(I wonder if there are slick ways to visualise the >3D case. Like, we can view 3D cross sections surely.

Or maybe could we follow a Lagrangian particle and have it change colour according to the D (or combination of D) it is traversing? And do this for lots of particles? And plot their distributions to get a feeling for how much of phase space is being traversed?)

This visualization also reminds me of the early debates in the history of statistical mechanics: How Boltzmann, Gibbs, Ehrenfest, Loschmidt and that entire conference of Geniuses must have all grappled with phase space and how macroscopic systems reach equilibrium.

Great work Shashank!

Comments URL: https://news.ycombinator.com/item?id=45766156

Points: 24

# Comments: 3

Comments URL: https://news.ycombinator.com/item?id=30818836

Points: 2

# Comments: 0

Comments URL: https://news.ycombinator.com/item?id=30239157

Points: 1

# Comments: 0

Comments URL: https://news.ycombinator.com/item?id=28013211

Points: 1

# Comments: 0

Comments URL: https://news.ycombinator.com/item?id=27384096

Points: 1

# Comments: 0

In it, there are long dialogues on Fermat's principle of least time (https://en.wikipedia.org/wiki/Fermat%27s_principle) and Faraday cages (https://en.wikipedia.org/wiki/Faraday_cage).

I wished the movie dwelled longer on those subjects though.

Michael Faraday's "Chemical History of a Candle" is a very readable masterpiece on the subject, despite its age.

The Engineering Guy has done much to revive Faraday's work: http://www.engineerguy.com/faraday/

> Imagine if scientists kept the result of every scientific study to themselves. The same work would have to be done over and over again as everyone was forced to reinvent the wheel countless times to do anything at all. Instead, scientists share their work and collaborate which benefits all of us.

raised my eyebrows. If only it were true. Aside from paywalled journals, we don't have a centralized repositories of data in most fields, probably because a lot of it is proprietary (or intends to be) in the first place.

A wishlist:

1) To be able to share maps with fellow researchers, not as pdfs or bib files, but as a url to the map so that they can interact with it. I can see that a "share link" is possible for an article, but not for a custom map. Such a link could also be used to embed such maps on sites like how one can with plots from https://ourworldindata.org/

2) To be able to get more metadata like sponsor, country, etc. like https://www.lens.org does.

3) To be able to upload pdfs and annotate them. I can see why this is dicey, but if possible, would be great to see an integration with something like https://fermatslibrary.com/margins

> It's currently in early access so it's free to use, and you don't need to create an account to get started.

I know software developers need to eat and totally respect your choice in making it a paid service in the future, but I will confess a deep desire for such a thing to be affordable, if not free.

It seems to me that innovations can come from two forces:

1) Fairness: Make teams operate fairly. Audit thoroughly, no slap on the wrist for violating Financial Fair Play, salary cap (I can dream can't I?), etc. Given how our society favors the capitalist over the regulator, all efforts on this front have amounted to mere asymptotic jokes.

2) Eliteness: Make the league the creamiest of the cream. Increase the magnitude of what happens when athletes with incredible talent are wedded with facilities that enhance and curate that talent. This was in fact the point of the premier league, but the Super league took it a step too far. The perception is that the "magic" in a game between Real Madrid and Manchester United (Goliath and Goliath) is more watchable than a game between Derby County and Manchester United (David and Goliath). Except that Derby County can win that game, have won that game, and the resulting dreams instilled in people (not just fans of Derby County, but fans of United) comprise the very source code that makes sports worth watching: a tale of the impossible that parallels and informs everyday life. Some men with $$$ in their eyes just don't seem to grasp that, for all their "finger on the pulse" bragging. Or they did, but felt that the source code could be rewritten and that's all that matters.

The "Eliteness" front tries to maximize the quality of a sport just short of steroid use: story of the goose that laid the golden eggs. But what about fairness? How can we set up incentives for that?

Why do we do this to ourselves?