The Fourth Dimension

GA 324a — 17 May 1905, Berlin

Third Lecture

My dear friends, today I will continue with the difficult chapter we have undertaken to take on. In doing so, it will be necessary to refer to the various things that I have already mentioned in the last two lectures. Then today I would also like to create the basic lines and basic concepts in order to [the more exact geometrical relationships as well as] the interesting practical aspects of theosophy, to make them our own.

You know that we have tried to imagine four-dimensional space in its potentiality for the very reason that we can at least create some kind of concept about the so-called astral realm as well as about the higher realms, about higher existence in general. I have already indicated that entering the astral space, the astral world, is initially something tremendously confusing for the secret disciple. For those who have not studied these things in detail, who have not even studied them theoretically, who have not even studied Theosophy theoretically, it is extremely difficult to even begin to form an idea of the very different nature of the things and entities that confront us in the so-called astral world. Let us once again point out how great this diversity is.

As the simplest thing, I mentioned that we have to learn to read every number symmetrically. The secret student, who is only accustomed to reading numbers as they are read here in the physical world, will not be able to find his way through the labyrinth of the astral. If you have a number in the astral, for example 467, you have to read it as 764. You have to get used to reading everything symmetrically, to seeing everything symmetrically (in a mirror image). That is the basic condition. This is still easy as long as we are dealing with spatial structures or numbers. It becomes more difficult when we come to time relationships. When we come to time relationships, the matter also becomes symmetrical in the astral, in such a way that what comes later appears to us first and what comes earlier appears later. So when you observe astral processes, you also have to be able to read backwards from front to back. These things can only be hinted at, because they sometimes seem quite grotesque to those who have never had an idea of them. In the astral, the son is there first and then the father; in the physical, the egg is there first and then the chicken. In the physical, it is different. In the physical, birth comes first, and then the birth is an emergence of a new thing from an old one. In the astral, it is the other way around. There, the old emerges from the new. In the astral, what is paternal or maternal nature devours what is filial or daughterly nature for the appearance.

In Greek, you have a pretty allegory. The three gods Uranus, Kronos and Zeus symbolize the three worlds. Uranus represents the heavenly world: Devachan; Kronos represents the astral; Zeus the physical. Kronos is said to devour his children.” So in the astral, one does not give birth, but is consumed.

But things get very complicated when we look at the moral aspect of the astral plane. This also appears in a kind of reversal or mirror image. And that is why you can imagine how differently things appear when we interpret things as we are accustomed to interpreting them in the physical. In the astral, for example, we see a wild animal approaching us. This is not to be understood in the same way as in the physical. The wild animal is choking us. This is the appearance that someone who is accustomed to reading things in the same way as external events has. But the wild animal is in truth something that exists within ourselves, that lives in our own astral body and that is choking us. What approaches you as a strangler is rooted in your own desire. So you can experience that when you have a thought of revenge, this thought of revenge appears to you as a strangling angel that approaches you from outside and harasses you.

In truth, everything radiates from us [in the astral realm]. We must regard everything that we see approaching us in the astral as emanating from us (Figure 18). It comes from the sphere, from all sides, as if from infinite space, it penetrates into us. But in reality it is nothing other than what our own astral body sends out.

We only really read the astral [and only then] find the truth when we are able to bring the peripheral into the center, to see and interpret the peripheral as the central. The astral seems to come at you from all sides. Think of it this way: in reality, it is something that radiates out from you in all directions.

I would like to familiarize you with a term that is very important in occult training. It appears in a wide variety of works on occult research, but is rarely understood correctly. Those who have reached a certain level of occult development must learn to see everything that is still karmically predisposed in them – joy, lust, pain, and so on – in the astral outside world. If you think theosophically in the right sense, you will realize that the outer life, our body, in the present age is nothing more than a result, an average of two currents coming from opposite directions and merging into each other .

Imagine a current coming from the past and one coming from the future, and you have two currents that merge and actually intersect at every point (Figure 19). Imagine a red current in one direction and a blue current in the other direction. And now imagine, for example, four different points in this intersection. [Then, at each of these four points, we have] an interaction of these red and blue currents. [This is an image for the interaction of] four successive incarnations, where in each incarnation something comes towards us from one side [and something from the other]. You can always say to yourself, there is a current that comes towards you and a current that you bring with you. Man flows together out of these two currents.

You get an idea of it if you think of it this way. Today you sit here with different experiences, tomorrow at the same hour you will have a different set of events around you. Imagine the events that you will have by tomorrow are already all there. It would then be the same experience as if you were looking at a panorama. It would be as if you were approaching these events, as if these events were coming towards you spatially. So imagine that the stream that is coming towards you from the future brings you these events, then you have the events between today and tomorrow in this stream. You allow the future flowing towards you to be carried by the past.

