I was asserting that anti-utilons do not increase linearly with pain but logarithmically: the scale of measurement of difference between a dust-speck in the eye, a splinter in your thumb, a stubbed toe, a broken toe, a stomache-ache, and torture is one such that it requires multiples of each ‘smaller’ event to accumulate a single equivalence of anti-utilons for the next-higher-”unit” (I.e.; orders of magnitude; a logarithmic scale.)
This is what I was saying when I was stating that the logarithmically additive was referring to the quantitative nature of the various suffering events in terms of their scale; such that a dust-speck would be equivalent to an infinitessimal number of tortures.
I was asserting that anti-utilons do not increase linearly with pain but logarithmically
Whether the increase is linear or logarithmic does not change anything—in both cases there could be a number N large enough that the disutility of N dust specks is larger than that of one torture. That is why Eliezer picked a mindfuckingly large number like 3^^^3 - to sidestep nitpicking over the exact shape of the utility function.
What would make a difference was if the disutility was a bounded function, hence Zack’s suggestion of the logistic function.
(Many people have been trying to tell you this in this thread, including TimS who seems to agree with your conclusions. You may want to update.)
Whether the increase is linear or logarithmic does not change anything—in both cases there could be a number N large enough that the disutility of N dust specks is larger than that of one torture.
This does not follow. One torture could possess effectively infinite disutility, potentially. But that’s irrelevant, as I was simply expressing the notion of logarithmic scaling of pain. Especially since we’re dealing with a nearly-negligible kind of pain on the lower end. A “mind-fucking large number” of nearly-0-value instances of pain would not necessarily find its way back up the scale to the “mind-fucking large number” of anti-utilons induced by the torture-for-fifty-years.
An infinitessimal amount of pain, multiplied by a non-infinite “mind-fuckingly-large number”, would not be guaranteed to exceed “1″, let alone achieve its own “mind-fuckingly large number” all over again.
That is the entire point of noting the logarithmic nature of pain—I was pointing out that the disutility experienced by the torture victimitself, according to that metric, was also a “mind-fuckingly large number”. I should have expected this to be obvious from the fact that logarithmic functions are unbounded.
That is why Eliezer picked a mindfuckingly large number like 3^^^3 - to sidestep nitpicking over the exact shape of the utility function.
And if disutility added linearly that would be a successful achievement on his part.
What would make a difference was if the disutility was a bounded function, hence Zack’s suggestion of the logistic function.
Zack’s suggestion was not appropriate to describing my position even slightly. I strongly disagree with the logistic function. My assertion is not that there is an upper bound to how much suffering can be received by dust-specking, but rather that there is no upper bound on the suffering of torture.
But that still only considers the primary consequences.
(Many people have been trying to tell you this in this thread, including TimS who seems to agree with your conclusions. You may want to update.)
Many people have been trying to tell me many things. Mostly that my premise is invalid in its face—but not a single one of them has provided anything resembling a non-illogical reason for their dismissal of my position.
I only update my beliefs when provided with legitimate arguments or with evidence. Nothing to this point has passed the muster of being non-contradictory.
There is further reason for my maintaining this position, however: even when I specifically stipulated the linear-additive—that is, when I stated that the direct suffering of the torture victim was less than that of the dust-speckings—by introducing the secondary consequences and their impact I STILL was left choosing the dust-speckings as the ‘lesser of two evils’.
And that, in fact, was the real “core” of my argument: that we must not, if we are to consider all the consequences, limit ourselves solely to the immediate consequences when deciding which of the two sets of outcomes has the greater disutility. I further object to the notion that “suffering” vs. “pleasure” is the sole relevant metric for utility. And based on that standard, the additional forms of disutility comparing between the dust-speckings as opposed to the torture strongly weigh against the torture being conducted; the dust-speckings, while nuisancesome, simply do not register at all as a result on those other metrics.
An infinitessimal amount of pain, multiplied by a non-infinite “mind-fuckingly-large number”, would not be guaranteed to exceed “1″, let alone achieve its own “mind-fuckingly large number” all over again.
That is the entire point of noting the logarithmic nature of pain
The term “logarithmic” does not capture that meaning. Your concept of “infinitesimal” such that you can never get to 1 by multiplying it by a number no matter how large is not a part of “standard” mathematics; you can get something like that with transfinite numbers and some other weirdness, but none of those are particularly related to logarithms and orders of magnitude.
