“The knowledge of which geometry aims is the knowledge of the eternal.”
Republic, VII, 52.
Plato’s theory of forms states that there are archetypal levels of reality that contain the blueprints of everything in the creation. According to Plato, human beings have knowledge of these archetypes from traveling in the spheres between incarnations. Learning ( anamnesis in ancient Greek,) consists of rediscovering that knowledge within. You simply remember or reconnect with the part of you that has a knowing of these archetypes. At Plato’s Academy, in ancient Greece (387 BCE), mathematics was stressed as a way of understanding more about the archetypal nature of reality. In particular he was convinced that geometry was key in unlocking the secrets of these archetypal levels. At the entrance of the academy there was a sign that read “Let no-one ignorant of geometry enter here”.
Now, I am a meditator and artist, not a mathematition! Yet I find that working with geometric forms does something beautiful to my state of mind. Geometric forms are a powerful language to describe the experiences of realms beyond the physical senses. States of consciousness that are difficult to capture in words can be expressed through a combination of the eternity of line, line segments, angles, and shapes.