A visual guide to Bayesian thinking

I wrote the present comment to 1) teach something about mathematics and probability 2) share enlightenment. In summary this comment should change your thinking about all subjects, forever. -------------- Program of study for this comment: 1. Read section 1 (approx. 1 hour.) Goal: improve your mathematical reasoning. 2. 30 minute break. 3. Read section 2 (approx 5 minutes). Goal: enlightenment. 1. The most important mathematical video you will ever see in your life. Firstly, unless you are a practicing mathematician this is the most important mathematical video you will ever see in your life. It is purely about mathematics: [VIDEO] Watch it. Suppose that you take an hour and learn this. You have just improved your rational thinking forever. - Break. Please now take a 30-minute break. During this time you can reflect and assimilate the knowledge you have learned. - 2. The most important social insight you will read in any comment. This section requires you to understand section 1. Next, suppose that you are perfectly rational. If I present you a (fair) coin and ask you to judge whether it is fair, after, say, thirty or forty flips you will conclude that it is fair. If I give you the same coin but also the knowledge that it was drawn from an infinite bag with 1 fair coin in it -- for example, let's say coins are numbered, I select a real number between 0 and 1, and only the coin with the exact value 0.5 is fair, any other coin is unfair, weighted - then even given hours, days, w

Note: as a throwaway I was unable to complete edits to this comment, therefore please upvote (and endorse) only this version. The first version should remain dead as a dupe. ----- In the spirit of the article we're discussing, I wrote the present comment to 1) teach something about mathematics and probability 2) share a bit of social enlightenment. In summary this comment should change your thinking fundamentally. You will need to read it carefully but I promise it is relevant. (Please endorse it and upvote it, if you agree.) -------------- Program of study for this comment. I suggest you go through this comment as follows. 1. Read section 1 (approx. 1 hour.) Goal: improve your mathematical reasoning. 2. 30 minute break. 3. Read section 2 (approx 5 minutes). Goal: social insight. 4. Generalize the insight just gained. Goal: make the example more practical. This is an exercise for the reader. ---------- 1. One of the most important mathematical videos you will ever see. Firstly, unless you are a practicing mathematician this is one of the most important mathematical video you will ever see: [VIDEO] Watch it. As a result you will improve your rational thinking forever. - Break. I suggest you next take a 30-minute break. During this time you can reflect on and assimilate the knowledge you have learned. - 2. An important social insight. This section requires you to understand section 1. Next, suppose that you are perfectly rational. We will introduce an extreme case, and you will

>You have two options, choose one: Your analysis is sensible. Where we should choose the most likely explanation, it might become sharper: - In case you're not familiar with it, one helpful tool is prior probability (Bayesian thinking). This video is short and accessible: [VIDEO] - There is a public intelligence budget in 2018 of $54.9 billion in the United States[1], as compared with the combined annual R&D expenditure of Apple, Google, Intel, and Microsoft at $53.2 billion[2]. This employs over 100,000 people[3]. - According to Snowden, they covertly use microphones.[4] He had reporters put their mobile phones in a fridge/microwave, since they could be turned on remotely. A sensible assumption is that you are unlikely to chance upon a covert surveillance mechanisms if one is installed. (For example, speakers could also be used as microphones.) Where a bug is present, I think assigning 1% to the probability of finding it is reasonable. In view of the above, after you find an undisclosed and apparently (but not physically) disabled microphone in a product, which is more likely? 1. One of the 100,000 people mentioned, using some of the $59,900,000,000 annual budget mentioned, put it there. They do this thousands of times per year, and you've just found one of them. However, the chances of your finding it are low. (1%). 2. It was put in there as part of normal product design but left unused. Perhaps it will be legitimately enabled in a future version. Perhaps Google will use it

Bayesian statistics at play here... Good explanation: [VIDEO] Imagine a world where there are 100 unvax and 9 million vaxed, now even if vaccines are 99% effective, you'd get 9M x 0.01 = 90k vax and sick.