OK, folks, listen. Newtonian mechanics has a slot in it for “what system are you evolving through time” and then it specifies the time evolution of that system. It, sadly, doesn’t come with a machine that spits that time evolution out, so we have to figure out how and if we can get that time evolution.
There’s a lot of detail that we don’t know about real world systems, and the more detail we have the harder it is to calculate the time evolution, so we come up with simplified systems that are kind of similar and, if we captured enough of the relevant details then the predictions should evolve in analagous ways. Whenever our predictions are wrong, it could be because of the misspecification error (i.e. that our simplified system was not like our real system in important ways) or because Newtonian mechanics was wrong.
This flexibility should indeed make you sus of Newtonian mechanics. And the smaller a slice of system space you have to hit to restrict to explain your observations, the more sus you should be of it you should be. But we’re not going to end up with that small a slice of the system space here.
I think your suspicion should be something like log(proportion of system space that explains the fallen pendulum)/log(proportion of system space of even simpler models that seem like they should work to model pendula). And waves hands frantically that’s an easily surmountable number of bits.
Gotta go, kids! Don’t do instrumentalist theories of philosophy of science and stay on LessWrong!
OK, folks, listen. Newtonian mechanics has a slot in it for “what system are you evolving through time” and then it specifies the time evolution of that system. It, sadly, doesn’t come with a machine that spits that time evolution out, so we have to figure out how and if we can get that time evolution.
There’s a lot of detail that we don’t know about real world systems, and the more detail we have the harder it is to calculate the time evolution, so we come up with simplified systems that are kind of similar and, if we captured enough of the relevant details then the predictions should evolve in analagous ways. Whenever our predictions are wrong, it could be because of the misspecification error (i.e. that our simplified system was not like our real system in important ways) or because Newtonian mechanics was wrong.
This flexibility should indeed make you sus of Newtonian mechanics. And the smaller a slice of system space you have to hit to restrict to explain your observations, the more sus you should be of it you should be. But we’re not going to end up with that small a slice of the system space here.
I think your suspicion should be something like log(proportion of system space that explains the fallen pendulum)/log(proportion of system space of even simpler models that seem like they should work to model pendula). And waves hands frantically that’s an easily surmountable number of bits.
Gotta go, kids! Don’t do instrumentalist theories of philosophy of science and stay on LessWrong!