The Capital Eventity. The capitalist enterprise, the "individual capital" -- the central 'logical individual', 'logical atom', or 'ontological unit'/'monad' and socio-economic object of contemporary "macro-economic" theories, and the universe of discourse of contemporary "micro-economic" theories -- may be grasped as an eventity which, in a helical self-process, "pulls-in" monetary capital, physical capital, and human capital. This collective-subject [ev]entity does so via capital stock sales and borrowings, plant and equipmental investment, purchases of raw materials, auxiliary materials, and power, plus procurement of employees, owners of various kinds and degrees of 'knowledge-capital' and 'skill-capital'. It designs to bring these "factors of production" into such interactions as "push out" specific, hopefully vendible commodities. In the process of producing these "internalities", it also produces "externalities", the totality of by-product impacts upon its "publics", i.e., that stakeholder/non-stockholder portion of the rest of the anti-physis comprising, in general, its non-employee, non-customer, non-supplier community, surrounding its operations, as well as upon the physis, the biospheric and sub-biospheric natural basis upon and from which society builds itself. This activity provokes a reflux. The capitalist firm receives a "return" -- on itself, to itself - metered, 'ratio-ed' vis-ˆ-vis its self-investment, its capital-value -- the monetary value of its capital asset content. This is a nounic way of describing that reflux. But this return, this 'self-refluxion', is better conceived as a transformed return on [and of] its own activity. Monetary consciousness fixes attention upon the financial quantity of this return. It fixates upon the revenue stream which flows back to the firm from the market in response to the stream of commodities that flows away from the firm to that market. In reality, the life-history of an individual capital, of a capitalist firm, is the rhythmic, pulsing self-refluxive process in which the total [self-]return to [and of] this activity-entity, plus its "accidents", continually determines and continually 're-determines' determines its fate. This total return includes refluxes of its externalities as well as of its 'internalities'. This _, the total profit, gain or loss in net, must thus include the total self-consequences of its impacts upon its publics and its natural basis. The firm's quanto-qualitative total "earnings" include public goodwill and ill-will, lawsuits and awards, strikes and alliances, regulatory legislation and deregulation, regulatory interventions and commendations, and damage or enhancement to its natural basis, in addition to its monetary revenue. They all eventually, on a variety of time-scales, affect that revenue. This total reflux, and its effect upon the firm, involves the qualitative as well as the quantitative aspects of all that returns. The firm's total output thus returns, albeit partially in a transformed, mediated, and usually partially-unrecognized form, and becomes re-input, as part of its total new input, which also includes streams of action flowing to it from other, "external" eventities as well. The total product of the firm, at the end of each natural period of its activity or production, is a total cause whose total effect includes the quality and quantity of the input to the firm's next round of existence _ [self-re-]production-activity. The capitalist firm produces commodities. It also produces, reproduces, and changes itself. It produces '''retarded''' or '''delayed''' causes which affect it, which [later] 'self-re-flex' or 'bend back' and act back upon it itself as well as upon others. The objects receiving its [past] action include itself, its present self, the very subject or agent which initiated those actions, as well as others. It operates now upon inputs which reflect its past outputs, and inputs. It is now producing outputs which, in part, will determine its future inputs. Thus, the 'eventity' known as the capitalist firm also fits well the 'cyclonic', or toroidal-vortical flow-form, paradigm discussed above. The capitalist firm, in each moment of its production - meaning both its production of its commodity output, and its production of itself, i.e., in each moment of its process of existence, of its essential, existential activity -- both consumes itself and produces itself, subtracts from itself and adds to itself. It thus continually transforms itself. It consumes, uses up, aspects of its inputs in producing its outputs. These inputs are not simply from its externity, but are partly 'internal', are partly self-inputs -- are partly itself. They include its total 'body', all of what it is -- its previously earned or purchased financial capital, raw and auxiliary materials, power, plant, equipment, and the portions of their daily lifetimes -- of their very lives -- that the firm has already purchased from its employees. Its output is not just the commodities it sends to market. Its output is also the changed state of its capital -- materials, work-in-process, fixed assets -- employees, community, and natural environment as a result of its use and partial consumption of all of them -- and partial reproduction of all of them -- in its just-previous round of production. These do not all vanish completely into the product /output of that round. The firm's un-owned assets appear among the firm's inputs, alongside the firm's direct, owned assets, its property-content. Many also re-appear, somewhat changed, partially or wholly among its outputs. The firm, by producing, and successfully selling, its nominal product, also reproduces itself, including all of these "elements", these "factors" of its self-reproductive activity. It thereby earns revenue required to repurchase, and thus replace, what it used up. In using its assets, it also alters, converts -- subtracts from /adds to -- those of its assets which persist as parts of its "body" beyond one production round; which thus do not yet require repurchase. The input upon which the firm works is thus, in part, itself -- itself as a whole. The means [of production] with which it works upon that input -- itself -- is also that firm as a whole -- itself. The output which emerges from this action of its means -- itself -- upon its input -- itself -- is also, in part, itself as a whole, but changed as a result, quantitatively and qualitatively. Again, because of the "squaring" operation it involves, the formula below describes only the "pure-qualitative" or "_" gain: ontological change in asset-category composition or content: itself "of" itself = itself[itself] = itself '''_''' itself = itself_ = itself + _[itself] itself, or, making explicit the relative timing or epochal order aspects of this process -- itself_[itself_] = ~itself_ = itself_ '''_''' itself_ = itself__ = itself_ + _[itself_] = itself____ itself_. We elide, for now, the moment of the 'other-determination' of the firm's existence. We focus on its moment of 'self-determination'. We ignore the independent impacts of its 'externity' -- its environment of other agents, i.e., of other subjects, collective or individual, including competing firms. In expanded self-reproduction, a firm "consumes" or "changes" the totality of its assets in ways which do not merely deplete them, but which, in the net, also "develop", enhance, or expand them, quantitatively, and often, crucially, qualitatively as well -- assets 'inter-operating', or 'operating among' themselves = the function: assets "of" assets = assets[assets] = ~assets = assets '''_''' assets = assets_ = assets + _[assets] assets, or, with explicit epoch-tagging and 'epoch-counting' via the symbol _ -- assets_[assets_] = assets_ '''_''' assets_ = assets__ = assets_ + _[assets_] = assets_______ assets_, wherein '_[_]' denotes 'pure-qualitative, ontic change of [_]'; wherein 'assets' describes the qualitative ontology of all of the human and non-human factors of production "owned" by or constituting that firm at the beginning of one "round" of production, at time-index value _, where assets__, or assets_ + _[assets_], or assets____ describes that same [sub-]totality, the ontic "content" of the firm, at the end of that round of production, at time-index value ____, and '_[assets_]', 'ontic change-in assets', denotes the ontic, qualitative aspects of the "total self-consequences profit" described above. I.e., _[assets_] denotes the ontic, qualitative increment to assets induced by the mutual interaction, that is, the intra-action, as well as by the self-interaction, of this 'assets meta-ÇarithmosÈ' or 'assets meta-organism' as it was at the start of the production round, at _, during that round of this [self-re-]production, of duration __. In contrast, the "change-in-assets" denoted by '_Assets_' describes the changes in ontic quality of these assets as well as their changes in quantity, during the time-period from _ to ____: _Assets_ _ Assets____ _ Assets_. This "increment" can be negative in the net, implying net loss, and consequent qualitative and quantitative self-contraction of assets. It can be positive, implying net profitability, quantitative and qualitative/ontological self-expansion of assets. It can even, at one extreme, approach near-zero change in the quantities of the assets, with non-zero change in the qualities of assets, or, at the opposite extreme, near-zero change in the qualities of the assets, with non-zero change in their quantities. But, typically, changes in qualities and changes in quantities of assets go hand in hand. Thus, the ongoing self-refluxive process that is the capitalist firm can, in the net, be either one of expanded or contracted self-reproduction. But it can hardly for long be one of both qualitative and 0 quantitative change -- a linear equilibrium, a 'Boolean' process of "simple reproduction" -- x_2 _ x_, _x_ _ , and x ___ _ x _, _x_ _ , wherein we have re-symbolized 'assets_' by 'x_', and Assets_ by x_. The "equilibrium" of "simple reproduction" is not "stable" -- is not an "attractor", but a "repellor" -- x_2 ( x_, _x_ ( ; x ___ ( x _, _x_ ( . Changes in quantitative attributes of Assets_ include changes in monetary value, as well as changes of quantity in non-monetary, including scale-of-operations, volumetric, attributes of the firm. Quality changes include emergence of new skills in the firm's workforce, installation of new technology in plant and equipment, and emergence of new features, e.g., design enhancements, in succeeding generations of the products previously offered for sale, as well as of innovations in the firm's product-line -- development of altogether new kinds of products. They also include "wear and tear" depreciation of the firm's assets - plant, equipment, and people -- i.e., of its owned assets and non-owned assets alike. The capitalist firm, the individual capital itself, forms part of the input to each round of its production, together with other means of production drawn into it from outside of itself. That individual capital, as a whole, is also the processor which processes the totality of those inputs, in producing its total output. That individual capital, as a whole, also forms part of the output from each round of its production, together with other products, which may leave it and accrue to the rest of the world. But what accrues from it to the rest of the world also determines, in part, what the rest of the world sends back to it, as its next-periods' input, including, but not limited to, its monetary revenues. The capitalist firm is thus, in part, a self-producer, a self-changer. It is a self-reflexive process and a self-refluxive process. The capitalist firm is a self-processor. An eventity. A toroidal-vortical flow-form. If the outputs of the capitalist enterprise are well-received, received as 'goods', its reflux may promote its quanto-qualitative expansion. It may grow, and prosper. If its outputs are received as damage, as toxins, as 'bads', its reflux may poison it in turn, subtract from its substance, and send it into a waning spiral of contracted self-reproduction eventuating in its self-liquidation, its extinguishment, its dis-existence. Indeed, a daily-life-scale example of the meaning of 'meta-evolution' versus that of 'mere evolution' in our usage herein can be exemplified via the 'meta-modeling' of this key object of micro-economic theory and practice, this entity or 'eventity' known as the capitalist firm, regarded within such a scale and partitioning wherein it constitutes a 'meta-dynamical meta-system' -- a sequence of distinct dynamical system-identities "bridged together" or 'meta-continuously connected' by 'self-bifurcation singularities', or 'metafinite transitions'. 