The author does not give sufficient credit for a particular difficulty in calculating the location of a solar eclipse. He mentions in pathing that "the rotation of the Earth is gradually slowing down" and that "exactly when a new leap second will be needed is unpredictable". More precisely, he should have said that the Earth's rotation has a tendency to slow down - in contrast to today, it accelerated somewhat in the last third of the 19th century, for example. But more significant in this context, however, is the aspect that the estimation of the degree of change for a given period of time becomes quickly more and more inaccurate when we go forward or backward in time. In the case of ancient eclipses we cannot calculate their exact location from a prior knowledge of the Earth's rotational speed. It is the other way round: since we have historical reports from a particular region about an eclipse we can deduce the change in the Earth's rotational speed between now and then.
I guess you would have to anchor those engines pretty deep. I would assume that even anchoring them to bedrock would simply cause unscheduled continental drift, and possibly only mountainous relocations.
Just walk down a hill to accelerate the rotation of the Earth a tiny bit. But when you need to walk up the hill again you decelerate it by the same amount. -- So building a dam preserves the rotational speed of the Earth with respect to the extent of the mass (or more exactly the angular momentum) of the retained water.
What a truly lovely piece of work. I'm so glad that Wolfram adores math and science, and history, so much and has the tools to craft an excellent precis like this. It's always good to go to original sources, and connect with the deep past of learning to which we are the grateful inheritors. Predicting eclipses, and the details of how it was and is done, is probably considered by many to be pointless, boring, or even harmful (stealing intelligent attention away from more pressing problems, or any number of other reasons). But I think it's beautiful to retell these stories and appreciate them and the minds behind them. There is something so entirely wholesome about a learned man appreciating the work of his forebears. Wonderful.
Agreed, it was a really nice read. Even simply in the role of an educator I've taken a liking to his blog posts. There is a certain combination of both breadth and depth that I've not found anywhere else. His overview of how LLMs work from last year was on of the first really good pieces describing them truly from first principles. And still shapes how I describe their workings to people outside of tech.
That's a good one, thanks. It gives me `18:09 UT`, which is `12:09 CST`.
The Precision Eclipse calculator does seem to provide correct results in the US (e.g., 1:40 PM for Dallas TX). So, it must be a Mexico timezone calculation error.
I have the Classic Wolfram app on iOS. I asked it, “When is the next partial Solar eclipse in New Hampshire?” It missed the 2024 one and started giving details about a 2026 eclipse in Spain.
I'm a big fan of Mathematica even though all commercial software irritates me on some level (transparency, cost, and licensing annoyance).
As a result I follow Stephen's blog and sometimes they come off as a little self serving and grandiose, but this one was terrific to me as a non physicist in better learning the history and challenges of all of this. It's hard to understand sometimes that celestial mechanics is simply not a "solved" problem these days.
I can’t believe that when the last time this eclipse happened my friends had to twist my arm into pausing whatever important thing I was doing to go outside and see it because this wouldn’t happen again for thirty years, in 2024. I would be SO OLD then and probably not living there anyway so seize the day!
Yes, great article and actually an astonishingly low amount of awkward-dad bragging by this particular author’s standards —- the closest he got was slipping in how he was ALSO at the Institute for Advanced Study “in Princeton” when Otto Neugebauer was there in the 1980s. And he probably considers himself a peer of Isaac Newton but hey, don’t we all from time to time?
Maybe he’s been reading the HN discussions of his articles and decided to tone down the boasting. One can hope.
See the "The Three-Body Problem" and several following sections. The fixed geometric approximations earlier in the article can have a closed form though.
For more information about the change of Earth's rotational speed see the Wikipedia article on "ΔT (timekeeping)": https://en.wikipedia.org/wiki/%CE%94T_(timekeeping)