The first experimental psychology laboratory (a predecessor of modern cognitive psychology) was established in Germany by Wilhelm Wundt, who applied Donders' ideas by building variety of clever machines capable of measuring different type of human responses and their reactions to various stimuli.
While the efforts of Wundt's laboratory were directed towards conscious human experiences (in line with the work of Fechner and Weber on the intensity of stimuli), the United Kingdom research group led by Francis Galton â a cousin of famous Charles Darwin - had focused its efforts on individual differences between humans using objective psychological parameters. Later James McKeen Cattell has adopted the Galtonâs methods and has created the foundation of Psychometrics and, ultimately of mathematical psychology.
The WWII gave a tremendous boost to developments in engineering, mathematical logic, computability theory, computer science, mathematics, information theory and the military applications of encryption and code breaking. All of this created the need to understand human performance and its limitations in those areas. Many experimental psychologists, mathematicians, engineers, physicists, and economists started to work together creating the mixture of different disciplines out of which mathematical psychology arose at the beginning of 50s and 60s. The developments in signal processing, information theory, linear systems, filter theory, game theory, stochastic processes and mathematical logic flourished immensely giving birth to Cybernetics, Artificial Intelligence and other disciplines in which psychological thinking was taking a major role.
The bell curve galton-- My close friend V. Niederhoffer is a huge proponent of Galton, going so far as naming one of his children Galt. surf
In 1950 a couple of ground breaking white papers on learning theory have appeared in âPsychological Reviewâ magazine. The paper by Bush and Mosteller that had introduced the linear operator approach to learning and the Estesâs paper dedicated to the stimulus sampling helped to establish the essential techniques of data processing in learning experiments. The 50s have produced a surge in mathematical theories of psychological processes. Luce's theory of choice, Tanner and Swets' introduction to the signal detection theory and Miller's approach to information processing are just a few examples of the information theories that were fueled by the USSR / US space race. As the result, by the end of the 50s, the number of mathematical psychologists had increased dramatically.
Among them was an English psychiatrist and a pioneer of cybernetics - W. Ross Ashby â whose contributions to the study of complex systems and to mathematical psychology in general cannot be overstated. It is a shame that his two groundbreaking books - âDesign for a Brainâ and âAn Introduction to Cyberneticsâ are still not very well known to general public and to even many scientists in the field of mathematical and cognitive psychology.
William Ross Ashby started working in 1930 as a Clinical Psychiatrist in the London County Council. From 1936 until 1947 he was a Research Pathologist in the St. Andrew's Hospital in Northampton in England. From 1945 to 1947 he served in India where he was a Major in the Royal Army Medical Corps. Between 1947 and 1959 he served as a Director of Research of the Barnwood House Hospital in Gloucester. In 1960 he went to the United States and became a Professor, Depts. of Biophysics and Electrical Engineering, University of Illinois until his retirement in 1970. Ross Ashby was one of the original members of the Ratio Club - a small informal dining club of young psychologists, physiologists, mathematicians and engineers who met to discuss issues in cybernetics and psychology. The club was founded in 1949 by the neurologist John Bates and continued to meet until 1958. Earlier, in 1946, Alan Turing wrote a letter to Ashby suggesting the use of Turing's Automatic Computing Engine (ACE) for his experiments instead of building a special machine. As the result, the Ashbyâs famous âHomeostatâ was born in 1948. Ashbyâs abilities to use formal mathematical equations to describe psychological aspects of our decision making processes were significantly ahead of his time. His astonishing âLaw of Requisite Varietyâ that he first published In his âAn Introduction to Cyberneticsâ is still one of the corner stones of todayâs science of complex systems; it has influenced and inspired countless researchers that later became major contributors to the various fields of Artificial Intelligence, cybernetics and psychology. Scientists like Stafford Beer who applied the Law of Requisite Variety to create the all-important Viable System Model, Gregory Chaitin who established the algorithmic information theory are just a few examples of Ashbyâs followers that have reshaped the field of Cybernetics.
For the purpose of creating tools that are capable of enhancing (amplifying) the abilities of stimuli detection mathematical and cognitive psychologists often focus on how a detecting system will process a signal, and where its threshold levels will be. Once a signal detection model is capable of explaining how changing the threshold will affect the ability to discern the stimuli it could be effectively used to create various methods of enhancing the stimuli detection process in both the operator and the machine. When the detecting system, however, is a human being, experience, anticipation, intuition, expectations, physiological state, and other factors can affect the efficiency and the accuracy of the stimuli detection process. For instance, a blind man can easily detect many of the sound patterns that normally are not sensed by an average person. By efficiently detecting and recognizing those subtle sounds a blind person could create a fairly accurate perception of his/her environment even without using visual receptors. By studying the ways of how our perception is formed mathematical and cognitive psychology offer unique approaches to creating many practical tools. Additionally, it provides formal methods for systematically enhancing such âillusiveâ human abilities as intuition, anticipation, skill development and associative pattern recognition.
The very latest significant boost to the scientific methods of mathematical and cognitive psychology came in 1990s from the development of Functional Magnetic Resonance Imaging (fMRI). fMRI is a technique for measuring brain activity. It works by detecting the changes in blood oxygenation and flow that occur in response to neural activity; it can be effectively used to produce activation maps showing which parts of the brain are involved in a particular mental process. Because of fMRI psychologists have received an unprecedented opportunity to study the working brain by non-invasive, accurate instruments. Thanks to the widely published results of brain scans many researchers (including myself) could use the fMRI images in their research even without the direct access to those expensive machines. http://www.bbc.co.uk/news/science-environment-21487016
Overall, both mathematical and cognitive psychology are a fairly young sciences, however, by utilizing many technological advances in computer engineering, Internet, signal analysis and mathematics it is one of the fastest and, in my opinion, the most promising areas of modern science. In upcoming posts we will be talking about many experiments and tools that were designed and performed using the modern achievements in cognitive and mathematical psychology.