Tag Archives: Jorge Luis Borges

Causality, Chance, and Connections

This essay introduces a topic I have been thinking about for a number of years. It also may allow me to connect the math impulse to a wider range of thoughts than just those based on math or even science.

It all begins with the perennial question of “why” that drives our curiosity about the nature of things and how various situations came about, such as our physical universe, our biology, the origin of life, or historical events. The explanations are usually couched in terms of causal links: such and such happened because some other thing happened. In the physical sciences we think the causal links follow certain physical, chemical, or biological laws that we provisionally hypothesize. In the historical realm we think there are still causes, such as the physical environment (geography, climate, weather, etc.) or the imprint of individuals. But the historical chains of events are often disrupted by chance and coincidences, and some supposed links degenerate into imagined connections or associations.

In the future I plan to write a number of essays that explore and illustrate these ideas. See Causality, Chance, and Connections.

The Essence of Mathematics

It is a bit presumptuous to think I could reduce the universe of mathematics to some succinct essence, but ever since I first saw a column in Martin Gardner’s Scientific American Mathematical Games in 1967, I thought his example illustrated the essential feature of mathematics, or at least one of its principal attributes. And he posed it in a way that would be accessible to anyone. I especially wanted to credit Martin Gardner, since the idea resurfaced recently, uncredited, in some attractive videos by Katie Steckles and James Grime. (This reminds me of the Borges idea that “eighty years of oblivion are perhaps equal to novelty”.) See the Essence of Mathematics.

Tupper’s Self-Referential Formula

Recently I viewed a startling video by Matt Parker about the Tupper Self-Referential Formula. It is a formula that visually represents itself when graphed at a specific location in the (x, y) plane. I found it difficult to fathom, so I looked it up on Wikipedia and Google. After reading different explanations, I finally think I have the idea. So thought I would add my version to the mix. See Tupper Self-Referential Formula.