functional information
Compiled with AI assistance and selectively reviewed. Please consult the cited passages; the books remain the authoritative source. About this companion
Editorial synthesis · provisional
Definition
Functional information is a function-relative measure of the rarity of configurations that attain at least a specified level of performance within a defined comparison space. The smaller the qualifying fraction, the greater the value in bits. Its value depends on the chosen function, threshold and system boundary. It quantifies a particular aspect of retained functional organization, rather than complexity in general or the process of in-formation.
Explanation
RB1 supplies the formula I(Ex) = −log₂ F(Ex), where F(Ex) is the fraction of configurations achieving at least the degree of function Ex. Function is specified within a constraint regime; it is neither an isolated structure’s intrinsic possession nor a purpose directing nature. AB’s glossary, PB’s aphorism and RB3’s development also call functional information retained achievement, constraint or viability. These are source-specific explanations of accumulated functional organization, not permission to treat arbitrary memory or complexity as a measured quantity.
The Law of Increasing Functional Information proposes conditions under which this organization accumulates; the measure itself is not that law, an agent or a guarantee of progress. Gains depend on variation, functional filtering and retention, and can be bounded, interrupted or lost. Broader LIFI+ applications remain separately qualified. RB1’s quantum extrapolation distinguishes outcome probability, persistence and functional information proper, and acknowledges that no operational quantum test has been specified. PB preserves domain-specific measures without a common numerical currency and warns that a nondecreasing running maximum is definitional, not by itself the substantive content of Law 3.
Scope and attribution
All five books contain meaningful treatment, but only AB and RB1 directly support the complete thresholded rarity definition/formula. Book filters display each book’s own statement and witnesses; PB/RB2/RB3 are not blanket-credited with an independently stated full formula.
Attribution
Author’s exposition and interpretation of the Hazen/Wong framework; named coauthors and native citations preserved.
Source scientific exposition, quoted law statements, AB glossary, PB aphorism, Letter correspondence, AI-assisted formal proposal and wider conjectural applications remain separately labeled.
AB — The Actual Book
AB explains functional information through the rarity of working configurations, then specifies function, system boundary, comparison space and performance level. Its glossary calls it retained achievement and connects it to Adaptive Complexity. The appendix relates the measure to selective retention while explicitly excluding measurement of form-taking itself.
The same variation/filtering/retention grammar uses different mechanisms across minerals, genes and ideas; no strict cross-domain identity.
LIFI is a proposed, still debated law under joint conditions, separate from the measure and not an ontological ground for in-formation.
Authorial exposition and glossary crediting Hazen, Wong and colleagues; source wording remains separately retained.
Occurrence locators: 59, 60, 144; Glossary: 223; Notes: 239, 244; Appendix: 263, 271, 272, 273.
PB — The Possible Book
The Tractatus compresses functional information into retained constraint, with non-monotonic accumulation. A Letter recounts discovering Wong and colleagues and identifies a quantum extension as the author’s own idea. Categoria introduces domain-specific measures and carefully limits its formal depiction of LIFI. PB does not independently state the complete thresholded rarity formula in these witnesses.
Retained-constraint aphorism, not a numerical definition of every kind of memory.
The reading history and proposed quantum extension remain the author’s personal intellectual account, not a result attributed to Wong or Hazen.
Measures IX belong to specified domains, with one form but no shared currency. A running supremum is nondecreasing by definition; this does not establish the law’s substantive claim. The extension across all scales is labeled a scale-equivalent conjecture/formal sketch. Source local tags and the global demand for verification remain; no independent mathematics is certified.
The proposed viability valuation for sense-making is distinguished from an increment of I; it is not a moral or experiential value automatically derived from functional-information magnitude.
Retain language-model drafting/verification caveat for Categoria.
Authorial aphorism, correspondence and qualified formal proposal remain distinct voices/genres.
Occurrence locators: 95, 137, 148, 151, 152.
