Arthur M. Young

The theory as it applies to nuclear particles

Having sufficiently prepared our tool kit, we are ready for further exploration. We have just described the priority of the experiential (threefold) world to the conceptual (fourfold) world, and the priority of both to the outer physical world of events, that unique "object" which we refer to as plainly and unquestionably out there in front of us, even though we often project upon it the substance of the threefold and the concepts of the fourfold.

Ordinarily, the fact that we project properties on objects needs only to be recognized when we make a mistake, as in a case of mistaken identity. The projection of substance, however, is an inevitable accompaniment to all perceptions, and the question of correctness does not properly apply. The quality of hardness, wetness, or solidity, even of goodness, beauty, or desirability, is supplied by an inner pressure that needs but the slightest excuse to throw itself upon the perceived object. Observe the projections of youthful love, which finds such desirable qualities in the object which it has singled out, as though it were only awaiting a container into which to pour what it itself has created. Or the play of children, where the crudest improvisations suffice to carry out the drama - a stick for a gun, a chair for a horse.

So the position we are taking, and calling upon the threefold operator to establish in formal fashion, is that this "substance" is a prior condition, supplied (perhaps by dreams or by imagination) before the lessons of life have trimmed and shaped it to conformity with actual circumstances. The latter operation is an enforced learning which, through the teaching of distinction and judgment, prunes the rank profligacy of projection and makes it possible for us to judge a situation objectively. Only in this way do we learn to distinguish, say, a bona fide antique from an imitation, or to make any wise purchase. We learn by mistakes and by careful application, even though the appetite for aesthetic experience is ready to leap at whatever moves.


Form versus substance in science

We are drawing up a scheme not just of psychology, but of the order of generation itself. So, to add greater scope to our inquiry, we should cast our nets in deeper waters.

In the physical sciences, we can find the same distinction between entities to which formulae apply (forms) and entities to which they do not (substance). But this distinction is not immediately apparent, for science is committed to the doctrine that substance is unnecessary. Locke first attacked the concept of substance by insisting that the real validity of knowledge is overthrown by the assumption of substance. Berkeley showed that the supposed material substance of things is not utilized either in science or in common life. Hocking, in paraphrasing Berkeley, states, "The chemist can always determine whether an object before him is gold, but he never does so by inspecting its 'substance.' He reaches his conclusion solely on the basis of its properties - its solubility in different acids, its combining proportions and weights. These are all he needs to work with. For is not the 'substance' of gold a mere name for the fact of experience that these properties belong together?"*

This is an excellent statement of the position of scientific objectivity, a position that has seen its most forceful exposition in logical positivism (only that which can be operationally tested is valid).**

*Hocking, William E., and Hocking, Richard B., eds. Types of Philosophy (p. 162). New York: Scribners, 1959.

**As another milepost in the history of this elevation of form as the objective and valid reality, we have relativity. Eddington says (in Mathematical Theory of Relativity, p. 9, Cambridge University Press, 1923), "If we describe the points of a plane figure by their rectangular coordinates, xy, the description of the figure is complete, but it is also more than complete because it specifies an arbitrary element, the orientation, which is irrelevant to the intrinsic properties of the figure and ought to be cast aside from a description of these properties . . ." Here, Eddington wants to toss out the orientation rather than the substance, but the statement illustrates well the vogue for form that relativity implemented.

But today, this reliance on relationship structure as the only truth with which science can deal is producing a rude shock in nuclear physics. As Gamow says:

"Although experimental studies of these new particles reveal new and exciting facts about them almost every month, theoretical progress in understanding their properties is almost at a standstill. We do not know why they have the masses they do. We do not know why they transform into another the way they do. We do not know anything."***

This was written in 1959, but the situation has, if anything, become more confused. A number of new particles have been discovered, and there is talk that the true elementary particles may be much smaller.

***Gamow, G. Scientific American, vol. 201, no. I, 1959. Compare Gamow's statement with Robert M. Eisberg's (in his Fundamentals of Modern Physics. New York: Wiley, 1961): "It is fair to say that the properties of the atom are completely understood . . . for the nucleus this is not the case."