'Evolution' of a Firm. Take the Chart Of Accounts of such a system-firm during a given time-period as an 'accounting-model' of that firm/system. By the 'evolution' of the firm, we mean its 'accounts-balances trajectory in accounts-balances state-space'. This potential evolution may be described as the "flow" or "vector-field" of the "purely-quantitative" changes, through time, of those accounts' balances, driven by transactions -- changes in their "pure quantitative" [currency-unit dimensioned, e.g., dollar-denominated], credit and debit contents as 'state' of the accounts of that firm, for those accounts that are 'extant' -- i.e., that "exist" within the given, fixed '[meta-]state' of its Chart Of Accounts, and that are 'populated' with debits and credits. These accounts collectively define, for this view, the 'state-space' of the firm, and their balances-contents at any given moment of time within the time-period in question collectively define the 'state' of this firm as a 'dynamical system' as of that moment, the coordinates of its position in its accounts-balances state-space as of that moment, via balances as "state-variables" -- as "functions of time". In particular, expansion/contraction of their quantitative, monetary-value-unit-ed "retained earnings" content may serve to index net cumulation/dis-cumulation of the "stocks", the net capital-assets-content, or "stockholder value" ["capital-value"] of this firm. 'Meta-Evolution' of a Firm. The 'meta-system' that is the firm passes 'meta-dynamically' from one system-identity or 'meta-state' to a new, next system-identity or 'meta-state' whenever its Chart Of Accounts "mutates". Adjunction of [typically a whole spate of] new accounts to the Chart Of Accounts occurs. 'Extinction' of some former accounts may also be observed to occur. 'Hybridization' of other former accounts via their definitional adjustment relative to the emergent existence/definitions of some of that increment of new accounts may also be observed. These latter types of change constitute the 'meta-evolution' of the firm as 'meta-system', e.g., the 'quanto-qualitative' expansion of the operations of a 'quanto-qualitatively growing' firm. These changes in the firm's Chart Of Accounts are largely 'evolute', cumulative changes in its content and/or "structure", not 'convolute', erasive ones [meaning total disappearances of all prior accounts/structures]. The 'meta-finite' character of such changes in the ['meta-state' of the] predecessor Chart Of Accounts can be seen via this consideration: No amount of finite quantitative change in the credit/debit contents/balances of any number of accounts in the old ['meta-state' of the] Chart Of Accounts can amount to or attain or represent the new form or structure of the successor Chart Of Accounts, let alone its incremental quantitative content. Nor can any "infinite" quantitative change concretely specify the successor 'meta-state', a 'meta-state' which is finite in content/structure, although it is also 'qualitatively' ['ontologically'] expanded vis-ˆ-vis its predecessor 'meta-state' -- the latter being also finite, and 'meta-finite' vis-ˆ-vis its predecessors. A growing firm's Chart Of Accounts can be seen as an existential assertion respecting the content of its operations, i.e., as an ontology. The accounts are the 'ontos'. Expansions of its Chart Of Accounts mirror an expansion in firm's practical 'ontology', results of its quanto-qualitative 'self-complexification', as of its "allo-complexification" in response to external forces impinging from its total, econo-politico-socio-ecological-climatological-... environment. Indeed, with accounts assigned as 'ontos', the ZU ideography can be applied to describe the 'quanto-qualitative' 'evolution' and 'meta-evolution' of firms as 'meta'-systems, by 'meta-modeling' of both the changing quantitative, debit and credit content of their accounts, and the changing qualitative / ontological content of their Charts Of Accounts, as per the Quanto-Qualitative Computation section of Dialectical Ideography, Part III. A 'Meta-evolution' model of the 'sub-chart(s) of sub-accounts' of such a Chart Of Accounts would constitute the '2nd-level meta-model', were the firm taken as 'first level' or primary universe of discourse, or the 'n_1st level meta-model', denoted {U_}, were 2 _ n ( N taken as denoting the level of the firm-eventity with respect to some whole-cosmos-model as 'first level' model, per a given partition-principle, denoted { ¶ }, for these nested universes of discourse. A 'meta-evolution' model of the 'sub-sub-chart(s) of sub-sub-accounts' of the 'meta-evolving' Chart Of Accounts then constitutes the 'n_2nd level', {U_} 'meta-model', or the 'third-level meta-model' relative to the individual firm taken as 'first-level' or primary universe of discourse. And so on. If we adopt f as our label for the individual firm being modeled, then the ZU 'meta-model' for the quantitative evolution and quanto-qualitative 'meta-evolution' of f looks like this, where ( ) enclose 'quantifiers', [ ] 'qualifiers', and 'quanto-qualifiers' -- nfU___= _____j_______nf__j(_)( nf_j _ nf__j(_)( nf_j( $__ = $___j_______(nf__j(_) __nf__j(_))( [nfj] = __ ___j___________[$]( ( nfBalancej(_) )( [nfj] = $___j___________nfBalancej(_)( nfj = $( nfBalance1(__( nf1 _ $( nfBalance2(__( nf2 _ $( nfBalance3(__( nf3 _ _____ -- wherein (1) $ denotes the 'quantifiable' 'metrical qualifier' for the currency unit -- here the $US -- the unit of ["continuous"] measure in which the account-balance 'quantifiers' are expressed; wherein (2) nfj denotes the 'metrically-qualifiable' 'ontological unit-qualifier' or 'ontic qualifier' of the jth account, as 'onto' or ontological category, in the 'meta-state' of the Chart Of Accounts as of _, and wherein (3) nf__j(_) denotes the period-cumulative credits to the jth account, and nf__j(_) the period-cumulative debits to that same account, as of "time" _, so that nfU__denotes the 'state' of the firm as the "set" or 'non-amalgamative sum' of the balances of all accounts extant and "populated" in the firm's Chart Of Accounts 'meta-state' as of _. Accounts not yet extant in the Chart of Accounts as of _ -- that is, accounts which belong to a later-manifesting 'meta-state' of the firm, or which, though possible for the firm in question at _, do not actualize -- are treated as having $0 balances, so that they accrue to , denoting the 'quanto-qualitative existential zero' which denotes the 'totum' of all ontological qualities, categories, or 'ontos' [and of their 'unmanifest quantities'] that are non-extant or 'unmanifest' at _, viz. -- $ ( 0 ( nf______ _ . Also, is 'Hridayamic' or 'all-absorptive', and 'additively idempotent' as well, i.e. -- z ( Z ( z ( = , and, ___ = . 'Extinct' accounts, formerly manifested during previous values of _, but not conserved, not carried forward -- no longer 'extant' in the Chart Of Accounts corresponding to the current value of _ -- are also treated as having $0 balances, and thus as also accreting to . The value is 'omittable' because it is an "additive identity" for ZU arithmetic: _ k _ k. The k meta-numbers are similar to the k, except that the k are "additively idempotent", like Boolean values, i.e., are 'unquantifiable', 'un-add-able', or 'non-additive' -- [ k _ k _ k ] -- whereas the k are 'quantifiable' or 'add-able' -- [ k _ k _ 2k ]. The nf_(j are 'bifurcation-functions' of control-parameter arguments -- (1) of other nf_(k(____i), k ( j, [already manifested in past epochs ____i]; (2) of their own past values, _f_(j(____i), for all levels of their [sub-]ontos, _ ( N, and; (3) of the past values of external [market, regulatory, climatic, etc.] parameters, quantifiers of the [sub-]ontos of all levels of other, (f, interacting, 'co-meta-evolving' meta-systems: nf_(j(_) _ nf_(j( { _f_(k(____i) }|k =_1, 2____; _ ( N, { p(f_m(____i)|m =_1, 2___; n ­ p ( N }, __(_i_(_N_). The 2_ potential new accounts that accrue at every transition from _ to ____1, allowing, e.g., up to every former account splitting into 2, may be dearth for some actual cases [and for some actual accountants!], surfeit for others. In both Q and U, units of unequal subscript or 'index' are "inhomogeneous" or 'qualitatively heterogeneous', so that they are also 'non-amalgamative', or 'mutually-orthogonal' in addition. That is, k ( m ( k m & k m, like the proverbial "apples and oranges", so that k _ m does not "reduce" to some x, and k _ m does not "reduce" to some x. Thus, for example, in this model of the 'meta-dynamics' of a firm, account balances are kept separate; are not "lumped together", just as distinct unit-vector "factors" or 'qualifiers' block "amalgamation" of "vector magnitudes" belonging to different "dimensions"/"directions". The symbol ZU denotes that arithmetical Rules-System which includes ZU, the "set" or 'space' of all b "such that" ["|"] all a, b, c are "elements of" ["("] the Integers, Z -- or, for short, | a, b, c_( Z -- just as ZQ denotes the Rules-System for the "set" or 'space' ZQ of all b | a, b, c_( Z: ZU ( { b | a, b, c__( Z }_ (_ { }; ZQ _ (__ {}. In the ZU arithmetic, minus signs can "travel around" from a to b to c, without changing a meta-number's value, i.e., additive inverses, multiplicative inverses, negative integer powers, and negative integer subscripts all coincide in operatorial meaning and effect, so that: __k_1 _ __k_1 _ __k_1 _ /__k_1 _ __k_1/, and therefore -- _k _ _k _ _k_1 _ _k_1 _ _k/ _ /_k _ _k _ k _ . Thus each term of the nfU_ summation ___j___________ nf__j(_)(_j _ nf__j(_)(_j takes a "balance", a difference of credits and debits, namely: ( nf__j(_) _ nf__j(_) )(j. We have focused so far on the single firm as "the capital eventity" -- on the local, the micro-economic, the individual capital scale. What of "the capital eventity" on the global, the macro-economic scale? What of the total, worldwide capital meta-system as that of "the production of commodities by means of commodities"12; of the production [& reproduction] of capital by means of capital? What of the 'quanto-qualitatively' self-expanding, "extended scale" self-re-production of capital, autocatalytically self-growing in both the quantity of capital value and of physical fixed capital extant, and in the quality or ontology of the new, unprecedented, but likewise in the to-the-new-adjusted kinds of old capital included in that "capital accumulation", that quanto-qualitative 'capital cumulum', or 'meta-social' cumulum, with global human society as a whole taking the form of the capital eventity? Planet wide Market 'Macro-Meta-Dynamics' -- 'Toroidal-Vortical' Model of Global Social Reproduction. Consideration of the capital-process at the "micro-economic" scale, that of the individual capital or firm, calls also for regress to the "macro-economic" scale, that of the "world market", as well. That scale, of globalized capital, is also that of the global self-reproduction of human society, mediated by the capital mechanism. It is that of the combined biological and politico-economic/cultural reproduction of the human civilization, or of the planetized humanity, of Earth. The focus for this scale should be that of the true unit of reproduction. The reproductive unit for the planetary human species is not the biological individual, nor the nation-state, nor even human society planet-wide. It is that global society together with the natural basis upon which it is founded, and upon whose reproduction its reproduction depends -- at minimum, the global biosphere. Models of global social reproduction must therefore encompass not just the planetary macro-economy, but the planet's dynamical econo-ecology as well. They must be anthropological-psychological, political-economic, econo-ecological models. This is not the place for a full discussion of such models. To introduce their formulation in the language of dialectical ideography would require a book of its own. We will return to these models in this book, with somewhat greater amplitude, in the section on Higher Level Applications. Our task here is to: (1) indicate how the 'toroidal-vortex paradigm' applies to the phenomenology of global social reproduction; (2) construct and name some key concepts that we will apply to this meta-scale of phenomena and to this epoch of cosmological meta-evolution, and; (3) use the example of the phenomena of this meta-scale to work out a major augmentation of our