I think the delivery could be greatly improved by introducing symbols and clarifying the logical environment where the derivation is happening. Allow me to do this, without using LateX I’ll assume /\ stands for logical conjunction and ~ for logical negation.
Proposition symbols
Our universe is normal: N We exist: E Our universe is magical: M
Logical environment
[1] The universe is either normal or magical: M = ~N [2] The magical universe is strongly biased to support our existence: P(E|M) = 1
I think the delivery could be greatly improved by introducing symbols and clarifying the logical environment where the derivation is happening. Allow me to do this, without using LateX I’ll assume /\ stands for logical conjunction and ~ for logical negation.
Proposition symbols
Our universe is normal: N
We exist: E
Our universe is magical: M
Logical environment
[1] The universe is either normal or magical: M = ~N
[2] The magical universe is strongly biased to support our existence: P(E|M) = 1
Derivation
By Bayes theorem:
P(N|E) = P(E|N) P(N) / P(E) <-->
P(N|E) = k P(E) /\ k = P(E|N)/P(E)
By partition of unity and [1]
P(E) = P(E|N)P(N) + P(E|M)P(M) ⇒ (by fact [2])
P(E|N)P(N) + P(~N) ⇒ (by law of probability)
P(E|N)P(N) + 1 - P(N)
If P(E|N) → 0 with P(N) fixed (say c), we get
P(E) → 0/c + 1 - c = 1 - c
From this
P(N|E) = k P(E) → k (1-c) /\ k → 0 / (1-c)
so that
P(N|E) → 0
I believe you can use latex in less wrong. It says so under “show help”. Let me try… $e^{i\pi}+1=0$
EDIT: Forget it. I just reread the help text. You have to use an external website to render the equation into an image...