Calendric Dominion (Part 6)


At the beginning of the 21st century, global cultural hegemony is on the move. For roughly 500 years, Western — and later more specifically Anglophone — societies and agencies have predominantly guided the development of the current world system. As their economic pre-eminence wanes, their cultural and political influence can be expected to undergo a comparable decline. In the early stages of the coming transition, however, the terminal form of active Western cultural hegemony – multicultural political correctness (MPC) – is well-positioned to manage the terms of the retreat. By reconfiguring basic Western religious and political themes as a systematic sensitization to unwarranted privilege, MPC is able to distance itself from its own heritage and to live on, in the resentment of ‘the other’, as if it were the neutral adjudicator of disputes it had no part in.

When MPC turns its attention to the Gregorian (or Western Christian) Calendar it is, of course, appalled. But it is also stuck. What could be more insensitive to cultural diversity than an ecumenical date-counting system, rooted in the ethnic peculiarities of Greek-phase Abrahamic religion, which unapologetically celebrates its triumph in the uncompromising words Anno Domini? Yet global convergence demands a standard, no alternative calendar has superior claims to neutrality, and, in any case, the inertial juggernaut of large-scale complex systems – ‘lock-in’ or ‘path-dependency’ – pose barriers to switching that seem effectively insuperable. The solution proposed by MPC to this conundrum is so feeble that it amounts to the completion of Gregorian Calendric Dominion, which is to be simultaneously rephrased (politely) and acknowledged in its irresistible universality as the articulation of a ‘Common Era’.

MPC supplants problems of cultural power with obfuscatory etiquette, and in absolute terms, its smug dishonesty is difficult to like. As a relative phenomenon, however, its appeal is more obvious, since radical ‘solutions’ to Gregorian Calendric Dominion, re-beginning at Year Zero, have generally reverted to mass murder. Lacking persuasive claims to a new, fundamental, and universally acknowledged historical break, they have substituted terror for true global singularity, as if fate could be blotted out in blood.

Since resentment gets nowhere, whether in its mild (MPC) or harsh (killing fields) variants, it is worth entertaining alternative possibilities. These begin with attention to real cultural differences, rather than mere ‘cultural diversity’ as it presents itself to the vacuously MPC-processed mind. Soon after Shanghai had been selected as host city for World Expo 2010 (in December 2002), countdowns started. For Westerners, these probably had space-age associations, triggering memories of the countdowns to ‘blast off’ that were popularized by the Apollo Program, and subsequent science fiction media. It is far from impossible that Chinese shared in these evocations, although they were also able to access a far deeper – which is to say civilizationally fundamental – reservoir of reference. That is because Chinese time typically counts down, modeled, as it is, on the workings of water clocks. The Chinese language systematically describes previous as ‘above’ (shang) and next as ‘beneath’ (xia), conforming to an intuition of time as descent. Time is counted down as it runs out, from an elevated hydraulic body into the sunken future that receives it.

Duration not only flows, it drips. Perhaps, then, an ‘orientalization’ of calendric perception and organization is something that significantly exceeds a simple (or even exceedingly difficult) renegotiation of beginnings. Re-beginning might be considered largely irrelevant to the problem, at least when compared to the re-orientation from an original to a terminal Year Zero. Whilst not exactly a transition in the direction of time, such a change would involve a transition in the direction of time intuition, simultaneously surpassing the wildest ambitions of calendrical re-origination and subtly organizing itself ‘within the pores’ of the established order of time. As modeled by the 2010 Expo, and previously by Y2K, the switch to countdown time does not frontally challenge, or seek to straightforwardly replace, the calendric order in being. Rather than counting in the same way, from a different place, it counts in a different way, within the framework of time already in place. It is a revolution with ‘Chinese characteristics’, which is to say: a surreptitious insurgency, changing what something already was, rather than replacing it with something else.

Both the 2010 Expo and Y2K also reveal the extreme difficulty of any such transition, since a futural Year Zero, or countdown calendar, must navigate the arrow of time and its cognitive asymmetry (between knowledge of the past and of the future), presupposing exact, confident, and consensual prediction.

