Here's the Wikipedia summary: https://en.wikipedia.org/wiki/Norton%27s_dome
The problem is simpler with time reversed. You can construct a dome such that you can roll a ball up it and it comes to a halt at the top in finite time. This is perfectly believable to me, and is I'm sure a proven fact.
The problem is that information is lost, the historical state cannot be reconstructed from the stationary ball at the top.
There are similar problems in Newton's laws, but as far as I know they are all non-general (have measure 0 in state space) so require an infinitely precise setup. So they don't affect real-world predictions.
Tom Lowe
npub1jj…pjlmk
2024-12-27 00:08:41 UTC
in reply to nevent1q…td0n
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2024-12-27 00:08:41 UTCEvent JSON
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