Lecture 2

Today it is extremely difficult for a personality who is involved in the current scientific establishment to find a transition from todays usual scientific approach into anthroposophy. Anthroposophy does not actually come into any contradiction with conventional science. It accepts the legitimate results of science and proceeds with them. The reverse however does not take place. Anthroposophy is rejected, its results are seen not to meet the strictly scientific criteria authorized today. It is still often thought that anthroposophy somehow takes its starting point from the nebulous condition of soul found in mysticism or occultism. One is mistaken if they ascribe to anthroposophy with such a questionable foundation, this view can only be held by those who know anthroposophy superficially or only from the side of its opponents. The basic orientation of Anthroposophic consciousness takes its start in an even more exact sense from what is actually the modern scientific field that is least contested today.

Famously one would like to say the Kantian statement that, in every science there's actually only so much true knowledge as there is mathematics. This state of mind is adopted by someone who mathematizes. Someone who lives within the activity of mathematical construction. We are in a very special state of mind when we do mathematics. This state of mind can best be characterized by geometry, the part of mathematics that has to do with the theory and treatment of space. In life we speak of three-dimensional space, we form the mental image of this space in such a way that its three dimensions are perpendicular, are right angles to each other. What we have before the eye of the soul as space is something which stands there quite independently of ourselves and of the rest of the world. The fact that space stands before our eyes independent of our being is evident to us from the fact that each of us determines ourselves as a separate individual according to these determinations of space. You can certainly say that you are so and so far away from any point you have in view, thus you incorporate yourself into space. You also integrate yourself into cosmic space by considering yourself as an earth being and by placing yourself at certain distances between planets and stars. In short, we all consider space as something objective as something that has nothing to do with our own inner being. This led to the fact that Kant spoke of. Our view of space as being a view that is innate to the human being from the beginning, we have no possibility of asking how we got this space. We simply have to accept it as something ready-made, as something we have to find our way into when we have come to the full consciousness of our existence on Earth.

But this is not the way it is in reality. As human beings we form a space out of our own being. Only we do not follow the formation of this mental image of space with consciousness. For this construction takes place during a time in our lives when we cannot yet think about ourselves and about our own activities. To be able to do so would require that we could with complete consciousness enlighten ourselves about the essence of space in relation to our own being. For we would not have the view we have of space if we did not experience these three dimensions of space within our own existence on Earth. We experience the one dimension by moving from helplessness after our birth to walking upright as a human being as placing ourselves into this vertical dimension. We simply learn about the existence of this dimension from the way we ourselves form this one dimension. You do not get to know just any dimension that simply happens to be perpendicular to the two other dimensions. We get to know this very special spatial dimension which is perpendicular to the surface of the Earth, we begin to Cognize it by the fact that we are not born upright. It is part of the laws that form our life on Earth that we first have to bring ourselves into this vertical dimension.

We also cognize a second dimension unconsciously. We individually form the ability to take our orientation from left to right and right to left. We only have to think of how we have the organization of speech in a certain part of our brain, the so-called Broca's area and on the other side of our brain does not have such an organization. Today it is known and recognized by science that the formation of this speech organization in the left part of the human organization is connected with the initial active mobility appearing in the right hand. So we know that there is an orientation from right to left. This orientation from right to left, this stimulation of activity on the left by activity on the right or vice versa, is something we experience within the laws that form us. Just like our rising into uprightness. It is in this symmetrical right and left orientation that as human beings we initially experience the second dimension of space.

We never actually experience the third spatial dimension completely we actually only visualize the so-called depth dimension in an estimating way. We are constantly accomplishing this, although fundamentally this accomplishment lies in the subconscious. If we cross our two eye axes at a point, we grasp with both eyes, we expand the space (which otherwise would have only two dimensions for us) into the third. With all the judging and estimating of spatial depth we actually unconsciously form the third dimension out of our own being, out of our own formative laws. We unfold the three spatial dimensions out of our own life, and the space we conceive and use in geometry is nothing but an abstraction of what we gradually learn to cognize concretely out of our own organism as the real 3 dimensions, which are fully connected with our subjective human nature. We omit in this geometrical abstraction in the very definite configuring of space, the very specific vertical, the specific horizontal and the specific depth dimensions all become indifferent to each other. Such processes always take place in abstraction, and then when we have formed this external space which we speak of in geometry, from an abstraction of our own inner 3-dimensional experience. We then extend our consciousness over this external space.