fundamental meta-evolution equation, our contender for a trans-Leibnizian, meta-dynamical version of Leibniz' Characteristica Universalis. The self-refluxive system paradigm, the toroidal vortex model, fits the phenomenology of the macroeconomic scale of the capital autocatalysis no less than it fits that of the microeconomic scale of the individual firm or household. The world economy likens to a multi-dimensional dynamical fractal, a macro eddy composed of many micro eddies, forming a self-enriching 'cumulum' containing a whole spectrum of scales of magnitude. As with the individual capital, so with the totality of capital: the self-reproduction of capital involves the self-operation of the capital eventity; the self-reflux, the flowing back to self, i.e., the self-re-input of previous self-output. In the process of global social reproduction, mediated by the capital mechanism, the capitalized means of production, subjective vs. objective, human capital/labor-power vs. artefactual capital [meaning raw materials, auxiliary materials, energy, financial capital/securities, objectified information capital and knowledge capital] -- all products of previous capital-production -- form the major input to each new whorl of capital-[re]production. Other input includes the changing state of potential of the natural basis of society and of the social basis to support that next round of reproduction. The latter potential may vary due to exo-noospheric and even exo-biospheric causes -- changes in climate due to Milankovitch and other insolation effects; exolithic impacts; volcanic eruptions, earthquakes, tectonodynamic or "continental drift" events; as well as due to plague/pandemic propagations, neglect of public social infrastructure, etc. Expanded self-reproduction of capital means the repositing, at the end of the current round of reproduction, of an equivalent of the capital-value laid out or input at its start, plus an increment of profit, retainable earnings, capitalized surplus product, etc., all in those physical, etc., forms suitable for further expanded reproduction. The total input to each current round of capital reproduction, described above, is input to what is in fact a part of the social reproduction processor itself, qua the global system of the [attempted] expanded self-reproduction of capital. That total system of 'society-[re]production' is thus also the processor which processes the totality of those inputs, in producing this system's total output. That global process of capital-reproduction, as a whole, also forms a main output of each round of its production, together with its other products, which leave it and accrue to the rest of nature, especially to the planetary biosphere. What accrues from it to that biosphere also determines, in part, what that biosphere sends back at it, as part of its next input, for the next annual round of global social reproduction, especially in the form of the potential of the natural basis of society to support further social reproduction. If those outputs to the biosphere, in the net, build-up and improve extra-human nature, add to its potential to support further human production, then future expanded social reproduction is made more likely. If the net effect of those outputs is to undermine that potential, then contracted social reproduction, even social extinction, may result. The global, social, capital-process is thus, in part, self-producer, and self-transformer. This capital-process is a self-reflexive process. Its action of production bends back upon itself and acts back upon itself, through the medium of its past output, which ever becomes its present input. It is a self-refluxive process, in that its outflow flows back to itself, as next inflow. It is a self-processor, an eventity, in that it cannot statically 'be' if it is to 'endure' or continue to exist, to 'extend' its body any further along the temporal, "4th", dimension. To continue to 'be' in this sense, it must 'do' its essential activity of self-reproduction, or continual 'production again of itself'. If production stops, eating, drinking, heating, and living stops. Society dies. If its society dies, so does capital. This process is toroidal vortex-like. What it pulls in at one end, it later emits, with modification, at the other end. It then pulls that outflow and/or its consequences back around and inflows it/them again. 'It' as totality-present takes in its own totality-past, and works upon [that past] itself, applies itself to [that past] itself. Its totality-present processes that intake - i.e., its [past] self -- then outputs that totality, __ gain/loss, again. Society is [part of] the 'raw material', society is the means of production, and society as a whole is [part of] the product of this global social reproduction. The generalized language-model for this process, of which the social reproduction process is a special case, is: processor[input] _ output, denoting that processor, acting upon input, produces output. Said better, the "product" of the "interaction" of processor and input is output. The conventional interpretation of this paradigm has it that these three terms are completely distinct, as in: means-of-production[raw-material] _ product. What is unusual about the Reflexivity Paradigm of Dialectical Ideography is that it sees the aspect in which only output is qualitatively distinct from processor and input. It sees processor and input as, in that aspect, forming an auto-dyad - two as one, one as two. It perceives an intra-dual but unitary eventity, notated doubly merely so as to 'explicitize' the internal tension of its 'verbic' aspect and its 'nounic' aspect, its 'subject' aspect and its 'object' aspect. This in-tension would otherwise be invisible, merely implicit, in a sequence of singular-occurrence, "first degree", "linear" symbols, viz., society _ society', or, society_ _ society____, so we instead employ a nonlinear, quadratic, 2nd degree notational self-doubling to denote this self-antithesis or ontological, onto-dynamical self-duality: society[society] _ society' _ _society _ society _ _[society]; society' society. The appropriate euphemism or 'pronoun' for global Terran human society today - since its reproduction is increasingly mediated entirely through the capital-relationship, comprising financial investment, profit, and the private exchange of wage and salary monies [also capital] for skill-based personal activity -- is capital_: capital_[capital_] _______ capital____ _ capital_ _ _[capital_] = capital_2 capital_. These partially phonetic formulae contain a 'formulaic picture' of the toroidal-vortical process. The medium, or ontological, onto-dynamical 'cumulum', which creates and sustains a toroidal vortical meta-dynamic as a self-mediation of its own bildung, is ingredient in, contained in all three moments of that process - the input, the input-transformer, and the output. In our present example, the self-developing medium or 'cumulum' is the human population together with its 'artefactual infrastructure' of "humanized nature" or "objectified humanity", meta-socially forming and self-re-forming; the self-globalizing Terran human society-process -- society...[society...] _ society.... -- wherein the "ellipsis dots" superscript denotes ever escalating numbers of "primes", '' '. An "ellipsis dots" subscript, denoting ever escalating values of _, would work here just as well in the above. We might imagine this "self-duality" as one which, during each epoch or round of self-transformation, ripens or matures, from a barely perceptible self-split at the beginning, to a full-blown, climactic one at its end; one that yields dramatic ontic, qualitative change, creating a categorically distinct, new epoch of the life-history of the eventity. This new epoch, once posited, thence begins its own, qualitatively new form of self-splitting: society_ _ society_[society_] _ society_ "of" society_ _ society_ "times" society_ _ _society_ _ society_ "squared" _ society_2 _ society___ _ society___ _[society_] society_. Notice again that, here, we are not dealing with "simple reproduction", with a "zero-net-change" "linear equilibrium" dynamic, whose "logic" is x2 = x. We are dealing, quantitatively and qualitatively, with either an expanded or a contracted self-reproduction, in which the ontology-cumulum 'society', operating upon itself, does return simply x, but also returns, in addition, an increment, a 'social profit'. This 'social profit' or 'socio-mass increment' is either 'positive' in the case of expanded self-production, of self-reproduction on an extended scale, or 'negative' in the case of contracted social reproduction. Substituting for the phonogramic symbol 'society' the (borrowed-from-the-phonetic-alphabet) ideographic symbol 'x', we obtain -- x _ _[x] ____ x[x] _ x _ x _ x_x _ xx _ x2 _ [x _ _x]; and _x x. While the x component of what 'x of x' returns is of like ontic quality to that of the x that was input, the increment, _x is of different quality than that input. The quantitative meaning of expanded social self-production is more of the same, more of the social surplus product in terms of the same kinds or ontos of products that also existed before, in x. The qualitative, ontological content of this 'pure-qualitative' incremental term, _x, denotes, in expanded social self-reproduction, the element of "surprise", the factor of "innovations", advances in social productivity, i.e., in the level of the social forces of [social self-re-]production, hence, in social reproductivity; emergence of new science, new knowledge, hence discovery of new natural resources; births of new subjective capacities, new skills, new kinds of human capital and labor-power; appearance of novel products/services and production technologies; mutation of social institutions, that is, of the social relationships of [social self-re-]production. Our model for expanded reproduction is not x2 _ x, nor even x2 ( x, restricted to x2 x, but x2 x. Global social reproduction in the form of the self-process of capital did not arise ex nihilo. Its existence presupposes a protracted sequence of prior social formations. These formations were both initially, temporarily self-reproductive and eventually self-destructive or self-superseding. They were "self-organizing systems" that self-consistently turned into 'self-dis-organizing systems'. Adequate modeling of the capital eventity requires, we hold, a model of human history. This model must encompass, for past time, not only the deterministic -- self-determined or essence-determined -- evolution and meta-evolution of those formations, but their accidents, and the choices among alternatives by their human[oid] populations as well. An overview of this 'model of history', encompassing the capital formation, and its predecessors, from the emergence of the biological or 'genotypological' human species on Earth, is addressed as part of the notational experiment which follows. Notational Experiment. Let's assign, to our meta-system variable m, the value humanity. Let's describe the internal, 'second-level' meta-evolution of this humanity, the sequence of its social formations, including global capital and its predecessors, as a succession of qualitatively different human species. They are different not so much 'genome-ically', but 'memenome-ically'; culturally, anthropologically, especially in terms of their modes of social reproduction. Each such 'instauration' of humanity is indexed and distinguished using consecutive values of an ordinal subscript, _. Hypothesis: _Starting from the last Ice Age, we find a blood-affinity, kinship-based, tribal Terran human species characterized by predation of plants and animals, "hunting and gathering". "Success" -- population expansion, hence relative densification and 'self-envelopment' -- of this predation of other multicellular organisms yields self-predation or self-hunting and self-gathering. Hunting of humans by humans arises. I.e., cannibalism and war appear. Hunting rises to nomadic herding, then to sedentary corralling, animal husbandry, and deliberate planting. Domestication of other multicellular and cellular organisms refluxes to the self-domestication of humans. Neolithic, agricultural humanities emerge, surrounded by hinterlands of predatory humanities. Self-herding unfolds as productivity rises sufficiently to sustain captives with a sufficient net gain. Practices of retaining prisoners of war alive for their labor-power appear. Social formations founded on "servile relations", herding and domestication of other human beings