by Arthur M. Young (1990)

One night I saw a TV program, Einstein’s Universe. I turned it on because it was narrated by Peter Ustinov, whom I admire, even though I’m tired of Einstein’s universe. The program was well done. A great effort was made to make a clear and convincing dramatization of the universe according to Einstein; just enough mystique to sugar the dull sterility of science.

What bothered me most was the subservient role of Peter Ustinov playing an average man who didn’t know science, feeling privileged to be let in on the secrets and instructed in the Sacred Doctrine.

Now Peter Ustinov, who probably has higher brain radiation that Einstein, at any rate a witty and delightful human, could only betray himself by an occasional inflection or intonation; as a good actor he could not depart from the script. So I got the message that the real meaning of the program was the takeover of one culture by another — like the Spanish missionaries building churches where an Inca temple had been before, or the Christians building churches with columns taken from a Greek temple. What remains of our human culture (represented by Peter) cowed and put to rout by the Legions of Science.

This is Medusa in modern dress, and if we’re going to deal with it we must do so as did Perseus. We need the shield of Minerva. We must use the mind to slay the mind.

The TV program discussed one of the major themes of the Einstein theory, which is to replace the force of gravity by the curvature of space. The program presented this visually with a table whose surface was shaped like the mouth of a trumpet with a grid of white lines which made the curvature visible. A ball was rolled by the obliging Peter to show how the curvature of space caused the ball to roll around the central sun: “The mass informs the space and the space informs the matter.”

I could not help protesting at this point, why then do we need “gravitons?” Why, in fact, is the curvature of space a better explanation than a force? Here we must realize that both gravitons and space curvature are inventions of science to avoid the “elusive” notion of force (Eddington’s phrase). Gravitons replace a force with a shower of particles, a desperate expedient to concretize with particles what is ontologically prior to particles. Curvature of space as the explanation of force is another expedient to describe what is prior to objectivity in objective terms. Of the two, space curvature is better because it is equivalent. If we drive a car around a curve, or take a corner at high speed, we are thrown violently to one side. The force and the curved path are equivalent.

What should not be forgotten, however, is that it is not curved space that is equivalent to force, but motion in a curved path. The effort to conceptualize force deludes us by a trick. We still have to invest this static picture with actual motion. Motion, of course, also cannot be conceptualized. In fact, it is not a sense datum, as the so-called paradox of Zeno disclosed, though even this point is overlooked by philosophers.

In other words, motion in a curved path is two removes from sense data. Sense data give us the position of an object in space. To know velocity we have to have two observations of position together with the elapsed time, and we can then compute the velocity (feet per second). But to know acceleration or to know that the body is moving in a curved path, we need three determinations. Three points determine a curve. As before, we must also have the time elapsed in order to say how rapidly the velocity has changed, or has changed direction, for a change in velocity or in direction are both acceleration.

Thus with acceleration or curvature of the path traveled, we are two removes from sense data. And if we recognize that velocity, because it must be computed from sense data, is essentially mental, velocity is one remove from position (the physical datum).

Now if we take seriously these removes and don’t just blur them all together as measures, we can recognize that each remove is a different category of measure. Position is a sensory measure, velocity is a mental one, and if we go a step further, acceleration is something we feel. Now of course we can compute acceleration, but it is a computation of a computation; it is one remove from mental, and this is the trick played on us by the substitution of curvature for force.

Readers familiar with my books will recall how often I’ve stressed these categories before, and that in the context of the ones just mentioned, position, velocity, and acceleration, there is a fourth: control. Control is not mentioned in the textbooks, but it is the basis of cybernetics (from the Greek cyberos, steersman), a science in its own right. And it is something we do all the time — with force, when we drive a car, when we make any physical movement; with speech, when we choose the right words to convey our meaning.

Science is dedicated to the principles involved in the design of machines (like Detroit) — to building cars, not driving them. But its neglect of control, the function that makes driving possible, shows that science is dedicated only to secondary causes.

