Putting Soul into Science

1. The nature of the quantum and subatomic worlds

We have seen in the last two chapters how the development of the sciences in the last few centuries has gradually led scientists more and more into the study of strange worlds very far from that of the everyday world of human experience. Basic assumptions were made starting at the time of Newton, about what really was and what really was not scientific. Physics was based on the study of bodies which exist in space and time, only taking into account their spatial properties and their properties in time as measured by clocks, that is, those properties which can be described by the space-like aspects of time. In addition physical phenomena were studied to a greater and greater extent by instruments, thus bypassing direct human perception as much as possible. Moreover, as the power of instruments was increased, it became more and more possible to study many phenomena which cannot be studied by other methods, such as those which occur on very small scales, which are generally believed by physicists to be fundamental. Therefore, what was studied was the interaction of the matter participating in a phenomenon with the matter associated with a measuring instrument. The following of this path by physics led to the crossing of a threshold at around the beginning of the twentieth century; we described in chapter 3 discoveries made after this threshold was crossed. The laws of other sciences including, for instance, biology, were supposed to be the consequences of the action of the laws of physics in various situations. As a result, the soul world of inner experience, that is the second world of Popper and Penrose, was eliminated, leading, as we saw in chapter 2, to quite paradoxical conclusions about the nature of the world. We shall now look at the discoveries made by the sciences in the twentieth century in different ways than those in which they have usually been looked at up till now, to see whether hitherto unknown soul aspects are not hidden behind them. We shall in particular look for the presence of the three aspects of the worlds of inner experience, discussed in section 4 of chapter 1. A certain effort of thinking will be required to do this, though it is not necessary to go into the technical details, which are only of interest to experts.

Let us start with the world of the very small, described by quantum physics, which as we shall find can teach us some very basic lessons. It is, as we saw in chapter 3, a world where different possibilities of successive events occurring co-exist; one of the possibilities will be realized in the large scale world, by what is called "wave function collapse" or according to the interpretation physicists now mostly accept, by interaction with the environment. Exactly What will be produced on the large scale by events on the small scales of the quantum world is unpredictable; in order to make the sort of prediction possible using Newton's laws, it would be necessary to know the values of physical quantities, that is, to be able to make physical measurements to an infinite accuracy (see the end of section 1 of chapter 2). This is impossible according to Heisenberg's indeterminacy principle. However it must be emphasized that the physics of the large-scale world is still closely connected with that of the small scale world; only certain possibilities are allowed by that world, which plays a fundamental role in the ideas of physicists about the nature of the processes of the world which can be directly perceived by humans.

As we saw in section 5 of chapter 3, the Heisenberg indeterminacy principle can be stated in different ways. It is a limit to the accuracy to which certain physical quantities can be simultaneously measured and even be thought of as having a meaning in physics. In the second form, the principle can be stated as being a limit to the accuracy in the measurement of the time of an event, multiplied by the accuracy in the simultaneous measurement of energy which must be present when the event occurs. Two examples of what is meant by an event and its energy in this context were given in that section of chapter 3. We spoke there about measurements being resisted by nature. More precisely, if what occurs is examined more closely we find that when an event which happens in a physical system is studied using a measuring instrument, we can suppose that there is resistance between the matter undergoing the event and the matter of the instrument with which it interacts. This can be seen because an experiment using instruments will measure more accurately the time of an event and less accurately the energy, while different experiments using other instruments will measure more accurately the energy and less accurately the time. Similarly the position of a particle will sometimes be measured more accurately and in different experiments the speed will be measured more accurately; there is also a resistance to both the latter quantities being simultaneously measured to an infinite accuracy. It is this basic resistance which limits the accuracy of measurement, while the highest possible accuracy in measuring all the properties possessed by any physical object according to pre-twentieth century physics, would be needed to predict its future behavior and so to know everything about it.

The Heisenberg indeterminacy principle is indicated in other sorts of resistance, described in section 6 of chapter 3. When combined with the Pauli exclusion principle, it can be partly related to a resistance between electrons and the nucleus of an atom, which prevents the electrons from falling into the nucleus and so maintains the atom's existence. In addition, atoms resist each other in their interactions. We saw in the same section of chapter 3 that the Heisenberg indeterminacy principle is also invoked in modern theories of the fundamental forces of nature (which are electricity and magnetism, the strong interaction. the weak interaction and gravitation); the principle permits the creation of "virtual particles", which produce these forces. The existence of the fundamental forces in nature may therefore also be thought of as a kind of resistance acting between particles. We may conclude that the Heisenberg indeterminacy principle is directly connected with the most basic characteristic of matter, which can also be observed on the scale of normal human experience. Matter resists matter; bodies made of matter act on other bodies made of matter in many different ways and so force them to have various sorts of behavior. For instance, to take a rather extreme case, it is very difficult to make a solid body pass through another solid body! It is possible to see in a more precise way how the Heisenberg indeterminacy principle is related to resistance and this is especially useful for its examination in the following discussion. We shall express it differently by making an extremely simple mathematical manipulation, that is, by taking the reciprocal of both sides of the expression in the form relating time and energy, given in the last chapter (this means that we take 1/each side of that expression). The result is

Here the symbol ≤ means less than or equal to, so this new mathematical expression states that the left-hand side must always be less than or equal to the right-hand side, the left-hand side containing the degree of precision of the value of time 1/Dt multiplied by the corresponding degree of precision in energy 1/DE. In the last expression the time is more precise if 1/Dt is large, while the energy is more precise when 1/DE is large. These precisions are limited by what we have just seen can be thought of as a form of resistance; their multiple can never be greater than the physical constant given on the right-hand side.

