along with their newly-emerged, qualitatively different products; that such "old" is most often not entirely 'erased' or 'extincted'/extinguished by its "new" offspring, but generally continues to be extant, albeit in "adjusted" form(s), adjusted via interaction with the "new", and continues to appear alongside that "new", as well as appearing as an internalized, in-folded foundation of, that "new". Indeed, such "old" often remains manifest in even greater "mass" or "volume" than that "new". Citing "pre-biological" stages of the meta-evolution of the ontology of this cosmos, 'Atomic onto-mass', populations of atoms, i.e., of matter/energy not organized beyond the atomic form of organization of matter/energy in the molecular sense, continues to exist, though molecules have long-since emerged in this cosmos. 'Molecular onto-mass', populations of molecules, i.e., of matter/energy not organized beyond the molecular form of organization of matter/energy in the cellular sense, continues to exist, though prokaryotic cells have long-since emerged in the cosmos, at least on -- and in[side]! -- planet Terra. Citing the human, meta-social evolution of forms of exchange, the emergence of money as medium of exchange did not initially, or even to this day entirely, extinguish the existence of commodity barter; even less so of the sea of commodities from which money , originally as money-commodity or "numŽraire" -- initially emerged. This emergence did, however, transform the context and thus the nature of the commodity as a form of exchange-value, in the process of forging the relationship of that older 'ontological category'; or 'onto' of exchange-value to this newly-emergent 'onto' in the ontology of the universe of exchange-value. Likewise, the emergence of mercantile capital -- of its circulation path, inverted with respect to that of the consumption-aiming circuit of the money-mediated circulation of commodities, does not extinguish the existence of either the onto of commodities or the onto of money, though it does transform their relationships in the formation of their relationships to the emergent exchange-value 'onto' of mercantile capital. By dint of thus modeling of the space-time-mass-energy "continuum" or "medium" of the cosmos as an 'evolute, multi-ontic cumulum', we see that 'cumulum' also as an 'irrepeatable' succession. Strict re-petition of meta-states is impossible. 'Second petition' must arise in a context no longer "pristine"; already altered by the consequences, the 'cumulum increment', of 'first petition'. h. Retention and 'Semantification' of 'Hybrid', Cross-Product Terms. Working Conviction: Previously-emerged, evolutely-conserved ontological categories, or 'ontos', continually undergo 'multi-mutual' or 'poly-mutual' readjustment, with respect to newly-emerged ontological categories or 'ontos', via the 'poly-interactions' among them, not just "between" them. Such adjustment processes can usefully be captured ideographically by retention of 'hybrid' or "cross" product terms in the possibility-space and actuality-space models, with the "assignment" and "interpretation" of those adjustment processes to and via these hybrid terms. Such hybrid or "cross product" terms are the very kinds of terms so typically dropped, or identified with zero, e.g., in the "scalar product" of vector 'meta-numbers', as well as in many other operations of 'linearist' mathematics. 'Hybrid' terms -- the terms in { Q__} models [of universes of discourse u, of order n, for evolutionary epoch counters or self-bifurcation index values or self-singularity counters __( W, of range 0 ( _ ( _(], generically denoted qk, such that k is not of the form 2_ -- can be interpreted, for some universes of discourse, as the mutual adjustments of the preceding and succeeding "purebred", non-hybrid, or 'self-hybrid' terms, those of the form q2_. These hybrid terms can also be interpreted, for some 'partition principles', or 'parsings' of universes of discourse and of the ontologies they involve, as describing populations of independent hybrid [ev]entities, or distinct material substrates, distinct qualities -- distinct organizations -- of "mixed states" of matter-energy. These 'Hybrid' or "half-breed" terms invoke an arena of empirical modeling where Terran science has tended to wax squeamish. As a small-scale psycho-historical experiment, observe your own emotional and other cognitive reactions to the connotations and associations of the words which describe mixes of materials, belonging to multiple levels of organization of matter-energy, that include some of the candidate 'interpretands' for the hybrid qk in { Q_ }: heterogeneity; humus, dirt, detritus; debris; deposits; dross; dregs; adulterates; alluvia; effluvia; entropies; exfoliations; effluent; sediment; scrap; shards; spume; scum; soil; slime; slop; slush; sludge; slag; swill; moraine; "mixed-up"; mess; mire; mush; mud; muck; mongrelize; guck, gruck, gushy; gunk; junk; jumbles; jetsam; goo; goop; glop; grit; grime; garbage; ooze; crud; crap; crumbs; crumble; corruption; corrosion; coagulum; fragments; froth; foam; filth; flotsam; offal; litter; loam, trash; rummage; rubbage; rubbish; rubble; ruins; remains; wreckage; recrement; residue; . . . No doubt there is, in part, a sound, Darwinian, genomic basis to the aversions that the word-symbols above, let alone their palpable referents, evoke. No doubt some of our reflex bodily and emotional recoil and even literal nausea in reaction to such actualities is part of an adaptive defense, via avoidance, against the pathogenic microorganisms that abound in many of the contexts connoted by the words listed above, part of the 'hybrid' adjustment of organisms co-constituent of the multicellular, metazoan onto to the massive if invisible presence of potentially pathogenic organisms of the earlier-emerged, prokaryotic and eukaryotic "unicellular" ontos. But the psycho-archaeology of Terran civilization reveals something more, something excessive, something extra-genomic; something memetic in this recoil, visible as early as the ancient Greeks: a tendency to seek refuge in "pure" ideas and "perfect, immutable" idealizations. It extremifies in the Nazi oxymoron of "pure blood", in Nazi fears of "mongrelization of the races"; in the Nazi's complete denial of heterosis, of "hybrid vigor". It manifests again in the epithets of modern science, e.g., in the naming "noble" of those elements which do not combine [chemically]. Many of the hybrid cumula we commonly encounter are 'catabolic' cumula. The dusts ever-accumulating on the floors of our houses, that need to be vacuumed away for the health of their human occupants, are cumula of elemental atomic mineral powders, of molecular debris, of prokaryotic bacterial spores, of eukaryotic molds and pollens, and of human skin-scales. A trans-nounic, 'eventity' view of the living human body sees it as a veritable walking fountain of skin flakes, exfoliating feasts for dust-mites. But are there not also 'anabolic' cumula in our cosmos -- again and again, starting even before those interstellar pre-atomic, atomic, and molecular nebular condensations which are the nurseries of new stars and even, perhaps, of new stellar-planetary systems? Are there not hybrid multi-ontic cumula whose existence qua activity is crucial to the catalysis of all of the 'meta-evolutionary', 'onto-generative' self-bifurcations? 'The Taboo Of The Hybrid', viz., the conceptual suppression and mathematical omission of these hybrid actualities, together with the grammatically-inculcated ideo-pathology of 'nounism', the semi-conscious belief that the objects we name using our nouns are as 'Parmenideanicly' actionless as the part of speech to which their names belong, weakens science. It blocks insight. Ontologically hybrid formations, from the bio-molecular lipofuscins that clog our cells, accelerating our bodily aging, to the plaques that clog our arteries, impending our premature deaths, to the geo-biological and meta-social hybrid cumulates we noted above, to the asteroidal, cometary, meteoric exolithic residuum of solar-planetary poiesis, which threaten to extinguish the progress of our planet -- are ignored at our peril. i. Goal: An Ideography of the ÇAufhebenÈ Operation. We seek 'meta-arithmetics' , 'meta-algebras', 'meta-geometries and a 'meta-analysis', in a sense distinct from the Hilbertian one, for trans-Hegelian versions of a quanto-qualitative Çaufheben È or "sublation" operation. This operation is central to Hegel's [unnecessarily restricted and still largely Parmenidean] version of dialectical logic. We seek arithmetics of "operations qua numbers" and "numbers qua operations", i.e., 'meta-arithmetics 'of 'meta-operators' which "simultaneously" (a.) annul, (b.) conserve, and (c.) elevate their operands. Such 'meta-arithmetics 'should codify an explicitly 'autopoiesic', self-reflexive version of the Çaufheben È operation. They thus reveal a conception of this operation as one which, as expressed herein via ideographic, "mathematical" symbols, models a mode of action that is primarily an 'essence-ial' self-operation of a dialectical [ev]entity upon itself, a 'self-critique' or self-/essence-induced 'immanent critique'; a "being-for-itself" 'self-re-flexion' and 'self-re-fluxion'. This is in contrast to a '[de-]flexion', a "being-in-itself" process -- an action upon that dialectical 'eventity' or Subject/agent by other agencies, by other Subjects/Actors, by other entities conceived as external/alien to its self/essence. The "elevation" moment of this operation is conceived as one of 'onto-generative', i.e., of 'qualitative' change. That moment thus supplies wherewithal for the description of a universe which is not just in a physical, spatial sense in acceleratory self-expansion, but which is also in a 'contental', 'typological', taxonomical, hence 'descriptional' -- in short, ontological -- acceleratory self-expansion: a universe which is constantly adding new "things" to itself, not just more "things" of the same [onto-]type (quantitative self-expansion), but "things" unprecedented in kind; new 'onto-mass' of new 'onto-type' ['qualitative self-expansion']; thus an 'onto-dynamical' universe. j. The 'Pseudo-Agents' "Pure Quantity", "Time", "Natural Law", & "Chance". Working Conviction: A 'conceptual- therapeutic' need exists for concerted application of a 'neo-Feuerbachian' version of the Feuerbachian 'righting', 'de-capsizing', or 'inversion of the inversion' operation with respect to current usages and "figures of speech", both phonogramic and mathematical- ideogramic , involving the concepts of "Time", "Law Of Nature", and "Chance". A 'neo-Feuerbachian' critique of 'deified', reified, hypostatized, and subject/object inverted linguistic expressions regarding abstract "Time" and "Natural Law", as well as regarding abstract "Quantity" and abstract "Quality", already resides at the very heart of this inquiry. Prevailing ideo-graphical notations for dynamical ["time-varying"] variables -- e.g., S((x, y, z), t) and X(t) -- present "time", denoted t, as ultimate independent variable, as if the final "cause" of all such dependent variable, function-value "effects". This semi-consciously inculcates a conception that "time changes all things". But that assertion places the real actors, the real agents, the real subjects, in the object position, and the real object(s) or result(s) of action in the subject-position of the sentence, hence of the [mis-]conception. It formulates, in that sense, an "inverted" proposition, 'standing the true description on its head' or "belly-up" in an "upside-down", subject/object-reversed formulation. It reifies the abstraction, "Time"; ascribes to "Time" a false causative status; falsely ascribing "Time" as "Subject" or "Agent" of change, as "Actor", thus making it a 'pseudo-subject' or false subject, while also ascribing the actual actor(s) or agent(s), the true subject(s), "all things", as mere objects of "Time" as if "Time" were an external cause of their changing natures, thus making them out to be 'pseudo-objects', ascribing to them a false "being-in-itself" passivity. Feuerbach's medicine for such mentality maladies was to reverse such reversals. Let us do so by performing a syntactical [and semantical] "180 degree rotation" on the sentence-string "Time changes all things". After re-righting the resulting upside-down letters, permuting the sub-strings "things" and "all", and dropping the "s" from the sub-string "changes", this yields the symbol- string 'All things change time' or 'Things all change time'. Such raw 'rection' or 'righting' of a more familiar, superficially more acceptable 'capsized' [in-]version, usually rings strange on first encounter. But, at length, for us, the results ring true, and have opened onto key insights that pervade this work, that help heal the subliminal ideo-pathologies of reifying, hypostatizing, 'apotheosizing', subject/object-inverting, pseudo-subject-concocting thought-habits, and that co-found a new time paradigm, one which we hope will help you to breach The Nonlinearity Barrier. Likewise, when we encounter [over-]turns of scientific phrases such as "The Schroedinger Equation governs the behavior of micro- physical objects", or "The laws of natural selection govern the evolution of the species", or "there may be general laws governing such nonequilibrium self-construction processes in biospheres and the universe as a whole", we 'turn them over' in mind, invert them into 'The behavior of micro-physical objects governs the Schroedinger Equation' or 'governs the "Laws" of Quantum Mechanics'; 'The observed patterns of the evolution of the species govern the "laws" of natural selection', etc. For "Natural Selection" is not a real and God-like super-Subject that accepts some species for continuance, and rejects others, but a name for some of the consequences of differential rates of self-reproduction of co-evolving and 'inter-evolving' populations of eventities. Neither