Mathematical Psychology: What It Is, And Main Representatives
Psychology draws on many other sciences. In this case, mathematics offers us a new and interesting point of view, to the point that The term “mathematical psychology” has been coined to talk about the contributions of certain authors.
We are going to see how both disciplines are intertwined and what benefits can be obtained from this relationship in order to develop different methodologies to achieve novel research in the field of studying the human mind.
Mathematical psychology is a way of conducting research in psychology based on the use of mathematical models in order to explain and predict thought processes, perception or any other psychological process. The objective would be to quantify the behavior and the stimuli that provoke it, finding the mathematical laws that underlie this relationship.
Therefore, mathematical psychology is a way to standardize psychological processes so that it is easier to measure them and be able to work with the relationships between stimulus and response, thus achieving much more precise and rigorous hypotheses and verifications. The way to quantify the individual’s behaviors is through a procedure in which they have to perform certain tasks.
The first rapprochement between psychology and mathematics took place much earlier than it may seem. They were extraordinary scientists like Galilego Galilei or Johannes Kepler, who In the 17th century they tried to verify if thought processes were governed by specific laws, just as it happened with physics. Logically, this approach was very diffuse, since psychology did not even exist as an independent science.
In the 18th century, some of the foundations on which mathematical psychology would later rest were laid. It is at this time that Blaise Pascal develops the argument of Pascal’s wager, within the theories of probability. Shortly after, Nicolas Bernoulli, for his part, developed the St. Petersburg paradox, to try to explain decision making from a mathematical point of view.
Thomas Bayes also made important advances in statistical studies of the time, proposing Bayes’ theorem, among many other contributions. Another author who continued to generate studies on which mathematical psychology would later be based is Robert Hooke. In his case, this English scientist carried out the first research on human memory, searching for predictive models.
It was in the 19th century that the great advances in psychology took place, taking on its own identity as a scientific discipline, led by the German Wilhelm Wundt, who founded the first experimental psychology laboratory It was therefore when we began to try to explain human behavior in a scientific way and therefore where mathematics made its definitive appearance to form mathematical psychology.
During these years psychophysics also developed, with authors such as Ernst Weber or Gustav Fechner, who develop Weber’s law and Fechner’s law, respectively. But even astrophysics had influence in some way on mathematical psychology. How can this be? Due to studies in which the distance at which the stars were was measured and to do so it was measured when they passed in front of the telescope.
The point is that it was observed that the reaction time of the different people in charge of taking the measurements was different. It was Friedrich Bessel the scientist who discovered these differences and developed personal equations from them in order to compensate for the characteristics of the observer who recorded the records and obtain the most precise data on the distance of the stars. Another step towards mathematical psychology.
Likewise, Hermann von Helmholtz was a prolific author who studied the speed of nerve impulses Together with Thomas Young, he developed the Young-Helmholtz theory or trichromatic theory, in which they explained how the three types of cones in the eyes perceived a specific part of the spectrum of visible light, giving rise to the color vision that we have. Humans.
Continuing with the contributions to mathematical psychology, Franciscus Cornelius Donders, Dutch author, led research to measure the time required at the brain level to perform some simple operations For his part, Johann Herbart also worked on mathematical models that could explain human consciousness, a truly ambitious work for his time.
Regarding the advances that came from England, the most notable begin with Francis Galton, a reference in the study of individual differences. In fact, Galton is one of the fathers of psychometrics. Likewise, many of the studies on the psychology of intelligence in England are based on the pioneering studies of Francis Galton.
Mathematical psychology during the 20th century
Another notable author who covers the last decades of the 19th century and the first decades of the 20th century is Charles Spearman. He is nothing less than the creator of factor analysis, a statistical system that uses variance and covariance to be able to study individual differences in a mathematical way Two others are added to this method, such as structural equation modeling on the one hand and ANOVA, or analysis of variance, on the other.
The first is the result of researcher Sewall Wright and the second was developed by Ronald Fisher. Together with factor analysis, these methods represent an important advance in the union between mathematics and psychology, crystallizing the branch of psychometrics, which is related to mathematical psychology. Psychometrics, therefore, was officially developed in the mid-1930s.
With the advances in the current of behaviorism, even more importance is given to variables such as reaction times. By then the Second World War also broke out, an event that enhances research related to mathematical science, logic or computing, concepts that apply to other sciences, such as psychology. Of course, mathematical psychology comes out stronger from this interaction.
This can be seen in the increasingly frequent use in psychology of mathematical concepts such as game theory, signal processing, filter theory, information theory or stochastic processes, among many others. Some of them had already been related in some way to psychology before, but the use of others represented a revolution in the field and a new way of doing science in the study of the human mind.
It was between the 50s and 60s when All the concepts of mathematical psychology were captured in a series of volumes and the publication of a scientific journal specialized in this branch began which meant the consolidation of it and a new and fundamental part in psychology.
Differences between mathematical psychology and psychometrics
It is important not to confuse mathematical psychology with psychometrics. Psychometrics refers to the statistical studies of quantitative measurements carried out in psychology studies On the other hand, mathematical psychology, as we have already seen, refers to the use of mathematical models that try to predict psychological phenomena such as cognitive processes.
Furthermore, psychometrics is especially responsible for explaining or classifying individual or population differences while mathematical psychology, for its part, tries to generate models that can offer an explanation for the behavior of any average individual, that is, predict the psychological behavior under certain conditions.
Likewise, psychometrics tries to find out the relationship between different variables of the population analyzed statistically. In contrast, mathematical psychology focuses on the creation of mathematical models into which all psychological phenomena recorded experimentally can fit.
This is why, although mathematical psychology has a certain relationship with psychometrics in some aspects, this link is more powerful with other branches of this science such as cognitive psychology and experimental psychology. It is also related to other aspects such as econometrics or computational neuroscience since it has in common with them the use of statistical optimization.
This question is generated by the premise that our brain, evolutionarily, must be configured to be able to deal with the different problems it encounters in an optimized way that increases the chances of overcoming them satisfactorily and with the minimum possible use of resources.
Returning to cognitive psychology, some of its most important studies, such as those that have to do with the dichotomy between limited or unlimited processing capacity, or also the different types of processing (parallel or serial, for example), are very present issues for the studies of mathematical psychology.
