Agreed that this points in the right direction. I think there’s more to it than that though. Consider for example a three-body problem under Newtonian mechanics. Then there’s a sense in which specifying the initial masses and velocities of the bodies, along with Newton’s laws of motion, is the best way to compress the information about these chaotic trajectories.
But there’s still an open question here, which is why are three-body systems chaotic? Two-body systems aren’t. What makes the difference? Finding an explanation probably doesn’t allow you to compress any data any more, but it still seems important and interesting.
(This seems related to a potential modification of your data compression standard: that good explanations compress data in a way that minimises not just storage space, but also the computation required to unpack the data. I’m a little confused about this though.)
Agreed that this points in the right direction. I think there’s more to it than that though. Consider for example a three-body problem under Newtonian mechanics. Then there’s a sense in which specifying the initial masses and velocities of the bodies, along with Newton’s laws of motion, is the best way to compress the information about these chaotic trajectories.
But there’s still an open question here, which is why are three-body systems chaotic? Two-body systems aren’t. What makes the difference? Finding an explanation probably doesn’t allow you to compress any data any more, but it still seems important and interesting.
(This seems related to a potential modification of your data compression standard: that good explanations compress data in a way that minimises not just storage space, but also the computation required to unpack the data. I’m a little confused about this though.)
Yeah, I think you’re right. There are two types of explanations:
those which compress information
those which provides us with faster algorithms to reason about the world
The three-body systems is the example of the latter. As is lots of math and computer science.