That is why it approximates so closely to conservative acceptance. If the countdown is to be sure of arriving at the scheduled terminus, the destination ‘event’ must already be a date (rather than an empirical ‘happening’). Nothing will suffice except a strictly arithmetical, rigorously certain inevitability, as inescapably pre-destined as the year 2000, or 2010, which cannot but come. From the perspective of the countdown calendar, that is what (Gregorian) Calendric Dominion will have been for. It is an opportunity to program an inevitable arrival.

But when? The sheer passage (fall) of time has assured that the opportunity for calendric revolution presented by the Y2K ‘millennium bug’ has been irretrievably missed (so that AD 1900 ≠ 0). The same is true of World Expo 2010, an event without pretense to be anything beyond a miniature ‘practice’ model of global-temporal singularity. As for the real (techno-commercial) Singularity – that is an imprecise historical prediction, at once controversial and incapable of supporting exact prediction.

A more appropriate prospect is suggested by the science fiction writer Greg Bear, in his novel Queen of Angels, set in anticipation of the mid-21st century ‘binary millennium’ (2048 = 2¹¹). This is a formally suitable, purely calendric ‘event’, deriving its significance from arithmetic rather than ideology or uncertain prophecy. He even envisages it as a moment of insurgent revolution, when artificial intelligence arises surreptitiously, and unnoticed. Yet arbitrariness impairs this date (why the 11th power of 2?), and no serious attempt is made to explain its rise to exceptional cultural prominence.

If an adjusted global culture is to converge upon a countdown date, it must be obvious, intrinsically compelling, and ideologically uncontroversial, in other words, spontaneously plausible. The target that World Expo 2010 suggests (anagrammatically) is AD 2100, a date that performs the final stages of a countdown (2, 1, 0 …). Reinforcing this indication, the Y2K ‘millennium bug’ threatened to re-set the date of AD 2000 to AD 1900, which would have tacitly reiterated itself at the exact end of the 21st century. If it continues to chatter about the calendar, perhaps this is how.

The impending Mayan Apocalypse, scheduled for 21 / 12 / 2012, offers a preliminary chance to indulge in a festival of countdown numbers – like 2010, it looks a lot like another digital singularity simulation. If the morning of December 22nd, 2012, leaves the world with nothing worse than a hangover, it could gradually settle into a new sense of the Years Remaining (to the end of all the time that counts, or the 21st century).

AD 2100 = 0 YR

AD 2099 = 1 YR

AD 2098 = 2 YR

AD 2096 = 4 YR

AD 2092 = 8 YR

AD 2084 = 16 YR

AD 2068 = 32 YR

AD 2036 = 64 YR

AD 1972 = 128 YR

AD 1844 = 256 YR

AD 1588 = 512 YR

AD 1076 = 1024 YR

AD 52 = 2048 YR

It’s difficult to anticipate what it looks like from the other side.

[No actual tomb, but retrieved from this]

Calendric Dominion (Part 4)

A Digression into the Reality Principle

Between the world we would like to inhabit, and the world that exists, there’s a gap that tests us. Even the simplest description of this gap already calls for a decision. ‘Ideologies’ in the broadest, and culturally almost all-consuming sense, serve primarily to soften it. Sense, and even compassion, is attributed to the side of reality, promising ultimate reconciliation between human hopes and desires and the ‘objective’ nature of things. Science, a typically despised and misanthropic discipline, tends to the opposite assumption, emphasizing the harsh indifference of reality to human interests and expectations, with the implication that the lessons it teaches us can be administered with unlimited brutality. We can dash ourselves against reality if we insist, but we cannot realistically anticipate some merciful moderation of the consequences. Nature does not scold or punish, it merely breaks us, coldly, upon the rack of our untruths.

