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Wellness Wednesday for December 13, 2023

The Wednesday Wellness threads are meant to encourage users to ask for and provide advice and motivation to improve their lives. It isn't intended as a 'containment thread' and any content which could go here could instead be posted in its own thread. You could post:

  • Requests for advice and / or encouragement. On basically any topic and for any scale of problem.

  • Updates to let us know how you are doing. This provides valuable feedback on past advice / encouragement and will hopefully make people feel a little more motivated to follow through. If you want to be reminded to post your update, see the post titled 'update reminders', below.

  • Advice. This can be in response to a request for advice or just something that you think could be generally useful for many people here.

  • Encouragement. Probably best directed at specific users, but if you feel like just encouraging people in general I don't think anyone is going to object. I don't think I really need to say this, but just to be clear; encouragement should have a generally positive tone and not shame people (if people feel that shame might be an effective tool for motivating people, please discuss this so we can form a group consensus on how to use it rather than just trying it).

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But I need something—I don’t think it’s healthy to live in a cold, unfeeling world ruled by randomness. (After all, that’s not how the West was won, was it?)

It's jarring and eye-roll-worthy when someone sneaks in a grand claim in an otherwise mundane post.


Anyway, I don't experience this all that much. The times that come to mind are;

  1. The Monty Hall problem. I understand probability theory well enough to Euler myself into the "correct solution", but I still FEEL like it should be 1/2 not 2/3s. And if you completely flipped the script with an alien scenario, I might fall for it again. I'm no stranger to probability puzzles and usually solve most of them or don't fall for the obvious trap, but the lizard in my brain can't accept reality in this specific case.
  2. I have a hard time accepting that things just are (the way they are) in the sociopersonal space. In that if you do X, the signal that you do X might predict that you do Y, but, that intuition is useless. In other words, knowing aggregate trends helps little on a single data point. Predicting aggregate -> aggregate is easy. Making a prediction is hard, this is almost always because (Lewontonins fallacy, minus the fallacy).

How do I cope with it? Just ignore it lol.

The Monty Hall problem. I understand probability theory well enough to Euler myself into the "correct solution", but I still FEEL like it should be 1/2 not 2/3s. And if you completely flipped the script with an alien scenario, I might fall for it again. I'm no stranger to probability puzzles and usually solve most of them or don't fall for the obvious trap, but the lizard in my brain can't accept reality in this specific case.

Code a simulation of it, and step through the logic, it helped me.

After grokking it, my conclusion was that a lot of the explanations are backwards. After they reveal the empty slot, you can only win by changing your decision, if you got it wrong the first time. So what are the chances of getting it wrong on the first go?

I have a hard time accepting that things just are (the way they are) in the sociopersonal space. In that if you do X, the signal that you do X might predict that you do Y, but, that intuition is useless. In other words, knowing aggregate trends helps little on a single data point. Predicting aggregate -> aggregate is easy. Making a prediction is hard, this is almost always because (Lewontonins fallacy, minus the fallacy).

I have a similar - perhaps reversed - experience as this. I chalk it up to my upbringing, being consistently taught and reinforced that stereotyping someone is only one notch above imposing something like literal chattel slavery on them. As such, as Arthur Chu might say, I was trained to periodically "mind-kill" myself to never predict the behavior of someone based on other signals without some specific independent evidence. If I ran into a burly man with face tattoos in a dark alley in an area known for gang activity, it would be evil to treat him any differently than if I ran into an old lady in her 70s who has to take deep breaths every few steps; the burly man could just be a tattoo and fitness enthusiast, and the old lady could be an armed robber with a hidden gun. The relative odds of these scenarios don't matter; in fact, even considering calculating it is, again, evil.

I've been trying to learn to think differently, since I noticed that even the people who push this stuff clearly don't believe it, as shown by their revealed preference and, more recently, just explicit praise of the moral virtuousness of stereotyping in [circumstances]. It's not easy to navigate out of decades of propaganda that started since grade school, though.

The Monty Hall problem. I understand probability theory well enough to Euler myself into the "correct solution", but I still FEEL like it should be 1/2 not 2/3s. And if you completely flipped the script with an alien scenario, I might fall for it again. I'm no stranger to probability puzzles and usually solve most of them or don't fall for the obvious trap, but the lizard in my brain can't accept reality in this specific case

Doesn't the feeling go away when you realise that what you're choosing is the odds of selecting the car the first time around, not the second, since the game show master always removes a goat? The removing of a goat isn't independent of your choice of door.

Or if you expand the number of doors. If there are a million doors, you choose one and the game show master removes 999998 doors and asks if you want to choose again, do you still feel like it doesn't matter what you choose?

I was never convinced by the "expand the number of doors" scenario because it's not obvious why 999998 doors would be removed in the new scenario. It feels like another euler trick.

Yeah me neither because of how hand wavy it is. It's trying to make a point about priors but that totally misses the point! The point of the Monty hall problem is that the door Monty Hall opens is DEPENDENT on you having made the choice before. That's what makes it 2/3. If he already opened a door and you walked up to the stage and chose the door after the fact, it would be 1/2. The lesson in Monty hall is a lesson of dependence not priors.

Another way I like to view it is that Monty Hall opening the door doesn't tell us anything at all about the door we initially chose. It's the illusion of information, my chances were 1/3 when I walked up to the stage, it's still 1/3. Because the dependence flows one way. You are not actually given any information to update on, so I think the bayesian explanation is kinda shoddy on that front.

Anyone who is actually good at probability theory, feel free mansplain it to me If my intuition is wrong.

Yeah, you’re right. When you pick door 1, Monty removes it from his little pre-game winnowing of the doors; he can only open door 2 or 3 now, which collectively have a 2/3 chance of containing the prize. If he opens 3 and it contains the car, you’ve automatically lost. The chance of this is eliminated when he reveals a goat, but the collective grouping of 2 and 3 retains 2/3 odds. Now door 1 is added back to the mix, it’s smart to switch.

What is sometimes confusing is realizing that there are actually two ‘games’, each with only two doors in play, with the second dependent on the first. The odds of a door having the car in a standard two-door scenario are 50/50, but the odds of your door having it are only 1/3, because there’s a 1/3 chance that you’re only still playing because Monty excluded your (goat) door from round one. Your door being ‘safe’ from Monty’s initial opening means your odds don’t improve, while door 2’s do, provided 3 doesn’t have the car.

When you frame it in terms of dependence (on you choosing the door before or after Monty showing a door with a goat) the Monty Hall problem isn't much of a problem at all.

This is a common thing in many many stats puzzles and the overall trend of why normies are so bad at probability/stats. The most important/pivotal part is formulating the correct problem statement. And in terms of inference, that means knowing exactly what the inference tells you and what it doesn't.

The above applies to most branches of math, but probability/stats is fundamentally at a level of abstraction above most other fields of math from the ground up.