“In the previous part, we discussed odour perception, the factors that affect it, and the importance of odour in life. Read Part 1.”
In this blog, let’s explore the mathematical correlations in odour perception. The mathematical relationship between odour concentration and odour perception without saying about two renowned German scientists – Ernst Heinrich Weber & Gustav Theodor Fechner.
Ernst Heinrich Weber
Ernst Heinrich Weber (1795–1878) was a German physician and physiologist. He is considered, with good reason, one of the founders of experimental psychology, especially in the field of sensory perception.
Ernst Heinrich Weber was born on June 24, 1795, in Wittenberg, Germany. He studied medicine at the University of Wittenberg and later became its professor. He had held different academic positions and was the professor of anatomy at the University of Leipzig. Though the work of Weber laid the foundation for the field of psychophysics, one of the biggest contributions in the context of odour perception is the mathematical formulation of the same – called the Weber’s law.. Weber’s law states that the “just noticeable difference (JND)” between two stimuli is proportional to the magnitude of the original stimulus. Mathematically, this can be expressed as:
ΔI/I=k
where:
- ΔI is the increment in intensity that can be detected (JND).
- I is the original intensity.
- k is a constant (Weber fraction) specific to the type of sensory input.
Ernst Heinrich Weber’s work has had a lasting impact on the fields of psychology and sensory physiology. His contributions are foundational to our understanding of how humans perceive and process sensory information.
Gustav Theodor Fechner
Gustav Theodor Fechner (1801–1887) was a German philosopher, physicist, and experimental psychologist. Fechner is considered one of the founders of psychophysics, study of quantitative relations between psychological events and physical events or, more specifically, between sensations and the stimuli that produce them.
Gustav Fechner was born on April 19, 1801, in Żarki Wielkie, Poland. He studied medicine at the University of Leipzig. Fechner spent most of his academic career at the University of Leipzig, where he held positions in physics and later in philosophy. Fechner’ law states that the perceived intensity of a stimulus increases as a logarithmic function of the actual stimulus intensity.
S=k log(I)
where:
- S is the perceived sensation.
- I is the physical intensity of the stimulus.
- k is a constant.
Gustav Fechner’s pioneering work bridged the gap between the physical and psychological worlds, laying the foundations for the scientific study of sensation and perception. His contributions continue to influence research in psychology, neuroscience, and related disciplines.
Weber-Fechner Law
While Weber provided the initial insights into the proportionality of sensory perception, Gustav Fechner expanded on these ideas to formulate the more comprehensive Weber-Fechner Law, the combined contributions of Weber and Fechner provide a comprehensive understanding of how we perceive changes in stimulus intensity. This law remains a key concept in sensory psychology and related fields. This law states that the change in a stimulus that will be just noticeable is a constant ratio of the original stimulus. Human perception of odour intensity (I) can be described by the equation:
I=k log (C)+C0
where:
- I is the perceived intensity.
- k is a constant that depends on the Odourant.
- C is the concentration of the Odourant.
- C0 is a baseline level of perception.
Implications of Weber-Fechner Law
The Weber-Fechner Law describes the human perception of the intensity of odors, just like with any other sensory stimulus.
Sensory Thresholds: The law helps in understanding the concept of sensory thresholds, for example, the absolute threshold, which is the minimum intensity at which a stimulus can be detected, and the difference threshold, which is the minimum difference between two stimuli that can be detected.
Perceptual Scaling: It tells why different sensory systems respond in a logarithmic relation to wide ranges of stimulus intensity. For example, our light and sound and odour perception can allow us to detect and then respond with a broad spectrum from very low to very high intensities.
Psychophysics: This is the study of the relationship between physical and perceived stimuli. The Weber-Fechner Law has been the basis for quantification of experiences created on senses as far as this field is concerned.
Logarithmic nature has to be perceived while understanding odour perception in environmental monitoring, perfumery, food, and beverages where the stringency in maintaining the odour intensity becomes very important. Odourants can be detected over a wide range of concentrations. At lower concentrations, small changes in concentration result in large changes in perceived intensity. At higher concentrations, much larger changes in concentration are needed to produce the same change in perceived intensity. This logarithmic relation may be used to explain why strong odours quickly appear to be overwhelming and why the differences between two very similar concentrations of a faint odour might not be easily distinguished. In other words, our sense of smell is more sensitive when the level of odourant is low and less sensitive when it is high—that is why we can effectively perceive and distinguish a wide range of odour intensities.
