by Arthur M. Young (Journal Extract)
With the theory of process it is necessary to make what amounts to a complete inversion of the scientific approach — to look not at objects and particles, but at forces, at motion, at change; to look at history or evolution rather than at fixed relationship or formulations — whereas in both Newton and Einstein the main emphasis is an extended geometry of space-time, whether curved or not, and a structure fixed in space and time.
As Eddington said in Fundamental Theory, “Curvature is a dodge.” To put this simply, relativity accounts for force as curvature of space-time. There is no doubt that this is valid as a correlation, but to substitute the curvature of something not itself visible or tangible to explain something as basic as force, which we are aware of without benefit of conceptualization, is indeed a dodge.
But Eddington did not dismiss curvature; he said its application to force was a dodge. He said curvature is uncertainty, and that complete uncertainty is 2 pi. Thus while the measures we apply to space, mass and other quantities have a range between zero and infinity, complete uncertainty is a circle of 360 degrees. Put another way, the certainty of a lens is measured by the angle between two points that can just be distinguished. It is not the distance between two points, because if the points were far away a given distance between them would subtend a smaller angle. Complete uncertainty is the widest possible angle, 360 degrees!
Eddington then correlates the uncertainty of the photon with the uncertainty of the universe, both of which are 2 pi.
I interpret this equivalence that Eddington points out to be a valid unification of relativity and quantum theory. Note that this is not a unified field. A field implies space, or space-time, something which has extension; but quantum phenomena preexist fields, whether space or time, and do not have extension.
Note that this primacy of uncertainty applies not only at the quantum level, and again at the cosmic level; it occurs at every level in between. In what direction will an atom or a molecule radiate a photon? What direction will an animal move? When and to what end will a person make a decision?
Finally note that this unification is the exact opposite of that sought by the unified field theory, which has not been found. It is well known that Einstein was not able to find a unified field theory that would reconcile quantum theory and relativity theory — but since he was looking for a field and did not accept quantum uncertainty it’s almost self-evident he could not find what would reconcile the two, which was not a field and did involve uncertainty.
Another subject that has to do with the limitations of science is that science, because it is dedicated to measurement, is restricted to a rather limited field — one that does not include what could be called qualitative distinctions. Even though science as measurement turns a deaf ear to qualitative distinctions, and has succeeded without them, there are still important distinctions in the nature of what is measured. For example time, despite Einstein, is different from space. This would be admitted to some extent, since time is a different “dimension.” But even to call time a dimension implies a resemblance to space which should not go unchallenged.
Confining myself to science, mass is another parameter which is measured. Since it is not thought of as a dimension it is even better evidence that science deals with attributes whose difference is not quantitative and so require different units. Charge is yet another; and magnetism, while it is due to the notion of a charge, requires another kind of unit.
That there is some uneasiness about the assumption that space, time and mass are the only parameters needed by science is reflected in recent work on particles which has made it necessary to postulate distinctions referred to as color, flavor, and charm. But here we are in a wholly speculative area, and it would be too soon to give these differences, which have no relevance to the rest of science, the status of different parameters.
Perhaps this is sufficient to at least open the discussion to the point I want to deal with — that the mathematical basis of science needs to be reexamined for the possibility that it can contribute to the qualitative differences found in physics.
Such a proposal would immediately be met with objections: “Mathematics is a purely quantitative science — the science of quantity”; “There is nothing in mathematics to suggest any attribute other than quantity”; etc., etc. If I say that mathematics needs to be reexamined I will receive the immediate reply that mathematics is what mathematicians say it is; it is not to be interpreted, nor does it owe any obligations, as does physics, to empirical fact.
Despite these protests I would persist. In fact I have already shown in a paper, “What’s Wrong with Mathematics,” that mathematics already includes qualitative distinctions and does owe some obligation to physical and empirical fact.
One defense of my position stems from Bohr’s principle of complementarity, which says that a measurement or observation cannot be carried out without an exchange of energy, a condition which would not be present in the realm of pure thought. This has further support from the physical impossibility of a dimensionless point (in space or time). In physics it has been found that the approach to a dimensionless point, either in time or space, requires an amount of energy inversely proportional to the size of the point. To locate a dimensionless point would require infinite energy. As Heisenberg said, this places a limit on smallness.
