THE SCIENTIFIC SYMBOLISM
OF PREHISTORIC CIVILIZATION

But what are they really,
the I Ching and the Cabala?

Up to this point we have seen how the I Ching and the Cabala were invented, what they meant for their creators, and how they believed they could be used. In this chapter we will try to explain the concrete significance of these maps of reality from an objective point of view. From Leibniz on, western science has been concerned with the mathematical structure of the I Ching and we have seen how its subdivisions are so rational and precise in their reproduction of the schemes of the human mind that they correspond exactly to abstract languages that were invented thousand of years later.

Leibniz, who around the end of the 1600's invented the binary number system, was astonished when a friend of his (Father Joachim Bouvet, a Jesuit missionary in China) showed him the 64 hexagrams of the I Ching. In fact, he noticed right away that, when arranged according to a certain logical order (called the "natural order" or FU-HSI) they are the written form of binary numbers of the figures from ZERO to 63. All we have to do is to substitute a ZERO and a 1 in place of the symbols Ying and Yang

to obtain the numeration 000001, 000011, 000111, etc. That constitutes the expression in binary terms of the numbers up to 63.

This fact astonished both Leibniz and Father Bouvet who thought that the Chinese had succeeded in discovering binary arithmetic by divine inspiration.
Sometime later, Z. D. Sung, while trying to find a way to rewrite the I Ching in a simpler manner, discovered that the 8 basic symbols could be the description of the vertices of a cube, according to the system of Cartesian coordinates. He noticed this while he happened to be handling a pack of matches and he thought that even primitive man could have reached a similar conclusion observing some other cubic form.

"Suppose that the three Cartesian coordinates of a unitary cube, x, y, z, indicate the first, second and third figures of a three figure binary number. Let's call 000 the vertex that constitutes the origin of the three coordinates. The other vertices are then indicated with three figure binary numbers from 0 to 7, where the 0 and the 1 indicate the distance of each single vertex from the point of origin in each direction of the coordinates.

The eight numbers correspond, obviously, to the eight trigrams, and the complementary trigrams can be found at the diametrically opposed vertices of the cube.
By following a similar procedure, the vertices of unitary hypercubes generate the higher order polygrams. The 64 hexagrams correspond to six figure binary numbers at the vertices of a hexadimensional hypercube."

Cube # 1	Cube # 2

The figures of the Cabala can also be used in this way. Arranged as we see them in cube # 2, they indicate the totality of the angles, sides and areas of a cube. In this case the three dimensionality of the cube is seen as the product, rather than of the single sides and angles, of sets of these elements; it is a kind of wholistic analysis of a cube. Within the cube, one can identify a first set composed of the three dimension and then other sets are formed by the angles, sides, and surfaces. In this way, we can obtain a description or a cube in terms fine the surfaces 3 dimensions, 6 faces (each or which is composed from three sets) and we get [3 + (6x3) 1 = 21 elements, plus the zero which represents the interior or the solid and we have the 22 symbols or the Cabala.

It is difficult to establish if the ancient Taoists, and Cabalists, really ever used the I Ching and the Cabala in this way, but in any case it is interesting that these systems adapt themselves so well to definition of an elementary solid body such as the cube, even in terms of descriptive languages which belong to modern abstract reasoning.
These examples are usually called into play by lovers of spiritualism and the occult to demonstrate the value of mystic consciousness, and the belief and superstitions which belong to all more or less religious traditions. I have cited them precisely to demonstrate the contrary, and that is, that the persistence over time of the logical sense of these diagrams does not depend on mystical illumination but on the good us by these ancient philosophers of a robust and unfailing rationality.
They, in contrast to many of their contemporaries who abandoned themselves to the imagination of devilry of every type and kind, investigated the real world while clinging faithfully to the most rigorous materialism.

These philosophers theorized only about things which they could experience and experiment; reality, time, movement, three dimensionality, the contradictions and the multiplicity of things, these were the facts that they observed and only on the basis of these facts did they erect their theories. There is nothing external to the materiality of things which intervenes to modify the objectivity of their thinking. Moreover, these philosophers were modest and had no pretensions of being able to explain everything.
They were well conscious of the fact that their knowledge, based as it was on limited physical perceptions, could not go beyond those aspects of reality that constantly repeat themselves in some visible way. (Their system didn't try to codify the whole but only these particulars that are easily identifiable, and it is only through these particulars that they tried to ascertain the skeleton of a phenomenon, its essential structure).

