Consider the duality

Consider the duality

A geometric dual graph was defined for graphs on the plane. It is a graph in which a point is drawn in an area bounded by edges, and the points of adjacent areas are connected by edges. Abstract dual graphs are not limited to graphs on the plane, but are extended to general graphs. In this dual graph, closed paths and cut sets are dual.

In Euclidean space, there is one straight line passing through two points, but the intersection of two lines cannot be said to be one. Because there are cases where they are parallel. In projective space, a point and a line are duals. Focus on Exceptions Exceptions are not failures, they are opportunities.

__BELOW_IS_AI_GENERATED__

Duality was discussed. He explained abstract dual graphs, which are extensions of geometric dual graphs in graphs on the plane to general graphs. He also discussed the duality between points and lines in Euclidean and projective spaces, and presented a viewpoint that views exceptions as opportunities.

The fragment "Create a Notation" shows the idea of pursuing visual beauty and ease of understanding by defining a new notation. This is related to the "viewing exceptions as opportunities" perspective described in the note. Creating a new notation may appear to be an exceptional act, but it becomes an opportunity for new perspectives and understanding.

deep thinking

The concept of duality is an important tool for understanding different sides of things. However, it does not always have clear boundaries, and exceptional situations and perspectives have the potential to bring about new understandings. This perspective can be applied to the act of creating a new notation.

The Pursuit of New Understanding through Duality and Exceptionalism."

extra info

generated: 2023-09-05 01:07

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