In this diagram the element Earth appears as a combination of the qualities Dry and Cold; Water of Cold and Moist; Air of Moist and Warm; Fire of Warm and Dry. As a result, Earth and Fire, besides representing opposite poles, are also neighbours in the diagram. Here we encounter a picture characteristic of all earlier ways of looking at the world: the members of a system of phenomena, when ranked in due order of succession, were seen to turn back on themselves circle-wise - or, more precisely, spiral-wise.

In what way do the qualities dry and moist form a polarity of the second order, and how do they represent the chemical polarity characteristic of sulphur and phosphorus as well as all the other secondary polarities dealt with in this book? To understand this we must submit the couple dry-moist to the same scrutiny as we applied to cold and warm in our earlier discussion of the four elements.

It lies in the nature of things that we instinctively associate these qualities with the solid and liquid states of matter respectively. This certainly agrees with the diagram given above, where the elements Earth and Water are distinguished precisely by their connexion with these two characteristics. Yet, in addition to this, the qualities dry and moist are found to be characteristic also of Fire and Air respectively, though with the difference that they are linked not with the quality cold, as in the case of the lower elements, but with the quality warm. So we see that the concepts Dry and Moist, as they lived in the old picturing of them, mean a good deal more than we understand by them to-day.

That these two respective attributes do not belong exclusively to the solid and the liquid states of matter can be seen at once by observing the different reactions of certain liquids to a solid surface which they touch. One need only recall the difference between water and quicksilver. If water runs over a surface it leaves a trail; quicksilver does not. Water clings to the side of a vessel; again, quicksilver does not. A well-known consequence of this difference is that in a narrow tube the surface of the liquid - the so-called meniscus - stands higher at the circumference than at the centre in the case of water; with quicksilver it is just the reverse. In the sense of the two qualities, dry and moist, water is a 'moist' liquid; quicksilver a 'dry' one. On the other hand, the quality of moistness in a solid substance appears in the adhesive power of glue.

Let us now see how, in accordance with the scheme given in Fig. 5, the four qualities in their respective combinations constitute the four elements. From the description we shall give here it will be realized how little such ancient schemes were based on abstract thoughts, and how much they were read from the facts of the world. Moreover, a comparison with our description of the four stages of matter, given in the previous chapter, would show how far the conceptual content of the old doctrine covers the corresponding facts when they are read by the eye of the modern reader in nature, notwithstanding the changes nature has undergone in the meantime.

The element Fire reveals its attributes of warm and dry in a behaviour which combines a tendency to dynamic expansion with a disinclination to enter into lasting combination with the other elements. Correspondingly, the behaviour of the element Earth unites a tendency to contraction with an inclination to fall out of conjunction with the other elements. Thus the attribute, dry, belongs equally to pure flame and sheer dust, though for opposite reasons. Distinct from both these elements are the middle elements Water and Air; with them the attribute, moist, comes to expression in their tendency both to interpenetrate mutually and to absorb their neighbours - the liquid element absorbing solid matter and the aeriform element taking up heat. What distinguishes them is that water has a 'cold' nature, from which it gains its density; while air has a 'warm' nature, to which it owes its tendency to expand.

In the most general sense, the quality 'moist' applies wherever two different entities are drawn into some kind of intimate relationship with one another; 'dry' applies where no such relationship prevails. Seen thus, they reveal themselves as a true polarity of the second order, for they describe the relationship between two entities which already exists, and, in the case of the four elements, are themselves a polarity. As such, they characterize precisely those polar relationships of the second order on which the threefold structure of man, we found, is based. For from the physical, as much as from the superphysical aspect the nerve-system represents the 'dry' part, and the metabolic system the 'moist' part of man's being. The same is true of the relationship between the soul and the surrounding world at both poles. Here we have the antithesis between the 'dry' onlooker-relationship of the intellect to the world, conceived as a mere picture whose essence remains outside the boundaries of the soul, and the 'moist' intermingling of the will-force with the actual forces of the world.

*

It needs no further explanation to realize that sulphur and phosphorus, by the way in which levity and gravity are interlinked in each of them, are representatives of these very qualities 'moist' and 'dry'. As such they are universally active bearers of these qualities in every realm of nature's varied activities, as their physical presence in such cases confirms. Consequently, sulphur is found in the protein-substances of the human body wherever they are bearers of metabolic processes, while the presence of phosphorus is characteristic of the nerves and bones. (Although its full significance will become clear to us only later, the fact may here be mentioned that the composition of the bone-material in the different parts of man's skeleton, as scientific analysis has shown, is such that the content of phosphate of calcium in proportion to carbonate of calcium is higher in all those parts which are spherically shaped, such as the upper parts of the skull and the upper ends of the limb-bones.)

In particular the plant reveals clearly the functional significance of phosphorus as the bearer of the quality 'dry'. For its healthy growth the plant needs the quality 'dry' in two places: at the root, where it unites with the element earth, and in the flower, where it opens itself to the fire element. Root and flower as distinct from the middle parts of the plant are both 'dry' formations. In a still higher degree this applies to the seed, which must separate itself from the mother plant to produce a separate new organism. All these are functions in the plant which, as was mentioned in the last chapter, require phosphorus for their healthy performance.

Our examination of phosphorus and sulphur from the functional point of view throws light also on their effect on the alternating conditions of waking and sleeping, necessary for the life of the higher organisms. This rhythmic change, which affects especially the nervous system, is an alternation between the qualities dry and moist. Disturbance of this alternation in one direction or the other makes it difficult for the organism to react in full wakefulness or normal sleep. It follows that treatment with phosphorus or sulphur in suitable preparations, according to the nature of the disturbance, can be beneficial.

If we study the functional properties of such substances we see that they can teach us a rational understanding of therapeutic practices, which otherwise must remain mere results of trial and error. The same applies to phosphorus and sulphur treatment in cases where in the functionally 'dry' bone system or in the functionally 'moist' metabolic system of the organism the wrong quality predominates. If the bones remain too 'moist' there is a tendency to rickets; against this, certain fish-oils are a well-known remedy on account of their highly phosphoric nature. Conversely, the application of sulphur can help where weakness of the metabolic forces produces rheumatic or gouty sediments in parts of the body whose function is to serve by their mobility the activities of the will. In this case the abnormal predominance of the quality 'dry' can be counteracted by the medical application of sulphur.

*

Having observed the action of sulphur and phosphorus in the laboratory and in living organisms, we will now turn to phenomena of a macrotelluric nature which reveal the participation of sulphur and phosphorus. There, sulphur points unmistakably to the earth's volcanism. It is a fact that, wherever mineral sulphur occurs in the earth, there we find a spot of former or present volcanic activity. Similarly, there is no such spot on the earth without sulphur being present in one form or another. Hence the name Solfatara for the fumarole described in Chapter IX.

Once again it is the Solfatara which offers us a phenomenon, this time in connexion with the special role sulphur plays in its activities, which, regarded with the eye of the spirit, assumes the significance of an instance 'worth a thousand'.

In spite of the very high temperature of the sulphurous fumes emitted from various crevices on the edge of the Solfatara, it is possible, thanks to the complete dryness of the fumes, to crawl a little way into the interior of these crevices. Not far away from the opening of the crevice, where the hot fumes touch the cooler rock surface, one is met by a very beautiful spectacle - namely, the continual forming, out of nothing as it seems, of glittering yellow sulphur crystals, suspended in delicate chains from the ceiling.

In this transformation of sulphurous substance from a higher material state, nearer to levity, to that of the solid crystal, we may behold an image of the generation of matter. For every physical substance and, therefore, every chemical element, exists originally as a pure function in the dynamic processes of the universe. Wherever, as a result of the action of gravity, such a function congeals materially, there we meet it in the form of a physical-material substance. In the same sense, sulphur and phosphorus, in their real being, are pure functions, and where they occur as physical substances, there we meet these functions in their congealed state.

One of the characteristics of the volcanic regions of the earth is the healing effect of substances found there. Fango-mud, for instance, which was mentioned in the last chapter, is a much-used remedy against rheumatism. This is typical of functional sulphur. We may truly characterize the earth's volcanism as being qualitatively sulphurous. It is the sulphur-function coming to expression through a higher degree of 'moistness' in the relationship between gravity and levity which distinguishes volcanic regions from the rest of the otherwise 'dry' earth's crust.

*

To develop a corresponding picture of the function of phosphorus, we must try to find the macrotelluric sphere where this function operates similarly to that of sulphur in volcanism. From what has been said in the last chapter it will be evident that we must look to the atmosphere, as the site of snow-formation. It is this process which we must now examine more closely.

