World Wide Whale:

Detecting Statistical Complexity in Marine Mammal Bioacoustics


Mathematical & computational research in information-theoretic measures of information, structure, semantics, and intentionality in acoustic signals, with a special emphasis on marine mammal communication.

Using modern theories of information and structure in complex systems, we are developing new signal analysis tools to analyze the informational, semantic, functional, and social communications within humpback whale populations. The long-term goal is to deepen our understanding of individual and group behaviors in ways that will improve their conservation.

Our strategy is to adapt recent mathematical innovations in meromorphic functional analysis [1], informational generalization of spectral analysis [2], and reproducing kernel Hilbert space representations of computational mechanics’ causal states [3] to acoustic signals [4]—that is, continuous-value, continuous-time series.

See the companion field work in the Voices of the Deep Project for one of the application domains in which we will prove-out the theoretical and algorithmic developments.

[1]  P. M. Riechers and J. P. Crutchfield. Beyond the spectral theorem: Decomposing arbitrary functions of nondiagonalizable operators. AIP Advances, 8:065305, 2018. doi:10.1063/1.5040705.

[2]  P. M. Riechers and J. P. Crutchfield. Fraudulent white noise: Flat power spectra belie arbitrarily complex processes. Physical Review Research, 3(1):013170, 2021. doi:10.1103/PhysRevResearch.3.013170.

[3]  N. Brodu and J. P. Crutchfield. Discovering causal structure via reproducing-kernel Hilbert space ε-machines. Chaos 32 (2022) 023103. Website.

[4] Principles of Marine Bioacoustics.


Jim Crutchfield, N Whales from M Hydrophones: Seminar, Complexity Sciences Center, Physics Department, University of California, Davis, California, 28 August 2019. (Video).