Determining Greek Architectural Design Units in the Sanctuary ofthe Great Gods, Samothrace: Application of and Extensions to theCosine Quantogram Method Public

Cox, Susan Margueritte (2009)

Permanent URL: https://etd.library.emory.edu/concern/etds/8910jv15j?locale=fr
Published

Abstract

Investigations into derivations of ancient Greek architectural units of measure have been limited in their statistical rigor. The primary method to find an indivisible unit, the quantum, has been D. G. Kendall's cosine quantogram analysis (1974), used by J. Pakkanen (2002; 2004a; 2004b; 2005) to calculate quanta based on architectural components. However, no inference has been conducted beyond simple point estimation and testing a quantum's existence. We expand Kendall's method by calculating standard bootstrap confidence intervals for point estimates and introducing a likelihood ratio-based hypothesis test for the equality of quanta between buildings at the same site.

As a case study, individual block dimensions from two Doric structures are considered from the Sanctuary of the Great Gods, located on the island of Samothrace: the Dedication and the Hieron. The cosine quantogram method yielded a quantum of 0.211 m. for the Dedication (95% CI: (0.070 m., 0.352 m.)) and the quantum for the Hieron is 0.253 m. (95% CI: (0.163 m., 0.343 m.)). There is no statistically significant difference between these two quanta (p = 0.270), although in architectural terms, they differ considerably. The possibility of a 0.208-m. quantum, which indicates that the Dedication may have been designed based on the interaxial distance between columns due to a 1:10 ratio between the quantum and the interaxial space, is also explored. A 0.253-m. quantum indicates that the Hieron was probably designed with the outer dimensions in mind since the ratio between the quantum to the building's width and length at the level of the stylobate is 1:50:155. Future directions of this method are presented as well as potential applications to biology and public health.

Table of Contents

1 Introduction 1.1 History of the Site and Excavations . . . . . . . . . . . . . . . . . . . . . 1 1.2 The Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3 1.3 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 Methods 9 2.1 The Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2 Block Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.3 Quantum Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.4 Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.4.1 Cosine Quantogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.4.2 Lower and Upper Bounds of q . . . . . . . . . . . . . . . . . . . . . . . .13 2.4.3 Unrounding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13 2.5 Hypothesis Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15 2.5.1 Monte Carlo Simulations and Bootstrapping . . . . . . . . . . . . . . .19 2.6 Diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .22 2.6.1 Conversion of Linear Data to Circular/Angular Data . . . . . . . . . .22 2.6.2 Goodness-of-Fit Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.6.3 Signicance Testing for μ (κ Unknown) . . . . . . . . . . . . . . . . . . 23 2.6.4 Homogeneity between Pairs of Subsets . . . . . . . . . . . . . . . . . 23 2.7 Software Packages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24 3 Results 25 3.1 Missing Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.2 Univariate Analysis of Block Subgroups between Buildings . . . . . . .28 3.3 Comparison of Quanta between Buildings . . . . . . . . . . . . . . . . . .30 3.4 Comparison of Quanta between Block Types within Buildings . . . . .36 3.4.1 Comparison of Quanta between Block Types of the Dedication . . 36 3.4.2 Comparison of Quanta between Block Types of the Hieron . . . . . 41 3.5 Diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.5.1 Goodness-of-Fit Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.5.2 Signicance Testing for the Mean Direction Parameter, μ . . . . . . 46 3.5.3 Two-Sample Tests of Homogeneity. . . . . . . . . . . . . . . . . . . . 50 4 Discussion 51 4.1 Art Historical Implications of the Calculated Quanta . . . . . . . . . . 51 4.2 Sources of Error in Block Dimensions . . . . . . . . . . . . . . . . . . . . 56 4.3 Limitations of Previous Studies . . . . . . . . . . . . . . . . . . . . . . . .57 4.4 Limitations of This Study . . . . . . . . . . . . . . . . . . . . . . . . . . . .58 4.5 Biological Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .59 4.6 Public Health Implications . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 4.7 Future Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .61 A Appendix: SAS Program for the Cosine Quantogram Method . . . . . . 64 References 74

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