Like other cultural institutions, calendars are saturated with ideologies, and tested to destruction against implacable reality. Their collision with nature is especially informative, because they express obstinate human desires as favored numbers (selected from among small positive integers), and they register the gulf of the real in a strictly quantitative form. Any surviving calendar relates the story of an adaptation to reality, or cultural deference to (and deformation by) nature, as numerical preferences have been compromised through their encounter with quantitative facts.

Pure ideology in the calendrical sphere is represented in its perfection by the fantasy year of the ancient Mesopotamians, 360 days in length, and harmonized to the sexagesimal (modulus-60) arithmetic of the Sumerians. Its influence has persisted in the 360 degrees of the geometric circle, and in the related sexagesimal division into minutes and seconds (of time and arc). The archaic calendars of Meso-America and East Asia, as well as those of the Middle East, seem to have been attracted to the 360-day year, as though to an ideal model. If the Great Architect of the Universe had been an anthropomorphic geometer, this is the calendar that would work.

Of course, it doesn’t (with all due respect to the engrossing Biblical counter-argument outlined here). Instead, in the mainstream world calendric tradition – as determined by the eventual global outcome – a first level adaptation systematized the year at 365 days – the Egyptian year. Unlike the 360-day archetypal year, which has all of the first three primes as factors, and thus divides conveniently into ‘months’ or other component periods, the 365-day year represents a reluctant concession to quantitative fact. The number 365 has only two factors (both primes, 5 and 73), but neither seems to have acquired any discernible calendrical valency, perhaps because of their obvious unsuitability to even approximate description of lunar periods. The Egyptians turned instead to an awkward but influential innovation: the intercalation. A five-day appendix was added to the year, as a sheer correction or supplementary commensuration, and an annual reminder of the gap between numerical elegance and astronomical reality. Whilst intercalations were invested with mytho-religious significance, this was essentially compensatory – a crudely obscured testament to the weakness of ideality (and thus of systematic priest-craft as a mode of reality apprehension, or efficient social purpose). If intercalations were necessary, then nature was not spell-bound, and the priest-masters of calendric time were exposed, tacitly, as purveyors of mystification, whose limits were drawn by the horizon of social credulity. Astronomical time mocked the meanings of men.

Over time, the real (‘tropical’) year discredits its calendrical idealizations by unmooring dates from the seasons, in a process of time drift that exposes discrepancy, and drives calendar reform. Inaccurate calendars are gradually rendered meaningless, as the seasonal associations of its time terms are eroded to utter randomness – by frigid ‘summer’ months and scorching ‘winter’ ones. Clearly, no priesthood can survive in a climate that derides the established order of the year, and in which farmers that listen to the holy words (of time) are assured inevitable starvation. Unless tracked within a tolerable margin of accuracy by a calendar that ‘keeps’ the time, the year reverts to an alien and unintelligible thing, entirely exterior to cultural comprehension, whilst society’s reigning symbols appear as a risible, senseless babble, drowned out by the howling chaos of the real.

With the introduction of the Julian Calendar, coinciding with the (non-event) of year zero, comes the recognition that the tropical year is incommensurable with any integer, and that a larger cycle of intercalation is required to track it. A kind of modernity, or structural demystification, is born with the relinquishment of the ideal year, and everything it symbolizes in terms of cosmic design or celestial harmony. The devil’s appendix is attached, irremovably.

Numeracy and time measurement divorce at the origin of caesarean Calendric Dominion, but it is easy to mistake accidents on this path for essential concessions to reality. Even allowing for the inescapable function of intercalations, there was nothing inevitable – at least absolutely or cosmically inevitable – about the utter ruination of numerical coherence that the Julian Calendar incarnated, and passed on.

To explore this (admittedly arcane) topic further requires a digression to the second power, into the relations between numbers and anthropomorphic desire. The obvious starting point is the 360-day calendar of ancient Sumer, and the question: What made this number appealing? Whether examining 360, or its sexagesimal root (60), an arithmetically-conventional attention to prime factors (2, 3, and 5), is initially misleading — although ultimately indispensable. A more illuminating introduction begins with the compound factors 10 and 12, the latter relevant primarily to the lunar cycle (and the archaic dream of an astronomically – or rather astrologically — consistent 12-month year), and the former reflecting the primordial anthropomorphism in matters numeric: decimalism. The 360-day calendar is an object of human desire because it is an anthropo-lunar (or menstrual-lycanthropic?) hybrid, speaking intrinsically to the cycles of human fertility, and to the ‘digital’ patterns instantiated in mammalian body-plans. A 360-day year would be ours (even if alien things are hidden in it).