In the atmosphere, to begin with, we find water in a state of vapour, in which the influence of the terrestrial gravity-field is comparatively weak. Floating in this state, the vapour condenses and crystallization proceeds. Obeying the pull of gravity, more and more crystals unite in their descent and gradually form flakes of varying sizes. The nearer they come to earth, the closer they fall, until at last on the ground they form an unbroken, more or less spherical, cover.

Imagine a snow-covered field glistening in the sun on a clear, quiet winter's day. As far as we can see, there is no sign of life, no movement. Here water, which is normally fluid and, in its liquid state, serves the ever-changing life-processes, covers the earth in the form of millions of separate crystals shaped with mathematical exactitude, each of which breaks and reflects in a million rays the light from the sun (Plate V). A contrast, indeed, between this quiet emergence of forms from levity into gravity, and the form-denying volcanism surging up out of gravity into levity, as shown by the ever-restless activity of the Solfatara. As we found volcanism to be a macrotelluric manifestation of functional sulphur, we find in the process of snow-formation a corresponding manifestation of functional phosphorus.

In the formation of snow, nature shows us in statu agendi a process which we otherwise meet in the earth only in its finished results, crystallization. We may, therefore, rightly look upon snow-formation as an ur-phenomenon in this sphere of nature's activities. As such it allows us to learn something concerning the origin in general of the crystalline realm of the earth; and, vice versa, our insight into the 'becoming' of this realm will enable us to see more clearly the universal function of which phosphorus is the main representative among the physical substances of the earth.

It has puzzled many an observer that crystals occur in the earth with directions of their main axes entirely independent of the direction of the earthly pull of gravity. Plate VI shows the photograph of a cluster of Calcite crystals as an example of this phenomenon. It tells us that gravity can have no effect on the formation of the crystal itself. This riddle is solved by the phenomenon of snow-formation provided we allow it to speak to us as an ur-phenomenon. For it then tells us that matter must be in a state of transition from lightness into heaviness if it is to appear in crystalline form. The crystals in the earth, therefore, must have originated at a time when the relation between levity and gravity on the earth was different from what it is, in this sphere, to-day.

The same language is spoken by the property of transparency which is so predominant among crystals. One of the fundamental characteristics of heavy solid matter is to resist light - in other words, to be opaque. Exposed to heat, however, physical substance loses this feature to the extent that at the border of its ponderability all matter becomes pervious to light. Now, in the transparent crystal matter retains this kinship to light even in its solid state.

A similar message comes from the, often so mysterious, colouring of the crystals. Here again nature offers us an instance which, 'worth a thousand', reveals a secret that would otherwise remain veiled. We refer to the pink crystals of tourmaline, whose colour comes from a small admixture of lithium. This element, which belongs to the group of the alkaline metals, does not form coloured salts (a property only shown by the heavier metals). If exposed to a flame, however, it endows it with a definite colour which is the same as that of the lithium-coloured tourmaline. Read as a letter in nature's script, this fact tells us that precious stones with their flame-like colours are characterized by having kept something of the nature that was theirs before they coalesced into ponderable existence. In fact, they are 'frozen flames'.

It is this fact, known from ancient intuitive experience, which prompted man of old to attribute particular spiritual significance to the various precious stones of the earth and to use them correspondingly in his rituals.

Crystallization, seen thus in its cosmic aspect, shows a dynamic orientation which is polarically opposite to that of the earth's seismic activities. Just as in the latter we observe levity taking hold of ponderable matter and moving it in a direction opposite to the pull of gravity, so in crystallization we see imponderable matter passing over from levity into gravity. And just as we found in volcanism and related processes a field of activity of 'functional sulphur', so we found in snow-formation and related processes a field of activity of 'functional phosphorus'. Both fields are characterized by an interaction between gravity and levity, this interaction being of opposite nature in each of them.

Here, again, sulphur and phosphorus appear as bearers of a polarity of the second order which springs from the two polarically opposite ways of interaction between the poles of the polarity of the first order: levity-gravity.

*

As in man there is a third system, mediating between the two polar systems of his organism, so between sulphur and phosphorus there is a third element which in all its characteristics holds a middle place between them and is the bearer of a corresponding function. This element is carbon.

To see this we need only take into consideration carbon's relationship to oxidation and reduction respectively. As it is natural for sulphur to be in the reduced state, and for phosphorus to be in the oxidized state, so it is in the nature of carbon to be related to both states and therefore to oscillate between them. By its readiness to change over from the oxidized to the reduced state, it can serve the plant in the assimilation of light, while by its readiness to make the reverse change it serves man and animal in the breathing process. We breathe in oxygen from the air; the oxygen circulates through the blood-stream and passes out again in conjunction with carbon, as carbon dioxide, when we exhale. In the process whereby the plants reduce the carbon dioxide exhaled by man and animal, while the latter again absorb with their food the carbon produced in the form of organic matter by the plant, we see carbon moving to and fro between the oxidized and the reduced conditions.

Within the plant itself, too, carbon acts as functionary of the alternation between oxidation and reduction. During the first half of the year, when vegetation is unfolding, there is a great reduction process of oxidized carbon, while in the second half of the year, when the withering process prevails, a great deal of the previously reduced carbon passes into the oxidized condition. As this is connected with exhaling and inhaling of oxygen through carbon, carbon can be regarded as having the function of the lung-organ of the earth. Logically enough, we find carbon playing the same role in the middle part of the threefold human organism.

Another indication of the midway position of carbon is its ability to combine as readily with hydrogen as with oxygen, and, in these polar combinations, even to combine with itself. In this latter form it provides the basis of the innumerable organic substances in nature, and serves as the 'building stones' of the body-substances of living organisms. Among these, the carbohydrates produced by the plants show clearly the double function of carbon in the way it alternates between the states of starch and sugar.

When the plant absorbs through its leaves carbonic acid from the air and condenses it into the multiple grains of starch with their peculiar structure characteristic for each plant species, we have a biological event which corresponds to the formation of snow in the meteorological realm. Here we see carbon at work in a manner functionally akin to that of phosphorus. Sugar, on the other hand, has its place in the saps of the plants which rise through the stems and carry up with them the mineral substances of the earth. Here we find carbon acting in a way akin to the function of sulphur.

This twofold nature of carbon makes itself noticeable down to the very mineral sphere of the earth. There we find it in the fact that carbon occurs both in the form of the diamond, the hardest of all mineral substances, and also in the form of the softest, graphite. Here also, in the diamond's brilliant transparency, and in the dense blackness of graphite, carbon reveals its twofold relation to light.

In Fig. 6 an attempt has been made to represent diagrammatically the function of Carbon in a way corresponding to the previous representation of the functions of Sulphur and Phosphorus.

*

By adding carbon to our observations on the polarity of sulphur and phosphorus we have been led to a triad of functions each of which expresses a specific interplay of levity and gravity. That we encounter three such functions is not accidental or arbitrary. Rather is it based on the fact that the interaction of forces emanating from a polarity of the first order, produces a polarity of the second order, whose poles establish between them a sphere of balance.

Through our study of levity and gravity in the matter-processes of the earth, a perspective thus opens up into a structural principle of nature which is actually not new to us. We encountered it at the very beginning of this book when we discussed the threefold psycho-physical order of man's being.

In the days of an older intuitive nature-wisdom man knew of a basic triad of functions as well as he knew of the four elementary qualities. We hear a last echo of this in the Middle Ages, when people striving for a deeper understanding of nature spoke of the trinity of Salt, Mercury and Sulphur. What the true alchemists, as these seekers of knowledge called themselves, meant by this was precisely the same as the conception we have here reached through our own way of studying matter ('Salt' standing for 'functional phosphorus', 'Mercury' for 'functional carbon'). Only the alchemist's way was a different one.

This is not the place to enter into a full examination of the meaning and value of alchemy in its original legitimate sense (which must not be confused with activities that later on paraded under the same name). Only this we will say - that genuine alchemy owes its origin to an impulse which, at a time when the onlooker-consciousness first arose, led to the foundation of a school for the development of an intuitive relationship of the soul with the world of the senses. This was to enable man to resist the effects of the division which evolution was about to set up in his soul-life - the division which was to give him, on the one hand, an abstract experience of his own self, divorced from the outer world, and on the other a mere onlooker's experience of that outer world. As a result of these endeavours, concepts were formed which in their literal meaning seemed to apply merely to outwardly perceptible substances, while in truth they stood for the spiritual functions represented by those substances, both within and outside the human organism.

Thus the alchemist who used these concepts thought of them first as referring to his own soul, and to the inner organic processes corresponding to the various activities of his soul. When speaking of Salt he meant the regulated formative activity of his thinking, based on the salt-forming process in his nervous system. When he spoke of Mercury he meant the quickly changing emotional life of the soul and the corresponding activities of the rhythmic processes of the body. Lastly, Sulphur meant the will activities of his soul and the corresponding metabolic processes of the body. Only through studying these functions within himself, and through re-establishing the harmony between them which had been theirs in the beginning, and from which, he felt, man had deviated in the course of time, did the alchemist hope to come to an understanding of their counterparts in the external cosmos.

