The Grail in Camelot College

Spreading out all the paper rings across my desk, I’m impressed with how many I’ve made. It’s only been three months an,d I have well over 100. Each one is a perfect circle of polygons. I marvel at their diversity. As I survey my handiwork, I pick one up, and my hands begin to shake. It's just a simple circle of hexagons that’s all—and yet it is the seed from which, like a grain of sand, a castle grows.

In that seed, I see structure, and from that structure, an architectonic vision rises up and into view. I see that castle in three stories. The first is built on the foundation of structuralism, optimizing creative diversity, like I learned constructing castles in college with plaster blocks. Then the second level is constructed with Da Vinci tables, optimizing creative efficiency like the one I found in Cracking Creativity. The top level is new. It’s where all the Da Vinci tables are organized in a nested hierarchy, just like the one I remember from biology. Altogether, there are three tables, one inside the other, corresponding to each level. What Da Vinci tables do for ideas, construct, multiply, and organize, nested hierarchies do for Da Vinci Tables. Thus, it amplifies their productive capabilities exponentially by multiplying tables by tables at each additional level (Figures 1-3).

I can see what this castle is, and what it is for. Camelot College—a model of a new university. Mirroring its architecture are disciplines at the top level, then categories of objects in the middle, and finally, at the base, objects themselves.

It’s the culmination of twenty-five years of work/play—a new vision of how to organize a university and make mathematics.

At a fever pitch, I begin to create. I use a 1×1 Da Vinci table to combine geometry and topology, forming the composite discipline of structural geometric topology.

Then, I define each of these at the second level of my castle in terms of the categories of objects they study. For geometry: points, lines, polygons, and polyhedra. For topology: knots, links, braids, and weaves. Placing them in a 4×4 Da Vinci table, it produces sixteen composite categories.

At the bottom level, I define each of the sixteen categories with four component objects and four component structures, producing sixteen tables with sixteen composite objects each—yielding a total of 256 objects.

I can feel that this is just the beginning—not just for mathematics, but for a new system of creating knowledge because it can be applied to more than just mathematics. It can be extended it to an entire university of departments including science, technology, engineering, art, and mathematics. This becomes the blueprint for Camelot College or STEAM University (Table 3).

With clarity and awe, I can see within my castle college, that ring of hexagons like a round table upon which sits the Grail filled with a new kind of creativity.