It is also the case that mathematics deals with positive and negative numbers. These numbers are fabricated by mathematics to get around the difficulty of including addition and subtraction in mathematics proper. Thus a lost sheep implies an actual world in which sheep exist or do not exist, whereas mathematics is not supposed to recognize anything other than its ideal world from which sheep could not disappear. This point can be raised about imaginary numbers as well, and mathematics quite peevishly replies that imaginary numbers are merely one part of number pairs — a description which neglects the origin and utility of complex and imaginary numbers, as well as their important difference from real numbers.
Another area is the number of dimensions. To mathematics there can be any number of dimensions; but this, I hope to show, is not true — and even if I can’t prove it the question is important because dimensions are essential to a manifest world, and it may be possible to show that some small number of dimensions could not be exceeded if such a world is to manifest, much as an unlimited number of letters could not be effective in the creation of words.
The mathematical assumption that the world could have any number of dimensions, and that our world is but one of many other possible worlds, rests on the definition of “dimension.” Another consideration is that if the world is a construct for learning it must be possible to transcend it — or for God to transcend it. Then we could ask: Why is there a universe? Why is there something and not nothing? Why need a universe have dimensions?
The last question has an answer that may clarify our whole approach. Time is obviously necessary to a universe of becoming. Such a world involves the learning process because there would have to be time to distinguish cause and effect. Without this distinction there could be no learning. Here the observer is really necessary. If cause and effect could not be observed, the universe could not produce life, which “knows” how to reverse entropy. The dimensions of space are also necessary to separate the agent of cause and effect from what is not the agent. Something equivalent to mass, if not mass itself, is necessary to evaluate the scope or significance of an effect.
Why is there something and not nothing? In other words, why are there things? If we define things as objects, and say why are there objects, it must be because there is something that is not an object — a ject, which the object gets in the way of or the object interferest with.
Why? Because the -ject, which could also be called “play” or purpose, requires objects to manipulate. Another answer is that the universe of potential requires that it create objects or things to manifest, much as a play requires actors, or a musical composition requires instruments.
This raises the question of why there should be purpose. To this there is no answer because purpose is first cause — there is nothing to come before it and to cause it because it is first cause. So the answer to our question, “Why are there things?” is that there is purpose, which requires things to manifest and to actuate its potential.
How then can science or math make a forward step? One possibility is that the ability of UFOs to go faster than light will stimulate efforts to discover how this could happen. But this is unlikely, since we already have teleportation, apports, precognition, distant viewing, etc., which require a like drastic revision of scientific assumptions, and such revision has not occurred. The Philadelphia Experiment is a case in point.
Another possibility is that astrology might inspire a new view of science. Here I would depend most on arcs, both primary and secondary, because they provide evidence of other time rates. To call these time dimensions would be a mistake, since the time we do accept is not a dimension in the sense that space is a dimension.
This makes it evident that we do not understand time — even the ordinary time. How then could we understand the two extra times that are so important to astrology — especially as these extra time dimensions, to which we are alerted by astrology, can be discovered in areas other than astrology?
Since I’ve already dwelt on the importance of these other times as they contribute to our lives, I will not do so here. It is more important to ask: what is time for?
Time is that which makes possible the phenomenal, the world of becoming. It makes history, it makes evolution. Its neglect by science — by which I mean the neglect by science of its important contribution in its effort to formulate time by means of space-time fields, including the morphogenetic fields of Sheldrake — is a clue to the major defect in science, the postulate that the world is objective. For time is not objective, which implies that the conceptual mind cannot cope with it.
