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The Structure of Cycles

Numerical Clues from Antiquity

The mathematical model used in the last chapter to illustrate cyclic properties is applicable only to the arguments to show that time as a whole is cyclic, in a way which remains confined to generalities. But this conception must be pursued into particulars if it is to connect with what is known about history. For this purpose it will be necessary to examine the structure of actual time-cycles as they have been understood in the past, though without any attempt to attach historical dates to them at this stage. Direct connections with history, although important, are often unsatisfactory because history always shows a greater complexity than can be accounted for in theory. Nevertheless, this still does not mean that the broad outline of history cannot be grasped theoretically, as I shall try to show later.

The most important quantity to be ascertained is the length of the cycle which contains the era of recorded history, a quantity which has frequently been given in chronologies, but nearly always by means of symbolical numbers. A study of such chronological periods shows them to be made up of shorter cycles, and these in turn are made up of yet shorter ones. This property alone makes it very difficult to determine whether the beginning of a given cycle really coincides with the origin of the human race, or whether that origin only goes back to the beginning of one of the lesser cycles of which it is composed. The subordinate cycle recapitulates within its own compass many of the features of the greater cycle, providing more grounds for confusion. To illustrate this, it may be useful to examine the symbolic quantity of 432,000 years, which has an important place in chronology because of the way in which it recurs in widely differing cultures apparently unconnected in time or place, and because of its astronomical connections.

A Universal Number

The writings of the Babylonian historian Berossos contain an account of ten kings who reigned in succession from ‘the descent of kingship from the courts of heaven,’ to the great Flood, a period corresponding to the biblical period from Adam to Noah, the age of the Patriarchs. He gives the length of each reign, which in each case is a period far in excess of any human lifetime measured in years, and their grand total comes to exactly 432,000 years. The figures seem to have a symbolic meaning, as also is the case with other ancient texts from Sumeria which give total periods of 241,200 and 456,000 years for these same antediluvian kings. These numbers are related to 432,000, moreover, inasmuch as all three are multiples of 1,200, the factors being 360, 201, and 380 respectively. (A period of 12,000 years also divides exactly into two of the above three numbers, and this period was reckoned to be a ‘divine year’ in some traditions, including that of India.) There is no apparent relation between these numbers and those given in the Book of Genesis for the same period, but I shall examine the meaning of this divergence in the next chapter.

When we turn to another tradition as different as possible from those of the Near East, that of the Icelandic Eddas, there appears an apocalyptic verse which is translated as follows:

Five hundred doors and forty there are,

I ween, in Valhall’s walls;

Eight hundred fighters through each door fare,

When to war with the Wolf they go.1

The ‘war with the Wolf’ is another expression for the last battle, the Ragnarök, when the powers of darkness overwhelm the gods. The number of combatants who are said to emerge here is thus 540 x 800 = 432,000. Appearing as it does in connection with the end of a world, this number will have a relation to its total duration, and such a recurrence is too much for coincidence. This number also appears in ancient tradition in higher multiples, including 4,320,000, and this number has a particular astronomical significance.

It has hardly been noticed that this number could have been found from an astronomy which required only naked-eye observation of the planets and records of them extending over one or two centuries. The planetary bodies, including the moon, have each at least one cyclic period after which they return to the same place in the zodiac on the same date as at the beginning of the cycle. For the moon, this is 19 years, the period of the Metonic Cycle. For Mercury and Mars, by a strange coincidence, it is 79 years in either case; while for Venus it is 8 years. For Jupiter it is taken to be 12 years, though this is less exact, being rounded up from 11.86 years, and for Saturn it is 30 years, this being rounded up from 29.45 years, and so also less exact.