treated as domestic "draft animals", i.e., slavery, serfdom, etc., emerge alongside the preceding formations. Barter between tribes, C_C', appears, alternating with feuding or war. Commodities C with specific physical characteristics sort-out as ÇnumerairesÈ or Money-commodities, M. Monetized exchange emerges alongside continued/money-modified barter. Inversions of the C_M_C' pattern of monetary exchange, to M_C_M', inaugurate mercantile capital. Loaning of specie, M_M', inaugurates usury capital. Capitalist humanity begins to emerge . Our generic formula for all of these 'human[oid]-social phase transitions', as for others not yet mentioned, is: humanity___ _ humanity_[humanity_] _ humanity_ "of" humanity_ _ humanity_ "times" humanity_ _ _humanity_ _ humanity_2 _ humanity___[humanity_] = humanity____ humanity_. A similar - "homeomorphic" -- model can be formulated in terms of a distinction between the "physis", or "growth dynamic" of pre-human and extra-human nature on the one hand, and, on the other hand, the newer, emergent 'neo-physis' of humankind, centered in the geographical region(s) of human[ized] nature, that is, of subjective/subjectified and objectified human nature, those patches of emergent noosphere within the biosphere, which the ancient Greeks termed the "anti-physis": anti-physis___ _ anti-physis_[anti-physis_] _ anti-physis_ "of" anti-physis_ _ _anti-physis_ _ anti-physis_2 _ anti-physis_ _ _[anti-physis_] _ anti-physis___ anti-physis_. By 'humanity' here we mean the developing [sub-]totality of humankind including all of its artefacts, all of its self-objectifications. That is, we mean the human social formation entire -- with all of its social-endosymbiotic, instrumental, and even effluent accouterments. Indeed, the entire character of the people themselves should be seen as, in part, an artefact -- their own artefact. An artisan who laboriously etches something new upon the outer world, also, simultaneously etches inward -- conceptually, emotionally, and bodily changing the embodied self of that artisan. Sculpting the material of the external world, human sculptors also sculpt the material of themselves, humanity. Reshaping the outer and exo-somatic world, they also reshape their somatic and inner worlds. Transforming extra-human Nature, they also transform their own nature, human-nature. Human [pre-] history is the historical labor of the self-production of humanity, of the self-construction of the human species as a 'trans-biological' onto, a meta-genomic, 'meme-nomic' meta--species. The labor of history, the labor of human history and of its pre-history, is that of the building and ÇbildungÈ of humanity; the labor of giving birth to humanity by pre-humanity -- by both proto-humanity and sub-humanity alike. Glorious fruition and hideous abortion are both still possible ends for Terran human kind. Thus, '_[humanity_]' includes the effects of conqueror upon conquered, and of conquered upon conqueror. It includes the subjective consequences of daily work/life -- the wounds, the healings, and the scars as well as the fruits of the mutually beneficial cooperations -- all of it. Another homeomorphism is framed via the term "noosphere", used by Vernadsky and Chardin to name the 'concentric' layer of "knowing" meta-socio-matter lately 'nesting' or enveloping and 'environmenting' the biosphere, the earlier envelope, of bio-matter [prokaryotic and eukaryotic uni-cellular onto-mass, meta-zoan / meta-phytan onto-mass, animal-society socio-onto-mass, plus their hybrids'] on whose 'shoulders' the noosphere is rising: noosphere___ _ noosphere_[noosphere_] _ noosphere_ "of" noosphere_ _ _noosphere_ _ noosphere_2 _ noosphere_ _ _[noosphere_] _ noosphere___ noosphere_. This meta-evolution of humanity, of it as "[anti-]physis", as "noosphere", is what we mean by the self-changing self-evolution of the "human species", or of 'human nature(s)', as a succession of quality-distinct social species: human-nature___ _ human-nature_[human-nature_] _ human-nature_ "of" human-nature_ _ human-nature_ "times" human-nature_ _ human-nature_ "_" human-nature_ _ human-nature_ "_" human-nature_ _ _human-nature_ _ human-nature_2 _ human-nature_ _ _[human-nature_] _ human-nature___ human-nature_, whereby; human-nature0 _ human-nature1_ human-nature2_ human-nature3_ human-nature4___... , or; sociocultural-species_ _ sociocultural-species_ _ sociocultural-species_ _ .... By "human-nature", or by its synonym as used here, "anti-physis", we mean that objective, empirically observable, self-expanding "patch" of "humanity-transformed nature" emerging initially within the biosphere. This includes the human population plus all the "objective infrastructure" produced by that collective subjectivity/activity. It includes all artefacts of the activity of those subjects. Originally upwelling locally, from Earth's biosphere, this zone of "human[ized] nature" has gradually grown global, spreading to engulf the entire surface of this planet, inaugurating a whole new layer of its own, the incipient global noosphere. An eventity, as a mode-of-action entity, has both object-like or "object-ive", and subject-like or "subject-ive" aspects. An eventity is a [sub-]hol or [sub-]totality, a unity of these [inter]twin[n][ed] aspects. Their duality is an indivi-duality, an 'indivisible duality'. It is "indivisible" or "uncuttable" in that the subjective aspect cannot be severed from the objective aspect without the disappearance, or mitosis, of both. The "south" polarity of a bar magnet is not severed from its "north" polarity by cutting the bar into two. On the contrary, such cutting induces a mitosis into two sub-wholes, into two new whole bar magnets, each with both an "N" and an "S" pole at opposite ends. Indivi-duality is internal-division-duality, intra-duality, intro-duality, endo-duality, or immanent duality, not the probably more familiar inter-duality or exo-duality of duals conceived as separable, mutually alien, and mutually external. The name of -- the noun denoting -- an individual eventity can properly fulfill 3 kinds of roles: (1) that of a "subject" in the grammatical sense -- denoting an initiator of action upon, an actor on, other objects, or, reflexively, upon itself as object; (2) that of a grammatical "object", a recipient of action from other subjects, or from itself as subject; (3) that of the verb denoting that "action" which is the essential, defining operation, process, or mode of doing, mode of self-doing, mode of self-reproduction/self-perpetuation of that eventity. Contemplating the construction of a model of history for the history of humanity brings up the fact that humanity is not the totality, the whole of nature, but only a part, a sub-totality, a sub-whole within that more encompassing whole. Humanity is not even an 'autarkic', fully-"autonomous" sub-totality within that totality; is not a universe-unto-itself. Human history is driven -- affected and effected -- by external causes as well as by internal causes. Human history is not entirely causa sui. The causa essendi of human history include causa transiens as well as causa immanens. Humanity's history is the joint product of self-activity and other-activity, of humanity's own activity upon itself, and of the activity of other agencies, of other subjects, of other eventities, upon humanity. The intra-action of humanity within itself in conjunction with the inter-action of humanity with the rest of nature is what generates that history -- our history. Our earlier formulations describe only the action of an x_ upon itself, where x_ denotes the state of activity of an eventity x during the _th instar of its meta-evolution, and where _ denotes an ordinal whole number. For the purposes of the present discussion, let's assign x_ (_ humanity_: x_ _ _[x_] _ x_[x_] _ _ x________ ______ x_2 = [x_ _ _x_] x_. Our model of history should take into account also the rest of the totality, the remainder of the universe - namely _ non-humanity_, the 'synchronic complement' of x___ humanity_ -- and the interaction-products it adds to the universe by its action upon humanity, as well as the interaction products which humanity adds to the universe by its action upon 'non-humanity'. In other words, our model must describe the action of the totality, including humanity, denoted T_, upon humanity, x_. At least a trichotomy of T_ into , x_, and a non-empty boundary eventity, ¶_, would be more coherent and consistent than a dichotomy, as we shall see. But if, for now, we partition T_ as the dichotomy ''humanity' '_' its 'synchronic complement', then T_____ [ x_ _ ], and x_ . Thus: x_ _ [ T_ _ ], and: _ [ T_ _ x_ ]. Our "Universal Characteristic" then becomes, from the point of view of the part x_ rather than of the totality: x____ + _[; x_] _ [[ T_ ][ T_____]] _ [ [ x_ _ ][ x_ ] ] _ [ x___ _x_ _ _[; x__] ] x_. Using our "syncopated rhetorical algebra", and assigning this x_ to human-nature_, we obtain: human-nature____ _ _[extra-human-nature_; human-nature_] _ totality_[human-nature_] _ hol_[human-nature_] _ universe_[human-nature_] _ nature_[human-nature_] _ whole-cosmos_[human-nature_] _ whole-cosmos_[whole-cosmos_ _ extra-human-nature_] ______T_[T_ __]_______T_[x_ ]____ [x_ _ ][x_] _ x____ _ _[; x_] x_, wherein we have to subtract the term denoting the 'complementary entity', 'extra-human-nature_', from the term denoting the totality, whole-cosmos_, if we want only terms involving human-nature_ to appear -- to be tracked -- per the 'aufheben evolute product' rule of the dialectical arithmetic described herein. This rule, to be detailed below, involves additive idempotency or 'non-addibility' for pure-ontic values of identical onto-type: x_ __ x_ ___ x_, not 2x_. Indeed, nx_ _ 2x_ _ 1x_ _ x_ [(n ( N]. This is rather like (___(___( and _((___(. Symbols like x_ do not denote "transfinite" values, in the sense of infinite quantities, nor do they belong to the realm of finite 'pure-quantitative' differences. They denote 'metafinite' values; qualitative finite differences. If we want to track the meta-evolution not just of the part, human-nature_, but of the totality, 'totality_______ [ human-nature_ _ extra-human-nature__]', in terms of our classification or partition of it into the two complementary parts, 'human-nature_' and 'extra-human-nature_', then no such subtracting-out of the synchronic complement is required, and we have: T____ _ _[T_]__________ T_[T_]________________ T_2_________________ T_______T_ T_. In the 'syncopated rhetorical equations' above, we employ rules of a 'non-Pythagorean arithmetic'. This arithmetic involves a partially 'genealogical', 'cumulative', or 'evolute' rule of '''multiplication''', an 'aufheben' product rule for the '''multiplication''' or "proliferation" of ontological types or qualities. This rule prescribes a "product" or result of the 'multiplicative' interaction between the denotations of two symbols which exhibits the 'ancestry' or source of that result as a part of that result, along with another part which qualitatively exceeds, augments, or increments that ancestry. The 'meta-numbers' or 'dialectors' of this arithmetic, denoted below by a, b, c, & d, when '''multiplied''', i.e., when 'interacting with' / 'operating upon' one another or themselves, behave as follows: a _ b _ a __b _ ab _ a[ b ] _ a 'of' b _ b _ _[ a; b ] _ b _ c; wherein b c, so b b _ c. The corollary of this behavior-rule, in the special case where a _ b, is: a _ a _ a __a _ a[ a ] _ a 'of' a __aa _ a2 _ a _ _[ a; a ] _ a _ _[ a ] _ a _ _a _ a _ d; a d. Note also that '''addition''', in this arithmetic, is the function which forms an aggregate or 'set' without any internal interaction or '''multiplication''' among the members of that aggregate: a _ b _ {a, b}. Thus, if a _ b, then: _[a, b] _ a _ b _ a _ a _ {a, a} _ {a} _ _a. That is, for this onto-logical arithmetic, the possible presence or present existence of any number - one or more -- of eventities of a given ontological type or quality, call it , is asserted by writing '' or '_'. The expression ' _ ' is, in this semantic context, but a redundant, prolix equivalent of just '', for which just '' can be substituted. The rule that _ _ is also termed that of "additive idempotency". The ontic, dialectical arithmetics share this rule with Boolean arithmetics. Note also that the '''sums''' above, such as 'b _ c' or '[ human-nature_ _ extra-human-nature__]', are also 'sets', or '''inhomogeneous sums''', that is, 'qualitatively heterogeneous' and therefore ''non-amalgamative'' sums. Just so, the general 'complex number' ar _ bri, or the 