This comment contains spoilers for Permutation City.

I agree that Peer's strategy, as described in Permutation City, is a very suboptimal strategy for maximizing fun, given both finite resources and finite time.

But Peer had an infinite amount of processing time, and (spoiler!) until the final chapter, believed that he had an infinite amount of computing resources as well. (In the final chapter, Peer found that he only had a finite, but large amount of computing resources - equivalent to a planet of computronium? a solar system? a galaxy? the story didn't say.)

Also, Peer had one strategically relevant belief which you may have overlooked: Peer believes that an experience has literally no value if someone has had exactly the same experience before. i.e. if the digital representation of a mind ever enters exactly the same state more than once.

(I personally disagree with this. A pleasure is still real, and still has positive value, the second time you experience it. A pain is still real, and still has negative value, the second time you experience it.)

Given this belief, Peer's strategy is the optimal: Randomly alternating between any experience that could even remotely be considered fun.

Given infinite time, this will eventually cover the entire volume of Fun Space. Or rather, all the parts of fun space that can be accessed by a mind running on the computing resources available to Peer.

If a mind really does have access to infinite computing resources, then that mind's Fun Space is truly infinite. (trivial proof, and a degenerate example: spend a year contemplating the number 1, then spend a year contemplating the number 2, then 3, then 4...)

All Peer cares about is that as much of Fun Space is covered as possible, and this strategy achieves that.

(another spoiler) In the final chapter, Peer decides that he doesn't even care who experiences the pleasure, and splits himself into a whole Solipsist Nation of minds that are each happy for their own wildly arbitrary reasons.

Other than a couple of major differences, Peer's philosophy matches mine quite well. Well enough for me to name myself after him. (After all, if my life is at all worthwhile, then Peer must have experienced the good parts of it at some point during his random explorations of Fun Space.)

Comment author:mcdowella
11 May 2010 07:16:04PM
0 points
[-]

If there are hidden variables and random noise, you can still be learning after repeating an experience an arbitrary number of times. Consider the probability of observed x calculated after reestimating the distribution on hidden variable t. We calculate this by integrating the probability of x given t, p(x|t), over all possible t weighted by the probability of t given x, p(t|x). We have

Integral p(x|t)p(t|x) dt = Integral p(x|t)p(x|t)p(t)/p(x) dt =
Expectation(p(x|t)^2)/p(x) =
Expectation(p(x|t))^2/p(x) + Variance(p(x|t))/p(x)
≥ Expectation(p(x|t))^2/p(x) = p(x).
Here the expectation is over the prior distribution of t. Note that we have equality iff the variance of P(x|t), according to our prior distribution on t, is zero, which is to say that the probability of x given t is constant almost everywhere the prior distribution on t is positive. If this variance is not zero, then p(x) in this calculation changes (increases) which means that we are revising our distribution on t, and changing our minds.

Right, but even with a digital brain, if you only have a finite number of bits to store the floating point number representing the probabilities, eventually you will run out of bits. What you just described gets you a whole lot of new experience, but not a literally infinite amount.

## Comments (65)

OldSPOILER WARNING!

This comment contains spoilers for Permutation City.

I agree that Peer's strategy, as described in Permutation City, is a very suboptimal strategy for maximizing fun, given both finite resources and finite time.

But Peer had an infinite amount of processing time, and (spoiler!) until the final chapter, believed that he had an infinite amount of computing resources as well. (In the final chapter, Peer found that he only had a finite, but large amount of computing resources - equivalent to a planet of computronium? a solar system? a galaxy? the story didn't say.)

Also, Peer had one strategically relevant belief which you may have overlooked: Peer believes that an experience has literally no value if someone has had exactly the same experience before. i.e. if the digital representation of a mind ever enters exactly the same state more than once.

(I personally disagree with this. A pleasure is still real, and still has positive value, the second time you experience it. A pain is still real, and still has negative value, the second time you experience it.)

Given this belief, Peer's strategy is the optimal: Randomly alternating between any experience that could even remotely be considered fun.

Given infinite time, this will eventually cover the entire volume of Fun Space. Or rather, all the parts of fun space that can be accessed by a mind running on the computing resources available to Peer.

If a mind really does have access to infinite computing resources, then that mind's Fun Space is truly infinite. (trivial proof, and a degenerate example: spend a year contemplating the number 1, then spend a year contemplating the number 2, then 3, then 4...)

All Peer cares about is that as much of Fun Space is covered as possible, and this strategy achieves that.

(another spoiler) In the final chapter, Peer decides that he doesn't even care who experiences the pleasure, and splits himself into a whole Solipsist Nation of minds that are each happy for their own wildly arbitrary reasons.

Other than a couple of major differences, Peer's philosophy matches mine quite well. Well enough for me to name myself after him. (After all, if my life is at all worthwhile, then Peer must have experienced the good parts of it at some point during his random explorations of Fun Space.)

related plugs:

a wiki page I wrote examining Peer's philosophy, and my own philosophy, in more detail: http://transhumanistwiki.com/wiki/Peer_Infinity/Quotes_from_Permutation_City

a dream I had, where I was Peer, that seemed almost good enough to write a short story out of, but not surprisingly ended up kinda lame: http://transhumanistwiki.com/wiki/Peer_Infinity/Short_Story_1

If there are hidden variables and random noise, you can still be learning after repeating an experience an arbitrary number of times. Consider the probability of observed x calculated after reestimating the distribution on hidden variable t. We calculate this by integrating the probability of x given t, p(x|t), over all possible t weighted by the probability of t given x, p(t|x). We have

Integral p(x|t)p(t|x) dt = Integral p(x|t)p(x|t)p(t)/p(x) dt = Expectation(p(x|t)^2)/p(x) = Expectation(p(x|t))^2/p(x) + Variance(p(x|t))/p(x) ≥ Expectation(p(x|t))^2/p(x) = p(x). Here the expectation is over the prior distribution of t. Note that we have equality iff the variance of P(x|t), according to our prior distribution on t, is zero, which is to say that the probability of x given t is constant almost everywhere the prior distribution on t is positive. If this variance is not zero, then p(x) in this calculation changes (increases) which means that we are revising our distribution on t, and changing our minds.

Right, but even with a digital brain, if you only have a finite number of bits to store the floating point number representing the probabilities, eventually you will run out of bits. What you just described gets you a whole lot of new experience, but not a literally infinite amount.