I remember coming across Amdahl's law in the grad school and thinking, "Why is this even a law? Isn't it something completely obvious?"
...later I became a developer. Turns out it's not obvious.
...later I became a developer. Turns out it's not obvious.
The only reason why it is non-obvious how to take advantage of it in practice is that problems in the real world very rarely break down so cleanly into a completely serial piece and a trivially, arbitrarily parallelizable piece and even if you are lucky enough to find such a problem at a certain scale, the very act of breaking down the problem almost always eventually results in other previously ignorable constant or scaling factors becoming important either as you chop the problem into smaller pieces or as you scale to bigger problems. The difficulty lies entirely in posing the problem to be "solved", not the application of the law itself.
E.g. pigeonhole principle -> no perfect compression (among other similar proofs)
Another a favorite one I have is understanding just how "weird" it is that pi, a constant, exists. Take a rope and tie it around the Earth so that it fits snugly on the Earth's surface. How much more length of rope does it take so that the entire rope circling the whole of the Earth can be lifted 10 feet off its surface? ~31 feet (this was at least surprising to me the first time I was asked this question, which was long after I first learned about pi).
It is similar to the ideal gas law, for example, which can be proved from the axioms of classical thermodynamics and yet fails when the molecules start interacting.
Laws span the whole spectrum from purely empirical to provable within some theories' frameworks.