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?”
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?”