So there are a couple interesting and meaningful changes at the event horizon, but it's not a mathematical singularity.

This understanding may be incomplete or outdated (things moving very fast right now). I'd love to hear from a someone with more experience using LLMs to do binary analysis about the level of 'binary annotation' needed for LLMs relative to humans.

It's gotten much easier to reverse engineer binaries in general, and security patches in particular. Basically, an LLM can turn binaries into 'readable' code, and then reason about said code.

The fact that they are holding some information back doesn't really strike me as unreasonable. The bug has yet to be released, so they should not provide identifying details. Let's see what happens with the CVE.

[0] https://www.cisecurity.org/ms-isac/services/words-of-estimat...

But for a perfect circle of diameter W, it will alway hit exactly two vertical lines.

I'll also say this: I greatly sympathize with Israel and Jews more generally here. The problem at the core remains global antisemitism; it's the reason Israel needed (and still needs!) to exist, and the reason Jews globally feel threatened. Antisemitism in the middle east is particularly pernicious, but it's not much better in Europe or the Americas. It doesn't just feel like a dangerous wolrd for Jews, it _is_ a dangerous world.

That doesn't change my opinion about the situation in Gaza---there's ample evidence that it's a genocide. But I hope this helps people see that we can, and should, hold these two truths at once. Jews are persecuted, and are in a precarious situation globally. In fear and in anguish, the state of Israel is performing unconscionable deeds in Gaza. A central cause is antisemitism; if we could somehow find a solution to that, you'd go a long way towards solving the whole conflict in the middle east. But good luck.

The Gaza genocide is the ongoing,[19][20] intentional, and systematic destruction of the Palestinian people in the Gaza Strip carried out by Israel during the Gaza war. It encompasses mass killings, deliberate starvation, infliction of serious bodily and mental harm, and prevention of births. Other acts include blockading, destroying civilian infrastructure, destroying healthcare facilities, killing healthcare workers and aid-seekers, causing mass forced displacement, committing sexual violence, and destroying educational, religious, and cultural sites.[21] The genocide has been recognised by a United Nations special committee[22] and commission of inquiry,[21] the International Association of Genocide Scholars,[23][24] multiple human rights groups,[c] state governments, numerous genocide studies and international law scholars,[30][31] and other experts.[32]

https://en.wikipedia.org/wiki/Gaza_genocide

To suggest that genocide is only possible when there is no civil life, no humanity, nothing to live for, no I do not accept your definition. If you kill 10% of a population... does it only count as a crime against humanity if the rest of the population cannot even be human?

A semblance of civilian life does not mean genocide did not or is not taking place. Wholesale population displacement, destruction of a significant percentage of civilian structures, bombings, raids, land and sea blockades, statements from leaders that suggest genocidal intent... these point in the other direction.

Would it only be genocide only if no child in Gaza was smiling? If no one was getting married, no one singing, no one relaxing amid the horror? Inhumanity of this level of extreme only occurs literally when everyone is dead. I guess that's the line you have in mind?

When I was in grad school, we learned about wavelets, but we did research on convex optimization for statistics. The first was an accomplishment of the last generation of mathematicians, and it would be hard to publish something groundbreaking. But nobody had really considered sparsity inducing optimization, so that was our problem.

In many ways, the situation is somewhat better for applied mathematicians because the problem space is wider. Ingrid Daubechies was an applied mathematician, and her work on wavelets was an outgrowth of work that originated in the petroleum exploration community. Wild how these connections get made.

If you don't allow rotations, but somehow still take a polygonal limit to circles, I suspect you'll end up with the same answer. But the limit is necessarily restricted relative to highly symmetric polygons going this route.

In general, rotational symmetry gives a ton of power to simplify the math, and leads to highly general results like arbitrary "noodles" having the same average crossing count as needles of the same length.

The point is that the "right" quantity to be considering for the problem is the average number crossings, since that naturally extends to curved noodles, lines of any length, and even circles. The number of crossings is also known as the Euler characteristic of the intersection, and there's a rather deep and beautiful theory of geometric probability that takes this as the jumping off point.

So taking the limit of a large number of segments converging to a circle of diameter W leads to the result that the average number of intersections must be 2L/\pi.

https://xcancel.com/wtgowers/status/2052830948685676605

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