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The Hidden Geometry of Emergence: How Structure Arises from Information
- SEFA, or Symbolic Emergence Field Analysis, finds structure by combining four features using information theory and self-calibrating to let data decide which features matter most based on their global information content.
- SEFA aims to detect emergence, which is the difference between noise and meaning, in various contexts such as neural bursts, social network clusters, and prime number distribution.
- It does not rely on fixed thresholds or domain-specific tricks, offering a universal and data-driven approach to reveal hidden order.
- SEFA breaks down the process into steps like constructing a base field, capturing the signal's essence with analytic methods, deconstructing geometry, normalizing features, and letting the data dictate importance through self-calibration.
- The SEFA score is a composite score that represents structuredness based on multiple informative features agreeing, prioritizing regions with high emergence.
- SEFA's weighting scheme is objective, allowing data to determine feature relevance without requiring manual tuning, ensuring robustness and minimizing false positives or biases.
- It can be applied to domains beyond number theory, such as EEG burst detection, social network clusters, and even uncovering hidden signals in non-coding DNA.
- SEFA's approach involves trusting the data over preconceptions, using entropy to weight features and detect meaningful patterns.
- It acknowledges limitations related to data stability, nonstationarity, and computational complexity, emphasizing the importance of cross-validation and critical analysis.
- SEFA offers a principled way to uncover meaningful structure in diverse datasets, encouraging curiosity, skepticism, and a deeper understanding of emergence in both data and life.
- SEFA is a self-calibrating mathematical method for detecting symbolic emergence in complex data, applicable in various fields beyond number theory due to its domain-agnostic nature.
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