Decibels are a relative quantity: they express the intensity of a signal relative to another. A 10x difference is 10 dB, a 100x difference is 20 dB, and so on. The ājust noticeable differenceā in amplitude of sound is ~1 dB, or a ~25% increase. But decibels can also be used in an āabsoluteā sense by quantifying the ratio of the signal to a reference value. In the case of sound, the reference value is the smallest value that most humans can hear (a sound pressure of 20 micropascals).[1]
Since pleasure and pain are perceived according to a log scale, the utility of a sensation could be approximated by:
U(S)=U0max(0,log(S/S0))
where S is the intensity of the sensation, S0 is the smallest perceptible sensation, and U0 is a constant that is positive for pleasurable sensations and negative for painful ones. (This is only an approximation because Fechnerās law, the principle that governs logarithmic perception of signals, breaks down for very strong and very weak signals.)
It seems very natural, therefore, to use decibels as the main unit for pleasure and pain, alongside utils for the utility of perceived sensations, as the relationship between decibels and utils is linear. For example, if a utility function is given by
U(D)=0.5max(0,D)
where D is the decibel amount, then we have 10 dB of pleasure = 5 utils, 20 dB = 10 utils, 30 dB = 15 utils, and so on.
It seems like decibels (dB) are a natural unit for perceived pleasure and pain, since they account for the fact that humans and other beings mostly perceive sensations in proportion to the logarithm of their actual strength. (This is discussed at length in āLogarithmic Scales of Pleasure and Painā.)
Decibels are a relative quantity: they express the intensity of a signal relative to another. A 10x difference is 10 dB, a 100x difference is 20 dB, and so on. The ājust noticeable differenceā in amplitude of sound is ~1 dB, or a ~25% increase. But decibels can also be used in an āabsoluteā sense by quantifying the ratio of the signal to a reference value. In the case of sound, the reference value is the smallest value that most humans can hear (a sound pressure of 20 micropascals).[1]
Since pleasure and pain are perceived according to a log scale, the utility of a sensation could be approximated by:
U(S)=U0max(0,log(S/S0))
where S is the intensity of the sensation, S0 is the smallest perceptible sensation, and U0 is a constant that is positive for pleasurable sensations and negative for painful ones. (This is only an approximation because Fechnerās law, the principle that governs logarithmic perception of signals, breaks down for very strong and very weak signals.)
It seems very natural, therefore, to use decibels as the main unit for pleasure and pain, alongside utils for the utility of perceived sensations, as the relationship between decibels and utils is linear. For example, if a utility function is given by
U(D)=0.5max(0,D)
where D is the decibel amount, then we have 10 dB of pleasure = 5 utils, 20 dB = 10 utils, 30 dB = 15 utils, and so on.
https://āāen.wikipedia.org/āāwiki/āāDecibel#Acoustics_2