Older alchemical writings, therefore, can be understood only if prescriptions which seem to signify certain chemical manipulations are read as instructions for certain exercises of the soul, or as advices for the redirection of corresponding processes in the body. For instance, if an alchemist gave directions for a certain treatment of Sulphur, Mercury and Salt, with the assertion that by carrying out these directions properly, one would obtain Aurum (gold), he really spoke of a method to direct the thinking, feeling and willing activities of the soul in such a way as to gain true Wisdom.1

*

As in the case of the concepts constituting the doctrine of the four elements, we have represented here the basic alchemical concepts not only because of their historical significance, but because, as ingredients of a still functional conception of nature, they assume new significance in a science which seeks to develop, though from different starting-points, a similar conception. As will be seen in our further studies, these concepts prove a welcome enrichment of the language in which we must try to express our readings in nature.

1 Roger Bacon in the thirteenth, and Berthold Schwartz in the fourteenth century, are reputed to have carried out experiments by mixing physical salt (in the form of the chemically labile saltpetre) with physical sulphur and - after some initial attempts with various metals - with charcoal, and then exposing the mixture to the heat of physical fire. The outcome of this purely materialistic interpretation of the three alchemical concepts was not the acquisition of wisdom, or, as Schwartz certainly had hoped, of gold, but of ... gunpowder!

CHAPTER XII

Space and Counter-Space

With the introduction, in Chapter X, of the peripheral type of force-field which appertains to levity as the usual central one does to gravity, we are compelled to revise our conception of space. For in a space of a kind we are accustomed to conceive, that is, the three-dimensional, Euclidean space, the existence of such a field with its characteristic of increasing in strength in the outward direction is a paradox, contrary to mathematical logic.

This task, which in view of our further observations of the actions of the levity-gravity polarity in nature we must now tackle, is, however, by no means insoluble. For in modern mathematics thought-forms are already present which make it possible to develop a space-concept adequate to levity. As referred to in Chapter I, it was Rudolf Steiner who first pointed to the significance in this respect of the branch of modern mathematics known as Projective Geometry. He showed that Projective Geometry, if rightly used, carries over the mind from the customary abstract to a new concrete treatment of mathematical concepts. The following example will serve to explain, to start with, what we mean by saying that mathematics has hitherto been used abstractly.

One of the reasons why the world-picture developed by Einstein in his Theory of Relativity deserves to be acknowledged as a step forward in comparison with the picture drawn by classical physics, lies in the fact that the old conception of three-dimensional space as a kind of 'cosmic container', extending in all directions into infinity and filled, as it were, with the content of the physical universe, is replaced by a conception in which the structure of space results from the laws interrelating this content. Our further discussion will show that this indeed is the way along which, to-day, mathematical thought must move in order to cope with universal reality.

However, for reasons discussed earlier, Einstein was forced to conceive all events in the universe after the model of gravity as observable on the earth. In this way he arrived at a space-structure which possesses neither the three-dimensionality nor the rectilinear character of so-called Euclidean space - a space-picture which, though mathematically consistent, is incomprehensible by the human mind. For nothing exists in our mind that could enable us to experience as a reality a space-time continuum of three dimensions which is curved within a further dimension.

This outcome of Einstein's endeavours results from the fact that he tried by means of gravity-bound thought to comprehend universal happenings of which the true causes are non-gravitational. A thinking that has learnt to acknowledge the existence of levity must indeed pursue precisely the opposite direction. Instead of freezing time down into spatial dimension, in order to make it fit into a world ruled by nothing but gravity, we must develop a conception of space sufficiently fluid to let true time have its place therein. We shall see how such a procedure will lead us to a space-concept thoroughly conceivable by human common sense, provided we are prepared to overcome the onlooker-standpoint in mathematics also.

Einstein owed the possibility of establishing his space-picture to a certain achievement of mathematical thinking in modern times. As we have seen, one of the peculiarities of the onlooker-consciousness consists in its being devoid of all connexion with reality. The process of thinking thereby gained a degree of freedom which did not exist in former ages. In consequence, mathematicians were enabled in the course of the nineteenth century to conceive the most varied space-systems which were all mathematically consistent and yet lacked all relation to external existence. A considerable number of space-systems have thus become established among which there is the system that served Einstein to derive his space-time concept. Some of them have been more or less fully worked out, while in certain instances all that has been done is to show that they are mathematically conceivable. Among these there is one which in all its characteristics is polarically opposite to the Euclidean system, and which is destined for this reason to become the space-system of levity. It is symptomatic of the remoteness from reality of mathematical thinking in the onlooker-age that precisely this system has so far received no special attention.1

For the purpose of this book it is not necessary to expound in detail why modern mathematical thinking has been led to look for thought-forms other than those of classical geometry. It is enough to remark that for quite a long time there had been an awareness of the fact that the consistency of Euclid's definitions and proofs fails as soon as one has no longer to do with finite geometrical entities, but with figures which extend into infinity, as for instance when the properties of parallel straight lines come into question. For the concept of infinity was foreign to classical geometrical thinking. Problems of the kind which had defeated Euclidean thinking became soluble directly human thinking was able to handle the concept of infinity.

We shall now indicate some of the lines of geometrical thought which follow from this.

*

Let us consider a straight line extending without limits in either direction. Projective geometry is able to state that a point moving along this line in one direction will eventually return from the other. To see this, we imagine two straight lines a and b intersecting at P. One of these lines is fixed (a); the other (b) rotates uniformly about C. Fig. 7 indicates the rotation of b by showing it in a number of positions with the respective positions of its point of intersection with a (P1, P2. . .). We observe this point moving along a, as a result of the rotation of b, until, when both lines are parallel, it reaches infinity. As a result of the continued rotation of b, however, P does not remain in infinity, but returns along a from the other side. We find here two forms of movement linked together - the rotational movement of a line (b) on a point (C), and the progressive movement of a point (P) along a line (a). The first movement is continuous, and observable throughout within finite space. Therefore the second movement must be continuous as well, even though it partly escapes our observation. Hence, when P disappears into infinity on one side of our own point of observation, it is at the same time in infinity on the other side. In order words, an unlimited straight line has only one point at infinity.

It is clear that, in order to become familiar with this aspect of geometry, one must grow together in inward activity with the happening which is contained in the above description. What we therefore intend by giving such a description is to provide an opportunity for a particular mental exercise, just as when we introduced Goethe's botany by describing a number of successive leaf-formations. Here, as much as there, it is the act of 're-creating' that matters.

The following exercise will help us towards further clarity concerning the nature of geometrical infinity.

We imagine ourselves in the centre of a sphere which we allow to expand uniformly on all sides. Whilst the inner wall of this sphere withdraws from us into ever greater distances, it grows flatter and flatter until, on reaching infinite distance, it turns into a plane. We thus find ourselves surrounded everywhere by a surface which, in the strict mathematical sense, is a plane, and is yet one and the same surface on all sides. This leads us to the conception of the plane at infinity as a self-contained entity although it expands infinitely in all directions.

This property of a plane at infinity, however, is really a property of any plane. To realize this, we must widen our conception of infinity by freeing it from a certain one-sidedness still connected with it. This we do by transferring ourselves into the infinite plane and envisaging, not the plane from the point, but the point from the plane. This operation, however, implies something which is not obvious to a mind accustomed to the ordinary ways of mathematical reasoning. It therefore requires special explanation.

In the sense of Euclidean geometry, a plane is the sum-total of innumerable single points. To take up a position in a plane, therefore, means to imagine oneself at one point of the plane, with the latter extending around in all directions to infinity. Hence the journey from any point in space to a plane is along a straight line from one point to another. In the case of the plane being at infinity, it would be a journey along a radius of the infinitely large sphere from its centre to a point at its circumference.

In projective geometry the operation is of a different character. Just as we arrived at the infinitely large sphere by letting a finite sphere grow, so must we consider any finite sphere as having grown from a sphere with infinitely small extension; that is, from a point. To travel from the point to the infinitely distant plane in the sense of projective geometry, therefore, means that we have first to identify ourselves with the point and 'become' the plane by a process of uniform expansion in all directions.

As a result of this we do not arrive at one point in the plane, with the latter extending round us on all sides, but we are present in the plane as a whole everywhere. No point in it can be characterized as having any distance, whether finite or infinite, from us. Nor is there any sense in speaking of the plane itself as being at infinity. For any plane will allow us to identify ourselves with it in this way. And any such plane can be given the character of a plane at infinity by relating it to a point infinitely far away from it (i.e. from us).

