Arthur M. Young

History assumes that thought has developed from a primitive state to the present advanced one.

This view may be justified in the case of science, but even here it is worth noticing that there is a difference between the body of science and the caliber of scientific thought. The body of science, depending as it does on the cumulative endeavors of all scientists, grows exponentially. The caliber of scientific thought, on the other hand, depends on persons, and rises or falls as individual talent varies. Even in persons, it may vary with age.

But something else goes on which a historical accounting would miss. Thought seems to become encumbered, rather than aided, by efforts to articulate itself. Someone asked the centipede which foot he started off with, and the centipede, trying to answer this question, became unable to walk at all.

In any case, we should study the disruption of innate understanding caused by the efforts of reason to justify its own legitimacy. In this sense, the growth of reason is a fall, first from the grace of instinctive motion, like that of a bird in flight, to that of a noisy machine, then to an erratic stagger, and finally, to a grinding halt.

The trouble began in Greece, with the "liberation" of thought from authoritarian teachings whose profundity rendered them too esoteric for "rational" explanation. These older teachings could never be explained, and such was their difficulty that the word "hermetic," which indicated their origin in the god Hermes, came to mean "closed off" or "sealed up."

Against this background of an unwritten tradition that was imparted only to initiates and understood by only a few, sometimes to be lost altogether, the use of reason must have burst like a flood of light. Certainly, the discovery of Pythagoras that musical notes bear the relation to one another of simple whole numbers was a triumph of rationality. ("Rational" literally means based on ratio, but it extends to mean any explanation which relates one thing to other things, especially to antecedents.)

But rationality is not always so effective. The ability of analysis to divide a thing into parts and compare them may engender absurdities when confronted with motion. Zeno's paradoxes the arrow at every moment is at rest, therefore it cannot move; Achilles cannot catch the tortoise because as soon as he reaches the place where the tortoise was, the tortoise will have moved on are, of course, absurd, but they are just as rational and make as much noise as better use of reason.

Indeed, the solution to the paradox of motion in the sense of a correct use of ratio had to wait for Newton. Meanwhile, there were brilliant philosophers like Berkeley to throw monkey wrenches into the machinery by insisting that a ratio between infinitesimals was an absurdity. We also had Hume at about this time, whose skepticism about the objectivity of causality we mentioned in the last chapter. That this should be considered significant by philosophers is an indication that the cogwheels of logic are highly vulnerable to monkey wrenches.

New impediments to thought are being discovered all the time. I will list only a few:

Dedekind's proof of continuity
Cantor's invention of a multitude of infinities
Russell's contribution to logic
Quantum theory's particle/wave enigma
Goedel's incompleteness theorem (an important step but still in its present state an impediment)

Still more recently, we have had other great discoveries. DNA, for example, while it undoubtedly does contribute to our knowledge, is responsible for an epidemic of nonsense subscribed to even by good scientists. We read that, any day now, science will produce Einstein's from a piece of his skin. (I hope later to show why this is a fallacy.)

Another is the computer and the madness it has engendered. Quite apart from that natural and perennial zeal for overdoing everything which characterizes American enterprise, computer mania is in the process of taking over people's imaginations. Science fiction looks forward to a future when its heroes will dispatch computers as their earlier counterparts did dragons. But what is alarming is that even good scientists (again) cannot distinguish computer activity from the mental processes of living creatures.

There are still other "remarkable advances" in science that, far from being an aid to thought, are incapacitating people for thought. Common sense has been so incapacitated by sophisticated obfuscation that we no longer even know how to pull our hand out of the fire when it's getting burned. In fact, it would almost seem that the progress of thought has reached a complete standstill, for we have not only more unanswerable questions and paradoxes than ever existed before, but a well-established staff of experts to preserve them for posterity and prevent any idle persons from presuming to solve them.

But it is for the outcasts, banned from the inner sanctum of science and without the prized qualifications, that I speak, for they have the necessary desperation required for the search I now urge them to make.

As Bacon said, it is the lighter stuff that floats on the river of time; the more profound sinks to the bottom. Such has been the fate of a very ancient symbolic concept, that of the four elements, whose deeper meaning has long since disappeared beneath the surface. I would like to bring this meaning to those who, surfeited with the meaningless pyrotechnics of science, seek some basic guidelines to help find their way through the jungle of sophistry that is our present culture.

The four elements, fire, water, air, and earth, originated long before the Greeks, for when the Greeks referred to them, the manner in which they did so indicates that they did not comprehend their full meaning. The Greeks apparently thought of the elements as states of matter, just as most modern thinkers do:

Earth = solid
Air = gaseous
Water = liquid
Fire = igneous (ionized)

But this is not their meaning. To say air is gaseous and water is liquid is simply to reiterate the words themselves. We can expect more than that of ancient wisdom. We must look deeper. As often happens with symbols, we can actually find them in use right now. For example, the economist speaks of liquid assets, by which he means assets that are readily negotiated, like cash, as distinct from real estate, which is the frozen (or earth) form of investment. Anything concrete is earth, so the element earth means that aspect of a situation that is practical and "down to earth." Air, by contrast, is the mental aspect, and fire the vital and initiating factor.