Now with these quantities it is possible to define a universal era by means of the time it takes for all six of these bodies to return to the same positions in the sky they had at the beginning of the era. One way of calculating this period would be simply to multiply all these numbers together, without attempting to take out common factors. The resulting figure would be exactly divisible by each separate planetary cycle and therefore common to all six bodies. Thus the time for the moon, Mercury, and Mars to return to their same relative positions would be 19 x 79 = 1,501 years, which for the present purpose will be rounded to 1,500 years. Likewise, the time for the moon, Mercury, Mars, and Venus to return to the same places would be 1500 x 8 = 12,000 years. For these four bodies and Jupiter so to return, it would be 12,000 x 12 = 144,000 years; and for these five together with Saturn, it will be 144,000 x 30 = 4,320,000 years.

Thus with slightly idealized and unsimplified factors, this fundamental cosmological quantity of 432,000 has a direct relation to the phenomena of the Solar System. It constitutes a measurement for what the ancients called the ‘mundane apocatastasis’, some estimates for which went into many millions of years. It can be seen that the separate factors of 12 and 30 for Jupiter and Saturn did not have to be included if the shortest period of recurrence was all that was required, since 12,000 (the period for the moon, Mercury, Mars, and Venus) is exactly divisible by either 12 or 30. This gives an additional reason for the importance of the 12,000-year period in ancient chronology, while underlining the symbolical nature of the 432,000 years. This is by no means the only astronomical explanation of it, as will be shown later.

Returning to the subject of apocalyptic images which contain numbers relevant to the cosmic periods, these appear in the New Testament in its account of the New Jerusalem, of which each side measures 12,000 furlongs, the height being also 12,000 furlongs.2 The area of each of the sides would thus be 144 million square furlongs, and its volume would be 123 or 1,728 million cubic furlongs (1,728 is also equal to 4 x 432). Elsewhere in the same text a similar number system arises where it is stated that ‘there were sealed an hundred and forty and four thousand of all the tribes of Israel,’3 that is, 12,000 from each of the twelve tribes. (The sacred significance of twelve in Jewish tradition is exoterically owing to there being twelve tribes of Israel.) There are twelve gates in the walls of the New Jerusalem, one for each of the twelve tribes, each numbering 12,000, again expressing the number 144,000. The connection between this number and the number in the Edda is a factor of three, as 144,000 x 3 = 432,000, and a second factor of three makes another of its astronomical connections, as will be shown.

To explain the significance of numbers made up of products of 12 and 1,000, it should be realized that 1,000 symbolizes totality since it is the cube of 10, and therefore a product of length, breadth, and height, and therefore in a sense the whole of space and the whole of creation. Twelve, on the other hand, symbolizes fullness in a more qualitative manner, being a product of three and four, where these numbers stand for the Forms and the material cosmos respectively. This aspect of twelve is acknowledged in innumerable groupings of twelve in both the Bible and in folklore.

If the factor of three is applied once more to this number system, i.e., 432,000 x 3 = 1,296,000, the result is 100 times 12,960, which is a very close approximation to a period in years which is of importance in astronomy as the semi-period of the precession of the equinoxes. This period is the time taken for the sun’s positions at the Spring and Autumn equinoxes to retreat halfway round the zodiac, and so change places. Thus, if the sun was at 0 degrees Aries at the spring equinox (as it was about two thousand years ago), and at 0 degrees Virgo at the autumn equinox, it would take nearly 12,960 years for these positions to move until the sun was at 0 degrees. Virgo at the spring equinox and at 0 degrees Aries at the autumn equinox. This relative shift between the sun’s circuit and the fixed stars is very slow, therefore, about one degree in seventy-two years.

However, this is the cosmic movement whose length is related to those of 432,000 and 144,000 years by simple factors. It also reappears in the so-called ‘Nuptial Number’ in Plato’s Republic, where it defines a cosmic period in accordance with which human affairs such as marriages should be arranged.4 In this discussion of number, the favorable times, which are presumably proportioned down to the measures of human lifetimes, are said to be governed by the product of 3, 4, and 5, raised to the fourth power. These three numbers are those of the first Pythagorean triangle, and their product is sixty: 3 x 4 x 5 = 60; 602 = 3,600, and the square of this, (3,600)2 = 12,960,000. Two ways of reaching this result are given, one of which involves squares, i.e., 362 x 1002, and the other involves a product of unequal quantities, i.e., 27 x 48 x 1002, from a different arrangement of the 3, 4, and 5.