Your whole use of “really small numbers” and “really large numbers” in this thread (notably in the discussion with paper-machine) is inconsistent with the ways those concept are usually used in maths.
Your concept of “infinitesimal” such that you can never get to 1 by multiplying it by a number no matter how large is not a part of “standard” mathematics; [and is not] particularly related to logarithms and orders of magnitude.
I’m pretty sure you meant to say finite number, here.
Are we talking about the same concept of orders of magnitude? (It might help to consider the notion that both torture and dust-speckings are distant from the same approximate “zero-magnitude” event which is the 1 anti-utilon.)
Your whole use of “really small numbers” and “really large numbers” in this thread (notably in the discussion with paper-machine) is inconsistent with the ways those concept are usually used in maths.
For any value of (finite) “really large number” n there is an equivalent “really small number” that can be expressed as 1/n. The notion of the logarithmic quantification of pain bears relevance to our discussion because of the fact that we have declared the dust-specking the “smallest possible unit of suffering”. This essentially renders it nearly infinitessimal, and as such subject to the nature of infinitessimal values which are essentially the exact inverse of “mind-fuckingly large” numbers.
It is furthermore worth noting that there is, since we’re on the topic of numbers and quantification, a sort of verbal slight-of-hand going on here: the ‘priming’ effect of associating 3^^^3 ‘dust-speckings’ with a “mere” 50 ‘years of torture’. I have repeatedly been asked, “If 3^^^3 isn’t enough, how about 3^^^^3 or 3^^^^^3?”—or questions to that effect. When I note that this is priveleging the hypothesis and attempt to invert it by asking what number of years of torture would be sufficient to overwhelm 3^^^3 dust-speckings in terms of disutility, a universal response is given, which I will quote exactly:
″ ”
This, I feel, is very telling, in terms of my current point regarding that “slight-of-hand”. Unlike units of measurement are being used here. I’ll demonstrate by switching from measurement of pain to measurement of distance (note that I am NOT stating these are equivalent values; I’m demonstrating the principle I reference, here, and do NOT assert it to be a correct analogy of the torture-vs-specking answers.)
“Which is the longer distance? 50 lightcone-diameters or 3^^^3 nanometers?”
Are you saying that 3^^^3 is not sufficiently large? Then consider 3^^^^3.
Whatever epsilon you assign to dust specks, there’s still a yet larger number such that this number of dust specks is worse than torture. Everything else is just accounting that we can’t feasibly calculate anyway.
there’s still a yet larger number such that this number of dust specks is worse than torture.
He (and I) deny this statement is true. There is no sum of sufferings that add up to torture. It is analogous to the fact that the sum of a countably infinite number of countably infinite sets is not as large as the set of real numbers.
I don’t know why Logos insists that logarithmic captures this idea.
Are you saying that 3^^^3 is not sufficiently large? Then consider 3^^^^3.
I’m saying that dust-specks are practically infinitessimal comparatively, and that’s in direct comparison. Ergo; a nearly or potentially truly infinite number of dust-speckings would be required to equal one torturing for fifty years, just in terms of direct suffering.
If we were to include the fact that such a torturing would result in the total personality destruction of several reconstructed psyches over the period of that 50 years, I don’t necessarily know that such a torture couldn’t rightly be called effectively infinite suffering for a single individual.
there’s still a yet larger number such that this number of dust specks is worse than torture.
In terms solely of the immediate and direct suffering, certainly. In terms of that suffering and the other consequences—individual self-determination, for example; or social productivity costs, etc., even an infinite number of dust-speckings begins to become insufficient to the task of equalling a single fifty-year torture. How much those additional elements ‘count’ as compared to the suffering alone is a question which is not immediately available to simple calculation; we have no means of converting the various forms of utility into a single comparable unit.
Everything else is just accounting that we can’t feasibly calculate anyway.
We’re already comparing two unimaginably large numbers against one another. For example; the adjustment of 3^^^3 to 3^^^^3 -- how would you decide on the torture vs. dust-speckings if we did the same to torture? What number of years of torture would need to “exceed” 3^^^3 dust-speckings? 51? 500? 50^50?
