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?”
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?”