A very similar connection between the precessional period and the 432,000-year period is to be found from the sexagesimal arithmetic of Babylonian astronomy, in which the longest period, the Great Saros, was equal to 60 x 60 x 60 = 216,000 years, and where two of these periods add up to 432,000 years. It is remarkable that the ancient chronologies should be linked so closely to a cosmic cycle which is supposed not to have been measured accurately until modern times, as Joseph Campbell has pointed out.5 Either there were sources of scientific knowledge in antiquity which are now unknown, or the arithmetic based on powers of sixty has given rise to an extraordinary coincidence.

The Period for the Kali-Yuga

Another source for this universal quantity is to be found in the chronology of ancient India, which gives a period of 4,320,000 years as that of a world-cycle, usually called a Manvantara or ‘era of Manu,’ who was India’s original lawgiver. (Guénon argues that he may also be the lawgiver of the Romans, since the Roman Numa is simply Manu with the syllables transposed. The name Minos in Greek tradition seems to be of the same origin.)

This universal era is said to be divided into four lesser cycles or Yugas, corresponding to the ages of Gold, Silver, Bronze, and Iron, as described in chapters 5 and 7. However, the Indian chronology assigns symbolic periods of time to each of the four Yugas, which are listed in order as follows:

The shortest of the four, the Kali-Yuga, is thus one-tenth the length of the total cycle. The order of these cycles, it should be noted, follows that of the Pythagorean Tetraktys in reverse: 4 + 3 + 2 + 1 = 10. This numerical symbol shows how the first four numbers are in a sense the equivalent of all numbers, as they produce the decad.

If these numbers are taken literally, the present era of Manu would extend far beyond the longest time assignable to recorded history, and this has resulted in this subject’s confinement to the realms of myth. But this attitude results from the loss of means of estimating the historical length of the present world, since the problem is precisely that of discovering what practical time values are contained in the symbolic periods. We are at least given an exact date for the beginning of the Kali-Yuga, i.e., February 16, 3102 bc, and it is obvious from the perspective of the present time that this cycle must have only just begun if the above numbers had to be taken literally; there would still be some 427,000 years more before its end. One reason for not taking such numbers literally is that mathematicians in antiquity preferred the use of very large numbers to the introduction of decimal points or fractions. By making the unit quantities small enough, exactness could be obtained with whole numbers.

Concerning the date, 3102 bc, it is a date which lies at the furthest limit of historical knowledge. Even the Pyramid Texts are dated only a little earlier than this time. The latter are an exception to the lack of intellectual contact with civilizations dating from before the present ‘iron age’. The general lack of evidence for still earlier civilizations is consistent with the discontinuities between cycles which are implied by the theory, although it is dangerous to support any theory on a mere absence of evidence. In fact this is not necessary because there are always at least vestiges of the long-lost ages. Both human remains and artifacts of an antiquity extending over many millions of years have been found, and however isolated and scattered they are, it should be clearly understood that just one such item of geological antiquity would be enough to explode the entire edifice of evolutionary theories as to man’s so-called ‘primitive origins’. One human bone or metal artifact dating from the Carboniferous era is all it would take, and in reality there are more than one. J. Davidson gives an account of a number of such finds which have been collected and described by geologists.6

The barriers between world-ages are thus by no means absolute, even though they rule out any spiritual or cultural transmission from one to another. They are formidable enough, even where they divide only secondary cycles like the Treta-Yuga and the Dvapara-Yuga, and this suggests the possibility that there may be more such barriers even during such cycles as these. This would be the case if they were made up of yet smaller cycles, for example if the Kali-Yuga itself went through four cycles of its own. That this should be so would follow from what was argued earlier in chapter 3. The shortest cycles of time in ordinary experience, like those of day and night, would truthfully reveal the nature of temporal change as it extends to even the longest periods. There would in this case be no reason why there should not be a continuous range of cycles from the longest, like the Manvantara, down to the shortest, like a year or a day. This would mean that the longest cycle would be made up of a very large number of cycles, and the effect of this would be a superficial disorder similar to that of a large number of musical instruments playing together. The note played by each instrument will make a regular pulsation, but the sum of all these regularities will be highly irregular, if a profile of the sound waves is constructed. Similarly to this, the superimposition of numerous time-cycles will account for much of the apparent disorder of history.

