Weber's Law is the most general and best proven quantitative rule in Psychophysics, the science that establishes relationships between the strength of physical stimuli and the sensations they generate in the mind. Although it was enacted 200 years ago, there was still no clear way to choose an explanation of this law among the many that have been proposed. But now, a team of scientists has shown that Weber's Law can be understood as the consequence of a new law of psychophysics that describes how long it takes sensory decisions to be made. The new rule allows for a robust and unique explanation of Weber's law.
For centuries, the world of the mind and the physical world were regarded as fundamentally distinct. While the movement of inanimate objects could be measured and therefore predicted with the help of mathematics, the movements of living organisms – that is, their behavior – seemed to be shaped by different forces, under the control of the will.
About 200 years ago, German physician Ernst Heinrich Weber made a seemingly innocuous observation. This later led to the birth of Psychophysics, the science that relates physical stimuli from the outside world to the sensations they evoke in a person's mind.
Weber asked his experimental subjects to decide which of two slightly different weights was heavier. From the results of his experiments, he found that the probability of a person making the right choice depends only on the ratio between the weights.
For example, if an individual gets it right 75% of the time when comparing a 1 kg weight and a 1,1 kg weight, he will also get it right 75% of the time when comparing a 2 kg weight and a 2,2 kg weight – and, more generally when comparing any pair of weights where one of them is 10% heavier than the other. This simple and precise rule opened the door to the quantification of behavior in terms of mathematical “laws”.
Weber's observations have since been confirmed in all sensory modalities and in many animal species, leading to what has come to be known as Weber's Law. It is the oldest and most strongly proven law of Psychophysics.
The laws of Psychophysics describe precise rules of perception and are important because they can be used to obtain mathematical explanations of behavior in terms of brain processes, just as the precise patterns of movement of planets in the sky were useful for understanding gravitation.
Many explanations of Weber's Law have been proposed and, although they all succeed in describing Weber's results, no experimental approach has been found to identify which of these models is right. The puzzle of the mathematical explanation of Weber's law has remained unsolved.
Now, a team of scientists from the Champalimaud Center in Lisbon, Portugal, has discovered that Weber's Law can be described as the consequence of a new law of Psychophysics that involves the time it takes to choose and not just the outcome of the decision. The team showed that this new rule is sufficient to obtain a unique and robust mathematical model that describes the cognitive process underlying Weber's Law. Their results were published in the journal NatureNeuroscience.
time is key
In this new study, Alfonso Renart, the principal investigator who led the work, and his team trained rats to discriminate between two sounds of slightly different intensities. For this they made tiny headphones, specially adapted to the rats' heads, and used them to transmit sounds simultaneously to both the animals' ears.
On each attempt, the volume of sound reaching one ear was slightly louder than the other. The mouse's task was to communicate its decision by orienting its head to the side where the loudest sound was coming from. “This is a natural behavior in rats, because they orient their heads towards the source of the sound, just like us”, explains José Pardo-Vazquez, one of the co-authors of the study. Rats were able to hear the sounds for as long as it took to decide. Therefore, each attempt provided a decision and a decision-making time.
“Our experiments confirmed that the animals' behavior followed Weber's Law,” says Pardo-Vazquez. His ability to determine which of the two sounds was louder just depended on the ratio between the intensities of the sounds. When the mouse compared the intensities of two soft sounds, its correct response rate was the same as when the two sounds were louder – as long as both pairs of sounds had the same intensity ratio.
Next, the team began to analyze in detail the time it took the rats to make their choices – a step that turned out to be crucial. “In general, Weber's Law studies focused on the accuracy of sound discrimination – which was what Weber had actually observed,” explains Pardo-Vazquez.
"Surprisingly, the time needed to decide has been very little studied."
The team then realized that the reaction times and the intensity of the pair of sounds were linked – the louder the sounds, the shorter the reaction time. What's more, scientists showed that the nature of this link was unique and mathematically accurate. This made the decision times observed, for example in the discrimination between two soft sounds, to be exactly proportional to the decision times measured when the subject discriminated two loud sounds – as long as their relative intensities were constant.
Beyond Weber's Law
The authors had, in fact, discovered a new “law of Psychophysics”, which they called “Time-Intensity Equivalence in Discrimination” (in English, Time-IntensityEquivalence in Discrimination or TIED), as it linked the global intensity of a pair. of sounds to the time it took to discriminate them. TIED is more stringent than Weber's Law, not only because it relates in terms of the accuracy of sound pair discrimination, but also in terms of the associated decision times. “The accuracy of this relationship between decision times in our experiments is unbelievable,” says Pardo-Vazquez. "It's not often animal behavior can be described with such a level of mathematical precision."
To determine whether TIED was also present under different experimental conditions, the team performed the same type of experiments on humans, obtaining similar results. The scientists also analyzed experiments carried out by other groups, on rats, where the animals had to perform olfactory discrimination when exposed to a mixture of smells. Again, the results were similar. “It is still too early to say that TIED is as general as Weber's Law, but the fact that we have obtained the same results in two species and in two sensory modalities is an encouraging first step”, concludes Pardo-Vazquez.
Looking for the right model
Dozens of mathematical models have been proposed over the years to explain Weber's Law, but until now there has been no clear experimental way of distinguishing them. Now, according to this study, TIED allows us to take that step. The analysis performed revealed that, to be consistent with TIED, the mathematical model of the sensory discrimination task would have to satisfy a set of strict conditions.
“It was fantastic,” says Juan Castiñeiras, co-author of the study. “TIED placed constraints on the universe of possible explanations and, therefore, resolved the ambiguity between the many models proposed to explain Weber's Law”. A model previously proposed by psychologist Stephen Link in the late 1980s was close to solution, but it lacked an important condition that described how the intensity of sensory stimuli is encoded by the activity of sensory neurons.
The final step was to apply this set of conditions to build a model and test how accurately this model accounted for the behavior of rats. “We analyzed the simplest model, with the fewest possible parameters,” explains Castiñeiras. And when they chose the values of these parameters in a way that maximized the similarity to the behavior of the rats, the scientists found that the model “fitted” the data remarkably, with almost zero error. “Even this simple model captured everything we could measure well. This made us much more confident that our model actually describes something true about how perception works,” says Renart.
guaranteed advance
These results are remarkable in their field due to the accuracy of both the new psychophysical law and the mathematical model that describes the experimental data. “Although less frequently observed in Biology and in the study of behavior than in Physics, precise experimental results allow precise explanations that resolve previous ambiguities and, therefore, constitute an advance”, says Renart. For example, the team's results suggest that one of the main theories in Psychophysics is not adequate to describe TIED.
“The production of mathematical explanations that exclude competing theories is very rare in Neurosciences, because there is always the possibility of slightly modifying a model to make it compatible with experimental data”, emphasizes Castiñeiras. “We showed that a very influential theory of Psychophysics (called Detection Theory) did not allow for modeling decision times and that, therefore, it could not describe TIED. It missed the essence of the explanation of Weber's Law”.
One of the scientists' next goals is to understand how the mathematical model they identified is implemented by the brain: "We want to systematically determine which brain areas are relevant to our sensory task and how the neurons in these circuits carry out the various computational elements of the model" , concludes Renart.
Author Champalimaud Center
Science in the Regional Press – Ciência Viva
Comments