THE FOUR ATOMS ACCORDING TO PLATO
Plato (c. 427 — c. 347 B.C.E.), were he was familiar with the atomism of Democritus, would have objected to its mechanistic materialism. He argued that atoms just crashing into other atoms could never produce the beauty and form of the world. In Plato's Timaeus, (28B – 29A) the character of Timeaus insisted that the cosmos was not eternal but was created, although its creator framed it after an eternal, unchanging model.
One part of that creation were the four simple bodies of fire, air, water, and earth. But Plato did not consider these corpuscles to be the most basic level of reality, for in his view they were made up of an unchanging level of reality, which was mathematical. These simple bodies were geometric solids, the faces of which were, in turn, made up of triangles. The square faces of the cube were each made up of four isosceles right-angled triangles and the triangular faces of the tetrahedron, octahedron, and icosahedron were each made up of six right-angled triangles.
He postulated the geometric structure of the simple bodies of the four elements as summarized in the adjacent table. The cube, with its flat base and stability, was assigned to earth; the tetrahedron was assigned to fire because its penetrating points and sharp edges made it mobile. The points and edges of the octahedron and icosahedron were blunter and so these less mobile bodies were assigned to air and water. Since the simple bodies could be decomposed into triangles, and the triangles reassembled into atoms of different elements, Plato's model offered a plausible account of changes among the primary substances.
A quadcopter, also called a quadrotor helicopter or quadrotor, is a multirotorhelicopter that is lifted and propelled by four rotors. Quadcopters are classified as rotorcraft, as opposed to fixed-wing aircraft, because their lift is generated by a set of rotors (vertically oriented propellers).
THERE ARE OTHER BLADE NUMBERS BUT SCHICK QUATTRO IS POPULAR BECAUSE OF THE COMMERCIALS- FOUR BLADES
Schick Quattro: a four-bladed razor for men, introduced in 2003. The Quattro Midnight and Quattro Chrome are models with redesigned handles and different color schemes from the original Quattro.
Quattro Power: A motorized version of the Quattro; it is supposed to reduce friction. The Quattro Titanium Power is a Quattro Power with a different color scheme and Quattro Titanium cartridges. The Quattro Power is powered by a single AAA battery.
Quattro Titanium: includes a titanium coating on the blades that is claimed to reduce irritation. There is also a Quattro Titanium Trimmer that includes a short face trimmer powered by a AAA battery.
Quattro for Women: A modified version of the Quattro with a feminine color scheme.
FOUR MODES OF CONFLICT BEHAVIOR
Typically, there are four recognizable stages in the conflict process :
Conceptualization and orientation
Frustration. The first step in any conflict process refers to the triggering event that set one or more people at odds. This event is referred to as perceived frustration—the belief that one party has frustrated or is about to frustrate some important concern of another. Frustration comes in many forms and approaches. Earlier, we identified several sources of frustration and hence conflict, and classified them into two categories: organizational and interpersonal. Frustrations occur in everyone's life on a daily basis. Therefore, there must be some reason why we choose to respond to certain frustrations in a confrontational manner. This choice is often predicated on our perception of how important an issue is to us. For example, while under normal circumstances a traffic jam would be a source of frustration, we would rarely deem it serious enough to actively confront the city's administration over the issue. On the other hand, in situations that involve slights to status, promotion possibilities, or public image, we tend to react to frustrations more directly. It is in these situations, where we attach a level of importance to the frustrated goal, that we are liable to respond in an aggressive and competitive manner.
Conceptualization and Orientation. Conceptualization means defining the issues underlying the source of conflict. When we analyze the causes of a conflict between ourselves or our team and another party, an interesting psychological process begins to occur: we see the conflict through the lens of egocentricity. Egocentricity refers to the predilection of most people to define issues solely in terms of their own concerns. In other words, when confronted with a situation in which we feel frustrated by another individual, we respond in a way that does not recognize the other party's perspective. That is, we perceive that the other person is thwarting us, without considering their point of view or why they are acting in a particular way.
The clear alternative to analyzing frustration in terms of egocentricity is to begin to develop a level of insight into the other party's concerns. There is an old saying that admonishes us to never judge another person unless we have walked a mile in his shoes. The implication of this chestnut is that until we are able to understand another person's motives, intent, and past experiences, we cannot objectively address the nature of the conflict episode. Rather, we will continue to be inclined to simply respond with an egocentric approach that only further solidifies the lines that separate the rival party's positions. Attempting to gain this insight into the underlying issues involves refusing to capitulate to the initial sense of frustration with another party and search for reasons why that person or group is operating the way they are. It is this search for the answer to “why” that can defuse many conflicts before they escalate. It requires the project manager or team member to be able to forego the appeals of egocentricity in order to try and analyze the problem from the other party's perspective. Depending upon the nature and degree of the conflict, this rational objectivity can be very difficult but it is an activity well worth the effort. If we are able to halt conflicts at this stage, many of the problems that will continually plague the project team throughout the remainder of the project development can be halted before they get too destructive.
While conceptualization helps us to initially define the terms of the conflict, orientation refers to the outlook we begin to adopt once a conflict episode continues to escalate. Ruble and Thomas  have argued that conflict orientation generally involves operating along two separate dimensions of concern: (1) the degree to which one party seeks to satisfy their own concerns, and (2) the degree to which a party seeks to satisfy the other person's concerns. Figure 1 shows Ruble and Thomas’ conceptualization of this two-dimensional model of conflict orientation. They argue that we make implicit tradeoffs in our willingness to seek our own gains versus our willingness to satisfy the other party to the conflict. They further posit that the underlying motive driving these two dimensions is our desire on one hand to be assertive and gain our own maximum advantage and on the other hand to be cooperative with the other party in order to maintain satisfactory relationships .
Within this two-dimensional model of conflict orientation and behavior, Thomas suggests that five distinct and recognizable types of conflict behavior are potentially possible. Figure 2 shows each of the five conflict-handling styles. The decision of which type of behavior to pursue resides solely with the party who is conceptualizing the nature and reasons for the conflict. The five conflict-handling styles are:
Competing behavior is basically assertive and uncooperative. Someone adopting a competing style has no regard for satisfying the other party's concerns, viewing conflict as a win-lose proposition in which they have resolved not to lose. Competing behavior is often used by insecure or power-hungry people who will use every technique or trick to get their way. It is often ironic to find that individuals who are high on the competing dimension have great difficulty in operating under any other style, no matter what the nature of the conflict. For example, highly competitive people take issues of resource allocation or the results of a game of gin rummy with the same degree of intensity. They often cannot distinguish between “important” conflicts and “unimportant” conflicts; indeed, the very creation of a concept such as an “unimportant” conflict is alien to their way of thinking.
At the opposite extreme from competing behavior is the accommodating style. As Figure 2 shows, accommodators enter conflicts from the perspective of seeking to first satisfy the other party's concerns over their own. Accommodators foster nonassertive and cooperative styles, usually in an effort to be true “team players.” They are quick to look for ways to either defuse a situation or to allow the other party to win. The accommodating style can be very useful when the issue of concern is seen as much more important for the other side than for the accommodatee. It may serve as an important goodwill gesture or a basis for “storing up” favors that the manager may need at a later point. The obvious problem with overuse of the accommodating style is that it tends to create passivity in a project manager, a state which can deprive subordinates or peers of useful viewpoints and contributions.
Figure 1. Conflict Orientation
The avoiding style is one that is at the same time unassertive and uncooperative. Individuals who rely on the avoiding style manifest no desire to either satisfy their own concerns or the concerns of the other party to the conflict. Avoiding tends to be an effective method for sidestepping a conflict that one party does not seek. It is the style of organizational diplomats and politicians who perceive that they can accomplish much more if they operate behind the scenes rather than out in the open, in conflict with another party.
Compromising behavior falls somewhere between assertive and cooperative behavior. It represents a desire by one party to satisfy some of their concerns and a willingness to give in on other points. A compromiser sees conflict as a win-lose situation, but believes that in order to get something, it is necessary to give something else up. A compromising style tacitly acknowledges the importance of making concessions in order to gain something from the conflict. As a result, while compromisers see conflict in terms of winners and losers, they generally feel that each party can win a little and lose a little.
Figure 2. Modes of Conflict Behavior
Modes of Conflict Behavior
The final style of conflict behavior, collaborating, rates high on both assertiveness and cooperativeness. Collaborators view conflict from a very different perspective than most managers in that they reject the win-lose argument that most of us believe underlies conflict. They always seek a win-win solution to conflict situations. In order to achieve such an outcome, collaborators readily work with the other party to see if it is possible to find a solution that fully satisfies both sides. This sort of joint problem-solving requires a great deal of flexibility, creativity, and precise communication between the parties to the conflict.
A collaborating style is usually necessary when the issue at hand is simply too important to be solved with a compromising approach. For example, in situations in which project leaders are seeking to make major product specification changes or determine resource allocation, they may be faced with two or more distinct alternatives. Rather than vainly attempt to satisfy these disparate viewpoints by offering a compromise that will please no one and do nothing to further the development of the project, these managers may seek to hold a series of project team meetings in order to get all positions on the table where they can be addressed in a problem-solving session. The results of this problem-solving meeting may be a new strategic focus for the project, with new tasks and responsibilities for each team member. In this example, the problem underlying the conflict could not be ignored and allowing one team member to dominate the others with a competing style could potentially result in an incorrect decision. The best alternative for the project manager is to seek, in active collaboration with the project team, a solution that offers a win-win alternative.
Because no one conflict-handling style is appropriate in every situation, insightful project managers will seek to develop flexibility in their approaches to dealing with conflicts, either their own or those of team members within the group. The benefits of a collaborative style are that, unlike competing or avoiding, a collaborative style emphasizes group relationships. That is, using this style offers a method for enhancing communication and creative problem solving. In doing so, a collaborating approach can bring team members in conflict closer together, rather than driving them further apart by solidifying the conflict situation.
Interaction. Once a conflict episode escalates, a number of different exchanges begin to occur between the two parties in conflict. This exchange process is referred to as the conflict interaction step. While there are a number of potential actions that conflicting parties can take during this process, we will focus on some of the more common dynamics of group conflict during the interaction stage.
One common occurrence that usually takes place early in the conflict process is reinforcement through stereotyping. When we perceive that another party is frustrating a goal we value, we may respond by attributing their intransigence to convenient (and often incorrect) motives. For example, in a budgeting disagreement with the project cost accountant, a project manager may react by saying, “What can you expect from a group of unimaginative bean-counters?” This reaction, while common, underscores the potential for reinforcing the disagreement by creating a self-serving stereotype of the other party. Under this process, all opponents are selfish, willfully ignorant, or malicious because these attributions allow us to hold the high ground in the dispute. At the same time, we attribute honorable motives to our own behavior. Through stereotyping other cultures, races, or the opposite sex, we create a convenient cause for our discontent without being forced to reexamine our own motives as a potential contributing cause of the conflict. The irony is that, as the name of this process suggests, when we initially perceive ourselves in a conflict, rather than attempting to defuse or suppress this tension, our first inclination is often to reinforce the conflict, making it that much more difficult to correct.
The second process that often occurs during the interaction phase is that conflict begins to heighten feelings of positive identification with our own group. There is a natural tendency, when we perceive ourselves in conflict with an external stakeholder, to close ranks and become more single-minded in our attitudes and dispositions. As a result of that process, it is very common for groups to develop a superiority complex vis a vis the other group. This superiority complex feeds our natural inclinations to regard our own position as sacrosanct and justified as opposed to our “devious” and “maliciously inclined” opponents.
