Dominic Calkosz
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dcalkosz.bsky.social
Dominic Calkosz
@dcalkosz.bsky.social
300 followers 210 following 4 posts
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
dcalkosz.bsky.social
I still don’t understand the contradiction in this proof. If you rearrange infinite points (surface of a sphere), you can get 2x infinite points (2 spheres), but that’s the same with the Naturals and the Reals right? Isn’t this just another case of human intuition about infinity being wrong?
April 30, 2025 at 3:14 AM
dcalkosz.bsky.social
Any tips for how one might give this as a gift, without coming across the wrong way?
November 24, 2024 at 6:38 AM
dcalkosz.bsky.social
I assume you’ve already counted them, but fun milestone: CMU GCS recently hit 200 games!
www.gamecreation.org/games
Games | Game Creation Society
Want to check out and play our games? Find them all here! This is a searchable and filterable list of the games GCS has made throughout its history.
www.gamecreation.org
November 15, 2024 at 12:54 AM