Aug 13 2019

Weber’s Law

I confess I have never heard (or at least don’t remember ever hearing) about Weber’s Law (pronouned vayber) until reading about it with this news item. It is the Law of Just Noticeable Differences. It deals with the minimum difference in a stimulus necessary to notice. While clearly established, and there are many hypotheses to explain the phenomenon, there has never been a way to test which hypothesis is correct. The news items relates to new evidence which may provide a mechanism.

Weber’s law applies to all sensory modalities – sight, sound, taste, smell, and tactile sense. For any sensory stimulus there is a minimum difference that a person can notice. For example, if you are visually comparing the length of two lines trying to determine which one is longer, or if you are holding two weights and trying to determine which one is heavier. There is a minimum difference that is necessary to be able to notice. Experimentally this means there is a relationship between the ratio of the difference and the probability of determining the correct answer.

So if you are trying to determine which light is brighter, an experiment may determine that for lights of 100 and 110 lumens there is a 75% chance of correctly detecting which light is brighter. What Weber’s law states is that one this relationship is determined, it holds true no matter what the absolute value of the stimulus is, as long as the ratio is the same. So for lumens of 200 and 220, or 1000 and 1100, there would still be a 75% probability of being correct. The only thing that matters is the ratio.

As you might expect, there is a lot of nuance to the law, such as subtle variations in the math and differences between vertebrates and insects, etc., which I won’t get into. They are not important for the current discussion, but know that they exist.

This observation was made about 200 years ago by Ernst Heinrich Weber. The eponymous law is referred to as a psychophysical law, because it describes mental behavior with strict mathematical precision. Weber’s law has been endlessly replicated, and holds true for many different animal species and different sensory modalities. The ratio is always the same within a specific task. It appears to be universal, which suggests to many neuroscientists that there must be an underlying reason. There has to be something about the way neurons process sensory information regarding intensity that results in Weber’s law. This has led to many hypotheses, mostly mathematical models of information processing.

The problem has been that no one could think of a way to test the various models. This is always a huge challenge in science. Hypotheses are a dime a dozen – what is valuable is a hypothesis that can be tested, especially if it can be tested in an objective and practical way, and one that will distinguish it from all the other hypotheses.

We don’t have that yet for Weber’s law, but recently a team of neuroscientists have added another piece to the puzzle. They tested another dimension to the phenomenon – decision making time. They exposed rats to sounds in each ear, one ear slightly louder than the other. Rats, like humans, will instinctively orient their heads toward a sound, so this can be used as a behavioral method for determining when the rats have noticed which ear has the louder sound. First, they replicated Weber’s law with this setup – the rats could notice which sound is louder based entirely on the ratio of the difference, not the absolute intensity.

But what they also did was record how long it took them to make the decision. They found that the louder the sounds, the shorter the decision making time. Further, there was a precise mathematical relationship between absolute intensity and decision making time. This means that once they determined the relationship, they could predict the decision making time at any intensity, as long as the ratio of the difference was held constant.

The researchers then replicated this experiment in humans, with similar results. Finally they analyzed data collected by other researchers looking at olfactory discrimination in rats, again with the same results. This is still a long way off from being confirmed through replication, and also from being established as universal. So far we have two species and two sensory modalities. We will need many more experiments to see how reliable and how widespread this new rule is. The researchers are calling their proposed new rule, Time-Intensity Equivalence in Discrimination’ (TIED).

Assuming this new observation (TIED) is correct, can this be used to determine which of the many proposed models are more likely to be correct. A scientific model is used to simulate a complex system, to see if we understand all of the component parts and how they interact. Models are tested against what is already known, and at the very least they are only valid if they correctly produce results that match this known reality. So up until now, sensory processing models only had to match Weber’s law, which is not very constraining. This means that many models could potentially fit.

Now there is a new piece of information that the models can be tested against. If a model also fits TIED then it may be closer to reality than one that does not fit TIED. The researcher tested one of the simplest models of Weber’s law against TIED and found that it fit very precisely. This was a good proof of concept.

Again, we are a long way away from having an established scientific theory that explains how vertebrate brains process sensory information in such a way as to produce all observed phenomena and experimentation. But this new research may, if validated, take us one step closer. We now have two criteria instead of one to test our models. That may not sound like much, but it can theoretically be a huge advantage. Having two tests allows for triangulation, so can be much more constraining than just one test. At the very least TIED may allow neuroscientists to dispense with many of the existing models, and narrow the choices considerably.

The best research produces more questions than answers and inspires further research. I think this study fits the bill. There is clearly a lot of research that now needs to be done, to see if the TIED rule holds, and across how many species and sensory modalities. Further, theoreticians have new data to plug into their models.

The research also may inspire other researchers to think along similar lines – what other aspects of Weber’s law can we look at? Decision making time added a new dimension, are there others to consider?

For example, I found a study that shows that Weber’s law does not hold for subjects with autism. Rather than scaling with intensity, perception decreased linearly with intensity. People with autism have long been known to have altered perception, so this is not entirely surprising. Perhaps, as we learn more about what is different between the typical brain and the autistic brain, we can compare this to our models of Weber’s law. This is another piece to the puzzle.

This research will also likely be helped (perhaps transformed) by the development of more and more accurate and sophisticated computer models of vertebrate brains. Once we have a virtual human brain, we can tweak the parameters and see what happens. We may be able to completely replicate Weber’s law just with computer algorithms.

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