The threshold of touch
In the 1830s at the University of Leipzig, the anatomist Ernst Heinrich Weber began a series of deceptively simple experiments to explore the sense of touch. His work established the foundation for psychophysics, the scientific study of the relationship between physical stimuli and the sensations they produce. One of Weber's concepts was the "just-noticeable difference" (JND), the minimum change in a stimulus that a person can detect half the time.
Through experiments involving subjects lifting weights, Weber discovered something significant. A person holding a 100-gram weight could typically notice a difference when a few grams were added. If that same person held a 1000-gram weight, they would need a much larger increase to perceive a change. The factor was not the absolute weight added, but the ratio of the added weight to the starting weight. This constant ratio became known as Weber's Law. Weber also mapped the sensitivity of the human body using a set of calipers in two-point discrimination tests. He systematically measured the smallest distance between two points on the skin that a person could feel as two distinct points, rather than one.
The logarithmic law of the mind
Gustav Theodor Fechner, a physicist and philosopher also at the University of Leipzig, saw a significance in Weber's findings. After a period of illness that forced him to resign his physics professorship, Fechner turned his attention to the relationship between the mental and material worlds. On the morning of October 22, 1850, he had an insight: Weber's work provided a way to measure sensation mathematically. He realized that for the intensity of a sensation to increase in an arithmetic progression (1, 2, 3, 4), the stimulus must increase in a geometric progression (2, 4, 8, 16).
This relationship is logarithmic. Fechner formulated it into an equation, S = k log R, where S is the magnitude of the sensation, R is the magnitude of the stimulus, and k is a constant. This became known as the Weber-Fechner law. He published his extensive research and theories in the 1860 book Elemente der Psychophysik (Elements of Psychophysics). This work is the foundation of experimental psychology, establishing that the mind itself was susceptible to measurement. Fechner's methods and mathematical laws influenced Wilhelm Wundt, who would go on to found the world's first formal laboratory for experimental psychology in the same city, Leipzig, in 1879.