Anthropomorphic decimalism suggests how certain numerical opportunities went missing, along with zero. ‘Apprehension’ and ‘comprehension’ refer understanding to the prehensile organs of a specific organism, whose bilateral symmetry combines five-fingered hands to produce a count reaching ten, across an interval that belongs to an alien, intractable, third. Triadic beings are monsters, and decimally ungraspable. The bino-decimal structure of the Yi Jing exhibits this with total clarity, through its six-stage time-cycle that counts in the recurrent sequence 1, 2, 4, 8, 7, 5 … Each power of three (within the decimal numerals) is expelled along with zero from the order of apprehensible time. There is no way that a ternary calendric numeracy could ever have been anthropomorphically acceptable – the very thought is (almost definitionally) abominable.

Yet astronomy seems hideously complicit with abomination, at least, if the years are twinned. The sixth power of three (3^6) approximates to the length of two tropical years with a discrepancy of just ~1.48438 days, or less than one day a year. An intercalation of three days every four years (or two twin-year cycles) brings it to the accuracy of the Julian Calendar, and a reduction of this intercalation by one day every 128 years (or 64 (2^6) twin-year cycles) exceeds the accuracy of the Gregorian calendar.

It might be necessary to be slightly unbalanced to fully appreciate this extraordinary conjunction of numerical elegance and astronomical fact. A system of calendric computation that counts only in twos and threes, and which maintains a perfectly triadic order of time-division up to the duration of a two-year period, is able to quite easily exceed the performance of the dominant international calendar (reaching a level of accuracy that disappears into the inherent instability of the tropical year, and is thus strictly speaking unimprovable).

How many days are there in a year? ((3 x 3 x 3 x 3 x 3 x 3) / 2) + ~0.74219

The horror, the horror …


Calendric Dominion (Part 3)

In Search of Year Zero

A Year Zero signifies a radical re-beginning, making universal claims. In modern, especially recent modern times, it is associated above all with ultra-modernist visions of total politics, at is maximum point of utopian and apocalyptic extremity. The existing order of the world is reduced to nothing, from which a new history is initiated, fundamentally disconnected from anything that occurred before, and morally indebted only to itself. Predictably enough, among conservative commentators (in the widest sense), such visions are broadly indistinguishable from the corpse-strewn landscapes of social catastrophe, haunted by the ghosts of unrealizable dreams.

Christianity’s global Calendric Dominion is paradoxical — perhaps even ‘dialectical’ — in this regard. It provides the governing model of historical rupture and unlimited ecumenical extension, and thus of total revolution, whilst at the same time representing the conservative order antagonized by modernistic ambition. Its example incites the lurch to Year Zero, even as it has no year zero of its own. Ultimately, its dialectical provocation tends towards Satanic temptation: the promise of Anti-Christian Apocalypse, or absolute news to a second power. (“If the Christians could do it, why couldn’t we?” Cue body-counts scaling up towards infinity.)

This tension exists not only between an established Christian order and its pseudo-secular revolutionary after-image, but also within Christianity itself, which is split internally by the apparent unity and real dissociation of ‘messianic time’. The process of Christian calendric consolidation was immensely protracted. A distance of greater than half a millennium separated the clear formulation of the year count from the moment commemorated, with further centuries required to fully integrate historical recording on this basis, digesting prior Jewish, Roman, and local date registries, and laying the foundation for a universalized Christian articulation of time. By the time the revolutionary ‘good news’ had been coherently formalized into a recognizable prototype of the hegemonic Western calendar, it had undergone a long transition from historical break to established tradition, with impeccable conservative credentials.

