A lay-friendly version of Montañez’s paper at BIO-Complexity translates from the math:

The paper gives a detailed mathematical theory of what specified complexity is, what it does and how it can be used to rule out proposed explanations. It defines a common and rigorous foundation for all specified complexity models. It demonstrates that specified complexity must be rare, and it shows how to create new specified complexity models for domains of interest (such as converting irreducible complexity into a quantitative form of specified complexity, as shown in the paper).

Given the explicit connection made between specified complexity and statistical hypothesis tests (by way of p-values), we can reverse the relationship to provide a minimum probabilistic baseline that any proposed explanation must exceed to be considered a plausible explanation, setting an objective quantitative bar (relative to a simple uniform distribution) by which we can measure the causal adequacy of any naturalistic explanation. As Dr. Montañez notes in the paper, meeting this requirement “is the entry fee for a probabilistic mechanism even to enter the tournament of competing explanations.” “BIO-Complexity Article Offers an Objective Method for Weighing Darwinian Explanations” at

Evolution News and Science Today

*See also:* A new unified model of specified complexity

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What stands out to me is ID theory has been in mainstream usage outside of ID for many decades.

Because canonical form is now defined, it puts previous research in a clear light, such as showing that a particular form of specified complexity (called the “algorithmic significance method” (Milosavljevi?, 1993)) has been used in machine learning and bioinformatics for over 25 years! This was brought to light by an ID critic (pointing out a similarity to algorithmic specified complexity). However, now that we have canonical specified complexity we can show it isn’t just similar, it is an actual mathematical specified complexity model. Specified complexity has therefore already found direct applications outside of ID for over a quarter century.