Janus

[Greg W. Goodwin]

The janitor (a word of the same origin) of gates, doors, passages and bridges in Roman mythology was the god Janus for whom the month January is named. Janus is depicted as a figure with a double face looking opposite directions, one face looking into the past and one facing the future. The underlying psychological concept seems to have been that of sensing a certain change of state as one room was exited and another room was entered, or one year was left behind and another year entered into. Janus is a double god with a masculine and feminine persona, Janus and Jana, the masculine persona representing the sun and the feminine persona representing the moon. According to legend Janus was granted by the god Saturn the gift of being able to perceive simultaneously both the past and the future. To the Romans Janus was the representative of time itself and of all beginnings in general. The month January dates back to the Roman calendar.

The origin or evolution of the Western calendar expressed briefly:

Athenian
Roman
Julian
Viking
Gregorian

Each of these calendar systems contributed something to the structure of the current Gregorian calendar. The Gregorian calendar was adopted as the official Western-Christian calendar by Pope Gregory XIII on 24 February 1582.

The Gregorian calendar is the international standard for civil use. It initially regulated the ceremonial cycle of the Roman Catholic and Protestant churches. Its original purpose was religious.

Years are divided into two classes: common years and leap years. A common year is 365 days in length; a leap year is 366 days, with an intercalary day, designated February 29, preceding March 1. Leap years are determined according to the following rule: every year that is exactly divisible by 4 is a leap year, except for years that are exactly divisible by 100; these centurial years are leap years only if they are exactly divisible by 400. Consequently the year 2000 is a leap year, whereas 1900 and 2100 are not leap years. Year 0 (1 B.C.) is considered to be exactly divisible by 4, 100, and 400; hence it is a leap year.

The Gregorian calendar based on a cycle of 400 years, comprising 146097 days. 146097 is equally divisible by 7 so the Gregorian civil calendar exactly repeats after 400 years. Dividing 146097 by 400 yields an average length of 365.2425 days per calendar year, this is a close approximation to the length of the tropical year. The Equation 1.1-1 reveals that the Gregorian calendar accumulates an error of one day in about 2500 years. As of yet no adjustments to the leap-year system have been proposed.

The months and days per month are adopted from the Julian calendar.


Just as an example of the complicated precision involved in this system the following is an algorithm for computing the date of Easter based on the algorithm of Oudin established in 1940. It is valid for all Gregorian years, designated as Y. All variables are integers and the remainders of all divisions are dropped. The final date is given by M, the month, and D, the day of the month.


C = Y/100,
N = Y - 19*(Y/19),
K = (C - 17)/25,
I = C - C/4 - (C - K)/3 + 19*N + 15,
I = I - 30*(I/30),
I = I - (I/28)*(1 - (I/28)*(29/(I + 1))*((21 - N)/11)),
J = Y + Y/4 + I + 2 - C + C/4,
J = J - 7*(J/7),
L = I - J,
M = 3 + (L + 40)/44,
D = L + 28 - 31*(M/4).

The main astronomical cycles are based on the rotation of the earth on its axis, a day. The revolution of the earth around the sun, a year. The third is the revolution of the moon around the earth, a month. Complexity develops due to the fact that these cycles of revolution do not involve an equal number of days. These astronomical cycles are not constant or exactly coordinated one with the other.

The astronomical year, also known as the tropical year, is the elapsed time it takes the sun to move from a direct overhead on one of the Tropics (the vernal equinox, March 21st in the Northern Hemisphere) and return. The astronomical year has a mean length of 365.2422 solar days, or 365 days, 5 hr, 48 min, 46 sec.”

The tropical year is defined as the average interval between vernal equinoxes. It is the cycle of the seasons. Based on the orbital elements of Laskar (1986) the following is used for calculating the length of the tropical year:

365.2421896698 - 0.00000615359 T - 7.29E-10 T^2 + 2.64E-10 T^3 [days] where T = (JD - 2451545.0)/36525 and JD is the Julian day number. The interval from a particular vernal equinox to the next may vary from this average by several minutes.

The length of a year is an averaged mean and as such is relatively constant. There are variables changing the length of a year from year to year, but the progressive and minute changes take place sporadically and these minor changes in the length of a year are corrected periodically:

A leap second is a second added to Coordinated Universal Time (UTC) to make it agree with astronomical time to within 0.9 second. UTC is an atomic time scale, based on the operation of atomic clocks. Astronomical time is based on the rate of rotation of the earth. Atomic clocks are more stable than the rate at which the earth rotates and leap seconds are added to equalize the two time scales in agreement.

On June 30, 1972 the first leap second was added. Leap seconds are added slightly less than one per year. A negative leap second is a possibility, the subtraction of a second because the earth sped up. As it is all leap seconds have been additions. A leap second was add for 2008. It is currently unclear exactly why the earth losses second every few years in relation the relative constant of atomic time.

The year, the average mean time it takes the earth to orbit the sun, is a reliable constant for all practical purposes. The concept of a year, the concept of a predictable traverse of time wherein the earth relative to a predicted position of the sun on the horizon returns to a point of origin but one period advanced, only varies by a second from year to year. In fact the earth is on average either speeding up or (theoretically) slowing down, but taken as an median there is no significant variation from the point of view of the scale of man’s sense of time. A year is 365 and a quarter days, fundamentally the same as it was thousands of years ago when the Egyptians built the pyramids.