But now comes the significant thing. What we have first gained out of ourselves is not applicable to external nature. First it is applicable to inorganic lifeless formations but also to the various positional relationships and movement relationships of organic formations. This is decisively determinative for our external world. Having made this transition/metamorphosis of space from a realm that lives only within us to what we usually call space. We now stand completely with our mental images of space our experiences of space within the outer world. We can then determine and reflect back on ourselves according to spatial dimensions, spatial measurements, in relation to our own location and movement. We actually go right out of ourselves by forming/constructing space in this way. That which we have first experienced in ourselves we carry out into the world outside our body, then we place ourselves at a point of view from which we then look back at ourselves filled with space. And by first objectifying space in this way, we can now study the outer movement and position of things with the mental images that we have formed geometrically within space. Thus, we really feel we are standing on a sure scientific foundation when we immerse ourselves in things by means of what we have formed out of ourselves. From these circumstances in regard to space we can never have any doubt and we can live inside things at the same time by means of what has come out of us in this way. If we judge the distance or the changing distance of two bodies in the outside world according to spatial relations, we never doubt that we are determining something completely objective, into which subjectivity cannot enter.

But there is an important problem there, the problem is that something which we have experienced subjectively in ourselves appears as belonging objectively to the outer world. By transforming it out of ourselves simply through a process of abstraction, space then becomes something which penetrates the outer world. When the subjective experience of space in three dimensions and the objectification of it is carried out, I stand inside the objective outer world with what I experience in myself. Our subjective experiences in that they are spatial experiences are at the same time objective experiences. By moving ourselves through space we carry out a subjective process, but it is at the same time an objective process because it takes place in the outer world. Whether we see a machine moving forward or a human being, subjectivity does not come into consideration. For the outer constellation of the world what takes place in so far as the human being lives spatially, is completely objective. You objectify space out of subjective experience by measuring space with your own self so that you then move in an objective space, by objectifying space you actually also carry this space within yourself.

If you consider what is actually present there, as a constitution of your soul unfolding in time, then you can say to yourself, if I could do the same with regard to other experiences as I can do with regard to mathematizing space then I would be able to carry the mathematizing constitution of my soul into other areas of experience. But let's assume that we not only could come to this during the unconscious course of life, (for learning to stand upright and to walk to orient left together with right belong to the unconscious course of life, and the way we measure the depth dimension of space is half unconscious), but rather that we could consciously transform other subjective experiences in such a way that we could stand outside ourselves and look back on ourselves with these transformed experiences. What if we could form other experiences just as we create and form the spatial experience out of ourselves. When we look at a salt cube, we bring with us the shape of the cube from out of our own geometry, and we know that a complete identification has taken place of the shape of the objective salt cube with what we have formed in our spatial conception. What if we could do this with our sense perceptions, with our sensations of sense qualities of colors sounds and so on, and when we confront external objects. In the same way project out into the world as it were what we first formed within ourselves. We would thus place ourselves outside our body and even be able to look back on ourselves.

With reference to sense perceptions however, science has come into true confusion. Science thinks that when we see red some kind of external vibration is transmitted to our organ of sight, then to the brain, then the actual red experience is triggered, or the tone C sharp is triggered in the same way by external vibrations. Here they are in confusion, because what lives in us within the boundary of our body can no longer be distinguished from what is outside. All sense qualities colors tones and warmth qualities are actually only subjective, the outer objective process is something completely different. If now we can also create from out of ourselves what appears in us as the sensations of sense impressions and then transfer them outside of us in order to find them again in and on things, just as we construct the three spatial dimensions out of ourselves, then in same way we would find again what we first found in ourselves, in and on things. And yes then looking back at ourselves we would find them again, just as we find would be experienced as space within us in the outside world and then looking back at ourselves we find ourselves belonging to this space. Thus we would have around us, as we have the world of space around us, a world of colours and tones flowing into each other. We would speak of an objectified colored sounding world, a flooding colored sounding world just as we speak of this space around us.

We can certainly achieve this. We can get to know this world as the world of our own construction. Just as we unconsciously, simply out of our human nature, form the shape of space in order to find it again in the world by first having metamorphosed it. So too can we through certain exercises that must now be carried out consciously, come to find out of ourselves all the qualities contained in the world and then find them again in looking back at ourselves. This is an ascent to what is called imaginative cognition. We all have a spatial world around us today, through exercises we can all experience what lives in us and in the world at the same time. We can add to the ordinary objective view of things, in which mathematics is a sure guide. The imaginative view is only a technical term and does not mean imagination in the ordinary sense. What must we have to do in order to arrive at such an imaginative contemplation, where we have an overall view of the qualities of the world?