We will now try to see what sorts of soul processes and actions of conscious beings can be behind this basic nature of matter as studied in physics. It will be necessary to examine more closely the three aspects of the soul possessed by many sorts of conscious beings, as described in chapter 1. Let us start as a first step by looking at what the simultaneous existence of different beings means. In fact, if more than one conscious being really exists, there must be a certain degree of separation between the different beings. This means that each being must possess something that is unpredicted and uncontrolled by other beings; on the other hand, the various beings can have relationships with each other. Each can then communicate something new to another being. If on the contrary everything in the world were under the control of just one being, a kind of supreme cosmic "dictator" (or God according to the ideas of religious extremists), it could in principle decide everything, as nothing else could have either the ability or even the desire to thwart it!

In order to see more clearly what is the role played by the three aspects or abilities of the soul, let us consider what happens if a being has a desire for something to happen. In order to realize the desire it needs the ability to act. However, it must also know what will be the results of any particular action; otherwise an action need not produce the desired result. This indicates that a desire is not enough; it must be accompanied by the two other soul aspects. Many examples of this exist in the most ordinary events of everyday life. For instance, suppose one wishes or desires to cut a circular cake into two equal halves; one must have the ability to use a knife, but also know enough about the geometry of a circle in order to place the knife in the right position and cut the cake correctly. If on a more difficult level one wants to build a house it is necessary to have available the force required to do the building work; but it is also necessary to know something about mechanics, so the house does not collapse. When a person wishes to make a journey by plane it is not only necessary to be able to go to the airport, but also to know where the airport is... We can conclude that without the ability to act, any amount of knowledge would be useless, while without knowledge any amount of ability to act would also be useless. In any case it is easy to see why one might expect the three abilities of the soul to be present very often in some form or other, when different conscious beings exist.

When independent beings exist, they can be expected to have different desires; it is in such a way that resistance can arise between them. Indeed the experience of resistance due to beings of the outer world might even be thought of as what gives rise to the consciousness of a particular being. Let us suppose that a class of beings exists who, when they interact with any other being of the same nature, always resist it to the same extent by limiting both its ability to act and its knowledge. In this way there could be a limit to the amount of ability to act multiplied by the amount of knowledge of each of these conscious beings and so there could be a limit to the realization of what is desired by each of them. In this way the feeling of contentment or happiness of each being would be limited. In that case we could have a situation where: the amount of knowledge times the ability to act is less than or equal to a certain value.

This is clearly very much like the last expression for the Heisenberg indeterminacy principle. This is easily seen because, as mentioned in section 2 of chapter 2, in physics energy is a form of ability to act. What is now involved is that if to produce a certain physical event one must not have either too much or too little energy, the ability to act will not be proportional to the total amount of energy available, but rather proportional to the precision with which the energy can be applied. Such situations can indeed exist in everyday life; when for instance a person in an office wishes to throw away some sheets of paper, in order that they fall into a wastepaper basket they need to be neither thrown too fast (with too much energy) nor too slow (with too little energy). The precision in the determination of the time of an event in the Heisenberg uncertainty principle can then be considered as being a form of the amount of knowledge which is available.

Our discussion indicates that the resistance of the quantum world, associated with Heisenberg's indeterminacy principle, is understandable as due to the interaction of conscious beings, which resist each other. According to this viewpoint the consciousness of such beings is, unlike what many people believe, not directly related to the consciousness of a human observer. These beings must in such a framework act when interactions occur between the objects which physicists think of as being very small particles. The beings, like these particles, must then not have the same relationships to space and time as the bodies and living organisms of the world of human experience. In this case, the physical constant on the right-hand side of the last mathematical expression for the Heisenberg indeterminacy principle must represent the maximum happiness attainable by each of the beings involved, when it uses all the means at its disposal to attain it. What for a human being would be a feeling of happiness is then limited by a constant of physics as the small scales of the quantum world are approached. We can now form a vivid picture in our minds of what appears to be a heartless inhuman world, which is the one we are considering here. There is no real love, but only a sort of resistance exists between beings, so the happiness of each of them is limited by or "imprisoned" inside a constant of physics.

It appears therefore that the small scale world we are now examining is not only without most of the qualities of human society, but that it is also without the qualities of nature as we directly experience it. Relations between animals like those between human beings (and between human beings and animals) are clearly not governed only by blind resistance. Animals have sexual relations and they often live in groups or herds. The social insects such as the ants and bees live in large communities. Symbiotic relations, where individuals of different species live together and help each other, also exist in nature. In this way the domain where the Heisenberg indeterminacy principle applies would seem to be at a level which is "lower" than the nature of human experience or, to use Rudolf Steiner's expression, a world of "sub-nature". In his last letter to those connected with the "anthroposophical" movement founded by him, written in March 1925 (see "Anthroposophical Leading Thoughts", Rudolf Steiner Press, 1973), he says that technical science and industry have entered a realm of sub-nature, from which among other things electricity is derived. At this point we may recall, as stated in chapter 3, that in the small-scale world we are now considering, electrical charges persist indefinitely.

