by Arthur M. Young
I would like to make a brief description of one of the basic ideas on which the theory of process is based. While I don’t see why the idea is difficult, and believe it to be essential to any understanding either of the nature of the universe or of the nature of the self, it is something not recognized by scientists and missing in the literature. Therefore it is urgent to make it known.
What I refer to first came to my attention back in college days when I read Bertrand Russell and encountered his logical types. As Russell, who had the knack of vivid expression, said, “The class of elephants is not an elephant.” Others have said, “The map is not the territory.”
When I met Gregory Bateson at a conference at Lindesfarne, he applied the notion of logical types to distinguish ratios (relationships) from objects. “The price of eggs is not an egg,” he said. But when I expressed the possibility of more logical types, Bateson said I was wrong — “violating the rule of logical types.” I know of no such rule. In fact, since Bateson had likened logical types to the derivatives (which also deal with ratios) and there is a rule for derivatives (successive divisions by time, i.e., ds, ds/dt, ds/dt², etc.), he had in effect provided just the rule needed to support more logical types.
Another giant of science, Eddington, placed great stress on the fact that science deals with the relationship structure of the universe, and distinguished between things and relationships between them. Thus a map might show the geographic position of towns and cities, and this would display one kind of relationship. A list of the populations of cities would also show relationship.
So far so good. But do these two logical types — elephants, and the class of elephants — have anything in common? Why should I ask this question? Because I need to show that since they do share one property there must be other types which do not have the property shared by a class and its members.
What then is this property? Both are objective. The animals that roam the jungle or inhabit the zoo are physical objects. The class of elephants, or the concept elephant, is a mental object in the sense that it can be communicated. This suggests that since there might be some aspect of an elephant that was not objective — in fact since we have both a physical and a non-physical aspect of the elephant — there might be a non-objective, physical and non-physical aspect.
Such would be the need for the elephant, which would be physical and something else that is non-physical and not objective. This I will venture to say (without proof) is the purpose of the elephant. It might be thought that this is physical, but I have to begin somewhere on what I propose to show, namely, that there are four and only four major aspects to the elephant (or to any object) and we can define the two that remain as opposites to the two we have already mentioned, the physical object and the mental object. While physical describes the animal itself, there is another term that is more appropriate to the description of logical types. This is the term particular, which stands as distinct from the class of elephants, which is general. I can now define four logical types:
- Particular objects correlate to physical things.
- Classes are general, correlating to concepts.
- Value is general, based on need.
- Purpose is particular.
The last two I will call projective, as distinct from objective. Here we must be careful because the mind would have no difficulty describing the value of an elephant, but this is not what I mean by value. Perhaps we could shift to eggs. The price of eggs is objective; it can be communicated. The value is something that will vary with persons; if you were dying of starvation an egg would have great value.
And purpose is different again. Your purpose might be to eat the egg, to raise chickens, to make Easter eggs.
|1. Particular objective||Solid||Object|
|2. General objective||Plane||Form|
|3. General projective||Line||Value, scale|
|4. Particular projective||Point||Purpose, direction|
But permit me to reverse the order and begin with purpose:
|Point||Purpose, direction||Particular projective||Origin, first cause|
|Line||Scale, time, value||General projective||Motivation|
|Plane||Form, concept||General objective||Identity|
|Solid||Physical object||Particular objective||Practice|
These four can also be correlated to other fours:
Having shown this with enough examples to indicate its wide application, we can add a description of their dimensionality.
Level I is zero dimension in the sense that it has no extension, yet it has all the angles. While in comparison to the other levels it can be thought of as a point, it is really a circle with a small radius. In the light of quantum physics, which teaches us that an infinitely short line would be associated with infinite energy, we cannot say the radius is zero; we say rather no extension. It is an origin, the origin of angle — it being understood that angle is a measure that does not require or is not concerned with the length of the lines which would describe an angle.
Level II is one dimension, a line, but it is not a finite line (a finite line is only possible in two dimensions which provide the cutoff points which define it; on one dimension these cutoff points are not available). As one line it measures absolute scale — temperature, time, far-awayness (which is also the radius in spherical coordinates).
Level III is two dimensions. It is important to realize the two dimensions are presented at once, in simultaneity; there is no time here. This is the space of comparison, measure. It is the blueprint, the form, the 3-view of a house or other shape to be made. It is outside of time or does not include time.
