Ah yes, you're right of course, and I haven't really thought about it in this way before - that either you're based on "real world" geometry, in which case thin

Ah yes, you're right of course, and I haven't really thought about it in this way before - that either you're based on "real world" geometry, in which case things are a bit harder to prove but make sense, or you're more abstract, in which case you can define things to be easier to prove e.g. Pythagoras, but the complexity is in the mapping between your definitions and the "real world". > In fact my masters thesis was about Hilbert spaces. And I find it pretty interesting that you can prove something like Pythagoras on the inner product form I mentioned at the end of my last comment. That's pretty cool, you're definitely more knowledgeable than I am, I'm just a math amateur :)