Simultaneously, however, the process of calendric consolidation sustained, and even sharpened, the messianic expectation of punctual, and truly contemporary rupture, projected forwards as duplication, or ‘second coming’ of the initial division. Even if the moment in which history had been sundered into two parts — before and after, BC and AD — now lay in quite distant antiquity, its example remained urgent, and promissory. Messianic hope was thus torn and compacted by an intrinsic historical doubling, which stretched it between a vastly retrospective, gradually recognized beginning, and a prospect of sudden completion, whose credibility was assured by its status as repetition. What had been would be again, transforming the AD count into a completed sequence that was confirmed in the same way it was terminated (through Messianic intervention).

Unsurprisingly, the substantial history of Western calendric establishment is twinned with the rise of millenarianism, through phases that trend to increasingly social-revolutionary forms, and eventually make way for self-consciously anti-religious, although decidedly eschatological, varieties of modernistic total politics. Because whatever has happened must — at least — be possible, the very existence of the calendar supports anticipations of absolute historical rupture. Its count, simply by beginning, prefigures an end. What starts can re-start, or conclude.

Zero, however, intrudes diagonally. It even introduces a comic aspect, since whatever the importance of the Christian revelation to the salvation of our souls, it is blatantly obvious that it failed to deliver a satisfactory arithmetical notation. For that, Christian Europe had to await the arrival of the decimal numerals from India, via the Moslem Middle East, and the ensuing revolution of calculation and book-keeping that coincided with the Renaissance, along with the birth of mercantile capitalism in the city states of northern Italy.

Indeed, for anybody seeking a truly modern calendar, the Arrival of Zero would mark an excellent occasion for a new year zero (AZ 0?), around AD 1500. Although this would plausibly date the origin of modernity, the historical imprecision of the event counts against it, however. In addition, the assimilation of zero by germinal European (and thus global) capitalism was evidently gradual — if comparatively rapid — rather than a punctual ‘revolutionary’ transition of the kind commerorative calendric zero is optimally appropriate to. (If Year Zero is thus barred from the designation of its own world-historic operationalization, it is perhaps structurally doomed to misapplication and the production of disillusionment.)

The conspicuous absence of zero from the Western calendar (count), exposed in its abrupt jolt from 1 BC to AD 1, is an intolerable and irreparable stigma that brings its world irony to a zenith. In the very operation of integrating world history, in preparation for planetary modernity, it remarks its own debilitating antiquity and particularity, in the most condescending modern sense of the limited and the primitive — crude, defective and underdeveloped.

How could a moment of self-evident calculative incompetence provide a convincing origin-point for subsequent historical calculation? Year Zero escaped all possibility of conceptual apprehension at the moment in the time-count where it is now seen to belong, and infinity (the reciprocal of zero) proves no less elusive. Infinity was inserted into a time when (and place where) it demonstrably made no sense, and the extraordinary world-historical impression that it made did nothing — not even nothing– to change that situation. Is this not a worthy puzzle for theologians? Omnipotent, omniscient, omnibenevolent, yet hopeless at maths — these are not the characteristics of a revelation designed to impress technologists or accountants. All the more reason, then, to take this comedy seriously, in all its ambivalence — since the emerging world of technologists and accountants, the techno-commercial (runway-industrial, or capitalist) world that would globalize the earth, was weaned within the playpen of this calendar, and no other. Modernity had selected to date itself in a way that its own kindergarten students would scorn.


Reign of the Tripod

China’s rise and the future of threedom

According to Arvind Subramanian, even conservative projections of comparative growth trends place China in a global position, by 2030, that is strikingly similar to that of Britain and of America at their respective moments of economic predominance, accounting for a share of the world economy roughly 150% the size of its closest rival. If this were to come to pass, such leadership would invoke ‘hegemony’ as a matter of sheer quantitative fact – quite irrespective of explicit intentions. The ‘Chinese model’ would promote itself, even in the complete absence of political and diplomatic reinforcement, and the magnetic power of Chinese culture would continue to strengthen in approximate proportion to its commercial influence. China would become the object of irresistible attraction – counterbalanced, no doubt, by resentments – and its example would burn incandescent, even in the offended eyes of its detractors. So what is this ‘example’?

