It’s interesting that most mountain systems, including the Rockies, Sierra Nevada, Alps, Andes, and even the Himalayas, have dense, continuous networks; but the Appalachians look like a big hole.

Other odd gaps are the upper Amazon, Poland, and east/central China.

Reminds me of Judge Holden in Blood Meridian, who sketched ancient artifacts in his personal notebook and then destroyed the originals.

The Works of Vermin by Hiron Ennes. Very reminiscent of Miéville and VanderMeer.

Or Salma Hayek.

If they make a sequel movie based on her current activities, who will they cast to play Julia Roberts in the in-universe version of the film based on the first movie?

The physical motion of the billiards is two-dimensional, but wouldn’t the phase space be four-dimensional (since it tracks both position and momentum)?

I think the reason chaos needs at least three-dimensional phase space for continuous-time systems is that the orbits in phase space can’t intersect (which the paths of the billiards in real space obviously do).

The article quotes a post from ISBNdb saying the issue is model collapse from training on synthetic data.

“Credit” implies something you can borrow against—I’m not sure what that would mean in the context of social media.

“Small government” only ever meant corporate deregulation—in all other respects they were already above the law.

Some further reading has led me to hyperchaos:

A hyperchaotic system is a dynamical system with a bounded attractor set, on which there are at least two positive Lyapunov exponents. Since on an attractor, the sum of Lyapunov exponents is non-positive, there must be at least one negative Lyapunov exponent. If the system has continuous time, then along the trajectory, the Lyapunov exponent is zero, and so the minimal number of dimensions in which continuous-time hyperchaos can occur is 4.

Do you continue being an idiot outside the context of the team?

I’d rather be surrounded by people more capable than me (at least if I care about the success of the task), but not at that cost.

I edited/clarified my comment before I saw your reply—apparently the restriction to three dimensions only apples to continuous-time systems, which is what I had in mind when I posted the question.

Hmm… the book I was reading (Complex and Adaptive Dynamical Systems by Claudius Gros) actually said strange attractors only occur in three dimensions or higher, but I changed that to “chaos” in the title to fit the character limit—I thought they were essentially synonymous.

Here’s the quote:

Strange attractors can only occur in dynamical system of dimension three and higher, in one dimension fixpoints are the only possible attracting states and one needs at least two dimensions for limit cycles.

Edit: I see that Gros clarifies a few paragraphs later:

Chaos may arise in one dimensional maps … but continuous-time dynamical systems need to be at least three dimensional in order to show chaotic behavior.

I guess I was mentally thinking of continuous-time systems, but there was no room to fit that in the title.

In the lyrics to the Beatles’ song Piggies, there’s the line “clutching forks and knives”. Is that just an Americanism they picked up?

Nah, that’s what got us the DMCA.

We need laws that are robust and universal enough to accommodate a spectrum of unforeseeable circumstances, not laws that are tailored to one expected future narrative.

Although it might be good to explore possible scenarios for how each law could be abused, and include provisions to void it if they occur.

Nationalism is the belief that the world should consist of ethnically-homogeneous nation-states—so it’s perfectly consistent for nationalists in one country to support other nationalist states outside their own.

That, and war makes for better narratives.

That war is the connective tissue of human history, rather than the holes in the tissue.

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The more abstract and general a theory is, the more different things it can be applied to. If you can figure out how to describe any problem in terms of sets, you immediately have all the theorems of ZFC at your disposal.