Level IV is best thought of as a combination of Levels II and III. It is the particular object, the result of “forming” (Level III) the “substance” of Level II. As Aristotle’s efficient cause it is the work of the carpenter forming the material of Level II (wood) into the form (Level III) of the table to make the object (Level IV).
This “dimensionality,” as I’ve described it, draws out the implications of dimension not usually expressed, and not possible to express in the most common application of dimension, that of Cartesian coordinates with x, y, and z axes. However, if we shift to spherical coordinates, we can see a use of dimension in the sense that I’m describing. Spherical coordinates include:
- An origin around which angle is measured.
- A radius which shows how far away.
- Longitude and latitude, which measures East-West as longitude, and North-South as latitude.
- Each of these dimensions is cumulative; it includes the one that precedes it.
Thus a distance near the north pole is expressed in angle modified by the cosine of the latitude, so gets shorter as we near the north pole. Likewise both the latitude and longitude measure greater distances as the radius increases. Thus scale is portrayed in spherical coordinates (which is not the case with Cartesian coordinates). The same is true for orientation, also not expressed in Cartesian coordinates. (See Constraint and Freedom: An Ontology Based on the Study of Dimension).
Thus we have a number of exemplifications of a fourfold division of things which is necessary for the complete analysis of any subject. The simplest of these fours is the metaphor of point, line, plane, and solid. When I first used this example I thought of it as a bare abstraction even though it was suggested in the Emerald Tablet, which described the descent of the spirit or monad into manifestation as the soul, as “like a point into a line.”
The Dogon myth of creation goes a step further when it describes the first word of God as like lines coming out of his mouth, the second word of God as lines crossing these lines as in weaving (making pattern or form possible).
Then I began to realize that the simplicity of point, line, plane, and solid contained a richness of meaning which could tell me much more about what is basic. What had first appeared to be an ultimate reduction at the same time opened the door to vistas of meaning that intellect had no access to.
Thus when we realize the point contains all the angles, that angles are directions and point to goals, we can then introduce purpose into a formulation that gives it the formal status it requires.
Similarly the line which is not a finite line between two points, but the line which begins at an origin and extends through another point to infinity, does not stop, because to do so there must be another dimension cutting across this line to terminate or define it.
If we let ourselves do so we can think of this cutoff function as what is referred to in the Cronos myth by Gaia having Cronos cut off the testicles of Uranus to put a stop to the endless birthing he was forcing upon her.
The extension introduced by this Level II line before it is terminated by Level III is thus not a length (a noun), it is longing (a verb). This makes it possible to see it as the origin of time, of force, of desire, of binding (as in force, but also as in spellbinding) as illusion (not delusion; by illusion I mean the feeling of reality, the investment of emotion we make when we see a good movie or play).
It is this powerful force that draws us into manifestation, into matter — it is what matters — and is the meaning of the very word matter, which comes from the Latin mater or mother, the Gaia of the Greek myth of creation. Even in the absence of pain or pleasure we feel it in the flow of time; we look forward to the future.
In contrast the third level forces us to stop and think. In fact the intercourse of time has to stop in order to think, to compare experience. This is reflected in myth where we have reference to the immobilized tree god, the castrated Uranus. Or if we return to the simple point-line-plane metaphor, we have three points, which determine a circle (as well as a plane). This circle makes a boundary between self and not-self; it gives identity. In physics this is the first entity to have an identity, the atom; in animals it is the stomach; in humans, the ego; in the spirit-soul-mind-body sequence it is mind as well as ego — not just awareness, but the con scio of consciousness, the knowing (scio) and con (together), knowing two things together, which ultimately makes possible inference, and from inference to the use of cause and effect, instead of being the victim of cause and effect, the beginning of the ascent.
But that is not my topic here. We must first lay the foundation for what we can build on later, and it is these same four levels that will become the steps to our higher evolution.
And there is still another description of the levels that can assist in comprehending their significance.
The first and fourth levels can be thought of as the world of Being and the world of Becoming respectively — Being because Level I just is: “I am that I am”; Becoming because it involves change: “I will be what I will be.” This change requires time to distinguish one state from another, and space to distinguish between what causes the change and what does not cause it. Thus, to refer once more to the learning cycle, at the second stage the child touches the hot stove and feels pain. Time is necessary to distinguish before and after. It is only after this experience, at Level III, that the pain is associated with the stove, an object having a location to be avoided. This is also the origin of consciousness, because it is more than awareness, it associates the pain with an object in space — con scio, knowing both together.