On a national level, this positive identification dynamic occurs quite frequently. To cite a recent historical example, in the early 1980s, just prior to the Falkland War between Great Britain and Argentina, the country of Argentina was in a state of tremendous political turmoil. Crowds in Buenos Aires and other large cities continually protested the right-wing rule of the military junta that controlled the government—right up until Argentina invaded the Falklands, creating a convenient external foe in the form of Great Britain. Literally overnight, the crowds that had been demonstrating against the government outside the Casa Rosada in downtown Buenos Aires became vast throngs supporting the actions of their leaders. This is another example of the positive identification effect that frequently occurs in the face of external conflict.
A final dynamic during intervention refers to the idea that while we exaggerate that positive nature of our own group and its members, we also seek to distort and exaggerate differences between our group and the opponent. In other words, once we find ourselves in a conflict situation, there is a real pressure to conform to group norms, to swallow internal differences in the face of outside aggression, and deny any degree of similarity with members of the opposing group. This separation serves to further solidify differences that prevent easy solutions to conflicts because they make it much harder for groups to seek common ground. In fact, we actively avoid the potential for identifying commonalties, preferring to focus on the differences and the reasons why we are justified in maintaining our beliefs.
Outcome. The final step in the conflict process is the outcome, during which time the two parties have come to some agreement in terms of resolving the conflict. It is important to bear in mind that no matter what the outcome— agreement, disagreement, or tacit agreement to let the issue drop—there will be residual emotions and ill will from the process. It seems an obvious point but it bears repeating that people simply do not forgive and immediately forget conflict episodes, particularly when the issues were significant or the emotional commitment of either party brought the conflict to a personal level. Project managers must be cognizant of the likely detritus of conflict. Playing down or smoothing over the problem when it has been “resolved” may be overly simplistic and ignores the potential for further tensions.
A final point about the outcome stage is to remember the difference between short-term and long-term outcomes. There is a familiar concept known as winning the battle and losing the war. When a manager wins a conflict, there is a strong potential for the other party to remember these experiences and look for retribution opportunities. This result is particularly true in the case of a manager who is prone to rely solely on the competing style in dealing with conflicts. As we have suggested, a competing approach that is based on assertiveness and unconcern for the other party is likely to create bad emotional feelings from the other party. Whether that party wins or loses the conflict, they are likely to remember the event and seek ways to repay the other group .
SOME OF ARTHUR YOUNGS FOURFOLDs
The dynamic confrontation between knower and known, with the addition of the two kinds of relation between them - the objective information (sense data) coming from the object, and the nonobjective qualities projected by the knower upon the object - may be represented diagrammatically:
At least four kinds of relationship are involved:
1. AA - The relationships contained within the object itself: that it is, for example, an equilateral triangle, having three equal angles and sides. Such interrelationship provides the definition of the object. It holds for all equilateral triangles.
2. AB - The data which the knower receives from the object as sensations: its weight, color, texture, etc. This is factual, and concerns the particular object. It tells us that one particular triangle is dented, or broken, or that another triangle is blue.
3. BA - The qualities which the knower projects upon the object: that the triangle is beautiful or ugly, good or bad. This includes characteristics like solidity because such qualities are in part projected by the knower. Solidity is not entirely objective since atomic structure is thought to be ninety-nine percent pure space.
4. BB- The function of the object for the knower: he uses the triangle for a watch fob or to illustrate an argument. This category consists essentially of relations of the knower to himself which he creates forthe object, and would include his purpose in making it.
Only the first category (AA) is considered valid and useful in the scientific view. I propose that a complete description necessarily includes the three alternatives to this view.
The first category, that of the relationships contained within the object, conforms to the scientific requirement for a valid description; i.e., one to which all observers agree: a square has four sides, etc. The second category, sense perception of the object, while also objective and the basis for all scientific experiments, provides only a transition to scientific knowledge. It comprises the immediate data obtained from a particular object or experiment and, before it is applicable to new situations, must be formulated and generalized.
Hence, scientific knowledge is derived from observations, but is different from them. The observations consist of particulars, while scientific knowledge is general and belongs in the first category, not the second.
Thus we may describe the objectivity of the first category as general, that of the second category as particular.
The third category consists of values projected upon the object; for instance, its beauty or ugliness. When Hamlet says, "There is nothing good or bad but thinking makes it so," the implication is that value is not inherent in the object itself. This is the usual view, which I do not contest. But the further implication that value, because it is not inherent in the object, is subjective, or limited to the particular consciousness of a particular knower, deserves closer scrutiny. For the moment, I will simply point out that I am replacing "subjective" with the more accurate word "projective" for reasons that will shortly develop.
The fourth category, the function of the object, we also refer to as projective. An alternative key word is orientation, which may be interpreted both metaphorically and literally. It refers not only to the function of the object, which we described as a relation projected for the object rather than upon it, but also to the way in which the object relates to a larger context. It concerns "which way up" the carburetor is installed in the engine or the key is inserted in the lock. This aspect of the object is not objective. We cannot determine it by inspection of the object alone, but only by an awareness of the larger context of which the object is a part.
Such reasoning indicates the appropriateness of supplanting the word "subjective" by "projective." "Subjective" implies a personal description, with the possibility of illusion, while "projective" implies only that which is not objective, and leaves aside the question of reality.
Thus we say that an image is projected on a screen, or that the earnings of a corporation are projected for the year to come. The projective aspect can be of very practical significance. When Thiokol, a synthetic rubber intended for tires, was proposed as rocket fuel (changing its projective aspect), the price of stock in the company soared.
The distinction between general and particular, demonstrated for the first two categories, also applies to the third and fourth. We may call the third projective and general, the fourth projective and particular.
In the third category, valid projections, such as "Where there's smoke there's fire," are possible only because such projection is general. The generality of projections also causes illusion. I see the beautiful tulips and imagine their smell and texture, only to discover that they are wax.
As for the fourth category, since function or purpose is an individual matter (my friend uses parking tickets to light the fire), the projection is particular. The word "orientation" implies this particularity; an orientation is by its very nature particular.
To illustrate the categories of knowing, let us use the example of an elephant:
1. The formal description. The structure of the elephant. The elephant as an object of scientific study. His anatomy, biology, behavior. Objective general.
2. The sense data which we experience by direct encounter with an elephant. The smell, the hairiness, the warm breath through the trunk. Objective particular.
3. The values we project on the elephant. How big he is! He seems kind, or patient, or terrifying, as the case may be. Projective general.
4. The function. The knower's interest in the elephant, what use he will make of him, as a circus attraction, a beast of burden, a zoological specimen, a source of meat or ivory. Projective particular.
The four aspects of a situation
In extending the method to deal with situations as well as objects, we must use more complicated examples. Suppose that a person is lost, but has a map. What kinds of information does he need to find his way?
1. The map itself. This, like the scientific description of the elephant, is an objective statement of the relationship of the distance between cities, of the location of roads, rivers, etc. The map is general and objective.
2. Where he is on the map. This information is different from the preceding. The person's position is particular as to place and time. It changes as he moves about. It is objective information but, unlike the map as a whole, it is particular and objective.
3. The scale of the map. Again, a different kind of information. It involves not just the scale in miles per inch on the map but the means of travel at the person's disposal. It is general and projective.
4. Orientation of the map. This different kind of information must be supplied by a compass. It also changes as the traveler moves about and is therefore particular. Note that it is an orientation, a direction, and that the direction of north and the direction in which the traveler wants to go are not necessarily the same. But in order to know in which direction to go, one must know how to orient the map. It is a relation of the map to the larger context. It is particular and projective.
In this example, there are again four aspects which correlate with four kinds of relationship:
Form correlates with the interrelationship of the parts of the known to one another.
Position correlates with the relationship of the traveler to points on the map.
Scale correlates with the relationship between a distance on the map and the effort the traveler is called upon to make.
Orientation correlates with the relationship of the traveler to a more ultimate reference which is not objective, his goal. This relationship is particular and projective.
The concept of four basic categories of knowing, or four aspects of a situation, is not new - as is evident by reference to the famous four causes of Aristotle. Aristotle described an object (for example, a table) as having:
1. A formal cause. The blueprint or concept of the table, its shape and proportion. Corresponds to the objective general.
2. An efficient cause. The work of the carpenter in making the table. Corresponds to the objective particular. His particular work produced this particular table.
3. A material cause. The wood or other raw substance of which the table is made. The projective general. Wood is general because it can make many things besides tables. There is some ambiguity here since one might choose a particular piece of wood to make a table. However, both the work and the wood have general and particular aspects.
4. A final cause. The purpose of the table. Its function of holding things. The projective particular.
Whether we refer to them as causes, categories, or kinds of relationships between an observer and an object, we can recognize that the examples we have listed all involve an observer and an object or situation.
We need not expect exact correspondences between the different examples, but notice only that they are all subject to analysis in terms of the particular-general and objective-projective dichotomies, and demonstrate the sufficiency of a fourfold analysis.
The next step is to display the four categories graphically. If, in fact, we call the categories aspects, the graphic portrayal is almost mandatory, since the word "aspect" implies a direction from which something is viewed. The apparent sufficiency of exactly four categories suggests representing them as pairs of opposites on a cross axis. But before we attempt this, we must decide which categories should be considered opposites. For instance, should the formal cause be opposite the material cause, or the final cause? Other alternatives, such as in what direction to have each aspect face, or in what order to have the aspects, are arbitrary.
To decide which pairs are opposite, we shall refer to the two dichotomies of general versus particular, and projective versus objective. Since formal cause is objective and general, and final cause is projective and particular, they are doubly opposite and hence their relationship should be represented by the maximum angle, a full diameter of difference. Thus we have:
Several important properties of the four categories are made apparent by this graphic representation which, by correlating the aspects with directions in space, permits us to say:
1. Four aspects are sufficient for the analysis of a situation. If there were a fifth, it would be compounded of two others.
2. Four aspects are necessary to a situation. If, for example, we know of three, we should expect to be able to find a fourth.
3. Aspects can be formally related. Aspects 90 degrees apart are independent of one another. On the other hand, aspects at opposite ends of an axis are mutually opposed. This idea can be illustrated by reference to the four directions. We can move due east without moving north or south, but not without moving away from, or negating, west.
The calculus, discovered simultaneously by Leibniz and Newton, is an important technical device which greatly enlarges the scope and power of the fourfold analysis. Since it is a foundation for the argument to come, I should describe it briefly.
The concept of the calculus consists of the recognition that, besides the measurement of space and time, we may also employ the ratio of space to time; that is, speed, or velocity. In these days of high-speed travel, it is difficult to understand why the discovery of a formal expression for such a household word as "velocity" raised such a fuss. But Bishop Berkeley, the philosopher, insisted that Newton's "fluxions," which were the ratio of an infinitesimally small increment of distance to an infinitesimally small increment of time, were "logical absurdities." "For," said the Bishop, "an infinitesimal is bad enough, but a ratio of infinitesimals is preposterous."
The person who insists he was not driving sixty miles an hour because he was traveling for only ten minutes is using the same reasoning.
Newton's great discovery was that we can speak of a velocity as having instantaneous value at a point, despite the fact that to measure velocity we have to take a finite distance and divide it by a finite interval of time.