Taoists and Cabalists stated explicitly the limits of their diagrams by the addition in both cases (as we have already seen) of the concept of the Zero; in this way they indicated the existence of the "other" that, because it could not be perceived by the observer, could not be considered within the scope of the diagram. Thus, they did not propose their diagrams as descriptions of everything but only as maps of that which the individual could perceive. (Maps of human perception).
This method, used by our Taoists and Cabalists, was a primitive version of the "experimental method" proposed by Galileo Galilei, which became the basis of scientific research. I believe, therefore, that in trying to define the nature of these ancient diagrams, we must consider them to be, not mere philosophical hypotheses, but true scientific hypotheses. The academic world has never tried to carefully evaluate the possibility that these ancient numerical theories contained elements of real scientific value.

This came about both because these ideas have always been associated with occultism, magic and religious tradition, and because modern scientists with all of their sophisticated instruments and apparatus thought it was impossible that a mere troglodyte could have understood something that was useful to 20th century science.
Another factor that tends to reduce the scientific credibility of these hypotheses is that the I Ching and the Cabala seem to contradict each other, in as much as the first divides reality into 64 parts while the second divides it into 22.
This fact leads us to think right away that one of the two theories must be mistaken and to suspect that the numbers were, in fact, chosen at random and that instead of 22 and 64 they could just as easily have been 17 and 65 or 23 and 49; this obviously removes any scientific value from the diagrams ad leaves them only with historic of philosophical value.

In my opinion such an evaluation is unjustified, and by reconstructing in this article an hypothesis of how these numerical systems came to be conceived I have tried to demonstrate how they were developed according to analogous approaches and methodologies.
Undeniably, the differences in the procedures depends only on the different paths that were followed. The Chinese disassemble reality on the basic of the two energy polarities (in terms of movement) and develop a binary number system to indicate the different polar sequences of which a particular thing is composed. Similarly, by breaking down language into concepts in ideogrammatic sequences, they invented their system of writing.

The Hebrews, on the other hand, subdivide reality by analysing only its most visible external aspects. Thus, they divided language into sounds and invented the alphabet. The differences that we encounter between the two systems stem from the differences in the type of research undertaken. The Chinese were into mathematical aspects of things, the Jews of the qualitative aspects: the former studied movement and the latter form.
It's clear that, in trying to produce maps of different things, came to construct different interpretive systems. But if the final results are different, the procedure, the general ideas and the numerical- geometrical-symbolic logic with which these diagrams were developed are absolutely identical. Up to this point I hope to have demonstrated the point that, in two very distant parts of the world, mankind, even in prehistoric times, succeeded in elaborating analogous interpretive systems.

From a certain point of view, this affirmation, that perhaps for some will make their hair stand on end, is even banal. In fact, the distance between these two civilizations was only metrical, in as much as in the era of the caveman they shared the same relationship with nature and the same scarceness of means of production; if it is true that it is their sociality that determines the culture of men, and if we want to give credence to historical materialism, then we must conclude that, in effect, it is quite probable that these two peoples would have arrived at analogous solutions, at least at an initial stage of the formation of their cultures.
Which would not only indicate an aspect of unity between Chinese and Hebrew culture but also between them and other primitive cultures; probably, in fact, if we were to extend this type of analysis to other primitive cultures, we would discover that, at least in the initial phases of each civilization, there exist the same criteria for the analysis and investigation of reality.

And in effect, at least superficially, we can see this right away if we think of how wide spread among primitive cultures is the attempt to interpret reality according to a numerical system. The Egyptians and the Atzecs developed the symbol of the pyramid, the Indians of Central America have legends that tell how the universe was created by two brothers who, while fighting over a girl, generated the energy that created matter; some African populations use systems similar to the Cabala based on 16 elements while the Arabs have 28.

I believe that, as we have seen with the Tao and the Cabala, all of these codifications, upon deeper investigation, would appear to be substantially similar. But the Cabala and the I Ching are not only similar. I submit that these two systems are exactly the same, and that their differences not only do not slow them to be contradictory, but instead confirm their coherence.
It's like listening to two doctors, one who explains the function of the liver while the other explains the heart. They say different things because they're talking about different things, but the approach, methodology and the principles that they expound are they same, and every point that one of the doctors makes about the heart confirms the points that the other doctor is making about the liver.

This claim is verified by the fact that these two cultural expressions, while following completely different paths, have led in many cases to exactly the same results. Even more convincing than the already cited case of the invention of writing is the example of the Chinese abacus.
In the invention of their system of counting, the Chinese showed the same diversity as they showed in the construction of their system of writing and the development of their interpretive model of reality. By applying to arithmetic a streamlined version of their binary system, they invented an abacus with which, as early as a thousand years ago, they were able to perform addition and multiplication with numbers of more than 10 figures, at the same speed as a modern computer.

The Chinese abacus is divided into a certain number of columns with seven balls in each column, divided into two groups of 5 and 2.