I’m saying that dust-specks are practically infinitessimal comparatively, and that’s in direct comparison. Ergo; a nearly or potentially truly infinite number of dust-speckings would be required to equal one torturing for fifty years, just in terms of direct suffering.
I don’t understand what you mean by “practically infinitesimal”. Are you saying the negative utility incurred by a dust speck is zero? Also, what do you mean by “nearly… infinite”? Either a quantity is infinite or finite.
there’s still a yet larger number such that this number of dust specks is worse than torture.
In terms solely of the immediate and direct suffering, certainly. In terms of that suffering and the other consequences—individual self-determination, for example; or social productivity costs, etc., even an infinite number of dust-speckings begins to become insufficient to the task of equalling a single fifty-year torture.
You’ve completely lost me. If X is the negative utility of N dust specks, and Y the negative utility of fifty years of torture, then the first sentence implies that X > Y. Then the second sentence defines a second kind of negative utility, Z, due to other consequences. It goes on to imply that X + Z < Y. All quantities involved are positive (i.e., the units involved are antiutilons), so there’s a contradiction somewhere, unless I’ve misread something.
Are you saying the negative utility incurred by a dust speck is zero?
Nearly zero. That’s part of the hypothesis: that it be the smallest possible unit of suffering. If the logarithmic scale of quantification for forms of suffering holds true, then forms of suffering at the maximal end of the scale would be practically infinite comparably.
Either a quantity is infinite or finite.
Correct, but a number that approaches infinity is not itself necessarily infinite; merely very large. 3^^^3 for example.
You’ve completely lost me. If X is the negative utility of N dust specks, and Y the negative utility of fifty years of torture, then the first sentence implies that X > Y.
The negative utility yet considered. Also, keep in mind that we’re at this point priveleging the hypothesis of torture being chosen: we are allowing the number of speckings to be adjusted but leaving the torture fixed. (While it doesn’t really change anything in the discussion, it bears noting for considerations of the final conclusion.)
Then the second sentence defines a second kind of negative utility, Z, due to other consequences. It goes on to imply that X + Z < Y.
No, it implies that Z(X) + X < Z(Y) + Y.
so there’s a contradiction somewhere, unless I’ve misread something.
My argument rests on the notion that the Z-function value of X is effectively zero, and my further assertion that the Z-function value of Y is such that it overwhelms, when added to Y, the value of X.
Nearly zero. That’s part of the hypothesis: that it be the smallest possible unit of suffering. If the logarithmic scale of quantification for forms of suffering holds true, then forms of suffering at the maximal end of the scale would be practically infinite comparably.
As long as it’s nonzero, then as I stated before, there exists some N such that N dust specks have greater negative utility than fifty years of torture. 3^^^3 and 50 are just proxies for whatever the true numbers are.
Correct, but a number that approaches infinity is not itself necessarily infinite; merely very large. 3^^^3 for example.
This is a category error. 3^^^3 does not approach infinity. It’s a fixed number, it’s not going anywhere.
The rest of your comment clarifies the offending inequality.
This is a category error. 3^^^3 does not approach infinity. It’s a fixed number, it’s not going anywhere.
Can you intelligibly grasp it? Or is it “unimaginably large”? For purposes of human consideration, I do not feel it necessary to differentiate between a truly infinite number and one that is “pseudo-infinite” (where by pseudo-infinite I mean ‘beyond our comprehension’). I admit this is an imperfect hack.
For purposes of human consideration, I do not feel it necessary to differentiate between a truly infinite number and one that is “pseudo-infinite” (where by pseudo-infinite I mean ‘beyond our comprehension’).
That way lies the madness of pre-Weierstrass analysis.
Why do you concede this? All the suffering you list after this is just as direct.
None of the things I listed afterwards were “suffering” at all. “Suffering” is not “the absence of pleasure”—it is “the antithesis of pleasure”. “Utility” is not synonymous with “enjoyment” or “pleasure”. (Also, please do recall that hedonistic utilitarianism is far from the only form of utilitarianism in existence.)
Saying that torture-without-most-of-the-things-that-make-it-wrong is not so bad might be true,
What.. ? Just… who are you reading in these threads? I am finding myself more and more convinced that you are responding to the writings of someone other than me. You seem to have a persistent habit of introducing notions to our discussions—in a manner as though you were responding to something I had written—that just bear in no way whatsoever to anything I have written or implied by my writings.
