## Kolmogorovs Axiomstheory

The Soviet mathematician Andrei Nikolaevich Kolmogorov (1903-1987) formulated the axiomatic theory of probability (also known as Kolmogorov's axioms) that provides four propositions concerning probabilities from which all major theorems may be derived: the probability of any event is equal to, or greater than, zero; the probability of a particular event is 1.00; if A and B are two mutually exclusive events (cf., principle of the excluded middle or excluded middle law - the law/principle which states that for any proposition p, the proposition p or not p is true according to logical necessity), then the probability of the disjunction (i.e., the probability of either A or B occurring) is equal to the sum of their individual probabilities; and the probability of a conjunction of two events A and B (i.e., the probability that both A and B occur) is equal to the probability of A (assuming that B occurs) multiplied by the probability of B. See also BOOLEAN SET THEORY; DECISIONMAKING THEORIES; EXCLUDED MIDDLE, PRINCIPLE OF; PROBABILITY THEORY/LAWS; SET THEORY. REFERENCE

Kolmogorov, A. N. (1933). Grundbegriffe der wahrscheinlichkeitsrechnung. Berlin: Springer.

KONIG'S THEORY. See COLOR VISION, THEORIES/LAWS OF.

KORTE'S LAWS. The German Gestalt psychologist Adolf Korte (1915) developed a series of general statements or laws that describe the optimal conditions for apparent motion when demonstrating the phi phenomenon (i.e., perceived motion produced when two stationary lights are flashed successively, where the sensation of apparent movement of the light from the first location to the second location occurs if the time interval between the flashing of the two lights is about 150 milliseconds). Korte's principles of apparent movement (phi) are: (1) when the intensity of the lights is held constant, the time interval for optimal phi varies directly with the distance between the stimuli; (2) when time is held constant, the distance for optimal phi varies directly with the intensity of the lights; and (3)

when distance between the stimuli is held constant, the intensity for optimal phi varies inversely with the interval of time that is used. Thus, Korte's laws state that it is more difficult to perceive apparent motion or phi when the spatial separation between lights is too wide, when illumination is too low, and when interstimulus interval is too short, even though decrements in one (or two) of the variables can be adjusted by increments in the other(s). The phi phenomenon may be observed in non-laboratory settings such as in motion pictures ("movies"), television, animated displays, and various neon sign displays where the sensation of motion is overwhelming and "irresistible." Korte's laws have been revised and extended in recent experiments (cf., Kolers, 1964), and several other stimulus variables that determine optimal apparent movement have been described. See also APPARENT MOVEMENT, PRINCIPLES/THEORIES OF; PHI PHENOMENON; UNCONSCIOUS INFERENCE, DOCTRINE OF. REFERENCES

Stratton, G. (1911). The psychology of change: How is the perception of movement related to that of succession? Psychological Review, 18, 262-293.

Korte, A. (1915). Kinematoskopische untersuchungen. Zeitschrift fur Psychologie, 72, 193-296. Neuhaus, W. (1930). Experimentelle untersuchung deer scheinbewegung. Archiv fur die Gesamte Psychologie, 75, 315-458. Fernberger, S. (1934). New phenomenon of apparent visual movement. American Journal of Psychology, 46, 309314.

Neff, W. (1936). A critical investigation of the visual apprehension of movement. American Journal of Psychology, 48, 1-42.

Kolers, P. (1964). The illusion of movement.

Scientific American, 211, 98-106. Graham, C. (1965). Perception of movement.

In C. Graham (Ed.), Vision and visual perception. New York: Wiley. Bell, H., & Lappin, J. (1973). Sufficient conditions for the discrimination of mo tion. Perception & Psychophys-ics, 14, 45-50.

Pantle, A., & Picciano, L. (1976). A multista-ble movement display: Evidence for two separate motion systems in human vision. Science, 193, 500-502. Beck, J., Elsner, A., & Silverstein, C. (1977).

Position uncertainty and the perception of apparent movement. Perception & Psychophysics, 21, 33-38.

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