3 ms·

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

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?

hengheng 9y ago
Not much of it should be robust to small input variations.
kurlberg 9y ago
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 http://www.ams.org/notices/199505/saari-2.pdf
- DamonHD 9y ago
  Interesting paper: I could just about follow it and the 'm3' particle accelerator is somewhat terrifying!
- aisofteng 9y ago
  Of course, that is physically impossible.
mathgenius 9y ago
I think Terrence Tao did something like this for fluid mechanics.
- IngoBlechschmid 9y ago
  Indeed, reported on at https://www.quantamagazine.org/20140224-a-fluid-new-path-in-grand-math-challenge/ https://www.quantamagazine.org/20140224-a-fluid-new-path-in-....
gue5t 9y ago
The Gravity esolang falls roughly along this line of thought: https://esolangs.org/wiki/Gravity https://esolangs.org/wiki/Gravity
jschwartzi 9y ago
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.

hengheng 9y ago

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

kurlberg 9y ago

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

DamonHD 9y ago
Interesting paper: I could just about follow it and the 'm3' particle accelerator is somewhat terrifying!
aisofteng 9y ago
Of course, that is physically impossible.

mathgenius 9y ago

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

IngoBlechschmid 9y ago
Indeed, reported on at https://www.quantamagazine.org/20140224-a-fluid-new-path-in-grand-math-challenge/ https://www.quantamagazine.org/20140224-a-fluid-new-path-in-....

gue5t 9y ago

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

jschwartzi 9y ago

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.