A Question About a Rotating Line Helps Reveal What Makes Real Numbers Special
The Kakeya conjecture sounds like a brain teaser. Place a needle flat on a table. How much area do you need in order to be able to turn it so that it points in all possible directions? The most obvious possible answer is a circle whose diameter is the length of the needle. But this is demonstrably wrong. And over the last century, the effort to understand the ways in which it’s wrong has revealed…
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