In every period of time, your life is an intersection of two currents, one from the future to the present and the other from the present to the future. Where the currents meet, a congestion occurs. Everything that a person still has ahead of him must be seen emerging as an astral phenomenon. This is something that speaks an incredibly impressive language.

Imagine that the secret disciple [comes to the point in his development where he] is supposed to look into the astral world, where the senses are opened to him so that he would see emerging around him as outer phenomena in the astral world that which he would still have to experience before the end of the present period. This is a sight that is very powerful for every human being. We must therefore say that it is an important step in the course of occult training for the human being to be confronted with the astral panorama, the astral phenomenon, of what he still has to experience until the middle of the sixth root race, because that is how long our incarnations will last. The path opens up before him. No secret disciple will experience it differently, except that he sees as an external phenomenon what he still has to face in the near future up to the sixth root race.

When the disciple has advanced to the threshold, the question arises: Do you want to live through all this in the shortest conceivable time? Because that is what it is about for the one who wants to receive the initiation. If you think about it, you have your own future life in front of you as an external panorama in a moment. That, in turn, is what characterizes our view of the astral. For one person, it is something that makes them say, “No, I'm not going in there.” For another, on the other hand, it is something that makes them say, “I have to go in there.” This point in the process of development is called the 'threshold', the decision, and the phenomenon that one has there, oneself with everything that one still has to experience and live through, is called the 'guardian of the threshold'. The guardian of the threshold is therefore nothing other than our own future life. It is ourselves. Our own future life lies behind the threshold.

You see in this another peculiarity of the astral world of appearance, namely, that when the astral world is suddenly opened to someone through some event – and such events do occur in life – that person must first face something incomprehensible. It is a terrible sight, which could not be more confusing for those people upon whom, unprepared, the astral world suddenly breaks in through some event. It is therefore eminently good to know what we have now discussed, so that in the event of the astral world breaking in, one knows what to do. It may be a pathological event, a loosening between the physical body and the etheric body or between the etheric body and the astral body. Through such events, a person may be unexpectedly transported into the astral world and gain insights into astral life. If this happens, the person will come and say that he sees this or that apparition. He sees it and does not know how to read it, because he does not know that he has to read symmetrically, that he has to understand every wild animal that approaches him as a reflection of what lies within himself. Indeed, the astral powers and passions of man appear in Kamaloka in the most diverse forms of the animal world.

It is not a particularly beautiful sight to see people in Kamaloka who have just been reaped. At that moment they still have all their passions, urges, desires and cravings. Such a person in Kamaloka no longer has his physical body or etheric body, but in his astral body he still has everything that connected him to the physical world, that can only be satisfied through the physical body. Imagine an average citizen of the present day who has achieved nothing special in his past life and has not made any effort to achieve anything, who has never done much for his religious development, who may not have abandoned religion in theory, but practically, that is, in his feelings and attitudes, has thrown it overboard. In that case it is not a living element in him. What then is in his astral body? There are only things that can be satisfied through the physical organism. For example, he craves palate enjoyment. But the palate would have to be there for that, so that this desire can be satisfied. Or man craves for other pleasures, which can only be satisfied by setting his physical body in motion. Suppose he had such a craving, but the body was gone. Then all this lives in his astral body. This is the situation in which man finds himself when he has died without astral purification and cleansing. He still has the desire for the pleasures of the palate and the other things, but not the possibility of satisfying them. This is what causes the torment and horror of the life in Kamaloka. Therefore, the desire must be laid aside in Kamaloka if man dies without astral purification. Only when this astral body has learned that it can no longer satisfy its desires and wishes, that it must unlearn them, is it freed.

[In the astral world] the instincts and passions take on animal forms. As long as the person is embodied in the physical body, the shape of their astral body is somewhat based on this physical body. But when the outer body is gone, then the instincts, desires and passions, as they are in their animal [nature], come into their own in their own form. So in the astral world, a person is an image of their instincts and passions.

Because these astral beings can make use of other bodies, it is dangerous to let mediums enter into a trance when there is no clairvoyant is present to avert evil.

In the physical world, the lion is a plastic expression of certain passions, the tiger is an expression of other passions, and the cat is an expression of yet other passions. It is interesting to see how each animal is the plastic expression of a passion, of an urge.

