8 Celestial Numbers & Terrestrial Numbers
The yang-yin duality also applies to numbers. According to the I Ching odd numbers are yang-that is, masculine or active-while even numbers are yin, feminine or passive. In fact there is nothing in this at all unique to the Far-Eastern tradition; on the contrary, these correspondences agree exactly with the teaching of all traditional doctrines. In the West, they are familiar to us through Pythagoreanism: in fact we have no doubt that there are people who think this way of categorising numbers is the exclusive property of Pythagoreanism and would be quite amazed to learn that exactly the same correspondences are to be found as far afield as China-without there being the slightest evidence of any 'borrowing', either by the West or by the East. It is, quite simply, a question here of a fundamental truth that will inevitably be perceived and accepted wherever the traditional science of numbers exists.
Because they are yang, odd numbers can be termed 'celestial'; even numbers, because they are yin, can be described as 'terrestrial'. But apart from this broad generalisation there are certain individual numbers that have a specific affinity either with Heaven or with Earth, and this fact calls for explanations of a different kind. To begin with, it is worth emphasising that it is chiefly the first odd number that is traditionally viewed as the number of Heaven and as an expression of the nature of Heaven-just as it is chiefly the first even number that is viewed as the number of Earth and as an expression of the nature of Earth. The reason for this is not hard to find: it is simply that each of these two numbers holds pride of place at the head of its own particular 'order', so that all the other numbers are in a sense merely derivatives of them, holding second place in relation to them in the particular series to which they belong. In other words, we could say that the first odd
number and the first even number are, respectively, representative of yang and of yin to the highest degree; or (which amounts to the same thing) we could say they are the purest expressions of the nature of Heaven on the one hand, and of the nature of Earth on the other.
Now what we must also bear in mind is the fact that unity, or the number one, is strictly speaking the principle of number and so cannot be counted as a number itself. The reality which it stands for must in fact be prior to the differentiation of Heaven and Earth; and we have already seen that this reality is none other than the principle common to both: namely T'ai Chi, that Being which is none other than the metaphysical Unity itself. So while the first even number is 2 , the first odd number is considered to be, not 1 , but 3 .
2 , then is the number of Earth, and 5 the number of Heaven. But this means that because the number 2 comes before the number 3, Earth appears before Heaven, just as yin appears before yang. In other words, in these numerical correspondences we find yet another, although fundamentally identical, expression of the cosmological point of view that we mentioned earlier when discussing yin and yang.
What would seem less easily justifiable is the additional fact that other numbers are also linked either with Heaven or with Earth, but in such a way as to produce-at least apparently-a kind of inversion. This is the case with 5 , an odd number, which is attributed to Earth; and with 6, an even number, which is ascribed to Heaven. Here again we have a case of two consecutive numbers within the series of numbers, the first of which (following the order of this series) corresponds to Earth and the second to Heaven. But apart from this one characteristic shared by the pair of numbers 2 and 3 with the numbers 5 and 6 , how can it possibly be the case that an odd yang number is associated with Earth and an even yin number associated with Heaven?
In this particular connection a 'hierogamic" exchange of attributes between the two complementary principles has been
suggested. [2] All in all, this explanation is quite appropriate; in fact the specific case of the numbers 5 and 6 is by no means an isolated exception, and many other similar examples could be cited from traditional symbolism. [3] However, it is actually necessary to carry the generalisation one step further. The reason for this is that the word 'hierogamy' can strictly only be applied to two complementary terms envisaged as masculine and feminine in relation to each other, and although this is the case with the example we are dealing with, we also find virtually the identical phenomenon occurring in situations where the complementary relationship between the two terms is of quite a different order. We have already discussed this elsewhere in connection with time and space and the symbols associated with them in the traditions of nomadic peoples and sedentary peoples. [4] It should be quite obvious that in a case such as this (where a temporal element and a spatial element are viewed as complementary) there can be no question of simply assimilating the relationship between masculine and feminine. It is, admittedly, quite true that this particular relationship, just like all other relationships between complementaries, is in a sense bound up with the relationship between Heaven and Earth. In this case, time is linked with Heaven through the idea of cycles-an idea that essentially has its basis in astronomy. As to space, its relationship to Earth is due to the fact that at the level of sensible appearances there is no better representative or embodiment of quantifiable extension than the earth's surface. But, granted these correspondences, it would still be wrong to conclude on the basis of them that all complementary
pairs can be reduced to one single type: hence the reason why it would be a mistake to speak of 'hierogamy' in this particular instance. The most that can actually be said is that all complementary pairs, whatever type they may be, are alike in having as their principle the first of all dualities which is the duality of universal Essence and universal Substance; or, in the symbolic language of the Far-Eastern tradition, the duality of Heaven and Earth.
