A dynamic system interpretation of irreducible complexity
Why this work is in the frame
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Bibliographic record
Abstract
Behe recently defined the idea of irreducible complexity for biological systems. Using the language of mathematics, we reinterpret his definition from a dynamical systems perspective. Our basic premise is that living organisms behave dynamically in a chaotic way while predictable periodic behavior reflects cessation of function. We consider the dynamics of a functioning system and altered versions of it to draw conclusions about the irreducible complexity of the original system. The dynamics of an organism is described by means of a discrete time transformation τ on the phase space of the system. The statistical behavior of τ is studied by means of its Frobenius–Perron operator which, in special cases, can be represented by a matrix. Using these matrices we rewrite our definition of irreducible complexity: M is irreducibly complex if it is primitive but no principal submatrix of M is primitive. The primitivity property implies chaotic behavior, while failure to have the primitivity property reflects periodic behavior. Examples of irreducibly complex dynamical systems are presented. We show that certain dynamical systems which are irreducibly complex have an additional property, namely that other systems arbitrarily close to it behave in a dramatically different way. Such behavior suggests that selective evolution by means of small perturbations may not be a general mechanism for achieving the dynamical behavior of a complex system.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it