2 · Standardization Scale

Coefficient of variation as a proxy for institutional scribal control

Paper section: Results §3.1 · Notebooks: 2.1, 2.2, 2.3

Overview

Beyond the directional shift in median h/w ratios, a second signal is encoded in the dispersion of those ratios: how tightly tablets in a period cluster around their period median. Eerkens & Bettinger (2001) proposed that artifact Coefficient of Variation (CV) below ~17% indicates motor-skill limits (standardization by habit), while higher CV indicates less-constrained production. We use CV as a proxy for the degree of institutional control over scribal format.

The Coefficient of Variation

For a period with median h/w ratio \(\tilde{r}\) and standard deviation \(\sigma\):

\[\text{CV} = \frac{\sigma}{\bar{r}} \times 100\%\]

where \(\bar{r}\) is the mean ratio. Lower CV = tighter clustering around the period norm = stronger scribal standardization.

Period standardization ranking

Code 
import pandas as pd

df = pd.read_csv("../../paper/figures/period_summary_stats.csv")
df_sorted = df.sort_values('CV').reset_index(drop=True)
df_sorted['Rank'] = range(1, len(df_sorted) + 1)
df_sorted['CV_pct'] = (df_sorted['CV'] * 100).round(1)
df_sorted['Median'] = df_sorted['Median'].round(3)

display_cols = ['Rank', 'Period', 'n', 'Median', 'CV_pct', 'Orientation']
df_display = df_sorted[display_cols].copy()
df_display.columns = ['Rank', 'Period', 'n', 'Median h/w', 'CV (%)', 'Orientation']

highlight = ['Ur III', 'Neo-Babylonian', 'Achaemenid']

def highlight_rows(row):
    if row['Period'] in highlight:
        return ['font-weight: bold; background-color: #fff3e0'] * len(row)
    return [''] * len(row)

df_display.style \
    .apply(highlight_rows, axis=1) \
    .background_gradient(subset=['CV (%)'], cmap='YlOrRd') \
    .format({'n': '{:,}'}) \
    .set_caption("CV standardization ranking — ascending order")
Table 1: Standardization ranking of all periods by Coefficient of Variation (ascending = most standardized). Bold rows are the three benchmark periods discussed in the paper.
(a) CV standardization ranking — ascending order
  Rank Period n Median h/w CV (%) Orientation
0 1 Ur III 22,504 1.125000 25.100000 portrait
1 2 Early Old Babylonian 2,560 1.268000 27.400000 portrait
2 3 Proto-Elamite 1,457 1.333000 27.900000 portrait
3 4 Uruk IV 1,808 1.276000 31.900000 portrait
4 5 Old Akkadian 3,397 1.280000 32.100000 portrait
5 6 Old Babylonian 15,884 1.282000 34.200000 portrait
6 7 ED IIIb 1,895 1.033000 36.300000 portrait
7 8 ED IIIa 414 1.559000 40.600000 portrait
8 9 Hellenistic 453 0.900000 41.200000 landscape
9 10 Middle Babylonian 3,023 1.000000 46.000000 landscape
10 11 Middle Assyrian 1,056 1.110000 50.000000 portrait
11 12 Uruk III 4,985 1.192000 50.200000 portrait
12 13 Hittite 161 1.000000 50.500000 landscape
13 14 ED I-II 457 1.733000 51.900000 portrait
14 15 Old Assyrian 1,124 1.106000 53.600000 portrait
15 16 Neo-Assyrian 3,379 1.158000 53.900000 portrait
16 17 Ebla 3,229 1.026000 56.900000 portrait
17 18 Lagash II 274 1.305000 60.500000 portrait
18 19 Middle Elamite 601 0.863000 74.000000 landscape
19 20 Achaemenid 1,718 0.786000 78.500000 landscape
20 21 Neo-Babylonian 7,133 0.741000 80.700000 landscape

