Natural computation measured as a reduction of complexity

Area of Science:

• Theoretical computer science
• Information theory
• Computational neuroscience

Background:

• Existing definitions of computation often focus on algorithms or information processing.
• A unified understanding of computation across natural and artificial systems remains a challenge.
• Statistical obstruction impacts predictive accuracy in complex systems.

Purpose of the Study:

• To propose a novel, unified definition of computation based on reducing statistical obstruction.
• To develop an explicit measure of computation applicable to diverse systems.
• To demonstrate the utility of this measure in analyzing dynamical and biological systems.

Main Methods:

• Derivation of a general measure of computation from the principle of reducing statistical obstruction.
• Application of the measure to well-characterized families of dynamical systems.
• Analysis of experimental time series data from cortical neurons.

Main Results:

• An explicit mathematical formulation for a computation measure is presented.
• The measure successfully quantifies computation in electronic circuits, mechanical devices, and neural networks.
• Validation through analysis of dynamical systems and real neural data confirms the measure's applicability.

Conclusions:

• Computation can be fundamentally understood as the process of overcoming statistical barriers to prediction.
• The derived measure offers a universal framework for quantifying computation across diverse systems.
• This work provides new insights into the nature of computation in both artificial and natural contexts.