This essay proposes mathematical answers to meta-scientific questions including "how much knowledge is produced by research?", "how rapidly is a field making progress?", "what is the expected reproducibility of a result?", "what do we mean by soft science?", "what demarcates a pseudoscience?", and many others. From two simple postulates - 1) information is finite; 2) knowledge is information compression - we derive a function \(K(y;x\tau)=\frac{T(y)-T(y|x \tau)}{(T(y)+T(x)+T(\tau)}\), in which the total information \(T()\) contained in an

This is a substantially updated and expanded version of the manuscript. It includes multiple new results in addition to various adjustments and clarifications of previous ones. Many more examples are offered throughout, and there is an entirely new section illustrating how the K function may quantify all forms of knowledge and biological adaptation. This new section and most mathematical details have been placed in a Supporting Information section at the end of the manuscript.

The author declares that they have no competing interests.

The following information was supplied regarding data availability:

The research in this article did not generate any raw data.