In exploring this question, one place to begin is the history of economic hegemony, and in particular that instantiated by the Anglo-American powers over their two ‘long centuries’ of global supremacy. This is a topic pursued with exceptional insight by Walter Russell Mead, most remarkably in his work God and Gold: Britain, America, and the Making of the Modern World.

Mead locates the key to ‘Anglosphere’ hegemony in the ‘Golden Meme’ of the invisible hand, originating in the religious idea of providence, and modernized in Newtonian celestial mechanics, Smithian political economy, and Darwinian evolutionary biology. At its most abstract, this idea is both an affirmation and a renunciation, with its potency and suppleness stemming from both. To acknowledge the invisible hand is to foster a special kind of positive fatalism, trusting in the spontaneous trend of history, which is embraced as a covenant, and an overt or implicit election (in the theological sense). Such themes are undisguisedly religious, and Mead does nothing to obscure their roots in the Abrahamic tradition, or meta-tradition, which lays out a providential vision of history as finite, progressive, and inevitable, tending inexorably to eschatological completion, structured by superhuman law, and (through its divine predestination) facilitating the function of prophecy.

The deep culture of the Anglosphere is not only generically Abrahamic, however, it is also specifically pluralistic. The invisible hand takes center stage because the center is otherwise vacated, or distributed. Esoteric providence supplants exoteric sovereignty because an inability to reach agreement is eventually institutionalized – or at least informally stabilized — in a triangular balance of power.

What the British ultimately did was to rely on what Burke called “convention.” Scripture, tradition, and reason – each had its place and each had its devotees. But all of them went wrong if you pressed them too far. You should respect the scriptures and defer to them but not interpret the scriptures in a way that led you into some weird millenarian sect or into absurd social behavior. You honored tradition but did not press it so far that it led you into the arms of royal absolutism or papal power. You can and should employ the critique of reason against the excesses of both scripture and tradition, but not press reason to the point where you ranted against all existing institutions., ate roots and bark for your health, or, worse, undermined the rights of property and the established church. One can picture John Bull scratching his head and slowly concluding that one must accept that in society there will be bible nuts, tradition nuts, and reason nuts – fundamentalists, papists, and radicals. This is not necessarily the end of the world. To some degree they cancel each other out – the fundamentalist zealots will keep the papists down and vice versa, and the religious will keep the radicals in their place – but the competition among sects will also prevent the established church from pressing its advantage too far and from forming too exalted an idea about the proper stature, prestige, and emoluments of the clergy. [p223]

Cultural hegemony follows from a semi-deliberate fatalization, as the sovereign center is displaced by a substantially automated social process, which no social agent is able to master or entirely impede. Each major faction steps back into its position in the triangle, from which it can strategically engage the others, but never fully dominate or eradicate them. The triangle as a whole constitutes a social and historical motor, without adequate representation at any identifiable point.

Pluralism, even at the cost of rational consistency, is necessary in a world of change. Countervailing forces and values must contend. Reason, scripture, tradition: they all have their uses, but any one of them, unchecked, will go too far. Moreover, without constant disputes, constant controversy, constant competition between rival ideas about how society should look and what is should do, the pace of innovation and change is likely to slow as forces of conservative inertia grow smug and unchallenged. [p231-2]

This blog has previously touched upon the Singlosphere, where aspects of Anglophone and Chinese culture converge in Manchester Liberal / Daoist acceptance of spontaneous order, or laissez-faire. Does this convergence extend to triadic pluralism, and apply to the Sinosphere core of the Chinese mainland? Mead’s analysis is highly suggestive in both respects.

