The famous Monty Hall problem in the field of statistics goes like this: Monty Hall is a game show host. You are given a choice of three doors. One has a car behind it, the other two have goats. If you pick the door with the car, you win it. Your odds are 1-in-3.

So you pick a door, but before it opens, Monty opens one of the other two doors to reveal a goat. He asks if you want to switch from the door you initially picked to the other closed door. Your brain says the odds are the same for any closed door, so you stay. But in fact, the odds are twice as good if you switch doors.

You can see the math of it here. But if you are normal, you'll never reconcile in your mind how one closed door could have better odds than the other. If there are two closed doors remaining, how can the odds be anything but 50-50?

This reminds me of the Schrodinger's Cat thought experiment in which a cat in a sealed box (presumably with air holes) exists in a state of being simultaneously alive and dead depending on the results of a randomized event happening inside the box. How can a cat be alive and dead at the same time? Math says it can happen, my brain says no.

The pattern recognition part of my brain is connecting the Monty Hall problem with the Shrodinger's Cat thought experiment because both situations feel like proof that our brains are not equipped to understand reality at its most basic level.

Most of us accept the idea that math is a better indicator of truth than our buggy personal perceptions. Math doesn't lie, but our brains are huge scam artists. The Monty Hall problem and Schrodinger's Cat are examples in which our perceptions of reality and the math of reality disagree in a big way. It makes me wonder how much of the rest of my so-called reality disagrees with math without me knowing.

If I were programming a computer simulation full of artificial humans who believe they are real, I would need to take some shortcuts in creating their context and history. It would be nearly impossible to invent consistent histories for seven billion people spanning back to the primordial ooze. A far smarter approach would be to craft the history as you go, based on the present, in whatever minimum way is necessary to make all histories consistent.

For example, let's say you learn that you are the grand winner of a lottery. At the moment you realize you are the big winner, history becomes limited to only the possibilities that got you to that winning moment. Before you learned you were a winner, the reality at the lottery headquarters was only a smear of possibilities - like Shrodinger's Cat - where you were both a winner and a loser, just like everyone else. As soon as you learn you won, your history and everyone else's harden to conform to it. No one else can perceive that they won the grand prize in that particular lottery.

If I were the programmer of this simulation that you call your reality, I would make the history dependent on the present just to streamline my work. All I need from my fake history is that it is consistent with all the other fake histories so there is no "tell" left by the programmer.

I realize the simpler explanation for my confusion about Monty Hall and Schrodinger's cat is "Math be hard." But I like the psychological freedom of feeling as though I am the author of my own history and not its bitch.

Here's the cool part: I get to keep my interpretation of reality - in which my history is a manufactured illusion - until something in my present experience is inconsistent with that view.

Recently I heard of two senior citizens with mild dementia who became friendly at a senior care facility. Their fragile minds concocted an elaborate history of being childhood acquaintances that had found each other through fate. No one tries to dissuade them of this illusion because it works for them. They successfully rewrote their histories without any repercussions.

I wonder how often the rest of us rewrite our histories. Our only limitations are that our new histories have to be consistent with whatever scraps of history have already hardened.

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Mar 28, 2013
I liked your explanation for a few minutes but then I again got confused.

Can you please explain how or why the combined 2/3 odds remain with the one door unopened by Monty and what prevents the 1/3 odds of the opened door being distributed amongst the two still closed doors.

Mar 28, 2013
Schrodinger's Cat is just a metaphor for how things work at the quantum level, and things at the quantum level defy our normal macroscopic frame of reference anyway.

The Monty Hall Problem is easier to grasp when you realize that your initial choice influences which door Monty opens. If you have picked the door with the car he'll open one of the remaining doors, but it you have picked one of the goat doors Monty is locked into opening the other goat door. Monty is a non-random factor so the two doors that remain closed are not equal to each other.
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Mar 28, 2013
The Monty Hall problem is trivial to comprehend, at least if you're a math person like me.

As far as Schroedinger's Cat, I thought it was actually meant to be sarcastic, as he prefaces it with "One can even set up quite ridiculous cases." I think he corresponded with Einstein about this idea and am given to understand that he (Schroedinger) was actually quite against the notion that a macroscopic system could be in two states at once.
Mar 28, 2013
I agree that our brains are not equipped to visualize quite a number of things which math can correctly predict. Monty hall problem although is not one of those and actually very easy to understand and visualize. The thing here is that the game host "knows" which door has the car. By opening one of the door which doesn't have the car he is giving out that information partly. That extra information changes the odds.

To visualize, two doors have combined odds of 2/3 of having the car while one door which player selected has 1/3. When the game host opens one of the two doors which he "knows" for certain is safe to open, the 2/3 odds applicable to combined door now applies to just one which the game host didn't select to open.

This doesn't change Scot's argument. Just that it's not difficult to fit Monty hall problem in our little brains :-).

Mar 28, 2013
[I wonder how often the rest of us rewrite our histories.]

Too often. There are cases where women have been honestly, seriously convinced that some guy raped them yet the physical evidence later proved they didn't. And cases where people have been convinced as kids that a parent abused them by questioners that didnt know what they were doing. I myself 'remember' a disturbing incident from my childhood that my mother-who I 'recall' as part of the incident-insists never happened and has no reason to lie about it.

I imagine there are lots of other similar cases out there we never hear about because they're less serious.

However I attribute this less to your programmer theory than to the limits of our brains to accurately record data. Our ability to imagine and rationalize also probably has something to do with it.
Mar 28, 2013
Schrodingers Cat was a zombie!!
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