Having thus dropped the one-sided conception of infinity, we must look for another characterization of the relationship between a point and a plane which are infinitely distant from one another. This requires, first of all, a proper characterization of Point and Plane in themselves.

Conceived dynamically, as projective geometry requires, Point and Plane represent a pair of opposites, the Point standing for utmost contraction, the Plane for utmost expansion. As such, they form a polarity of the first order. Both together constitute Space. Which sort of space this is, depends on the relationship in which they are envisaged. By positing the point as the unit from which to start, and deriving our conception of the plane from the point, we constitute Euclidean space. By starting in the manner described above, with the plane as the unit, and conceiving the point from it, we constitute polar-Euclidean space.

The realization of the reversibility of the relationship between Point and Plane leads to a conception of Space still free from any specific character. By G. Adams this space has been appositely called archetypal space, or ur-space. Both Euclidean and polar-Euclidean space are particular manifestations of it, their mutual relationship being one of metamorphosis in the Goethean sense.

Through conceiving Euclidean and polar-Euclidean space in this manner it becomes clear that they are nothing else than the geometrical expression of the relationship between gravity and levity. For gravity, through its field spreading outward from an inner centre, establishes a point-to-point relation between all things under its sway; whereas levity draws all things within its domain into common plane-relations by establishing field-conditions wherein action takes place from the periphery towards the centre. What distinguishes in both cases the plane at infinity from all other planes may be best described by calling it the all-embracing plane; correspondingly the point at infinity may be best described as the all-relating point.

In outer nature the all-embracing plane is as much the 'centre' of the earth's field of levity as the all-relating point is the centre of her field of gravity. All actions of dynamic entities, such as that of the ur-plant and its subordinate types, start from this plane. Seeds, eye-formations, etc., are nothing but individual all-relating points in respect of this plane. All that springs from such points does so because of the point's relation to the all-embracing plane. This may suffice to show how realistic are the mathematical concepts which we have here tried to build up.

*

When we set out earlier in this book (Chapter VIII) to discover the source of Galileo's intuition, by which he had been enabled to find the theorem of the parallelogram of forces, we were led to certain experiences through which all men go in early childhood by erecting their body and learning to walk. We were thereby led to realize that man's general capacity for thinking mathematically is the outcome of early experiences of this kind. It is evident that geometrical concepts arising in man's mind in this way must be those of Euclidean geometry. For they are acquired by the will's struggle with gravity. The dynamic law discovered in this way by Galileo was therefore bound to apply to the behaviour of mechanical forces - that is, of forces acting from points outward.

In a similar way we can now seek to find the source of our capacity to form polar-Euclidean concepts. As we were formerly led to experiences of man's early life on earth, so we are now led to his embryonic and even pre-embryonic existence.

Before man's supersensible part enters into a physical body there is no means of conveying to it experiences other than those of levity, and this condition prevails right through embryonic development. For while the body floats in the mother's foetal fluid it is virtually exempt from the influence of the earth's field of gravity.

History has given us a source of information from these early periods of man's existence in Traherne's recollections of the time when his soul was still in the state of cosmic consciousness. Among his descriptions we may therefore expect to find a picture of levity-space which will confirm through immediate experience what we have arrived at along the lines of realistic mathematical reasoning. Among poems quoted earlier, his The Praeparative and My Spirit do indeed convey this picture in the clearest possible way. The following are relevant passages from these two poems.

In the first we read:

'Then was my Soul my only All to me, A living endless Ey, Scarce bounded with the Sky Whose Power, and Act, and Essence was to see: I was an inward Sphere of Light, Or an interminable Orb of Sight, Exceeding that which makes the Days . . .'

In the second poem the same experience is expressed in richer detail. There he says of his own soul that it -

... being Simple, like the Deity, In its own Centre is a Sphere, Not limited but everywhere.

It acts not from a Centre to Its Object, as remote; But present is, where it doth go To view the Being it doth note ...

A strange extended Orb of Joy Proceeding from within, Which did on ev'ry side display Its force; and being nigh of Kin To God, did ev'ry way Dilate its Self ev'n instantaneously, Yet an Indivisible Centre stay, In it surrounding all Eternity. 'Twas not a Sphere; Yet did appear One infinite: 'Twas somewhat everywhere.'

Observe the distinct description of how the relation between circumference and centre is inverted by the former becoming itself an 'indivisible centre'. In a space of this kind there is no Here and There, as in Euclidean space, for the consciousness is always and immediately at one with the whole space. Motion is thus quite different from what it is in Euclidean space. Traherne himself italicized the word 'instantaneous', so important did he find this fact. (The quality of instantaneousness - equal from the physical point of view to a velocity of the value - will occupy us more closely as a characteristic of the realm of levity when we come to discuss the apparent velocity of light in connexion with our optical studies.)

By thus realizing the source in man of the polar-Euclidean thought-forms, we see the discovery of projective geometry in a new light. For it now assumes the significance of yet another historical symptom of the modern re-awakening of man's capacity to remember his prenatal existence.

*

We know from our previous studies that the concept of polarity is not exhausted by conceiving the world as being constituted by polarities of one order only. Besides primary polarities, there are secondary ones, the outcome of interaction between the primary poles. Having conceived of Point and Plane as a geometrical polarity of the first order, we have therefore to ask what formative elements there are in geometry which represent the corresponding polarity of the second order. The following considerations will show that these are the radius, which arises from the point becoming related to the plane, and the spherically bent surface (for which we have no other name than that again of the sphere), arising from the plane becoming related to the point.

In Euclidean geometry the sphere is defined as 'the locus of all points which are equidistant from a given point'. To define the sphere in this way is in accord with our post-natal, gravity-bound consciousness. For in this state our mind can do no more than envisage the surface of the sphere point by point from its centre and recognize the equal distance of all these points from the centre. Seen thus, the sphere arises as the sum-total of the end-points of all the straight lines of equal length which emerge from the centre-point in all directions. Fig. 8 indicates this schematically. Here the radius, a straight line, is clearly the determining factor.

We now move to the other pole of the primary polarity, that is to the plane, and let the sphere arise by imagining the plane approaching an infinitely distant point evenly from all sides. We view the process realistically only by imagining ourselves in the plane, so that we surround the point from all sides, with the distance between us and the point diminishing gradually. Since we remain all the time on the surface, we have no reason to conceive any change in its original position; that is, we continue to think of it as an all-embracing plane with regard to the chosen point.

The only way of representing the sphere diagrammatically, as a unit bearing in itself the character of the plane whence it sprang, is as shown in Fig. 9, where a number of planes, functioning as tangential planes, are so related that together they form a surface which possesses everywhere the same distance from the all-relating point.

Since Point and Plane represent in the realm of geometrical concepts what in outer nature we find in the form of the gravity-levity polarity, we may expect to meet Radius and Sphere as actual formative elements in nature, wherever gravity and levity interact in one way or another. A few observations may suffice to give the necessary evidence. Further confirmation will be furnished by the ensuing chapters.

The Radius-Sphere antithesis appears most obviously in the human body, the radial element being represented by the limbs, the spherical by the skull. The limbs thus become the hieroglyph of a dynamic directed from the Point to the Plane, and the skull of the opposite. This indeed is in accord with the distribution in the organism of the sulphur-salt polarity, as we learnt from our physiological and psychological studies. Inner processes and outer form thus reveal the same distribution of poles.

In the plant the same polarity appears in stalk and leaf. Obviously the stalk represents the radial pole. The connexion between leaf and sphere is not so clear: in order to recognize it we must appreciate that the single plant is not a self-contained entity to the same degree as is the human being. The equivalent of the single man is the entire vegetable covering of the earth. In man there is an individual centre round which the bones of his skull are curved; in the plant world the equivalent is the centre of the earth. It is in relation to this that we must conceive of the single leaves as parts of a greater sphere.

In the plant, just as in man, the morphological polarity coincides with the biological. There is, on the one hand, the process of assimilation (photosynthesis), so characteristic of the leaf. Through this process matter passes over from the aeriform condition into that of numerous separate, characteristically structured solid bodies - the starch grains. Besides this kind of assimilation we have learnt to recognize a higher form which we called 'spiritual assimilation'. Here, a transition of substance from the domain of levity to that of gravity takes place even more strikingly than in ordinary (physical) assimilation (Chapter X).

The corresponding process in the linear stalk is one which we may call 'sublimation' - again with its extension into 'spiritual sublimation'. Through this process matter is carried in the upward direction towards ever less ponderable conditions, and finally into the formless state of pure 'chaos'. By this means the seed is prepared (as we have seen) with the help of the fire-bearing pollen, so that after it has fallen to the ground, it may serve as an all-relating point to which the plant's Type can direct its activity from the universal circumference.