This in turn brings out that experience, which occurs in time and therefore depends on time, is a different way of knowing than intellect or conceptualization, which depends on space. There are thus two ways in which we know the actual world, through experience, and through intellect — the former phenomenal, the latter noumenal — a distinction which is clearly set forth in the Timaeus of Plato, between the world of Being and the world of Becoming. Note however that the Timaeus refers to four — the world of Being and the world of Becoming, plus two means which connect them. The Loeb edition likens the latter to the two means between the extremes of a³ and b³, which are a²b and ab². This too I’ve discussed elsewhere, and have shown that if we translatea as freedom and b as constraint, a³, a²b, ab² and b³ describe precisely the four levels of the theory of process. I might add that I did not know of the Timaeus until after I’d so described the four levels of process.
I have often wondered about the fact that the complete expression for the expansion of (a+b)³ is a³ + 3a²b + 3ab² + b³ rather than a³ + a²b + ab² + b³
Why the coefficients of 3 for the a²b and ab² terms? It now occurs to me that the 3 coefficient of a²b refers to three dimensions of time, and the 3 coefficient of ab² refers to the three dimensions of space.
This seems all very pat and algebraic and therefore like science, until we realize that the three time dimensions are utterly unlike the three space dimensions and therefore quite unlike science. How does this unlikeness show? How does it manifest in life?
It shows in that the time dimensions are not like space — not different directions, but are nested within one another. The dimensions of space display relations in simultaneity. The dimensions of time program one another. This radical difference would make little sense if we did not see the universe as a device for learning rather than a purposeless machine, as it is now considered to be by science. Incidentally, have you ever known of a machine that did not have a purpose?
Because the time dimension is essential to history and to evolution, it is also essential to life. Life is not something that can be expressly formulated as can the motion of inert particles, nor is it something that is implied by the laws that science has discovered. On the other hand it does not violate these laws. What then is it? Life is that which takes advantage of the laws of nature to create constructs that transcend these laws. These constructs gradually evolve through self-organization — depending on the hierarchy of cells, tissues, organs, organ systems created and controlled by the super molecule, DNA. Essential to this hierarchy is control, the third derivative implied by the Newtonian calculus and recognized by cybernetics but neglected by theoretical science.
Control is yet another function or aspect of the world that would not be possible without time. The world of becoming deals with change, and control is what causes intentional change. So here again we must acknowledge purpose. In fact it is an error in control (“sin”) that makes the world a school for learning. If this seems too anthropomorphic, we can say “that makes a world in which evolution is possible.”
But where are we to put purpose in the scheme of things? It is certainly not in the conceptual world of science, and it is not in the world of becoming, since purpose is more properly described as noumenal rather than phenomenal. (A purpose which varies is feeble indeed.) We must place purpose as noumenal, because as Aristotle said, it is the final cause (i.e., first cause).
The next stap is to ask: If science emphasizes the noumenal, and purpose is noumenal, why does science exclude purpose? I can only contribute that purpose, which is like curiosity, and science which gives answers and thus neutralizes curiosity, are the two poles of the noumenal, which could also be called the nonphysical. Because these poles, like plus and minus, necessarily neutralize one another.
To confirm this, consider the poles of the phenomenal (or physical) axis. One pole is the world of objects and of facts. Its opposite is the world of non-objects, or, more positively expressed, of the forces and desires for objects or between objects. These forces and desires bring the world of objects into existence, much as curiosity, the desire or appetite for information, brings the conceptual world into existence.
But this discussion is becoming too pat, too tied up in a bundle, to expand science. We should return to the different kinds of time. We know that the time of science, even if not appreciated for its contribution to becoming (and to evolution and life), does do its job in the derivatives with respect to time — velocity and acceleration, momentum and force, energy and power — all of which are time derivatives. Surely there is here no neglect of time. Right; but this is the recognized time dimension. What about the others?
I have said that these others are the dramatic time of plays, games, conversations and other human interactions, and the generic time of planned endeavors, learning courses, etc. But this does not give them other than anthropomorphic status.
Not quite so, because all vegetation operates to a great extent on about a two-month growing time, not only for annuals but also for the seasonal change in perennials. And all animals in their mobility have to move in the more rapid dramatic time, in their pursuit of food and evasion of enemies. So it would therefore appear that the extra times are essential to living creatures. The question then arises, are they significant cosmologically? Would they affect atoms and particles? I do not think so.
©1996 Anodos Foundation