Further Numerical Relationships

The numbers given for the four Yugas give a hint of this possibility of further subdivision in the number of zeros they contain. By the repeated division by ten which they allow, we can reduce the four Yugas to further sets of lower sub-cycles. Thus if the Krita-Yuga or Golden Age is also divided in the same ratios of 4 : 3 : 2 : 1, the last and shortest of them will likewise be one-tenth of the whole:

Similarly, further divisions of the cycle by 100 and then by 1,000 will yield yet smaller cycles, still with the same ratios as those of the first ones. This is how it could be said that the Krita-Yuga or Golden Age has its own golden age, and then its own silver, bronze, and iron ages. Likewise the three other Yugas will have their own golden, silver, bronze, and iron ages, and in this way all the permutations will be worked out until the final limit is reached with the iron age of the Iron Age. Such a process of recapitulation inherent in time would be a natural cause of confusions between remote periods and later ones in which they re-emerge on a different scale. There may also be confusions between critical events which may be the same in form while differing widely in their range of effects, as with various major inundations which have been taken for the biblical Flood. Such confusions could not be resolved until the durations of the cycles divided by such events were ascertained.

The cyclic recapitulation as described so far can be expressed much more economically by means of numbers. Taking the Manvantara as the primary cycle, one may represent the secondary cycles, i.e. the Golden, Silver, Bronze and Iron Ages by 4, 3, 2, 1. The same numbers will then also be used to denote the next subordinate cycles with the same qualities, which we may call the tertiary cycles. Thus the Silver Age of the Golden Age would be denoted by 4 + 3, and the Iron Age of the Bronze Age would be denoted by 2 + 1. The numbers 4 to 1 will be added in turn to the numbers 4 down to 1. By this means, sixteen tertiary cycles can be expressed as follows:

Golden Age

4 + 4,

4 + 3,

4 + 2,

4 + 1

Silver Age

3 + 4,

3 + 3,

3 + 2,

3 + 1

Bronze Age

2 + 4,

2 + 3,

2 + 2,

2 + 1

Iron Age

1 + 4,

1 + 3,

1 + 2,

1 + 1

Each cycle is represented here as a composite of secondary and tertiary cycles by a sum of two numbers which stand for the respective qualities of the parts in question and fix their place in the whole order. The highest sum, 8, is found only in the first, and the lowest, 2, only in the last, whereas all the others are repeated once, twice, or three times, as the following summary shows:

Golden Age

Silver Age

Bronze Age

Iron Age

8, 7, 6, 5

7, 6, 5, 4

6, 5, 4, 3

5, 4, 3, 2

This sequence with its partial reversals shows a vital aspect of the cyclic rise-and-fall pattern, which can be summed up in a law that the first and highest state of a lower sub-cycle always comprises a return to a higher state than that of the lower parts of the next-higher sub-cycle before it. It is essentially owing to this naturally self-reversing property of time that belief in progress finds confirmatory evidence, as every advance into a lower range of possibilities will be compensated by the realization of values in it which went unrealized before. Such changes deflect attention from what has been lost in order to make these new relative goods possible, so that lost values fall into oblivion while things gained have immediate evidence. Different ages can thus vindicate their own value in relation to others thanks to the reascending movement of time, though this is always deceptive by absolute standards because the reascending movements are always incomplete, while the descending movement goes further each time.

