The Weber-Fechner law is a simple yet intriguing finding that may have far more implications for understanding physiological and biophysical phenomena that produce our receptor responses to stimuli such as light, taste, sound, touch and smell.

The following six paragraphs are from -http://embryology.med.unsw.edu.au/History/page5c.htm

They provide a view about the Weber-Fechner law that suggests a reluctance to fully embrace its finding because it invades the sacred territory of mind.

FECHNER EXPOUNDS WEBER'S LAW

The chief purport of this classical book of the German psycho-physiologist was the elaboration and explication of experiments based on a method introduced more than twenty years earlier by his countryman E. H. Weber, but which hitherto had failed to attract the attention it deserved. The method consisted of the measurement and analysis of the definite relation existing between external stimuli of varying degrees of intensity (various sounds, for example) and the mental states they induce. Weber's experiments grew out of the familiar observation that the nicety of our discriminations of various sounds, weights, or visual images depends upon the magnitude of each particular cause of a sensation in its relation with other similar causes. Thus, for example, we cannot see the stars in the daytime, though they shine as brightly then as at night. Again, we seldom notice the ticking of a clock in the daytime, though it may become almost painfully audible in the silence of the night. Yet again, the difference between an ounce weight and a two-ounce weight is clearly enough appreciable when we lift the two, but one cannot discriminate in the same way between a five-pound weight and a weight of one ounce over five pounds.

This last example, and similar ones for the other senses, gave Weber the clew to his novel experiments. Reflection upon every-day experiences made it clear to him that whenever we consider two visual sensations, or two auditory sensations, or two sensations of weight, in comparison one with another, there is always a limit to the keenness of our discrimination, and that this degree of keenness varies, as in the case of the weights just cited, with the magnitude of the exciting cause.

Weber determined to see whether these common experiences could be brought within the pale of a general law. His method consisted of making long series of experiments aimed at the determination, in each case, of what came to be spoken of as the least observable difference between the stimuli. Thus if one holds an ounce weight in each hand, and has tiny weights added to one of them, grain by grain, one does not at first perceive a difference; but presently, on the addition of a certain grain, he does become aware of the difference. Noting now how many grains have been added to produce this effect, we have the weight which represents the least appreciable difference when the standard is one ounce.

Now repeat the experiment, but let the weights be each of five pounds. Clearly in this case we shall be obliged to add not grains, but drachms, before a difference between the two heavy weights is perceived. But whatever the exact amount added, that amount represents the stimulus producing a just-perceivable sensation of difference when the standard is five pounds. And so on for indefinite series of weights of varying magnitudes. Now came Weber's curious discovery. Not only did he find that in repeated experiments with the same pair of weights the measure of just-{p}erceivable difference remained approximately fixed, but he found, further, that a remarkable fixed relation exists between the stimuli of different magnitude. If, for example, he had found it necessary, in the case of the ounce weights, to add one-fiftieth of an ounce to the one before a difference was detected, he found also, in the case of the five-pound weights, that one-fiftieth of five pounds must be added before producing the same result. And so of all other weights; the amount added to produce the stimulus of least-appreciable difference always bore the same mathematical relation to the magnitude of the weight used, be that magnitude great or small.

Weber found that the same thing holds good for the stimuli of the sensations of sight and of hearing, the differential stimulus bearing always a fixed ratio to the total magnitude of the stimuli. Here, then, was the law he had sought.

Weber's results were definite enough and striking enough, yet they failed to attract any considerable measure of attention until they were revived and extended by Fechner and brought before the world in the famous work on psycho-physics. Then they precipitated a veritable melee. Fechner had not alone verified the earlier results (with certain limitations not essential to the present consideration), but had invented new methods of making similar tests, and had reduced the whole question to mathematical treatment. He pronounced Weber's discovery the fundamental law of psycho-physics. In honor of the discoverer, he christened it Weber's Law. He clothed the law in words and in mathematical formulae, and, so to say, launched it full tilt at the heads of the psychological world. It made a fine commotion, be assured, for it was the first widely heralded bulletin of the new psychology in its march upon the strongholds of the time-honored metaphysics. The accomplishments of the microscopists and the nerve physiologists had been but preliminary--mere border skirmishes of uncertain import. But here was proof that the iconoclastic movement meant to invade the very heart of the sacred territory of mind--a territory from which tangible objective fact had been supposed to be forever barred.

I've discovered that there is a fundamental equation of equilibrium that can be simply derived from an analysis of unequal weights on a two-pan balance http://www.bio-balance.com/Simple_Balance_PartII.pdf. These simple physical experiments demonstrate something very profound about a two-pan balance that to my knowledge hasn't been adequately explored before now. This fundamental equation may revolutionize how scientists view everything from cellular receptor activation to complex, nonlinear systems (see - Weber's law or http://www.bio-balance.com/Weber's_Law.pdf and Graphics and http://www.bio-balance.com/A_Question_of_Balance.htm). Digesting this requires some time, but only a basic understanding of algebra. Those who try will be rewarded by the elegant simplicity of the fundamental equation of equilibrium that may hold the key to several complex problems today.

Weber's Law Modeled by the Mathematical Description of a Beam Balance, Mathematical Biosciences 122: 89-94 (1994) - Link: http://www.bio-balance.com/Weber%27s_Law.pdf

Weber–Fechner law http://en.wikipedia.org/wiki/Weber%27s_law

http://ombamltine.blogspot.com/2008/05/welcome.html

http://ombamltine.blogspot.com/search?q=Weber%27s+law

## No comments:

Post a Comment