The threefold operator and the nuclear realm

To me it is deeply significant that the nuclear particles have remained inexplicable, whereas atoms, once the key was found, have been completely explained. Atomic structure, mass, chemical properties, radiation spectra, etc., have all been accounted for and even predicted with great accuracy, but nuclear particles defy explanation by rational theory.

The reason, I believe, is that the realm of nuclear particles precedes form. It is the realm of raw substance: the possibility of form has not emerged, and will not emerge, until the atom exists. Form, which involves two dimensions of constraint, is conceptual and can be formulated, but that which precedes form, namely, substance, cannot be formulated.

However, it is appropriate to apply the threefold operation to nuclear particles. The nuclear realm introduces mass (rest mass) and motion (measurable and extrinsic motion, as distinct from the intrinsic and constant velocity of light). Both of these characteristics reflect the threefold. It also exhibits irreversibility (one-wayness) and other forms of asymmetry, such as parity (right- or left-handedness) and the fact that the proton has a much greater mass than the electron.

Further, and more significantly, the permanent nuclear particles, the proton and electron, do not possess identifiable structure as do atoms. This is because the principle of form does not exist prior to the atomic realm. Nuclear particles do not have form as do atoms, whose structure and behavior are so completely in accord with rational theory. Since the nuclear realm is prior to form, it cannot be accounted for in terms of form, and requires a different kind of description.

The threefold realm has two degrees of freedom, and since, as we said, forms or shapes require two degrees of constraint, they cannot exist at this level. In other words, a law here can deal only with linear measure; it cannot supply or impose a shape.

Like the bank, whose only requirement is that you may not overdraw your account, this "law" puts no stricture on how you "spend your money." Hence, we find with nuclear particles conservation laws of several sorts: conservation of mass, of energy, of momentum, etc. But we do not find laws like the Pauli exclusion principle, which dictates the configuration of electron shells in the atom.

This correlation with the threefold reveals a wider significance in the realm of nuclear particles. I believe that it may shed light upon cosmological and even metaphysical questions which science has heretofore felt outside its province, questions of ontogeny, or the order of generation from first cause.

This vague hunch on my part has prompted me to try to grasp something of the strange new world that now is being uncovered: the physics of nuclear and subnuclear particles. What could be the laws of this world?

I had a few additional hints from the threefold operation:

1. Asymmetry. According to our theory, we would expect nuclear particles to have one degree less symmetry than atoms. Since atoms have radial symmetry - a central axis with symmetrically disposed electron orbitals - nuclear particles would have the bilateral symmetry of a helix or screw. This has at least been indicated by the parity experiments of Lee and Yang. This discovery of asymmetry, disconcerting to physics, is a confirmation of the threefold operator, whose one-wayness is similar to that of a screw (right- or left-handed).

2. Behavior. Since nuclear particles have two degrees of freedom as against one for atoms, they should exhibit this difference in their behavior. (Behavior is a manifestation of freedom.) When nuclear particles radiate, or rather, dissipate into radiation (for they do not remain particles), the disintegration products are other particles as well as radiation, adding thus an extra "dimension" to the product. Extremely interesting to me is that the difference in degrees of freedom manifests in a literal fashion, in that the radiation spectrum of atoms, displayed on a photography plate, is a one-dimensional array of frequencies:

whereas the radiation of nuclear particles displayed on a photographic plate is two-dimensional:

3. An additional consideration that brings out the difference between the nuclear and atomic realms is of a rather abstract nature. It is so novel to our accepted notions that I'm happy to have found a statement Eddington made some forty years ago that can now be interpreted as anticipating this subject, the generation of nuclear particles. He says:

"The fundamental basis of all things must presumably have structure and substance. We cannot describe substance, we can only give a name to it. Any attempt to do more than give it a name leads at once to an attribution of structure . . ."*

*Eddington, Arthur S. The Mathematical Theory of Relativity. London: Cambridge University Press, 1923 (p. 221 ff., in Section 98, "General Relation Structure").