I’ll concede that suffering might not be the right word. But everything later in that sentence are essential parts of why torture is wrong. If torture didn’t imply those things (i.e. wasn’t torture), then it would be the right choice compared to dust-specks.
But everything later in that sentence are essential parts of why torture is wrong.
Of course those things are essential parts of why torture is wrong. They would have to be, for my argument to be valid.
If torture didn’t imply those things (i.e. wasn’t torture), then it would be the right choice compared to dust-specks.
Are you simply unaware that the conventional wisdom here on Less Wrong is that the proper answer is to choose to torture one person for fifty years rather than dust-speck 3^^^3 people?
Are you simply unaware that the conventional wisdom here on Less Wrong is that the proper answer is to choose to torture one person for fifty years rather than dust-speck 3^^^3 people?
Yes, that is the conventional wisdom. I agree with you that it is wrong, because the features of torture you describe are why the badness quality of torture cannot be achieved in the sum of huge amounts of a lesser badness.
You seem to think that someone could think dust-specks was the right answer without taking into account those essential parts of torture. Otherwise, why do you think that the secondary effects of allowing torture were not considered in the original debate?
As you noted in your post, people in the original thread objected to choosing torture for reasons that basically reduce to the “non-additive badness” position. For me, that position is motivated by the badness of torture you described in your post. So I read the other commenters charitably to include consideration of the sheer wrongness of torture. I simply can’t see why one would pick dust-specks without that consideration.
Now you say I’m reading them too charitably. I’ve been told before that I do that too much. I’m not sure I agree.
I see. I’ll rephrase.
I was asserting that anti-utilons do not increase linearly with pain but logarithmically: the scale of measurement of difference between a dust-speck in the eye, a splinter in your thumb, a stubbed toe, a broken toe, a stomache-ache, and torture is one such that it requires multiples of each ‘smaller’ event to accumulate a single equivalence of anti-utilons for the next-higher-”unit” (I.e.; orders of magnitude; a logarithmic scale.)
This is what I was saying when I was stating that the logarithmically additive was referring to the quantitative nature of the various suffering events in terms of their scale; such that a dust-speck would be equivalent to an infinitessimal number of tortures.
Whether the increase is linear or logarithmic does not change anything—in both cases there could be a number N large enough that the disutility of N dust specks is larger than that of one torture. That is why Eliezer picked a mindfuckingly large number like 3^^^3 - to sidestep nitpicking over the exact shape of the utility function.
What would make a difference was if the disutility was a bounded function, hence Zack’s suggestion of the logistic function.
(Many people have been trying to tell you this in this thread, including TimS who seems to agree with your conclusions. You may want to update.)
This does not follow. One torture could possess effectively infinite disutility, potentially. But that’s irrelevant, as I was simply expressing the notion of logarithmic scaling of pain. Especially since we’re dealing with a nearly-negligible kind of pain on the lower end. A “mind-fucking large number” of nearly-0-value instances of pain would not necessarily find its way back up the scale to the “mind-fucking large number” of anti-utilons induced by the torture-for-fifty-years.
An infinitessimal amount of pain, multiplied by a non-infinite “mind-fuckingly-large number”, would not be guaranteed to exceed “1″, let alone achieve its own “mind-fuckingly large number” all over again.
That is the entire point of noting the logarithmic nature of pain—I was pointing out that the disutility experienced by the torture victim itself, according to that metric, was also a “mind-fuckingly large number”. I should have expected this to be obvious from the fact that logarithmic functions are unbounded.
And if disutility added linearly that would be a successful achievement on his part.
Zack’s suggestion was not appropriate to describing my position even slightly. I strongly disagree with the logistic function. My assertion is not that there is an upper bound to how much suffering can be received by dust-specking, but rather that there is no upper bound on the suffering of torture.
But that still only considers the primary consequences.
Many people have been trying to tell me many things. Mostly that my premise is invalid in its face—but not a single one of them has provided anything resembling a non-illogical reason for their dismissal of my position.
I only update my beliefs when provided with legitimate arguments or with evidence. Nothing to this point has passed the muster of being non-contradictory.
