Future Filters [draft]

post by snarles · 2011-05-16T12:42:02.466Z · LW · GW · Legacy · 12 comments

Contents

  "Dr. Evil's Machine"
  Future Filter Model I
None
12 comments

See Katja Grace's article: http://hplusmagazine.com/2011/05/13/anthropic-principles-and-existential-risks/

There are two comments I want to make about the above article.

First: the resolution to God's Coin Toss seems fairly straightforward.  I argue that the following scenario is formally equivalent to 'God's Coin Toss'

"Dr. Evil's Machine"

Dr. Evil has a factory for making clones.  The factory has 1000 separate identical rooms.  Every day, a clone is produced in each room at 9:00 AM.  However, there is a 50% chance of malfunction, in which case 900 of the clones suddenly die by 9:30 AM, the remaining 100 are healthy and notice nothing.  At the end of the day Dr. Evil ships off all the clones which were produced and restores the rooms to their original state.

You wake up at 10:00 AM and learn that you are one of the clones produced in Dr. Evil's factory, and your learn all of the information above.  What is the probability that that the machine malfunctioned today?

In the second reformulation, the answer is clear from Bayes' rule.  Let P(M) be the probability of malfunction, and P(S) be the probability that you are alive at 10:00 AM.  From the information given, we have

P(M) = 1/2

P(~M) = 1/2

P(S|M) = 1/10

P(S|~M) = 1

Therefore,

P(S) = P(S|M) P(M) + P(S|~M)P(~M) = (1/2)(1/10) + (1/2)(1) = 11/20

P(M|S) = P(S|M) P(M)/P(S) = (1/20)/(11/20) = 1/11

That is, given the information you have, you should conclude that the probability that the machine malfunctioned is 1/11.

 

 

The second comment concerns Grace's reasoning about future filters.

I will assume that the following model is a fair representation of Grace's argument about relative probabilities for the first and second filters.

Future Filter Model I

Given: universe with N planets, T time steps. Intelligent life can arise on a planet at most once.

At each time step:

1. each surviving intelligent species becomes permanently visible to all other species with probability c (the third filter probability)
2. each surviving intelligent species self-destructs with probability b (the second filter probability)
3. each virgin planet produces an intelligent species with probability a (the first filter probability)

Suppose N=one billion, T=one million.  Put uniform priors on a, b, c, and the current time t (an integer between 1 and T).

Your species appeared on your planet at unknown time step t_0.  The current time t is also unknown.  At the current time, no species has become permanently visible in the universe.  Conditioned on this information, what is the posterior density for first filter parameter a?

 

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