david brodie photography
david brodie photography
visual thinking
God, Nature and Humanity
this is not an apple
useful delusions
the one true way
stepping not flowing
Zeno's singularity
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David Brodie photography
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Stepping not flowing
Numbers do not flow, they step. There is a gap between the values of 1 and 2, and between 2 and 3. From the origins of numbers in practical experience, and of counting observable objects like apples, then if we simplify by supposing one apple to be much the same as another, the gaps between 1 and 2 and between 2 and 3 are the same – one apple. The gap can be filled with other numbers, such as 2.718 and 2.719. (For apples, we need to apply a knife for such numbers to become more meaningful.) Indeed, there is a gap between these into which other values can fit (such as 2.7184). There is no end to the number of numbers that can fill the gap. Likewise, two points in space have gaps between them, and in any gap between any pair of points there is room for an infinite number of other points. Numbers and points can be thought of as stepping stones, or as knife edges that are so sharp that they have vanished.