That science has elevated this dedication into a religion takes us back to the division of functions which the ancients represented as different gods. In Christianity this survives in the recognition that Satan, who rebelled and was cast into hell, still has the status of a god. In Egypt this was Set, who brought about the fall of Osiris. In Greece it was Cronos who ate his own children. Prometheus brought fire to man, which in one sense was a transgression for which he was punished, yet in another sense it was fire that enabled man to evolve. Science has this Promethian role — but Prometheus brought fire, which is the spirit of science. And this is not what we are presently concerned with. It is the face or mask of science that is turning us to stone. It is science as a Medusa that freezes us in the dogma of determinism. If we look behind this mask of certainty, which science adopts, we find uncertainty; if we question the frozen shape of space-time we find force, which we humans know through feelings more directly than science can know it. But let us spare the polemics lest we spoil the problem.

What are we to say to this beautiful but frozen concept of curved space-time?

For answer, let us hold the mirror up to Einstein. Here I can draw on Eddington, who carried the theory of relativity to its ultimate conclusion. We can take advantage of Eddington’s determination of the number of particles in the universe, 1079, an obviously mad idea for which he has been rebuked (as Eddington answered, he did not offer this number on the supposition that someone was going to count them); nevertheless, Eddington’s figure has been generally adopted.

Let us set up a diagram in which the principal features of the universe are set forth. Note first that the diagram has the four measures: Position (on the right), Velocity (at the bottom), Acceleration (on the left), and Control (at the top). For the maximum length or distance we have 1027 cm, the diameter of the universe. For the minimum distance we have the diameter or radius of the proton, 10-13 cm. The latter as a radius of curvature represents a curvature of space-time and hence is equivalent to a force — in this case, probably the electromagnetic force, 10-39 times gravity.

The corresponding force on the right will be proportional, that is, will be less as the radius is greater = 1027+13 = 1040 times weaker = gravity. (We don’t bother about one order of magnitude in this kind of picture, so the fact that gravity is 1039 times the electromagnetic force, rather than 1040, can be overlooked.)

We now invoke the speed of light (at the bottom). How long will it take light to go round the proton? We divide the speed of light by the proton circumference:

3 x 1010 cm per sec = 1022 times per sec.

6 x 10-13

This is the frequency of the photon that would create a proton.

How long will it take light to go across the universe?

2 x 1027 cm per sec = 2.1017 seconds = 56 billion years

3 x 1010

This is close to the computed age of the universe, 40 billion years, and I will not try to improve it because the model does not purport to establish what this will be. (It probably has to do with what it is now.)

The electromagnetic force is that which would keep the photon in an orbit 10-13 cm. What is gravity? It is the force which keeps light from escaping from the universe! How great is it? Well it’s 10-40 times the electromagnetic force. What is it due to? It’s due to the matter in the universe. We can consider this matter to be concentrated at the center of the universe. Now, if one proton can confine light to moving in a circle of 10-13 cm, how many protons would it take to confine light to a radius of 1027? A lot. (Because the pull of the force varies inversely as the square of the distance.) So to exert the same force (as in the proton) at the much greater distance, i.e., 1027 x 1013 = 1040, it would take (1040)22 = 1080 protons.

But the force required is less because the radius of curvature is greater. How much less? Less by the ratio of the radii, i.e. 1027/10-13 = 1040. Gravity is this weaker force.

So there must be 1080 protons in the universe to cause light, under the pull of gravity, to stay within the universe!

Recall that the ratio of the electromagnetic force to gravity is known (actually 1039), as are the speed of light, the diameter of the proton, and the frequency and wave length of the photon which would create the proton. The diameter and age of the universe are speculative, but are thought to be approximately what I’ve given. The number of protons is that computed by Eddington on the basis of other considerations.

But what should we put at the top of the figure? This is the position for control, but there is no figure for control in science, so we must find some other measure to put there.

It so happens that mass has the same ultimate dimensionality, L4, (see The Geometry of Meaning), so we can put mass here.

The obvious mass would be that of the proton, and when I first showed the diagram I put the proton mass here. But someone said, why not the mass of the universe? This troubled me; it was just as much an absolute as the other “constants” such as the speed of light, and was of equal status as the proton.