'Real Cartesian vector' 5x _ 3y _ 11z, or the oft-cited '''apples + oranges''' represent 'multi-unit-of-measurement additions' or 'poly-qualinomial sums' which do not reduce to a single, "purely-quantitative", cardinal number. Carrying out the '''multiplications''' indicated in the equation-models above, we obtain: { human-nature_ _ extra-human-nature_ }[human-nature_]___ _ [human-nature_]2 _ extra-human-nature_[human-nature_]____ _ [human-nature_ _ _[human-nature_] _ _[extra-human-nature_; human-nature_]. Synonymously assigning x_ ( anti-physis_ yields a model homeomorphic to the last model -- { anti-physis_ _ physis_ }[anti-physis_]____ _ [ anti-physis_]2 _ physis_[anti-physis_]_____ _ anti-physis_ _ _[anti-physis_] _ _[physis_; anti-physis_] anti-physis_. Synonymously assigning x_ ( noosphere_ yields another homeomorphic model -- [ noosphere_ _ non-noosphere_][ noosphere__] _ [ noosphere_ ]2 _ non-noosphere_[ noosphere__] _ noosphere_ _ _[ noosphere__] _ _[ non-noosphere_; noosphere__] noosphere_; x_ _x_ _____[; x__] __. . . . The 'hybrid' term denoted _[; x__], or _[ non-noosphere_; noosphere_], etc., stands for the products of interaction of with x_, of non-noosphere_ with noosphere_, etc. Hybrid products 'belong' to both 'parent' processes or, alternatively, to neither. They form a non-empty ontological boundary, ¶_, a tertium quid, "between" _& x_. Per the computational rules of the dialector algebra/arithmetic set forth herein, hybrid [ev]entities differ qualitatively, or ontologically/taxonomically, from both of their 'parent' eventities, denoted above by _and x_, as well as from the 'non-hybrid' or 'self-hybrid', 'parthenogenetic', reflexive increments, or self-increments [self-developments], of each 'parent' eventity, denoted above by __&__x_, respectively. Examples of constituents of the _[non-noosphere_; noosphere_] instantiation of the generic _[; x_] term include the fossilized skeletal remains of individual human bodies. They also include moldering archaeological ruins -- fossils of humanity's collective, societal body; skeletal remains of societal infrastructure. These qualify as such hybrid entities especially when in those meta-states in which they existed before being unearthed, that is, before their re-mining and re-minding by archaeological excavation, and their reincorporation into the museums and laboratories of contemporary societal infrastructure. They qualify as such, i.e., in that meta-state in which they were buried in, and assimilated into, the lithosphere/biosphere boundary of socio-bio-geo-sedimentary rock. Though useful for the present purpose, the above models represent a rather biased, anthropocentric way of 'parsing' and conceptually partitioning the universe. The relative physical magnitude of the Terran noosphere is miniscule, even if measured in rather indiscriminate, inertial terms, comparing the 'meta-sociomass' or 'nšomass' of this, Earth's latest self-lamination, to the remaining biomass of Earth's biosphere, let alone to the remaining mass of the cosmos. The imbalance between the physical minuteness of what x_ denotes in the above, and the physical vastness of what is there lumped together under , is egregious, to say the least. And yet the potential of this x_ to transform all of T_ -- both x_ and , quantitatively and qualitatively, in the future, and in league with other planetary instances of x__and beyond -- is immense. Another approach to a 'model of human history', at a different 'meta-fractal' scale, might begin as a project of economic archaeo-anthropology, of archaeo-economics via archaeological reconstruction of ancient human[oid], including Neanderthal, economies. This approach forms 'meta-dynamical Leontief Input/Output models', i.e., 'self-expanding inter-activity flow matrices', for past-to-present Terran human economies, starting with the most primitive that can be empirically grounded. Formed partly in the "closed", Br—dy format [Andr‡s Br—dy, Proportions, Prices, and Planning, Elsevier, 1970, ISBN 444-10006-7], counting labor-powers/skills/human-capitals of various onto-types as both 're-products' and 're-producers' of other products/themselves, such meta-models would map both evolution and meta-evolution of Terran humanity as its [pre-]historical quanto-qualitative net expansion of the social inventory of products ( social ontology of activities/skills/occupations ( social division/ontology of labor. Economic evolutions map to changes in magnitude of matrix entries [productivities], meta-evolutions to changes-of-matrix; changes in its dimensionality or rank; mitosis of rows/columns; appearance of new / disappearance of old categories _ rows/columns as entry-quantifier values cross critical thresholds, with net gain in rows/columns counts as _(. Thus evolutions, at self-bifurcation quantifier thresholds, yield meta-evolutions, with new onto-qualifier emergence. Why 'Psycho-Historical'? [forthcoming]. Personal Psyche/Soma Meta-Dynamics. From childhood, humans engage a personal dialectic of social and moral/experimental learning. A child may notice that delivering slaps to the faces of playmates provokes slaps in return. Snatching their toys makes it likely that they will do the like in response. Giving them gifts that bring their smiles may motivate them to actions that bring smiles to the giver's face as well. A person, as subject, operates upon the world, acting [mainly] upon a part thereof. This makes the world, via that part [mainly], the object of that operation. Later, the tables turn. That world, via [mainly] a[nother] part thereof, as subject, operates similarly upon that person, thus making that person the object of a similar operation. Human personal growth involves growing sensitivity to such 'justitial' and temporal symmetries. The toroidal vortex model serves here too. Output becomes input. Giving becomes receiving. "Dishing it out" becomes "taking it". Acts of one self, imposing experiences upon other selves, engender later acts by said others imposing like experiences upon that self. Action flows back to its source "in kind" - in the same quality. The action of an individual subject or self upon the world 'reflects' -- 're-flexes' & 're-fluxes' -- upon that self via the consequences of that action. That person receives back, after varying lapses of time, 'mirrorings' of that person's earlier actions; refluxes, back-flows, return-flows, re-actions which reflect the qualitative content of those earlier actions. As do echoes and boomerangs, actions emitted by a subject to its environment return as actions transmitted back from, feedbacks emitted by, that subject's environment, back to that subject. Action is requited. A crucial step in the process of personal ethical [meta-]evolution arrives in that moment of insight wherein the person's critique of others, of environment, progresses to the point of reaching back around to self; the moment when exclusive critique of others is transformed to include self-insight and critique of self. The person may thenceforth become increasingly sensitized to the internal dynamics within self which chronically lead self to actions damaging to the rightful interests of other selves, and, ultimately therefore, damaging to self as well. Once the internal dynamics of this "iblis" attain to self-awareness, qualitatively new possibilities for accelerated self-development emerge. Thereafter, noticings whose elicitation require, in childhood, the most dramatic or traumatic refluxes, may evolve, in adult development, to a highly tuned perception of the subtlest nuances of consequence in the interpersonal "politics" of the family and the work group, the cooperative labor arena of the adult person. Hypothesis. For any being of human [or of 'humanoid'] genome to become truly human, the phenotype must overcome the genotype. "Nurture" -- especially 'self-nurture' -- must overcome "nature". For each emergent planetary humanity as a whole to survive, to flourish, and to continue to evolve and 'meta-evolve', to pass its 'planetary selection test', the 'Meme-nome', or the 'Phenome', must overcome the Genome, and not in the sense of repression, or even suppression, but in the ÇaufhebenÈ sense, and the sense of conscious, freely-chosen self-destiny and self-destination. The dialectic of moral learning outlined above is continual and incessant, operating at the most intimate, personal scales of individual evolution and meta-evolution. In this process, moral insight may be born, even in ever increasing degree. Insight thus gained into cause and consequence may extend beyond the time-scale of immediate and short-lag refluxes, slap for slap, interpersonal or political slight for interpersonal or political slight, to encompass greater stretches of time, the scale of human history, even that of cosmological meta-evolution itself. If self-discovery, self-location, self-identification, self-identity expands, beyond the boundaries of skin-envelope, family, tribe, religio-ethnicity, company, industry, nation-state, planet . . . then even moral intelligence may awaken. Thus may human subjects become fitted to participate, with self-awareness, in, and with all-beneficial contribution to, evolution and meta-evolution at ever larger [meta-]scales. If, at a given locus of humanization, this process occurs in sufficient proportions of human subjects and at the right times, then another planetized humanity may achieve the moral fitness to survive, and to live on, into the meta-evolutionary stages of full planetization, and beyond. The I_AM[I_AM], tetragrammaton-like quanto-qualitative expansion-process of the personally self-recognized self-identity-ontology of a human[oid] individual may be modeled as: I _ _[I] _ I[I] _ _ II _ I2 _ [I _ _I] I, or as: I_ _ _[I_] _ I_[I_] _ _ I______________ I_2 _ [I_ _ _I_] I_, where _I_ denotes an increment of qualitative, ontological expansion of the 'I' of the self, and I_ denotes an individual human[oid] identity-ontology in its _th epoch, with I_h(q256 per our standard ¶ partitioning . Personal Meta-Evolutions -- Life-Habits, Skill-Levels, Persona. Partitioning on aspects of the psyche-ological meta-evolution of the human person, instead of the meta-evolution of the total psyche/soma as sub-totality, one may gain insight by modeling each of these aspects in distinction, applying the putative 'Universal Characteristic', x_ _ x___ _ x_[x_] _ _[x_] _ x_2 _ x_ _ _x_ x_, to each. Partitioning upon the development of 'habit-formations' -- those systems of mental/physiological 'software' and 'self-automation' which form a key infrastructure of human personhood, and whose acquisition begins in earliest childhood, we might encode this aspect of the self-induced and other-induced expansion of 'personal ontology' thusly -- habituation_ _ habituation_[habituation_] _ _[habituation_] _ [habituation_]2 _ habituation_ + _[habituation_] _ habituation_ habituation_ .... Similarly, parsing on training, informal as well as formal, and the meta-evolution / ontological expansion of personal "skill-sets", we obtain -- skill-level__(_skill-level_[skill-level_] _ _[skill-level_] _ [skill-level_]2 _ skill-level___[skill-level_] _ skill-level___ skill-level_[skill-level_] _ _[skill-level_] _ [skill-level_]2 _ skill-level___[skill-level_] _ skill-level___ skill-level_[skill-level_] _ _[skill-level_] __[skill-level_]2 _ skill-level___[skill-level_] _ .... If, instead, we partition upon the succession of personas of the developing, 'meta-evolving' personality and personality-ontology, we obtain -- persona_ _ persona_[persona_] _ _[persona_] _ [persona_]2 _ persona_ _ _[persona_] _ persona_ _ persona_[persona_] _ _[persona_] _ [persona_]2 _ persona_ _ _[persona_] _ persona_ _ persona_[persona_] _ _[persona_] _ [persona_]2 _ persona_ _ _[persona_] _ ... , wherein: persona_ persona_ persona_ persona_ .... Personal Meta-Evolutions - Nature and Nurture. The self-iterations above are doubly-omissive: (1) they describe 'partials' or aspects of the developing human psyche/soma eventity, and (2) they describe it with reference to the moment of self-causal or reflexive ontological elaboration alone. They address the self-impacts of the 'internities' of these various 'natures'. They make no reference to "nurture", to the impact of the 'externity', the "environment" of these features, either in terms of other features of the psyche/soma, or of the features of the non-psyche/soma. In short, the formulae set forth above address the moment of self-determination, of re-flexion, of intra-action or self-interaction, but not that of flexion, of other-action, of