What we commonly call a year, the complete orbit of the earth around the sun, with its current beginning and end in January, a convention arrived at over a period of thousands of years of human experience and codified as civilization developed refinements, is significant to the psychological sense of men. This is subjective, but it is not entirely an isolated idea. The ancients built most notably Stonehenge, Machu Picchu and hundreds of other astronomical sites in order to keep track of the recurrence of the stars, the sun and the moon in relation to the same reference location in time and space. The beginning of the new year, often referred to by the convention “New Years” (no apostrophe), is a universal psychological beginning of an octave of time (the word “octave” is a Fourth Way term indicating an activity that begins with one DO and ends with another DO) recognized through the cultural mentality of modern nations.

Just on the simplest scale, the midnight revelers celebrate in Times Square on one winter night and then one year later, 365 days later, they do the same thing again, but unavoidably older and filled with experience that they did not possess the year before. This is an octave. The tradition of the “New Year’s resolution” is just one cultural indicator that men in general recognize this time, the first day of January, as a new beginning.

This is an obvious and simple point that all reasonable people will agree to. Here are some thoughts on the subject from Rodney Collin (a student of Ouspensky and unaffiliated with Gurdjieff, other than following some of the principles of Gurdjieff’s teaching):

III THE CALENDAR: SUPERHUMAN AND SUBHUMAN TIMES

“Nevertheless, men - their own inner clocks set each at a different and personal time have to live together, and in living together to set up a convenient common measure of time in which all can concur, however misleading that common time may be. For this purpose they quite naturally have recourse to a unit of the time of the higher cosmos which embraces them. They measure their own, each others’, and their ancestors’ lives by the breathing of the Earth, that is, by the time the Earth takes to revolve about the Sun, by years.

“Now a year is an extremely interesting and complete unit of time, full of inner connections and relations, and which may perhaps be taken as the classical pattern of an organic time-form. For since, as we established in the second chapter, the dimensions of space and time become interchangeable as we pass from one cosmos to another, then evidently certain patterns in time must represent organic forms just as certain patterns in space do. A year is such an organic time-form, with its own functions or festivals and its own inner circulation between them. So that, although different individuals will pass through a year at different speeds according to their own personal time, that year will nevertheless bring them all comparable experiences and possibilities, and will represent a fixed common relationship for all of them.

“Thus, for all men on one half of the earth, the same day of the year will be shortest, the same days will mark the waxing of the sun’s power, the same day its longest light. Definite fractions of the year will separate seed-time and harvest, moisture and drought, the flower and the fruit. If a man and a woman engender a child, seven-ninths of a year will bring about its birth, no matter how different their personal times may be. The year in fact represents a great dance in which all men, animals, birds, trees and plants upon the surface of the Earth take part, no matter how quickly or how slowly they themselves pass through it.

“Let us mark 360 days of the year round the 360° of a circle, leaving uncounted and ‘outside time’ the five days between Christmas and New Year, between the end and the beginning. In this circle of the year tradition marks three major points - the festival of the midwinter solstice or Christmas, when all life is hidden and invisible; the festival of rebirth or Easter; and the festival of harvest. These three festivals are typified by the three stages of natural growth - root, flower and fruit - and in a very general way their intermediate periods represent, not only for plants, but for all living beings an ever-repeating cycle of gestation, ripening and reaping.

“Thus once again we come to the now-familiar figure of the triangle within the circle. If we make the centre of this circle to represent the Earth, and place about the triangle the twelve signs of the zodiac against which the Sun moves in the course of the year, we see also that this divine triangle represents the Sun’s path. And if we further add the six intermediate points and the strange movement between them, which in the Solar System we found to represent the invisible circulation of light, we find the pattern of a year indeed to correspond with this fundamental pattern of all truly cosmic beings and forms.

“Many calendar-systems - the Aztec one of eighteen twenty-day months with five ‘dead’ days, for example - evidently derive from this conception of the year as a nine-pointed circle. For each division thus represents forty days. In modern times these organic divisions of the year are clearly indicated by certain moveable feasts - Ash Wednesday oscillating between points 1 and 2, Easter between points 2 and 3, and Whitsunday between points 3 and 4. Forty days - Christ’s sojourn in the wilderness - thus represents a definite period in which certain things can be achieved, matured or fixed. While multiples of forty days, joined together by the line of invisible inner circulation, remain connected across time by unseen processes of germination or understanding.

“Winter wheat, sown at point 7 (October 6), following the mysterious motion 142857, is harvested at point 4 June 9); spring corn, sown at point 2 (March 21), is in turn reaped at point 7. The soil, frozen or desiccated at one date, must be thawed or softened with rain at another date innerly connected with it. While to human beings, all unwitting, memories, moods and the result of long-forgotten actions, emerge suddenly out of invisibility along this hidden circulation between one part of a year and another. A given day in a given spring must certainly be experienced at the speed appropriate to the observer’s age and type. But apart from this it will also bring him echoes from the same day in all other springs, and it will be connected in yet another way with a certain day of that summer and all other summers, with a certain day of that autumn and all other autumns. In this way, a year represents for man not a line but a rippling and scintillating web of trans-temporal echoes.

“A year is not at all a unit of individual time, as we often suppose, but rather the scenery through which personal time passes. For man’s time moves against the background of the Earth’s time, itself also moving, yet so relatively slowly that it seems to him motionless - as a background of moving clouds appears motionless in contrast to a swift-sailing ship in the foreground.”