The Weber-Fechner law

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This law hails from the middle of the nineteenth century. It is mainly founded on experiments where persons were given two nearly identical stimuli (for example, two similar weights) and tested whether they could notice a difference between them. It was found that the smallest noticeable difference was roughly proportional to the intensity of the stimulus. Ie, if a person could consistently feel that a 110 g weight was heavier than a 100 g weight, he could also feel that 1100 g was more than 1000 g.

Since a constant relative difference in the intensity corresponds to a constant absolute difference in the logarithm of the intensity, Weber and Fechner suggested that R is proportional to the logarithm of S:

R = k log (S/S₀)

which corresponds to a curve of this type:
 

There is a lot of sense in the Weber-Fechner law, but in the long run it has turned out to be too inflexible. It is therefore rarely used nowadays, but it is very vulgar not to know about it.

Nowadays, the formula most used is Stevens' formula. 

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