abstract "Time" nor natural "Law" is the "energizing principle" of universal self-movement or of cosmological meta- evolution. Science consists in a meta-social community of comprehension of experientially, experimentally faithful, apt, fittingly reconstructive, and predictive operational descriptions of empirically-given phenomenologies. The "laws" in science are empirically-disciplined formulae, in phono-picto-ideo-graphic language(s), whose formulation by human subjects is "governed by" the actualities they seek to homeomorphically, if forever imperfectly, re-present. Such "laws" are not entities operating in the external, 'exo-mental' world as actual agents, subjects, empirical actors in their own right, who "govern" those actualities, or manipulate the actual actors in any way, with the partial exception of the 'self-sciences' of human meta-society, wherein observor and observed [partially] coincide. We have therefore chosen to practice a praxis of thought designed to re-condition our conscious, semi-conscious, and pre-conscious thought-habits by pursuing an account of actual time as constituted of and by concrete action, by the other-action and the self-action of concrete sub-totalities, 'ev-ent-ities' which are the actual subject-verb-objects or causes of "Time", not its mere "objects" or "effects". We thus search for alternative formulations of the dynamical and 'meta-dynamical' "Laws" of nature in which the time variable emerges as ultimate dependent variable, as ultimate effect, rather than as the ultimate independent variable, as if the ultimate cause, of cosmological self-development or autopoiesis. Thence arises a key concept, that of quanto-qualitative 'temporal acceleration'. We therefore also pursue an account of "The Laws Of Nature" in terms of 'meta-gnomonic', 'spatio-temporal meta-fractals', quanto- qualitatively different but self-similar patterns or "habits" [Peirce] of action, evincing the self-refluxive self-constraint of the self-burgeoning processes and populations of [ev]entities ever-pouring forth from universal self-production. We thus also seek for alternative conceptions and verbal expressions regarding such "Laws", which do not connote that they "govern" the actions of concrete actors, but conceive them as linguistic portrayals of the self-created patterns of change expressed by, and expressing the 'dynamical essences' of, those very concrete actors. Such patterns of evolution and 'meta-evolution', conceived as concrete operations embodied in externity, may thus themselves change, and even change themselves, in the sense of the metafinite self-bifurcation process: in their turn, meta-evolve, and even self-meta-evolve! Reflecting back upon some of the deeper historical, cultural, civilizational roots of the cumulum of conceptions upon which Modern Science has drawn in framing its conceptions of "Time" and "Natural Law", we should say that Abstract "Time" is not the creator-god of all change, nor is a static, changeless God the decreeing source of immutable, changeless, Parmenidean "Natural Law", Who created the Creation, and legislated that "Law" in the process, once-and-for-all. Nor should the "Tetragrammaton" of the Judeo-Christian testament, the "I AM [that] I AM", the "JHVH", be interpreted as the ultimate assertion of Parmenidean changelessness. On the contrary, it is a consummate expression of 'Non-Linear, Self-Reflexive Divinity': AM ( AM[AM] _ AM(AM _ ~AM _ AM_ _ AM _ _AM AM; jH[vH] _ jH_ _ jH _ _jH jH; Being_ ( Being_[Being_] _ Being__ _ ~Being_ _ Being_ _ _Being_ _ Being___ Being_, or better; Becoming_ ( Becoming__ _ ~Becoming_ _ Becoming_ _ _Becoming_ _ Becoming___ Becoming_. It describes 'continuing Creation' -- the ongoing Cosmo-Genesis/Chrono-Genesis of ever-growing, eternally-progressing Deific Being in 'Self-Continuing Self-Creation', including the ever-new generation/transcendence of ever-new "Laws"/Patterns of becoming. k. The Concept of 'Meta-Finite, Conversion-Singularity Self-Bifurcation'. Working Conviction: The paradigm of unitary control-parameter-space /state-space 'self-bifurcation' provides an appropriate conceptual and mathematical tool-kit for describing, in both past-reconstructive and future-preconstructive modes, the 'generics' of outwardly diverse physical mechanisms of the combined, "being-in-itself", 'flexive' development and "being-for-itself" 'self-reflexive', 'self-refluxive' self-development of populations of eventities. This paradigm includes the quanto-qualitative self-transformations of human societal formations, the revolutions, "sudden evolutions", sudden depopulations, and also the "renaissances" which are ontologically generative at the level of human social ontologies, and also "revolutions" in human idea-systems, including the historically-observable 'meta-evolutions' of mathematics. That is, this paradigm also applies to human society; to that sub-realm of natural history which is '[proto-]human[oid], meta-social nature' qua eventity; to its partially other-/"environment"-generated, partially self-generated, self- engendered history. 