Print

Please login or register.
1 Hour 1 Day 1 Week 1 Month Forever
Login with username, password and session length

[Dozebôm Lolumzalìs]

Not really. You can't quantify the difference in pain of pain A and pain B; all you can say is that one is worse than the other.

Why do you think that?

We could classify the set of all pains as a partially ordered set. That is, we have an operation <= with the following properties:

A<=A for all A in our set of pains.
If A<=B and B<=A then A=B for all A and B in our set of pains.
If A<=B and B<=C then A<=C for all A, B, and C in our set of pains.

For us to be able to take operations such as A-B, we would need a metric. As you said, such a metric would depend on the individual interpretation (such as it is, a subjective measure), and so such a set would not have a single metric but a set of all possible metrics such that the partial ordering is respected (that is, while everyone may agree that pain A is worse than pain B, the degree of which may scale from infinitesimal to infinite).

Ah, but you see, the same argument applies to your mathematics! Not everybody agrees on whether Pain A is worse than Pain B, so the partial ordering is subjective, just like my metric.

What you are claiming is specifically that for all possible metrics d for every epsilon>0 there exists an integer N such that n>N=>d(torture, dust_n)<epsilon.

I'm not quite getting you here. What does d(something) mean?

This is the definition of a limit of a sequence under an ambiguous metric, with a sequence {dust_n} which you claim converges to torture for all possible metrics.

I don't think that's what I claimed. I think that dust_n converges to infinity.

Now, I did not assume that dust simply increases by scaling, since our metric is undefined here- d(dust, 2*dust) can equal anything, we do not know. You claim it is 1, but that requires an explicit metric, which you said yourself is a subjective evaluation.

But... but you're saying that the second person to receive a dust speck matters less than the first! Why would you think that?!

So, what do we know about our lovely infinite dust sequence? Well, we know it is monotonic increasing, or else at some point more people suffering makes the suffering better, which makes no sense. We would like for it to converge- hence, it is bounded.

"I want it to be bounded, therefore it is bounded." What? Anyway, I don't think it converges. I think that an arbitrarily large group receiving dust specks feels an arbitrarily large amount of suffering.

Now it is a question of what it converges to. We know that the definition of convergence is as follows:

For every epsilon>0 there exists an N such that n>N=>d(a_n,a)<epsilon

We would like to claim that dust converges to torture under all metrics. We know that d(x,z)<=d(x,y)+d(y,z), since it is part of the definition of a metric. Hence, d(dust_n,torture)<=d(dust_n,dust_m)+d(dust_m,torture), for all m>n. Or, to rearrange, d(dust_n,torture)-d(dust_m,torture)<=d(dust_n,dust_m), for all m>n. So let's look at the sequence of d(dust_n,dust_m), with n fixed and m increasing.

We know that the sequence is monotonically increasing. We do not know if it is strictly increasing, and we do not know that it is bounded. If, under a metric, it is not strictly increasing (that is, there exists an m₁ and an m₂ such that d(dust_n,dust_m1)=d(dust_n,dust_m2), then we would consider all pains by dust equal to torture. If we consider that we do not know the number of dust-sufferers at any given point in time, and there is ambiguity in our n's and m's, then it is inherently monotonic across all evaluations (since n versus n+1 would be effectively the same because they are indistinguishable, but n versus n+100 would be distinguishable), and we would get this result.

The main issue arises if it is bounded- that is, there is a limit to what we can consider to be "suffering" by dust. There exists an M such that |dust_n|<=M for all n. This is not to say that we necessarily "stop caring" about additional pain- there is no explicit requirement that we have equality, only that we have less than or equality, so it is entirely possible that |dust_n|<M for all n. If M<torture, then d(dust_n,M)<=|torture|, which violates are triangle inequality. There are an infinite number of metrics where this can be true, even if in the one you originally worked with, your metric was Euclidean distance. Ergo, there are an infinite number of metrics where there does not exist a finite number of dust-sufferers such that torture would be a viable alternative.

And this is why armchair mathematics as a philosophical system is absolutely ridiculous. Especially when the people making the arguments don't actually have a proper understanding of the mathematics involved.

I can't really respond to this until I know what d(something, something else) means, but it feels like you're just pulling numbers and concepts out of thin air. Why the hell should infinite pain be bounded?!

[Sergarr]

That's true. I guess it's not really feasible to apply Bayes here.

