Paper section: Results §3.1 · Notebooks:2.1, 2.2, 2.3
Overview
This section documents the primary measurement approach: height-to-width (h/w) ratios derived from the binary silhouettes of 94,936 cuneiform tablets. It is the simplest possible shape descriptor — a single number — yet it carries the clearest long-run historical signal in the corpus.
Why ratios, and why log-scale?
Physical tablet dimensions (height and width in cm) are not systematically available in the CDLI catalogue. We therefore use pixel-based h/w ratios from the photographs, which encode relative proportions rather than absolute measurements.
We work with the natural log of the h/w ratio throughout for statistical analyses. The log transformation:
Is symmetric around 0 (log(1) = 0 = square; portrait positive, landscape negative)
Corrects the asymmetry of the raw ratio (portrait side: 1 → ∞; landscape side: 0 → 1)
Enables additive decomposition of shifts
All medians and IQR in tables are reported in the original ratio scale.
The three-millennium shift
The core finding: the median h/w ratio of the corpus falls from 1.125 (Ur III, most representative 2nd-millennium period) to 0.741 (Neo-Babylonian) and 0.786 (Achaemenid), a log-ratio shift of approximately −0.27 over the 2nd-to-1st-millennium transition.
Code
import pandas as pdimport matplotlib.pyplot as pltimport matplotlib.image as mpimgimport osfig_path ="../../paper/figures/fig_ratio_by_period_log.pdf"if os.path.exists(fig_path):# Display the pre-computed figurefrom IPython.display import Image# Convert PDF to PNG for display if needed img = plt.imread(fig_path) if fig_path.endswith('.png') elseNoneprint(f"Figure available at: {fig_path}")print("Run notebook 2.2 to regenerate.")else:print("Figure not found. Run notebook 2.2 to generate.")
Figure available at: ../../paper/figures/fig_ratio_by_period_log.pdf
Run notebook 2.2 to regenerate.
Figure 1
Figure 2: Height-to-width ratio by period (log scale)
The portrait-to-landscape transition is robust across all three measurement approaches. The Spearman rank correlation between chronological rank and median log-ratio is statistically significant (p < 0.001), and the same directional signal emerges from three independent measurement regimes.
Note
Next:Standardization Scale → — how the CV of h/w ratios measures institutional control over scribal format.
Source Code
---title: "1 · Corpus & Height-to-Width Ratios"subtitle: "The three-millennium portrait-to-landscape shift"sidebar: analyses---> **Paper section:** Results §3.1 · **Notebooks:** `2.1`, `2.2`, `2.3`## OverviewThis section documents the primary measurement approach: height-to-width (h/w) ratiosderived from the binary silhouettes of 94,936 cuneiform tablets. It is the simplestpossible shape descriptor — a single number — yet it carries the clearest long-runhistorical signal in the corpus.## Why ratios, and why log-scale?Physical tablet dimensions (height and width in cm) are not systematically availablein the CDLI catalogue. We therefore use pixel-based h/w ratios from the photographs,which encode relative proportions rather than absolute measurements.We work with the **natural log of the h/w ratio** throughout for statistical analyses.The log transformation:- Is symmetric around 0 (log(1) = 0 = square; portrait positive, landscape negative)- Corrects the asymmetry of the raw ratio (portrait side: 1 → ∞; landscape side: 0 → 1)- Enables additive decomposition of shiftsAll medians and IQR in tables are reported in the **original ratio scale**.## The three-millennium shiftThe core finding: the median h/w ratio of the corpus falls from **1.125** (Ur III,most representative 2nd-millennium period) to **0.741** (Neo-Babylonian) and **0.786**(Achaemenid), a log-ratio shift of approximately −0.27 over the 2nd-to-1st-millenniumtransition.```{python}#| label: fig-ratio-period#| fig-cap: "Height-to-width ratio distributions by period, log scale. Vertical dashed line at log(1) = 0 marks the square/isometric boundary. Blue = portrait-dominant periods (median > 1); red = landscape-dominant (median < 1)."#| code-fold: trueimport pandas as pdimport matplotlib.pyplot as pltimport matplotlib.image as mpimgimport osfig_path ="../../paper/figures/fig_ratio_by_period_log.pdf"if os.path.exists(fig_path):# Display the pre-computed figurefrom IPython.display import Image# Convert PDF to PNG for display if needed img = plt.imread(fig_path) if fig_path.endswith('.png') elseNoneprint(f"Figure available at: {fig_path}")print("Run notebook 2.2 to regenerate.")else:print("Figure not found. Run notebook 2.2 to generate.")```{#fig-ratio-period}## Period summary statistics```{python}#| label: tbl-period-stats#| tbl-cap: "Period-level h/w ratio statistics: median, 95% bootstrap CI, IQR, CV, and orientation classification."import pandas as pddf = pd.read_csv("../../paper/figures/period_summary_stats.csv")df['Median'] = df['Median'].round(3)df['IQR'] = df['IQR'].round(3)df['CV'] = df['CV'].round(3)df['95% CI'] = df.apply(lambda r: f"[{r['CI_95_low']:.3f}, {r['CI_95_high']:.3f}]", axis=1)display_cols = ['Period', 'n', 'Median', '95% CI', 'IQR', 'CV', 'Orientation']df[display_cols].style.background_gradient(subset=['CV'], cmap='YlOrRd') \ .format({'n': '{:,}'}) \ .set_caption("Physical pixel-ratio statistics by period")```## Diachronic trend```{python}#| label: fig-diachronic#| fig-cap: "Diachronic trend in median log h/w ratio with Spearman rank correlation. Each point = one period."import matplotlib.image as mpimgprint("Figure: ../../paper/figures/fig_diachronic_trend.pdf")```{#fig-diachronic}## Three-method convergenceThe same trend is observed across three independent measurement strategies:- **Physical pixel ratio** (this notebook, from bounding-box pixel measurements)- **Image-derived pixel ratio** (notebook 2.3, larger subsample)- **VAE dimension X2** (notebook 2.4, latent-space coordinate; Spearman ρ = +0.655, *p* = 0.001){#fig-three-method}## Key resultThe portrait-to-landscape transition is robust across all three measurement approaches.The Spearman rank correlation between chronological rank and median log-ratio isstatistically significant (*p* < 0.001), and the same directional signal emergesfrom three independent measurement regimes.::: {.callout-note}**Next:** [Standardization Scale →](02-standardization.qmd) — how the CV of h/w ratiosmeasures institutional control over scribal format.:::