There is further reason for my maintaining this position, however: even when I specifically stipulated the linear-additive—that is, when I stated that the direct suffering of the torture victim was less than that of the dust-speckings—by introducing the secondary consequences and their impact I STILL was left choosing the dust-speckings as the ‘lesser of two evils’.
And that, in fact, was the real “core” of my argument: that we must not, if we are to consider all the consequences, limit ourselves solely to the immediate consequences when deciding which of the two sets of outcomes has the greater disutility. I further object to the notion that “suffering” vs. “pleasure” is the sole relevant metric for utility. And based on that standard, the additional forms of disutility comparing between the dust-speckings as opposed to the torture strongly weigh against the torture being conducted; the dust-speckings, while nuisancesome, simply do not register at all as a result on those other metrics.
The term “logarithmic” does not capture that meaning. Your concept of “infinitesimal” such that you can never get to 1 by multiplying it by a number no matter how large is not a part of “standard” mathematics; you can get something like that with transfinite numbers and some other weirdness, but none of those are particularly related to logarithms and orders of magnitude.
Your whole use of “really small numbers” and “really large numbers” in this thread (notably in the discussion with paper-machine) is inconsistent with the ways those concept are usually used in maths.
I’m pretty sure you meant to say finite number, here.
Are we talking about the same concept of orders of magnitude? (It might help to consider the notion that both torture and dust-speckings are distant from the same approximate “zero-magnitude” event which is the 1 anti-utilon.)
For any value of (finite) “really large number” n there is an equivalent “really small number” that can be expressed as 1/n. The notion of the logarithmic quantification of pain bears relevance to our discussion because of the fact that we have declared the dust-specking the “smallest possible unit of suffering”. This essentially renders it nearly infinitessimal, and as such subject to the nature of infinitessimal values which are essentially the exact inverse of “mind-fuckingly large” numbers.
It is furthermore worth noting that there is, since we’re on the topic of numbers and quantification, a sort of verbal slight-of-hand going on here: the ‘priming’ effect of associating 3^^^3 ‘dust-speckings’ with a “mere” 50 ‘years of torture’. I have repeatedly been asked, “If 3^^^3 isn’t enough, how about 3^^^^3 or 3^^^^^3?”—or questions to that effect. When I note that this is priveleging the hypothesis and attempt to invert it by asking what number of years of torture would be sufficient to overwhelm 3^^^3 dust-speckings in terms of disutility, a universal response is given, which I will quote exactly:
″ ”
This, I feel, is very telling, in terms of my current point regarding that “slight-of-hand”. Unlike units of measurement are being used here. I’ll demonstrate by switching from measurement of pain to measurement of distance (note that I am NOT stating these are equivalent values; I’m demonstrating the principle I reference, here, and do NOT assert it to be a correct analogy of the torture-vs-specking answers.)
“Which is the longer distance? 50 lightcone-diameters or 3^^^3 nanometers?”
Are you saying that 3^^^3 is not sufficiently large? Then consider 3^^^^3.
Whatever epsilon you assign to dust specks, there’s still a yet larger number such that this number of dust specks is worse than torture. Everything else is just accounting that we can’t feasibly calculate anyway.
He (and I) deny this statement is true. There is no sum of sufferings that add up to torture. It is analogous to the fact that the sum of a countably infinite number of countably infinite sets is not as large as the set of real numbers.
I don’t know why Logos insists that logarithmic captures this idea.
I’m saying that dust-specks are practically infinitessimal comparatively, and that’s in direct comparison. Ergo; a nearly or potentially truly infinite number of dust-speckings would be required to equal one torturing for fifty years, just in terms of direct suffering.
If we were to include the fact that such a torturing would result in the total personality destruction of several reconstructed psyches over the period of that 50 years, I don’t necessarily know that such a torture couldn’t rightly be called effectively infinite suffering for a single individual.
In terms solely of the immediate and direct suffering, certainly. In terms of that suffering and the other consequences—individual self-determination, for example; or social productivity costs, etc., even an infinite number of dust-speckings begins to become insufficient to the task of equalling a single fifty-year torture. How much those additional elements ‘count’ as compared to the suffering alone is a question which is not immediately available to simple calculation; we have no means of converting the various forms of utility into a single comparable unit.
We’re already comparing two unimaginably large numbers against one another. For example; the adjustment of 3^^^3 to 3^^^^3 -- how would you decide on the torture vs. dust-speckings if we did the same to torture? What number of years of torture would need to “exceed” 3^^^3 dust-speckings? 51? 500? 50^50?
