There have been, in the last few weeks and months, some a-ha moments I've experienced. One happened yesterday. The others had to do with Calculus and Physics. But yesterday's was particularly satisfying. You see, there was a problem posted somewhere a long time ago and it was eventually answered by Marilyn vos Savant. Now, Marilyn is a genius with and IQ, apparently, higher than that of Einstein. (I don't know how they measure such things but lets just say she is special).
The puzzle she solved was the Monte Hall Door Problem where there are three doors and behind one is a big prize. The other two have bogus prizes. You're asked to pick a door but aren't shown what's behind it. Then, Monte reveals a remaining door that has one of the bogus prizes. He offers you a chance to stick with your first choice or switch.
Marilyn says you should always switch. Most people balk at that saying that it's a 50-50 choice at that point and switching doesn't increase your odds...so why switch.
She was right, though. It's been proven through computer simulations and Myth Busters did a piece on it.
I never understood her logic until yesterday. I don't know why it clicked for me. I'm certainly not as Hi-Q as her, but maybe in my older brain, some synapse dislodged enough to make room for understanding.
The other A-HA's had to do with understanding differential calculus, and whether photons really are both waves and particles. There's that and I like to look at funny YouTube videos.