Phil Gibbs

Interested in Diophantine m-tuples, perfect cuboids, Bellman's escape problem, Ulam numbers.

Last Notes

2025-12-24 00:00:49 GMT

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I looked a little deeper and found that Feynman was just popularising the work of Edward Fredkin and Tommaso Toffoli who are cited in this paper even though Feynman isn't. Fredkin and Toffoli showed that classical billiard ball dynamics as a basis for computation is Turing complete. This already seems to cover the title of the new paper, which leaves me wondering what their new result is.
Perhaps there method is different and more robust? The abstract does not clarify. I am sure there must be something new and worthwhile there, but I wish they would state what it is. Looking a little further again, they seem to be looking at a system with just one billiard ball and a complicated table shape, which is very different from the prior system of colliding multiple billiard balls.

2025-12-23 17:06:21 GMT

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I find it surprising that such a paper can be written without even a passing mention of Feynman's very well known billiard ball model of reversible computing from the Feynman Lectures on Computation.

2025-10-28 07:33:23 GMT

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Hawking proved that the total area of the horizons of black holes always increases. The theorem assumes that there are no naked singularities, and no exotic matter, i.e. no white holes, and no magic donuts (see John's recent video)
Hawking proposed the cosmic censorship conjecture that no naked singularities form in GR given realistic starting conditions. There is evidence from numerical simulations that this is false.
Furthermore the big bang singularity is completely naked in standard cosmological models. Some mental gymnastics is needed to argue that the big bang is OK but white holes are not.
How nature resolves these paradoxes remains a puzzle. Possibly the answer requires quantum gravity.
Another way to look at this is that white holes break the second law of thermodynamics. If we accept the view that the entropy of a black hole is given by the area of its event horizon, then the increase of its area is part of the second law of thermodynamics.
If you time-reverse a thermodynamic system the entropy should be the same, so we also need to accept that the entropy of a white hole is equal to the area of its anti-horizon. This means that unforming or unmerging white holes violate the second law of dynamics and are therefore ruled out.
There is a possible exception to this. If a white hole emitted matter with high enough entropy to counter-balance the decreasing horizon area then it might not violate the second law. The white hole would then be physically indistinguishable from a black hole evaporating via Hawking radiation.
Hawking considered the idea that a black hole might transition to a white hole in quantum gravity, but he eventually abandoned the idea.

2025-10-27 22:26:10 GMT

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Yes it should be time reversible, but as John says it wont look the same. It would look like an unmerging. These questions can help build an intuition for what is going on.
Your next question might be about what happens if two white holes merge. Then what happens if you time reverse that scenario. Wont it look like a black hole splitting into two smaller black holes? That is supposed to be impossible in GR.
My guess is that this paradox is avoided because two white holes merging makes then immediately unform instead of merging to make a bigger white hole, but I am not very sure if that is right.

2025-10-27 21:54:13 GMT

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That is a thought provoking question. In principle it must have an answer in classical GR. You could set up the initial conditions and simulate the outcome up to the singularity.
It is not too hard to work out some limiting cases. If a small white hole falls into a black hole, the white hall enters and hits the singularity. It would be possible for the white hole to unform and then the matter it ejects would fall on the singularity.
If a small black hole fell towards a large white hole, then the black hole is frozen onto the white hole anti-horizon until the white hole unforms. Eventually it should reappear with the matter from the white hole. Some of that matter could fall into the black hole.
The question for two equal size bodies is harder to predict, but my best guess is that the white hole unforms inside the black hole and the matter hits the singularity. From outside it would look like two black holes merging. It is possible that the white hole starts to unform before it enters the black hole in which case some of its matter could escape.
Feel free to make the case for a different outcome.

2025-10-27 15:37:00 GMT

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That is a very comprehensive analysis which looks like it could answer many questions, thanks.

2025-10-27 15:23:46 GMT

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On the subject of AI I have very mixed feelings. I foresee a continuing rapid development which seems like it could lead to AGI quite soon. I am excited that this could mean the resolution of many problems in mathematics and science in my lifetime. Already I see how I can use it as a research assistant to extend my useful life as someone able to follow what is going on, though I appreciate that it still makes many errors.
On the other hand, the implications for society are terrifying. AGI coupled to robotics can potentially replace everyone's job. There are big issues with alignment, security and use of energy and water. I am very worried that this will not go well given everything else that is happening.
I think that the momentum is now such that there would be no way to stop it or even slow it down if pessimistic outlooks are correct.

2025-10-27 13:35:08 GMT

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I think this can be analysed in Schwarzschild coordinates for the interior.
Assuming that is correct, you can consider a trajectory in the Schwarzschild metric with dt = 0. Also take ds = 0 making the world line lightlike representing the limit of how fast they can go. Fix theta at pi/2. This gives a relation between dr and d(phi) which can be integrated as r goes from r_s down to zero. I did this and got the result delta(phi) = pi. If they both agree to move in the opposite direction they only need delta(phi) = pi/2 so they can comfortably meet up.
Even if they fall in at different times, the first in can almost hover just inside the horizon until the other one enters, so they can always meet up.
I am looking for a reference to confirm that this is right because I am certainly capable of getting it wrong.

2025-10-27 10:40:07 GMT

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Another interesting question is about two astronauts that cross the event horizon at the same time, but different places. Can they always meet up inside and shake hands before hitting the singularity, or does it depend on the angular separation around the black hole?

2025-10-12 11:53:58 GMT

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It was a quote from the Futurism report you linked. I did not mean to imply that you were endorsing that claim, just that anyone following the link should be aware. Sorry for the confusion.

2025-10-12 09:57:19 GMT

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interesting stuff but ask your favourite AI to fact check that "Generative AI now accounts for roughly 40 percent of the United States’ gross domestic product." It is very inaccurate.