Newton went further. "Not only may we speak of the rate of change of distance with time, which is velocity," he said, "but we may speak of the rate of change of velocity with time, which is acceleration." Velocity is expressed as dl/dt, which means the derivative (or ratio) of length (distance) with respect to time (dlsignifies an arbitrarily small increment of length, dt an arbitrarily small increment of time); acceleration is expressed as (d/dt)(dl/dt), the derivative of a derivative, or As position is measured by length (l), we will
use the words interchangeably.
The calculus enabled Newton to solve the problem of planetary motion. Even more significant is the fact that the calculus, through its concept of derivatives, is able to give a precise definition to elusive notions like force, and hence makes possible the whole science of motion.
In following the use of the calculus to explore the four categories of knowing, the non-mathematically grounded reader should not permit a horror of formulae to spoil what can be an interesting adventure. Readers familiar with mathematics will hopefully be tolerant if their equipment is borrowed for a purpose that takes it beyond its usual employment.
To illustrate the interrelation of the concepts of the calculus - position, velocity, and acceleration - let us take the example of a swinging pendulum.
Assume that the bob of the pendulum is released at point A and swings from Athrough midpoint B to point C opposite A and back again. When it is to the right of midpoint B, its position is positive; when to the left, negative. A and C are thus its maximum positive and negative positions.
If we chart the position of the pendulum with respect to the passage of time, we may refer to the completion of one swing to the left and its return to A as a cycle of action, the halfway point of which is C and the first quarter of which is midpoint B. The third quarter will be B again but, to distinguish the midpoint of the return swing from that of the outgoing swing, the latter is called D. This can be represented by a new diagram on which the right and left positions of the pendulum are represented by a vertical distance above and below a horizontal line upon which A, B, C, D, A' represent successive time intervals.
This vertical distance, or swing, will be maximum positive at A, zero at B,maximum negative at C, zero at D, and back to maximum positive at the end of the line, A'. A smooth curve is drawn through these points.
Note the slope, or "steepness," of this curve, which represents the rate at which the position changes.* At A it is zero (fiat) because the position of the pendulum is changing very slowly; at the 1/4 point B, the slope is steep and downward (negative), at midpoint C it is zero again, at the 3/4 point D it is steep and upward (positive), and at the end it is again zero. These values are marked on the same diagram to obtain a new curve, which represents the value of the slopeof the first curve.
*If we take a short section of the position curve, for example, where it first crosses the line, we can see that slope is the ratio of the vertical distance dl to the horizontal distance dt. and this ratio has a definite value.
In the diagram we have made dl and dt large for visibility. But when dl and dtare large, the curve between them is not a straight line. However, if we make dland dt small enough, the curve between them will approach a straight line, and the slope of the curve at point B will equal the ratio dl/dt, which is called the derivative of l with respect to t. Since l is distance and t is time, dl/dt is velocity. This was Newton's discovery. It permits us to deal with an entity that is not an immediate fact of sense experience. (Since an instantaneous picture of the pendulum would not reveal its velocity or even that it is moving, we have to take at least two pictures and plot their relationship.)
This second curve, showing the rate at which the position changes, depicts the velocity of the pendulum. Since position has been designated as positive when the pendulum is to the right, velocity is negative (moving to the left) in the first half of the swing. This is shown by the curve of velocity being below the line in the first half.
Going a step further, the slope of the velocity curve, which is to say the rate at which velocity is changing, is charted. This produces a third curve, which represents acceleration.
Observe that the acceleration curve is exactly opposite to the position curve. At the start, position is maximum and positive, acceleration maximum and negative. One may experience this by holding the pendulum at position A (positive), and feeling it pull back (negative). The pull is acceleration. If one lowers the pendulum into a vertical position, this pull reduces to zero (at B). The pull becomes maximum and positive (pulling toward A) when in position C and so on.
Note that these curves are all of the same shape but the curve for velocity is displaced 114 of a cycle* back from the position curve, and the curve for acceleration is displaced 114 cycle back from the velocity curve and therefore 112 cycle from the curve of position. Acceleration is thus "out of phase" with position by 112 cycle. Velocity is out of phase with both acceleration and position by 114 cycle. Note that the peak of velocity comes at D, acceleration at C and so on.
*A to A' is a full cycle, so A to B is 1/4 cycle.
The cycle of action
To take a final step, the cycle of action is represented as a full circle. To do this, we simply bend the line ABCDA' around into a circle, with A' falling on A, and the points of maximum positive position, velocity, and acceleration falling on three points 90 degrees apart.
This charting presents the phase relationship between the three measures under discussion. Velocity lags behind position by 90 degrees, acceleration by 180 degrees, making acceleration opposite to position. The fourth point on the circle has no measure assigned to it. What could this measure be?
Since it is 90 degrees "beyond" acceleration, and each right angle has signified an additional derivative of position, we could expect it to be the third derivative, That is to say, the rate of change of acceleration.
But what name and what meaning can we give to this?
The name given to the third derivative by aeronautical engineers is jerk, probably because when acceleration is changed by an automatic control, it does so in an all-or-nothing fashion which results in a jerk. But in the general case, as in human control, it need not be a jerk.
In any case, because this control factor is not described in the textbooks, we should give it special attention. Let us take the case of driving an automobile.
To increase the speed of an automobile, we push on the accelerator, causing positive acceleration. To decrease the speed, we step on the brake, causing negative acceleration. We may also alter the direction of the car by steering.*What is the process by which the accelerator, brakes, and steering change the acceleration of the car? Clearly, a change of acceleration is what we mean by the word control, which now goes in the diagram's fourth position.
Reading clockwise, each measure is the change of the one before. This raises a question: what factor changes control?
*This is also a change of its acceleration, which may be understood as follows: Suppose we are traveling at a constant speed and make a U-turn without slowing down. We are now moving in the opposite direction, and our velocity, as measured from a point outside the vehicle, has changed from positive to negative. As this implies, a change of direction of velocity is, in fact, an acceleration. The force of this acceleration is what pushes objects in the car toward the outside of the curve. If we hold the wheel in one position so that the car travels in a circle, we are not changing the acceleration - we have simply imposed a constant acceleration.
What causes us to turn the automobile, or start it in the first place, or finally to stop it? The answer is "the destination." The destination is a place, or position. Thus the fifth step, the fourth derivative of position, that which determines control, is the same as the first step. This position is not the same position we started with but has the same category of measure (distance, or length), just as the direction in which the traveler wants to go is not a new category in the example of the map.
The examples of the map and the automobile both demonstrate the sufficiency of four categories. We need no fourth derivative. Position and its three derivatives are sufficient for analysis; and, I might add, necessary when there is control, human or otherwise.
It may be recalled that the problems of classical mechanics always exclude the possibility of a free agent "interfering with" the system. These problems employ only position and its two derivatives, velocity and acceleration, and in the case where friction can be ignored, may even omit velocity (for friction depends on velocity).
Thus the basic predictive equation that is used for treatment of the motion of all bodies, from atoms to spaceships, is:
The presumption in excluding a free agent is that there could be no prediction in such a case - the equation would be too complicated or would not apply.
However, the above argument shows that there is a formal expression which covers the "free agent," namely, the third derivative. This, of course, does not mean that prediction is possible. On the contrary, it means that freedom (or unpredictability) is part of the system. In certain cases, prediction is theoretically possible, as in the case of feedback wherein a predetermined position regulates control. One example of this is a target-seeking missile - but even here, although the control is not itself free, it has been set in advance by an agent who is free to choose the target.
One might suppose such a situation altogether too complicated for complete analysis, but at least it can be shown that the four categories are again sufficient:
1. To know the position of a body in space, we need one instantaneous observation (for instance, the photo finish of a race).
2. To know its velocity, which is computed from the difference in position of the body and the difference in time between the two observations, we need two such observations.
3. To know its acceleration, we need three observations.
4. To know that a body, for example, a vehicle, is under control, and thus distinguish it from one in which the controls are stuck, we need at least four observations. That is, we need three to know acceleration and one more to know that acceleration has been changed. (This still does not tell us the body's destination or goal.)
5. To know the destination, provided the operator does not change his mind or try to fool us, we need five observations.
6. To know the operator has changed his mind or is trying to fool us, we need six observations.
Note that the fifth observation is to establish a position (the destination) and the sixth a change of position. Thus categories five and six repeat the cycle, the fifth falling into the position category and the sixth into the velocity category. As in the case of the map, the sufficiency of four categories is demonstrated.
Use of the measure formulae
We have shown that the motion of a body, even one controlled by an operator, may be formally described by the four categories of measure. The form we have used to represent these measures is that employed in the calculus:
There is an alternative, and simpler, representation in which the d's are omitted and capital letters employed; thus:
This is the form used in so-called measure formulae, the ten formulae used in physics to describe the motion of a body. Since I will discuss these formulae at some length, I will use the simpler representation.
In describing these measures - position and its derivatives we have sought to establish:
1. That four categories of measure are necessary and sufficient for the analysis of motion of a moving body.
2. That the graphic representation of these measures as four right angles dividing the circle has a special significance - each right angle is a phase shift of 90 degrees and correlates with the derivative of the one before.
In the course of the above demonstration, we uncovered another point which has philosophical significance and suggests further implications:
3. That the measure technique of science can be extended to include free will, an aspect of a situation generally thought of as nonscientific.
What is going on? We have been standing on the sidelines watching the scientist ply his trade with some technical measurements that do not appear to concern philosophy; they are just the tools of his trade. But one of these, the third derivative, turns out to be the very thing discredited by science - the human, or free will, factor!*
*It has been suggested that rather than saying the third derivative is free will, I should say that the third derivative is where free will enters - but I would protest that this implies free will is something more than control.
Perhaps we should take a closer look at these measure formulae. Do they have a more general significance?
Categories of knowing represented by the measure formulae
What are these measure formulae, position and its derivatives, velocity and acceleration? Are they just the simple "physical quantities," as they are referred to in the textbooks?
Not so. Closer examination reveals fundamental qualitative differences between them. To understand this, consider how each of these measures is known. Position can only be observed visually or by less direct processes. Velocity is an intellectual abstraction: it cannot be known from direct experience. It must be computed. To know velocity, we must make two observations of position, determine their differences, and divide the time elapsed, thus obtaining a ratio. (Though velocity can be read from a speedometer, the only accurate speedometer, a chronometric tachometer, is itself a computer.) The velocity of the airplane even at six hundred miles an hour is something that one is completely unaware of. The earth is "hurtling" through space at eighteen miles per second, yet we have no feeling of it.
Acceleration, however, is felt. For example, when an elevator suddenly starts down, you feel it in the pit of your stomach; when the airplane comes in for a landing and the jets are reversed, you are thrown forward in your seat. Acceleration may also be computed, but it can be directly and physically experienced by the knower because the nervous system registers change, not a steady state.
The notion of velocity is so far removed from direct human experience that it was not until after Newton's discoveries that it became a formally recognized concept. And for all its acceptance by modern civilizations, velocity is nevertheless denied by many philosophers, because it is neither an "event" nor an "individual."*
*For an example of the confusion that exists over this question. see Smart. J. J. C.. Problems of Time and Space. New York: Macmillan. 1964.
We may deny the reality if we wish, although it would then be hard to know which of the formulae we might endow with reality. In any case, this misses the point. What is important is that:
1. Position, velocity, and acceleration are separate and different aspects of the total situation.
2. They are all necessary.
3. They are included in the scientific description.
4. And most important, they are different categories of knowing. Position is observed, velocity is computed, acceleration is felt. Control, the fourth category, is essentially indeterminate.
