The Consolidation

During the rest of June I devoted myself intensely to applying the garden metaphor to the educational process as a whole - thinking about how the corresponding concept-formation system ought to be structured.

The environment of the garden gave a natural background for the presentation of various elements and phenomena , as well as a possibility to supply a variety of different tools to experiment with these. From the start I imagined the elements divided into two classes - depending on whether they belonged to heaven or earth. Among the 'heavenly elements' were of course the sun, the moon, the stars and the planets, and among the 'heavenly phenomena' e.g. appearance, motion and disappearance of light. Among the 'earthly elements' were air, water, solid (soil), fire and vacuum, and among the 'earthly phenomena' were light, sound, heat, electricity and magnetism [Figure (27)].

In the garden I also envisaged a number of experimental tools, i.e. different types of computer programs, to support the interactive exploration of various elements and phenomena. There would e.g. be a Lyre and a Drum for performing musical experiments, and a set of Canonballs to build pythagorean pyramid-figures. There would also be a set of tiles - to represent the exploration of geometrical patterns in general. As a basis for this activity we already had the program MacWallpaper. The lyre was associated with the analogue part of the music (= its tone), while the drum represented the digital part (= its beat). The lyre would be connected to the pythagorean monochord, and futher - through time travel - to the Bach piano, and the modern synthesizer. The drum would work as an entrance to the 'rythm-laboratory' - where one could experiment with building various types of rythm instruments, e.g. with the help of the so called 'Chinese remainder theorem' - which is of fundamental importance within the field of fast computing (= 'modular arithmetic').

Towards the end of June I had a meeting with Kenneth (27/6), where I presented him with these concepts. Since he had not been present at the Apple meeting, this was the first time that I had the opportunity to introduce him to the concept of a Pythagorean garden of knowledge.

Heavenly and earthly elements and phenomena (96-06-27)

Kenneth was instantly positive and very responsive to these ideas. He proposed that we should make use of a (brick) wall instead of a drum - partly because it harmonized better with the concept of a neglected garden, and partly because we could extend it into a type of rythm tool that made use of bricks of different length in order to represent different time intervals. I liked this idea a lot, and we discussed many types of mathematical connections, as e.g. the representation of various number sequences by the corresponding rythmical processes.
It was a very constructive meeting. For the first time I felt some real enthusiasm for my thoughts about the GOK from somewhere else than the part of the students. We definitely had an interesting set of connections between mathematics and music to explore!