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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 position to an objective – a hypotenuse.

·        You have found the intersection of your approach and your opponent’s.

·        The base of the candidate’s knowledge does not measure up to the job requirements.

·        You may think of your knowledge about a topic forms a sphere of all possibilities.

·        For some very complex topics, you may think in terms of higher or infinite dimensionality of knowledge, realizing the unboundedness of complexity.

·        You intend to “circle back” to make a response to an issue you don’t know currently.

·        You have an acute sense of a situation indicating a perceptive understanding or insight.

·        Your employer has the highest degree of understanding of their competition.

·        Often you think of knowledge values as coordinates of a possible set of information needed.

·        After some deliberation, the ambassador concluded his views to be congruent with those of his neighboring state.

·        On another tack, we often hear of fuzziness of thought and knowledge. We don’t know it precisely, but in some fuzzy way. Not blurry. Not random.  Note there is an entire area of math referred to as fuzzy.

 

Now, this all this because you know some geometry and begin to classify or arrange knowledge in geometrical terms for convenience? For descriptiveness? By cleverness? By transparency?


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