In the first place, it encourages considerable equanimity in regards to the prospective global transition, even when attention is focused upon the political and ideological heartland of contemporary China. It might seem, superficially, that the passage from a leading world culture dominated by tacit Christian attitudes to one in which unfamiliar Sino-Marxist ideas rise to unprecedented international prominence must be characterized by an immense – even near-absolute – discontinuity. Can such a leap take place without succumbing to catastrophic culture-shock and unmanageable friction? When examined from a broader perspective, however, such alarmism is far less than fully warranted.

For better or for worse, the over-arching cultural continuity of the coming shift is ensured by the profound kinship tying Marxism into the broad family of Abrahamic belief systems. Theologically rooted in the dialectical engagement with Judeo-Christian spirituality, initiated by Hegel and Feuerbach, the basic framework of Marxist thinking only trivially perturbs the structure of prophetic, eschatological, redemptive, and providential history. Its millenarian expectations are no more terrifying than those of Jewish and Christian apocalypticism before it, its prophetic certainties no more irrational, its submission to the iron laws of history no more constraining, and its moral enthusiasm no more zealous or impractical.

The specter of a totalitarian Marxist resurgence in China is as realistic as the fear of a theocratic putsch in the United States of America, which is to say, it has no reality at all. In both cases, maturity, pluralism, and established traditions protect against the domination of society by any particular intolerant faction. It is unnecessary to be either Christian or Marxist to recognize the continuing world-historical momentum of a broad Abrahamic meta-narrative, or to accept the consistency of such large-scale social storytelling with the perpetual regeneration of practical impetus, or to see a settled, spontaneously improvised social solution – and incarnation of dynamic conservatism – in the enduring triangular stand-off between Marxist scriptures, Communist Party institutional traditions, and market radicalism in today’s China. As with Mead’s Anglospherean pluralism, the reciprocal limitations that each of these factions imposes on the others will inevitably disappoint many, but there is no reason for them to horrify anybody.

Insofar as Mead is correct in identifying Anglosphere hegemony with the reign of the tripod, or the socio-cultural realization of pluralism (as triangular dynamic stability), the disruptive potential of emerging Chinese leadership should be considered as massively discounted, because the tripod is a Chinese native. Every temple in the country is equipped with a three-footed incense burner, every museum bronze collection is dominated by three-legged cauldrons, and each of these tripods has definite, explicitly conceptual cultural meaning. This is not only based upon the obvious practical and intuitive truth that the simplest model of stability comes from the tripod, but also from a recognition that triangular stand-off exemplifies sustainable dynamism in its elementary form, disintegrating the universe into strategic possibility.

For literary elaboration of this theme, one need only turn to the Romance of the Three Kingdoms, perhaps the most widely read of China’s four great classical novels. Its most conspicuous instantiation as popular entertainment is seen in the game of paper, scissors, stone, which dates back (at least) to the Chinese Han Dynasty (206 BC – AD 220), when it was known as shoushiling.

The ultimate expression of triangular dynamic stability, not only in China, but worldwide, is undoubtedly presented by the Classic of Change, the Yi Jing, or Zhouyi. It is upon this work of singular, inhuman genius, in which sheer arithmetic speaks more purely than it has ever done before or since, that all of China’s ceremonial bronzes, literary flights, and childhood games converge.

In the numerical system of the Yi Jing, the tripod finds a source more basic than the Abrahamic meta-tradition can provide, regardless of how Trinitarian this latter has become. That is because, in this Chinese cultural ur-stratum, unity does not figure as an original unity, subsequently disintegrated into a theological, dialectical, or sociopolitical triangle but is, on the contrary, derived. As the Confucian commentary explains: “The number 3 was assigned to heaven, 2 to earth, and from these came the (other) numbers.” In the beginning were numbers – primordial dispersion.

The ‘language’ of the tripod finds its most convenient expression in the trigram, whose three lines constitute an elementary unit. To grasp the Yi Jing as a complete arithmetical model of the dynamic triad, however, it is necessary to proceed immediately to the structure of the hexagram.