The world in which the Heisenberg indeterminacy principle acts with what we can understand as being blind resistance and the "imprisonment" of happiness inside a constant of physics, appears to us as a world without love and without morality; it is, however, not immoral but rather amoral. In any case, it cannot be thought of as a "good" world. At this point it is possible to go much further in understanding that world, by using certain conceptions formulated by Rudolf Steiner to explain the phenomena we are considering. He often describes what can become two sources of evil for human beings when they are not faced in the right way. These sources of evil which oppose human beings are, according to him, two beings which have opposite natures and whom he calls, taking names from different religious traditions, Lucifer and Ahriman. According to Rudolf Steiner, Lucifer, which in the Christian tradition is a name for the devil, tempts a human being through pride and through producing all sorts of illusions about the apparent beauty and wonderful nature of many aspects of the world around him or her, which in reality are very different, such as false ideals. Ahriman or Angra Mainyu is the name of the devilish being of the Zoroastrian religion, which was practiced in Persia before the rise of Islam. According to that religion, as a spirit of evil, he resists Spenta Mainyu, who is the son of the supreme God Ahura Mazda (see "Zoroastrianism: the Religion of the Good Life" by Sir Rustom Masani, Collier Books, New York, 1962). Let it be noted that Zoroastrianism is sometimes described somewhat differently; I have here mainly followed the description in the book just mentioned, written by a twentieth century follower of this religion, that is, by an Indian "parsee". Rudolf Steiner gave the name of Ahriman to a being associated with matter, the materialism and philistinism common among human beings, who also tries to imprison human behavior through rigid rules and through what is cold and impersonal in the world. According to Rudolf Steiner both Lucifer and Ahriman are necessary elements in the evolution of the world; a human being must strike a balance between them. I should also point out that Lucifer and Ahriman have only been described here in a very simplified way; Rudolf Steiner's descriptions of them are much more subtle, involving many situations where both are present and complex interactions occur between the two.

In the framework of these two sources of evil the Heisenberg indeterminacy principle has an important role. The world where this principle is important can be clearly pictured as being a world of cold resistance with happiness imprisoned inside a constant of physics, and can also be conceived of as a world of Ahriman. Indeed, it was through such a picture that the author of this book was able to more clearly understand what Rudolf Steiner meant when he discussed the nature of Ahriman.

Quantum physics is closely connected with the physics of the world of human experience and in particular with the human experience of matter. The physics of the very small acts on the physics of the world in which we live. In fact certain spiritual traditions have considered matter to be evil and to be the domain where the devil acts. In this connection we should mention various Gnostic movements which existed in the first few centuries of the Christian era, the Manicheans (from the third century onwards) and the Cathars. All these movements were violently opposed by the Church. Catharism, which became widespread early in the eleventh century, later became particularly influential in south-western France. The Cathars were heretics as far as the Roman Catholic church (and also the Orthodox Church) was concerned, to be brutally exterminated by burning its adherents at the stake. Though great crimes were committed against such movements, we need not agree with all that they stood for; in particular their view of the world appears to be somewhat one-sided. As already mentioned, the nature in which we live is not the same as the world of quantum physics; nature does not seem to contain only evil.

As is well known by people who have some acquaintance with science, the other aspects of nature studied by physicists do not show love or morality either. This amorality of physics leads to a kind of freedom for human beings in the world on the human scale. It is not necessary to "persuade dead objects" to do what we want them to do by being "kind to them"; we can make them do what is possible according to the laws they obey. To give an example, a chair will not play games with somebody who wants to sit on it, as happened in a film made by students I saw many years ago.

Before ending this section, it is useful to briefly look again at the Pauli exclusion principle. As we saw in section 6 of chapter 3, "fermions", which are the particles which obey this principle, produce the structure of matter. No two particles can have exactly the same properties. In the framework of the present discussion concerning the possible soul properties of beings acting in quantum physics, this might be understandable if it is considered as being due to a refusal of any being connected with fermions to imitate another such being. Such a property might appear to be another kind of resistance.

We shall now examine some other aspects of science before returning to quantum physics later in this chapter.

2. Where can soul be found in the phenomena of Chaos?

As stated in the last section, the nature which is inhabited by human beings does not have the properties of the quantum world, though the latter clearly has what is an extremely important role in determining the physical processes of the world on the human scale. It is possible, however, as we shall now see, to understand certain aspects of nature if we consider it to be the stage on which other kinds of conscious beings can also act. Such beings include humans, who have an inner experience of being free to act, as well as many other types of beings. These beings must possess different forms of what for humans are the three soul abilities.

As we have seen, according to present interpretations of quantum theory, different possibilities of successive events co-exist in the quantum world. All but one are eliminated at the boundary between that world and the world we experience; as a result a unique sequence of events occurs in time, which must obey the logic of our large scale world. The nature of time, already discussed at the end of chapter 2, is in fact essential for understanding that world on the human scale.

We shall now return to the examination of what is called "chaos". In situations of chaos which can occur in the world directly experienced by human beings, physical events are unpredictable because their occurrence is extremely sensitive to the exact physical conditions and indeed to any minute perturbation from outside. As stated in chapter 3, chaotic systems can be thought of as being "vessels" able to receive what cannot be grasped in the framework of physical predictability. For instance, there are indications that chaos is present in living organisms, which could be such "vessels"; something could be present in the phenomena of life which cannot be grasped in this framework of physical predictability. The future development of such a chaotic system would, among many other things, be dependent on the exact time at which a particular small event in the system occurred. In this way a system in a state of chaos, like a system obeying the laws of quantum physics, also resists attempts to make it have a particular behavior. However, we shall now see that this resistance can be directly connected with the nature of time. As described in chapter 3, chaos plays a role on time scales much longer than the Lyapunov time; it is difficult to influence the behavior of a chaotic system on such a time scale. This type of system is so sensitive to minute infinitesimal perturbations, that the results of an action very close to a particular time are unpredictable on such relatively long time scales. Indeed, if these time scales are sufficiently long, the behavior of the system is influenced by the indeterminacy of the Heisenberg principle.