I don’t understand what you mean by “practically infinitesimal”. Are you saying the negative utility incurred by a dust speck is zero? Also, what do you mean by “nearly… infinite”? Either a quantity is infinite or finite.
You’ve completely lost me. If X is the negative utility of N dust specks, and Y the negative utility of fifty years of torture, then the first sentence implies that X > Y. Then the second sentence defines a second kind of negative utility, Z, due to other consequences. It goes on to imply that X + Z < Y. All quantities involved are positive (i.e., the units involved are antiutilons), so there’s a contradiction somewhere, unless I’ve misread something.
Nearly zero. That’s part of the hypothesis: that it be the smallest possible unit of suffering. If the logarithmic scale of quantification for forms of suffering holds true, then forms of suffering at the maximal end of the scale would be practically infinite comparably.
Correct, but a number that approaches infinity is not itself necessarily infinite; merely very large. 3^^^3 for example.
The negative utility yet considered. Also, keep in mind that we’re at this point priveleging the hypothesis of torture being chosen: we are allowing the number of speckings to be adjusted but leaving the torture fixed. (While it doesn’t really change anything in the discussion, it bears noting for considerations of the final conclusion.)
No, it implies that Z(X) + X < Z(Y) + Y.
My argument rests on the notion that the Z-function value of X is effectively zero, and my further assertion that the Z-function value of Y is such that it overwhelms, when added to Y, the value of X.
As long as it’s nonzero, then as I stated before, there exists some N such that N dust specks have greater negative utility than fifty years of torture. 3^^^3 and 50 are just proxies for whatever the true numbers are.
This is a category error. 3^^^3 does not approach infinity. It’s a fixed number, it’s not going anywhere.
The rest of your comment clarifies the offending inequality.
Can you intelligibly grasp it? Or is it “unimaginably large”? For purposes of human consideration, I do not feel it necessary to differentiate between a truly infinite number and one that is “pseudo-infinite” (where by pseudo-infinite I mean ‘beyond our comprehension’). I admit this is an imperfect hack.
That way lies the madness of pre-Weierstrass analysis.
Why do you concede this? All the suffering you list after this is just as direct.
Saying that torture-without-most-of-the-things-that-make-it-wrong is not so bad might be true, but it isn’t useful.
None of the things I listed afterwards were “suffering” at all. “Suffering” is not “the absence of pleasure”—it is “the antithesis of pleasure”. “Utility” is not synonymous with “enjoyment” or “pleasure”. (Also, please do recall that hedonistic utilitarianism is far from the only form of utilitarianism in existence.)
What.. ? Just… who are you reading in these threads? I am finding myself more and more convinced that you are responding to the writings of someone other than me. You seem to have a persistent habit of introducing notions to our discussions—in a manner as though you were responding to something I had written—that just bear in no way whatsoever to anything I have written or implied by my writings.
Why is this?
I’ll concede that suffering might not be the right word. But everything later in that sentence are essential parts of why torture is wrong. If torture didn’t imply those things (i.e. wasn’t torture), then it would be the right choice compared to dust-specks.
Of course those things are essential parts of why torture is wrong. They would have to be, for my argument to be valid.
Are you simply unaware that the conventional wisdom here on Less Wrong is that the proper answer is to choose to torture one person for fifty years rather than dust-speck 3^^^3 people?
Yes, that is the conventional wisdom. I agree with you that it is wrong, because the features of torture you describe are why the badness quality of torture cannot be achieved in the sum of huge amounts of a lesser badness.
You seem to think that someone could think dust-specks was the right answer without taking into account those essential parts of torture. Otherwise, why do you think that the secondary effects of allowing torture were not considered in the original debate?
Because I read the original submission and its conversation thread.
This is a bit of Meta-Comment about commenting:
As you noted in your post, people in the original thread objected to choosing torture for reasons that basically reduce to the “non-additive badness” position. For me, that position is motivated by the badness of torture you described in your post. So I read the other commenters charitably to include consideration of the sheer wrongness of torture. I simply can’t see why one would pick dust-specks without that consideration.
Now you say I’m reading them too charitably. I’ve been told before that I do that too much. I’m not sure I agree.