Perception is an active process in which an individual’s cognitive system constructs an internal representation of the environment through the organisation and interpretation of the sensory information. What an individual perceives is not an accurate or direct representation of reality as it can be influenced and distorted by memory and high-level knowledge. Perception occurs outside an individual’s conscious awareness and more or less, shapes their experiences. This process involves both bottom up and top down processing. Bottom up processing occurs when the sensory information is processed as soon as it is coming in, whereas top down processing refers to the perception which is driven by cognition. Psychophysics investigates the relationship between sensation in the psychological domain and stimuli in the physical domain, e.g. what is happening inside the brain and outside the brain. Fechner’s Law and Weber’s Law are two attempts in psychophysics to explain human perception, but more specifically are interested in determining the relationship between the actual change in a physical stimulus and the change that the individual perceives. However, short-comings and limitations of the Weber-Fechner Law led to further development of alternative methods of linking sensation to perception. Steven’s Power Law is a proposed relationship between the magnitude of a physical stimulus and the intensity that people feel.
Fechner’s Law is a psychological law quantifying the perception of change in a given stimulus and most importantly, explaining its relationship with sensation/perception. Similar to Weber’s Law, Fechner’s Law proposes the idea that the just noticeable change in a stimulus will be a constant ratio of the original stimulus. Fechner derived the equation S=klogI to explain how the sensation and perceptual magnitude is a logarithmic function of stimulus intensity. He believed that as the stimulus intensity grows larger, the individual’s perception of it grows linearly, equally. Fechner proposed different thresholds in an attempt of explaining how individuals perceive stimuli. He noted that the absolute threshold is the level of stimulus intensity that the observer can just barely detect, meaning that intensities below the absolute threshold cannot be perceived, whilst intensities exceeding this threshold are easily detected. The difference threshold, also known as the just noticeable difference, is the minimum change in intensity that is required to be perceived or noticed by the observer. Following the same rules as the absolute threshold, a change in intensity that is smaller than the difference threshold, will be undetectable. It is important that the potentially detectable stimulus is of sufficient intensity to cause the degree of neural activation required to sense it.
Weber’s Law explains that the difference between two stimuli is better and more easily perceived as the ration between the magnitude of two stimuli increases. Derived from his law, Weber’s Fraction is based on the equation where the difference threshold is divided by the baseline weight providing a result which is constant. However, Weber also noted that for the most part, if the standard weight is not too close to the absolute threshold, then the Weber Fraction is likely to be constant and will stay the same. The smaller the Weber’s Fraction, the smaller the change in the stimulus necessary to produce a just noticeable difference. Most importantly, rearranging Weber’s Fraction from DL/S=K to S*K=DL allows us to predict a linear relationship between the absolute threshold and the background intensity. He used the equation deltaI=KI to show that the difference threshold is a constant proportion (k) of a particular stimulus. He noted that most importantly, these constant proportions are different for different sensory modalities. Thus, this gives us the impression that to some extent, perception can be quantified and summarised using equations, whilst also equipping us to predict the detection threshold.
Despite the Weber-Fechner Law being highly regarded as a method of measuring perception, it was believed to have a few limitations. The Weber-Fechner law was not 100% accurate and was unable to account for all perceptual modalities, for example, the perception of time. Empirical evidence shows that this law was very limited in being able to quantify the relation between sensation and stimulus. Further limitations are found in the assumption that the just noticeable differences are all equal. An example where this fell short is where a tone that is 20 JND above the absolute threshold should appear to be twice as loud as a tone that is 10 JNDs above the threshold, however, this was found that it is actually much louder. Similarly, Weber’s assumption that the constant will be consistently the same every time was found to be very limited in application when dealing with much weaker or much stronger stimuli.
Whilst the Weber-Fechner law provided a great attempt and account of measuring the relationship between the stimuli and how we as observers perceive them, their limitations led to the development of Steven’s Power Law. Stanley Steven’s was the first to challenge Fechner’s assumption that there is a logarithmic relationship between the stimulus intensity and the magnitude of sensation. Whilst Fechner’s Law was unable to account for all types of stimuli, Steven’s was interested in doing so by rethinking the relationship between stimuli and perception. Steven’s law took a different approach to Fechner’s, where instead of using thresholds to measure perceptual experiences, he attempted to estimate these perceptual experiences using a statistical approach. Steven’s idea was that presenting stimuli to individuals and asking them to assign numbers to what they perceive allowed the exploration of how those numbers change as stimuli changers. This was believed to have granted the exploration of other aspects of perception that the Weber-Fechner Law was not able to explore, e.g. beauty and attraction. Steven’s Power law aimed to quantify the connection between stimuli and how we perceive them, as a threshold cannot be used to measure all motions. The approach of direct scaling was also adopted where the change in what individuals perceive is measured in numerical terms. Despite this being a subjective measure, where some may believe this is a limitation, the quantitative nature of this method allows us to monitor regularities in judgments. Steven’s Power Law is an establishment of a mathematical relationship between stimulus intensity and sensation magnitude. His equation s=kI^a was developed to explain that the perceived strength of stimuli increases in proportion to its physical intensity to some power. The exponent (a) is a crucial parameter of the equation as it is a reflection of the connection between the sensory and stimulus magnitude, whilst being unique to the modality being measured.