In 1834, the German physiologist Ernst Weber ... 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. ... 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.
Modern Information theory is generally considered to have been founded in 1948 by Shannon in his seminal work, "A mathematical theory of communication." Shannon's formulation of information theory was an immediate success with communications engineers. Shannon defined mathematically the amount of information transmitted over a channel. Meanwhile, psychophysics is the study of quantitative relations between psychological events and physical events or, more specifically, between sensations and the stimuli that produce them. It seems that Shannon's information theory bears no relation to psychophysics established by German scientist and philosopher Fechner. To our astonishment, it is possible that we combine two fields. And therefore we come to be capable of measuring mathematically perceptions of the physical stimuli applicable to the Weber-Fechner law.