In order to find the corresponding morphological polarity in the animal kingdom, we must realize that the animal, by having the main axis of its body in the horizontal direction, has a relationship to the gravity-levity fields of the earth different from those of both man and plant. As a result, the single animal body shows the sphere-radius polarity much less sharply. If we compare the different groups of the animal kingdom, however, we find that the animals, too, bear this polarity as a formative element. The birds represent the spherical (dry, saline) pole; the ruminants the linear (moist, sulphurous) pole. The carnivorous quadrupeds form the intermediary (mercurial) group. As ur-phenomenal types we may name among the birds the eagle, clothed in its dry, silicic plumage, hovering with far-spread wings in the heights of the atmosphere, united with the expanses of space through its far-reaching sight; among the ruminants, the cow, lying heavily on the ground of the earth, given over entirely to the immensely elaborated sulphurous process of its own digestion. Between them comes the lion - the most characteristic animal for the preponderance of heart-and-lung activities in the body, with all the attributes resulting from that.

Within the scope of this book it can only be intimated briefly, but should not be left unmentioned for the sake of those interested in a further pursuit of these lines of thought, that the morphological mean between radius and sphere (corresponding to Mercurius in the alchemical triad) is represented by a geometrical figure known as the 'lemniscate', a particular modification of the so-called Cassinian curves.2

1 For further details, see the writings of G. Adams and L. Locher-Ernst who, each in his own way, have made a beginning with applying projective geometry on the lines indicated by Rudolf Steiner. Professor Locher-Ernst was the first to apply the term 'polar-Euclidean' to the space-system corresponding to levity.

2 For particulars of the lemniscate as the building plan of the middle part of man's skeleton, see K. König, M.D.: Beitrage zu einer reinen Anatomic des menschlichen Knochenskeletts in the periodical Natura (Dornach, 1930-1). Some projective-geometrical considerations concerning the lemniscate are to be found in the previously mentioned writings of G. Adams and L. Locher-Ernst.

CHAPTER XIII

'Radiant Matter'

When man in the state of world-onlooker undertook to form a dynamic picture of the nature of matter, it was inevitable that of all the qualities which belong to its existence he should be able to envisage only those pertaining to gravity and electricity. Because his consciousness, at this stage of its evolution, was closely bound up with the force of gravity inherent in the human body, he was unable to form any conception of levity as a force opposite to gravity. Yet, nature is built bipolarically, and polarity-concepts are therefore indispensable for developing a true understanding of her actions. This accounts for the fact that the unipolar concept of gravity had eventually to be supplemented by some kind of bipolar concept.

Now, the only sphere of nature-phenomena with a bipolar character accessible to the onlooker-consciousness 'was that of electricity. It was thus that man in this state of consciousness was compelled to picture the foundation of the physical universe as being made up of gravity and electricity, as we meet them in the modern picture of the atom, with its heavy electro-positive nucleus and the virtually weightless electro-negative electrons moving round it.

Once scientific observation and thought are freed from the limitations of the onlooker-consciousness, both gravity and electricity appear in a new perspective, though the change is different for each of them. Gravity, while it becomes one pole of a polarity, with levity as the opposite pole, still retains its character as a fundamental force of the physical universe, the gravity-levity polarity being one of the first order. Not so electricity. For, as the following discussion will show, the electrical polarity is one of the second order; moreover, instead of constituting matter as is usually believed, electricity turns out to be in reality a product of matter.

*

We follow Goethe's line when, in order to answer the question, 'What is electricity?' we first ask, 'How does electricity arise?' Instead of starting with phenomena produced by electricity when it is already in action, and deriving from them a hypothetical picture, we begin by observing the processes to which electricity owes its appearance. Since there is significance in the historical order in which facts of nature have come to man's knowledge in the past, we choose as our starting-point, among the various modes of generating electricity, the one through which the existence of an electric force first became known. This is the rousing of the electric state in a body by rubbing it with another body of different material composition. Originally, amber was rubbed with wool or fur.

By picturing this process in our mind we become aware of a certain kinship of electricity with fire, since for ages the only known way of kindling fire was through friction. We notice that in both cases man had to resort to the will-power invested in his limbs for setting in motion two pieces of matter, so that, by overcoming their resistance to this motion, he released from them a certain force which he could utilize as a supplement to his own will. The similarity of the two processes may be taken as a sign that heat and electricity are related to each other in a certain way, the one being in some sense a metamorphosis of the other. Our first task, therefore, will be to try to understand how it is that friction causes heat to appear in manifest form.

There is no friction unless the surfaces of the rubbed bodies have a structure that is in some way interfered with by the rubbing, while at the same time they offer a certain resistance to the disturbance. This resistance is due to a characteristic of matter, commonly called cohesion. Now we know that the inner coherence of a physical body is due to its point-relationship, that is to the gravitational force bound up with it. Indeed, cohesion increases as we pass from the gaseous, through the liquid, to the solid state of matter.

Whilst a body's cohesion is due to gravity, its spatial extendedness is, as we have seen, due to levity. If we reduce the volume of a piece of physical matter by means of pressure, we therefore release levity-forces previously bound up in it, and these, as always happens in such cases, appear in the form of free heat. Figuratively speaking, we may say that by applying pressure to matter, latent levity is pressed out of it, somewhat like water out of a wet sponge.

The generation of free heat by friction rests on quite similar grounds. Obviously, friction always requires a certain pressure. This alone, however, would not account for the amount of heat easily produced by friction. To the pressure there is in this case added a certain measure of encroachment upon the unity of the material substance. In the case of friction between two solid bodies, this may go so far that particles of matter are completely detached from the cohesive whole. The result is an increase in the number of single mass-centres on the earth, as against the all-embracing cosmic periphery. This diminishes the hold of levity on the total amount of physical matter present on the earth. Again, the levity thus becoming free appears as external heat. (In the reverse case when, for instance through melting, a number of single physical bodies become one, free heat becomes latent.)

Both the diminishing of spatial extension and the breaking up of a whole into parts entail an increase in the quality 'dry'. This applies not only in the sense that the parts which have become independent units are 'dry' in relation to each other - formerly coherent matter being turned into dust - but also in the other sense, and one valid in both cases, that levity and gravity are losing part of their previous inter-connexion. If this twofold process of 'becoming dry' reaches a certain intensity, the substances concerned, provided they are inflammable, begin to burn, with the result that dry heat escapes and dry ash is formed. We note that in each case we are dealing with a change in the relationship between the poles of a polarity of the first order.

We will now apply this picture of the process of friction to the instance when, as a result of this action, electricity appears.

Originally the evoking of the electric condition was ascribed solely to the nature of amber, the only substance known to possess this property. To-day we know that not the amber alone, but its coming together with another substance of different nature, in this instance an animal substance of the nature of hair or silk, is required. Whatever substances we use for friction, they must always be different in nature, so as to allow both kinds of electricity to appear at once. Which of the two kinds imposes its presence the more strongly upon the observer depends on purely extraneous conditions which have nothing to do with the process itself.

Obviously, if we wish to understand the qualitative difference between the two kinds of electricity, we must investigate the qualitative difference in the material substances, which give rise to electricity when they are rubbed together. We shall again follow the historical line by examining the two substances which first taught man the polar nature of electricity. They are glass and resin, after which, as we mentioned, the two electricities were even named in the beginning.

Our functional conception of matter, developed earlier (Chapter XI), allows us to recognize in these two substances representatives of the Salt-Sulphur polarity. Indeed, glass as a mineral substance, which actually owes its specific character to the presence of silicon in it, clearly stands on the phosphoric-crystalline side, while resin, being itself a sort of 'gum', on the sulphurous-volcanic side. In fact, sulphur itself was soon found to be a particularly suitable substance for producing 'resin'-electricity.

Now the usual way of producing one kind of electricity is by rubbing resin (or sulphur, or ebonite) with wool or fur, and the other by rubbing glass with leather. At first sight, it does not seem as if the two counter-substances represent the required alchemic counter-poles to resin and glass. For both hair and leather are animal products and therefore seem to be of like nature. Closer inspection, however, shows that they do obey the rule. For hair, like all horny substances, is a dead product of external secretion by the animal organism. An ur-phenomenal example of it, showing its kinship to glass-like substances, is the transparent cornea of the eye, close to the crystal-lens. Leather, on the other hand, is a product of the hypodermic part of the body and, as such, belongs to those parts of the organism which are filled with blood, and, therefore, permeated with life. (Note as a characteristic of leather that it requires a special treatment, tanning, to make it as immune from decay as hair is by nature.) Hair and leather, therefore, represent in themselves a salt-sulphur polarity, and thus fulfil the corresponding function when brought together with resin or glass respectively.

