I sometimes feel guilty in just writing the "easy" stuff, but I know there are also folks like you out there who are grinding out some great, important stuff like the math behind the phenomenon. I was very into math during high school and even carried a little of that with me, but at some point I realized I was sort of out of balance and needed to work on other areas.
Ha, actually "doing the math" is very niche -- from popping out a few articles, I can't imagine the work involved in writing a new piece *every day*. Nothing remotely "easy" about that! I'm still on a sort of writing vacation, so love catching up on your stuff. :)
Thanks, Tad! I'll admit that there's a lot of work in what I do, but it's just so rewarding to finally fully understand something well enough to have a real conversation with other thoughtful folks about that thing.
Do you know what his insight was? Lagrange added those two non-planar points off at right angles at equilateral triangles, and of course Euler conceptualized and proved that there were those first three points. What did Poincaré add to the body of knowledge? Now you have me super curious, and that's one of the best things about when I write something!
It was not exactly an "insight" but a long-term relationship with Euler's and Lagrangian methods. For example there is the Euler-Poincaré formula for topological property. This allows the "point" to be expanded to a "region" which is closer to the way we calculate things today.
Poincaré was a polymath and calculations for astronomical reasons were definitely within his bag.
I am doing Logical systems especially in the lare modern period. As I can only write about one to 2000 words a, I need to concentrate on one thing at one time. The stroke has its limitations.
Enjoyed this! And a personal shout-out to the haunting scene in "2010" where the protagonists find the Discovery spinning silently at the inner Lagrange point between Jupiter and Io. Gorgeous visuals (I now understand the depiction of physics was in places a bit iffy, but to hell with it), and that whole scene still does things to my inner ear that no movie should be able to do. https://www.youtube.com/watch?v=y52hcNbdCiQ&t=70s
I use Lagrange points in book two of the singularity chronicles.
Nice article! Euler was a monster.
There might be a tiny group of people interested in the math behind calculating where these points are; if so, here's a little write-up:
https://open.substack.com/pub/firstexcitedstate/p/lagrange-points?r=em9w0&utm_campaign=post&utm_medium=web&showWelcomeOnShare=true
That's great, Tad! Thanks for sharing this.
I sometimes feel guilty in just writing the "easy" stuff, but I know there are also folks like you out there who are grinding out some great, important stuff like the math behind the phenomenon. I was very into math during high school and even carried a little of that with me, but at some point I realized I was sort of out of balance and needed to work on other areas.
Ha, actually "doing the math" is very niche -- from popping out a few articles, I can't imagine the work involved in writing a new piece *every day*. Nothing remotely "easy" about that! I'm still on a sort of writing vacation, so love catching up on your stuff. :)
Thanks, Tad! I'll admit that there's a lot of work in what I do, but it's just so rewarding to finally fully understand something well enough to have a real conversation with other thoughtful folks about that thing.
I'm glad you're here!
Excellent article! Having written an article on Lagrange myself this week, I can relate to it even more!
Dude, we have to stop doing that.
Actually, we don't!
Euler and Lagrange were way wicked smaht but the are other pieces. Henri Poincaré for one.
Did Poincaré work on Lagrange points too?
Very earlier on he did Lagrange Points for the solar system, part of his dissertation or a PhD.
Do you know what his insight was? Lagrange added those two non-planar points off at right angles at equilateral triangles, and of course Euler conceptualized and proved that there were those first three points. What did Poincaré add to the body of knowledge? Now you have me super curious, and that's one of the best things about when I write something!
It was not exactly an "insight" but a long-term relationship with Euler's and Lagrangian methods. For example there is the Euler-Poincaré formula for topological property. This allows the "point" to be expanded to a "region" which is closer to the way we calculate things today.
Poincaré was a polymath and calculations for astronomical reasons were definitely within his bag.
Nice, thanks. Have you written about him yet? I need to at some point!
I am doing Logical systems especially in the lare modern period. As I can only write about one to 2000 words a, I need to concentrate on one thing at one time. The stroke has its limitations.
This is what came to mind from this article, Andrew. Math was not my strong point. https://www.youtube.com/watch?v=Gg9cNGHl-bg
Ohhhh yeah! Classic.
Enjoyed this! And a personal shout-out to the haunting scene in "2010" where the protagonists find the Discovery spinning silently at the inner Lagrange point between Jupiter and Io. Gorgeous visuals (I now understand the depiction of physics was in places a bit iffy, but to hell with it), and that whole scene still does things to my inner ear that no movie should be able to do. https://www.youtube.com/watch?v=y52hcNbdCiQ&t=70s
LOL @ "John Lithgow Breathing Heavily in Space" - amazing title for that video!
I'm glad this one resonated with you. Gravity is one of the things I don't think I'll ever get tired thinking about.
March 13, 2024: The day I learned that "L1" and "L2" aren't just buttons on a Playstation controller.