How do we quantify the relationship between the physical and the mental? An Introduction to Psychophysical Laws

Psychology and cognitive science have at their foundation the notion that we can somehow measure the mental world. But can we? It is unclear, at least to the naïve observer, how such a goal could be achieved given that the mental is unobserved and private to each individual that has a mental capacity. However, there is good reason to think that we can relate the mental to the physical in a meaningful way. The methods for doing so were first developed by Gustav Fechner in the 1800s and were called Psychophysics (psycho meaning mental and physics meaning physical). Psychophysics is still studied and used today and has served as the foundation for much of experimental psychology and cognitive science.

A basic psychophysics experiment is designed to determine the relationship between a particular sensation and a particular physical stimulus. Ernst Weber used this type of experiment to look at the relationship between the sensation of heaviness and the actual weight of a weight lifted by the observer. Weber varied the magnitude of standard and comparison weights held in turn by the observer, who made reports of whether the comparison was less than, equal to or greater than the standard weight. It was discovered that the change in the weights that was just noticeable by the observer (called the “just noticeable difference” or JND or “difference threshold”) was a constant fraction of the magnitude of the standard stimulus. This meant that for larger weights, more weight was required to get the observer to notice a change compared to when they were lifting smaller weights.

Weber investigated further and found that this relationship held for most human senses (e.g., sight, sound, taste, touch). Weber’s law states simply that the JND is proportional to stimulus magnitude. Gustav Fechner proposed another law, using Weber’s law for the foundational assumptions. Fechner’s law looks specifically at the relationship between stimulus intensity and perceived magnitude. It assumes that Weber’s law holds (i.e., JND is a constant fraction of magnitude) and also that the JND is the fundamental unit of perception, meaning that one JND in one sense is “perceptually equivalent” to one JND in another sense. With these assumptions in mind he hypothesised that the perceived magnitude of a stimulus can be calculated by adding up JNDs. Mathematically, this leads to the formula:

P = k.log.I

, where P is perceived magnitude, k is the Weber fraction and I is actual stimulus intensity/magnitude. Fechner’s law allows you to calculate whether a light that is twice as bright (in terms of physical magnitude) will appear so to the observer. However, work since Fechner has cast doubt on the second foundational assumption of the law (that the JND is the fundamental unit of perception), and this has led to the conceptualisation of Fechner’s law as a special case of the more general “Power law” or “Steven’s power law”, expressed mathematically as:

P = k.I^n

, where P is again perceived magnitude, k is again the Weber fraction and I is again stimulus intensity/magnitude. However, in this case, I is raised to a power n, which specifies the relationship between P and I — that is, does a doubling in P lead to a doubling in I (a linear relationship with n of 1) or is there more or less of a doubling in I for a doubling in P? Steven’s law has been found to better quantify the relationship between P and I for many senses, compared to Fechner’s law.

In this article I have briefly touched on psychophysical experiments as originally conceived and the laws that have been derived from such experiments. In my next article, I will focus on varieties of psychophysical experiments and how they can help us quantify the relationship between the mental and physical.



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