Thanks for the relevant discussion, Jim and Wladimir. Wladimir, in your framework, is resolution i) the total number of distinct welfare intensities, ii) the ratio between i) and the difference between the maximum and minimum welfare intensities, or iii) something else?
Thanks. In our framework, resolution is not simply (i) the number of distinct welfare intensities, nor (ii) a strict ratio relative to the total range. It refers to the functional granularity with which differences in intensity can be discriminated and behaviorally prioritized.
The key point we raise in the post is that resolution is orthogonal to range: a system can evolve high resolution while maintaining a modest range, expand its range while keeping coarse resolution, or increase both simultaneously.
I thought ii) in my past comment was the resolution over the whole range of welfare intensities. The image below of the post suggests “resolution from welfare intensity A to B” = “number of different welfare intensities between A and B”/(B—A)? More precisely, it looks like resolution is the derivative of the number of different welfare intensities with respect to welfare intensity. This still leaves open how ii) relates to the whole range of welfare intensities. A system can have high resolution, and a narrow whole range of welfare intensities in the same way that a car can move fast over a short distance (even though the average speed over a distance can be calculated from the ratio between the distance covered, and time spent covering it).
Thanks, Vasco — I see where the confusion is coming from.
The difficulty is that in our framework, resolution is not defined as a mathematical density of bins over a fixed, external intensity axis (e.g., dN/dI). That framing assumes there is already a continuous welfare scale “out there,” and resolution simply tells us how finely the organism partitions it.
In our usage, resolution refers to the organism’s internal discriminative granularity — how finely differences in affective magnitude can be distinguished and behaviorally prioritized within whatever range the organism has.
So resolution is not the derivative of category-count with respect to an external intensity variable. Rather, it is a property of the encoding architecture itself.
That’s why it is orthogonal to range. A system may:
• Have a narrow range but very fine discriminative structure within that range. • Have a wide range but coarse internal discrimination. • Increase both independently.
Your car analogy is actually helpful. A car can move very fast over a short distance — speed is not determined by total range. Likewise, high resolution does not require a wide affective range, and vice versa.
So resolution is better understood as internal discriminative power, not as bin density over a pre-specified global welfare scale.
I was not clear, but I meant the image suggests “organism’s resolution from welfare intensity A to B” = “number of different welfare intensities the organism can experience between A and B”/(B—A), which depends on the organism, A, and B. Is this what you have in mind?
In our upcoming post, we introduce human-anchored reference categories (Annoying(h), Hurtful(h), Disabling(h), Excruciating(h)) to provide a pragmatic shared coordinate system for cross-species discussion. So if one wants to talk about “acuity/resolution between A and B,” it’s reasonable to treat A and B as positions (or intervals) on that human-anchored scale.
But no — we’re not defining acuity as #levels/(B−A), because that requires meaningful distances between A and B. At this stage the (h) scale is best treated as ordinal: it supports “higher/lower ceiling” comparisons, not subtraction or ratios.
I worry just 4 human-anchored pain intensities are not enough for reliable comparisons, even for an early stage. For shrimp-anchored annoying pain 10^-6 times as intense as human-anchored annoying pain (the ratio between the individual number of neurons of shrimps and humans), and this 10^-6 times as intense as human-anchored excruciating pain, shrimp-anchored annoying pain would be 10^-12 (= (10^-6)^2) times as intense as human-anchored excruciating pain. It seems super hard to cover such a wide range of pain intensities with any significant reliability using just 4 values?
Thanks for the relevant discussion, Jim and Wladimir. Wladimir, in your framework, is resolution i) the total number of distinct welfare intensities, ii) the ratio between i) and the difference between the maximum and minimum welfare intensities, or iii) something else?
Thanks. In our framework, resolution is not simply (i) the number of distinct welfare intensities, nor (ii) a strict ratio relative to the total range. It refers to the functional granularity with which differences in intensity can be discriminated and behaviorally prioritized.
The key point we raise in the post is that resolution is orthogonal to range: a system can evolve high resolution while maintaining a modest range, expand its range while keeping coarse resolution, or increase both simultaneously.
I thought ii) in my past comment was the resolution over the whole range of welfare intensities. The image below of the post suggests “resolution from welfare intensity A to B” = “number of different welfare intensities between A and B”/(B—A)? More precisely, it looks like resolution is the derivative of the number of different welfare intensities with respect to welfare intensity. This still leaves open how ii) relates to the whole range of welfare intensities. A system can have high resolution, and a narrow whole range of welfare intensities in the same way that a car can move fast over a short distance (even though the average speed over a distance can be calculated from the ratio between the distance covered, and time spent covering it).
Thanks, Vasco — I see where the confusion is coming from.
The difficulty is that in our framework, resolution is not defined as a mathematical density of bins over a fixed, external intensity axis (e.g., dN/dI). That framing assumes there is already a continuous welfare scale “out there,” and resolution simply tells us how finely the organism partitions it.
In our usage, resolution refers to the organism’s internal discriminative granularity — how finely differences in affective magnitude can be distinguished and behaviorally prioritized within whatever range the organism has.
So resolution is not the derivative of category-count with respect to an external intensity variable. Rather, it is a property of the encoding architecture itself.
That’s why it is orthogonal to range. A system may:
• Have a narrow range but very fine discriminative structure within that range.
• Have a wide range but coarse internal discrimination.
• Increase both independently.
Your car analogy is actually helpful. A car can move very fast over a short distance — speed is not determined by total range. Likewise, high resolution does not require a wide affective range, and vice versa.
So resolution is better understood as internal discriminative power, not as bin density over a pre-specified global welfare scale.
I was not clear, but I meant the image suggests “organism’s resolution from welfare intensity A to B” = “number of different welfare intensities the organism can experience between A and B”/(B—A), which depends on the organism, A, and B. Is this what you have in mind?
In our upcoming post, we introduce human-anchored reference categories (Annoying(h), Hurtful(h), Disabling(h), Excruciating(h)) to provide a pragmatic shared coordinate system for cross-species discussion. So if one wants to talk about “acuity/resolution between A and B,” it’s reasonable to treat A and B as positions (or intervals) on that human-anchored scale.
But no — we’re not defining acuity as #levels/(B−A), because that requires meaningful distances between A and B. At this stage the (h) scale is best treated as ordinal: it supports “higher/lower ceiling” comparisons, not subtraction or ratios.
I worry just 4 human-anchored pain intensities are not enough for reliable comparisons, even for an early stage. For shrimp-anchored annoying pain 10^-6 times as intense as human-anchored annoying pain (the ratio between the individual number of neurons of shrimps and humans), and this 10^-6 times as intense as human-anchored excruciating pain, shrimp-anchored annoying pain would be 10^-12 (= (10^-6)^2) times as intense as human-anchored excruciating pain. It seems super hard to cover such a wide range of pain intensities with any significant reliability using just 4 values?