> The prototypical example in my mind has always been the Monty Hall problem, where you often see convoluted explanations or detailed probabilistic calculations, but the solution is just plain as it can be when you consider that if you switch you win iff you chose a goat and if you stay you win iff you chose the car.
The problem here is, when two people disagree, they both think the problem is simple and they both think their answer is trivial. The thing is, they haven't solved the same problem.
In the standard formulation, where switching is the best strategy, Monty's actions are not random: He always knows which door has the good prize ("A new car!") and which doors have the bad prize ("A goat.") and he'll never pick the door with the good prize.
If you hear a statement of the problem, or perhaps a slight misstatement of the problem, and conclude that Monty is just as in the dark as you are on which door hides which prize and just happened to have picked one of the goat-concealing doors, then switching confers no advantage.
A large part of simplicity is knowing enough to state the problem accurately, which circles back to your paragraph about Feynman: Understanding his initial understanding of QED required understanding everything he knew which lead him to his original understanding of the problem QED solved; for his final formulation of QED, he understood the problems in terms of more fundamental concepts, and could therefore solve them using those same concepts.
Actually, if Monty chooses randomly and just happens to pick a door with a goat you should still switch, because it's still true that you will win if you switch iff you chose a goat but you'll win if you stay iff you chose the car already. The host's method of selection is not relevant given a priori the observation that the host selected a goat. The host's method is relevant if we forgo that observation and iterate the game repeatedly.
The problem here is, when two people disagree, they both think the problem is simple and they both think their answer is trivial. The thing is, they haven't solved the same problem.
In the standard formulation, where switching is the best strategy, Monty's actions are not random: He always knows which door has the good prize ("A new car!") and which doors have the bad prize ("A goat.") and he'll never pick the door with the good prize.
If you hear a statement of the problem, or perhaps a slight misstatement of the problem, and conclude that Monty is just as in the dark as you are on which door hides which prize and just happened to have picked one of the goat-concealing doors, then switching confers no advantage.
A large part of simplicity is knowing enough to state the problem accurately, which circles back to your paragraph about Feynman: Understanding his initial understanding of QED required understanding everything he knew which lead him to his original understanding of the problem QED solved; for his final formulation of QED, he understood the problems in terms of more fundamental concepts, and could therefore solve them using those same concepts.