The question is - Is it possible for conscious beings possessing soul abilities to act on chaotic systems such as those of living organisms? Such beings would need to have behavior which could not be completely predicted and controlled by other beings, that is, which would have to be not predictable according to the laws of pre-twentieth century physics.

The control of chaos has interested a number of scientists (for a mathematical treatment see "Using Small Perturbations to Control Chaos" by T. Shinbrot, C. Grebogi, E. Ott and J. A. Yorke in "Nature" vol. 363, p. 411 1993). It is possible to apply a succession of small perturbations to make a chaotic system stay in the same state, in order to overcome the consequences of changes due to small influences from outside the system. Alternatively it is possible to slightly change basic properties (mathematical constants) of the system, so that in its unpredictable behavior a state near that which is desired is attained fairly quickly, without using large quantities of energy. This type of manipulation clearly has practical applications, for instance in changing the chaotic orbits of spacecraft.

A being who wished to influence a chaotic system on a time scale much longer than the Lyapunov time, without being hindered by the rigid laws of cause and effect of pre-twentieth century physics, that is, without needing significant quantities of energy produced by physically predictable processes, could not use such methods to control chaos. It would appear that if such beings existed, they would need to "see" what the results of any possible action are, that is, to "see" and also act in the future! In that way they would be able to "select" the future they wanted. Their perceptions would need not to be confined to one instant of time; these perceptions would have to be "extended" over an interval of time. In fact, the satisfaction or feeling of happiness obtainable by such beings would be proportional to their ability to act times the ratio of the amount of time they could "see into" the future divided by the Lyapunov time.

In many situations of this sort the ability to act would no longer be the precision with which an energy can be applied as in our discussion in section 1 of this chapter about how to understand the Heisenberg indeterminacy principle, but rather the amount of energy required to perform the action. If the ratio of the two times were sufficiently large, knowledge of the future would be very great and the energy required would be very small or even in the domain of quantum uncertainty. In such a way, beings of the sort we are now considering would, it appears, be limited in the satisfaction they could obtain by something which again looks like the Heisenberg indeterminacy principle, though knowledge and ability to act are now represented by different physical quantities. The three aspects or abilities of the soul world described in chapter 1 again appear here. However, the limit to the present kind of satisfaction or happiness is not necessarily a constant.

Some readers might at this point think that the author of this book has become completely irrational! Why think of beings able to "see" the future, why think that any other beings act in chaotic systems? Why suggest something as far-fetched as beings whose perceptions are extended in time? A simple reason for considering this kind of possibility is what is directly experienced by a human being. A human has the experience of being able to act, of being able to use his or her will to at least partly obtain what he or she wants. In particular, it is possible to act on the body, to move the limbs for example. As described in chapter 3, there are indications that certain processes in the human body and particularly in the brain are chaotic, that is, sensitive to infinitesimal perturbations from outside. The present discussion offers a possible framework for a human to possess something which, in order to act on the body and control it, "sees" very slightly into the future or which is slightly "extended" in time. Other living organisms are also partly chaotic, or are at the border between chaos and predictability, so the same situation might to some extent also exist for them. The same could also be true for some other examples of chaotic systems which are not thought to be associated with life. In this way beings which are not governed by the laws of deterministic physics could be present in the world and possess aspects corresponding to the soul abilities. This is far from a rigorous proof, but rather something which appears to be not completely unreasonable if we free ourselves from conventional materialistic ways of thinking.

We can see two possibilities if we consider the role of chaos in living organisms: either the situation is as suggested here, that the world of human inner experience or the soul is really significant and at least partly independent of "normal" physics, ; or the matter of which the human body is composed plus the matter outside the body which can produce minute perturbations in it, act in their own unpredictable and uncontrollable ways. Matter would, according to the second possibility in the framework of what might be seen to be a more "consistent" sort of materialism, have to possess additional soul abilities, which however are not those which can be thought of as being behind quantum physics. The alternatively even less satisfactory materialistic explanation is that the human experience of being able to act is only an illusion. Though we cannot rigorously "prove" that matter in a state of chaos is acted upon by beings extended in time, what is here suggested does not, in view of such considerations, appear to be irrational.

In fact the present conception of the action of beings extended in time on chaotic systems might also help to resolve an old philosophical problem of what is called "dualism". If both a material body and a non-material "soul" exist, as is the case according to dualism, it is not clear how this soul could act on the body. However, it may be possible to overcome such a difficulty if what is involved is a being extended in time, acting on a chaotic physical system. In the framework of the point of view presented here, strong interactions can be expected between a chaotic brain and what is extended in time. In such a way, quite a good correlation could exist between brain processes and the world of inner experience, which is then "reflected". Studies of the brain do indeed show such a correlation.

At this point certain objections might be raised against what is being proposed here. The three soul abilities appear at first sight to be directly related to consciousness, while modern psychology emphasizes the role of the unconscious and subconscious, at least in humans. However it is easy to realize that the conscious human being need not be alone even in his or her body, whose chaotic processes may be also continually influenced by many other beings. The latter could then be expected to be unpredictable and uncontrollable, being able to resist the human, by limiting his or her amount of knowledge and ability to act. Such beings then can be thought of as influencing the unconscious and subconscious. The effects of such influences would be complex, thus explaining the complexities of human psychology, including mental illnesses. If a human felt guilty about a past action which he or she had performed, for example, it might be possible to "forget" it, while other beings "retained" the knowledge contained in the memory. The awareness of this memory or apparently irrational actions based on it, could then be "returned" to the human in certain circumstances.