inter-action with exterior otherness. Less omissive model-making maps the co-meta-evolution of the individual self and of its "environment"-- x_ _ the ontological ['pure-qualitative'] meta-state of the psyche / soma self as of stage _; __ _ the ontic meta-state of the not-self; of the self-complement, of the self's environment as of stage _; T__ _ ontic meta-state of the totality @ _, here as 'parsed' from the point of view of x_; T____ [ x_ _ ]; T____ _ _[T_] _ T_[T_] _ T_2 _ T_______T_ T_. [ x____] ( [ x_____ ___ _ _[x_; ] _ _[; x_] ] _ [ x_ _ ][ x_ _ ] _ [ x_ _ ]2 _ [ x_ _ _[x_] _ _ _[]_ _ _[ x_; ] _ _[; x_] ] -- in which calculation we have applied, again, the rules of the ontological or onto-dynamic arithmetic. We have applied, in particular, the rule of 'ontological' or 'ontic' 'multiplication'; of the 'aufheben' 'vestigial' and 'evolute' product rule, and of "idempotent" addition, glossed above, and explored with greater amplitude in subsequent sections below. In the products-sum expression above, _[ x_; ] denotes the pure-ontic products or consequences of the action(s) of the _th ontic meta-state of this individual upon the _th ontic meta-state of this individual's environment, and _[; x_ ] the pure-ontic products of the action(s) of the _th ontic meta-state of this individual's environment upon that of this individual, so that, in toto, per this calculus of qualitative differences: T___ __ T_______[T_] _ [ x_ _ _[x_] _ _ _[]_ _ _[ x_; ] _ _[; x_] ] _ _ [ x_ _ _] _ [ _[x_] _ _[]_ _ _[ x_; ] _ _[; x_] ]; T_____________[ x_ _ _] _ ['nature of x_' _ 'nurture of x___'] _ ['self-nurture and exo-nurture of x___']; _T_ ___ [ _[x_] _ _[]_ _ _[ x_; ] _ _[; x_] ]. Though useful in some applications, the 'partitioning' employed in the above may manifest a rather "egoistic", "egocentric", "narcissistic", or self-distorted, if not self-deluded, emphasis in that a single self is singled-out, and the vast 'remainder' of the totality, T_______x_, including all other such selves, is lumped together into the single term . This yields a special kind of 'homeomorphic defect' accordingly. More adequate models generally require a more proportionate representation of reality; a vastly more detailed sub-'parsing' of . The ontological partitioning principle, { ¶ }, applied in a given modeling effort, is at least as much a map of modeler, the modeling subject, as of objective/external reality. It maps the perceptual organization and priorities of that subjectivity. Many partitionings are possible. Each exacts its own price in homeomorphic defect. The Q Characteristica Universalis aims to accommodate and facilitate a great diversity of such "points of view". Personal Meta-Evolutions -- Judgment and Mode of Cognition [ÇOrganonÈ]. The ideation process in creative mentation, and the "waves" or "trains" "of thought(s)" which meta-evolve thereby, involve a dialectic in which the thinker, as subject, reflects upon re-presented previous meta-states of that subject's own subjectivity, of that subject's own thought, of the previous thought-contents of that self, thus objectified in this re-minding self-reflection or self-re-thinking of/by those contents. Reflection of the subject as thinking-process-present upon an object which is the self-dual, self-other, self-previous self-representation and self-object-ification of the meta-state of that self-same subject as thinking-process-past, is a self-reflexion and self-refluxion of one and the same thinking-eventity or thought-eventity. Self-confrontation of present/"living" thinking-capacity with representations of itself as its own past/'dead' thought-product may evoke into awareness previously unnoticed self-inconsistencies and self-inadequacies of that previous thought-product, as well as previously unnoticed inter-connexions, and intra-connexions within, that network of idea-objects, idea-eventities, or idea-ontos. Such 're-cognitioning' may thus amount to an 'immanent- or self-critique of thought by thought itself' yielding a meta-finitely, qualitatively advanced, ideo-ontologically self-expanded thought-product as its next outcome -- 'Thought thoughting thought'; 'thinking thinking thinking'; thinking rethinking thinking [dialectic of ideation]: idea_ _ idea_[idea_] _ [idea_]2 _ _[idea_] _ idea_ _ _[idea_] _ idea_ _ idea_ idea_ ... thought_ _ thought_[thought_] ___[thought_]__thought_____[thought_] __thought____thought____... thinking_ _ thinking_[thinking_] _ _[thinking_] _ thinking___ _[thinking_] _ thinking_ _ _... Another generic name for the product/producer of such mental objects or mental products is "judgment". We can model the immanent improvement, or self-critique, of the quality of a judgement which is being embodied or simulated by the mind of a thinking human[oid] subject via the same kind of succession -- 'Judgment judgment'; 'judgment of judgment'; 'self-judgment of a judgment'; (a) 'judgment of 2nd degree': judgment_______ [judgment_]2 _ _[judgment_] _ [judgment_____[judgment] ] judgement_. Again, bringing in the influence of external forces - such as the effects of external experiences or experiments in the meta-evolution of a scientific hypothesis -- requires that the 'non-autonomous' as well as the 'autonomous' moments of this self-iteration of judgement be modeled. Shifting 'meta-fractally' to a larger scale of observation of the developing mental processes of a meta-evolving human[oid] person, we may model the meta-evolution of the organon or 'technology of thought' of that person; their metafinite succession of modes of cognition or ÇmentalitŽÈ, { m__}, after the fashion of Piaget: c ( concrete operations, or 'use-value' stage of personal cognitive development; f ( formal operations, 'cardinal operations' 'monetary operations', or 'exchange-value operations' stage; d ( dialectical operations, or quanto-qualitative, meta-dynamics-, historicity-, & negentropy-cognizant stage. m_ _ c ; m___ _ m_2 _ c[c] _ cc _ _c _ c2 _ c _ _c _ m_ _ f c _ m1; m___ _ m_2 _ f[f] _ ff _ _f _ f2 _ f _ _f _ m_ _ d f ; ... ; in summary, m_ m_ m_ ...; m___ _ _m____ m_2 __ m_ _ _m_ , & m___ _ m_2___ m_2_. Personal Meta-Evolutions -- The Somatic Dialectic. [forthcoming] Personal Meta-Evolutions - Methodologies and Technologies of The Sciences of Subjectivity. We earlier alluded to formulae of the following form as formulations of 'anthropogenesis' or 'anthropopoiesis', wherein the meanings of 'awareness of awareness' or 'meta-awareness', and of 'awareness of self' qua 'self as awareness', converge -- sentience _ sentience[sentience] _ [sentience]2 _ self-sentience sentience; or awareness _ awareness[awareness] _ [awareness]2 _ self-awareness awareness. The next step in this progression might thus be modeled as the self-reflexion of this 'meta-sentience' itself - self-awareness _ self-awareness[self-awareness] _ _[self-awareness] _ [self-awareness]2 _ self-awareness _ _[self-awareness] _ 'self-awareness of self-awareness' _ 'self-awareness of higher (2nd) degree' self-awareness; [self-awareness]2 _ [sentience]2_ _ [sensory-awareness]2_ _ [mere-consciousness]2_, wherein the meanings of 'meta-self-awareness' or 'self-awareness of self-awareness' and of 'awareness of meta-self' qua 'meta-self as self-awareness itself' converge. Traditions endure, descending from ancient times in Earth's Orient and Occident alike, which remain semi-esoteric and partly hidden to this day, and which may be grasped as protocols of a self-reflexive, dialectical psycho-physiological praxis; as forms of individualized self-activity accelerating the immanent development of the infrastructures of human self-awareness. These traditions involve the cultivation of forms of profound or intensified attention that arise to 'meta-attention' -- 'attention to attention', 'attention of the second degree', 'the self-attention of attention itself', and of the self-amplification of attention. They involve the cultivation of a profound concentration that becomes 'meta-concentration' -- 'concentration upon concentration itself', 'the self-concentration of concentration', self-amplified concentration. They require a contemplation that intensifies to 'meta-contemplation' or 'self-contemplation' - 'the contemplation of contemplation itself by contemplation itself'. These psycho-physiological practices include psycho-physiological technologies which accomplish a self-refluxion and self-reflexion of will/attention. They apply the will to turn attention back upon the physiological organs that appear, phenomenologically, to generate or manifest will-attention. They thereby produce -- much as the feeding of a loudspeaker's output back into its microphone produces a crescendo of sound -- a crescendo of consciousness, a self-intensification of will-attention, 'meta-will', a 'willing of will itself', a change of willingness, a simultaneous gain in the willingness to change and in the capability to change: will_[ will_] _ will_2 _ _[ will_] _ will_ _ _will_ _ will___ will_. These practices amount to a 'nonlinearization of self-awareness', to a deliberate induction of a self-refluxion of self-awareness, and a self-reflexion of self-reflection itself; a bending-back-upon-itself again of 'proprio-perception'. Other and deeper secrets of the self-reflexivity of 'inner Nature' in general, and of subjective human[oid] nature in particular, are discoverable within these traditions of practice, such as those known as Raja Yoga, Kriya Yoga, and Tantra Yoga. We present nothing further of them here. We believe that comprehension is better served - for those who choose for themselves to conduct such a program of self-research -- to encounter such discoveries in the full-context experience of their own self-experiments, carried out in the laboratories of their own psyches/somas, rather than to first confront them as verbal formulae, representing phenomena never yet experienced by them, in abstraction from any such context of experience and personal experiment. Indeed, in some variants of these traditions, the theory and practice of such exercises of consciousness forms an extensively elaborated science of 'internal nature', or science of subjectivity, complementary to the lately more familiar science of 'external nature', or science of objectivity. In those variants, these meditative practices amount to a methodology and technology of the science of subjectivity. Self-humanizing individuals, at a certain stage in the course of their psyche-ological/somatological development, tend to discover or rediscover such practices, which may then lend celerity to their further personal meta-evolution. Personal Meta-Evolutions: An Enormous Discovery, The Revelation of Iblis, The Discovery of an Enormity and of an Enemy Within. The awakening of insight into the self-reflexive moment of the constitution of personal life/experience, of the partially self-refluxive or echoic content of personal occurrences, may, at length, precipitate a crucial discovery. This discovery is potentially enormous in its implications and in its consequences, for the life of the discoverer and for the experience of every other person whose life is touched by that discoverer's life thenceforth; the revelation of self-infliction -- Ç . . . Culprit, c'est moi È. 'The main culprit in my life is me'. 