biology zoology blog benno meyer Making Sense of Sensors

Making Sense of Sensors

The Laws of Weber-Fechner and Bloch

Of the courses I teach, I love “Animal Senses and Behaviour” the most. A study of behaviour does not make much sense to me, unless we first examine how an individual detects a stimulus and that requires some knowledge about the sensory structures involved, namely their anatomical organization and their physiological (= functional) properties plus the nerve centres involved in processing. In this context the meaning of two so-called “laws”, known as Weber-Fechner Law and Bloch’s Law, are important.

Often the Weber-Fechner law is expressed mathematically as it says that the relationship between stimulus and perception is logarithmic. The consequence is that for multiplications in stimulus strength, the strength of perception adds. If this sounds a little abstract, let’s take an example: if the smallest perceivable difference in weights that you can distinguish when tested with two weights is 1 g (one weighing 10 g and the other 11 g), then you might think you can sense the difference between 100 g and 101 g. Not so: Under these scenarios the difference in the sensation is due to the pressure (or stretch) receptor’s threshold sensitivity. But when tested to distinguish the two heavier weights (100 g versus 101 g) you don’t notice a difference unless the weight difference becomes 10 g (one the weights being 110 g). Using a 1000 g weight, you won’t notice a difference between it and a 1010 g heavy weight: only when the second weight is 100g heavier you sense the difference.

Another way of showing how this relationship affects our judgement (and in this case our sense of vision) is a test I always ask the students to carry out in the lab. What they have to do is very simple: they need to visually determine the centre of some straight lines: a short one of 1 cm; a longer one of 10 cm; and an even longer one of 1 m. To hit the centre of the 1 cm line is usually done with considerable accuracy and an error of less than 1 mm is the result. The 10 cm line’s centre is usually found with an accuracy of ± 1 mm, which is still not bad, but the centre of the long 1 m line is often missed by as much as 1 cm. If we would have had a line 100 m long, the error might well be 10 cm. It is said that the Weber-Fechner relationship works best for weight and light intensity assessments and neuronal responses to different stimulation strengths do reflect the law across a certain range, but not at the higher and lower extremes.

The other law our sensory physiology students are usually confronted with is Bloch’s law (also known as Bunsen-Roscoe law, which simply states that the product of the intensity of a stimulus and the duration of the stimulus is a constant). One can demonstrate this law with recordings from neurons that transmit responses elicited by stimuli of flashes of light. If for example one uses as a stimulus a flash of light and records the nerve spikes that it generates and then decreases the intensity of the stimulus by one log unit, i.e. a factor of ten, then one can still obtain the same number of spikes in the neuron if the duration of the stimulus is increased tenfold. This relationship does work well if relatively short flash durations are used, e.g. 0.1, 1, 10, 100 or maximally 1,000 milliseconds. Almost certainly camera and photography enthusiasts know that in order to compensate for the reduction of the size of the aperture in your camera (using a smaller f-stop) you need to increase the exposure time in order to obtain the same brightness in your photo.

Stimulus-response relationships like those briefly explained above play an essential role in comparative sensory physiology and psychophysics and I found that it is actually a wonderful field to get students of biology interested in physics. My student H had obviously understood what I had explained, for she told me after class that now she knew why 1 hour of a deep sleep felt as good as 10 hours of a light sleep. Monsieur Adolphe-Moïse Bloch who had published his work in 1885 would have been glad to hear that.

© Dr V.B. Meyer-Rochow and, 2020.
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