Newtonian mechanics was systematized as a special case of general relativity.
One of the things I found confusing early on in this post was that systemization is said to be about representing the previous thing as an example or special case of some other thing that is both simpler and more broadly-scoped.
In my opinion, it’s easy to give examples where the ‘other thing’ is more broadly-scoped and this is because ‘increasing scope’ corresponds to the usual way we think of generalisation, i.e. the latter thing applies to more setting or it is ‘about a wider class of things’ in some sense. But in many cases, the more general thing is not simultaneously ‘simpler’ or more economical. I don’t think anyone would really say that general relativity were actually simpler. However, to be clear, I do think that there probably are some good examples of this, particularly in mathematics, though I haven’t got one to hand.
Yeah, good point. The intuition I want to point at here is “general relativity was simpler than Newtonian mechanics + ad-hoc adjustments for Mercury’s orbit”. But I do think it’s a little tricky to pin down the sense in which it’s simpler. E.g. what if you didn’t actually have any candidate explanations for why Mercury’s orbit was a bit off? (But you’d perhaps always have some hypothesis like “experimental error”, I guess.)
I’m currently playing around with the notion that, instead of simplicity, we’re actually optimizing for something like “well-foundedness”, i.e. the ability to derive everything from a small set of premises. But this feels close enough to simplicity that maybe I should just think of this as one version of simplicity.
One of the things I found confusing early on in this post was that systemization is said to be about representing the previous thing as an example or special case of some other thing that is both simpler and more broadly-scoped.
In my opinion, it’s easy to give examples where the ‘other thing’ is more broadly-scoped and this is because ‘increasing scope’ corresponds to the usual way we think of generalisation, i.e. the latter thing applies to more setting or it is ‘about a wider class of things’ in some sense. But in many cases, the more general thing is not simultaneously ‘simpler’ or more economical. I don’t think anyone would really say that general relativity were actually simpler. However, to be clear, I do think that there probably are some good examples of this, particularly in mathematics, though I haven’t got one to hand.
Yeah, good point. The intuition I want to point at here is “general relativity was simpler than Newtonian mechanics + ad-hoc adjustments for Mercury’s orbit”. But I do think it’s a little tricky to pin down the sense in which it’s simpler. E.g. what if you didn’t actually have any candidate explanations for why Mercury’s orbit was a bit off? (But you’d perhaps always have some hypothesis like “experimental error”, I guess.)
I’m currently playing around with the notion that, instead of simplicity, we’re actually optimizing for something like “well-foundedness”, i.e. the ability to derive everything from a small set of premises. But this feels close enough to simplicity that maybe I should just think of this as one version of simplicity.