We achieve this in just in the same way as we come to experience space. Thus, when we can confront the world in this imaginative way we are already within supersensible vision, we are at the first stage of super senseble vision. Normal sense perception seeing with our sense of sight for example, where we simply stare at things and only take in their forms externally, can be distinguished from seeing mathematically geometrical structures in things where we see triangles and squares within them. The vision that occurs in imagination is really an interweaving with the inner essence of things, just as mathematical contemplation is an interweaving with those world relations that are absolutely accessible to mathematics. Whoever approaches mathematics with the right attitude will come to see a model for everything that is to be achieved for a higher, a super sensible contemplation. For mathematics is simply the first stage of supersensible perception, what we see as the mathematical structures of space are supersensible perceptions. We only do not acknowledge this because we've gotten used to it and merely accept it. But one who knows the actual nature of his mathematizing, knows that what we find given within the structure of space completely bears the character of all that one can demand from Clairvoyance in the true sense of the word. This is the anthroposophic sense of Clairvoyance, without nebulous mysticism or confused occultism, but simply with the aim of ascending to supersensible worlds in an exact and scientific way. On the whole it is precisely mathematicians the ones who should know the process that takes place when they are mathematizing, who do not actually bring a deeper understanding toward what necessarily appears as a higher qualitative mathematizing in clairvoyant research.

For imaginative cognition the first stage of this research attained through exercises is nothing other than an insight into still other areas of existence than mathematizing usually allows for. But many things change with respect to human observation, if we look at the whole inner nature of mathematics with true self cognition, there we come for example to the following, we look back on how we came to the structure of space in early childhood through walking and standing upright by orienting left and right by determining the depth dimension, by connecting with all this we get to know from inner experience what is otherwise only an abstractly viewed geometrical space. We also learn to recognize the fateful consequences if one cannot look back to this living emergence of space, in the mental picturing and contemplation of space from out of the human being. For there are consequences if we simply accept space already in a metamorphosed form independent of the human being. Today science has come to regard space in its three dimensions in such a way that they have gone over purely mathematically to a fourth and to further dimensions. These muti-dimensional spaces and the geometries that refer to them have today become generally known in scientific circles. However, for someone who has gotten to know the living formation of space it is extremely interesting to follow this pursuit of mathematical calculations and function operations carried out in respect to three-dimensional space. By extending certain things one then gets the fourth dimension which is no longer visible and so on. These things are mathematically logically not only interesting but also completely correct.

However, for someone who knows how our vision of space comes about, there is something very special here. For example, we can have a pendulum and see the pendulum swing out and up, in looking purely externally at a moment of a pendulum swing you could think that this pendulum might swing on and on outward and upward, but it does not, when it has reached a certain point it swings back again in the opposite direction. If we know the force relations that live in the pendulum then we know that the pendulum oscillates that it cannot simply go on because of the force relations that lie within it. In the same way you can learn to cognize such force relations in your own soul condition in relation to space. Then matter becomes different, then you actually logically mathematically participate in what forms the transition from the calculations in three dimensional to four-dimensional space. Only you then notice it does not proceed further, it does not proceed into an indefinite 4th, but you must turn back at a certain point and the 4th dimension becomes simply the third dimension with a negative sign, you come back again through the third dimension. This is the mistake that is made in multi-dimensional geometries. There we simply continue to run abstractly from the second into the third from the third into the fourth dimension and so on. But what is happening here is not simply continuous but oscillating, our view of space must again return into itself, in truth we destroy the third dimension by taking it negatively. The 4th dimension is the negative third which annihilates the third and actually makes space two dimensional. And likewise we can find a process for the 5th and 6th dimensions which is quite real in itself although one that is logically mathematically algebraically simply continuous. If we are to form mental images according to the reality of the space that is simply present before us, we must with the 4th 5th 6th dimension come back again and with the 6th dimension we have simply canceled space altogether, we've arrived at the point.

What is actually present now in our current culture? Our age has become abstract with respect to thinking, one simply continues the course that one has taken by thinking from plane emetrics to steryometry. While in reality the 4th dimension leads back again into space, but by returning now, we are not at all in the same situation in which we were when we emerged into a vision of the third dimension, by returning we are spirit laden. If we find the possibility to think of the fourth dimension in such a way that we return with it again by being the negative third back into space, then this space becomes spirit filled, while three-dimensional space is matter filled. We find space filled with higher and higher spirit forms. If we go along from the negative third and 2nd and 1st dimension up to the point, where we have no more spatial extension but stand completely in the extensionless, purely within the spiritual.