This reference to the learning cycle suggests that we here have the origin of time and space, which is much too drastic a view to accept. Nevertheless let us look at another venerable reference with this in mind. I refer here to the Timaeus of Plato. Timaeus says that the Creator God made two worlds, the world of Being and the world of Becoming. But it was necessary to have means connecting them. Then comes the remarkable part: “Because of the three dimensions of space there must be two means.” Here the reference shifts to mathematics, explaining that the “means” between the extremes of a³ and b³ are a²b and ab². No further explanation is given.
Since I had already described Level I, or a³, as three degrees of freedom, and Level IV, or b³, as three degrees of constraint (the time and place), it would follow that a²b represents one constraint (that of time), and ab² two constraints (that of space)! So time and space are the means connecting the world of Being and the world of Becoming. Both Being (“I am”) and Becoming (“I will be”) are particular, whereas means must be general. This is evident in Russell’s distinction between a class and its members which we started with. The elephant is a particular member of the class of elephants, so the class is general. So too value is general. “I like music” implies more than one musical composition.
This may not be what was meant by “means” in the Timaeus, but the description there is like a blank check; it allows one to fill in what conforms to the definition a²b and ab². Time with its one dimension and space with at least two dimensions conform to the requirements. If it be objected that space is three-dimensional, I can point out that in the more sophisticated treatment of dimensions involved in spherical coordinates, one of the three space dimensions is the radius, which always includes time, and/or scale. It is also the case that three dimensions can always be described by three of more “views” of a house — for example, plan view, front view, side view. These views are two-dimensional. The eye too sees two dimensions in the image on the retina. One doesn’t “see” depth, which requires two eyes and measurement of small differences of direction (parallax).
Another tradition views the world of Being as including thinking or concepts, which are referred to as Non-Being. This might strike the modern reader as too negative a description of consciousness, but let’s take this other view as a kind of medicine. Why do scientists insist that spirit and soul do not exist? The word exist must mean to be out of “isting” or being. Thus we speak of the ex-president as the person who was president and no longer is.
Or think of the present moment; does it exist? The very thought of the present is a verb in the present tense; we don’t know what it is until it’s over. So it is correct for the scientist to say the soul and spirit do not exist. Spirit is, soul is; it is concepts that exist, and science deals in concepts, maps, relationships which are derivatives of what is. A relationship between things can be established only after the “things” have been identified.
So we could say both the world of Being and the world of Becoming include aspects that don’t exist. Eddington asks if a bank overdraft exists. I would prefer to place the bank account, whether overdrawn or not, in the world of Becoming, and perhaps replace the word becoming by having. This makes it easy to see that not having has a positive aspect in that it creates need, and need is the human equivalent of a force. In science the photon’s creation of the first so-called particles, or protons (called pair creation) also creates an enormous force 1039 times gravity. This force is so great that nothing can exist until it neutralizes itself in the joining of positive and negative “particles” (proton and electron) in atoms that do exist.
Translated as having, we can define force or desire as “not having,” and just as important as having, because it and Being (both of which don’t exist) supply the dynamic that makes the universe evolve, not only making it go but creating it in the first place.
Perhaps you will say this is mere play on words. Yes, but it’s better to play on words than let them play on you — and this is just what makes the statement of the scientist that spirit does not exist mean the opposite of what he intends, since even the present doesn’t exist, which, in the present context, is a truism, but was not so intended.
But to take this out of mere play on words, I can refer to the greatest book on the truth behind manifestation, the truth of spirit, The Cloud of Unknowing, of unknown authorship. It recommends that we go about with a cloud of unknowing around our head. “In all other things,” it recommends, “use discretion, but in this none.”
Those who favor Eastern tradition will find the same testimony in Zen philosophy and the Tao.
Perhaps I’ve gone too far. Maybe, but my point is to show that what is not objective, what does not exist, is also important just because it has no outward and static permanence; it is dynamic and creative.