The scientific basis for the human faculties
The fundamental differences between the measure formulae, demonstrated by the different ways they are known, suggest that the origin of feeling, thought, and sensation may not be merely human, but may lie much deeper.
When we describe the human organism in this way, however, we are in double jeopardy. The behaviorist says: "You see, the human organism is merely a machine"; while the vitalist counters: "When you try to prove that man is merely a machine, you deny free will."
We would answer both points of view by referring to the fourth aspect, control. In a machine, this would include all the devices provided for its control: the accelerating, braking, and steering mechanisms. But all the mechanisms, no matter how elaborate, do not complete the control. Control must be initiated by an operator. And this absolutely essential element is indeterminate and unknowable to an observer.
Thus the complete account, far from denying free will, shows both the possibility of free will and the requirements for its effective operation. For if any of the three "mechanical" aspects does not function properly or is tampered with by an enemy agent or even a behaviorist, free will cannot manifest itself.
The learning cycle
The learning cycle further illustrates the cycle of action. An infant begins with a spontaneous act. He reaches out to grab something (1). Then he encounters a painful contact, perhaps a hot stove, and he reacts by withdrawing his hand (2). After the pain subsides, he takes stock, associates the stove with pain, observesthe situation (3). Finally, he controls his action by avoiding hot stoves (4).
The four types of action in the learning cycle correspond to the four measure formulae:
Spontaneous act (impulse) = acceleration
Reaction (also spontaneous) = velocity (i.e., change)
Observation = position (the observable factor)
Control = control
The same diagram that we used to depict the cycle of action may be used to represent the learning cycle, but it is necessary to reverse the clockwise order and to start at the left:
While it is satisfying that the same scheme serves to represent such dissimilar activities as an operator's controlling a machine and a child's learning about the world, the fact that the order must be reversed is important and will be discussed later. Another indication of incompleteness is that, so far, we have dealt only with actions, each of which is part of a larger cycle which begins with a stimulus and leads to a result. The behaviorists, in their dependence on the duality of stimulus and response (a form of action), fail to recognize the necessityof a third factor: when a dog's hunger is satisfied, it may no longer respond to the stimulus of food.
But when the stimulus causes wrong action and the result is not achieved, the learning cycle becomes necessary. Thus the learning cycle occurs only when there is an obstacle in the larger, threefold cycle.
THE ROSETTA STONE OF MEANING
The method developed in the foregoing chapters has shown the interrelationship underlying the complete basic vocabulary of science. Since we have already found that some of these scientific measures (in the cycle of action) have equivalents in human terms, we may likewise expect to find that the others have equivalents in human terms.
This is an area to which the specialist, philosopher, mathematician, or even psychologist, has no better access than the unskilled human being.
I should point out that the diagram we are evolving - which I call the "Rosetta Stone" because of its similarity to that famous tablet which bears inscriptions in three languages, providing the key for the translation of Egyptian hieroglyphics - is not just a translation of meaning, but is a generation of meaning. It is the relationships between the words we must use, not their definitions, that give them their meaning. With this in mind, we will now attempt to uncover the relationships underlying the basic human vocabulary.
The learning cycle has given us four basic categories of act:
1. Spontaneous Act
2. Change (reaction)
Considering the threefold cycle, we may expect each kind of act to have a preceding stimulus and an ensuing result or, as we generalized, an appropriate relationship and state. But in Chapter I, we already disclosed four categories of relationship, so now we need only reexamine these four and see to which acts they properly correspond. We may then find states corresponding to the four acts.
Our analysis of the four relationships is best done through the two dichotomies of objective-projective and particular-general. By considering the permutations of these dichotomies, we can explore the meaning of each kind of relationship, and then look for an appropriate word to describe it.
I. Objective general. General information which is objective, definitions, scientific laws, etc., we will simply call KNOWLEDGE, in the sense of a "body of knowledge."
2. Objective particular. Particular objective information, on the other hand, such as "This triangle is dented," is factual. We will call this category FACT.
3. Projective general. Knowledge which is projective and general, such as "All redheads are talkative," might be called belief. Since "belief' suggests a particular situation, however, we would use the more generalized word FAITH, remembering that the projection can be correct or incorrect.
4. Projective particular. This category is inherently subtle and difficult, containing relationships within the person himself. For the moment, we will leave it unnamed, but later we will find that it is possible to name it.
We must now decide which of the four acts corresponds to each of these relationship categories, and what would be the state resulting from each act.
1. KNOWLEDGE. The act immediately appropriate to knowledge (as it is meant here-a body of knowledge) is OBSERVATION. By observation we mean not only "looking," but other kinds of consideration as well. A body of general knowledge is useless until it is considered.
The state immediately resulting from the consideration of knowledge is SIGNIFICANCE.
2. FACT. The act appropriate to a particular fact is CONTROL. Upon encounter with fact - the traffic light is red - one controls the situation by stopping the car. Recall that control cannot become manifest without certain objective facts at its disposal.
The word I have tentatively chosen for the state resulting from control is ESTABLISHMENT. It could also be called "accomplishment" or "consolidation."
3. FAITH. Because faith is a presumption or an expectation, it is likely to produce CHANGE (reaction) upon confrontation with actuality: I meet a redhead who isn't talkative. (Change here is in the passive sense of being changed, the active sense, producing change, would be "control.")
The state immediately resulting from change is the TRANSFORMATION of one's original faith.
4. IMPULSE. This is the name which, in deference to our method, we refrained from assigning to the "projective particular" relationship. Now we can see the difficulty: what is the antecedent to a "spontaneous act"? Here we must think of spontaneity as being in the relationship category, where we will call it "impulse." Other possibilities would be "insight" or "intuition." Since a spontaneous act is projective, directed toward the future, its stimulus is not apparent. It is equivalent to purpose (within the person himself).
The state which results from the spontaneous act, for instance, a playful act, is very simply BEING.
The foregoing is summarized thus:
Relationship Act State
Impulse (purpose) Spontaneous act Being
Faith Change (reaction) Transformation
Knowledge (form) Observation Significance
Fact Control Establishment
To complete the "Rosetta Stone," we must show the correspondence of these twelve human categories to the twelve measure formulae. We shall use the cross axis as a format for analysis to bring out the meaning implicit in the angular relationship between the terms. Recall that factors at opposite ends of an axis are mutually opposed, that those at right angles to one another are independent, and that rotation signifies change in time.
The four relationships
Impulse/Action : In physics, the quantum of action exists in its pure state as a quantum (discrete particle) of radiation, having an undividedness which makes it unique among physical measures. These "quanta of action" are the origin of matter, and in having the power to alter the state of an atom, they are the origin of change.
Impulse, like the quantum, is the initiating factor in a process. Also like the quantum, it is instantaneous and quantized - occurring in discrete units. Two of its forms, decision and recognition, emphasize this - you cannot recognize somebody, nor make a decision, one and a half times.
Impulse and action are particular, potential, unknown, projecting into the future.
Faith/Moment of inertia : In science, the moment of inertia is the tendency of a thing to continue in a given state of rest or motion. In mechanical systems, it serves the function of maintaining steady motion and canceling outfluctuations, as with the flywheel of an engine.
Its human equivalent, faith, is the tendency to maintain a given credo without examination. Like the flywheel, it serves to maintain steady motion, carrying us through the vicissitudes of life.
Faith and inertia are in the present. Faith is the projection we put upon the present situation.
Fact/Work Work is energy - the amount of energy expended to perform a task. It is opposite to inertia.
For the mind, work is the readjustment of its implicit beliefs when confronted with fact. Like work, it is a physical exchange of energy, as when a scientist tests his theory on physical objects.
Work and fact are in the present - they are the impingements of the physical world upon the person. Fact is equivalent to work because the word is derived from factus, past participle of facere, "to make," as in "factory."
Knowledge/Power Knowledge, or data, is objective descriptive information which sits in the library or in our minds until it is used.
Power is an objective measure - the description of the dimensions of an engine, for example. By itself it is nothing; power has no actuality until it operates for a time to produce work. Power x time = work.
Knowledge and power manifest through application.
The four relationships
The foregoing diagram should be compared with the four types of relationships outlined earlier. It is worthwhile to play around with the interrelationships involved in order to get a sense of how together they constitute the totality of the object.
Note that faith and fact are opposite. This does not imply that all belief is false, but that the element that operates in faith is a projection of what has gone before. Like inertia, faith is the continuation of the state of rest or motion that has held before, whereas fact is the confrontation with what is particular to the present.
Similarly, function and form are opposite. Function is the purpose which the self projects for the object (I use a stone for a hammer). Form is the definition that would limit this freedom (I ask for bread and you give me a stone). Again, we may note that either form or function may mediate to determine whether something is or is not what it is called. Are these your glasses? No, mine are bifocal (form or definition decides). No, but they will do (function decides).
A difference between vertical and horizontal is that the horizontal is bound to time. It concerns what is immediate or phenomenal. The vertical axis is not bound to time. It concerns the ideal, either the definition, which is ideal in the sense of a standard for manufacture; or the function, which is ideal in the sense of the cause that gives the object its value.
The four acts
Control/Control Control is the final stage of the learning cycle, and in a moving body it is the rate of change of acceleration. Control is free; it is at the disposition of an operator and correlates with will.
As the reaction to observation, it is conscious action.
Spontaneous act/Acceleration The spontaneous act is primary and simple, without antecedent. In motion, the initiating factor is acceleration, as in starting a car from rest.
Both the spontaneous act and acceleration are unconscious action.
Observation/Position (L): The midpoint in the learning cycle is observation - the consideration of what has taken place. For the scientific term, we may equate it with the thing observed: position.
All the other measures ultimately involve a measure of observable position, such as a needle on a dial.
The observation of position is a conscious reaction.
Change/Velocity Velocity is the change of position, and we may generalize it as the change of any observable property. In the learning cycle, it is the point of reaction to the initial act.
Velocity and change (passive) are unconscious reaction.
The four acts
Here too there is value in drawing out the implications of opposite and of complementary aspects. It is clear that observation on the right is opposite spontaneous act on the left, and it is also clear that control at the top is the opposite of the passive change at the bottom of the chart.
This oppositeness is confirmed by the literal oppositeness, in the case of the pendulum, of acceleration and position. When the pendulum is at the extreme position, acceleration is at a maximum and is pulling in the opposite direction.
If one experiments with a pendulum hung from the hand, it will be found that one can control the pendulum by timing the motion which produces control so that it is exactly opposite to the velocity. In other words, control is most effective at the midpoint of the swing. Here a control motion in the direction
of the pendulum will stop it, and a motion in the opposite direction will increase its swing.
Such control motions, which do not have to lift the pendulum, can be effected with a minimal energy reduceable in theory without limit. This, of course, confirms the independence of the control aspect and the motion aspect, because were the control not independent of the motion, it would not be possible to induce motion in either direction.
The four states
Because they are not conceptual, the human states must be apprehended through feelings. While each physical state is the rate of change of the one before. it would appear that the human states do not change into one another except through the appropriate relationships and acts; and we are reminded that the fourfold is essentially secondary to the threefold.
Significance/Moment (ML): These two terms come together when we refer to "matters of great moment." meaning significance. In a broader sense, it is the extent to which things come into focus on an issue. In science, moment is leverage - the "state" of a mass at a distance - as when a man uses a crowbar to move a stone many times his own weight.