What is true for the particular substances which originally led man to discover the dual nature of electricity, holds good equally for any pair of substances capable of assuming the electric state when rubbed against each other. If we examine from this point of view the series of such substances, as usually given in the textbooks on electricity, we shall always find a substance of extreme salt-character at the one end, and one of extreme sulphur-character at the other, the substances as a whole forming a gradual transition from one extreme to the other. Which kind of electricity appears on each, when submitted to friction, depends on whether the counter-substance stands on its right or left, in the series. It is the particular relation between the two which makes them behave in one way or the other.

There are cases which seem to elude this law, and investigation has shown that other characteristics of the rubbed bodies, such as surface quality, can have a modifying influence. For lack of a guiding idea they are treated in the textbooks as 'irregularities'. Observation led by a true polarity concept shows that in these cases also the rule is not violated. In this respect, interesting information can be gained from the observations of J. W. Ritter (1776-1810), an ingenious Naturphilosoph from the circle round Goethe, but to whom, also, physical science is indebted for his discovery of the ultra-violet part of the spectrum and of galvanic polarization. Among his writings there is a treatise on electricity, giving many generally unknown instances of frictional electricity which are in good accord with our picture and well worth investigating. According to Ritter, even two crystalline substances of different hardness, such as Calcite and quartz, become electric when rubbed together, the softer playing the part of 'resin' and the harder that of 'glass'.

These few facts connected with the generation of frictional electricity are enough to allow us to form a picture of the nature of the polarity represented by the two kinds of electricity.

We remember that in the case of the generation of heat through friction, as a result of an encroachment upon the cohesion of the material body involved, the relationship between levity and gravity in it changes from 'moist' to 'dry' and that the effect of this is the appearance of 'fire' and 'dust' as poles of a primary polarity. This process, however, is altered when the bodies subjected to friction are opposed to each other in the sense of a salt-sulphur polarity. The effect then is that the liberated levity, under the influence of the peculiar tension between the two bodies, remains bound in the realm of substance and becomes itself split up polarically.

Clearly, then, in the case of electrical polarity we encounter a certain form of gravity-bound levity, and this in a twofold way. Owing to the contrasting nature of the two bodies involved in the process, the coupling of gravity and levity is a polar one on both sides. The electrical polarity thus turns out to be itself of the nature of a secondary polarity.

Two more recently discovered means of evoking the electric condition in a piece of matter confirm this picture. They are the so-called piezo-electricity and pyro-electricity. Both signify the occurrence of the electrical polarity at the two ends of an asymmetrically built (hemimorphous) crystal, as the result of changing the crystal's spatial condition. In piezo-electricity the change consists in a diminution of the crystal's volume through pressure; in pyro-electricity, in an increase of the crystal volume by raising its temperature. The asymmetry of the crystal, due to a one-sided working of the forces of crystallization, plays the same role here as does the alchemic opposition between the two bodies used for the production of frictional electricity.

*

It is typical of the scientist of the past that he was dependent on phenomena brought about by a highly developed experimental technique for becoming aware of certain properties of the electrical force, whereas for the realistic observer these properties are revealed at once by the most primitive electric phenomena. We remember Eddington's description of the positron as 'negative material', and his subsequent remarks, which show the paradoxical nature of this concept if applied to the hypothetical interior of the atom (Chapter IV). The quite primitive phenomenon of electrical repulsion and attraction shows us the same thing in a manner of which it is not difficult to form a conception.

Modern physics itself, with the help of Faraday's field-concept, describes these phenomena as caused by pressure - resulting from the meeting in space of two similar electrical fields - and suction - resulting from the meeting of two dissimilar fields. In the first case the space between the two electrically charged bodies assumes a degree of density, as if it were filled with some elastic material. In the second instance the density of the space where the two fields intermingle is lower than that of its surroundings. Here, clearly, we have a state of negative density which acts on the electrically charged bodies just as a lowering of pressure acts on a gas: in both cases movement occurs in the direction leading from the higher to the lower density. Electricity thus shows itself capable of producing both gravity and levity effects, thereby once more confirming our picture of it.

*

Our next task will be to examine the galvanic form of generating electricity, in order to gain further light on our picture of the electrical polarity.

Galvanism, as it became established through Volta's work, rests on certain properties of the metallic substances of the earth. Compared with the substances which may be used for producing electricity through friction, the metals hold a mid-position. They are all essentially mercurial substances. (In quicksilver, which for this reason was given the name 'mercury' by the alchemists, this fact comes to an ur-phenomenal appearance.) Among the many facts proving the mercurial nature of the metals, there is one of particular interest to us. This is their peculiar relationship to the processes of oxidation and reduction.

Metals, in their metallic state, are bearers of latent levity, which can be set free either through combustion or through corrosion. They differ from one another by their relative degree of eagerness to enter into and remain in the metallic, that is, the reduced state, or to assume and keep the state of the oxide (in which form they are found in the various metallic oxides and salts). There are metals such as gold, silver, etc., for which the reduced state is more or less natural; others, such as potassium, sodium, etc., find the oxidized state natural and can be brought into and kept in the reduced state only by artificial means. Between these extremes there are all possible degrees of transition, some metals more nearly resembling the 'noble', others more nearly the 'corrosive', metals.

We remember that it was the different relationship of sulphur and phosphorus to reduction and oxidation which led us to envisage them as ur-phenomenal representatives of the alchemic polarity. We may therefore say that there are metals which from the alchemic point of view more nearly resemble sulphur, others more nearly phosphorus, whilst others again hold an intermediary position between the extremes. It is on these differences among the various metals that their galvanic properties are based.

Let us from this point of view contemplate the following series of chemical elements, which is a representation of the so-called voltaic series:

Graphite, Platinum, Gold, Silver, Copper, Iron, Tin, Lead, Zinc, Aluminium, Magnesium, Sodium, Potassium.

Any two of these metals constitute a voltaic cell. Its electromotive force is determined by the distance in the series between the metals used. Just as in the case of frictional electricity, the kind of electricity which is supplied by a certain metal depends on whether the other metal with which it is coupled stands to the right or to the left of it in the series.1

Let us now see what happens in a galvanic cell when the two different metals are simultaneously exposed to the chemical action of the connecting fluid. Each metal by itself would undergo oxidation with greater or less intensity, and the calorific energy hidden in it would become free in the form of heat. This process suffers a certain alteration through the presence of the second metal, which sets up an alchemic tension between the two. Instead of a proper segregation of the primary polarity, heat-dust (in this case, heat-oxide), the heat remains matter-bound and appears on the surface of the two metals in a secondarily split form as positive and negative electricity.

The similarity between this process and the frictional generation of electricity is evident.

*

Our observations have shown that the emergence of the electric state, whether it be caused by friction or galvanically, depends on matter entering into a condition in which its cohesion is loosened - or, as we also put it, on its being turned into 'dust' - and this in such a way that the escaping levity remains dust-bound. This picture of electricity now enables us to give a realistic interpretation of certain phenomena which, in the interpretation which the physicist of the past was bound to give them, have contributed much to the tightening of the net of scientific illusion.

Some sixty years after Dalton had established, purely hypothetically, the theory of the atomistic structure of matter, scientific research was led to the observation of actual atomistic phenomena. Crookes found electricity appearing in his tubes in the form of discrete particles, with properties hitherto known only as appertaining to mass. What could be more natural than to take this as evidence that the method of thought developed during the past era of science was on the right course?

The same phenomena appear in quite a different light when we view them against the background of the picture of electricity to which our observations have led. Knowing that the appearance of electricity depends on a process of atomization of some sort, we shall expect that where electricity becomes freely observable, it will yield phenomena of an atomistic kind. The observations of electricity in a vacuum, therefore, yield no confirmation whatsoever of the atomistic view of matter.

The same is true of the phenomena bound up with radioactivity, which were discovered in direct consequence of Crookes's work. We know that the naturally radioactive elements are all in the group of those with the highest atomic weight. This fact, seen together with the characteristics of radioactivity, tells us that in such elements gravity has so far got the upper hand of levity that the physical substance is unable to persist as a spatially extended, coherent unit. It therefore falls asunder, with the liberated levity drawn into the process of dispersion. Seen thus, radioactivity becomes a symptom of the earth's old age.

*

Before entering into a discussion of the question, which naturally arises at this point, as to how levity and gravity by their two possible ways of interaction - 'sulphurous' or 'saline' - determine the properties of so-called positive and negative electricity, we shall first study the third mode of generating electricity, namely, by electromagnetic induction. Along this way we shall arrive at a picture of the magnetic force which corresponds to the one already obtained of electricity. This will then lead us to a joint study of the nature of electric polarity and magnetic polarity.

