Black and white photo of a young Alfred Tarski . He wears dark pant and jacket, with a very prominent white collar. His hands are folded in his lap, and he is seated in an ornate armchair.

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1. Robert McNees (mcnees@mastodon.social)'s status on Sunday, 14-Jan-2024 20:14:11 UTC Robert McNees

   Mathematician Alfred Tarski was born #OTD in 1901.

   The Banach-Tarski paradox asserts that a ball in three dimensions can be decomposed into a finite number of pieces which, after translation and rotation, can be reassembled into *two* distinct copies of the original ball.

   The paradox also works in more than three dimensions, but not in one or two without significant technical modifications.