Dominic Calkosz
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dcalkosz.bsky.social
Dominic Calkosz
@dcalkosz.bsky.social
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Senior Game Designer on Hearthstone Battlegrounds. Tweets represent my two cats. he/him
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dcalkosz.bsky.social
I think I found what I was looking for (also Wikipedia), and I just misinterpreted the paradox from the beginning: It’s not intended to show a contradiction.
Screenshot of text: “The theorem is a veridical paradox: it contradicts basic geometric intuition, but is not false or self-contradictory. "Doubling the ball" by dividing it into parts and moving them around by rotations and translations, without any stretching, bending, or adding new points, seems to be impossible, since all these operations ought, intuitively speaking, to preserve the volume. The intuition that such operations preserve volumes is not mathematically absurd and it is even included in the formal definition of volumes. However, this is not applicable here because in this case it is impossible to define the volumes of the considered subsets. Reassembling them reproduces a set that has a volume, which happens to be different from the volume at the start.” Source: https://en.m.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox
April 30, 2025 at 6:22 AM