Establishment/Mass control (): Recent aeronautical practice refers to this product of mass times control as "power control," but strictly it is "force control" or "mass control." One can recognize the difference between controlling a small mass, say, a pencil, and bringing a ship into dock. The control of a greater mass is a greater accomplishment. "Establishment" is a tentative general name for this product. We could also use "accomplishment" or "consolidation."
Transformation/Momentum (): By "transformation," we mean the state resulting from a change - a certain condition within an overall "state of flux." It is distinct from "establishment," which is a final state of control, usually changeless. Thus the woman admiring her new hairdo is celebrating a transformation, rather than the possession of beauty. In science, this "state of changing" is called "momentum," as the momentum of the hammer drives the nail, or the momentum of the car breaks the telephone pole.
Being/Force (): Like "impulse" and "spontaneous act," "being" is elusive as a concept. Insofar as it can be objectively described, it is the result (within the actor) of a spontaneous act - the incorporation of spontaneous action. It is helpful to contrast it with "having." It may be more easily understood in its scientific guise as force, a condition which is caused simply by the presence of something - as the force of gravity is caused by the presence of the earth. So "being" is like the force of personality.
The four states
The four states can be seen most simply as the dichotomies of being and nonbeing and of having and not having.
Establishment, or mass control, is easily correlated to having, but many things that one may have are not desirable, for example, sickness, impediments, flaws. Transformation is the state in which such undesirable limitation has been
removed (not having). Transformation includes the destruction necessary to construction; in addition, it includes the breakdown of waste products, making them available for new growth.
Nonbeing is consciousness of being because it is opposite to being. But to be conscious of being is to realize the significance of being; hence, nonbeing is significance.
This use of negation (as in giving importance to nonbeing) is perhaps awkward in comparison with the usual words, but it is a technique that can handle meaning and can reduce two words to one or even four words to one, if we could find word pairs as we did for relationships and action.
The four states are difficult because they are, as noted, not conceptual, nor are they apparent in the sense that actions are. It is especially important to recognize that states are represented in the measure formulae, and hence have status in science coequal with the relationships and actions. So great is their importance in current science, in fact, that it is sometimes stated that science consists solely in the observation of states.
We have had examples of actions and of relationships, so we should have one of states. We can think of the four stages of an internal combustion engine as bringing about four different conditions, or states, of the contained gases.
First there is the compression stroke in which the mixture of fuel and air is compressed, second the firing stroke in which the gases explode and push the cylinder to do work, third the exhaust stroke in which the waste products are discharged, and fourth the intake stroke in which new fuel and air is drawn in. These follow the sequence in counterclockwise order:
Compression Gases compressed (Establishment)
Ignition Explosion and expansion (Being)
Exhaust Wastes discharged (Transformation)
Intake Gas is drawn in (Non-being)
The diagram above is the same as that at the end of Chapter IV, except that to it have been added the words that we have been dealing with in this chapter. As with the measure formulae, we can move around the circle in threefold or fourfold manner.
We have now completed the diagram by adding the four stimuli and the four results (or relations and states).
We should also realize - a point which will be discussed in more detail later - that there are two directions in which to go around, counterclockwise and clockwise. The motion is counterclockwise for the learning cycle, moving from blind action (acceleration) through reaction to control. It is clockwise in the operation of a machine because the operator anticipates what happens.
The learning cycle is natural or naive, but teaches control; the other is informed and applies the knowledge gained.
Illustration from Peirce
I will close this chapter with an analysis by the philosopher Charles Sanders Peirce (referred to in the Introduction). In his essay "How To Make Our Ideas Clear,"* Peirce describes four steps which lead to action. We begin with sensations, of which we are immediately conscious. These, he maintains, occur in succession and create a thought, just as the succession of musical notes creates a melody. The goal of thought is belief; we continue the activity of thought until we reach a belief, the "demi-cadence which closes a musical phrase in the symphony of our intellectual life." He goes on to say that belief establishes a rule for action, so that the final upshot of thinking is the exercise of volition.
*Philosophical Writings of Peirce (p. 314). Justus Buchler, ed. New York: Dover Publications, Inc., 1955.
Thus we have the sequence: sensation --» thought --» belief --» action.
This is precisely the sequence we would have on a diagram of the four relationship categories if we were to proceed clockwise from "fact":
Here, as with the aspects of motion, each right-angle shift is the slope or trend in the previous category. With relationship, we have, first, awareness of isolated facts; then, with repetition of fact, knowledge of generalities; then, confidence in such knowledge; and finally, we decide on action based on this confidence.
This succession moves in the direction of a conscious search for valid principles of action (clockwise); it is opposite to the learning cycle (counterclockwise), which advances by trial and error.
Piaget has found this sequence in children. Over a period of years, they become able to (1) move from observation to recognition of law, (2) act on the assumption that law holds despite counterfactual evidence.
YOUNG HAS A CHAPTER DEDICATED TO THE THREE AND FOUR DYNAMIC- AND HE DISCUSSES FOUR TYPES OF FOLDS
The threefold and fourfold operators, then, may be thought of as using up orremoving the freedom implicit in the three dimensions. The combination of three- and fourfold applies to the physical space-time world of objects and events. This is the world of determinism, subject to all the laws of classical physics.
We may diagram the situation thus:
Level Character Freedom
I Unity Three dimensions free
II Threefold One dimension committed, two free
III Fourfold Two dimensions committed, one free
IV Twelvefold Three dimensions committed, determinism
The threefold has one dimension committed (time). The fourfold has two dimensions committed (mental space). The twelvefold has three dimensions committed (actual space-time).
To clarify the distinction between the threefold and fourfold operators, as applied to ontology, I have listed them in a comparison chart:*
Threefold (experience, feeling) Fourfold (concepts, intellect)
Indefinite, infinite Finite
One dimension committed, Two dimensions committed,
two dimensions free one dimension free
Exists in time (sequence) Exists in space (simultaneous)
Ordering can be taken only Ordering possible in any
one way direction
The matrix of experience The matrix of mind
Supplies substance,* Supplies measure, form,
motion, and value and concept
Requires three dimensions Requires only two dimensions
for full representation for full representation
*Substance will be described in Chapter VIII.
We may sum this up by saying "Time supplies content - space supplies measure." The magnitude of space depends ultimately on time to traverse it. The measurement of time depends on treating it like space.
YOUNGS FOUR LEVELS
We have already, in Chapter VII, shown the progressive loss of freedom at successive levels.
I (Light) Unity Three dimensions free
II (Nuclear) Threefold Two dimensions free
III (Atoms) Fourfold One dimension free
IV (Molecules) Twelvefold No dimensions free
This declension, however, depicts only the process of generation produced by the counterclockwise rotation, toward manifestation. The clockwise rotation, away from manifestation, is of course toward goals; but it is also toward greater freedom (more degrees of freedom, fewer degrees of limitation).
At the fourth, or molecular, level, a reversal can occur in the evolutionary process, and the appropriate direction moves now toward goals (what we have called clockwise rotation). Further counterclockwise rotation results only in molar aggregates, which do not participate in the process. The molar aggregates do not comprise another level because they are not fundamentally different from molecules in terms of the theory. As aggregates, they have lost that trace of the original potency which appeared in individuals on the molecular level as the phase dimension, or choice of timing. They constitute the inert "furniture" which is used by process to fulfill itself.
We can now realize the reason for the non productiveness of the clockwise rotation at levels II and III. When the clockwise rotation occurs at the nuclear and the atomic levels, before the complete loss of freedom at the molecular level, it cannot harness means (matter and law) to its purposes. The opportunity to use means comes at the fourth level, in the physical world. This is the world of commitment, where the initial freedoms have changed into restraints; the world of determinism.
This world is characterized by the increase of entropy. Entropy is the tendency of differences to average out, of stones to roll down from the mountains and fill valleys. In other words, it is the tendency for energy to become more uniformly distributed and hence unavailable.
In the molecular world, the reversal of direction permitted by the twofold operator does have significance, and a crucial one. It makes possible the decrease of entropy.* A small system can store order or energy which it draws from its environment, and build this order into itself. Such a system is the living plant.
*The decrease, that is, of local entropy. While the total entropy of a particular system always increases, it is possible in living systems to circumscribe a localregion where entropy decreases; in inert systems no such region exists.
YOUNGS FOUR LEVELS
C. Seven Stages (and Substages) of Process
Most simply stated, the theory of evolutionary process consists of seven sequential, cumulative stages, each associated with a particular essential property or Power (Figure 1a.). Each of these seven stages of evolution, in turn, contains seven substages with the same sequential powers (developed over the same four levels) as the major stages.
Loss of Freedom (an illustration)
In the descent, process loses its freedom in three downward steps. Let us imagine that you are trying to capture a wildcat that has climbed a tree. You lasso him with a rope and make the rope secure. The wildcat can still move about, but he can't get away. Then you lasso him again and make the second rope fast. The wildcat can still move, but whereas his movement was first confined to a sphere, the pull of the two ropes will constrain it to a circular orbit on a plane. (A circle is the locus of a point equidistant from two given points.) A third rope will complete the process and hold the wildcat in one position.
Similarly, the step down from light to the level of nuclear particles constrains the particle to motion within a sphere (which is the orbit of uncertainty of the electron as described by Heisenberg); the second downward step confines the electron to movement in a circle around the nucleus of the atom; the third to a fixed position of the atom, as in a crystal.
Levels of Descent
The descent is not continuous; it occurs in three steps. But why necessarily three? In the case of the wildcat, it is clearly because there are three dimensions of space. In the case of process, this three-dimensionality carries over into something more abstract, but still threefold. To demonstrate, I would like to present three ways of describing the entities of physics in four stages involving three downward steps. The individual levels will be described in more detail later in the book; here we are concerned only with a method for structuring this concept.
1. Division of initial unity
Described one way, the descent is, as we've mentioned (see pp. 18ff.), a division of the initial unity or wholeness in the quantum of action into Energy times Time, and Energy into Length times Force.
2. From homogeneity to heterogeneity
But there is another kind of division. This is the decline from homogeneity to heterogeneity of the entities themselves:
1. One kind of photon, which has unit spin 2 and no charge.
2. Two kinds of nuclear particles, which have half-spin
and are charged positively or negatively; i.e. proton and electron.
3. One-hundred-odd kinds of atom, with various chemical properties.
4. Countless kinds of molecule, with many kinds of properties: mechanical,
electrical, chemical, physiological.
3. Change in degrees of certainty
The levels also represent the degrees of certainty which it is possible to have about the entities at the respective stages of process, and these degrees can be correlated to electron volts, a measure of energy.
Level I. The photons at level I are complete in their uncertainty: they are unpredictable. As we have noted, the observation of a photon annihilates it, so that there is nothing left to predict. The energy of a photon that can create a proton is about a billion electron volts, to create an electron about one-half million volts. All photons have total freedom.
Level II. The nuclear particles, electron and proton, created by photons, are the first occurrence of permanent mass and charge, the basic substance of the universe, as compared with the activity of the light that created them. But not all of this activity (or, more correctly, angular momentum) is condensed into mass. For reasons which are still unknown, 1/137 of the angular momentum remains uncommitted, and free. (This 1/137 is known as the fine structure constant.) It is this "freedom" which manifests itself in the uncertainty of position and momentum that characterizes the fundamental particles.
Level III. The atom entails a further reduction, not only in the sense that the charge of the contributing particles is neutralized, but in that the free energy which it radiates or absorbs is drastically reduced to about 10 electron volts (for hydrogen).