'Self-bifurcation' involves actual 'singularities', finitary, but 'metafinite' and "catastrophic" behavioral "discontinuities". These are often seen as marking the outermost temporal boundaries of the existences/identities of systems, via self-transformations so deep that the preceding system-identity may be perceived and conceived as being lost, and a new, successor system-identity as being born. The model occurrence of self-bifurcation arises when the value of a system control-parameter shifts across its bifurcation-inducing, critical value threshold, but driven not just by some external, environmental, non-self mechanism, but by the internal , self-changes described by the state-space trajectory of that system itself. Such 'metafinite singularity' arises, in __-'requalified' or 'onto-metrically qualified' dynamical "evolution equations", at that t value for which a denominator-resident 'conversion-function' involving a self- bifurcation parameter-value indicates complete conversion/depletion of the 'material negentropy' that had 'fueled' the evolutionary epoch thus ending within the 'driver loci' of that evolution, by means of a (0)([ ]( __ denominator. The 'meta- system' concept bridges the "catastrophic" identity-loss boundaries cited above; sees predecessor and successor "systems" as united within a single, deeper, 'meta-continuing', meta-system' identity. Thus, successive generations of stellar "births" and novae-"deaths" meta-continue as the [especially planetary-nebular] self-development of the 'meta-system' of the galactic interstellar medium. The 'atmo-/litho-synthetic', chemosynthetic, photosynthetic, and 'industrio-synthetic' epochs of the Terran biosphere meta-continue as the 'meta-system' of Earth's bio-noospheric meta-evolution. The ancient/'chattelist', medieval/feod-based, and modern/capital-based epochs of Western history meta-continue as the 'meta-system' of Terran Occidental meta-social meta-evolution. This meta-system level of theory and of ideographical, mathematical modeling is neglected in contemporary science, even in that science's most "nonlinear, dynamical" mental, conceptual and mathematical models, which all tend to model 'systems', but not their 'meta-systems', and also not their "meta-system transitions" [Turchin]. This 'meta-system' level of identity, locus of 'meta-space'; and of the unified, state-space /- control-parameter-space 'meta-dynamics' of 'metafinite, conversion-singularity self-bifurcation', constitutes that level of natural phenomenology which the logic, arithmetic, algebra, dynamical geometry, and analysis of dialectical ideography targets for capture. _. The Concept of 'Self-Duality' or 'Di-act-icity'. Working Conviction: The primary formations of every to-us-known epoch of the 'meta-evolution' of this cosmos are globally characterized by inherent, ineluctable, self-induced instabilities. By this, we mean that, apart from external "accidents" which may terminate their existences prematurely, their own immanent, 'essence-ial', 'self-nature-al', thus "necessary", internal self-maturation self-terminates them 'maturely'. We mean that, precisely because of what they are [and therefore of how they are and of what they do, including especially 'because of what they do to themselves'], and not only because of what other "things" may or may not do to them; "things" cannot stay the same; that this is the most radical, fundamental source of change, and, thereby, even of "time" itself. The incompatibility of each meta-state of each such system-self with the continuation of that meta-state, this 'self-incompatibility', is the 'dialectical force' that drives change, the "energizing principle" behind the '(' in the 'universal characteristic' process expression: x_ ( x____ _ x_[x_] _ _[x_] _ x_2, wherein _ denotes the 'self-bifurcation index' or 'metafinite singularity countor' for the universe of discourse spanned by { x__}. For example, the continued existence of a Hydrogen-fusioning star is inconsistent/incompatible with its later continued existence as such, beyond the critical values of its core Hydrogen-density and Helium-density self-bifurcation control parameters. This is because its "existence" as a Hydrogen-fusioning star IS the continuous depletion of core