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Tallis in Wonderland

On Points

Raymond Tallis pinpoints the mathematics/reality divide.

Readers of this column will have had a hint of my views on the limitations of the ability of maths and physics to capture lived experience – in particular in ‘Time, Tense and Physics: The Theory of Everything But…’ in Issue 81. Here, I want to focus on something absolutely central to the interpretation of the world in which we live in terms of mathematics: the notion of a point – in particular, a point in space. Points, which lie at the heart of the mathematisation of space (and, subsequently, of space-time), achieved this elevated status via the discipline of geometry.

Those of you who remember your early encounters with Euclid may recall, amidst memories of fear, humiliation, boredom and the other accompaniments of the pedagogic experience, that Euclid begins with a series of definitions and axioms. Some of them seem so obvious that you may have wondered, “Why is this guy telling me this? Did I really need to be informed that ‘Things equal to the same thing are equal to each other’ or that ‘A whole is greater than any of its parts’?” You stop wondering when, as if by magic, he conjures from these ideas a series of theorems that are far from obvious.

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