It then occurred to me that since the acceleration of a curve of the radius of the proton is 1040 times that of the radius of the universe, and these two are one diameter apart, then 180 degrees involves multiplication by 1040 (this is also apparent in the ratio of the universe — 1027 cm — to the smallest particle in it — 10-13).

Well, if 180 degrees = 1040, then 360 degrees = 1080 (the mass of the universe)! Both the mass of the proton and the mass of the universe are predicted by the point at M.

We are now ready to go further, and again I draw on Eddington. I quote once more from a remarkable passage in Eddington’s Fundamental Theory (also see The Reflexive Universe, Appendix III):

The usual equations of wave mechanics postulate flat space. I do not think there is anything to be gained by trying to extend wave mechanics to curved space. Curvature and wave functions are alternative ways of representing distributions of energy and momentum; and it is probably bad policy to mix them.

We have introduced the curved space of molar relativity theory as a mode of representation of the extraordinary fluctuation, and have obtained the fundamental relation between the microscopic constant s and the cosmological constants Ro,N. Having got what we want out of it, space curvature no longer interests us; and we return to flat space to pursue the specialized development of microscopic theory. That does not mean that henceforth we neglect curvature; we merely refrain from using the dodge that introduces it. The scale uncertainty, instead of being disguised as curvature, will be taken into account openly; so that there is no loss of rigour.

Realize that Eddington wrote two books on the theory of relativity, The Mathematical Theory of Relativity and Relative Theory of Protons and Electrons. But now he says, “Having got what we want out of it, space curvature no longer interests us.” What a line! But he goes on to say, “The scale uncertainty, instead of being disguised as curvature, will be taken into account openly, so that there is no loss of rigour.”

I have already commented on this remarkable passage in The Reflexive Universe, where I quoted it at even greater length, because it was in this passage I found sanction for two important ideas of The Reflexive Universe:

1. That complete uncertainty is a circle.

2. That the 3/4 which Eddington calls stabilization of scale I call control.

While my interpretation of Eddington in point #2 has not been challenged in the years since The Reflexive Universe was published, I will still take the responsibility for a possible misinterpretation — which does not mean that what would in that case be my idea, is invalid. The validity of interpretations is impossible to prove.

In any case, for the present I can leave out #2 and consider only #1: uncertainty is a circle.1

Eddington, as I understand him, equates the curvature of space to the curvature or circle of the quantum of action. As I said in The Reflexive Universe, this recognition reconciles quantum theory and relativity, a goal still not acknowledged by science as having been achieved, because the goal was misnamed “a unified field theory” and Eddington’s solution does not involve a field but circularity.

Relativity and quantum theory are regarded as two mutually incompatible theories, which deal with different areas. Relativity deals with large-scale phenomena and quantum theory with small-scale, or microphenomena. Paradoxically, quantum theory deals with wholes and relativity deals with parts. Actually it could not be otherwise, because the micro-world of quantum physics is the level at which only wholes exist. While the atom, once thought to be indivisible, has been divided, the quantum of action cannot be divided. It is the true atom — an atom not of matter, but of activity. To deal with the universe in these terms is not humanly possible, because to do so we would have to have a life cycle billions of years in duration in order to encompass the “life” cycle of the universe.

Relativity deals with pieces of curvature, and it fails to emphasize the cycle of time where all this curvature is put together into one great cycle of action. Let me point this out another way. What is called the “volume” of the Einstein-Eddington hypersphere — which is to say, the volume of the universe in the sense both of the space it encloses and the time which is in process of being enclosed — this “volume” has the formula:


An ordinary physical sphere has the volume:


Without any special knowledge one can see that:

1. There is no “t” (for time) in the hypersphere.

2. There is, however, an extra pi.

Could it be the case that pi takes the place of time? Suppose for simplicity we represent the ordinary (physical) universe, or the instantaneous universe, as a circle. The area of this circle has the equation pR2. Suppose now we multiply this by time:

piR2 x time = piR2T, a cylinder

Now suppose we bend this cylinder around to meet itself, that is, into a circle like a doughnut.

