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.
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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:
Watch it. Suppose that you take an hour and learn this. You have just improved your rational thinking forever.
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Break. Please now take a 30-minute break. During this time you can reflect and assimilate the knowledge you have learned.
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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, weeks, or years of flipping, you will come to me with the same conclusion: there is a 0% chance that the coin is fair and 100% chance that the coin is weighted. This includes your running every test for randomness, flipping it millions of times and analyzing the result, anything you want.
So let's look at what happened. You have been moved from being able to quickly decide whether a coin is fair, to being completely unable to accept that the coin is fair. No matter how much evidence you can collect, you can only conclude with 100% certainty that the coin is unfair.
The only thing that changed is the understanding of the population it was drawn from.
Why is this a problem? For the simple reason that the coin labelled 0.5 exists.
If you reflect on the plight of coin 0.5 you forever understand why it is very wrong to talk about the bag from which it was drawn or how.
Appreciate you trying to share some insight. But from the hype, I was expecting some kind of world changing revelation. But basically you're just explaining the basics of bayesian statistics?
A lot of people already know this stuff. It's part of an intro course in probability/stats that you'd take while doing a CS degree, or a course about experiments for other science degrees.
In summary this comment should change your thinking about all subjects, forever.
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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:
https://www.youtube.com/watch?v=BrK7X_XlGB8
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, weeks, or years of flipping, you will come to me with the same conclusion: there is a 0% chance that the coin is fair and 100% chance that the coin is weighted. This includes your running every test for randomness, flipping it millions of times and analyzing the result, anything you want.
So let's look at what happened. You have been moved from being able to quickly decide whether a coin is fair, to being completely unable to accept that the coin is fair. No matter how much evidence you can collect, you can only conclude with 100% certainty that the coin is unfair.
The only thing that changed is the understanding of the population it was drawn from.
Why is this a problem? For the simple reason that the coin labelled 0.5 exists.
If you reflect on the plight of coin 0.5 you forever understand why it is very wrong to talk about the bag from which it was drawn or how.