Level IV. In the molecule, it is the bonds that have energies, which cover a wide range. We will be interested in the energies of approximately 1/25 of an electron volt, which is that of the average molecule at room temperature. Why? Because according to our theory, it is at this energy level that life becomes possible.
This last energy level, it would appear, is the working base that process has to reach before it can start building up again. By this, we mean building the complex organic molecules such as proteins and DNA that are the basis of life, which requires a temperature between O and 45 degrees centigrade.
Necessity for Free Will
The reader may perhaps be familiar with current ideas of how life arose from electrical discharges in the early atmosphere of methane. Such discharge has been experimentally tested and found to produce minute amounts of many of the amino acids necessary to life. This may indeed have been an important step in the creation of life, but in our view it could by no means have been sufficient. Our position is that life requires, in addition to materials and conditions, an act of will comparable to the purposiveness of the quantum of action. I am afraid this will seem unscientific, but I hope to show the contrary: that the hypothesis I am setting forth requires a minimum of assumptions. And it does not hide the problem under the rug, as do current interpretation of the Darwinian theory.
Neither of the preceding ways of distinguishing the levels lends itself in any clear-cut fashion to the higher kingdoms, plants, animals (man). (I am putting man in parentheses to indicate that he is not to be thought of as the sole representative of the seventh kingdom. In fact, part of the job is to arrive at a definition of the seventh kingdom, or at least a description that will distinguish it categorically from the others. It is not enough to make man a "naked ape" or "an ape with a club" or even an animal that "communicates through language" or "is capable of abstract thought." We have in the theory a tool that provides for more basic distinctions, and we should use it. This is what the levels provide. And it is perhaps not too early to point out that what is emerging is a scheme of the cosmos in which life, far from being "a green scum on a minor planet," as one scientist put it, is inherent in several levels of organization that are intrinsic to cosmology. The seventh kingdom, which includes man, is one of these levels of organization.)
So how can we show that the higher kingdoms are categorically distinct and occur on separate levels?
Symmetry of Descent and Ascent
There are several possibilities, but the one that is clearest, because it is visual, draws on the well-known, though neglected, symmetries of minerals, plants, and animals. This was first brought to my attention by Fritz Kunz, who discussed the subject in his article "On the Symmetry Principle." 3
While D'Arcy Thompson in Growth and Form4 devotes a large part of his thousand-page work to the subject of symmetry, he does not appear to notice the eloquently simple fact that the kingdoms may be distinguished by symmetry.
Molecules--level IV, stage four:
Crystals, in the molecular kingdom, have what is known as complete symmetry: they comprise molecules in rows, columns, and layers monotonously and indefinitely repeated; three axes of symmetry and no freedom. By the term "axis," I mean a direction of symmetry.
It seems beyond comprehension how a virus molecule, having a molecular weight in the millions, can be marshaled into the strict order of a crystal, yet this is true. All molecules can occur as crystals.
Plants--level III, stage five:
Plants exhibit their one degree of freedom by growing vertically. The top of the plant differs from the roots, but right and left are similar, front and back are similar. This is known as radial or cylindrical symmetry; two axes of symmetry.
Animals--level II, stage 6:
Animals differ front and rear, and also top and bottom, but are similar right and left. This is bilateral symmetry; one axis of symmetry.
Note that the greatest symmetry (three axes) occurs with molecules, the least with animals, suggesting a correlation of symmetry with constraint. We have here a simple way to make a quantitative distinction among these three kingdoms by counting the axes of symmetry, or conversely the degrees of freedom. We may say of crystals that they have no freedom, while plants have one degree of freedom (their ability to grow) and animals two degrees of freedom (their ability to move about two-dimensionally on the surface of the earth). The flight of birds is also two-dimensional in the present sense, since birds steer vertically or horizontally.
But there is a position open for a kingdom with three degrees of freedom and no symmetry. (Kunz indicates a tendency toward asymmetry in the human face. There is also left- and right-handedness and the recently discovered fact that the two sides of the human brain have different functions. As already mentioned, however, the seventh kingdom is not to be thought of as limited to humans.)
The question now arises: can a similar quantitative distinction be applied to the left-hand side of the arc--to atoms, to nuclear particles, and to light?
Atoms. level III, stage three
While the image of electrons traveling around a central nucleus like planets around a sun has been supplemented by more abstruse models, the radial symmetry of the atom still holds, as is brought out by its magnetic properties.
What gives the atom one degree of freedom (like the plant) is the fact that it can absorb or release energy without any prompting from outside. Its energy state is unpredictable (or free). The same can be said of plants, since growth correlates with energy storage by carbohydrates, etc.
Nuclear particles. level II, stage two
Let me first take up freedom. Recall Heisenberg's observation that we are uncertain of the position and momentum of the nuclear particle: hence it has two "degrees" of freedom. The product of the uncertainty of position and momentum is a unit of action and may not be less than the value h. The formula for this is L x ML/T = ML2/T = h. This situation is similar to that of an animal at large: we can know only an area (L2) in which the animal (M) would be after a given time (1/T). The product cannot be less than a given value, ML2/T = h.
As to the symmetry, this question cannot be answered with finality, but the experiments proposed by Lee and Yang, and completed by Mme. Wu, which discovered that chirality, or handedness, characterizes nuclear particle reactions, suggest this possibility, for only that which has bilateral symmetry can have handedness. (One could not have a right-handed circle or cone, but one can have a right-handed thread or spiral.)
Light: level I, stage one
To carry out the scheme, we should show that light has no symmetry and complete freedom. I can't see how to establish its asymmetry. 5 Light is certainly the most completely free form of existence there is: a photon released at a certain point could be anywhere within a radius of 186,000 miles a second later. In addition, we can again point out that since observation annihilates the photon, it cannot be predicted.
As for the seventh kingdom, we will make lack of symmetry and complete freedom a definition of the kingdom. Since this is the highest form of existence, we cannot expect to define it anyway, and this, while a negative definition, is as good as we can expect.
We may put this all together in a chart:
There are four possible bosonic string theories, depending on whether open strings are allowed and whether strings have a specified orientation. Recall that a theory of open strings also must include closed strings; open strings can be thought as having their endpoints fixed on a D25-brane that fills all of spacetime. A specific orientation of the string means that only interaction corresponding to an orientable worldsheet are allowed (e.g., two strings can only merge with equal orientation). A sketch of the spectra of the four possible theories is as follows:
OVIDS FOUR AGES OF MAN
Plato in his Cratylus referred to an age of golden men and also expounded at some length on Ages of Man from Hesiod's Works and Days. The Roman poet Ovid simplified the concept by reducing the number of Ages to four: Gold, Bronze, Silver, and Iron. Ovid's poetry, known to schoolboys from Antiquity through the Middle Ages and beyond, was likely a prime source for the transmission of the myth of the Golden Age during the period when Western Europe had lost direct contact with Greek literature.
There are analogous concepts in the religious and philosophical traditions of the South Asian subcontinent. For example, the Vedic or ancient Hindu culture saw history as cyclical, composed of yugas with alternating Dark and Golden Ages. The Kali yuga (Iron Age), Dwapara yuga (Bronze Age), Treta yuga (Silver Age) and Satya yuga (Golden Age) correspond to the four Greek ages. Similar beliefs occur in the ancient Middle East and throughout the ancient world, as well.
The Golden Age by Lucas Cranach the Elder.
The Golden Age by Lucas Cranach the Elder.
Lamborghini uses the bulls left horn and left rear leg to form a cross. The badge is encircled and uses a golden or sunlight color for the trim, lettering and bull.
Holden --The lion's right arm and body make the horizontal line. The head and left arm make the vertical line of the cross. The cross-shaped lion sits on the red sun.
Peugeot -- same concept as Holden (and the beer logos: Lowenbrau, Strohs, Modelo, Hamms)
Ferrari --same concept as Holden and Peugeot.
The Pontiac logo fits the sun/cross symbolism simply because of the cross in the middle. Plus it’s surrounded by red color.
BENTOV WAS A JEWISH MYSTIC WHO SAID THAT THE SWASTIKA WAS BOTH THE CREATOR AND THE CREATION
BUT what did Itzhak write in his book A Brief Tour of Higher Consciousness that he knew the mundane profane world was not ready to hear on TV?
And it reveals the work of Itzhak more profound because Itzhak was Jewish too.
He loved to meditate and this is what he ‘saw’ when meditating and it is central to his theory, his story recovered, part of the narrative recovered that effects you and me.
“This desire resulted in the process of creation, symbolized by the swastika within the creative center, representing a four-dimensional rotating universe.
It is interesting to note that if you merge your consciousness with that of the Creator, you discover within Him a rotating swastika.
In other words, swastika stands for both the Creator and the Creation – they are inseparable”
ACCORDING TO HINDUS THE NAME OF KRISHNA IS NARAYANA- THEY SAY THAT THE FOUR SYLLABLES OF THE NAME WERE DERIVED BY BRAHMA FROM THE FOUR VEDAS
THE FOUR SYLLABLE MANTRA
Gaura-gopala mantra-mantra composed of the four syllables ra-dha-krs-na.
Gaura Mantra the four syllable mantra is ”gau-ra-an-ga”
Srila Bhaktivinoda Thakura explains the Gaura-gopala mantra in his Amrta-pravaha-bhasya. Worshipers of Sri Gaurasundara accept the four syllables gau-ra-an-ga as the Gaura mantra, but pure worshipers of Radha and Krsna accept the four syllables ra-dha krs-na as the Gaura-gopala mantra. However, Vaisnavas consider Sri Caitanya Mahaprabhu nondifferent from Radha-Krsna (sri-krsna-caitanya radha-krsna nahe anya). Therefore one who chants the mantra “gauranga” and one who chants the names of Radha and Krsna are on the same level.
Ajamila chanted the four syllables of the hari-nama Narayana,and therefore the order carriers of Narayana, the Visnudutas, also immediately arrived there. By chanting the four syllables of the name Narayana, he was saved from the gravest danger of falling down.
The Visnudutas therefore instructed that because he had chanted the four syllables of the name Narayana at the time of his death, he was freed from all sinful reactions.
” Although calling the name of his son, he nevertheless uttered the four syllables na-ra-ya-na. Simply by chanting the name of Narayana in this way, he sufficiently atoned for the sinful reactions of millions of lives.
Extracting the four syllables that are the heart of the four Vedas, Lord Hari makes the word Narayana. Day and night chanting this name, we become purified. We do not know any other better way to please Lord Hari.
THE FOUR SYLLABLES OF NARAYANA FROM THE FOUR VEDAS
FOUR IS THE HIGHEST DEGREE
The proof that four is the highest degree of a general polynomial for which such solutions can be found was first given in the Abel–Ruffini theorem in 1824, proving that all attempts at solving the higher order polynomials would be futile. The notes left by Évariste Galois prior to dying in a duel in 1832 later led to an elegant complete theory of the roots of polynomials, of which this theorem was one result.
Edinger says that Ahab and his three officers represent the four functions of Jungian theory. “Ahab, as captain, stands for the superior function, which is thinking.” Thinking isn’t the superior function for everyone, only for “thinking types,” such as Melville.
These four officers tell us about Melville himself:
We might outline Melville’s personality through the officers he created for the Pequod: thinking, his superior function; intuition, its well-developed auxiliary; sensation, a rather poorly developed third; and feeling, his fourth function, undifferentiated and inferior. Moby Dick shows a striking lack of differentiated feeling. It is notable that the novel contains no significant female (anima) figure! And Melville’s personal relationships and feeling adaptations were correspondingly precarious. Likewise, his relatively inferior sensation function was evident in his life — in his shaky relation to reality, requiring support by relatives.