'The primary cause of the mischief in my life is my way of doing me'. Once attained with clarity, this discovery offers the meta-evolving person a new and far more powerful methodology for the investigation and amelioration of personal difficulties: to probe first for causes of those difficulties in the past-to-present action of that self-same causal agent and subjectivity. The self itself, not some other, becomes the self's prime suspect. The self itself is typically the greatest offender against its own experience. If [other-and-self-]offending action is thereby uncovered, the subject may endeavor to re-design its practice of self, promulgating a program of reformed self-activity whose refluxes, or 'returns-to-self', are more congenial for all concerned, self included. Deepening insight into one's own misdeeds, and into their deep-seated and difficult-to-exorcise origins within, tends also to awaken a salutary compassion for one's fellow mis-doers; for the disfiguring, tragic, and even horrific personal consequences of undiscovered, unacknowledged, and unchecked iblis; for the enormous inner war which each must undertake to acknowledge, check, and overcome the enormity within. Capacity may thus develop to not only, at times, "be hard with your "beast"", but also, at times, to be gentle with others', though they harbor this "beast" no less than do you. This iblis is the reason why: "Power corrupts, and absolute power corrupts absolutely". Evil has an embassy in every psyche borne of this cosmos. Abuse of power, parasitism and sadism - the pitiless, vampiric emotional, sexual, and economic exploitation and torture of other beings, by an exploiter who is not only not appalled by, but takes perverse pleasure in, the horrific suffering that it causes - these are the invariant 'marks' of this 'beast' of iblis in its [re-]crudescence full-blown. Thus, the elimination of unchecked power, the building-in of elaborate controls, checks, and balances, is a key moral principle for the design of viable social institutions. Yet all of that is in vain unless a sufficient proportion of individual members of society choose to struggle to build sufficient "checks and balances" into their own psyches. A major crossroads looms, often in late adolescence, when self-knowledge breaks through to recognize, within self, the seeds of the corruption up 'til then known only externally, in social institutions and in other beings, often figures of authority within those very institutions. When this crossroads is reached, the being may take up the arduous path of self-reform. Or, that person may "surrender" to iblis, taking a willing place among the willingly corrupt; spending the remainder of life bickering over the spoils of corruption. The latter path is not hopeless. Some who take it first are later overcome by self-revulsion, and propelled by that self-revolt to the path of self-reform. The former path is not dauntless. Many snag along its way. Some revert. In either case, the aftermath of this crossroads is to re-confront its likes again and again. Progress in self-reform is far from popular. Synthesis appears to be mere antithesis -- and, at least at first, anathema -- to both thesis and anti-thesis. What a terrible shock of recognition when self-exploration reveals the hideous face of iblis -- the horrific adversary that one has fought so hard for so long in the outer world -- hidden and harbored, aided and comforted within one's own psyche, a psyche thus traitor to itself! One discovers -- seeded in oneself -- the monstrosity so malignantly manifest in even the most infamous of 'human' monsters who litter the history of humankind. These inner seeds need but to fall on the fetid soil of times too hard - or too easy - to sprout in hideous fruition. This discovery is a trauma both salutary and indelible: one which can incent, incite, and insight to further meta-evolution! Strong motive is required. The path that leads from the 'life' of iblis to greater life passes through the valley of the shadow of death. Self-Reflexivity/Self-Refluxivity as the Essence of Dialectical Meta-Dynamics. Dialectics is most essentially about those processes described in, e.g., English phonetic or phonogramic language, by sentences in which the subject and the object are identical; i.e., in which the same noun -- the same name, or a pronoun standing for that name -- holds both the subject place and the object place; sentences describing processes in which the subject acts upon itself as its own object, through a verb which is also an action-name of that self-same subject-object, naming a mode of action which inheres in the very nature or essence of that three-way-named -- subject-verb-object-named -- eventity. What such a sentence describes is a self-reflexive process by which the eventity denoted by the subject-verb-object of the sentence changes itself quantitatively and qualitatively [i.e., ontologically], or [in a 'dialectized' version of the language of dynamical systems theory], partially controls its own control-space, via its own states, and thereby self-induces its own self-bifurcation(s). The "nonlinear terms" of the extant ideographic mathematical language -- the components that make mathematical equations "nonlinear" and typically also "unsolvable" within the extant epoch of mathematical meta-evolution -- are mathematical expressions and ideographic formulations of dynamical [and, in some cases, of meta-dynamical] self-reflexivity. Terms like x(t)( x(t) ) __ x(t) ( x(t) _ x(t)x(t) _ x(t)2 and w(x,y,z,t)( w(x,y,z,t) ) _ w(x,y,z,t) ( w(x,y,z,t) _ w(x,y,z,t) ( w(x,y,z,t) _ w(x,y,z,t)w(x,y,z,t) _ w(x,y,z,t)2 denote the self-application or reflexive application of a[n "unknown"] mathematical operation; the operation upon themselves of the function-values, here denoted x(t) or w(x,y,z,t), of a function-valued or operation-valued function-"unknown"; an operation or function here denoted x or w. As expressions of self-reflexive process, they are expressions of dialectical process. The term 'self-reflexion' connotes a 'bend-ing' ['flex-ion'] again or back [re] upon self. Hence, the phonogramic term 'self-reflexivity' is one we use to name the quality of a 'self-consequential' operation, an operation or mode-of-activity which applies itself to itself, or acts back upon itself; i.e., to name the quality of self-activity. We identify this quality as the defining attribute of dialectical processes, that is, of dialectical eventities. In relation to classical nonlinear dynamics, dialectics constitutes a meta-dynamics. It does so because it deals with changes not restricted to changes of location within a given "state-space", and to changes in 'trajectory-morphology' within a quantitatively and qualitatively unchanged "state-space". It deals with epochal, revolutionary changes. It deals with system-induced, state-trajectory-induced change of "state-space"; with the change to a different and qualitatively expanded [not just quantitatively expanded] "state-space" and coupled "control-space" or "parameter-space", i.e., one in which new dimensions, not just new volume or new flows are added. Such 'changes of space' arise because the "control parameters" of nonlinear, 'self-reflexive', 'self-refluxive', dialectical or meta-dynamical 'meta-systems' -- parameters often [mis-]described as "constant coefficients" in the equations of state-evolution -- are not truly constant, hence are not truly "constants". They too are variable, are variables, are even self-variables. They too, not just the "state-variables", are dynamical. 'Change of space' may result when cumulative changes in one or more control-space parameter-values reach and cross their critical threshold values, "bifurcation" values. 'Dialectical' 'meta-systems' are dynamical systems whose own essential behavior, as expressed/described by their state-space trajectories, partially control their control-space positions, and which thus self-induce "bifurcations" of their state-space behavior. Relatively sudden, deep, qualitative self-change results from movements in the system's control-space which are driven by the self-movement of the system through its state-space, that is, by the system's integral, internal, self-propulsion -- in both its state-space and its parameter-space or control-space, or better, in its unified 'state/control meta-space'. Such unified state/control meta-dynamics exhibit a generic phenomenology which we term self-bifurcation. This phenomenology is explicated in the section on self-bifurcating systems in the sequel, and is homeomorphically encoded in the 'arithmetical' Rules-Systems of the Q, U, & am dialectical ideographies, and beyond. Again, in summary: dialectics is about processes most readily and naturally described by sentences in which subject, verb, and object name different aspects of the self-same process-entity or 'eventity'. Such sentences are traditionally characterized, in the technical terminologies of 'grammatics' [grammar] and linguistics, as "reflexive" or "self-reflexive" sentences, connoting the "bending [flex] back [re] upon self" [self-re-flex-ion] of the sentential subject upon itself, as sentential object, through the mediation of [its own self again, as] the sentential predicate or verb/verbal phrase. We believe that The Nonlinearity Barrier has its thickest historical root in Western classical antiquity, in the promulgation and codification of a logic that ruled out, by assumption, time and change, and therefore also self-change. At least one major shoot off that tap-root can be traced to the incipient recovery of Western Civilization from the horrific and protracted episode of contracted social reproduction known as the "Dark Ages"; can be traced to the first great resurgence of light after the break in that darkness, at the base of the Medieval period, in the 1200s; at the start of the Dim Ages of Terran humanity, which have not yet ended. Thus, Aquinas: "Now the same thing cannot at the same time be both actually x and potentially x, though it can be actually x and potentially y: the actually hot cannot at the same time be potentially hot, though it can be potentially cold. Consequently, a thing in process of change cannot itself cause the same change: it cannot change itself. Of necessity therefore anything in process of change is being changed by something else."13 However, returning to our earlier example of stellar evolution, a proto-star -- in the process of its formation from a self-gravitating, self-concentrating, self-densifying mass of inter-stellar gas and dust -- is, at many points in its self-development, both "actually hot" and "potentially hotter still". It can -- and does -- move itself from "hot" to "hotter". A typical proto-star moves itself from the state "partially hot" to the state "fully hot", in that its state converges, through a succession of transient, proto-stellar temperature regimes, to its "essence-ial", long-lasting "main-sequence" temperature regime, reflecting sustained Hydrogen-fusion in its core. The primary causes of this transition and convergence are internal to this stellar eventity, not external to it. The primary causes of this self-convergent or essence-convergent behavior arise from, arise as, and operate within the physical internity, the interior substance-and-dynamic of this "automorphogenesis" and "auto-metamorphosis" -- this self-shaping, "self-forming content", the proto-stellar body. The primary causes are not located in the proto-star's exterior environment, in the surrounding externity of matter-energy-process. The "something" which causes this "heating-up" is the proto-star itself, not "something else". The proto-star "causes" the star; causes itself to become the star, causes the transition from proto-star to main-sequence star: protostar[protostar] = protostar2 = star = not-protostar = _protostar protostar. More generally, and contrary to Aquinas' [unknowing] implication, nonlinear differential equations can have solutions. In terms of their state-spaces, that is, in terms of the 'dynamical analytical geometry' of such equations, and of their 'geometries-of-solution' or 'solution-geometries': a dynamical system can have an "attractor" structure as its solution-geometry. That attractor may be a single state-point or an orbit-of-state-points in its state-space, toward which its trajectory tends regardless of its initial position in that state-space [or within the sub-region of that state-space which is the "basin" of that attractor]. The existence of such an 'essence-ial' behavior or "dynamic" implies no teleology, no causation of present states by future, not-yet-existent states. It simply implies existence of cybernetic "self-steering" mechanisms. Such confluences of negative and positive feedbacks -- such self-refluxions -- self-constrain the system's behavior in every present moment so that its states converge upon this 'essence-ial' behavior. Similarly, the rule of a finite sequence may make it always end presently with the same value, via computations carried out in 'presents-past-up-to-present-present', rather than via anything carried from some [presently-nonexistent] future backward. By the term 'eventity', we name an ontological conception of beings as subject-verb-object unities, whose continuing self-activity induces continuing and self-consistent, directional -- essence-directed -- self-change, or self-development. By 'eventities', i.e., we mean "beings" that self-induce changes that are in accord with their natures, essences, or [meta-]attractors. We mean activity-entities whose essential activity constitutes a process of graduated "self-attainment"; a "self-creation", "self-making", or "self-production"; an autopoiesis. Eventities are thus self-meta-evolving entities comprehended as dialectical self-becomings or essence-becomings. The characteristic mode of activity of an eventity, its active character, is not optional. To be itself, it must do this, and do this to itself. A star cannot stop the fusion at its core and remain a star. The essence-process of an eventity is its essence-process, its essential process, its necessary process, its [self-]defining process, its existential process, the process of its existence, the process which is its existence. A star cannot both be a star and stop the process of depletion of its most vital resource, its internal fusion fuels. Yet their consumption by that star itself at length brings that star's existence -- as such, as star -- to an end. 