That's why Bayes is so rarely used in practice - the results of applying Bayesian reasoning are heavily influenced by how you set the priors, and the knowledge of how to set the priors  properly to reflect information available to you is very much non-trivial.

[inteuniso]

tl;dr (that's a lie I read all of it) there are no easy answers

[inteuniso]

Can I agree with you that torture isn't the desired outcome and we would much rather spend some time making cloaks for people to protect against dust?

[Dozebôm Lolumzalìs]

d is the metric (or rather, the pair (d,M) is our metric space with d:MxM->R being our distance function). We're on a metric space, ergo we have a metric. Literally the definition of a metric space.

Ah, it was familiar enough that I thought I understood it well enough not to need to research it, but I didn't quite understand it enough to get your post. Or something. Sorry. d(x,y) is the distance or difference between x and y.

As for the partial ordering bit, I never said my approach wasn't relying on the metric being subjective. Literally my entire post was a matter of handling this using a general notion of a metric rather than an explicit assumption about what this metric may entail, as you did.

If I understand this correctly, you're trying to reduce the subjectivity of the pain-model, while recognizing that some subjectivity still remains. That is a good point - it is parallel to degrees of wrongness.

Why I insist that it must be bounded is because we are talking about the evaluation of pain, not the existence of pain- as you said, subjective measurements. Humans cannot comprehend the infinite. Hence, their comprehension of an infinite number of individuals suffering pain must not be infinite- ergo, bounded.

I'm not talking about how sad I will feel if 3^^^3 people receive dust. I'm talking about the suffering that will result from 3^^^3 people receiving dust. Only the latter is relevant.

[Dozebôm Lolumzalìs]

I'm not talking about how sad I will feel if 3^^^3 people receive dust. I'm talking about the suffering that will result from 3^^^3 people receiving dust. Only the latter is relevant.

So is it subjective, or objective? You keep saying it is subjective, and then keep assuming that there is some objective measurement here, so which is it? Does it change based on personal interpretation or doesn't it?

This is kind of confusing for me, but there's a difference between:

• The total reported individual utility
• The personal emotional impact of a decision
• The expected overall utility of a decision, as judged by yourself but considering all people

I think that the last one, taking into account the first one, is important. The middle one is only relevant insofar as it affects the expected overall utility.

I mean, I can't actually comprehend a million people, but I know that a million people's lives being saved is better than ten lives being saved. This is similar.

[martinuzz]

Urists. Utility is universally expressed in Urists

[ChairmanPoo]

What the hell is a LW

[ChairmanPoo]

Eh, even avoiding the silly dust debate, the website does give a cult-like vibe

[MetalSlimeHunt]

Every post in this thread before mine must, by necessity for the universe to exist, burn in Hell for all eternity.

However, I crash-read Unsong after Doz posted this and enjoyed it a good deal, so you should also read it. Just don't make any heuristic systems that are dedicated to reading Unsong unless they're safely contained in your brain. I certainly enjoyed it a great deal more than Worm, which I have made two separate herculean efforts to read and enjoy but both times failed.

[inteuniso]

Unsong is existential purpose, Worm is will-to-live. One is happy about living despite the circumstances,  while the other is living through the circumstances despite them (no, really, wildbow actually rolled dice to see if Leviathan [that dude is EVERYWHERE] would kill Taylor.)

P.S. Just played a riveting game of the grouchy ladybug with my sister. It features ladybugs collecting aphids (don't forget to say please) around -- you guessed it -- a whale.

[Dozebôm Lolumzalìs]

Eh, even avoiding the silly dust debate, the website does give a cult-like vibe

Well, I agree that there is a somewhat disturbing amount of Yudkowsky-worshipping.

Every post in this thread before mine must, by necessity for the universe to exist, burn in Hell for all eternity.

However, I crash-read Unsong after Doz posted this and enjoyed it a good deal, so you should also read it. Just don't make any heuristic systems that are dedicated to reading Unsong unless they're safely contained in your brain. I certainly enjoyed it a great deal more than Worm, which I have made two separate herculean efforts to read and enjoy but both times failed.

This. Scott wrote this by putting his connection-making module into overdrive and turning off his coincidence-detector module. In real life, there really are coincidences. If you aren't careful, well, this is how people become New Age Mystics who speak about the connectedness of everything. Also, taking LSD.