Beyond Zipf’s Law: Equifinality and Mechanistic Inference from Scaling Laws

Earlier this year, I was reading Arnon et al.’s Science paper, “Whale song shows language-like statistical structure,” which reports statistical regularities in humpback whale song that resemble those found in human language, including a frequency distribution close to Zipf’s law. It brought me back to a simple question: even if we observe a Zipf law, what can we really infer about the mechanism…