And we do not have to wait for science to discover this unpredictable unknowing. Science has already found it in the quantum of action, alias uncertainty, and I would be repeating myself to refer to what John Archibald Wheeler, perhaps the most eminent physicist now living, said of this quantum of action (1982): “For all we know it may someday turn out to be the fundamental building block of all that is, more basic even than the particles or fields of force or space and time themselves.”
And I must again point out Bacon’s remarkable prediction in his essay “Cupid or the Atom” (1609) of the quantum of action discovered by Planck almost 400 years later. This Cupid, said Bacon, father and most powerful of all the gods, was born of an egg of night. This Love, he says, is introduced without any parent at all (and was therefore first cause). The attributes which are assigned to him are in number four: he was always an infant; he is naked; he is depicted as blind; he is an archer.
Bacon goes on to interpret these attributes: an infant, because at the origin of things; naked because without properties; the blindness, he says, “makes the supreme divine providence all the more to be admired, as that which contrives out of subjects peculiarly empty and destitute of providence . . . to educe . . . all the order and beauty of the universe.”
His last attribute, says Bacon, is archery, “meaning that which acts at a distance, for all operation at a distance is like shooting an arrow . . . and without this no motion could be originated.”
As I said in Foundations of Science (1984), this is an exact description of the quantum of action. It is at the beginning of things (since it creates particles); it is without properties — no mass, no charge, outside of time and space; it is uncertainty (blind); and it is responsible for all action at a distance.
To conclude then, this first level or first cause, this quantum of action, this Cupid, is what can also be called purpose. It has been omitted from science because it is ineffable, uncertain, cannot be measured. It is also a whole. Only when it is divided into its components is there something to measure, space, time, and mass. Thus the quantum is not another measure; it is the whole whose parts can be measured.
The next step might be to assign the parts or components to the three remaining levels. But we need a rationale for so doing.
This rationale has the advantage that it uses division to supply the meaning of the levels — most easily seen in what we mentioned at the beginning of this essay, the derivatives. I said that Bateson’s reference to the derivatives as logical types gave me the right to correlate the second derivative to the value of eggs (Bateson had already correlated the eggs to position, and the price of eggs to its first derivative). This gave me permission to extend the correlation to make the second derivative correlate to the value of eggs, and the third derivative to their purpose.
Since the goal is a position, and position is what we started with, there can be no more than four — position and its three derivatives. We can confirm this in another way. Since derivatives are obtained by successive divisions by time, this limits them to four. Why? Because they are independent measures, and independence requires that they be at right angles. There can be only four right angles in a circle; therefore time has the ultimate dimension (in terms of angle) of 90 degrees. This then is the fourfold of Level III.
Level II can be recognized as threefold because it deals with time: past-present-future. This requires a measure that has the ultimate dimension of 120 degrees (because 3 x 120 degrees = 360 degrees). I have found mass can be given this measure, and so can L x T, which would be the “longing” (the extension that includes time but is not cut off by time). This is still not a proof, so I have to make it an hypothesis that Level II is division by three.
We can then see that Level IV, which was the combination of substance and form, or of time and space, correlates to the combination of these measures 1/3 and 1/4, whose product is 1/12, and assign this measure to the measure that remains, i.e., length.
Most easily understood is Level III. I had for some time before I met Bateson recognized that there are four derivatives. The third must be that which changes or controls acceleration, and the fourth that which controls or governs control It is through this third derivative that we control a car (by pressing the brake or pressing the accelerator). Our control in turn is governed by position of the car, and we stop the car when we get to our goal. The goal is a position, so we are back to the same category we started with, a position in space. This means that there are only four time derivatives.
Similarly Level II divides the whole into three — past, present, and future — or stimulus, act, and result. One of Newton’s first realizations after he devised the derivatives was that acceleration times mass equals force. In similar fashion we can say that velocity times mass equals momentum, and position (or length) times mass equals moment, and a fourth, recognized in aeronautics, control times mass equals mass control.
Since the derivatives are actions, and their multiplication by mass leads to states or conditions of matter, we can think of mass as a kind of embodiment, result, or manifestation of the four derivatives. Thus:
- Mass x acceleration = Force
- Mass x velocity = Momentum
- Mass x position = Moment (as in leverage)
- Mass x control = Mass control
But we are talking about Level II, so there must be a third term to stimulate the action.
©1996 Anodos Foundation