This shows how a spiritual path unfolds in reality. This is in contrast to the path which has become so accustomed, only to material appearances. This external path naturally no longer works materially in the souls constitution, but it works within mathematics by continuing on in abstractions to enter an imperceptible world, in which it can at most calculate or form imaginary mathematical structures. Here you see that living completely into the mathematical leads you to receive into yourself the inner nature of the spiritual in accordance with the world through mathematics, a true understanding of the mathematical state of the soul leads us directly into the concept of clairvoyant experience and then we ascend to imagination. In order to comprehend the spiritual it cannot be comprehended in the usual way, it must be described the way I have, when we passed from the third to the 4th dimension and so on up to the dimensionless realm to the point. This leads us spiritually to the highest we can reach not as an empty point but as a fulfilled point.

How do you first become aware of this difference between seeing the sense world and seeing the supersensible world? At the moment I got to know the inner sense of the so called viewer or synthetic geometry, that's when you pass from analytical to synthetic geometry, it allows you not only to approach its constructions externally but also to grasp their mutual relations. This synthetic geometry starts from these constructions themselves and not from external coordinates, for if we only construct spatial coordinates we have not grasped these structures but only the end points of the coordinates and then we connect these ends and get the lines, but we can't actually get to these structures with analytical geometry. While with synthetic geometry, we live within the constructions, with this we receive the stimulus to study the soul constitution, which when for the developed leads to a penetration into the super sensible world.

Natural science uses a ready-made formalized mathematics, anyone who wants to understand the clairvoyant process must seek it out where it is most primitively present, in the form of mathematics. If you can then carry it up into higher realms you develop something that relates to the elementary primitive basis of mathematics in the same way as the later mathematical realms relate to their first axioms. The first axioms of clairvoyance are alive and if we succeed in training mathematically through exercises we will not only see spatial relations in our environment but we'll get to know the spiritual beings who reveal themselves before us with spiritual inwardness, just as we can know the inner cube nature of rock salt. We get to know spiritual beings when we carry in this way what we form in mathematics up into higher realms. This is the foundation of what must be recognized within anthroposophy as clairvoyant research. We will then see how this clairvoyant research can be applied to the individual fields of knowledge both to the fields of natural science and to the fields of Medicine, Historical Science and so on, and we will see how the sciences are not challenged but enriched by introducing into their fields the knowledge that can be cognized in super sensible vision, super sensible cognition.

However, for a correct understanding of what is actually meant here, it can help to consider the course of human development over a certain period of history in order to see how it led to the formation of our present scientific thinking. Let us considered this scientific thinking which recognizes the mere formalism of mathematics and yet has learned inner certainty and exactness of research from mathematics. It actually regards the laws of nature as justified only if they are capable of such a mathematical formulation. At least this is a kind of ideal of today's scientific inquiry but it was not always so, that which we recognize today as the scientific spirit has only developed over the long course of human evolution, I will present only three stages of this developing human spirit at which we are in the third today.

If we go back to the ancient orient we find a principle of cognition that has been preserved there, in those older times human beings looking back on themselves did not feel as we do today. Our self-consciousness is firmly taken hold of by thinking on the one hand and the observation of what is mechanistic on the other hand. A person from the Orient was not able to feel like this. They felt themselves as breathing beings. The human being was a breather and the process of breathing was that to which they preferably looked for self cognition, for self perception. They even associated immortality with the breathing process, a kind of exhalation of the soul was its entrance into death. Why did they feel in this ancient state of soul that the human being was a breathing being? Because in the breathing process life was really felt in inhalation and exhalation. They felt the vibrations, the rhythms of life in breathing. Breathing was felt then the way we feel hunger and thirst today, but this breathing process was a continuous feeling in the waking state. They felt the act of looking in such a way that the breathing movement flowed through it. It was likewise with a movement of the will, a stretching out of the hand was felt as if it were something that was connected to movements of the breath, a spreading of the breath into the whole body was felt as an inner life process. Thus, perception was then felt to be animated by the breath, over against our more theoretical perception of today of the outer world through the senses. They also felt their impulses of will to be animated by the breath, they felt themselves to be breathing beings. Because of this they could have said their breath was modified in such a way by seeing through their eyes, by hearing through their ears, by perceiving effects of heat, they experienced everywhere through sensory perceptions a differentiated modified metamorphosed refined breathing process. Because of this for them the path of cognition also involved a regular training of the breathing process.

