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.
Hearing occurs when your ear drum vibrates from a sound. When a sound occurs, the drum vibrates with it. When two identical sounds play, the drum vibrates more intensely. When 10 identical sounds play, the drum vibrates twice as intensely compared to a single sound.
Your eyes perceive light waves similar to the way your ears hear sound waves. One difference between these body parts is that your eyes have different mechanisms to alter or interpret the light waves before it reaches your brain. Light is scattered or focused through your clear jelly lens. The amount of light let in is controlled the black hole called the pupil. Then the cones and rods interpret this signal to build an image.
Sound is mainly interpreted by the intensity of air pressure in the drum.
1 lion and 2 lions look very different.
99 lions and 100 lions look about the same.
The difference in still one lion, but one lion matters less when there’s already 99.
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