Last email: 5 April 2010
Dear Christopher Hitchens:
I wonder if you have a quick answer to these questions:
• What is the most-simple, three-dimensional, finite structure?
Some argue for a sphere. That is a special case and as a result of sphere stacking, the tetrahedron emerges and generally wins the day.
• What perfectly fills out the inside of a tetrahedron?
It is a kindergarten question that most adults have not a clue, including our finest scientists and philosophers. Why is it important? It is what is. It is immutable. There are four tetrahedrons, one in each corner and one octahedron in the middle.
• What perfectly fills out the inside of an octahedron?
Even the inventor of surreal numbers and “geometer par excellence” John Conway of Princeton, hesitated momentarily to answer that question. No one else even tried. Most believe it to be of no significant import. I think that is so mistaken.
We see here three “penultimates” of life, continuity/order, symmetry/relations and dynamics/harmony and we begin to see the reasons for both Aristotle and Plato (I am working on the “For more…”).