In 1834, the German physiologist Ernst Weber (pictured above) carried out a series of experiments to determine the limits of sensory perception. He gave a blindfolded man a mass to hold and gradually increased its weight, asking the subject to indicate when he first became aware of the change.
These experiments showed that the smallest increase in weight that a human can perceive is proportional to the initial weight. The German psychologist Gustav Fechner later interpreted Weber’s work as a way of measuring the relationship between the physical magnitude of a stimulus and its perceived intensity.
The resultant mathematical model of this process is called the Weber-Fechner law and shows that the relationship between the stimulus and perception is logarithmic. (For a straightforward derivation see Wikipedia.) The Weber-Fechner law is important because it established a new field of study called psychophysics.
The logarithmic relationship between a stimulus and its perception crops up in various well known examples such as the logarithmic decibel scale for measuring sound intensity and a similar logarithmic scale for measuring the visible brightness of stars, their magnitude.
Today, Haengjin Choe at Korea University in South Korea, says there is an interesting connection between the Weber-Fechner Law and the famous mathematical theory of information developed by Claude Shannon at Bell Labs in the 1940s.
Shannon’s work is among the most important of the 20th century. It establishes the limits on the amount of information that can be sent from one location in the universe to another. It is no exaggeration to say that the world’s entire computing and communications infrastructure is based on Shannon’s work.
Choe points out that the law developed by Shannon that links the amount of information that can be transmitted by a single symbol is also logarithmic. In fact, it takes exactly the same form as the Weber-Fechner law.
What that means is that psychophysical phenomena can be treated mathematically in the same way as any other form of information transmission and so opens up a new and extensive mathematical toolbox that may provide new insights into the nature of perception .
Of course, the idea that sensory perception is a form of communication and so obeys the same rules, is not entirely surprising. What’s astonishing (if true) is that the connection has never been noticed before.
Ref: arxiv.org/abs/1002.3909: Connection Between Shannon’s Information Theory And The Weber-Fechner Law