He goes on to describe structure, and then continues:

"There is a certain hiatus in the arguments of the relativity theory which has never been thoroughly explored. We refer all phenomena to a system of coordinates, but do not explain how a system of coordinates (a method of numbering events for identification) is to be found in the first instance. It may be asked, What does it matter how it is found, since the coordinate system is entirely arbitrary in the relativity theory? But the arbitrariness of the coordinate system is limited. We may apply any continuous transformation; but our theory does not contemplate a discontinuous transformation of coordinates such as would correspond to a reshuffling of points of the continuum.* There is something corresponding to an order of enumeration of the points which we desire to preserve, when we limit the changes of coordinates to continuous transformations."

*My italics.

Now it has recently been discovered that nuclear particles are permutations, reshufflings, of several quite esoteric factors or parameters. Some of the parameters are little more than symbolic: spin, strangeness, charge, atomic mass. But these permutations produce a number of distinct entities: pi and kappa mesons, lambda, sigma, and xi hyperons, etc., all of which are transitory; i.e., they disintegrate almost immediately. Only two permutations are permanent: the proton and the electron.

Another recent development has been the notion of "quarks," elemental carriers of spin, isospin, and strangeness, whose combinations in groups of three account for the recognized particles with mass equal to or greater than that of the proton.

The fact that three quarks are necessary echos the threefold theme again. And recall our discussion at the end of Chapter IV, in which we recognized that mass was a threefold entity; and our discussion of cube roots, in which we saw that the threefold can be expressed in unitary fashion only by using the three dimensions of space.

Eddington's first statement, that we cannot describe substance because "any attempt to do more than give it a name leads at once to attribution of structure," is essentially negative in that it says we cannot describe substance, but by this very acknowledgment it sets us on the right track and leads to the second statement, about a "reshuffling" of the continuum. Did Eddington connect the two thoughts? Whether he did or not, I would like to make the connection, and assert that substance correlates with the ordering of the points of continuum.*

*Manifest, perhaps, as the inversion of time in the world of antimatter.

I would further claim that recent developments in nuclear physics, in which the several kinds of particle are accounted for as permutations of some more basic entities, are a confirmation of this insight of Eddington's some twenty-five years before the complexity of the subnuclear world was known.

The fact that Eddington is talking about points in a continuum, while the entities of nuclear physics are not points but quarks or the like, does not affect the validity of the correlation. We must realize that "points" are undefined entities. And so are quarks. We cannot endow these elements themselves with spatial or even substantial nature, because they are only carriers of abstract properties. It is the ordering of quarks that produces what we recognize as mass or charge.

So much, then, for substance. We can well realize why the subject has not been pursued by science until recently, and why the present research of nuclear particles is encountering such difficulty. But while we do not have the gadgets of science, its synchrotrons, cyclotrons, etc., we are engaged simply as living creatures in a continuing interaction with our environment, and thus have direct access to the substance of the universe. For what occurs in the cosmos at the nuclear level, the realm of substance (mass), the realm of asymmetry manifesting the threefold operator, corresponds to nothing other than experience itself. We feel, we fear, we hunger, we value. Even that universal conveyor of information, light, is taken into us, into our consciousness, consumed and converted, much as it is by plants through their photosynthesis. It becomes our understanding, coloring our imagination and lighting our dreams.

At the risk of seeming to wander far afield, I would like to end this chapter with a distinction between threefold and fourfold drawn from another area - human experience. This is the distinction between the emotional and the intellectual. A very good example of the former is the experience described by Carlos Castaneda in The Teachings of Don Juan and A Separate Reality.

By way of resume, we may now say the encounter with reality consists of steps that follow and build on one another:

The first step is awareness itself.

The second is experience in time, a sequence of events accompanied by feelings. The second level - threefold: past, present, future - presents memory of past feelings and their relation in time.

The third step occurs when a present and a past experience are compared and a concept is found which measures or identifies an experience or what is common to experience. These concepts permit laws or generalizations to be formed about events, and the distinction between internal and external (objective) becomes possible.

The knower can now test these generalizations or laws.


The Geometry of Meaning