Originally Posted by Dave in Green
I've just gone back and read some of the original posts in this thread, and it's weird and spooky how new forum members keep entering the thread with the same misguided intuition about the physics of projected images.
I may regret bringing this up, but this whole subject reminds me of a somewhat famous statistical problem, that many call the Monte Hall problem.
Wikipedia has an explanation of the problem here:
Here is how it was asked of Marilyn vos Savant in Parade magazine:
Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?
I remember seeing it there in 1990. This was a couple of years after I had first heard it though.
My first exposure to the problem was during a statistics class in college. The teacher laid out the question, I thought for maybe a minute, then turned to somebody I knew next to me and told him that people should switch because then they would have a 2/3rds chance of winning.
I considered this one of our easier problems in that class. To me it seemed obvious. I was shocked that after the teacher explained it for the whole rest of the class time, the class still left with many people believing the odds were 50/50.
People can learn all sorts of rules, but if they don't understand the underlying reasons for things then they are likely to mess up when given a problem where those rules don't apply.
To me this was an easy problem because when you pick a door you have a 1/3rd chance of picking the car, there is a 100% chance that the host can pick a door with a goat that isn't your door, so the odds that you picked the right door to begin with don't change one bit when the host opens a door. And the odds that the car is behind a door you didn't pick don't change just because you were shown one of the doors. The odds were 2/3rds that the car was behind a different door than you picked to begin with, and they stay at 2/3rds when you are shown what is behind one of the doors, which has 0% chance of containing the car, because the host knew which door to open.
The host showing you a door not changing the odds that you picked the car to begin with is the kind of thing I was referring to in the original post in this thread when I said:
Originally Posted by darinp2
I view this as like test questions in school where the teacher would put irrelevant information and part of the class would change their answer based on it. In this case the irrelevant information is whether the left and right side are shown at the same time or at different times when each is being shown at higher frequency than the viewing system can perceive.
Much like the way Dave Harper claims we have to believe his expert and that I am just a weekend warrior who hasn't used physics in this area since college, despite the fact that Dave's expert can't even answer the questions without contradicting himself, in the Monte Hall problem many people with great credentials claimed that Marilyn vos Savant was wrong and others claimed that we had to go with what those with great resumes said. As it says on the Wikipedia page:
Many readers of vos Savant's column refused to believe switching is beneficial despite her explanation. After the problem appeared in Parade, approximately 10,000 readers, including nearly 1,000 with PhDs, wrote to the magazine, most of them claiming vos Savant was wrong (Tierney 1991). Even when given explanations, simulations, and formal mathematical proofs, many people still do not accept that switching is the best strategy (vos Savant 1991a). Paul Erdős, one of the most prolific mathematicians in history, remained unconvinced until he was shown a computer simulation demonstrating the predicted result (Vazsonyi 1999).
Sometimes being a certain kind of thinker matters more than what it says on a person's resume.
For those who use their intuition to think that eShift must have the same lens requirements as the native resolution because that is all that goes through the lens at a moment in time, and also that the odds in the Monte Hall problem must be 50/50, here is one that I consider a pretty easy proof of the Monte Hall problem.
Start with 6 people playing the game with the car behind the same door, but without seeing the other 5 people play, having the host go through all 6 people, who are taking all 6 possibilities a contestant can take. Those 6 combinations of choices are:
1: Stayer, starts with door A.
2: Stayer, starts with door B.
3: Stayer, starts with door C.
4: Switcher, starts with door A.
5: Switcher, starts with door B.
6: Switcher, starts with door C.
Now, there are only 3 possibilities for the car. Door A, B, or C. Here are the winners for every one of those possibilities.
A: 1, 5, 6
B: 2, 4, 6
C: 3, 4, 5
In other words, no matter where the car is, out of those 6 people one stayer wins and two switchers win. One out of three stayers and two out of three switchers. There are only 18 possibilities in the game and stayers win 6 of those, while switchers win 12 of them.
In short, if you are a stayer and want to win the game, you have to pick the car. If you are a switcher you always win if you pick a goat. The odds of picking a car are 1/3 and the odds of picking a goat are 2/3, so it is better to be a switcher than a stayer, at least based on the odds, since you are twice as likely to win as a stayer is.
I learned some things about human intuition there, since to me my intuition was very different and was what turned out to be the right answer, while I've talked to people who I consider extremely intelligent who got the wrong answer to that problem. I enjoyed problems like that since I was young, so I probably had some advantage there by the time I heard it.
One thing that the Monte Hall problem should tell anybody who hasn't been paying enough attention to notice this already in life, is that just because a person can point to a great resume that doesn't mean they are always right, especially when the problem isn't as a straightforward as the problems they've been used to getting.
For the Monte Hall problem a very simple rule fits. If you are a stayer and want to win you have to pick the car to begin with, which you have 1/3 chance of doing. Those who think that being shown a door means the odds of the car being behind your door change are a lot like those who think that all you have to do to show smaller details with higher fidelity through a lens is to only show part of the image at a time, IMO. Those who think those things can take solace that a lot of very smart people thought the first one too, and would likely be true if enough people were asked about the 2nd one also. Lots of people having the same intuition doesn't change the truth though.