In the above numerical illustration, the end of the Golden Age is followed by the Silver Age which begins with a tertiary cycle (its own golden age), equivalent to the second tertiary cycle of the previous cycle, and it is represented by 7 in either case. The highest and lowest members of the whole set, represented by 8 and 2 respectively, are both unique in the set, whereas the one represented by 5 occurs in all four secondary cycles, showing among other things an equivalence between the lowest part of the highest of the four secondary cycles and the highest part of the lowest secondary cycle. The numbers 6, 4, and 3 are repeated in a similar way, but less frequently. From these facts, there follows another cyclic law to the effect that when history enters an age which is in a category of its own in relation to the past, it must be the last part of the total cycle.

The total numbers which denote the tertiary cycles, 8, 7, 6, 5, can be seen to follow another numerical rise-and-fall pattern which has already been observed in connection with degrees of complexity in chapter 3, as the intermediate order of possibilities has the greatest frequency in either case. Again there is a symmetry of extremes and a maximum development at the center. The example worked out above concerns only the tertiary degree of complexity, but there is no reason why it should not be pursued next into quaternary cycles in the same ratios as before, as follows:

4 + 4 + 4,

4 + 4 + 3,

4 + 4 + 2,

4 + 4 + 1,

4 + 3 + 4,

4 + 3 + 3,

4 + 3 + 2,

4 + 3 + 1,

4 + 2 + 4,

4 + 2 + 3,

4 + 2 + 2,

4 + 2 + 1,

4 + 1 + 4,

4 + 1 + 3,

4 + 1 + 2,

4 + 1 + 1,

3 + 4 + 4,

3 + 4 + 3,

3 + 4 + 2,

3 + 4 + 1,

3 + 3 + 4,

3 + 3 + 3,

3 + 3 + 2,

3 + 3 + 1,

. . .

. . .

. . .

. . .

1 + 1 + 4,

1 + 1 + 3,

1 + 1 + 2,

1 + 1 + 1.

On this basis, each member of the previous sixteen-term sequence acquires a set of four changes of its own, giving a new set totalling 64 members. A further set, developed in the same way would therefore have four times as many members again, that is, 256. In the above example, the first and last numbers total 12 and 3, and are unique in their set in the same way as 8 and 2 were in the previous one. The first four three-number totals in this set are 12, 11, 10, 9, and the last four are 6, 5, 4, 3. This system again shows an increasing frequency for numbers the closer they are to the average between 12 and 3, similarly to the pattern for the set which ranged from 8 to 2. This method of cyclic division can be pursued as far as required, or until the smallest sub-cycles come down to a length approaching, say, a year.

All that can be done at this stage is to find how the cyclic order can be divided, without attempting to link its divisions to historical dates. However, one application to history is possible, in view of the fact that no other period has had so little continuity with past centuries as the present one. This historically singular character of the past hundred years means it can reasonably be identified with either of the final and unique terms 2 and 3 in the above examples. Here is a possible clue as to the length of the Kali-Yuga and consequently of the Manvantara, since the essential changes that gave rise to the modern world date from no more than four hundred years ago at most. If a length of three, four, or five centuries could be assigned to the last tertiary cycle or ‘iron age of the iron age,’ the lengths of all the other cycles could be calculated, as they are all related by proportion. However, that would only be the solution for one system of cycles, which would not rule out other kinds of cycle acting at the same time.

1. Joseph Campbell, The Masks of God, Oriental Mythology, chap. 3.

2. Rev. 21:16.

3. Ibid., 7 :4–8.

4. Rep. viii, 546.

5. Joseph Campbell, The Masks of God, Oriental Mythology, chap. 3, iii ‘Mythic Time’.

6. John Davidson, Natural Creation or Natural Selection?, chaps. 9 and 10. According to this author, ‘A human skull, completely mineralized to iron and manganese oxides and hydrates was found in a 100 million year old coal bed near Freiberg [East Germany] and described in detail by Karsten, in 1842.’ Fossilized shoe prints of a similar period have also been described.

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