The research studied the role of perceptual factors in Pythagorean definition of even and odd as opposite numbers. The purpose was to analyze whether this opposition is based upon precise visual features of the Pythagorean figural numbers (gnomons). The ten pairs of opposites used by the Pythagoreans and reported by Aristotle (Methaphysics A5, 985b, 22) were used as scales of a semantic differential. Participants were 66 undergraduate students. Three conditions were studied within subjects: words “odd” and “even”; rectangular and squared dot lattices, representations of the square and oblong Phytagorean numbers; rectangular and squared margins, representations of the two right angled segments composing the gnomon. The results demonstrate that the semantic description of even and odd, as words, turn out to be opposite in the ten scales, but in an inverted direction with respect to the one predicted by Pythagoreans (even is polarized in the positive sides of the scales, while odd is in the negative), confirming the influence of cultural factors. When the description is based on the visual structures, the opposition turned out to be visible only in the gnomonic margins and not at the dot lattices. It is argued that this result experimentally supports the hypothesis (Zellini, 1996) that the origin of number is in the Greek idea of ratio as diastema (ratio between length), better than in the idea of ratio as logos (ratio between discrete quantity).

THE VISUAL STRUCTURE OF EVEN AND ODD. PERCEPTUAL ORIGIN OF THEIR OPPOSITION.

BIANCHI, IVANA;
2001

Abstract

The research studied the role of perceptual factors in Pythagorean definition of even and odd as opposite numbers. The purpose was to analyze whether this opposition is based upon precise visual features of the Pythagorean figural numbers (gnomons). The ten pairs of opposites used by the Pythagoreans and reported by Aristotle (Methaphysics A5, 985b, 22) were used as scales of a semantic differential. Participants were 66 undergraduate students. Three conditions were studied within subjects: words “odd” and “even”; rectangular and squared dot lattices, representations of the square and oblong Phytagorean numbers; rectangular and squared margins, representations of the two right angled segments composing the gnomon. The results demonstrate that the semantic description of even and odd, as words, turn out to be opposite in the ten scales, but in an inverted direction with respect to the one predicted by Pythagoreans (even is polarized in the positive sides of the scales, while odd is in the negative), confirming the influence of cultural factors. When the description is based on the visual structures, the opposition turned out to be visible only in the gnomonic margins and not at the dot lattices. It is argued that this result experimentally supports the hypothesis (Zellini, 1996) that the origin of number is in the Greek idea of ratio as diastema (ratio between length), better than in the idea of ratio as logos (ratio between discrete quantity).
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11393/110802
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