Three benchmark periods

The standardization landscape is anchored by three historically significant periods:

Period Median h/w CV Interpretation
Ur III 1.125 25.1% Tightest portrait norm — bureaucratic mass production
Achaemenid 0.786 78.5% Widest overall, but pixel IQR = 0.150 (tight central tendency)
Neo-Babylonian 0.741 80.7% Loosest dispersion — diverse archive genres

The apparent paradox of Achaemenid high CV alongside tight pixel IQR is resolved by distinguishing two kinds of standardization:

  • Orientation standardization: the central mass of tablets clusters tightly around the landscape norm (IQR = 0.150), suggesting the landscape format was institutionally enforced for canonical documents
  • Global shape standardization: a tail of outlier formats expands the overall CV — likely non-canonical genres (astronomical diaries, school texts, ritual tablets) that did not conform to the administrative format

The standardization curve

Code 
import pandas as pd, matplotlib.pyplot as plt, numpy as np

df = pd.read_csv("../../paper/figures/period_summary_stats.csv")

chron_order = ['Uruk IV','Uruk III','Proto-Elamite','ED I-II','ED IIIa','ED IIIb',
               'Ebla','Old Akkadian','Lagash II','Ur III','Early Old Babylonian',
               'Old Babylonian','Old Assyrian','Middle Assyrian','Middle Babylonian',
               'Middle Elamite','Hittite','Neo-Assyrian','Neo-Babylonian',
               'Achaemenid','Hellenistic']

df['_rank'] = df['Period'].map({p: i for i, p in enumerate(chron_order)})
df = df.sort_values('_rank').dropna(subset=['_rank'])

fig, ax = plt.subplots(figsize=(10, 4))
colors = ['#b5622e' if p in ['Ur III', 'Neo-Babylonian', 'Achaemenid'] else '#4a6fa5'
          for p in df['Period']]
ax.bar(range(len(df)), df['CV'] * 100, color=colors, alpha=0.85,
       edgecolor='white', lw=0.5)
ax.set_xticks(range(len(df)))
ax.set_xticklabels(df['Period'], rotation=45, ha='right', fontsize=7.5)
ax.axhline(17, color='grey', ls='--', lw=1.2, alpha=0.7,
           label='Eerkens & Bettinger (2001) motor-skill threshold (17%)')
ax.set_ylabel('CV of h/w ratio (%)', fontsize=9)
ax.set_title('Scribal standardization by period — lower CV = tighter institutional control', fontsize=10)
ax.legend(fontsize=8)
plt.tight_layout()
plt.show()
Figure 1: CV of h/w ratio by period, sorted chronologically. High CV = low scribal control over format; low CV = tight institutional standard.

Eerkens & Bettinger framework

Eerkens & Bettinger (2001) proposed that artifact CV ≤ 17% signals production under cognitive templates — mental representations of a target form that constrain production even without measurement tools. CV 17–57% indicates reduced copying fidelity; above 57%, variation is essentially unconstrained.

Applied to tablet morphology:

  • No period reaches the 17% threshold, confirming that scribal shape was always more variable than true standardized craft production (e.g., mass-produced ceramics)
  • Ur III (25.1%) comes closest — consistent with the interpretation of Ur III as the most bureaucratically controlled period of cuneiform writing
  • Neo-Babylonian (80.7%) and Achaemenid (78.5%) fall in the “unconstrained” range globally, but the Achaemenid pixel IQR signal suggests local standardization within the dominant genre

George’s (2010) concept of “fixed balance” — scribal templates for geometrically harmonious proportions — complements this framework: the portrait norms of the 3rd and early 2nd millennium (h/w ≈ 1.1–1.3) and landscape norms of the 1st millennium (h/w ≈ 0.75–0.85) represent two successive cognitive templates, each maintained with varying institutional force.

Note

Next: Period Classification → — how well machine learning models recover historical periods from silhouette shape alone.