ln the previous chapter, the figure of the lemniscate was used several times in order to help the reader picture and experience how polarities can be turned inside out. Drawing exercises were also given to clarify the process of thinking one's way through from one polarity into the other. Chapter 4 discussed the polarity between what anthroposophy calls the spiritual world and the material world. Anthroposophy sees these areas as complementing one another, yet forming a unity. In this chapter an attempt will be made to give the reader an experience of the reality of this polarity – and mutual interdependence - by means of geometrical descriptions and representations. This may seem a rather theoretical pursuit, far-fetched and removed from daily reality. Yet these mathematical imaginations are a help to gain access to this realm which is hard to penetrate. Therefore this should be regarded as practice material.
This chapter's approach aims to make clear that the anthroposophical concept of a 'spiritual world' is neither grounded in free associations of the imagination, nor in unclear raptures about 'energy clouds' and the like. We have the capacity to get to know a spatial world of a different kind from the material world with its characteristic measurable quantities. This capacity rests on mathematical thinking, which all of us can use to a certain degree. We can get an initial glimpse of the supersensory world when we try to do this with the kind of clarity which is only granted by mathematical thinking. Mathematics is the only exact science which is totally perspicuous, by virtue of the fact that it is completely unconnected to the senses (it is abstract) and basically cannot error.* Through the inner power of the activity of thinking we can thus transcend the inherent limits of the sense world.
In anthroposophy the level of life, which lies directly next to sense perceptible reality, is called the ‘etheric’ world.’ Although it is invisible, it can be grasped as an idea. Theexamples dealt with III this chapter aim to get to the beginning level of an initial experience of this etheric world, as it relates to physical-material reality.
Like to read more? Open the link below.Polarities and Projective Geometry 2009 EN chapter.pdf