There are reasons to believe that the soul abilities of a human being have quite subtle relationships with time. As already stated at the end of chapter 2, willing is connected with action on the future from the present, while it is possible for the human in the present to reflect on the past. In the present the possibility to act on the future dies. These considerations might suggest that things are rather more involved than stated up to now, if what is happening is the action on chaotic situations of a being extended in time. The human action of willing could in this case act on times which tend to be slightly to the future of what is experienced as the present, while the person would only be able to consciously see and think about what tends to be slightly in the past (see fig. 4.1).

Fig. 4.1 - Separation of thinking, feeling and willing in time.

This suggestion is not, as it might first appear to be, empty speculation, as it may be possible to explain in such a way the surprising results of certain psychological experiments involving stimulation of the brain, mentioned in particular in the book "Shadows of the Mind" by Roger Penrose. Among the people who carried out these experiments, we should mention H.H. Kornhuber, while later ones were performed by B. Libet. Kornhuber's experiments indicated, among other things, that if a human being decides to perform an action, the electrical activity of the brain starts to change one to one-and-a-half seconds before he or she is conscious of having made the decision to act. It may be possible to understand this result from the nature of that which in a human being is, as suggested here, slightly extended in time, with a will acting slightly in the future on the brain, while conscious perceptions of these actions of the will are only possible if they are slightly in the past. This means that awareness of a decision, that is the possibility of thinking about it, could only come after the act of willing, when the act was no longer slightly in the future. In this way, a human could bridge a "gap" between the near future and the near past. This gap is in fact a form of the gap between causes and effects possessed by chaotic systems. A more detailed investigation is clearly required to see whether the explanation given here works. Let it be noted finally in this connection that Roger Penrose mentions in "Shadows of the Mind" as a possibility a similar explanation for the psychological experiments discussed here, involving a spread in time of consciousness.

To what extent the same situation could exist for other living organisms, is a more open question. It is not so clear whether corresponding beings extended in time acting on various chaotic processes, would need to have the same structure in time as that which is proposed here for humans. If the time structure is similar, the nature of what is associated with life, the "etheric" in certain occult traditions, might be closely associated with the nature of time.

Another aspect may also be mentioned before the end of this section. Human society is very complex and certainly chaotic and unpredictable, with a strong dependence on interactions between individuals, though this is difficult to prove mathematically. This is clear if we examine history and wonder how a very small event might have completely changed it. For instance, if an accident had badly injured the nineteenth century German statesman Bismarck in early childhood, Germany might not have needed a war with France in order to attain unification (the Franco-Prussian war of 1870), which led to the loss of Alsace-Lorraine by France, French desires for revenge, the First and Second World Wars and the tragic events which followed them. The idea of a very small event changing the course of history has been used in fiction. Smaller groups of people similarly may also be influenced by almost imperceptible events. Even the stock exchange appears to be sensitive to very small perturbations, which unfortunately can have an extremely large effect on present-day economies. Benoit Mandelbrot, who invented the expression "fractal" for the geometry associated with chaos, has emphasized the role of chaos in the mathematical description of what happens at the stock exchange. It is for such reasons that we may suppose that various sorts of other beings, who are not directly perceived by the senses, may be able to act within groups of people. In fact, Rudolf Steiner, like other spiritual teachers, speaks of both beneficial and harmful invisible beings which act in the world, including some which act in human society. Rudolf Steiner uses the names of angels and archangels, which are also known to Judeo-Christian tradition. The presence of such invisible beings is evident in rather subtle ways.

3. Is there a soul content in the domain of pure ideas?

Reasons have just been given suggesting the possible existence of beings which have a component extended in time. We may wonder whether beings can also exist which are completely outside time. The existence of such beings might be expected to be related to a behavior which other beings could neither completely predict nor completely control. In fact as we saw at the end of the last chapter, a sort of "indeterminacy" exists even in mathematics, in the realm of eternal ideas outside time, thus at least suggesting the existence there of separate beings! The great monotheistic religions state that God is outside time; the question is whether we can see real indications for the existence of other beings outside time. In addition would such eternal beings possess something corresponding to the three soul abilities?

This question can be stated in another way. Indications have been found for the presence of soul in physics, that is of Popper's and Penrose's second world of mental experience within their first world of physical states. Do there then also exist indications for the presence of soul in their third world, that is in that of Penrose's third world of pure ideas, which includes the ideas of mathematics?

Let us start our present considerations with the relationship between the mathematician and the mathematical concepts which he or she studies. What is involved is the relationship of a human being with a part of the world of eternal ideas. The mathematician can discover something about certain aspects of mathematics, but if he or she tries to apply the discovery to prove something else, the mathematical contents or "objects" studied will "resist" this being done. In fact, certain mathematical statements such as Fermat's last theorem mentioned in chapter 3, are very simple. If such a theorem is stated as a hypothesis, one does not have to be a great mathematician to understand it; however the proof can be extremely difficult. There is, as we saw, no standard mechanical procedure to prove all theorems, or even to know whether certain theorems are provable. In order to prove a theorem a mathematician must know about other relevant theorems as well as having the ability to act in the world of mathematical ideas, that is to use will power. Once the theorem is proved, its truth is known in addition to previously proved theorems, and the mathematician is satisfied. Again contentment or happiness equals knowledge times an ability to act. Therefore the mathematician needs soul abilities in order to overcome the resistance of the objects of mathematics. This implies that mathematical ideas, including numbers, are real and not just a human invention. The very great, if not the greatest of Greek philosophers, Plato, considered pure ideas to be real and what is perceived by the senses to be imperfect reflections of these ideas. Many if not most mathematicians (but very few contemporary philosophers of mathematics) are "Platonists"; they believe in the reality of what they study.