RB1 — The Real Book, Volume I: The Possible Is Real
RB1 gives the rarity/effectiveness definition and the explicit negative-logarithm formula in native note 559. Function is contextual within constraint regimes. It develops chemical, biological, technological and cultural uses, while stating that functional information is descriptive, not an agent or hidden selector. Its stronger LIFI+ and quantum extensions are expressly interpretive and require separate qualification.
Enzyme rarity supplies a biological illustration; language, computing and scientific-theory cases are the author’s broader applications. Their explanatory comparisons are not automatically cross-domain numerical measurements. Local biological simplification remains possible.
The manuscript proposes quantum functional information as an analogy, then distinguishes Born probability, persistence and functional information proper. It admits no specified operational quantum measurement capable of falsifying that extrapolation, and calls the stronger ontological reading an extrapolation beyond the metric.
No agent, teleology or guarantee of universal/monotonic progress follows. Conditional trajectories may be bounded, intermittent or absent; source discussion acknowledges unresolved mechanisms and system-boundary dependence.
Hazen/Wong framework as presented by the manuscript author; quoted law statements, metric and the author’s broader conjectural extensions remain distinct.
Occurrence locators: 179, 203, 204, 205, 206, 207, 208, 209, 210, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 251, 253, 254, 256, 257, 258, 259, 260, 261, 262, 263, 264, 266, 267, 268, 269, 270, 271, 272, 273, 281; Notes: 204, 269.
RB2 — The Real Book, Volume II: Becoming Is Being
RB2 relates LIFI to Law 6: rare functionally successful configurations may be retained through irreversible history. A protein example illustrates the relevant specificity. The discussion expressly permits loss and ecological destruction, and separates functional information’s scope from the broader historical emergence of lawfulness.
An informational arrow of retained form is distinct from the thermodynamic arrow; this is the author’s proposed relationship, not an identity of measures.
No inevitable increase or benevolent progress; functional information can be lost.
Function must be specifiable; the measure/LIFI does not exhaust historical lawfulness.
Authorial Law 6/Meta-Law development, citing Wong and Hazen; no blanket attribution of the complete core metric definition to RB2.
Occurrence locators: 221, 223, 253, 257, 271, 272.
RB3 — The Real Book, Volume III: Murmurations
RB3 interprets function as retained efficacy under constraint and functional information as selectively retained viable organization. Its rarity-based explanation connects this with LIFI. It expressly limits the measure to specified functional configurations and distinguishes it from in-formation’s metaphysical operator. Chemical and linguistic cases remain domain applications, not a common numerical currency.
Function does not mean purpose, and Shannon, genetic/functional and cultural information do not constitute one invariant measure.
LIFI is presented as proposed and contested rather than settled science.
The measure illustrates one aspect of the broader account but does not measure in-formation.
Authorial generative-realist interpretation drawing on Hazen, Wong and colleagues; illustrative applications and empirical assertions remain attributed to the manuscript.
Occurrence locators: 23, 24, 26, 64, 69, 71, 81, 82, 83, 87, 92, 93, 123, 134.
Sense distinctions
function relative rarity measure
One primary quantitative sense, with separately exposed authorial retained-achievement/constraint/viability glosses. Do not turn the broad glosses into unconditional numeric identities or silently merge the measure with its proposed law or extensions.
AB directly joins the retained-achievement wording to rarity in its glossary; PB and RB3 compress or develop that interpretation. These passages justify source-local explanatory treatment within the entry, not an unsupported independent measure or a new universal information currency. Existing separate LIFI, LIFI+, quantum functional information, ordinary information and in-formation records remain separate.
Background used in the editorial explanation
Domain-specific mechanisms and wider analogies remain distinguished. Original definitions retain their scope; local cross-references do not rewrite them. Named theories and mechanisms are distinguished from neighboring background, homonyms and the author’s own synthesis. Reproduced AI passages retain their separate voice.