Now what we need to understand very clearly if we are accurately to appreciate the different significance of the two pairs of numbers mentioned above-in both of which one number is ascribed to Heaven and the other to Earth-is that an exchange such as the one in question can only occur when the two complementary terms are considered not in themselves and as separate units, but in relationship to each other or (if it is a genuine case of 'hierogamy') as actually united with each other. From this we see that whereas 2 and 3 represent Earth and Heaven in themselves, 5 and 6 represent Earth and Heaven in their reciprocal action on and reaction to each other. In other words, 5 and 6 represent Earth and Heaven from the standpoint of manifestation, which is in fact the product of this action and reaction. We find this very clearly expressed, for example, in the text that says: 'In 5 and 6 we have the central union (chung ho, that is, the union occurring at their centre [5]) of Heaven and Earth. [6]
The truth of what we are saying here emerges with even greater clarity if we look at the actual constitution of the numbers 5 and 6 . Both numbers alike are formed from 2 and 3 ; but in the case of 5 , these two numbers are combined by addition $(2+3=5)$ whereas in the case of 6 they are combined by multiplication $(2 imes 3=6)$. Here we have the reason why 5 and 6 , both of them products of the union of even and odd numbers, are very commonly regarded in the symbolism of completely separate traditions as each having a fundamentally 'conjunctive' nature. [7]
To carry our explanation a stage further, we need now to ask ourselves why, in the case of Earth envisaged in its union with Heaven, the two numbers 2 and 3 are added together, whereas in the case of Heaven envisaged in its union with Earth the numbers are multiplied. The answer is that although each of the two principles receives through this union the influence of the other in such a way that that influence becomes as it were a part of its own nature, each principle receives this influence from the other principle in an altogether different way. The action of Heaven on Earth gives rise to a straightforward addition of the celestial number 3 to the terrestrial number 2 , for the simple reason that the action of Heaven is strictly 'actionless', [8] and can be described as an 'action of presence'. As to the reaction of Earth with regard to Heaven, this gives rise to multiplication of the celestial number 3 by the terrestrial number 2 , because the potentiality inherent in substance is the very root of multiplicity. [9]
It can also be said that whereas 2 and 3 are an expression of the intrinsic nature of Heaven and Earth, 5 and 6 are merely an expression of their 'measure', or extension. This is just another way of stating that, as mentioned earlier, the numbers 5 and 6 represent Heaven and Earth viewed not in themselves but specifically in relation to manifestation: for as we have explained elsewhere, [10] the very notion of 'measure' is directly associated with manifestation. As and in themselves, Heaven and Earth cannot be measured for they do not belong to the domain of
manifestation. We can only speak of 'measure' in relation to the visible determinants of Heaven and Earth which enable manifested beings to perceive them; [11] and these determinants can be referred to as celestial influences and terrestrial influences or, in other words, as the actions or effects of yang on the one hand and of yin on the other.
To gain a clearer picture of how this idea of 'measure' is to be applied, we must cast another look back at the geometrical symbols for these two principles. As we have already seen, the geometrical shape corresponding to Heaven is the circle, and the shape corresponding to Earth is the square. [12] Now the square is the prototype of all rectilinear shapes, and these are measured by 5 as well as by multiples of 5 ; circular shapes, on the other hand, are measured by 6 and its multiples. When we speak of the multiples of these two numbers we have in mind primarily the first of these multiples-that is, twice 5 or 10 and twice 6 or 12 . In fact the natural way of measuring straight lines is by using a decimal division, while the natural way of dividing circular lines is duodecimal. It is not difficult to perceive in this the reason why these two particular numbers- 10 and 12 -are made the bases for the principal systems of numbering. In fact both systems are sometimes employed concurrently, and this is precisely the situation in China. The reason for their being used concurrently in this way is that they actually have quite different applications, so that their co-existence-even within one and the same formal traditionhas absolutely nothing arbitrary or superfluous about it. [13]
By way of bringing these observations to a close we would like also to point to the significance attributed to the number 11. As
the sum of 5 and 6 itis the symbol of that 'central union of Heaven and Earth' that we mentioned above. Consequently it is 'the number that establishes the perfection (ch'eng) [14] of the Ways of Heaven and Earth. [15] This significance, ascribed both to the number 11 and to its multiples, is also a point on which-as we have already shown on another occasion [16]-the most diverse of traditional doctrines are in complete agreement; although for reasons that are not very clear this fact goes largely unnoticed by those moderns who claim to study numerical symbolism. [17]
There is virtually no end to the lengths to which we could go in developing these basic observations on numbers. So far we have only concerned ourselves with the subject of Heaven and Earth, the first two terms of the Great Triad. It is time now to pass on to a consideration of the third term of this triad: Man.