Grasped in operation, the Yi Jing is not only a binary arithmetical system (as Leibniz interpreted it), but a bino-decimal conjunction. This is demonstrated by the fact that it systematically rewards the application of decimal digital reduction, and reveals its dynamic pattern only under these conditions. (This might, quite reasonably, be considered a highly surprising suggestion, since digital reduction – as it arose within the history of Western Qabbalism – seems to have been generated, automatically, from the interference of the decimal Hindu numerals with older alphabetical number systems, or ‘gematrias’, that attached cardinal values to specific letters, without use of place value. It is immediately obvious that this historical account cannot be translated into a Chinese context, where alphabets have no traditional root.)

Digital reduction is an extremely simple numerical technique, involving nothing besides single-digit additions and neglect of decimal magnitude. A multi-digit number is treated as a string of single digit additions, and the process is reiterated in the case of a multi-digit result.

Expressing the series of binary powers in decimal notation yields the familiar sequence 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192 … When this series is compressed to a string of single digits by reduction, it proceeds: 1, 2, 4, 8, (1 + 6 =) 7, (3 + 2 =) 5, (6 + 4 =) 1, (1 + 2 + 8 = 11 = 1 + 1 =) 2, (2 + 5 + 6 = 13 = 1 + 3 =) 4, (5 + 1 + 2 =) 8, (1 + 0 + 2 + 4 =) 7, (2 + 0 + 4 + 8 = 14 = 1 + 4 =) 5, and repeatedly, through the 6-step cycle 1, 2, 4, 8, 7, 5. This process exposes the arithmetical necessity of the Yi Jing hexagram, as an archetypal exhaustion of the phases of time.

To excavate the triadic or tripodic, it is helpful to turn to the classical (and now integral) Confucian commentary, the ‘Ten Wings’ (Shi Yi), which explore the structure of the trigrams and hexagrams in various ways. These include an explicit formula for folding the six lines of the hexagram back into a triad, by coupling the lines: first and fourth; second and fifth; third and sixth. These dyads have a consistent arithmetical order, when calculated in accordance with the reduced bino-decimal values generated above: 1 + 8 = 9; 2 + 7 = 9; 4 + 5 = 9. “What these six lines show is simply this, the way of the three Powers.”

Summation to nine regularly serves as a confirmation within the Shi Yi. For instance, in the section translated by Legge as ‘The Great Appendix’:

52. The numbers (required) for Khien (or the undivided line) amount to 216; those for Khwan (or the divided line), to 144. Together they are 360, corresponding to the days of the year.
53. The number produced by the lines in the two parts (of the Yî) amount to 11,520, corresponding to the number of all things.
54. Therefore by means of the four operations is the Yî completed. It takes 18 changes to form a hexagram.

144 = 1 + 4 + 4 = 9

216 = 2 + 1 + 6 = 9

360 = 3 + 6 + 0 = 9

11,520 = 1 + 1 + 5 + 2 + 0 = 9

18 = 1 + 8 = 9

There is much more to say on the importance of the number nine in traditional Chinese culture, and beyond, but this is not the time. For now, it suffices to note that nine, or ‘Old Yang’, represents the extreme point of maturity or positive accumulation in the Yi Jing, and thus incipient transition. It thus echoes the function of the same numeral within a zero-based decimal place-value system, strongly reinforcing the impression that the Yi Jing assumes cultural familiarity with such numeracy, and thus indicating its extreme antiquity within China.

The six-phase cycle collapses into a triadic dynamic, whose stages are the dyads 1&8, 2&7, 4&5. It is thus exactly isomorphic with the paper, scissors, stone circuit, or rather, this latter can be seen as a simplification of the Yi Jing dynamic tripod, treating each stage as simple, rather than twinned. Where the bagua, or set of trigrams, merely enumerates the set of 3-bit variants in static fashion, the system of hexagrams rigorously constructs a triangular dynamic, which is presented as a model of time.

If this is the ‘Chinese example’ at its most quintessential, then it is exactly the Anglosphere example, as determined by Mead, except carried to a far more exalted level of abstraction, or proto-conceptual purity. Dynamic pluralism is under no threat from a Chinese future, insofar as deep-cultural evidence counts for anything. The reign of the tripod has scarcely begun.