In observing the growth of the plant, Goethe had perceived that this proceeds simultaneously according to two different principles. On the one hand the plant grows in an axial direction and thereby produces its main and side stems. To this growth principle Goethe gave the name 'vertical tendency'. Were the plant to follow this principle only, its lateral shoots would all stand vertically one above the other. But observation shows that the different plant species obey very different laws in this respect, as may be seen if one links up all the leaf buds along any plant stem; they form a line which winds spiral fashion around it. Each plant family is distinguishable by its own characteristic spiral, which can be represented either geometrically by a diagram, or arithmetically by a fraction. If, for example, the leaves are so arranged in a plant that every fifth leaf recurs on the same side of the stem, while the spiral connecting the five successive leaf-buds winds twice round the stem, this is expressed in botany by the fraction 2 / 5. To distinguish this principle of plant growth from the vertical tendency, Goethe used the term 'spiral tendency'. To help towards a clear understanding of both tendencies, Goethe describes an exercise which is characteristic of his way of schooling himself in what he called exact sensorial fantasy. He first looks out for a phenomenon in which the 'secret' of the spiral tendency is made 'open'. This he finds in such a plant as the convolvulus; in this kind of plant the vertical tendency is lacking, and the spiral principle comes obviously into outer view. Accordingly, the convolvulus requires an external support, around which it can wind itself. Goethe now suggests that after looking at a convolvulus as it grows upwards around its support, one should first make this clearly present to one's inner eye, and then again picture the plant's growth without the vertical support, allowing instead the upward-growing plant inwardly to produce a vertical support for itself. By way of inward re-creation (which the reader should not fail to carry out himself) Goethe attained a clear experience of how, in all those plants which in growing upwards produce their leaves spiral-wise around the stem, the vertical and spiral tendencies work together.