QUATERNITIES IN MOBY DICK
Six years ago, when I discussed Conrad’s Heart of Darkness, I pointed out that Conrad uses the very word “shadow” to refer to Kurtz. Likewise, Melville compares Fedallah to a shadow: “Ahab chanced so to stand, that the Parsee occupied his shadow; while, if the Parsee’s shadow was there at all it seemed only to blend with, and lengthen Ahab’s.”(Ch. 73). In Chapter 130, Melville says that Ahab and the Parsee often stared at each other, “as if in the Parsee Ahab saw his forethrown shadow, in Ahab the Parsee his abandoned substance.” Jung didn’t choose the word “shadow” at random; man seems naturally disposed to apply the word “shadow” to the unconscious, the dark side of human nature.
But while there are similarities between Fedallah and Queequeg, there are also differences. Queequeg is the noble savage, Fedallah the diabolical savage. Queequeg’s fortitude complements Ishmael’s weakness, while Fedallah’s “moral inferiority” complements Ahab’s “conscious sense of nobility.” So Moby Dick has two pairs — Ishmael-Queequeg and Ahab-Fedallah — and these two pairs add up to a quaternity. (Edinger mentions in passing that Pip also forms a “character pair” with Ahab; Pip’s weakness complements Ahab’s strength.)
THE FOURTH TRANSCENDENT PERSON IN JOB
In chapter 32 a change takes place. Job’s three companions
have finished and now we are introduced to a fourth man, pre-
viously unmentioned, named Elihu. He claims he had refrained
from entering the discussion previously because of his youth. This
brings up the theme of “3 and 4” to which Jung has drawn at-
tention. If Elihu can be considered as the previously missing
fourth function. Job’s totality has finally been constellated. This
interpretation also fits the nature of Elihu’s discourse which is
largely a prelude to Yahweh’s appearance and presents many of
the same ideas Yahweh is to express even more forcefully. Par-
ticularly noteworthy are Elihu’s remarks about dreams:
TRANSCENDENT FOURTH IN DANIEL
Intense moods and emotional states will also yield up their mean-
ing if the relevant symbolic image can be found. For example, a
man was in the grip of an angry mood. Things were not as he
wished but he could neither act out the affect nor repress it. Finally
he prayed for understanding of its meaning. Immediately the image
came to him of the three men in the fiery furnace as described in
the Book of Daniel. He read this passage in the Bible and as he re-
flected on it, his mood disappeared. The third chapter of Daniel
describes the decree of Nebuchadnezzar that all people on signal
shall fall down and worship his golden idol. Shadrach, Meshach
and Abednego refused and Nebuchadnezzar in a state of rage had
them thrown into the fiery furnace. But they remained unharmed
and a fourth figure was seen walking with them in the fire, “like a
son of God.”
This image resolved the angry mood because it expresses sym-
bolically the meaning of the mood. King Nebuchadnezzar represents
an arbitrary, tyrannical, power-driven figure who would usurp the
prerogatives of God and rages when he is not treated as deity. He
is the ego identified with the Self. His rage is synonymous with the
fiery furnace. Shadrach, Meshach and Abednego, by declining to
give transpersonal value to a personal motivation, expose themselves
willingly to the fire of Nebuchadnezzar’s frustration. This would
correspond to the patient’s ability to avoid identification with the
affect but instead endure it and finally seek its meaning in active
imagination. The fourth figure that appears in the furnace “like the
son of God” would represent the transpersonal, archetypal com-
ponent that was actualized in the experience. It brings meaning,
release and wholeness (as the fourth).
THE TRANSCENDENT FOURTH WISE MAN AND THE FOUR SIDED ZIGGURAT
Here is another dream which is a beautiful example of the ego-
Self axis and of the numinous impact it can have. The patient had
this dream about one year prior to beginning analysis, during a
time of considerable distress. Although his psychotherapy was
long and arduous, this dream portended eventual success: I am
on the roof of a room completely surrounded by water when
I hear wonderful music coming across the water. The music is
being brought by four “wise men’ standing in small boats and
each is coming from one of the four directions. They are mag-
nificently robed and as they proceed across the water through a
blue-gray dawn I realize that the music each one brings bears
the characteristics of the “ direction ” from which he comes. These
four musical qualities blend and merge into a sound which affects
me powerfully in writing about it three years later as it did when
it occurred in the dream. The four “wise men” ascend stairs at
each corner of the room. I am overcome with a feeling of great
reverence and excitement, and as they reach the roof it has grown
lighter. The nearness of them is overwhelming. I realize they have
come to prepare me for the doing of some work. I then must go
downstairs and complete some task which requires prolonged
diligence and concentration. When I come back I see the four
“wise men” going back across the waters in their small boats.
Though there is a sense of disappointment the music seemed more
glorious than before, even triumphant. There teas definitely a
sense of having succeeded or passed the test. Then l saw that in
the place where each “ wise man” had stood there was note a stone
idol which though abstract not only intrinsically represented the
“wise man” but indeed all that teas implied by the culture and
mores of the direction from which he had come. There was a sense
of being tlumkful that I would be able to prove that they had been
Then l turned my attention to the four “ wise men” each return-
ing to his own direction in the small boats, and the music became
even greater. Once more I heard with special clarity the special
personality of each of the four directions blending mysteriously
The Search for Meaning
Picture 32. THE GREAT
OF UR, Reconstruction.
into a “supermusical” sound and the day became brighter until
an electric blue surrounded me and a sense of the most intense
well-being I had ever known filled me as the dream ended.
I do not want to discuss this dream in its personal aspects but
only to the extent that it illustrates the function of the ego-Self
axis. The drama of the dream takes place on the roof of a room
which is a kind of platform raised above the water with steps
at each of its four comers. This reminds one of the early Egyptian
concept of the God Atum. He was represented as the world mound
rising out of the primeval ocean. According to Clark, this primordial
mound symbol “was soon formalized into an eminence with sloping
or battered sides or a platform surrounded by steps on each
side. . . It is probably what the step pyramids represent.” 8 Another
analogy is the Babylonian ziggurat, likewise a holy mound with
steps on four sides leading to a platform on top which housed the
shrine of Marduk. (Picture 32) The top of the holy mound was
thought of as the navel of the world, the point where divine
creative force is manifested, and the place of meeting between god
and man. The same ideas were associated with the pyramids of
the Mayas (Picture 33).
8 Clark, R. T. R., Myth and Symbol in Ancient Egypt, New York, Grove
Press, i960, p. 38.
The Search for Meaning
The image of wise men bringing gifts reminds us of the story
of Jesus’ nativity and the three wise men. This theme of bringing
gifts to the newborn child is part of the myth of the birth of the
hero which, we can add, is also the myth of the birth of the ego . 9
But what is the significance of four wise men instead of three?
There is a legend that when Jesus was bom, not three but four
wise men were supposed to have come to him from the four
corners of the world, but the fourth was delayed and did not
arrive in time. The fact that there are four wise men coming
from the four directions alludes to mandala symbolism and in-
dicates that the wise men are a function of the Self, or psychic
totality. The wise men thus represent a fourfold ego-Self axis.
They are messengers and gift-bringers from the land beyond the
sea come to establish communication with the ego. We are re-
minded of the previous priest-rabbi dream where likewise an old
wise man served to connect the dreamer with her suprapersonal
I would draw your attention to the light symbolism in this dream.
The dream begins at dawn. It grows lighter as the wise men reach
the roof and becomes still brighter at the climax of the dream.
Light represents consciousness. All peoples have myths of creation
which depict it as the creation of light. Such myths refer to the
creation of the ego which is the light pf consciousness bom out
of the darkness of the unconscious. Similarly, dawn is the daily
birth of the light of the sun and is an apt image to represent
emerging consciousness. Thus we can understand this dream as
referring to a growth or increase of consciousness on the part of
the dreamer. This interpretation would also correspond to the sig-
nificance of the wise men whose attribute is wisdom. Wisdom is
light in the psychological sense. The wise men are bringers of
the light of consciousness.
THE FOURTH WISE MAN
The Story of the Other Wise Man is a short novel or long short story by Henry van Dyke. It was initially published in 1895 and has been reprinted many times since then.
The story is an addition and expansion of the account of the Biblical Magi, recounted in the Gospel of Matthew in the New Testament. It tells about a "fourth" wise man (accepting the tradition that the Magi numbered three), a priest of the Magi named Artaban, one of the Medes from Persia. Like the other Magi, he sees signs in the heavens proclaiming that a King had been born among the Jews. Like them, he sets out to see the newborn ruler, carrying treasures to give as gifts to the child - a sapphire, a ruby, and a "pearl of great price". However, he stops along the way to help a dying man, which makes him late to meet with the caravan of the other three wise men. Because he missed the caravan, and he can't cross the desert with only a horse, he is forced to sell one of his treasures in order to buy the camels and supplies necessary for the trip. He then commences his journey but arrives in Bethlehem too late to see the child, whose parents have fled to Egypt. He saves the life of a child at the price of another of his treasures.
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In literature, 40 is the number of thieves Ali Baba clashes with in Arabian Nights.
10. In religion, 40 seems to be shorthand for “a long time.” Jesus spent 40 days fasting in the wilderness being tempted by the devil; the great flood lasted 40 days and 40 nights; the Jewish people wandered the desert for 40 years.
11. And if you need more evidence that 40 sounds like a lot, please see the standard American workweek: 40 hours.
7. It took chemists 40 attempts to develop the magical spray we know as … wait for it… WD-40 (full name: Water Displacement, 40th formula).
The Number 40
In my Torah studies I keep running across the number 40 - for example, Moses on Mount Sinai for 40 days. Is there an underlying message of the number 40?
The Aish Rabbi Replies:
The number 40 has great significance throughout the Torah and the Talmud. The number 40 represents transition or change; the concept of renewal; a new beginning. The number 40 has the power to lift a spiritual state. Consider:
When a person becomes ritually impure, he must immerse in a ritual bath, a mikveh. The Talmud tells us that a mikveh must be filled with 40 se'ahs (a measure of water). Immersion in a mikveh is the consummate Jewish symbol of spiritual renewal.
It is no accident that in the story of Noah, the rain poured for 40 days, and submerged the world in water. Just as a person leaves a mikveh pure, so too when the waters of the flood subsided, the world was purified from the licentiousness which had corrupted it in the days of Noah.
Moses was on Mt. Sinai for 40 days and came down with the stone tablets. The Jews arrived at Mt. Sinai as a nation of Egyptian slaves, but after 40 days they were transformed into God's nation.
According to the Talmud, it takes 40 days for an embryo to be formed in its mother's womb.
In Kabbalah, 40 represents the four sides of the world, each side containing the ten Sefirot (esoteric powers).
When a rabbinical court finds someone guilty of a crime, the punishment is sometimes lashes, prescribed in the Torah as "forty less one." The purpose is to bring the offender to a point of change, transition and atonement.
There are 40 days between the first day of Elul, when we begin to blow the Shofar to prepare for Rosh Hashana, until Yom Kippur, the end of the annual teshuva (repentance) period. These 40 days are the most auspicious time for personal growth and renewal.
