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Mathematical psychology is a form of mathematical modeling applied to psychological concepts and research. It is used to study and draw conclusions on motor processes, task performance, and quantifiable behavior. The application of mathematical psychology is utilized in various approaches to the science of the mind, including the fields of clinical psychology, cognitive psychology, and social psychology. Mathematical psychology draws its unique approach from classic studies of math and psychology as well as physics and biology.
The roots of modern mathematical psychology can be traced to two 19th century researchers, physician Ernst Heinrich Weber and psychologist Gustav Theodor Fechner. These two individuals were the first to study psychology from a mathematical perspective, considering issues of weight, sound, and vision on various psychological processes. The two men devised the Weber-Fechner Law, which aimed to illuminate the bond between the physicality of a particular stimuli and how that stimuli is perceived by the individual.
In addition to the Weber-Fechner model of mathematical psychology, the Stevens' Power Law is another commonly utilized approach to the science. It is based on the same general ideas as Weber and Fechner's format, but Stanley Smith Stevens expanded the technique to include other variations. The additional sensations Stevens included in his law encompass a wider berth of psychological experience, such as brightness, loudness, and taste. Stevens then added measurements to these sensations in order to better deduce how they affect an individual's experience.
A more basic type of mathematical psychology is the signal detection theory. In this theory, researchers study how the brain measures and distinguishes noises from signals. This approach is primarily used by psychologists who are seeking to understand how the brain makes the decisions it does in unsure or tentative situations. For example, all human brains have the same general shape, and when a tumor forms on the brain, it can alter that general shape. A physician examines the shape and scope of the tumor, and, relying on his or her training and instinct, is able to make decisions on how to treat the tumor.
There are several other widely utilized models of mathematical psychology. These include stimulus identification approaches, such as the study and measurement of neural networks, simple decision making models, and the gauging of error response times. The study can also be applied to how the brain learns, deducing with mathematical precision the various ways the brain is able to absorb, retain, and disseminate information.