Radius = R’

The circumference of this new circle will be 2piR and the volume of the cylinder bent into a circle will be:

2piR’ x piR2 = 2pi2R’R2

Now let R’ be the same as R, and we have:


In other words, instead of “t” we have 2piR. Time is replaced by a cycle of action. The measure of this cycle of action in terms of time varies with the entity. If the photon, it is 1/1022 seconds (the photon that can create a proton). If a bacterium like E. coli, then about 20 minutes (the time required for it to reproduce, or create two cells from one). If a person, it has its life cycle in a physical body, perhaps 80 years, but if we include reincarnation, a much greater figure, which may be the age of the universe or may be greater.

While we may not care to extend this cycle for the monad to the figure I’ve given, which takes us into unknown territory, we can at least appreciate the point implied by Eddington, the equivalence of curvature with the cycle of action (or uncertainty).

Before leaving this subject, which I confess has been speculative, let me not neglect a comment on the question of the “unified field theory” which I hope can stand independently of my vagaries on human evolution, and which can apply to Eddington’s “Space curvature no longer interests us.” The issue is the reconciliation of relativity and quantum physics. Eddington saw the key to be curvature, which was present in both theories but in different forms, or rather, on very different scales. Quantum theory dealt with the micro world, relativity with the whole universe.

But now note what made it impossible for Einstein to reconcile the two theories. He called the theory he hoped to find the “Unified Field Theory.” We have already pointed out that the notion of a field is a concession to conceptual thinking. We can form the concept of a field, but we cannot form a “concept” of force. Force is a different category. The quantum of action is also in a different category. Under its other name, quantum of uncertainty, it is, by definition, impossible to conceptualize.

If the reader finds this difficult, I have two alternatives, either to accept as a fact of life that quantum physics has stumbled upon something that cannot be conceptualized — that is, take it as would a child, that Daddy said so — or take the route that I’m trying to open through the jungle, that there are different categories, aspects, or causes of things.

Since this is a venerable tradition, echoed, for example, in Aristotle’s four causes, I hesitate to repeat it again, but here in the failure to obtain a unified theory we have a lesson. Not only did Einstein doom his search to failure by calling his goal a field theory, thereby excluding what was not a field, but he insisted that quantum theory was invalid. (Why then did he seek to unify it with relativity?)

We need to uncover what it is that gives science the authority it has come to have in order to go beyond the blind spots in the current world view.

We have already mentioned that the “god” of science is physical law — determinism and reductionism — which we can classify as secondary causes. This is inverse hierarchy, the “worship” of Set, of what pulls down into manifestation.

There is also the accord given to physics because it is an exact science. This exactness is quantitative. When the scientist says the speed of light is 299,792,456.4 meters per second, Peter Ustinov says, “Zero point four?” and the other replies, “Well, the English would say 0.5.”

It is impressive that it is possible to test Einstein’s theory of the advance of the perihelion (which, for Mercury, is only a few seconds per century) on a quasar some hundreds of millions of light years distant. In fact even to be able to see such an object is profoundly impressive.

Or again, to photograph the rings of Saturn.

Now, the pursuit of exact measures is an important aspect of physics, but it is to be credited not so much to science as to technology, and we have to ask whether the technical achievement represented by gene splicing is not equally impressive. There must be something more than just the accuracy that gives physics its prestige.

I have the feeling it is irrelevant, and possibly irreverent, to say such information (perihelion advance of distant quasars, etc.) has little to do with important problems. Man is the only creature to pursue goals beyond his immediate necessities, and to demand “practical” results would eliminate his most creative efforts. The astronomer, when asked, “What is the use of astronomy?” said, “Of what use is a baby?” It is because astronomers and the other branches of science are dedicated to “unworldly” goals that they command our respect.

Nor can science be faulted on the grounds that it is always cold and sterile. It has its own mystique, quite as compelling as that of religion. Black holes, for example, are now credited to Einstein, although LaPlace predicted them 150 years ago; yet no black hole has ever been discovered. One might ask, if there were black holes, defined as matter so dense that light cannot radiate from them, how is it that they can exert a gravitational influence (since gravity is assumed to be radiated at the speed of light)? The answer I got from a physicist was that the gravitons, like light, are slowed down, they exert an influence before the black hole becomes invisible. This answer conflicts with the thesis that black holes account for the missing mass of the universe.

