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The Geometry of Thought

It is sometimes better to think in terms of the shape of knowledge and thought in terms of geometry. This renders many geometric metaphors. They help us to categorize and understand how we understand, in a visual way. A few examples come to mind.   ·         You often think in terms of some knowledge encompassing a topic – you’ve got it covered from all perspectives. ·         You may think of some topics as disjoint from or orthogonal to other knowledge. ·         You may see your knowledge triangulates a topic allowing you to narrow it down to some essential facts. ·         Your point of reference is distant from hers. ·         You square up the situation, understanding all questions and a proper and complete perspective. ·         You may see someone's train of thought is parallel to yours, proceeding along similar lines, but noting no intersection is possible. ·         You may think of the best possible thinking is the best or fastest way to move from one pos