The discovery of the phenomena we call electromagnetic depended on the possibility of producing continuous electrical processes. This arose with Volta's invention. When it became necessary to find a concept for the process which takes place in an electric conductor between the poles of a galvanic cell, the concept of the 'current', borrowed from hydrodynamics, suggested itself. Ever since then it has been the rule to speak of the existence of a current within an electric circuit; its strength or intensity is measured in terms of a unit named in honour of Ampere.

This concept of the current has had a fate typical of the whole relation of human thought to the facts connected with electricity. Long after it had been coined to cover phenomena which in themselves betray no movement of any kind between the electrical poles, other phenomena which do in fact show such movements became known through Crookes's observations. Just as in the case of atomism, they seemed to prove the validity of the preconceived idea of the current. Soon, however, radiant electricity showed properties which contradicted the picture of something flowing from one pole to the other. The cathode rays, for instance, were found to shoot forth into space perpendicularly from the surface of the cathode, without regard to the position of the anode. At the same time Maxwell's hydrodynamic analogy (as our historical survey has shown) led to a view of the nature of electricity by which this very analogy was put out of court. By predicting certain properties of electricity which come to the fore when its poles alternate rapidly, he seemed to bring electricity into close kinship with light. Mathematical treatment then made it necessary to regard the essential energy process as occurring, not from one pole to the other, but at right angles to a line joining the poles (Poynting's vector). This picture, however, satisfactory though it was in the realm of high frequency, failed as a means of describing so-called direct-current processes.

As a result of all this the theory of electricity has fallen apart into several conceptual realms lying, as it were, alongside one another, each consistent in itself but lacking any logical connexion with the others. Although the old concept of the electric current has long lost its validity, scientific thought (not to speak of the layman's) has not managed to discard it. To do this must therefore be our first task, if we want to attain to a realistic picture of electromagnetism.

*

While keeping strictly to the historical order of things, we shall try first to form a picture of what happens when we connect two electrically charged bodies by a conductor. We know that we rightly describe the change of the dynamic properties of the part of space, in which the two bodies are present, by saying that a certain electric field prevails in it. This field possesses different 'potentials' at its various points and so there exists a certain potential difference between the two electric charges. What then happens when a so-called 'conductor' is brought into such a field?

From the point of view of the field-concept, conductivity consists in the property of a body not to allow any change of potential along its surface. Such a surface, therefore, is always an equipotential. In the language of alchemy, conductivity is a mercurial property. In the presence of such a body, therefore, no Salt-Sulphur contrasts can obtain. In view of what we found above as the mean position of the metals in the alchemic triad, it is significant that they, precisely, should play so outstanding a role as electrical conductors.

If we keep to pure observation, the only statement we can make concerning the effect produced by the introduction of such a body into the electric field is that this field suddenly disappears. We shall see later in which direction this vanishing occurs. For the present it is sufficient to have formed the picture of the disappearance of the electrical condition of space as a result of the presence of a body with certain mercurial properties.

Nothing else, indeed, happens when we make the process continuous by using a galvanic source of electricity. All that distinguishes a galvanic cell from the sources of electricity used before the time of Volta is its faculty of immediately re-establishing the field which prevails between its poles, whenever this field becomes extinguished by the presence of a conductor. Volta himself saw this quite correctly. In his first account of the new apparatus he describes it as 'Leyden jars with a continuously re-established charge'. Every enduring electrical process, indeed, consists in nothing but a vanishing and re-establishment of the electrical field with such rapidity that the whole process appears continuous.

Here, also, pure observation of the effect of a conductor in an electric field tells us that its action consists in the annihilation of the field. There is no phenomenon which allows us to state that this process takes place along the axis of the conductor. If we wish to obtain a picture of the true direction, we must consider the condition of space which arises in place of the electric condition that has disappeared.

With the possibility of turning the cancellation of the electrical condition of space into a continuous process, it became possible to observe that the neutralization of electric charges entails the appearance of heat and magnetism. We must now ask which are the qualities of electricity on the one hand, and of heat and magnetism on the other, which account for the fact that where electricity disappears, the two latter forces are bound to appear. Since magnetism is the still unknown entity among the three, we must now deal with it.

*

Unlike electricity, magnetism was first known in the form of its natural occurrence, namely as a property of certain minerals. If we follow the same course which led us to start our study of electricity with the primitive process of generating it, we shall turn now to the basic phenomenon produced by a magnetic field already in existence. (Only when we have learnt all we can from this, shall we proceed to ask how magnetism comes into being.) Obviously, we shall find this basic phenomenon in the effect of a magnet on a heap of iron filings.

Let us, to begin with, compare a mass of solid iron with the same quantity of it in powdered form. The difference is that the powder lacks the binding force which holds the solid piece together. Now lei us expose the powdered iron to the influence of a magnet. At once a certain ordering principle takes hold of the single particles. They no longer lie at random and unrelated, apart from the inconspicuous gravitational effect they exert on one another, but are drawn into a coherent whole, thus acquiring properties resembling those of an ordinary piece of solid matter.

Read thus, the phenomenon tells us that a part of space occupied by a magnetic field has qualities which are otherwise found only where a coherent solid mass is present. A magnetic piece of solid iron, therefore, differs from a non-magnetic piece by giving rise in its surroundings to dynamic conditions which would otherwise exist only in its interior. This picture of the relatedness of magnetism to solidity is confirmed by the fact that both are cancelled by heat, and increased by cold.2

By its magnetic properties iron thus reveals itself as a substance capable of assuming the condition of solid matter to a degree surpassing ordinary solidity. As an exceptional kind of metal it forms the counter-pole to mercury, in which the solid-fluid condition characteristic of all metallic matter is as much shifted towards the fluid as in iron it is to the solid. (Note in this respect the peculiar resistance of iron to the liquefying effect which mercury has on the other metals.)

This picture of magnetism enables us to understand at once why it must occur together with heat at the place where an electric polarity has been cancelled by the presence of a conductor. We have seen that electricity is levity coupled in a peculiar way with gravity; it is polarized levity (accompanied by a corresponding polarization of gravity). An electric field, therefore, always has both qualities, those of levity and of gravity. We saw a symptom of this in electrical attraction and repulsion, so called; the attraction, we found, was due to negative density, the repulsion to positive density, imparted to space by the electrical fields present there. Now we see that when, through the presence of a conductor, the electrical field round the two opposing poles vanishes, in its place two other fields, a thermal and a magnetic, appear. Clearly, one of them represents the levity-part, the other the gravity-part, of the vanished electric field. The whole process reminds one of combustion through which the ponderable and imponderable parts, combined in the combustible substance, fall apart and appear on the one hand as heat, and on the other as oxidized substance ('ash'). Yet, between these two manifestations of heat there is an essential qualitative difference.

Although, from our view-point, magnetism represents only one 'half of a phenomenon, the other half of which is heat, we must not forget that it is itself a bipolar force. Thus, despite its apparent relation to gravity it does not represent, as gravity does, one pole of a primary polarity, with heat as the other pole. Rather must it carry certain qualities of levity which, together with those of gravity, appear in a polarically opposite manner at its two poles. (Details of this will be shown later when we come to investigate the individual qualities of the two poles of magnetism and electricity.) Hence the heat that forms the counterpart to magnetism cannot be pure levity either. As the result of a certain coupling with gravity, it too has somehow remained polarically split.

This can easily be seen by considering the following. Unlike the levity-gravity polarity, in which one pole is peripheral and the other point-centred, both Doles of the electrical polarity are point-centred; both are located in physical space, and thereby determine a definite direction within this space. It is this direction which remains a characteristic of both the magnetic and the thermal fields. The direction of the thermal field as much as that of the magnetic is determined by its having as its axis the conductor joining the poles of the antecedent electrical field. Both fields supplement each other in that the thermal radiation forms the radii which belong to the circular magnetic lines-of-force surrounding the conductor.3

Our picture of the process which is commonly called an electric current is now sufficiently complete to allow us to make a positive statement concerning the direction in which it takes place. Let us once more sum up: In order that this process may occur, there must be present in an electrically excited part of space a body which does not suffer the particular polarization of space bound up with such a field. As a result, the electrical field disappears, and in place of it appear a thermal field and a magnetic field, both having as their axis the line connecting the two poles. Each of them spreads out in a direction at right angles to this fine. Obviously, therefore, it is in this radial direction that the transformation of the electrical into the thermo-magnetic condition of space must take place.

This picture of the electro-thermo-magnetic happening, as regards its direction, is in complete accord with the result obtained (as indicated earlier) by the mathematical treatment of high-frequency phenomena. Once more we see that quite primitive observations, when properly read, lead to findings for which scientific thought had to wait until they were forced on it by the progress of experimental technique - as even then science was left without a uniformly valid picture of the dynamic behaviour of electricity.