'Meta-Monadology': A Unitary Conception of "The Dialectic Of Nature" [The Ubiquity of the 'Graduated Cumulum' of '''being-for-itself''' Proto-Subjectivity] -- of the 'Self-Bifurcative' Processes of Human Nature, Pre-Human Nature, and Extra-Human Nature -- in Relation to the Concept of 'Meta-Dialectics', The 'Higher Degree' Dialectics of Dialectics Itself; of Its Own Self-Activity, Self-Reflexion, & Self-Refluxion. Indo-European "natural" languages abstract, or conceptually separate-out, subject and object, nominal aspects, from one another, and from verb/predicate aspects, of their sentential descriptions of each single eventity. This forces their users to redintegrate their descriptions by talking and writing in terms of an interaction, a two-way communication of information, negentropy, energy, forces, or effects, among as if separate subject, object, and predicate/verb aspects of that self-same eventity. Metaphorically, using the interpersonal and intrapersonal processes with which human beings are most intimately familiar as the ground of this metaphor, this redintegration can be likened to a material dialogue, a self-conversation and a self-dispute or self-controversion between the subjective and objective aspects of this unitary eventity. Per age-old Terran human philosophical convention, human subjectivity is taken to be the collective, historical subjectivity proper, and sometimes as the sole historical subject/agent with which dialectics should be concerned. When observing that convention, one might refer, for the dialectics of pre-human nature, to meta-dynamical eventities which emerged in the natural history prior to the emergence of human[oid] subjects, but as part of the meta-evolutionary sequence allegedly leading to humankinds, variously as that of 'pre-subjects', 'proto-subjects', or 'sub-subjects', hence also as 'pre-objects', 'proto-objects', or 'sub-objects' in their 'object-ive' aspects. One might, in the same vein, refer to their self-bifurcations, that is, to their metafinite transitions or conversion-singularity meta-dynamics as a 'pre-dialectic', 'proto-dialectic', or 'sub-dialectic' -- the dialectic of pre-human[oid] nature. One might also refer to the ongoing, partially independent or 'parallel' self-reflexive development of cosmological extra-human nature, synchronic with self-developing human nature, but, in large portions, substantially isolated from direct human[oid] impact, as a 'co-subjectivity' and as a 'co-objectivity'. One might refer to the meta-dynamics of this contemporary sub-realm of the cosmos as a 'co-dialectic' -- the dialectic of extra-human nature. When not observing that convention, we will refer to each eventity discussed, according to the operatorial or sentential role of its name or other symbol in its descriptions -- its grammatical "moment", regardless of its location in 'the great chain of [evolute] self-becoming' -- as simply a "subject"/'agent' and an "object", or, in totality, as a 'subject/verb(s)/predicate(s)/object'. The first of these conventions tacitly implies that an eventual meta-evolutionary self-supersession of the presently-extant, 'meta-social' Terran humanity, emerging, by self-reflexion, from within that humanity, if it should arise, would be conceived of and addressed in terms of a 'super-subjectivity', a 'super-objectivity', and of a 'super-dialectic' or 'hyper-dialectic' -- the dialectic of post/meta-human[oid] nature. In short, in the perspective of this theory of dialectics, dialectics also applies to itself. There is also a 'dialectics of dialectics', a 'meta-evolution' of the dialectic itself, and that 'meta-evolution' is also 'dialectical'. The "laws" of dialectics, the 'meta-patterns' codified in dialectical logic, are subject to their own 'meta-dynamics'. 'Dialectics', used to mean the conceptual praxis of the collective subjectivity of the Terran human community of dialecticians, if it exists as such, must continually self-revolutionize itself. This continuing self-revolution is its ongoing, open-ended attempt to keep up with cosmological actuality in the context of the ever-expanding possibility-space/actuality-space multi-ontic cumulum arising from ongoing universal 'onto-dynamasis'/'meta-dynamasis' at all 'meta-fractal' scales/levels, for all ontic levels, and the consequently ever-growing 'knowledge deficit'. This meta-evolution of dialectics is intimately bound up with the emergence of new ontology, of qualitatively different historical 'subject[ivitie]s' or 'agen[cie][t]s' in the course of the history of nature. If we hold that human history/society is the realm of dialectics proper, then we have the following relationship of that "dialectics" to its immediate epochal predecessor and successor: proto-dialectics _ proto-dialectics[proto-dialectics] _ [proto-dialectics]_ _ _[proto-dialectics_] _ [ proto-dialectics _ _[proto-dialectics] ] _ [ proto-dialectics _ [meta-proto-dialectics] ] _ dialectics; dialectics _ dialectics[dialectics] _ [dialectics]_ _ _[dialectics_] _ [ dialectics _ _[dialectics] ] _ [ dialectics _ [meta-dialectics] ] _ hyper-dialectics_ _ . . . Otherwise, we might simply formulate this meta-dynamics of dialectics via the following formulae: dialectics__ _ _[dialectics_] _ dialectics_ _ _[dialectics_] _ dialectics_ _ . . . subject__ _ _[subject_] _ subject_ _ _[subject_] _ subject_ _ . . .. The 'Operator' Concept within Operatorial Ideography and the Ideography of 'Eventity' and of 'Self-Duality'. In the mathematical ideography already extant, there has emerged the concept of an "operator". This concept is a synthesis of the conceptions of "pure number", "pure quantity", or "mathematical noun" -- supposedly, for "pure quantity" conceptions, exemplified by ideas such as those denoted by the ideograms 2, 3, or 4 -- and of "pure operation", or "mathematical verb" -- again, supposedly, for such "purist" conceptions, exemplified by the ideas denoted by, e.g., the ideograms (, (, (, (. The operator conception means that the meaning of a "sign of operation", like ( in an algebraic expression like y ( z _ y(z) _ yz, is no longer necessarily "times". That meaning is no longer independent of the meaning of the "numeral" -- or of the "algebraic literal" standing for a "numeral" -- i.e. of the "[meta-]number" denoted by the ideogram to its left, here y. If, for example, y denotes the "Real" number 2.000 . . . , then the ( denotes our familiar "Real" multiplication operation. However, if y denotes the "Imaginary" number _i, a value of the square root of _1, then ( in y ( z _ y(z) _ yz, does not denote "Real" multiplication. It denotes the 'function' or "operation" that defines _i, the operation that _i denotes, describable analytic-geometrically as a 90¡ counter-clockwise circular rotation in the plane-space of the "Complex" ["Real" _ "Imaginary"] numbers. An operator is a 'mathematical eventity'. [cf. the "object" concept of "object-oriented programming"]. Certain mathematical operators -- or 'meta-number-ized' functions/operations -- can aptly model physical eventities. We employ this convention of general operatorial ideographies in the dialectical ideography, and for essence-ial reasons. Use of ( as a separate ideogram denoting "pure operation" is rendered redundant. It is obviated by the simple juxtaposition or contiguity of operator symbols, as in yz. The action of the operator or operation y upon the operator or operation z, and the product of the interaction of y and z, is known from the definition, nature, or essence of y and z -- from their operational meaning, from the choreography, the form of analytic-geometric motion, the kind of number, the type or quality of "quantity", that each symbolizes. Operatorial ideography is an 'arithmetic' of functions applied to functions, of operations applied to operations, of 'meta-numbers' applied to 'meta-numbers'. Operatorial ideographies are about functions taking other functions, and themselves, as "arguments". They are about operations operating upon other operations; 'ideographic verbs' operating upon other 'ideographic verbs', plus the special case of operations/verbs operating upon themselves. Adjacency, contiguity, juxtaposition -- the absence of space or separation between two symbols -- signifies their 'multiplicative interaction' or '''multiplication'''. This is already the convention in ordinary algebra, in matrix linear algebra, and in calculus/analysis. However, its usage in operatorial ideography generalizes this tacit meaning and concept. The literal symbols of ordinary algebra are assumed to represent but one kind of operator, one 'quality of "quantity" ' -- namely, the "Real" or at most the "Complex" number kind. In operatorial ideographies, many different kinds of operators may interact. This touching of two operator signs thus signifies the activation of the operations they denote, the one upon the other. But, if the operators are not Real numbers, the operation activated is no longer "times" or standard "multiplication". We need a new name, one that covers all cases. We use the term 'flexion', or 'inter-flexion', connoting the mutual "bending" or "de-flection" of the trajectory, or characteristic number-space motion, definitive of each operation, by that of the other. Expressions like yz may thus be read off as 'y flexion z', or as 'y flex z', or as 'y (de)flects z', instead of as 'y times z', when y, z _ R. When y _ z, so that yz _ yy _ zz, we may read this as 'y flex y' or 'y flex itself'. We may thus also term that which such self-juxtapositionings denote variously as 'intra-flexion', 'self-flexion', 're-flexion', 'self-de-flection', or 'self-re-flexion'. This 'operator' concept -- this synthesis of the concepts of 'number' and of 'operation' -- is radically fundamental to all that follows, both notationally and epistemologically. Operatorial ideography is the very ideography of eventity. We employ underscored boldface black letters, phonograms like x, as ideograms to denote a new kind of 'operator', also called (1) 'ontological' or 'ontic' 'unit-qualifiers', '(2) unquantifiable qualifiers', (3) [especially the 'evolute'] 'meta-numbers', (4) 'dialectical operations', (5) dialectical 'meta-vectors', or simply (6) 'dialectors'. This usage of x is serendipitously fitting, providing mnemonic and connotative support to the eventity concept. On the one hand, this usage continues the tradition of classical algebra, where the phonogram x, used as an ideogram, denotes an unknown value to be solved-for, a general variable, or a generalized "pure number". This usage of x also simultaneously evokes the traditional "pure operation" ideogram for multiplication, namely, _. This is a sign for the operation of "taking the product" of two numbers, that is, for multiplication, or 'produc-tion'. Such 'product-tion' means the positing of a new number, or "product", as a result of this action upon one number by another, or of this mutual action between two numbers. We will also employ _, a pure-qualitative take-off from the quantitative "boundary operator" or "partial differential" operator, _, as an ideographic modifier of phonogramically-symbolized English words. We use it as shorthand for the epithets "partly" and "partial", and as an acknowledgment of the insights of fuzzy set theory. That is, we use it as an assertion of the non-extremal nature of most phenomena we will be describing, their status as neither all nor none of the totality to which they belong, i.e. as but some of that totality. The meta-evolutionary models which the language of the dialectical ideography renders via ideogramic, mathematics-like formulae are dialectical models in this sense: they are semantically hyper-condensed shorthand for -- ideogramic 'translations' of -- what would, in e.g., English phonogramic form, be expressed via subject-verb-object-identical sentences of great length and complexity. 57 Dialectical Ideography I- Distributed ÇSamizdatÈ by Foundation Encyclopedia Dialectica Dialectical Ideography I- F.E.D.