As I read this, I get stuck on the form of the solutions they wish to solve. For example, in the lava examples, presumably at a static time snapshot, the mathematicians wish to generate a function of space point in; temperature out. Then, maybe, do this at multiple time points, or evolve the system over time. Or maybe generalize classes of how a lava system could evolve.
This is a very complicated model of the real world, and I think this sort of problem comes up whenever we move from "spherical cow" physics and math to modeling or simulating something? There's chaos in the system, and sensitivity to initial conditions which aren't known. It's like reading about the "3 body problem is unsolvable".
Maybe you look at this without the framework of PDEs, and simulate it. But the article implies that lava is heterogeneous, so you don't know how to model how each part of it interacts with the rest. I struggle understanding, for example, how the author uses the word "equation" to describe something this complicated.
So, maybe the ideal solution is a set of coarse descriptions of the lava flow's temperature distribution, likelyhoods for each, predictions of which you get depending on how much you know about the initial conditions. Probably fractal?
It's often the case that describing how a complex system changes with its input variables is much easier than writing the function from the variable to the state.
A PDE is a precise description of some unknown function in terms of how it changes, so it's really the ideal framework for doing the kind of simulation you're talking about.
I should have added this in my original note, but as a programmer, if you’re interested in learning about this I highly recommend Steve Brunton’s course in differential equations and dynamical systems on you tube https://youtu.be/9fQkLQZe3u8?si=Cu7F5QQyljjiG4K8
He’s a really amazing teacher and he goes through all the maths on a lightboard and then writes simulations of all the systems he talks about in python and matlab. All the course materials are available free online. It’s quite extraordinary.
PDE can simulate Kelvin helmhotlz instability and if you want to go even smaller, you can go to particle in cell methods. And the distribution thing you are talking about is similar to lattice boltzmann methods.
This is roughly what I've been doing. I consider it a duty: Occasionally (once or more a day) review "new". Flag any spam articles, or generic LLM hype articles; update science or non-LLM-focused technology ones.
I even upvote AI or LLM-centered articles if they're not centered on "How agents and vibe coding have/haven't/will/will not changed everything about coding" - it's these that have grown intolerable in the past few weeks.
I've made a similar observation. I'm clearly in camp #2: No agents, and use ChatGPT or Gemini to ask specific questions, and feed it only the context I want it to have.
I have a parallel observation: Many people use code editors that have weak introspection and refactoring ability compared to IDEs like JetBrains'. This includes VSCode, Zed, Emacs etc. I have a suspicion there is a big overlap between this and Group 1. It is wild to me that people are generating AI code while skipping in-IDE error checking, deterministic autocomplete, and refactoring.
TailScale is a VPN, and the article highlights a recent increase in user base. This is likely due to VPNs being required to access pornographic materials for residents of many US states.
Notably, it's a VPN for connecting your own devices together, so unless you're deploying a server elsewhere for access to porn it's probably not for that.
It could also be that Tailscale users have many kids, who then also use Tailscale. Although if the header is meant to represent that, it's showing the wrong position.
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