Hydrogen and the continuous accumulation of core Helium, via the nucleosynthetic continual conversion of the one into the other, to the eventual degree where core Hydrogen burning sputters out, and the accelerated, "catastrophic" self-gravitational implosion/contraction-collapse of the star resumes [until stellar core compression is sufficient to ignite Helium-fusion]. A 'dialectical [meta-]system' is 'diactic' or 'dually self-active'. The self-same self-generated acts which change its state, the kind of change depicted by its continual change of position in its state-space, i.e., which create its "state- space trajectory", also shift its key control parameter value(s). This shift typically occurs in a gradual, mounting, progressive, cumulative, and acceleratory way, until those parameters are thereby driven to their critical threshold values, representing a complete conversion of the negentropy base whose conversion has driven system state-evolution for the entire epoch now therefore closing. The resulting, denominator-resident zero value of the function representing the net remaining available store of that base resource in the 'driver-loci' of system evolution, models a threshold-crossing which induces a 'via-singularity bifurcation', a 'metafinite', 'onto-qualitative change' in the very topology; in the axial, dimensional, metrical content, of the state-space flow-field. This 'complete conversion self-bifurcation' thus involves changes in the very dimensionality, in the state-variable and control-parameter metrics, of the appropriate post-bifurcation state-space/[self-]control-parameter-space, i.e., in the unified, state-control meta-space of meta-states, which is, in toto, a geometric depiction of the 'meta-dynamic' [meta-"law" of motion] of this meta-system. Such bifurcation is thus self-induced mediately, as opposed to externally-induced immediately or instantaneously. It is represented, in the state-space/-control-space metaphor, as a cumulative effect of the successive state-spaces motions of the meta-system upon its 'paths' in its successive control-parameter-spaces. We thus term such a bifurcation a self-bifurcation. Such self-bifurcation is typically associated with a change of ontology, reflected in the irruption of the new metrics of the new state-variables' and control parameters' axes, i.e., normally with a net expansion in ontology, and with a problem-self-induced change in the specification of the problem and of its model. "Withering-away" of metrics/axes/dimensions, and interchange of axes between state-space and control- space, may also manifest. We memorialize this 'diacticity' via a phonetic formula which is rather a mnemonical than a truly etymological one: 'Individuality entails indivi-duality', meaning 'indivi-sible [inner, endo-, 'intra-] duality', as opposed to 'divi- duality'; 'divi-sible', external, inter- or 'exo-duality'. We identify this generic internal tension, or 'in-tension', as that 'between' the subject-aspect/moment and the object-aspect/moment of each [ev]entity. It manifests ideographically as the syntactical self-duality, self-confrontation, self-interaction, or 'self-double-ness' expressed in the "nonlinear term" x_2 in x_1 ( x_2 _ x_[x__] _ _[x__] _ x___. The x_[ _ ] component of x_[x___] denotes the 'for-itself', 'operator', 'movor', and 'pattern-of-movement in [meta-]number-space'; in toto, the subject-aspect, of x_2. The _ [x__] component of x_[x___] denotes the 'in-itself', 'stopping-point previously attained in [meta-]number-space', in short, the object- aspect, of x_2 _ x_[x__]; indeed of the entire self-dual, self-evolving, self-iterative [ev]entity modeled by { x__} as a whole. Timing. A tradition of thought, developing from the deeps of Earth's antiquity; appearing, with variations, in both the oriental and the occidental hemispheres of human habitation and self-cultivation, and with varying degrees of staticist, 'Parmenidean' impairment, has come down to us under the name "dialectics". We find it potentially serviceable for the requisite breakthrough. Sober consideration of the potential of this organon has been blocked, planetwide, for most of the twentieth century. Early this century, Terran humanity cleaved against itself in a new way. A "First World", the portion of that humanity first self-transitioned to the industrial capital-based 'meta-attractor' of human 'meta-evolution', engendered, and entered into protracted conflict with, a "Second World". The latter comprised the portions of this humanity who recoiled against their social cannibalization by [what their recoil constituted as] the "First World". The latter then reactively/transiently unveiled