According to the Talmud (Avot 5:26), at age 40 a person transitions from one level of wisdom to the next. After Moses led the Jewish people for 40 years in the wilderness, he told them: "God has not given you a heart to know, and eyes to see, and ears to hear, until this day" (Deut. 29:3-4). From here we see that it took the Jewish people 40 years before reaching a full level of understanding.
FORTY, THE NUMBER:
By: Morris Jastrow, Jr., I. M. Casanowicz
Table of Contents
Forty in Counts and Measures.
Forty in the Talmud.
Forty in Temple History.
In the Bible, next to the number seven, the number forty occurs most frequently. In Talmudical literature it is often met with, in many instances having been apparently used as a round number or as a concrete and definite expression in place of the abstract and indefinite "many" or "some," and hence becoming a symbolical number. As regards the period of forty years, the Jews seem to have shared with other peoples, especially the Greeks, the notion that the fortieth year was the height or acme of man's life; and from this fact forty years came to represent a generation (compare Nöldeke, "Untersuchungen zur Kritik des Alten Testaments," p. 188).
The rain which brought about the Deluge lasted forty days (Gen. vii. 4, 12, 17); the same period passed between the appearance of the mountain-tops and the opening of the windows in the ark (Gen. viii. 6). For the embalming of Jacob forty days were required (Gen. 1. 3). Moses was without food on Mount Horeb for forty days (Ex. xxiv. 18). Elijah wandered without food for the same period (I Kings xix. 8; compare also the fasting of Jesus previous to his temptation, Matt. iv. 2). Ezekiel was ordered to lie on his right side forty days, to represent the forty years of the sin of Judah (Ezek. iv. 6). Forty days were spent by the spies in Canaan (Num. xiii. 25); Goliath challenged the army of Israel for forty days (I Sam. xvii. 16; compare Soṭah 41b). The same number of days was granted Nineveh for repentance (Jonah iii. 4). They also form the period required for purification after thebirth of a male (Lev. xii. 2, 4), while after that of a female it is twice that number of days (ib. 5).
Isaac married when forty years old (Gen. xxv. 20); so also Esau (Gen. xxvi. 34). Caleb was of the same age when sent as a spy (Josh. xiv. 7); and so was Ish-bosheth when commencing his short reign (II Sam. ii. 10; compare Acts vii. 23, where the age of Moses, when he was called to become the deliverer of his people, is given at forty years). Israel sojourned forty years in the desert (Ex. xvi. 35, and frequently elsewhere). The same period is given for the rule of each of several of the judges (Judges iii. 11), and for that of Deborah (v. 31, viii. 28; I Sam. iv. 18), as also for the reigns of David, Solomon, and Joash (II Sam. v. 4; I Kings ii. 11, xi. 42; I Chron. xxvi. 31, xxix. 27; II Chron. ix. 30, xxiv. 1). So also Israel was oppressed by the Philistines forty years (Judges xiii. 1). In Ezek. xxix. 11-13 a desolation of forty years is predicted for Egypt. A multiplication of 40 by 3, or three generations, is seen in the 120 years of the life of Moses (Deut. xxxiv. 7; compare Gen. vi. 6). Some (compare Wellhausen, "Prolegomena zur Geschichte Israels", 2d ed., 1883, i. 285) are inclined to see in the 480 years which are stated (I Kings vi. 1) to have passed between the Exodus and the building of the Temple of Solomon a multiplication of forty by twelve, or the round number of twelve generations.
Forty in Counts and Measures.
Among the presents sent by Jacob to Esau were forty cows (Gen. xxxii. 16). Ben-hadad sends "forty camels' burden" as a gift for Elisha (II Kings viii. 9). The governors before Nehemiah extorted from the people forty shekels of silver (Neh. v. 15). Abdon had forty sons (Judges xii. 14); Solomon, forty stalls of horses (I Kings v. 6). Barak's army consisted of forty thousand men (Judges v. 8); as many Syrian footmen were killed by David in battle (I Chron. xix. 18); and forty stripes were inflicted on certain evil-doers (Deut. xxv. 5). In the Tabernacle forty sockets of silver supported the twenty boards (Ex. xxvi. 19 et seq.; xxxvi. 24, 26); in the Temple of Solomon each of the ten lavers of brass contained forty baths; and in the Temple described by Ezekiel the "hekal" and the side-courts measured forty cubits in length (Ezek. xli. 2, xlvi. 22).
Forty in the Talmud.
The fortieth year is the age of reason ("ben arba'im la-binah," Ab. v. 26). Hillel (Sifre, Deut. xxxiv. 7; ed. Friedmann, 150a), Johanan ben Zakkai (R. H. 31b), and Akiba (Ab. R. N. vi.) set out upon their rabbinical careers when they were forty years old. To them, as also to Moses, is ascribed a life of 120 years, being divided in each case into three divisions of forty years each (Sifre, l.c.). Hillel's disciples were eighty in number (Suk. 28a). A woman marrying after forty can not bear children (B. B. 119b). Marriages are made in heaven by the announcement of the Bat ḳol forty days before birth (Sanh. 22a; compare Soṭah 2b). Forty times' repetition renders a thing unforgettable (Pes. 72a; compare Yer. Giṭ. vi. 47d). The extravagance of Pekah is characterized by his consuming forty measures of pigeons for dessert (; Sanh. 94b; Pes. 57a). Forty measures was the weight of each stone carried into the Jordan (Josh. vi.; Soṭah 34a). In connection with Ps. xcv. 10 it is said that the Messianic age would last forty years (Sanh. 99a).
Forty in Temple History.
The number forty had a fatal significance in connection with the destruction of the Second Temple. Forty years before this catastrophe the Sanhedrin "went into exile," that is, left the premises of the Temple (Shab. 15a; 'Ab. Zarah 8b). Rabbi Zadok spent forty years in fasting to avert the calamity (Giṭ. 56a). In the war of Bar Kokba forty measures of phylactery-blocks () were found on the heads of the slain at Bethar (Giṭ. 58a).
The ritual purification-tank ("miḳweh") must hold forty measures of water (Miḳ. ii. 1 et seq.; compare 'Er. 14a). The measure of the heave-offering ("terumah") for a generous person () is a fortieth part of the produce (Ter. iv. 3). A dry season of forty days is the condition for ordering a public fast (Ta'an. 19a). On the other hand, the forty stripes of Deut. xxv. 5 are reduced to thirty-nine (Mak. 22a; compare II Cor. xi. 24). Forty is also given as the number is of the "principal labors" () which are forbidden on the Sabbath (Shab. 69a, 73a).
QUARANTINE FORTY DAYS
Because the number 40 appears so many times in both the Old Testament and the New Testament, we would expect to see the number in many Christian Traditions. For example, the observance of Lent mimics the fasting of Jesus in the wilderness. The number 40 also appears in a few superstitions. According to some versions of Physiologus the serpent does the following:” when he grows old, his eyes become dim and, if he wants to become new again, he abstains and fasts for forty days until his skin becomes loosened from his flesh. And if it does become loosened with fasting, he goes and finds a narrow crack in the rock, and entering it he bruises himself and contracts and throws off his old skin and becomes new again”. According to the Etymologies of Isidore of Seville , the sarcophagus stone consumes the body of the deceased person in 40 days. Also, there was the tradition to keep a ship in a quarantine for 40 days.
The number 40 also appears as the number of various groups of martyrs. The 40 martyrs of Sebaste or the Holy Forty, were 40 Roman soldiers that were killed because of their Christian faith.
J.K. Rowling published a new short story today about the North American equivalent to Hogwarts, called Ilvermorny, and along with a new hero, classes of creatures and magical history, also introduced four new houses for people to be sorted into.
Here’s the thing: The comparisons between houses in Hogwarts and houses in Ilvermorny are going to come up for multiple reasons, but they’re designed to. According to Rowling’s short story, the founders were obsessed with creating a school that would give students a similar experience to Hogwarts, so the four houses at Ilvermorny are going to match Hogwarts’ originals pretty closely.
Four Temperament Ensemble / Western Animation
The Fashion Club: Quinn (melancholic), Sandi (choleric), Stacy (sanguine), and Tiffany (phlegmatic).
Daria's family: Quinn (sanguine), Helen (choleric), Daria (melancholic), and Jake (phlegmatic).
As far as Lawndale High School: Mr. DeMartino (choleric), Mr. O'Neill (phlegmatic), Kevin and Brittany (sanguine), and Mack and Jodie (melancholic).
Finally, there's Mystik Spiral: Trent Lane (phlegmatic), Jesse Moreno (melancholic), Max Tyler (choleric), and Nicholas Campbell (sanguine).
The four main kids in Doug: Doug (melancholic), Skeeter (sanguine), Patti (phlegmatic), and Beebe (choleric).
Neighbors: Peter (sanguine), Joe (melancholic), Cleveland (phlegmatic), and Quagmire (choleric).
The Flintstones: Fred (choleric), Betty (melancholic), Wilma (phlegmatic), and Barney (sanguine).
Futurama: Fry (melancholic), Leela (phlegmatic), Bender (choleric), and Farnsworth (sanguine).
Star Wars: Republic Commando: The four Clone Commandos of Delta Squad are this. Delta-38, "Boss", is choleric, showing good leadership instincts. Delta-07, "Sev", is melancholic, being the Cold Sniper of the group and showing great care to place each round for maximum effenciency. Delta-40, "Fixer", is phlegmatic, being, as Taun We put it, "A pure and uncomplicated soldier." Delta-62, "Scorch", is sanguine, showing much enjoyment in blowing the CIS forces apart.
In Street Fighter II, the four members of Shadaloo: Balrog (choleric), Sagat (phlegmatic), M. Bison (melancholic), and Vega (sanguine).
The Four Apprentices of Master Goutetsu: Gouken (melancholic), Akuma (very choleric), Ryu (phlegmatic), Ken (sanguine).
THE QUARTET OF MEN ON FAMILY GUY - JOE IS THE TRANSCENDENT FOURTH WHO WAS ADDED LATER
THE QUATERNITY THREE PLUS ONE IN DIGIMON
Most continuities of Digimon utilize a simple triangle—Vaccine beats Virus, Virus beats Data, and Data has higher average stats than the other two (effectively beating Vaccine by default.) However, Digimon Tamers introduces as its final villain a being that doesn't fit any of the three types because it's not a Digimon at all, and is strong against them all. The protagonists wind up having to change the type designation of their own Digimon in order to fight it properly.
CRUCIATUS CURSE AND THE CRUCIFIXION- HARRY POTTER
The Cruciatus Curse, which inflicts excruciating pain upon the victim, requires the verbal incantation and the use of a wand. The effects of the curse depend upon the desires and emotions of the character — to produce the excruciating pain implied by the name, the caster must, according to accomplished caster Bellatrix Lestrange, truly despise the victim. The extreme pain inflicted by the curse makes it uniquely suited as a form of torture, and was used regularly by the Death Eaters.
When Harry Potter was made the victim of the curse in June 1995, he described it as feeling like his head was being split open while having his bones set on fire. However, since this is the only time Harry is known to have been inflicted with the Curse, and as no one else has ever given a description of its effects, it is unknown if this is how the Curse always feels.
The Cruciatus is the curse which caused Alice and Frank Longbottom such suffering that they were admitted to the permanent ward at St Mungo's Hospital for Magical Maladies and Injuries as cases of insanity. This was carried out by: Barty Crouch Jr, Bellatrix Lestrange, Rodolphus Lestrange, and Rabastan Lestrange.
Lord Voldemort torturing Harry Potter with the curse, causing Harry excruciating pain