New periodic orbits of the three-body problem (opens in new tab)

In fact the more general N-body problem is perhaps one of the most classical uses of high order Taylor methods, in particular for studying the long term stability of the solar system. Here is a paper from 1993: http://adsabs.harvard.edu/full/1993A%26A...272..687L. Rigorous error analysis of Taylor methods for ODEs goes all the way back to Moore's original work on interval arithmetic in the 1960s; in the early 2000s Makino and Berz developed so-called Taylor models which combine rigorous error bounds with accurate long-term propagation of changes due to perturbations in the initial values (see http://bt.pa.msu.edu/index_TaylorModels.htm); they used it to study the dynamics of the solar system among other things. R. Barrio and others have published several papers about reliable solution of ODEs using Taylor methods; leading to the development of the TIDES software. See several references listed on http://cody.unizar.es/tides.html. In particular the paper https://doi.org/10.1016/j.amc.2004.02.015 from 2005 investigates using variable order Taylor series with extended precision for the solutions of dynamical systems. The paper http://dx.doi.org/10.1155/2012/716024 from 2012 is specifically about obtaining periodic solutions of dynamical systems using a high order Taylor method with multiple precision arithmetic.

Actually, I made the first comment after I checked the second author's earlier paper https://arxiv.org/abs/1109.0130 where they essentially made the claim about inventing "CNS" as the first-ever reliable technique for long-term solutions of dynamical systems, without referencing any of the earlier work I mentioned above.

However, I just checked the actual text of this new article on the three-body problem (through sci-hub) and there the authors do cite the earlier work I mentioned above, giving proper attribution to others for the basic ideas behind what they call "CNS"! So all is actually well, and the peer review presumably did work (or the authors found out about the earlier work even before writing the new paper). It is just the press release that is misleading, as usual.

To answer your question, I'm not really familiar with the research on the N-body problem, so I can't say why or whether no one tried looking for periodic solutions in this way before. Perhaps no one actually thought of it, or they didn't try since they didn't expect to find anything, or they didn't have the computational resources, or they just couldn't figure out the details of how to do it (which the present authors did, and deserve credit for). Again, I was not trying to downplay the significance of this work, and finding new applications of existing methods (and making even tiny improvements along the way) is how science progresses. It also happens all the time that methods get rediscovered/reinvented independently.

>Many (too many) parts are "here's a scientific theory I learned about, let me give you a brief Wikipedia-style description.

So? Doesn't sound that different from 90% of classic sci-fi, especially Asimov.

>- No person in the history of this world has ever spoken like characters in the book. Dialogs are just people explaining things to each other

Ditto.

Have you read Nexus yet?

much what? Don't leave me hanging.

Could you elaborate? I usually read positive stuff about this book, so I'm very curious to hear diverging views.

Part two and part three are both exceedingly more brilliant. Very much advise you to read them.

I, for one, found it a masterpiece.

Books 2/3 are waaaay better! You’re missing out

Maybe the laws of our math and physics are not invariant to space and time :)

String theory is unproven, and AI is a technology, not a scientific theory.

There are hints of that concern in TFA where they state the importance of accurate simulations over a long time. On the other hand, a simple two body system is very stable but will diverge in a simulation using a simple Euler integrator.

Yes, that does work. In the literature this is called a "heirarchical system"

The very simplest version is called the Euler problem. Two fixed masses and a third moving in the "dipole field". All the solutions can be explicitly determined (although only in terms of e.g. Jacobi elliptic functions and other elliptics). There's a book "Integrable Systems in Celestial Mechanics" by Mathuna.

I recently added the Euler problem to my iOS app ThreeBody: https://appadvice.com/app/threebody-lite/951920756

Some day I'll get around to adding these 600 solutions...

Yeah, but that doesn't always turn out so well :(