6. Anthroposophy and Agnosticism

Rudolf Steiner: If I have the usual coordinate system, I have characterized three-dimensional space. Now, let us just discuss it schematically, we proceed from certain algebraic assumptions by abstractly continuing the same process that leads from the plane into three-dimensional space, and we arrive at the fourth dimension, the fifth and so on, at an n-dimensional space. And then it is even possible, let's say, to construct bodies – Hinton did that – to construct the tessaract, but that is not a real body, but the projection of the real tessaract into three-dimensional space. Now the thing is this: in purely theoretical-abstract terms, of course, there is nothing to be said against such derivations. In theory, one can also pass from three-dimensional space to the fourth dimension of time, if one proceeds within the calculation formulas in such a way that one takes into account the leap that is actually made, because it is different after all, if one passes from the first to the second dimension and to the third dimension of space, than if one passes into time. But if you refine it, ... then you can pass over into time. In this way one arrives at an abstract four-dimensional space. If one remains abstract, one can go on doing this as long as one remains in the purely intellectualistic, as long as one is not compelled to follow the matter vividly. But then one is confronted with a problem which, while the purely abstract train of thought leads to a regressus ad infinitum, vividly becomes an elasticity problem. We could also think of the pendulum as continuing to swing forever. But in the dynamic, we will get a state of vibration. That is how it is in reality. If you can get into imaginative thought, you simply can no longer carry out the process in infinitum by assuming a fourth and so on dimension. Then, if I call the first dimension +a, the second +b, the third +c, if I take real space, I am obliged not to write the fourth +d, but by the nature of things I am obliged to write -c. So that the fourth dimension simply cancels out the third bit by bit and only two remain. So instead of four, I end up with two dimensions. And so I am also forced, if I assume the fifth, to set - b, and with the sixth - a. That is, I come back to the point. Elasticity has struck back to the starting point. And that is not something that exists only in the imagination, for example, that is, a subjective experiment, but it is realized in the way I described the day before yesterday. As long as we have, let us say, the earth here and look at the root of the plant, we are really dealing with a special formation of gravity. Here one is in the ordinary dimensionality of space. But if one wants to explain the form of the blossom, then one cannot get away with that. Then, instead of taking the point of origin of the co-ordinates, one must take infinite space, which is, after all, only the other form of the point. And then one comes to going in centrifugally instead of going out centrifugally. You come to this wave surface. Instead of the thing spreading out, it pushes in from the outside, and then you get those movements, which are sliding or scraping movements or pressure movements, where you would go wrong if you took coordinate axes from the center of coordinates, but you have to take the infinite sphere as the center of coordinates and then all the coordinates going towards the center. So, one also gets the qualitatively opposite coordinate axis system as soon as one enters the etheric. The fact that this is not taken into account is the mistake in the ordinary ether theory. Herein lies the difficulty in defining the ether. Sometimes it is seen as liquid, sometimes as gas. The mistake here is that one starts from the coordinate system seen from the center. But as soon as one enters the ether, one must take the sphere, and construct the entire system not from the inside outwards, but the other way around.