These simple facts are for children and students, yet really for all of us. Here we engage part of work of Plato, Buckminster Fuller, and John Conway. It is all just to keep opening new conduits to natural creativity. When adults grasp these facts, a possible new synthesis for one’s genius may well open.
Editor’s Note: There are obvious facts – not just ideas – that could stimulate a child’s natural creativity simply because these facts exercise part of the brain that engages spatio-temporal relations in basic ways. These all seem to be “basic-basics” that do not have much currency within education today. – Bruce Camber
Perhaps engaging these questions is a little like listening to Beethoven before one learns how to speak. Adults might benefit by exercising one’s brain in ways that expand one’s commonsense logic structure. More…
Fact #1: A most-basic, three-dimensional object in space-and-time is the tetrahedron.
We all should know the object very well. Some adults may be a little familiar with the object, but generally it has no particular importance. It should. It is the one of the most basic building blocks of the sciences. Children should play with tetrahedrons and octahedrons as well as other kinds of building blocks. Now here is a postulate; it is also one of the most basic building blocks of epistemology and heuristics.
This image comes from our Small Business School television series back in 1997 when we were trying to model “People, Products, and Processes” of business. Look at the tetrahedron just above. There are four tetrahedrons within each corner. The center face is one of the four exterior faces of an octahedron. The other four faces of the octahedron are interior.
Fact #2: Most adults cannot tell you what is perfectly enclosed within the tetrahedron.
This is not just a lack of insight into geometry, it is a lack of insight into the basic structures of biology, chemistry and physics. It all starts with the sphere; connect the center points of just four spheres and you have begun the simple process of making a tetrahedron.
From Wikipedia: An animation of close-packing lattice generation. This image file (right) is licensed under the Creative Commons Share-Alike 2.5 Generic license.
Fact #3: The octahedron is magical. It is also one of Plato’s forms, a most basic three-dimensional object.
From the octahedron we start seeing squares for the first time. Yes, the ubiquitous square is derivative. Now most scientists, logicians, and geometers cannot tell you what is perfectly enclosed within the octahedron.
That is a profound educational oversight.
Within each corner there is an octahedron. There are six corners. With each face is a tetrahedron. There are eight faces. The tape inside defines four hexagonal plates and everything shares a common center point. Notice the tape comes in four different colors, red, white, blue, and yellow.
The internal structure of the octahedron is simple but opens the way to complexity quickly. By making it a practice to look inside basic structure, the mind gets exercised in very special ways. Quickly, this simplicity-that-is-complexity becomes metaphorical. The mind begins seeing similarities, analogies, and metaphors everywhere. The mind begins making the strange familiar and the familiar strange. By going inside the octahedron one learns basic order, then basic relations that become functions that move the mind further within the interior world.
Using base-2 exponential notation, take the smallest measurement, called the Planck length (ℓP), and multiply it by two. There are 101 steps (“doublings”) to reach the width of a human hair and 101+ additional steps to reach the edges of the observable universe. It begs the question, “Is this a meaningful way to organize data?” And, it inherently asks another question using the five platonic solids: “Is there a basic structural support created by nesting objects within all 202+ steps?” At the very least, it helps to organize data. In the smallest scale, there is conceptual richness. From step 1 to 65, the sum of the distances is equal to one-Planck-Length-less-than-the-diameter-of-a-proton, yet there are over 36 quintillion primary points to make every conceivable model, of any object or thing in existence. Now that opens up an interesting thought experiment. More…