Over 150 new families of Newtonian periodic planar three-body orbits

Re:Over 150 new families of Newtonian periodic planar three-... by GregBuchholz on Saturday May 06, 2017 @11:33AM (#14280659)

Has anyone explored the computational nature of Newtonian gravity? That is, if you carefully setup a set of masses in some manner, and let them interact though their gravitational pull, what kinds of things can you compute? Is gravity Turing complete? Is it a push down automata? Finite state machine? Can you use choreographies like these, coupled together to create register machines, or simulate cellular automata?

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Re:Over 150 new families of Newtonian periodic planar three-... by kurlberg on Saturday May 06, 2017 @12:44PM (#14281085)

Not quite a computation, but there is a striking example (due to Xia) where 5 particles interact and "kicks" off one particle to infinity in finite time. Further details can be found in

http://www.ams.org/notices/199505/saari-2.pdf

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Re:Over 150 new families of Newtonian periodic planar three-... by aisofteng on Saturday May 06, 2017 @11:17PM (#14283663)

Of course, that is physically impossible.

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Re:Over 150 new families of Newtonian periodic planar three-... by DamonHD on Saturday May 06, 2017 @01:08PM (#14281219)

Interesting paper: I could just about follow it and the 'm3' particle accelerator is somewhat terrifying!

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Re:Over 150 new families of Newtonian periodic planar three-... by jschwartzi on Saturday May 06, 2017 @05:56PM (#14282476)

There might be some way to devise an analog computer, although it's not clear to me how you would implement arithmetic operations.

Operational amplifiers can be configured to generate analogous orbits by using them to differentiate one of their inputs. By wiring multiple op-amps together and measuring voltages at different points it's possible to observe chaotic behavior in the measurements, just as if you were to directly differentiate from some initial condition on paper using a differential equation. This configuration is an analog computer. In fact, I wouldn't be surprised if op-amp circuits existed with perfectly analogous mathematical behavior to the orbits described in the paper.

The problem with gravitational computing using n bodies probably lies with establishing initial conditions, and with inhibiting the effects of neighboring systems.

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Re:Over 150 new families of Newtonian periodic planar three-... by mathgenius on Saturday May 06, 2017 @02:04PM (#14281505)

I think Terrence Tao did something like this for fluid mechanics.

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Re:Over 150 new families of Newtonian periodic planar three-... by IngoBlechschmid on Saturday May 06, 2017 @02:32PM (#14281606)

Indeed, reported on at https://www.quantamagazine.org/20140224-a-fluid-new-path-in-....

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Re:Over 150 new families of Newtonian periodic planar three-... by gue5t on Saturday May 06, 2017 @03:56PM (#14281955)

The Gravity esolang falls roughly along this line of thought: https://esolangs.org/wiki/Gravity

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Re:Over 150 new families of Newtonian periodic planar three-... by hengheng on Saturday May 06, 2017 @11:46AM (#14280733)

Not much of it should be robust to small input variations.

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