Such inconsistencies of science are paraded as paradoxes which only experts can understand, and these paradoxes contribute to the mystique of science. It might be worthwhile to attempt an enumeration. It would include:


If gravity is explained by the bending of space-time, why is it necessary to have gravitons at all? Actually, the whole question needs an airing. Gravitons are postulated (they have not been observed) because, since the photon can be interpreted as an exchange particle which explains the electromagnetic force, there should be another exchange particle that explains the gravitational force.

But is it correct to interpret the photon as responsible for force? What actually occurs is that when a charge (i.e., an electron) is accelerated a photon is radiated. But this would not account for the force between two particles that are not accelerated (at rest).

Again, the electron orbits the nucleus. It is certainly being accelerated. But it does not radiate a photon unless it changes to a different orbit. This is the prequantum problem, which was solved by saying the electron is accelerated without radiating a photon, provided it does not change orbit.

Furthermore the force in question is between the electron and the nucleus. There is no radiation to or from the nucleus when the electron does change orbit and radiates or absorbs a photon.


There are endless criticisms of this slippery bit of juggling introduced to balance the books in what is known as beta decay, when a neutron releases an electron and becomes a proton. (Not all the energy is accounted for.)

The latest absurdity is to explain the “mass deficiency” (not enough mass in a galaxy to account for its rate of rotation) by the mass of the neutrino. But it is easy to show that to explain the missing mass would require there to be millions of times more neutrinos than there are particles. This, it should be evident, is absurd. But if the absurdity is not evident, why does the existence of so many neutrinos, which cannot be at rest and must therefore by flying about in all directions, not show up in the experiments to detect neutrinos from the sun? In fact, why does it not cause there to be so many neutrino events that those caused by neutrinos from the sun would be lost in the shuffle?

The unification of the four forces

One of the projects that physicists are given to praise with hallelujahs that fall on my ear like musical instruments out of tune is the proposal to unify the four forces — the electromagnetic, the gravitational, the strong and the weak forces.

The idea got its initial impetus from the prediction by Yukawa of the meson, which did indeed turn up. This was a short-life “particle” or bundle of energy of such amount as would account for the binding of nuclear particles. Such binding is, of course, energy, because it takes energy to break the particles apart.

Then it became the vogue to explain electromagnetic force as due to photons, as I mentioned above. Thence to the postulations of gravitons for gravity and a W particle for the weak force. These particles had in common that they were bosons, which are defined as having integral spin (not 1/2 spin), but gravitons have spin 2, photons spin 1, W particles spin 0. Meanwhile mesons, which started the club, have been dropped from membership, for what reason I cannot make out. So their definition as bosons does not mean bosons have much in common. And of course there could hardly be a greater disparity than there is between electromagnetic force (emf) and gravity!

1. The emf is 1040 times gravity, a number which is so large that it would require the smallest dimension possible in matter, the diameter of the proton, versus the diameter of the universe to represent it. 2. The emf comes as repulsion and attraction, whereas gravity and the other forces are attractive. 3. The strong and weak force are short-range, extending only 10-12 cm from the nucleus, whereas the emf and gravity extend to infinity.

This gross disparity is not reconciled by any account I’ve seen. While I’m given to mixing categories in the sense that I can find a method by which four categories can be shown to be interrelated, this method depends on the recognition that the categories can be defined as the permutation of two dichotomies, a and non-a, b and non-b, a and b being independent.

The method also requires something in common between opposite ends of the diameters. This is not evident in the case of the forces. There should be something in common at upper right and at lower left.

Elegance has always been what fascinated me about physics, especially the elegance of explaining atoms as multiples of protons, the line spectrum of hydrogen, the Mendeleev table, etc.; but I’ve not heard any such harmony since the neutrino. Physics has become a patchwork of ad hoc assumptions, and quarks are more like Ptolemaic circles than good explanation.

