{'fraction_non_alphanumeric': 0.02403846153846154, 'fraction_numerical': 0.0, 'mean_word_length': 5.017341040462428, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Great circles: the analysis of a concept in mathematics and poetry

This article looks at analysis of concepts as a search for conditions of intelligibility, where intelligibility is recognized to be a value. Choosing the circle as an exemplary concept, we trace the discovery of a quadratic polynomial equation, the sine and cosine functions, and the nth roots of unity ‘inside’ the circle, as mathematicians discover new conditions of intelligibility for the abstract notion of a circle. Then we trace the uses of circles in poems by Marlowe, Shakespeare and Keats. What we discover ‘inside’ the circle there is of course quite different (a devil, a planet, a sleeping girl), for what the poet seeks are really conditions of the meaningfulness (intelligibility) of human life. The notion of containment and of intelligibility changes as we move from the investigation of mathematical problems to that of problematic human beings. Still, the circle remains as part of experience and part of our best conceptualization of the natural world.