Practical Implications
- Environmental Monitoring: The logarithmic nature of odour perception is important in understanding how regulatory standards for air quality and odour control should be set.
- Perfumery and Flavor Science: Logarithmic perception of odour intensity assists the formulation of products where precise control over odourant concentrations must be made to achieve the desired sensory effect.
- Health and Safety: Odour thresholds are of use in the industrial sphere for monitoring the levels of unsafe substances and maintaining their concentrations at levels that will not injure health.
The application of the Weber-Fechner Law is vital in the case of environmental monitoring, particularly odour detection and control.
Environmental Monitoring Applications
- Setting Odour Thresholds:
- Regulatory Standards: Environmental agencies set permissible levels of certain Odourants in the air. Using Odours logarithmic perception, they could determine threshold values that one can easily detect but also find acceptable to the human nose.
- Odour Units: Often odours are measured in “odour units” derived from the amount of Odourants which can be detected by 50% of a panel of human testers. This follows the Weber-Fechner Law, focusing on the sensitivity of human perception rather than pure chemical concentration.
- Odour Complaints and Impact Assessment:
- Quantifying Complaints: When odour complaints are filed by residents around industrial facilities or waste treatment plants, monitoring systems are able to quantify odour intensity on logarithmic scales. This helps to check whether the perceived intensity of odours justifies mitigation measures.
- Impact Zones: Knowing how Odour intensity decreases by a logarithmic rule, depending on distance, the environmental scientist would draw circles of impact around Odour sources and predict how far the Odours will travel and are perceived at different distances.
- Odour Mitigation and Control:
- Effective Dispersion: Odour control technologies, such as scrubbers and biofilters, can be designed and evaluated based on their ability to reduce Odourant concentrations logarithmically. The knowledge that small reductions in high concentrations yield noticeable benefits assists in optimizing these systems.
- Monitoring Technologies:
- Electronic Noses: These devices can mimic the human olfactory system and very often use algorithms incorporating the logarithmic perception model for the detection and quantification of Odours in real-time.
- Real-Time Data: Monitoring systems can provide real-time data about Odour levels, translating chemical concentrations to perceived intensities by means of logarithmic scales. Further, this output can be used to trigger automatic responses, such as the activation of ventilation systems or adjusting the levels of chemical treatment.
- Health and Safety:
- Hazardous Substances: Some hazardous substances are even harmful at low concentrations. A logarithmic perception model helps in setting lower detection thresholds so that such substances can be identified well before dangerous levels are reached.
- Exposure Limits: Occupational exposure limits for odours can be set for both the actual concentration and perceived intensity to avoid exposure of workers to odours that are unpleasant or harmful.
Sensory Adaptation
The concept of sensory adaptation is one in which the responsiveness of the sensory receptors gradually decreases toward continuously present or unchanging stimuli. This enables us to focus on changes in the environment, rather than detecting unchanging background stimuli constantly.
Examples of Sensory Adaptation
Vision:
(a)Dark Adaptation: When moving from a brightly lit environment to a dark one, the sensitivity of photoreceptors in the retina increases, allowing better vision in low light. This process can take several minutes to complete.
(b)Light Adaptation: Conversely, when moving from a dark environment to a brightly lit one, the sensitivity of the photoreceptors decreases, preventing overexposure to light.
Smell:
(a)Olfactory Adaptation: When continuously exposed to a particular Odour, the olfactory receptors in the nose become less sensitive to that Odour. For instance, when entering a room with a strong smell, you may initially find it overpowering, but after a while, you stop noticing it.
Touch:
(a)Tactile Adaptation: When you wear clothing, you feel the fabric against your skin at first, but as your tactile receptors adjust to the continuous pressure, the experience gradually fades.
Hearing:
(a)Auditory Adaptation: When exposed to a constant noise, such as the hum of an air conditioner, your auditory system becomes less sensitive to that noise, allowing you to focus on other sounds.
Sensory adaptation allows organisms to become less sensitive to constant stimuli, while the Weber-Fechner Law explains how changes in stimulus intensity are perceived relative to the initial intensity. Together, they illustrate the complex mechanisms of human perception and how we interact with our environment.
Let us close the description by showing a small illustration on the different mathematical relationships from linear to logarithmic to cosine and so on.
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