The comments above demonstrate some of the inconsistencies and absurdities in science, all of which make it difficult for non-scientists to venture into such areas and form their own judgments or viable questions.

I am often criticized for “answering questions that haven’t been asked.” But the problem is that people have become too intimidated by science to ask questions. This doesn’t mean they don’t sense the error of science, but this awareness drives them away from science — into the consciousness movement, into Eastern philosophy, into protest marches and other tactics that are essentially regressive in that they fail to meet science on its own grounds, correct its errors and make it a servant in the general human quest for understanding and wisdom rather than a god.

It takes both courage and wit to ask questions of science — courage because for a long time now we have had “this nonsense knocked out of us.” I’ve seen many biology books which start out by a statement that science doesn’t deal with questions like, “What is the purpose of life?” The unmistakable message this carries is that such questions are naive, beneath contempt, not only not worth asking but definitely in bad taste.

As for the wit needed to question science, this requires the perception that science is not the immaculate perfection of knowledge that its press gives out. Even technical questions from within the establishment are difficult to ask because much of scientific training consists of learning to swallow pills that are distasteful to chew. It takes about three years to get the nuclear physicist to go through the ritual movements that are recognized by other scientists, and to depart from this would result in being thrown out of the club. Yet it is difficult not to depart from the ritual because it is the ritual that is inadequate.

In fact, both my handicap and my advantage in dealing with physicists is that I’ve not swallowed the requisite pills. I can’t remember the simplest formulas; I have to figure them out each time. In aerodynamics I avoided the complex German formulas, but could approach the problem from the more basic level of laws of similitude. This was of importance for helicopters, which required a more basic investigation than that which had sufficed for airplanes.

A critique of science takes a combination of understanding science plus the ability to see through the smokescreen of gobbledegook which obscures its errors from scientists themselves.

I think a thorough reappraisal of science must be done if we are to reach the next stage. It may not be done; we may regress to the prescientific, or our culture may split up with scientists becoming more zombie-like and the protestors more cut off from the rest. In my work I have tried to bridge the gap, by which I mean account for the disparity between the scientific picture of life, and life from the standpoint of the meaning universe. I’ve found there is one key link in the bridge. It was introduced earlier in this essay, when I showed that the reconciliation of quantum mechanics with relativity can be achieved by the recognition that the curvature of space-time and the uncertainty of quantum physics are both cycles of action, the one on the micro and the other on the macro scale. Generally speaking, the measures of science deal only with whole cycles — a 60-cycle current; a 20-megacycle radio signal; middle C is 256 cycles, and so on — though in some applications science does have to deal with phase, but this usage is rare.

However, human life is mostly concerned with phase relationship — it’s time for lunch; it’s bedtime; the timing of a stock purchase; the player’s timing is off (which could apply to sports or to music); dancing, etc. Again, a person’s age can be counted in years, but the differences which develop — childhood, puberty, youth, maturity, etc. — are positions in the cycle from birth to death.

We may refer to this cycle by different names — quantum of action, quantum of uncertainty, free will, life cycle, learning cycle, etc. — realizing of course that it has many octaves; it can be the instantaneous act of decision, a moment of realization, a day, a year, or a life, or even a day in the life of Brahma (4 billion years).

Perhaps the most suitable term is the learning cycle, not only for its implication of phases within the cycle, but for its suggestion of something achieved. Unlike the measures of science, this cycling does not get back to the starting point and repeat. Rather, it provides for the progress of evolution and the cumulative, generative nature of life. The evolution of life as viewed by science has nothing to do with life! What is missing in science is the recognition of the concept of phase (in the cycle of action) which the quantitative or reductionist approach cannot accommodate. This phase is the completely unpredictable, freedom of choice, option, also known to us as meaning — in contrast to measure. It is the link between human spiritual awareness and knowledge of the physical world.

1 Our certainty can be described as it is with a lens, as the angle between two distinguishable points; the greater the angle, the greater the uncertainty, hence maximum, i.e. complete, uncertainty is the maximum angle, 360 degrees, or a full circle. This is the phase dimension.

©1998 Anodos Foundation