Monty Hall is a game show host, and he is famous for the eponymous problem. It is a probabilistic puzzle masquerading as a game show; here's how it goes:
- You are the participant in a game show where you can win a car or a goat. You want the car, NOT the goat.
- There are three closed doors in front of you; behind one of the closed doors is a car, while the other two hide a goat each.
- You are asked to guess behind which is the car.
- The host, who knows everything, opens one of the doors revealing a goat behind it. So now you're left with two doors.
- Do you want to stay with your choice or switch?
At first sight, it doesn't seem prudent to switch because probabilities have not changed - the initial likelihood of picking the door with a car is 1/3. However, now that new data is revealed, it sets in motion a new game and you have to update your probabilities. You were 2/3 likely to have picked the goat in the first round of guessing, so by revealing a goat Monty is telling you where the car is. If you had chosen the door with the car, though, you would lose by switching, but the probability of that from the previous game was lower, at 1/3. So if you approach the problem from a Bayesian perspective, where new data updates the decision model, you would benefit by switching.
This was not intuitive for a long time; I couldn't see how the game changed if irrelevant data was revealed (the car door is never opened). More fundamentally, I did not see how a new game was set in motion. A basic understanding of quantum mechanics, notably string theory helped the concept click into place.
In the nano-scale world of quantum mechanics, the most fundamental particles are probabilistic waves passing down time-strings (approximation). It is the act of observation that determines their position, and in the process transforms the wave function.
The wave looking thing is a string vibration passing along minding its own business, and the little clock is what we use to observe the particle. Notice how the wave was smooth, but the instant we observe and thus "determine" it, the wave function changes. Our observation changes the waveform, and if we are all waves, then that change affected the nearby vibrations. These changes propagate through adjoint strings and affect reality.
That's what happens when the host opens one of the doors, new information is revealed, and the change wrought about by observing, ripples through to start a new game. The impact of observation on creating new realities is profound when you attempt to wrap your head around. It was interesting how my mind immediately went to the Monty Hall Problem and updated my understanding. In a way, my watching it changed me.
Many questions persist around why watching that had that impact on me and not say on my friend. What about the time-string configurations in my body led to that specific response.