Comments by "Wiczus" (@wiczus6102) on "3Blue1Brown" channel.

  1. I actually did that 2 years back. Let's say you have 6 plausible mechanism and no tests yet. Since we have no tests, the probability of every mechanism is equal and the sum of the product of the mechanism result and mechanism probability will be as follows: 0%/6+20%/6+40%/6+ ... =50%. if you have 1 positive test. Now every mechanism will have a different likelihood, namely the square of its positive rate, divided by the sum of these squares (hence all probabilities should add up to one). if instead of quantizing our mechanisms by 6, we can do infinity. Which would mean that instead of a Riemann Summ we use an Integral. Funnily enough the x to any power will always be 1 (since our integral ends at 1), so the only important thing in these integrals will be the resulting divisor. If you play things through a few times you'll see a very elegant property that the empirical probability equals (1+p)/(2+t) where p are the positive results and t are the total trials. So if I flip the coin 8 times and get heads 5 times then there is 60% chance to get heads again. if I flip 8 times and get heads 8 times, the chance is then 90%. Dope if you ask me.
    1
  2. Quaternions are evil I KNEW IT!
    1