"(2) any posthuman civilization is extremely unlikely to run a significant number of simulations of their evolutionary history (or variations thereof)"
Should this have said "likely" instead of "unlikely"?
There are many non-simulation-hypothesis explanations for a sequence of coin tosses with many heads (or tails) in a row. ("The coin is a trick coin" being one of the simpler ones.)
P(H | S) > P(H) _is not enough_. You must also have P(H | S) > P(H | M) for _all_ other Mundane hypotheses.
For an explicit example.
I have a prior of S=10^-6, and M=10^-4.
(In the below I'm using lowercase X to mean ~X. So e.g. Sm means 'Simulation and not Mundane')
I know the following probabilities:
P(H | SM)=4/5
P(H | sM)=4/5
P(H | Sm) = 3/4
P(H | sm) = 1/2
I flip a thousand heads in a row. What is my resulting posterior?
1000 heads:
SM: 1e-06
Sm: 9.359075874475835e-31
sM: 0.999999
sm: 7.585312510276936e-201
S_: 1e-06
_M: 1.0
...oh. The dominant hypothesis is the mundane explanation.
"(2) any posthuman civilization is extremely unlikely to run a significant number of simulations of their evolutionary history (or variations thereof)"
Should this have said "likely" instead of "unlikely"?
There are many non-simulation-hypothesis explanations for a sequence of coin tosses with many heads (or tails) in a row. ("The coin is a trick coin" being one of the simpler ones.)
P(H | S) > P(H) _is not enough_. You must also have P(H | S) > P(H | M) for _all_ other Mundane hypotheses.
For an explicit example.
I have a prior of S=10^-6, and M=10^-4.
(In the below I'm using lowercase X to mean ~X. So e.g. Sm means 'Simulation and not Mundane')
I know the following probabilities:
P(H | SM)=4/5
P(H | sM)=4/5
P(H | Sm) = 3/4
P(H | sm) = 1/2
I flip a thousand heads in a row. What is my resulting posterior?
1000 heads:
SM: 1e-06
Sm: 9.359075874475835e-31
sM: 0.999999
sm: 7.585312510276936e-201
S_: 1e-06
_M: 1.0
...oh. The dominant hypothesis is the mundane explanation.