To the pure geometer the radius of curvature is an incidental characteristic - like the grin of the Cheshire cat. To the physicist it is an indispensable characteristic. It would be going too far to say that to the physicist the cat is merely incidental to the grin. Physics is concerned with interrelatedness such as the interrelatedness of cats and grins. In this case the cat without a grin and the grin without a cat are equally set aside as purely mathematical fantasies.

Summary

This quote highlights the contrasting perspectives of a pure geometer and a physicist when considering the radius of curvature. The geometer sees it as an unimportant aspect, comparable to the fleeting grin of the Cheshire cat. However, for the physicist, the radius of curvature holds crucial significance in understanding the physical world. It suggests that while the pure mathematician may see things in isolation, physics recognizes and investigates the interconnectedness of various elements, like the relationship between a cat and its grin. Without this interrelatedness, both the cat without a grin and the grin without a cat hold little meaning beyond abstract mathematical concepts.

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