The reasoning used up to now does not however directly throw light on the question as to whether the pure ideas of mathematics themselves possess something corresponding to the soul abilities, nor even whether they actually resist each other. This question is less easy to investigate than that of the relation of a mathematician to mathematics. What can be stated, however, is that the fact that it can be impossible to prove a theorem from any other known theorem, without one even being able to prove this characteristic, as we saw in section 7 of chapter 3, appears to indicate a great "distance" between different aspects of mathematics which contain the proofs of different theorems. A mathematical statement is not "dominated" by other "far away" statements. As noted in that section, at one time people wondered whether Fermat's last theorem was provable. One might think of such a "distance" and "lack of domination" as revealing a kind of resistance between these different aspects of mathematics.It is then this resistance which must be overcome by the will of the mathematician, who wishes to use what he or she already knows about certain aspects of mathematics to prove something which can only be done by understanding other aspects of mathematics. What could be the soul content of what then appears to be a resistance between different aspects of mathematics and of associated beings, needs however to be investigated further. Let it be noted in this connection that various soul qualities have been associated with numbers in spiritual traditions at least since the time of the ancient Greek teacher Pythagoras. The book written by the author's father mentioned in the preface is a more modern approach to this concept.

The ideas of mathematics are of course not the only eternal ideas which exist. Abstract words such as, good, beauty, love, wisdom, freedom, happiness, desire, selflessness and selfishness, represent ideas which are very hard to define. In fact a dictionary will define a word in terms of other words and it is possible by looking at the definition of the words used in the definition of the original word to find again the original word! In this way the attempt to understand the meaning of a word can lead one around in circles... In any case understanding what an abstract word may mean, what the ideas behind it are, is a task for the philosopher; such ideas will resist being understood as the ideas and theorems of mathematics resist a mathematician. This again suggests the presence of conscious beings who are connected with ideas of this kind.

The question of whether universal ideas or "universals" exist independently of individual objects (or the bodies of living things when living organisms are considered) whose nature and properties are describable using universals, was the subject of a great philosophical debate in Europe during the middle ages. An example of this type of question is: does happiness exist by itself or only because individual human beings and animals are happy? The "realists" believed in the real existence of universals independently of individual objects, while for the nominalists following Roscelin, they were only words.

The contents of the third world of Penrose can be seen to correspond to the spirit and to one or more eternal beings of the spirit. This world would be a world where the basic constituents of the other two worlds or their archetypes exist. We may expect that at least many of these constituents or rather separate beings are far beyond what can be grasped by ordinary present-day human thinking. Such archetypes were perceived by the spiritual experiences of, for example, Rudolf Steiner. In this framework the ideas of mathematics may be thought to contain the least "indeterminacy". Mathematical proof works in very many situations; it is only in the twentieth century that limits have been found to the power of mathematics. This is similar to what happens in physics; many properties and events are predictable in what on the human scale appears to be the almost "dead" processes of physics. It is therefore not surprising that almost "dead" mathematics with relatively little indeterminacy, was very successfully applied to almost "dead" physics, which has also relatively little indeterminacy. The relation of mathematics - and the discovery of new concepts in general - to the spirit and to spiritual teachings can be seen in another way. Great discoveries tend to be made following a certain sequence of events (described in the already mentioned book "The Quark and the Jaguar" by Murray Gell-mann). The nineteenth century German physicist Herman von Helmholtz stated that the birth of a new idea needed three stages -saturation, incubation and enlightenment. Murray Gell-mann describes the first stage as one of filling oneself with the difficulty of a problem and making attempts to overcome it. During the second stage conscious thinking becomes useless,even though the problem is still within oneself all the time. One might think that in the second stage the problem is still tackled unconsciously, or at least according to the interpretation of the unconscious given in the previous section of this chapter, by other beings with whom the human being is in contact. In the third stage a solution suddenly appears, while one can be doing something which is completely different. This is a sudden enlightenment or illumination. The French mathematician Henri Poincaré added a fourth stage, that of verifying that the solution really was correct. Another French mathematician, J. Hadamard, studied how mathematical discoveries were made.

This process in the discovery of new concepts, including those of mathematics, can be compared with the process of spiritual development of a human being who wishes to experience spiritual worlds, which cannot be perceived through the senses, as described by Rudolf Steiner in the book "An Outline of Esoteric Science" (Anthroposophic Press 1997). He describes several stages of perception of "invisible worlds", leading to what is really spiritual perception. These stages are "imagination", "inspiration" and "intuition". The stage of "imagination" (not to be confused with "imagining" unreal things) is reached through various exercises involving the formation of mental images of things not perceived by the senses, followed by concentration on these images. In this stage spiritual realities appear through living images, but are not directly perceived. The stage of inspiration where spiritual realities are perceived is attained by making the images disappear, while retaining only the effort made to produce these images. In that stage truths appear immediately without it being necessary to think about what is observed. The following stage of intuition, that is of direct contact with spiritual beings, is also reached through the effort in making the images of imagination disappear.

It might appear that the process of performing exercises to reach the stage of imagination corresponds to the filling of oneself with a scientific or mathematical problem, or what Helmholtz called saturation. The "inspiration", or perhaps even the "intuition" of the solution, follows a stage when awareness of the problem disappears from consciousness. Poincaré's fourth stage might then be related to living in a world of spiritual realities. However, we must remember that the spiritual experience described by spiritual teachers like Rudolf Steiner goes far beyond the processes of scientific and mathematical discovery. As we have mentioned, spiritual archetypes may be far beyond what can be grasped by ordinary present-day human thinking.