This was for those older epochs of human development what our university study is for us today. But we study in a different way, in those days when they wanted to gain religious satisfaction, when they wanted to gain knowledge they studied by training and transforming their breathing process. In other words they developed what was later called yoga breathing, Yoga exercises, and what was thus trained. If you follow what was achieved by practicing yoga breathing in order to reach higher levels of cognition, you will find something strange. Those who had become scholars through yoga exercises had taken hold of something in their soul constitution that in later times, for example in the Greek and Roman times, was experienced as the world of ideas. Later for the Greeks this world of ideas simply arose there as if by itself. Thus for the Greeks the human soul constitution no longer needed yoga. That is the interesting thing, what one has to strive for through all kinds of exercises during an earlier epoch is there by itself in the development of later epochs. Later it no longer means what it used to mean, thus we see that what was practiced as a path of cognition in the most ancient times through regulated exercises of the breath resulted in a certain vivid conceptual world. This is what was given to people as a matter of course in that age, and which was achieved in still older times through yoga. It was always through exercises that one strove for the higher knowledge of an age, thus the perception of the world was experienced in later epochs in such a way that one now no longer perceived the breath when reflecting upon oneself. At that time of the Greeks it was still the case that people did not form separate thoughts about the world, rather their ideas formed a unity with their sense experiences. They saw their thoughts outside in the world as we today see red or blue outside or hear c sharp or b flat. Thoughts were part of the outside world, thus they then perceived only spirit penetrated by sense perceptions or sense perceptions penetrated by spirit, and no longer the differentiation of the breathing process.

However, humanity again strove to reach a higher level of cognition in all those fields where they had already striven for higher cognition, and this new level was again reached by exercises. Today we have rather vague ideas about the times of the early Middle Ages, about the spiritual life of the early Middle Ages. Such abstract learning as we practice today was not what medieval students did. They also had to do exercises, the usual learning process was then also connected with doing exercises. It was an inner practice they went through, but not in such a robust way as the practice of yoga breathing, it was a more inward practice but still a practice. A legacy little understood today has been preserved in what in the Middle Ages was called the seven liberal arts. At that time anyone who sought a higher cognition had to undergo a training in the following subjects; Grammar which meant the practical handling of language, Rhetoric which not only meant the proper use but also the beautiful handling of language, Dialectic the manipulation of language from out of the inner power of thinking, and when they and when they had gone through these three inner practice as exercises then came Arithmetic. Not our abstract arithmetic, but that arithmetic which lived within things, which led to a clear consciousness of the fact that we form everything inwardly. Then they learned inwardly practiced Geometry. A geometry that was fully inter woven within them, becoming a practical capacity. Then the whole thing led into what was called Astronomy. Here they integrated their being into the Cosmos. They learned to Cognize how their head related to the Cosmos, how their lungs and their heart were a result of the Cosmos. They did not have an astronomy separated from the human being, but an astronomy within which the human being stood fully. And then Music, they got to know the weaving and working of Divine Being, which weaves and wells through the world. Not the music of today, but a higher living development of what was active more in thought form in astronomy. And so in these later times students exercised an inner practice, what used to be breathing exercises was now more an inner practice of the soul.

Gradually in the course of the history of human civilization we came to have thoughts separated from sense perceptions. We grasp a thought as something produced by us as a thing that is not contained in things. What we feel in this way, what our souls condition is today, is a result of practicing grammar rhetoric and so on up to music in earlier times. Thought became detached from things, when one learned to move freely in thought. This finally has brought about what is now natural to us, what we have to day without having to do exercises. It is what we find today in our schools and is offered in the individual sciences. Thus from the yoga breathing exercises one got as a matter of course the Greco Latin world view and then today's scientific point of view arose from the exercises that went from grammar to music.

Now this can be continued, Indeed the best and surest way is to start from mathematics. We must therefore internalize the process still further. We must know how the course of humanity has been up to now and how it must continue. This historical consciousness, this consciousness of being inside the whole process of humankind, is what is added to the insight that comes to us when we inwardly not outwardly take the present scientific spirit into our souls. Thus, on the one hand anthroposophy knows the peculiarity of todays science, and it rejects all denialism, all amateurism, and builds on from what is true science. On the other hand, it knows the historical necessities, it knows how the path of humanity must continue from what has been achieved at present if we do not want to stand still, just as all our ancestors where they had a share in the development of civilization wanted to move forward. We must know which steps have to be taken from the present standpoint of the scientific spirit. We are in accelerating times, may that which humanity wants to achieve in the cognition of the supersensible be achieved as quickly as is necessary for the salvation of humanity.