In the astral, in Kamaloka, man is therefore approximately similar to [animal nature] through his passions. This is the source of the misunderstanding regarding the doctrine of transmigration of souls that has been attributed to Egyptian and Indian priests and teachers of wisdom. You should live in such a way that you do not incarnate as an animal, says this teaching. But this teaching never speaks of the physical life, but of the higher life, and its only aim was to persuade people on earth to lead such a life that after death in Kamaloka they would not have to develop their animal form. Those who develop the characteristics of a cat will appear in Kamaloka as a cat. The fact that one also appears as a human being in Kamaloka is the meaning of the rules of the doctrine of the transmigration of souls. The true teachings have not been understood by the scholars; they only have an absurd idea of them.

Thus we have to deal with a complete mirror image of what we actually think and do here in the physical world in every area – in the areas of number, time and moral life – when we enter the astral realm. We must get used to reading symmetrically, because we must be able to do so when we enter the astral space.

The easiest way for a person to get used to reading symmetrically is to build on such elementary mathematical ideas as we have hinted at in the previous lecture and as we will get to know more and more in the following discussions. I would like to start with a very simple idea, namely the idea of a square. Imagine a square as you are accustomed to seeing it (Figure 20). I will draw the square so that the four sides are drawn in four different colors.

This is the physical appearance of the square. Now I would like to draw the devachan aspect of the square on the board. It is not possible to do this exactly, but I would like to give you an approximate idea of what a square would look like in the mind. The mental counter-image [of a square] is approximately like a cross (Figure 21).

We are dealing here mainly with two perpendicular intersecting axes. Two lines that pass through each other, and that's it. The physical counter-image is created by drawing perpendicular lines on each of these axes. The physical counter-image of a mental square can best be imagined as a congestion [of two mutually intersecting currents]. Let us imagine these perpendicular axis lines as currents, as forces that act outwards from the point of intersection, and let us imagine countercurrents to these currents, only now in the direction from outside to inside (Figure 22). A square then enters into the physical world by imagining these two types of currents or forces - one from the inside, the other from the outside - as accumulating against each other. The currents of force are thus limited by accumulations.

With this, I have given a picture of how everything mental relates to the physical. Likewise, you can construct the mental counterpart for any physical thing. The square here is only the simplest of examples.

If you could construct a correlative for every physical thing that corresponds to the physical world in the same way that two perpendicular lines correspond to a square, then you would obtain the devachan or mental image for every physical thing. With other things, it is of course much more complicated.

Now imagine a cube instead of a square. The cube is very similar to the square. The cube is a body that is bounded by six squares. Mr. Schouten made these six squares that bound the cube specially. Now, instead of the four bounding lines that are present in the square, imagine six bounding surfaces. Imagine that instead of vertical lines we have vertical surfaces as a kind of congestion, and then assume that you have not two but three axes standing on one another [vertically], and you have the boundary of the cube. Now you can also imagine what the mental correlate of the cube is. You have again two things that challenge each other reciprocally. The cube has three perpendicular axes and three surface directions; we have to think of congestion effects in these three surface directions (Figure 23). We cannot imagine the three axes and the six surfaces, as before the two axes and four lines, in any other relationship than by thinking of a certain contrast.

Anyone who reflects on this will have to admit that we cannot imagine this without forming a certain concept of the opposition, namely the opposition of activity and an obstruction, a counter-activity. You have to introduce the concept of opposition here. The matter is still simple here. By entwining ourselves around geometric concepts, we will be able to construct the mental counter-images of more complicated things in an appropriate way. Then we will find the way and to some extent reach higher knowledge. But you can already imagine the colossal complexity that arises when you think of another body and look for its mental counter-image. Many complicated things come to light. And if you were to imagine another person and their mental counterpart, with all their spatial forms and their activity, you can imagine the complicated mental structure that this produces. In my book 'Theosophy', I was only able to give a rough idea of what mental counter-images look like.

We have three dimensions, three axes in the cube. On each axis we have the corresponding perpendicular planes on both sides. So you must now be clear about the fact that the contrast I have spoken of is to be understood in such a way that you imagine each face of the cube as having come into being in a way similar to the way I described human life earlier, as the intersection of two currents. You can imagine currents emanating from the center point. Imagine space in one axial direction, flowing outwards from the center, and in the other direction, flowing in from infinity, another current. And this [imagine] flowing in two colors, one red, the other blue. At the moment they meet, they will flow into a surface, a surface will arise, so that we can assume the surface of the cube to be the meeting point of two opposing currents in a surface. This gives a vivid idea of what a cube is.

The cube is therefore an intersection of three currents acting on each other. If you think about it, you are not dealing with three, but with six directions: forward-backward, up-down, right-left. So you have six directions. And indeed, that is the case. Then the matter becomes even more complicated by the fact that you have two types of currents: One in the direction of a point, the other coming from infinity. This will give you a perspective on the practical application of the higher, theoretical theosophy. I have conceived every direction in space as two opposing currents. And if you then imagine a physical body, then you have in that physical body the result of these two currents running into each other.