These meanings emerge in the use of the words as verbs, thus:

To fire = to arouse, to start, "to throw out"
To air = to make known
To water = to nourish
To "earth" = to get down to earth; to materialize

This should give us a start, for it is not so much a question of defining the elements precisely, as it is of understanding the meanings in terms of their classically assigned quadrate relation, with air opposite fire and water opposite earth.

The elements designate directions in space, as they do in the signs of the zodiac. These directions in space are also associated with people's poetic understanding of the seasons. Thus, taking the four signs of the zodiac assigned to the equinoctial points (the first day of spring and of fall) and the solstices (the first day of summer and of winter), we have four signs: Aries or spring, Cancer or summer, Libra or fall, and Capricorn or winter.

Spring begins the yearly cycle, just as the east initiates the diurnal cycle; thus people associate spring with the east. The astrological sign for spring is Aries (fire). It signifies increasing heat. Its meaning is spontaneous outrush, symbolized by the ram which charges with its head down.

The outrush of Aries awakens the response of summer growth represented by Cancer. The floodwaters of spring assume their nurturing level. Cancer is symbolized by the crab with its protective shell for the growing form within. The autumnal sun is in the sign of Libra (air). The harvest is weighed, evaluated. Autumnal winds take the turning leaves. It is the time of mental awakening and judgment, symbolized by the scales.

The sun enters Capricorn (earth) in winter, when its heat is at a minimum. Dormant nature gives us the meaning of conservation and control. Lessons learned in the seasonal cycle are absorbed during the winter; the watery element is congealed. Capricorn's symbol, the goat, denotes the surefootedness of this animal, but other goat-like references are available: the scapegoat that voluntarily takes the "blame," the self-assurance of the goat, its ability to digest, and so on.

Spring and fall are opposites, as are fire and air; so too summer and winter and their associated elements. Our temporal awareness of the seasons finds correspondence in the spatial notation of astrology.

These astrological meanings, it will be noted, fit the four types of action in the learning cycle at the end of Chapter II. On the left, corresponding to the first day of spring, is acceleration or unconscious action, precisely what is happening in spring. At the bottom we showed velocity, which is change of position, but it will be recalled that we generalized this to cover all unconscious reaction. On the right we had position, which we equated to observation, conscious reaction. This is the function of Libra, looking to see where one is at. At the top we had control, or conscious action, which is as good a meaning for Capricorn as can be made in two words.

Quite apart from the validity of astrology, we can therefore see that the signs denote, and derive their meaning from, the critical points in a cycle dealing with velocity and acceleration. Relating this to our subject, the geometry of meaning, we can see that there is an underlying and abstract four-foldness in the signs.

Note that the four meanings are defined by one another. Unconscious action on the left is doubly opposite conscious reaction on the right. Likewise, the two cross products, unconscious reaction and conscious action, are on bottom and top. 

This should make it clear that the elements occur together. Like the directions in space, they coexist. One can emphasize one element at the expense of another, just as one can travel west instead of east, but this does not mean the other element or direction ceases to exist. One cannot imagine space extending only to the west. Space is omni-directional, and so is everything else. It is true that a thing moves only one way at a time, but the cyclic nature of all occurrences makes it inevitable that the complete development of anything takes it through all four phases. Like the pendulum we started with, the phases of the cycle derive their nature from this sequential interrelation.

The elements, as expressed in the cardinal signs which we have just outlined, are thus four kinds of action. For example, the action of the soldier typifies Aries (Mars), or fire, as compared with the observational action of the scientist, which typifies Libra, or air. The engineer or manager, who makes and controls, contrasts with the passive consumer, much as Capricorn (earth) contrasts with Cancer, water.

But these are all forms of action. To fully explore the elements, we should draw on the other two sets of four, making three signs in each element. Taking them in sets as we did in the case of the measure formulae, the next set are what are known as the fixed signs which "incorporate" the activity of the cardinal signs and produce states:

Action (leads to)                                                         States

Fire Outrush (Aries)                                                       Being (Leo)

        Water Change (Cancer)                                              Transformation (Scorpio)

        Air Observation (Libra)                                                Significance (Aquarius)

        Earth Control (Capricorn)                                              Establishment (Taurus)

We can also place states in opposition, as we placed measure formulae in opposition. Transformation as the opposite of Establishment gives us no difficulty. But Significance as the opposite of Being may seem strange.

Here is where the deeper insights afforded by the elements are a help, for in recognizing Leo (being) as fire, we may characterize it as centrifugal, throwing out. This, in fact, is what the basic symbolism suggests, for the sun is symbolized by a circle with rays going out from it. The lion has probably become its representative because his mane, springing from his head, also depicts an outgoing, or centrifugal, motion.