4. Comments on the concept of "energy"

At this point it may be useful to consider in more detail the concept of energy. Its role in pre-twentieth century physics was discussed in section 2 of chapter 2. The word "energy" is often used by certain spiritual movements and is frequently believed to be directly connected to spiritual realities. Some speak of different forms of energy including "spiritual" energy. Unorthodox types of medicine speak in addition about "energies of the body". We shall look at the concept of energy in physics whereby we can see how much of what is said on this subject is the result of unclear thinking and is in some ways materialistic.

Let us start by looking at the origin of the word. According to the French "Robert" etymological dictionary ("Dictionaire de l'etymologie du francais" by Jacqueline Picoche, 1973), the word energy (energie in French) is derived from an indo-european root which means to act. This root "werg" or "worg" is at the origin of the English word "work" and the German word "werk". In the development which led to the word "energy", we find the Greek word "ergein", which means an acting force. For the great Greek philosopher Aristotle "ergein" was contrasted with "dynamis", which is a possibility of action. We can therefore see that the word energy is derived from the idea of action which, we should remember from our previous discussions, is not the only defining aspect of the world.

In elementary physics a fixed amount of energy can, in principle, be converted to mechanical "work", that is, enable an object to move against a force which is acting on it. In fact there exist many forms of energy in physics such as light, heat and electrical energy. The principle of the "conservation of energy", mentioned in chapter 2, states that one form of energy can in principle (not always in practice) be converted to another form; a fixed quantity of one form is convertible to a fixed quantity of the other. Einstein's famous equation E = mc2, mentioned in chapter 3, states that even the mass of a body can be converted to other forms of energy. The energy of physics is the ability to act in the realm of physics or, in the words of the "Encyclopedic Dictionary of Physics" (Pergamon Press 1961), "energy may be defined as the capacity for producing effects".

However, the perception of different forms of energy, that is the inner experience of them by human beings, is not at all the same. Though the conservation of energy is accurate when numerical measurements of energy are made, it does not describe the human experiences associated with different forms of energy.

The total quantity of energy available in a certain form may often be the appropriate ability to act in the type of physics relevant to the human scale, as mentioned in section 2 of this chapter, where a possible action of beings extended in time on chaotic systems was considered. However we saw that this is not the case in situations where the Heisenberg indeterminacy principle needs to be taken into consideration; there in the sphere of quantum physics it is the accuracy with which a fixed quantity of energy can be applied, which appears to be equal to the ability to act. It is in such ways that the ability to act need not be the same in different situations. The ability to act is almost certainly not the available quantity of physical energy, nor the accuracy with which this energy is applied when a human body is cured of an illness. It is therefore better not to call all forms of ability to act "energy".

The role of the total quantity of energy for conscious beings acting on physical chaotic systems can be compared with that of something which intervenes when human beings have relations with each other. Money plays a similar role to that of energy in relations between people and groups of people!. Its possession gives human beings the ability to act. Money can also be expressed in the forms of different currencies used in different countries, each of which can be converted to another through an exchange rate. There is then something corresponding to the conservation of energy when one currency is converted to another one, though the rate of conversion, that is the exchange rate, is not constant. In any case different currencies are not equivalent; the relative prices of different products are not the same in different countries, these prices depending on the economy and culture of a particular country. This reminds us of the fact that human perceptions of different forms of energy are not the same. This suggests that energy is not necessarily spiritual; in certain physical situations it plays the role played by money in human society. I must admit that I am tempted to connect the present excessive concern with energy in certain circles with the excessive preocupation with money at the present time in most of the world. Indeed certain individuals who pretend to be "gurus" are especially interested in the money they earn through their activities....

5. Is there a kind of trinity behind the various conscious beings?

There is a further step which may be taken if many different sorts of conscious beings exist. The idea of the existence of a divine trinity behind the phenomena of the world is present in more than one culture. Hinduism speaks of three supreme gods: Brahma, who creates, Vishnu who maintains and Shiva who destroys. We should note that such a concept is closely related to the time trinity of past, present and future, although it is not quite the same. The creation of an object which exists in the present occured in the past. The object was maintained in the past after being created, is being maintained in the present and will be maintained in the future, until it is destroyed. However, three gods of this sort cannot be thought of as existing separately in the world of eternal ideas, which is neither created nor destroyed.

The Greek philosopher Heraclitus, mentioned in the last section of chapter 2, asserted that there were three fundamental principles in the world. They were "Theon", a kind of divinity, the "Logos", which can be thought of as the words or language of the Universe and of philosophers, while the last principle was perpetual change. It may be noted that the English word "logic" is based on the idea of the Logos. A few centuries after Heraclitus, the Logos was a basic concept in stoic philosophy. The author of St. John's gospel quoted the same principle of Heraclitus in the prologue at the start of the gospel, saying that the Logos or word, which was in the beginning, was made flesh and lived among human beings in the form of Jesus Christ. Thus one of the basic doctrines of Christianity is related to what had been previously taught by Heraclitus. It might be possible to extrapolate such an interpretation; in that case, Theon would represent the Father and perpetual change the Holy Spirit. It seems however that Heraclitus was influenced, at least to a certain extent, by teachings of the Greek mysteries. His three principles might indeed also be related to Rudolf Steiner's stages of spiritual perception, briefly described in section 3 of this chapter. Perpetual change is then the basic property of the living images of the stage of imagination, while the direct perception of truth is attained in the stage of inspiration. Direct contact with spiritual beings in the stage of intuition can then be related to perception of the divine. It may therefore even be possible to connect Rudolf Steiner's stages of perception with the Trinity.

