Simple ideas, complex possibilities, elegant and beautiful results

Possibilities of great subtlety, elegance, and power can follow from the simplest ideas. Leonardo da Vinci is often credited with offering a variation on this theme, but the basic idea is much older. Philosophy, for instance, began with Plato’s distinction between name and concept. This realization that words are not the things they stand for has informed and structured each of several scientific revolutions.

How so? It all begins from the reasons why Plato required his students to have studied geometry. He knew that those familiar with the Pythagorean theorem would understand the difference between any given triangle and the mathematical relationships it represents. No right triangle ever definitively embodies a perfect realization of the assertion that the square of the hypotenuse equals the sum of the squares of the other two sides. The mathematical definition or concept of a triangle is not the same thing as any actual triangle.

The subtlety and power of this distinction became apparent in its repeated application throughout the history of science. In a sense, astronomy is a geometry of the heavens, Newton’s laws are a geometry of gravity, Ohm’s law is a geometry of electromagnetism, and relativity is a geometry of the invariance of mass and energy in relation to the speed of light. Rasch models present a means to geometries of literacy, numeracy, health, trust, and environmental quality.

We are still witnessing the truth, however partial, of Whitehead’s assertion that the entire history of Western culture is a footnote to Plato. As Husserl put it, we’re still struggling with the possibility of creating a geometry of experience, a phenomenology that is not a mere description of data but that achieves a science of living meaning. The work presented in other posts here attests to a basis for optimism that this quest will be fruitful.

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