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 …