The opposite tendency or mode would be centripetal, converging to a point. The astrological symbol of Aquarius is the water bearer, sometimes shown pouring water from a jug. That Aquarius is an air sign, not a water sign, makes sense if we realize that Aquarius represents precipitation or rainfall -- the return to center of that which heat has caused to evaporate -- and hence the opposite of Leo. Another probable reference to Aquarius suggested by Eric Schroeder,* an authority on symbols, is the unicorn, a mythical beast whose single horn twists to a point, and thus literally portrays the centripetal. Its opposition to Leo is shown in the British royal coat of arms. As the nursery rhyme says "The lion and the unicorn are fighting for the crown." This convergence to a point, or focus, of the power of the head (the horn) confirms the mental nature of this air sign and stresses its meaning as significance. 

*Muhammad's People. Portland, Maine: Bond Wheelwright Co., 1955.

Since the contrast between centrifugal and centripetal forces is clearer than that between words like "being" and "significance," we are justified in using it to explain or define their meaning. The contrast between centrifugal and centripetal implies oppositeness, and hence exemplifies the geometry implicit in meaning.

We can discover a similar oppositeness between establishment (Taurus, earth) and transformation (Scorpio, water). Here the point is to recognize these states as possessive (in contrast to the states of being and not being). Establishment is having, and transformation its opposite, not having. In a negative sense, this means the destruction of the former, but in a positive sense, its reconstitution. Taurus, or the bull, is the zodiacal symbol and corresponds to the month of May. We can sense the "bull market" feeling of this time of the year when the spirit of increase is bursting forth everywhere. -The opposite sign, the scorpion with its poisonous sting, does not so much symbolize destruction as the intensity of reappraisal necessary to transformation. Death, which is associated with this sign, is destruction, but only of the form, since there is in cosmic symbolism no true death. This vital renewal is emphasized in the other symbol of Scorpio, the eagle.

There remain what are called the mutable signs, which, like the third set of measure formulae, have to do with kinds of relationship. These are Gemini (air), Virgo (earth), Sagittarius (fire), and Pisces (water). All except Virgo deal with forms of two-ness, and this recognition makes it possible to relate them in quadrate relationship. Thus Gemini, or the twins, are two out of one (mother), whereas Sagittarius, the archer astride a horse shooting an arrow, is one (arrow) out of the two. Since Sagittarius rules the hips, the point where the two legs come together to form the spine, this again is one growing out of two, and hence synthesis. Similarly, Virgo is one out of one, and Pisces, the two fishes pulling against one another, are two out of two (which helps bring out the tendency of this sign to confusion and delusion).

The word pairing which we used earlier in the book for the four forms of relation is also apt:

Sagittarius, the arrow, is the particular projective; Gemini opposite it, the general objective. The criterion for objectivity in science is that an experiment be repeatable. One must be able to "duplicate" it and obtain the same result, an emphasis suggested by the twins.

The particular objective, which we earlier related to empirical fact and to the work required to determine it, corresponds to Virgo, which is the sign that stands for discrimination, separation, purification, and in astrological usage rules the "house" of work. (The "houses" are the twelve kinds of relationship possible to the self, and have a correspondence to the signs.) "Work," it will be recalled, is the equivalent in science to energy, whose measure formula is MLsquared/Tsquared, and was positioned at four o'clock, which is where Virgo falls in the conventional disposition of the signs. 

Pisces, as opposite Virgo, is lack of discrimination, but its positive reading is faith. There is also in Pisces the connotation of sympathy, of going along with, which is again a positive reading of the opposite of the separation and purification (negative hypochondria) implied in Virgo. 

We can now survey the three sets or modalities -- cardinal, fixed, and mutable -- which combine with the four signs or elements, fire, air, water, and earth, to produce the twelve modes of being set forth in the zodiac.

The origins of the zodiac go further back in time than Greek philosophy, or even the I Ching. The zodiac is, of course, the basis for astrology, currently regarded as a, pseudo-science (largely because its critics misinterpret what it actually purports to do). Apart from the question of whether astrology is or is not valid, one can hardly question the zodiac. Spring is the time of physical acceleration; autumn is the opposite, the time of mental stimulus. Summer is the time of physical change, and winter the time when growth has ceased.

"So what," says the modern mind, putting its faith in the constructions of science.

But, as I have been at pains to show and have obliged my patient reader to witness, the measure formulae, which are the very basis of science, draw their meaning from the same angular relationships, from dispositions about a circle, from the opposition and complementarity that thousands of years ago were evident to the ancients. This circle of the zodiac (not constellations, which are quite arbitrary pictorial projections hardly even resembling the stellar configurations to which they refer) is basic. It is at once the cycle of action, the progression of the seasons, directions in space, the measure formulae. Even more importantly, it is the whole whose various aspects are the signs, the measure formulae, or the seasons.

And because it is the whole (and does not let us forget it), it is a more valid reference than science, for science, which is knowledge, not wisdom, is not the whole story. Scientific knowledge, in fact, can be rather mischievous and even dangerous in that it is at best partial. In the next chapter I propose to show how, with the help of the four elements, we can break the spell which the evil magician has cast over the enchanted princess.


The Geometry of Meaning