Further, we can now see that when we apply electricity to practical purposes, we are in fact seldom using electricity itself, but other forces (that is, other combinations of gravity and levity) which we make effective by making electricity disappear. The same is true of most of the methods of measuring electricity. As a rule, the force which sets the instrument in motion is not electricity but another force (magnetism, heat, etc.) which appears in the place of the vanishing electricity. Thus the so-called intensity of an electric current is actually the intensity with which the electricity in question disappears! Electricity serves us in our machines in the same way that food serves a living organism: it gets itself digested, and what matters is the resulting secondary product.

Just as alterations in the electrical condition of space give rise to the appearance of a magnetic field, any alteration of the magnetic state of space gives rise to the appearance of an electrical field. This process is called electromagnetic induction. With its discovery, the generation of electricity through friction and in the galvanic way was supplemented by a third way. By this means the practical use of electricity on a large scale became possible for the first time. If our picture of the two earlier processes of generating electricity is correct, then this third way must also fit into the picture, although in this case we have no longer to do with any direct atomization of physical matter. Our picture of magnetism will indeed enable us to recognize in electromagnetic induction the same principle on which we found the two other processes to rest.

Magnetism is polarized gravity. Hence it has the same characteristic of tending always to maintain an existent condition. In bodies subject to gravity, this tendency reveals itself as their inertia. It is the inertia inherent in magnetism which we employ when using it to generate electricity. The simplest example is when, by interrupting a 'primary current', we induce a 'secondary current' in a neighbouring circuit. By the sudden alteration of the electric condition on the primary side, the magnetic condition of the surrounding space is exposed to a sudden corresponding change. Against this the magnetic field 'puts up' a resistance by calling forth, on the secondary side, an electrical process of such direction and strength that the entire magnetic condition remains first unaltered and then, instead of changing suddenly, undergoes a gradual transformation which ideally needs an infinite time for its accomplishment (asymptotic course of the exponential curve). This principle rules every process of electromagnetic induction, whatever the cause and direction of the change of the magnetic field.

We know that electromagnetic induction takes place also when a conductor is moved across a magnetic field in such a way that, as the technical term goes, it 'cuts' the field's lines of force. Whereas the process discussed above is employed in the transformer, this latter process is used in generation of electricity by dynamo. We have seen that a magnetic field imparts to the relevant part of space qualities of density which otherwise prevail only in the interior of solid masses. We remember further that the appearance of electricity, in the two other modes of generating it, is caused by the loosening of the coherence of the material substance. A similar loosening of the coherence of the magnetic field takes place when its field-lines are cut by the movement of the conductor across it. Just as heat occurs when we move a solid object through a liquid, electricity occurs when we move a conductor across a magnetic field. In each case we interfere with an existing levity-gravity relationship.

*

Having established thus far the picture of both electricity and magnetism which shows each as an outcome of certain levity-gravity interactions, we now ask how, in particular, negative and positive electricity on the one hand and north and south magnetism on the other are determined by these interactions. Let us again begin with electricity.

We remember that Galvani was led to his observations by the results of Walsh's study of the electric fishes. While Galvani clung to the view that in his own experiments the source of the electrical force lay within the animal bodies, Volta saw the fallacy of that. He then conceived the idea of imitating with purely inorganic substances the set-up which Galvani had come upon by accident. The paradoxical result - as he himself noticed with surprise - was that his apparatus turned out to be a close replica of the peculiar organ with which the electric fishes are endowed by nature. We must now take a closer view of this organ.

The electric organ of such a fish consists of many thousands of little piles, each made up of a very great number of plates of two different kinds, arranged in alternating layers. The two kinds differ in substance: in one case the plate is made from a material similar to that present in the nervous system of animals; in the other the resemblance is to a substance present in the muscular system, though only when the muscles are in a state of decay. In this way the two opposing systems of the animal body' seem to be brought here into direct contact, repeated many thousands of times.

In the electric fishes, accordingly, sensation and will are brought into a peculiar interrelation. For the will-pole is related to its bodily foundation in a manner which otherwise obtains only between the nervous system and the psychological processes co-ordinated with it. These fishes then have the capacity to send out force-currents which produce in other animals and in man 'concussion of the limbs', or in extreme cases paralysis and even death. Through describing the process in this way we realize that electricity appears here as metamorphosed animal will, which takes this peculiar form because part of the animal's volitional system is assimilated to its sensory system in an exceptional manner.

It is known to-day that what nature reveals so strikingly in the case of the electric fish, is nothing but the manifestation of a principle at work in the bodies of all beings endowed with sensation and volition - in corporeal terms, with the duality of a nervous and a muscular system - and therefore at work also in the human body. Observation has shown that the activities of these two systems in man and animal are accompanied by the occurrence of different electric potentials in different parts of the body. Plate A, Fig. iii, shows the distribution of the two polar electric forces in the human body. The bent lines in the diagram stand for curves of equal electric potential. The straight line between them is the neutral zone. As might be expected, this line runs through the heart. What seems less obvious is its slanting position. Here the asymmetry, characteristic of the human body, comes to expression.

If we remember that the nervous system represents the salt-pole, and the metabolic system the sulphur-pole, of the human organism, and if we take into account the relationship between levity and gravity at the two poles, we can see from the distribution of the two electricities that the coupling of levity and gravity at the negative pole of the electrical polarity is such that levity descends into gravity, while at the positive pole gravity rises into levity. Negative electricity therefore must have somehow a 'spherical' character, and positive electricity a 'radial'.

This finding is fully confirmed by electrical phenomena in the realm of nature most remote from man (though it was an effort to solve the enigma of man which led to the discovery of this realm). Since Crookes's observations of the behaviour of electricity in a vacuum it is common knowledge that only the negative kind of electricity occurs as a freely radiating force (though it retains some properties of inertia), whereas positive electricity seems to be much more closely bound to minute particles of ponderable matter. Here again we find gravity-laden levity on the negative side, levity-raised gravity on the positive.

The same language is spoken by the forms in which the luminous phenomena appear at the two poles of a Crookes tube. Fig. i on Plate A represents the whole phenomenon as far as such a diagram allows. Here we see on the positive side radial forms appear, on the negative side planar-spherical forms. As symbols of nature's script, these forms tell us that cosmic periphery and earthly centre stand in a polar relation to each other at the two ends of the tube. (Our optical studies will later show that the colours which appear at the anode and cathode are also in complete accord with this.)

At this point in our discussion it is possible to raise, without risk of confusing the issue, the question of the distribution of the two electric forces over the pairs of substances concerned in the generation of electricity both by friction and in the galvanic way. This distribution seems to contradict the picture to which the foregoing observations have led us, for in both instances the 'sulphurous' substances (resin in one, the nobler metals in the other) become bearers of negative electricity; while the 'saline' substances (glass and the corrosive metals) carry positive electricity. Such a criss-crossing of the poles-surprising as it seems at first sight - is not new to us. We have met it in the distribution of function of the plant's organs of propagation, and we shall meet a further instance of it when studying the function of the human eye. Future investigation will have to find the principle common to all instances in nature where such an interchange of the poles prevails.

While the electric field arising round an electrified piece of matter does not allow any recognition of the absolute characteristics of the two opposing electrical forces, we do find them revealed by the distribution of electricity in the human body. Something similar holds good for magnetism. Only, to find the phenomena from which to read the absolute characteristics of the two sides of the magnetic polarity, we must not turn to the body of man but to that of the earth, one of whose characteristics it is to be as much the bearer of a magnetic field as of gravitational and levitational fields. There is significance in the fact that even to-day, when the tendency prevails to look for causes of natural phenomena not in the macrocosmic expanse, but in the microscopic confines of space, the two poles of magnetism are named after the magnetic poles of the earth. It indicates the degree to which man's feeling instinctively relates magnetism to the earth as a whole.

In our newly developed terminology we may say that magnetism, as a polarity of the second order, represents a field of force both of whose poles are situated within finite space, and that in the macro-telluric mother-field this situation is such that the axis of this field coincides more or less with the axis of the earth's physical body. Thus the magnetic polarization of the earth as a letter in nature's script bids us rank it alongside other phenomena which in their way are an expression of the earth's being polarized in the north-south direction.

The Austrian geographer, E. Suess, in his great work The Countenance of the Earth, first drew attention to the fact that an observer approaching the earth from outer space would be struck by the onesided distribution and formation of the earth's continents. He would notice that most of the dry land is in the northern hemisphere, leaving the southern hemisphere covered mainly with water. In terms of the basic elementary qualities, this means that the earth is predominantly 'dry' in its northern half, and 'moist' in its southern.