Let us now denote these six currents, these six directions, with six letters a, b, c, d, e, f. If you could visualize these six directions or currents — we will come to being able to do this next time — and you would imagine the first and last, a and f, erased, then you would be left with four. And that is what I now ask you to take into account: these four that remain are the four that you can perceive when you see the astral world alone.

I have tried to give you an idea of the three [ordinary dimensions] and of three [further] dimensions that actually behave in the opposite way. It is through the interaction of these dimensions and their counteraction that physical bodies arise. But if you think a little way away from the physical [dimension] and a little way away from the mental on the other side, you are left with four dimensions. These then represent the astral world existing between the physical and mental worlds.

The theosophist's view of the world is such that it necessarily has to work with a higher sense of geometry that goes beyond ordinary geometry. The ordinary geometer describes the cube as bounded by six squares. We must understand the cube as the result of six currents running into each other, that is, as the result of a movement and its reversal, of the interaction of opposing forces.

I would like to show you another such concept outside in nature, where a real contrast has taken place that contains a deep secret of the world's development before the eyes of man. In the “Fairytale of the Snake and the Lily”, Goethe speaks of the “revealed secret”, and that is one of the truest and wisest words that can be spoken at all. It is true, there are secrets in nature that can be grasped with hands, but are not seen by people. We are dealing with reversal processes in nature in many cases. I would like to show you one such reversal process.

Let us compare humans with plants. When compared to plants, humans behave as follows. What I am about to say is not a game, even if it initially seems like one. It is something that points to a deep mystery. What does a plant have in the ground? Its roots. And upwards it develops stems, leaves, flowers and fruit. The main part of the plant, the root, is in the earth, and the organs of reproduction it develops upwards, towards the sun, which we can call the chaste way of reproducing. Imagine the whole plant turned upside down, with the root becoming the head of a human being. Then you have the opposite of the plant in the human being, who has his head at the top and his reproductive organs at the bottom. And the animal is in the middle of it all, as a stowage. If you turn the plant upside down, you get a human being. That is why the occultists of all times draw this with three lines (Figure 24).

One [line] as the symbol of the plant, one as the [symbol] of the human being, and one in the opposite direction as the [symbol] of the animal – three lines that together form the cross. The animal has the transverse position, it thus crosses what we have in common with the plant.

You know that we speak of an all-soul, of which Plato says that it is crucified to the cosmic body, that it is chained to the cross of the cosmic body.? Imagine the world soul as plant, animal and human being, and you have the cross. By living in these three realms, the world soul is chained to this cross. As a result, you will find the concept of congestion expanded. You will find it expanded by something in nature. Two complementary, diverging, but interlocking currents form plants and humans, with congestion being the animal. Thus, the animal actually places itself between an upward and a downward current. In this way, the Kamaloka [astral sphere] interposes itself between Devachan and the physical world. Thus, something interposes itself between these two symmetrical worlds, between Devachan and the physical world, and acts between them, acting on both sides like a dam. The outer expression of this Kamaloka world is the animal world.

Those who already have organs for this world, which must be grasped with strength, will recognize what we see in the three kingdoms in their mutual relationship to one another. If you understand the animal kingdom as emerging from a congestion, if you understand the three kingdoms as mutual congestion, then you will find the position that the plant kingdom has to the animal kingdom and the animal kingdom to the human kingdom. The animal is perpendicular to the other two directions, and the other two are two complementary currents that merge into each other. The lower realm serves the higher realm as food. This is something that allows a small glimpse of the very different kind of relationship between humans and plants and between animals and humans. Those who feed on animals are therefore related to a congestion.

The real effect consists in the encounter of opposing currents. This is the beginning of a series of thoughts that you may later see in a strange and very different way.

We have seen that the square is created when two axes are intersected by lines. The cube is created by intersecting three axes through surfaces. Can you now imagine four axes intersecting through something? The cube is the boundary of the spatial structure that is created when four axes are intersected.

The square limits the three-dimensional cube. Next time, we will see whose boundary the cube itself is. The cube bounds a four-dimensional structure.

Answering Questions

[What does it mean to] imagine six currents, of which two must be imagined as having been extinguished, and so on?

The six currents must be thought of as two times three currents: three acting from the inside out according to the three axial directions, and the other three as flowing towards these from infinity. For each axial direction, there are thus two types, one going from the inside out, the other coming from the outside in the opposite direction. If we call the two categories positive and negative, plus and minus, we have:

math figur

And of this [in order to get to the astral space, we have to] imagine an entire direction, [for example the] inner and outer flow, erased, so for example +a and -a.