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My entire undergraduate degree in Physics was derivation from first principles. The verification issue comes about when you need to run the experiments yoursel

by throwaway22032 5y ago

My entire undergraduate degree in Physics was derivation from first principles. The verification issue comes about when you need to run the experiments yourself to prove that your equations don't just match with fudged data. You can pretty much prove that calculus works from a purely logical basis (I might be using incorrect terminology here but you get the point, pure math is self-proving.).

foldr 5y ago
> You can pretty much prove that calculus works from a purely logical basis (I might be using incorrect terminology here but you get the point, pure math is self-proving.). Right, but it’s pretty clear from your use of terminology here that you personally haven’t studied the foundations of calculus deeply. Which is 100% fine. You understand roughly why it works and you trust that specialists have checked it out more thoroughly. A lot of people on this thread keep pointing out that various things can be verified. But they are saying this precisely because they themselves have not verified the things in question and yet trust that it is possible to do so. The point is that this is perfectly reasonable in most contexts. You do not have to take on the burden of proving for yourself every mathematical theorem that you make use of.
- throwaway22032 5y ago
  I'm not great at explaining this, but let me try: There are shades between full formal verification of literally everything and then "trust the elders". You can know a little bit about a lot and use that as a sort of statistical verification because you're basically running a monte carlo sim to find holes in the logic, if you find no holes then you can reasonably assume that the rest is true and that's not based on trust. It's a bit like having a 500-dimensional jigsaw puzzle, once you show that most of the pieces fit together the other ones have nowhere to go any more except to fit.

foldr 5y ago

> You can pretty much prove that calculus works from a purely logical basis (I might be using incorrect terminology here but you get the point, pure math is self-proving.). Right, but it’s pretty clear from your use of terminology here that you personally haven’t studied the foundations of calculus deeply. Which is 100% fine. You understand roughly why it works and you trust that specialists have checked it out more thoroughly. A lot of people on this thread keep pointing out that various things can be verified. But they are saying this precisely because they themselves have not verified the things in question and yet trust that it is possible to do so. The point is that this is perfectly reasonable in most contexts. You do not have to take on the burden of proving for yourself every mathematical theorem that you make use of.

throwaway22032 5y ago
I'm not great at explaining this, but let me try: There are shades between full formal verification of literally everything and then "trust the elders". You can know a little bit about a lot and use that as a sort of statistical verification because you're basically running a monte carlo sim to find holes in the logic, if you find no holes then you can reasonably assume that the rest is true and that's not based on trust. It's a bit like having a 500-dimensional jigsaw puzzle, once you show that most of the pieces fit together the other ones have nowhere to go any more except to fit.