It is perhaps dangerous to try to relate a divine trinity to what may be discovered through scientific research. There is a story about the great teacher Alain de Lille who was called the "Doctor Universalis" and who lived in the twelfth century. He was walking along the banks of the Seine in Paris in 1168, the day before he was due to talk about the Trinity, when he saw a small boy trying to make all the water of the Seine enter a small hole. Alain de Lille told the boy that this was impossible, whereupon the boy replied that it was also impossible to speak about the Trinity. According to the story, Alain de Lille was so shocked that he abandoned teaching the following day.

In order to proceed further, we shall again look at quantum physics. We saw in chapter 3 that quantum physics can only describe the different possibilities of what may happen; one of the possibilities is realized by "wave function collapse". It is in this way that the occurrence of real events in time on the human scale is related to the quantum world. We saw that this phenomenon is now understood by many physicists through the interaction of small systems obeying the laws of quantum physics with a very large "environment", that is, with the outside world, which is indeed virtually infinite when compared with the quantum system. This process is usually extremely rapid. We can think of each interaction or meeting of all the small quantum systems which exist with particles of the environment as being a kind of "death" process of a host of possibilities possessed by the beings associated with quantum physics, whose existence was proposed in the first section of this chapter. This is very similar to the way the human experience of the present was described as a sort of death of the possibilities of acting on the future in the last section of chapter 2. In interactions the particle-like properties of the components of a quantum system should be taken into account, the particle needs to be in a certain region of space near another particle if it is to interact. After an interaction with the environment many different possibilities again appear, almost all of which will again die in the next interaction. It is in such a way that interaction with the environment makes us think of a continual process of birth, followed by death associated with confinement to a small region of space, which is followed in its turn by re-birth. The world on the human scale then appears to make the quantum world of "sub-nature" die when it interacts with the human world.

Interaction or meetings occur when the path of a particle with quantum properties crosses the paths of other particles belonging to the environment. It is possible to picture this through Christian symbolism. We may view the death process of the quantum world as a process of continual "crucifixion", as a quantum system is crossed by something belonging to the environment. Beings of sub-nature are crossed or met by the large scale world. In this way real events can be produced in time and the rhythm of the succession of these events is a language or "logos". The original world of possibilities is that of the Father, death is connected with the Son and the re-birth of possibilities with the Holy Spirit. What is associated with the Holy Spirit then plays the role of Father in later interactions. This can be directly connected with the spiritual stream of the Rosecrucians and the way they related to the Trinity, involving birth in the Father, death in Christ and re-birth in the Holy Spirit:

Ex Deo nascimur
In Christo Morimur
Per Spiritum Sanctum reviscimus

In section 2 of this chapter it was proposed that beings other than those connected with the Heisenberg uncertainty principle act in the large scale world. Such beings are also associated with what is unpredictable. In this case when two such beings meet the result of the meeting must be unpredictable. Only one of the many possibilities of interaction between them will become real; the other possibilities die. Death is then a necessary part of the realization of possibilities in the partly unpredictable universe in which we live. Without death there could be no re-birth. The Son or cosmic Christ may, following what has been said, be seen to be present in meetings. This way of understanding what happens in the universe need not and indeed does not, at first sight, suggest the existence of an all-powerful God.

It may be possible to conceive of the Trinity as consisting of three (or one) independent consciousness(es), which manifest themselves (itself) through what is accomplished by all the different conscious beings of the universe, without controlling all of what is performed by those other conscious beings.

What has been said here can be stated in another way through Rudolf Steiner's "Foundation Stone" meditation. This is the basic meditation for members of the Anthroposophical Society, founded by him. The idea of the Trinity of Father, Son and Holy Spirit is fundamental in this meditation. The second part is directy connected with the idea of the environment, though the meditation was given to members of the Anthroposophical Society in 1923, many decades before physicists thought of linking the environment to quantum physics:

For the will of Christ rules in the periphery,
Blessing the soul in cosmic rhythms..

Denn es waltet der Christus-Wille im Umkreis
In den Weltenrhythmen Seelen-begnadend..

The human being, unlike lower beings, is self-conscious; he or she can say "I am". In this way it is possible for a human to meet his or her inner self. It is in such a manner that the meeting with the inner self may also be connected with the Son or Christ. Further consideration of this question is outside the scope of this book.

Let it be emphasized that the role of the Trinity proposed here does not "prove" the doctrines and dogmas of the different churches concerning the historical incarnation of Christ. In any case the aim here is not to make the reader believe any particular doctrine or dogma and even less to make him or her submit to the hierarchy of a church.

© 2000 Michael Friedjung

Michael Friedjung was born in 1940 in England of Austrian refugee parents who had escaped from the Nazis. He was already deeply interested in science at eleven years of age, and uniting science and spirituality eventually became his aim. He studied astronomy, obtaining a Bsc in 1961 and his Phd in 1965. After short stays in South Africa and Canada, he went to France in 1967 on a post-doctoral fellowship and later was appointed to a permanent position at the French National Center for Scientific Research (CNRS) in 1969, where he is now Research Director. After living with the contradictions between official science and spiritual teachings, he began to see solutions to at least some of the problems, which are described in this book.

E-mail: [email protected]

The last chapter of "Putting Soul into Science" will appear in the next issue of the SouthernCross Review. To read the previous chapters, click here: Back Issues

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