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Introspection is the examination of one's own conscious thoughts and feelings. [1] In psychology, the process of introspection relies on the observation of one's mental state, while in a spiritual context it may refer to the examination of one's soul. [2]
Mathematical psychology is an approach to psychological research that is based on mathematical modeling of perceptual, thought, cognitive and motor processes, and on the establishment of law-like rules that relate quantifiable stimulus characteristics with quantifiable behavior (in practice often constituted by task performance).
The introspection illusion is a cognitive bias in which people wrongly think they have direct insight into the origins of their mental states, while treating others' introspections as unreliable. The illusion has been examined in psychological experiments, and suggested as a basis for biases in how people compare themselves to others.
The surface structure is the way a problem is framed. The deep structure is the steps for the solution. For example, when a math story problem changes contexts from asking how much it costs to reseed a lawn to how much it costs to varnish a table, they have different surface structures, but the steps for getting the answers are the same.
Clever Hans performing in 1904. Clever Hans (German: der Kluge Hans; c. 1895 – c. 1916) was a horse that appeared to perform arithmetic and other intellectual tasks.. In 1907, psychologist Oskar Pfungst demonstrated that the horse was not actually performing these mental tasks, but was watching the reactions of his trai
Differential equations are an important area of mathematical analysis with many applications in science and engineering. Analysis is the branch of mathematics dealing with continuous functions, limits, and related theories, such as differentiation, integration, measure, infinite sequences, series, and analytic functions. [1] [2]
Mathematics makes up that part of the human conceptual system that is special in the following way: It is precise, consistent, stable across time and human communities, symbolizable, calculable, generalizable, universally available, consistent within each of its subject matters, and effective as a general tool for description, explanation, and prediction in a vast number of everyday activities ...
The formula game that Brouwer so deprecates has, besides its mathematical value, an important general philosophical significance. For this formula game is carried out according to certain definite rules, in which the technique of our thinking is expressed. These rules form a closed system that can be discovered and definitively stated. [11]