Twenty-Second Meeting

Dr. Steiner: Well, that is a more general question. It is not a good idea to use things in projective geometry that do not exist. There are no light rays and still less shadow rays. It is not necessary to work with such concepts in teaching projections. You should work with spatial forms. There are no light rays and no shadow rays. There are cylinders and cones. There are shadows that arise when I place a cone at an angle and illuminate it from a point and allow a shadow to fall upon an appropriately angled plane. Then I have a shadow form. The form of the shadow as such is the boundary of the shadow, and even a child should understand that. It is the same later in projective geometry when the child learns what occurs when a cylinder cuts through another with a smaller diameter. It is very useful to teach children that, but it does not detract from the artistic. It guides children into the artistic. It makes their imagination flexible. You can imagine flexibly if you know what section occurs when two cylinders intersect one another. It is very important to teach these things, but not as abstractions. A teacher asks about plane geometry.