Thanks for the reply! This has been gnawing at me. Couldn't sleep very well last night.
However, I did get a few hours and I think my subconscious did some leg work for me. I don't prefer math. I think it's an incredibly powerful tool, but without the right logic it's like firing a gun without the right direction. Also, I won't allow a theory into my worldview unless I can understand it on a fundamental level. I think it would be akin to simply taking it on someone's word, and I won't do that with deep philosophical and rational thoughts.
But now that I've slept! I've begun to see a path to reason this out for myself. And you helped a bit as well. I had earlier said:
Now I'm seeing a different way to interpret what I wrote above. There's a sort of redundancy there. The first two possibilities are Pick a car, shown either goat, switch to goat and LOSE. The possibilities that these two things can happen are equal BEFORE either goat is shown. But time and the unique conditions do a weird trick. As everyone is saying, there's a 2/3 chance of winning if you SWITCH.
You can't pick the car twice with one goat shown anymore! It becomes irrelevant whether the host showed g1 or g2. The possibilities collapsed in such a strange and UNINTUITIVE manner! It's almost like the reason I couldn't figure it out was that I was stuck in the past! I am grateful to "TakenItSeriously" for starting this thread. I don't actually care about who is correct, the very question of why it seems so obvious at first is confounding!
The psychological implications of this have got to be profound. As I was trying to transition to the new paradigm in "opened door world", my brain was screaming halt! I hadn't resolved the issue yet. It would've been 50/50 with 2 doors before, but now it's not. The host hasn't moved anything, we should still be on the same course. Immediately my brain agreed, it was time to put away the question and move forward. Don't let those devious Switchmen slow you down!
HOWEVER, my elder brother was convinced otherwise and I had spent the hours previous arguing without convicting him. He's fairly open minded in the philosophical realm, so this meant something.
I walked away from the phone call, immediately discussed it with a close friend at hand. We reassured eachother. "These people were confusing the issue!" " Most of these people haven't reasoned it out themselves, they're just a bunch of parrots adopting the supposed intellect of others!"
But there was something deep within me unsettled. I read the thoughts of others, tired of the antagonism of forums, and eventually posted my own thoughts CONVINCED that I was right and walked away. But it wasn't enough. I shivered with nervous energy. I laid awake until 5am without thinking of anything in particular.
Then I woke. Suddenly I could think differently.
Before, the noise from my mind was so loud I had trouble even moving forward in thought. Now I woke with a sudden suspicion that I had been wrong. And here I am.
WHAT AN EXPERIENCE! I've crossed so many psychological mechanisms to get here! Although I'm still not entirely convinced, with enough empirical data I could be convinced now (that may not have been the case before), and I'm leaning Switchmen. Before I would question the source, it's methods and intentions, ad infinitum.
What happened in my mind? Is this a matter of right brain/left brain hoopla? Was the right brain doggedly focused on expediently executing judgement based on my own known theories, while the left brain waited for it to loosen up and chime in? What is the nature of conscious/subconscious? How is it that I can only be convinced of something asleep?! Also, it's quite fascinating how the probability DOES seem to change. This might have more implications in physical reality than I realize.
I'm sure my peers think to themselves that I would have been the more intelligent had I grasped the concept sooner-that I was stubborn in my thinking. That I should've been convinced by the empirical data alone! BAH! Studies lie! I'm a chemist who's seen group bias and the manipulation of data! Hell, I was a highschooler who'd seen those things as well! There's value in conservatism! If you can't understand a theory, don't bed it! Although ironically it was sleep that opened me to the idea...Nevertheless! Skepticism is healthy!
Perhaps you'd had won and I lost. Perhaps you're driving that brand new Mitsubishi Mirage right now! But I'll take my goat. I love and understand goat. And I'll walk away a rich man in my experience. I'm still thinking about it...