The two balls represent the two quintals between 1 and 10 and the 5 balls represent the 5 units in each quintal. Each of the 7-ball columns represents the increasing decimals (10, 100, 1000, 10.000 etc). To write 4 I will move 4 balls in the bottom row in the group that represents the first five units:

To write 7 I will move 2 balls in the group of the 5 units and I ball in the group of the second quintal. Now the speed of this system stems from the fact that, by writing a number to add to 7 I will already have reached the result.
Let's take the example of 9 + 7. To write 9 I will move 4 balls in the lower group of 5; since I've already moved 2 in writing seven, I will move the second ball of the group of 2 and I will write the units that are left after I have moved one ball of the group of 5.

Then I will add the quintal, that together with the 4 units, forms the number 9. Since the two balls in the first row that indicate the quintals have been moved I'll put them back in place. I will mark this ten that I have removed from the lower row by moving one ball in the second row, the row that represents the tens, from the group of five in that row. I will indicate the quintal that was left by moving of the 2 balls (of the quintal of units). In this way I get the result of the addition, that is, 7 + 9 = 16

(one ball from the tens + 1 quintal and a unit from the level of the numbers from 1 through 10).
Now let's try 3,697 + 4,209:
First let's write 3,697:

then let's add 4,209

and we get 7,906

This process may appear to be somewhat complex but our minds are capable of doing it very quickly because it is based on very easy subdivisions of the numbers. Once we've learned it this system proves to be much easier than our own method because we can perform all of the operations using only the first five units.
The use of the Chinese abacus demonstrates how the mathematicians of this culture conceived a way of representing numerical reality and a way of manipulating it that was much different from the methods of their western colleagues. The indisputable precision of the numbers and the mathematical operations dispels any doubts about whether the two systems of counting are of equal value.
They are in perfect correspondence, 2 + 2 always equals 4, and multiplication, division, addition and subtraction are always the same, even if the methods used by the two systems reveal significant differences.

With this example I have certainly not demonstrated that the I Ching and the Cabala are the same thing, but I think I have been able to confirm that hypothesis at least enough to overcome the objection that their diversity is certain proof that they are contradictory.
Having done this, we must now try to establish, very rigorously, to what extent these two diagrams of reality are capable of being unified into one unitary "scientific" theory of reality.
I know that some will smile at this idea. It's difficult to entertain the idea that those little numbers and those odd little symbols could constitute a scientific theory, even if the formulas of modern physics should have gotten us used to imagining the content of similar symbolic languages.
To be sure the I Ching and the Cabala were not written by a loth century university professor and, therefore, to understand their content it is indispensable to translate them into a modern and explicit language. I (as the dean of the shabbiest university in the world) will try to imagine what I would say if I was a Cabalist of 3000 years ago who had to explain his theories to a conference of modern scientists. First of all, since I would be talking to a group of famous professors I would not try to explain all of my hypotheses but I would try to go quickly to the heart of the matter. I would start by saying that my research was accomplished by observing the ways in which the human mind perceives reality. Very modestly I would define my theory as a hypothesis in the field of perception.

Then I would say that by studying the form of perception I had discovered that the human mind is capable of distinguishing and recognizing 22 different qualities. I would add that this particular form of human perception allows us to subdivide in ways useful to mankind every particular aspect of the universe.
In support of this theory I would offer my own personal invention of a system (which the human mind is capable of mastering with incredible speed) which allows us to express with symbols, all human thoughts and arguments; amidst the general envy I would announce to the world that I have called "writing" the act of drawing symbols and "reading" the act of interpreting them.

And as indisputable proof of the validity of my theory I would ask, as author's royalties, to be paid 1 lira every time someone used my invention to write a love letter or a novel. Journalists would hate me, women would be crazy about me. And the amount of money that I would make every day would convince any great scientist of the validity of the cabalist theory.
Unfortunately, because our friendly cabalist lived long before the copyright laws, nobody gives him a lira and nobody wastes time paying attention to his ideas; anyway he's dead and the alphabet is ours for free. (The same is true for the Taoists).
In the chapters to come I will try to render justice to our cabalist by discussing his ideas and treating them with respect; by trying to understand the possible scientific significance for today's world that is contained in the ideas of the 22 qualities and the 64 polar combinations. I will try to discover the extent to which these numerical diagrams can be unified into a single logical system and how the concept of the world implied by that system might be expressed in modern terms. Hoping that you will be consumed with curiosity while you wait. I advise you, to pass the time between issue of this magazine, reading an exceptional book that is fundamental to a better understanding of the argument: The Tao of Physics by Friotjof Capra (Ed. Adelphi).
Capra, a physicist, explains, in an inspiring style, the whole of ancient oriental philosophy by comparing it to the latest discoveries in nuclear physics. (It is through comparison, above all, that both ideas become much clearer).