It seems that the literature supports the intuition that to meaningfully relax (i.e. exercise the brain with fewer pressures of time, success or similar, and with a relatively low information bandwidth) is really good for cognitive health. And it's very good to destress, which we can all benefit from!

So even if there are more cars than birds outside my own window... I'll make sure to spend a few more moments each day by it :)

[0] https://www.youtube.com/watch?v=Q-25c8Rsobw

But Excel is not a relational database: for simple cases, having an extra table for a non-scalar column is awfully confusing to present to an end-user. From that angle this makes total sense. There's still 1NF for more complex embeddings, anyhow

The killer feature is that you can put the two together for a rotation axis (~ vector) and angle (~ scalar).

With just three gimbals (rotating circles), if gimbals A and B are aligned, you only have two degrees of freedom (rotating A is the same as rotating B). Because of this, interpolating angles is unwieldy in vector space. 'Gimbal lock' confounds animation (in hilarious but unrealistic ways) but also aerospace (four hours before 'one small step for man', just after landing, Collins joked he would like a fourth gimbal for Christmas).

I'd love to see just how Lipschitz continuous, how smooth, the potential field can be; how adding features puts it closer to or further from solutions that fit the consecutive-no-duplicate constraint, say. Adding a smooth 'hill' is probably viable; is a 'river'?

One little critique I have is in the latter third. Using LLMs for proof is pretty standard now, but the way the text focuses on their tribulations was distracting. It might have been cleaner to use the mathematician's "we" after introducing the 'co-authors', so that the casual reader might sink their teeth into the math rather than be reminded LLMs can sometimes cost money and go around in loops.

But otherwise this is a really gorgeous article! The visualisation is really powerful, and something about how the symmetries impose a kind of conservation (which looks like hot soup but actually has a smooth potential) are very exciting, and curiously very physicsy.

Might be useful to

- add a wordle-style 'SHARE' button, and/or

- make the canonical URL that of the puzzle (and only the attempt on completing/abandoning it)

Confusingly, "more" means "please add more terms"...

[0] https://oeis.org/wiki/Keywords

As a current juror I really do not feel for how long jury selection might have taken here, and I can imagine deliberation will take longer yet.

Let the funding go to some actual charitable foundation which offsets the very real negative externalities of large-scale AI, I say. That seems most likely to benefit humanity.

[0] https://www.theguardian.com/technology/2026/apr/27/elon-musk...

I am also sick of handling port numbers - I end up allocating them on a schema to different services, so for testing I can spool any VM/service combination and avoid crossover. But if I want the same service twice, ah...

It always fascinated me that ports don't have any kind of textual resolver, so you can bind to `:1234` and also say "please also accept `:foobar`". But that would itself require some kind of "port resolver" on a device, and that's another service to break and fix :)

"OS-efficient cross-platform HTML-based UI toolkit" is a great technological thing, but neither PyWry and Tauri's sites make that clear, or meaningfully advertise what they do. Which is a shame, because there is myriad software which might benefit all to use this.

[0] Tauri is akin to Chromium, I think? https://tauri.app

[1] and also a rather large amount of LLM integration; the source for PyWry has a whole section for Claude bindings

[2] the Webview Rendering librarY (WRY) used in Tauri https://github.com/tauri-apps/wry

“Symmetric” user reporting is dearly needed in some websites; as you say something can be mass-reported with no real recourse.

> Why create yet another physics engine? Firstly, it has been a personal learning project.

which is really rather wonderful and inspiring to see.

[0] https://github.com/jrouwe/JoltPhysics

Certainly a terrifying amount of responsibility and upkeep for each individual website. If the UK wishes to establish this and not want it to lead to an insane amount of privacy leaks, it should consider developing a technology that makes it work in a privacy-respecting way, like the European Age Verification Solution [0]'s Zero-Knowledge Proofs.

[0] https://ageverification.dev

For... some in the comment section, please recall the HN guideline: "Comments should get more thoughtful and substantive, not less, as a topic gets more divisive."

The only link is the person -- that their acts inform their thoughts and habits, which informs future acts. In this case "good deed math" is likely a post-hoc rationalisation, predicted by the Franklin model but not exactly encouraged.

"Fantasy or faith? One company's AI-generated Bible content stirs controversy" https://www.npr.org/2025/09/07/nx-s1-5518263/ai-bible-christ...

It's ice that burns: cages of water trapping methane, and indeed the largest non-atmospheric store of it on earth. It forms interesting fractals under a microscope, has subtle and historical climate effects, fosters methanotroph communities. It has commercial interest for methane extraction and may work well for static methane storage.

A fascinating topic to stumble upon!

Comments URL: https://news.ycombinator.com/item?id=45427866

Points: 4

# Comments: 2