a dual, quasi-autarkic vs. [proto]-state-monopolized/nationalized-capital-competing-in-world-market meta-state of bureaucratic-nationalist politico-economic [mal-]praxis. Locked for the last 80 years in this global battle, humanity could not clear-sightedly address the nature and utility of dialectical thought. One partial fruition of dialectics, the post- and contra-Hegelian school of Karl Marx and Frederick Engels, was central to the ideology of this conflict. We use the term "ideology" advisedly. The ruling plutocracies of both combatant parties only pretended to embrace, or to denounce, dialectics. What the Second Party upheld, and what the First Party rejected, was not the actual dialectical tradition. Two competing, deeply corrupt [with crucial individual exceptions], supra-national, extra-constitutional, oil/financial/espionage/secret-police/mafia/arms-cartel / drug-cartel / slavery-cartel / asset-"bubble"-orchestrating / 'designer-disease'-propagating plutocracies, two factions of a global 'dictatorship of petroleum', seized power, one more overtly; the other, more covertly; but each equally committed to the suppression of universal humanity, of global human social individuality, of human individual sovereignty, of global human prosperity, and of political-economic democracy. The "dialectical thought" about which they ideologized was but a diverting camouflage for their competing but antagonistically-cooperative social parasitisms; a counterfeit within a facade. It was the waxing democratic spirit of the greater people of the Earth, East and West, North and South, that brought this paralyzing impasse to a pause. Earth's people know the value of what they have gained [even if some of their present rulers do not know, or do not want them to know]. They will not trade the degree of democracy -- and of freedom of creative enterprise -- that they have attained, at such great price, for something less. And why should they? What they have gained is the achievement of the generations -- generations of labor, discovery, building; of hardship, struggle, sacrifice, and death. It has cost them the lives of countless heroines and heroes to make it this far. At the same time, they know that all that they have gained is in growing jeopardy. They know that the only way to sustain what they and their foremothers and forefathers have built, is to build, with it, something better. They will work for, and hold out for, something better than what they have, for themselves, for their children, and for their children's children...something more, not less democratic; with greater justice, and greater opportunity, not less, for all. Not the unchecked power of bureaucratic dictatorship, of government monopoly, whether in Hitler's version, or in Stalin's; nor the faceless, all-devouring "welfare state" [which winds up in 'state welfare'; "welfare" for the public bureaucracy and its plutocratic private patrons]; nor the attempted re-impositions of dark ages "fundamentalist" theocracies, whether pseudo-Christian, pseudo-Islamic, or pseudo-Hindu, etc., with all their endless bloody inquisitions, nor the guilt-feeding, anti-science, anti-"technology", pro-superstition, pro-dark-ages, '''people are pollution''', Malthusian/Ur-Nazi negative economic growth, negative population growth, humanocidal pseudo-religion of 'Earthism'. The latter are but co-optations by, and covers for, a single strategy: "globalization" or "new world order" as global destruction /- 're-Third-world-ization' of middle classes and democracies; 'multinational-corporation internal-command-economy Private Stalinism'; supranational dictatorship of the petroleum/finance plutocracy, bought, in the society of universal prostitution, by the wholesale buying of governments, legislature, executive, and judiciary; lock, stock, and barrel, disguised as "free trade" and "free market, laissez-faire capitalism", with re-monopolization sold as "deregulation". Note the mounting tide of plutocracy-faction-sponsored, openly genocidal neo-Nazi experiments and dress rehearsals, foundered upon literally sub-human - less than human - ethnic distinctions and exclusivities? That better future: the people of Earth are reading and taking heed of what they have written in their own blood, in this century, now passing, and in centuries past, about what it is not. But what is it? We believe that the time for a true and global consideration of the organon of dialectics has begun. Sophya St. Germain # Karl Seldon Foundation Encyclopedia Dialectica Stars' End, New York, 25 November 1999 C.E./B.U.E. Dialectical Ideography Prescripts Distributed ÇSamizdatÈ by Foundation Encyclopedia Dialectica