I’m not sure if this is a weird quirk of my particular brain or just a side-effect of coming of age around the time the Matrix was released, but I’ve always found it easy to see the underlying “ones and zeros” beneath a coat of paint.
Wait, let me go back and start a little differently.
I play a lot of board games. If you ask someone what a particular board game is about, you often get one of two very different kinds of answers. The more common answer is something like “Oh, this is a game about fighting dragons, and you’re trying to save the kingdom from all these evil dragons, but sometimes there are good ones, and you get a bunch of cool magic swords and stuff, and the winner is whoever bags the biggest dragon!” That’s perfectly true, but the less common (and equally true) kind of answer is something like: “This is an auction game; you have various different kinds of resources and you bid on things you want, and the winner is whoever bid most effectively.”
The first answer is the window dressing. The coat of paint. It’s describing the theme of the game. The second answer is describing the underlying mechanics. You bid currency for a resource you want. The “currency” could be “cool swords” or “your knight’s health,” and the thing you want to “buy” is “a dead dragon.” But if you stripped away all the stuff about swords and dragons, you could still play the game, in the same way you can play chess without caring about what ancient warrior class each piece was meant to represent.
Now, for a lot of people, the game is very boring without all the window dressing. I’m not one of those people. I like swords and dragons! But I don’t care if my sudoku puzzle is like, sushi-themed or whatever. I’m just there for the math. And I can see right through everything else to the math pretty easily.
Okay, tangent time. I think a lot of what it takes to understand math, philosophy, science, and psychology is the ability to see two situations as equivalent even when their window dressing is very, very different.
The full trolley problem isn’t just “do you hit one person or five.” It’s asking if you’re willing to pull the lever to switch the train to only kill one person, and then asking if you’d push someone in front of the train to stop it from killing the five original people, and then asking if you’d murder a homeless man and harvest his organs to save five dying hospital patients, and then asking people what the actual difference between those three scenarios is.
And that’s the point: there isn’t any. If you strip away the window dressing and get down to the math, all three scenarios are asking the same question: “Is it okay to actively make the choice to murder one person to save five lives that would end if you make the passive choice to do nothing?” Every scrap of your moral intuition will try to scream at you that the scenarios aren’t different, but if you can look past the paint and see the ones and zeroes, that’s what’s at stake.
I started thinking about this today because of the Monty Hall problem. Here’s a quick summary: You’re on a game show, trying to win a new car, which is randomly behind one of three doors. You pick a door, let’s say Door #3. Before opening the door, the host opens up one of the other doors, say Door #1, and shows you that the car is not behind that one. He then asks if you want to stick with Door #3, or switch to Door #2. Should you switch?
The intuitive answer is “no, it doesn’t matter,” but that’s actually incorrect. The correct answer is that you should switch: you have a 1 in 3 chance of being right the first time, but you have a 2 in 3 chance of being right if you switch.
That’s not the debate – that’s settled and proven. What trips people up is that even if they believe the answer (and of course, a huge number of people don’t believe it) is that they can’t find an easy, intuitive way of explaining or understanding why. They can look at the mathematical proof, but they can’t just grok it.
I have (what feels to me like) an intuitive explanation, so let me see if it works on you:
You pick Door #3, correctly understanding that you have a 1 in 3 chance of being correct and getting the car. Before opening Door #3, the host asks if you want to switch to Doors #1 & #2 together. If you switch, and the car is behind either door, you get the car. Assuming that the host isn’t deliberately trying to trick you or anything and this is just always how the game show goes, do you get that switching would give you a 2 in 3 chance of getting the car? You do, right? Because obviously 2 doors is 2/3 of the doors, and so if you could bet on the car being behind either of them, that’s a better deal.
Well, “Opening Door #1 and showing you it has nothing, then offering you to swap to Door #2” is exactly the same as “Offering to let you swap to Doors #1 & #2 together.”
If you get offered the chance to swap to Doors 1 & 2, and you take it, you already know that at least one of those doors has to be empty. There’s only one car. So dramatically opening one of the doors to show you is just window dressing for suspense, it doesn’t change anything.
Here’s another way the host could make the exact same offer, but phrase it differently: “Okay, you picked Door #3. Before we open it, I’ll give you a chance to pick a different door. But I’ll sweeten the deal: if you choose to swap and you pick an empty door, I’ll let you mulligan and pick again!” Again, you end up with the same information before making the final choice, but surely you see how getting an extra pick increases your odds from 1 in 3 to 2 in 3, right? You get two picks!
Anyway, I genuinely don’t know if that made it clearer for you. One of the problems with intuitively seeing an answer like that is that you can have a hard time explaining it to someone who doesn’t see things the same way. So really, that’s what this is for me – practice. If you understand the Monty Hall problem any better, let me know!
The Opportunity Machine 