I’ve always heard that the decibel scale for hearing is logarithmic, and I’ve recently learned that our eyes view and compare objects logarithmically as well. How exactly does this process work, and is it different between the eyes and the ears?
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It is, of course, different. The ears work somewhat “mechanically” (ear drums etc) while the eyes work “photonically” in that it is a response to light. The relevant organs translates the different input into nerve signals which are “electrical” in nature. (very ELI5)
The logarithmic scale is a very natural response. It is the inverse of the exponential scale. You can think of it like two different ways of saying the same thing. For example: if object A is 1 meter high and object B is 2 meters high, one can say that A is half the height of B or B is twice the height of A – they are saying the same thing simply from different perspectives.
The exponential/logarithmic response occurs (typically but not always) when the rate of change of some measure is proportional to the measure itself. An example of this would be how quickly the temperature of a hot object drops when left to cool down naturally in air. This relationship happens a lot in natural systems. It happens when we try to measure intensity and/or power responses – which is what sound and light happen to be. Measuring the intensity of sound pressure waves or light energy is what our ears and eyes do.
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