**From:** Matt Mahoney (*matmahoney@yahoo.com*)

**Date:** Mon Mar 17 2008 - 16:31:13 MDT

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--- John K Clark <johnkclark@fastmail.fm> wrote:

*> On Sun, 16 Mar 2008 "Matt Mahoney"
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*> <matmahoney@yahoo.com> said:
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*>
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*> > N is the number of trials, not the number of agents.
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*>
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*> Then I’m not very interested in N, I don’t really care how often an
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*> identical being performs an identical experiment and gets an identical
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*> result.
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*>
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*> > A robot zombie with no qualia or consciousness
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*> > [blah blah] then the robot is killed
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*>
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*> That does not compute. Perhaps you mean quantum erasure is used to wipe
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*> the robot’s memory clean, but then you can’t say in your thought
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*> experiment that the robot saw this and that because even the universe
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*> doesn’t know what the robot saw.
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Consider a robot whose entire mental state is 2 counters: n_heads and n_tails,

both initialized to 0. The only observation that the robot can make is that

of a coin flip, in which case one of the two counters is incremented depending

on the outcome. The robot's output is a prediction p(heads) =

(n_heads+1)/(n_heads+n_tails+2), i.e. Laplace's derivation of the maximum

entropy prediction of the next coin flip assuming an a-priori bias uniformly

distributed between 0 and 1.

1. A robot flips a coin with unknown bias 100 times and counts 99 heads. What

is its prediction p(heads) of the next coin flip?

2. A robot flips a coin with unknown bias 100 times. If it is heads, it and

the coin are copied 100 times. All coins are actually fair (p(heads) = 0.5).

What is its expected estimate of p(heads) of the next flip for a robot

randomly chosen from the resulting ~ 50^100 robots?

3. 50^100 robots start with 1 coin each with unknown bias (but actually fair).

Whenever a coin comes up tails the robot is killed with probability 0.99.

After 100 flips, only one robot remains. What is its expected estimate of

p(heads)?

4. Start with 50^100 robots. Divide them into groups of 100 robots with 1

coin each. Flip the coin. If it comes up tails, then hold a lottery and kill

99 of the robots in that group. Repeat 100 times, after which one robot is

left. What is its expected estimate of p(heads)?

5. One robot flips a coin with unknown bias (but actually fair) until n_heads

+ n_tails = 100. Whenever a coin comes up tails, both counters are reset to 0

with probability 0.99. What is its expected estimate of p(heads) when

finished (about 50^100 coin flips later)?

Is it possible for a robot to distinguish between these 5 cases? What about a

human?

-- Matt Mahoney, matmahoney@yahoo.com

**Next message:**Heartland: "Re: Atoms"**Previous message:**John K Clark: "Re: Atoms"**In reply to:**John K Clark: "Re: Is a Person One or Many?"**Next in thread:**Lee Corbin: "Re: Is a Person One or Many?"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

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