📄 Statistical Structure in Indus Sign Sequences

Summary

The Indus script is still undeciphered. Scholars disagree on whether its short sign strings record language or act as non-linguistic emblems. This paper does not try to settle that dispute. It asks whether the sequences show measurable regularities, and how they compare with a known writing system and a rule-bound non-linguistic one.

Using 6,579 inscriptions compiled from published catalogs (Mahadevan, 1977; Wells, 2011), the author combines four analyses:

• unsupervised clustering of glyph images (Hu Moments and HOG features, UMAP, HDBSCAN and agglomerative clustering);
• conditional entropy and a positional rigidity score, benchmarked against Linear B and a synthetic heraldic system;
• KL divergence between forward and reversed transition statistics;
• a categorical HMM and a BiLSTM tested on deliberately altered synthetic inscriptions.

Reading in the original direction is more predictable than reading in reverse, and final positions are tightly constrained. On rigidity, Indus falls between Linear B and the heraldic baseline. This points to non-random structure without establishing linguistic status. Following Sproat's (2014) critique, the work offers a multi-baseline template for studying undeciphered symbol systems.

Key points

• Data and visual clustering: The corpus has 6,579 inscriptions and roughly 400 distinct signs, averaging 4–5 signs per text. It uses an 80/20 split stratified by object type. Visual clustering selected k = 8 families (silhouette 0.414). These clusters serve only for interpretation; all statistics use the full sign inventory.
• Directional asymmetry: Bigram entropy is 3.60 bits forward versus 4.11 reversed, and trigram entropy is 1.42 versus 1.61. KL divergence between forward and reversed distributions is 16.45 bits for bigrams and 21.43 for trigrams.
• Positional rigidity at the last position (R5): Indus scores 0.740, Linear B 0.014 and the heraldic baseline 1.780. The author reads this as evidence that terminal signs may act as delimiters.
• Sequence models: BIC favoured a 4-state HMM, with distinct states dominating sequence starts and ends. The BiLSTM (embedding 128, hidden 256, 10 epochs) reached a perplexity of 2.60 on the real test set. Mean perplexity was 1.10 for suffix replacement, 1.39 for concatenation and 2.42 for prefix-core swaps (p < 10⁻¹²).
  • All synthetic sets therefore had lower mean perplexity than the real data.
  • The author's claim that the model tolerates edits to terminal signs but resists edits to the core rests mainly on differences in variance.
• Limitations and availability: The study cannot show whether the script encodes language, and short texts limit higher-order inference. The processed data and scripts are promised in an open repository upon publication.