## Zeilers Theory See Spences Theory

ZEISING'S PRINCIPLE. This generalization refers to a term - golden section - that was used by the German mathematician Adolph Zeising (1810-1876), and called attention to the aesthetic value of the geometric relationships inherent in a rectangle. That is, the golden section is the division of a line or area into two parts, or the relations of the sides of a rectangle, in such a manner that the ratio of the smaller to the larger equals the ratio of the larger to the whole. This principle of proportion was investigated experimentally by the German physicist/mathematician/philosopher Gustav Fechner (1801-1887) in the area called experimental aesthetics. Fechner's seminal research on preferences for shapes gave experimental aesthetics its "reductionistic" quality (i.e., examining aesthetics from "below" from a structural point of view). Investigations have been made by researchers for an aesthetic formula (cf., Birkhoff, 1933). In one case, the aesthetic measure (M) of balance or unity (represented by the number 1) is defined as the ratio of order (O) to complexity (C): in the resulting formula, M = O/C, the various components of an artwork can be physically specified, measured, and evaluated where the closer it is to 1, the more "harmonious" the object. Zeising 's principle attempts to answer the persistent question in aesthetics concerning the dimensions of preferred shapes such as encompassed in the concept of the golden section. See also EYE PLACEMENT PRINCIPLE; FECHNER'S LAW; GESTALT THEORY/LAWS; WEBER'S LAW. REFERENCES

Zeising, A. (1855). Aesthetische forschungen.

Frankfort, Germany: Breitkopf & Haertel.

Zeising, A. (1884). Der goldene schnitt. Leipzig: Breitkopf & Haertel. Fechner, G. (1897). Vorschule der aesthetik.

Leipzig: Breitkopf & Haertel. Archibald, R. C. (1920). Notes on the logarithmic spiral, golden section, and the Fibonacci series. In J. Ham-bridge (Ed.), Dynamic symmetry. New Haven, CT: Yale University Press.

Birkhoff, G. (1933). Aesthetic measure. Cambridge, MA: Harvard University Press.

Valentine, C. (1962). The experimental psychology of beauty. London: Methu-en.

Zusne, L. (1970). Visual perception of form.

New York: Academic Press. Hintz, J. M., & Nelson, T. M. (1976). Golden section: Reassessment of the peri-metric hypothesis. American Journal of Psychology, 83, 126-129. Child, I. (1978). Aesthetic theories. In E. Car-terette & M. Friedman (Eds.), Handbook of perception. Vol. 10. New York: Academic Press. Plug, C. (1980). The golden section hypothesis. American Journal of Psychology, 93, 367-387. McWhinnie, H. J. (1987). A review of selected research on the golden section hypothesis. Visual Arts Research, 13, 73-84.

Davis, S. T., & Jahnke, J. C. (1991). Unity and the golden section: Rules for aesthetic choice? American Journal of Psychology, 104, 257-277.

ZEITGEIST THEORY. See NATURALISTIC THEORY OF HISTORY.

ZEN BUDDHISM. See BUDDHISM/ZEN BUDDHISM, DOCTRINE OF.

ZENO, ACHILLES ARGUMENT OF. The; Greek philosopher Zeno of Elea (early 5th century B.C.) was the author/originator of the sophism (i.e., a clever and plausible but fallacious argument or form of reasoning) called the Achilles argument to prove, theoretically, that motion is impossible. According to the argument, Achilles (who was the fastest possible runner) could never overtake the tortoise (who was the slowest moving animal) if the tortoise had ever so short a start. The reasoning behind the argument is that because the distance between them consists of an infinite series of parts, and when Achilles, by traversing one of these parts, comes to where the tortoise was, the latter will always have gone further. A variation on Zeno's famous "Achilles-tortoise" philosophical paradox or scenario is the equally-paradoxical or specious argument that an arrow shot from a bow will never truly reach its target because, theoretically, it will always have gone only half the existing distance to the target at any given moment. See also PROBLEM-SOLVING AND CREATIVITY STAGE THEORIES. REFERENCE

Baldwin, J. M. (Ed.) (1901-1905). Dictionary of philosophy and psychology. New York: Macmillan.

ZIPF'S LAW. This proposition was developed by the American philologist George Kingsley Zipf (1902-1950), and states that an equilibrium exists between uniformity and diversity in examining various psychological phenomena. In general, Zipf's law describes the relationship between the frequency with which a certain event occurs (e.g., the frequency of usage of a word in a language) and the number of events that occur with that frequency. In particular, Zipf's law states that when examining certain aspects of language, it is predicted that there are a very large number of very short words (e.g., "auto") that occur with high frequency and progressively fewer longer words (e.g., "automobile") that occur with lower frequency. Zipf hypothesized that such uniformities or "tendencies" in language usage are the result of a biological principle of least effort. Although this latter notion has not been validated by other researchers (these uniformities are now known to be merely the necessary result of particular stochastic processes), Zipf's linguistic hypothesis that frequency of word usage and word length are inversely related seems to be a pervasive phenomenon of language usage, especially in the present age of computers and the perceived need for rapid communication. See also LEAST EFFORT, PRINCIPLE OF. REFERENCES

Zipf, G. K. (1935). The psycho-biology of language. Boston: Houghton Mif-flin.

Zipf, G. K. (1945). The repetition of words, time-perspective, and semantic balance. Journal of General Psychology, 32, 127-148; 33, 251-256.

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