The Φ Atlas

Fields orbit the transformation. Structures form the inner ring.

Φ is project-defined notation for a constrained transformation of the library’s state: not the golden ratio, not integrated information (IIT Φ), and not any other established phi quantity.

Switch the map between disciplines and structures. Select a node, or one of each, to open an intersection with its concept, its limit and its sources. Every state has its own address: copy it to share exactly what you are looking at.

The correspondences are graded: 72 solid paths (STRUCTURAL CORRESPONDENCE), 23 dashed paths (EXPLORATORY HYPOTHESIS) and 35 intersections where nothing is drawn. Featured intersections:

Psychology × Higher Order
Hermeneutics × Recursion
Library & information science × Invariance
Cybernetics × Agency
Epistemology × Transformation
Complex systems × Emergence
Phenomenology × Provenance
Ethics × Humility
Semiotics × Provenance

Select a field or a structure. Arrow keys move around a ring; select one of each to open their intersection. A solid path is a documented correspondence; a dashed path is an exploratory hypothesis; where nothing is documented, nothing is drawn. The disciplines stay distinct lenses: a shared structure does not make them interchangeable, and no theory proves the product.

Φ sits at the centre: our notation for a constrained transformation of the library’s state, not the golden ratio and not integrated information. Thirteen fields orbit it; ten structures form the inner ring. Solid paths are documented correspondences; dashed paths are exploratory hypotheses. Choose one to begin.

Disciplines

Structures

The whole atlas as a table (the same information and order as the map)

The Φ Atlas as a table: thirteen lenses × ten structural primitives. ● a documented correspondence (a solid path, STRUCTURAL CORRESPONDENCE); ○ a qualified analogy (a dashed path, EXPLORATORY HYPOTHESIS); · no documented correspondence, so nothing is drawn. 72 solid, 23 dashed, 35 undrawn.
Lens	Transformation	Relation	Recursion	Invariance	Emergence	Provenance	Feedback	Higher Order	Agency	Humility
Mathematics & theoretical computer science	State-transition function; discrete dynamical systemSTRUCTURAL CORRESPONDENCEAlso described as: state transition	Graphs; temporal (time-stamped) networksSTRUCTURAL CORRESPONDENCE	Recursive definition; iteration of a mapSTRUCTURAL CORRESPONDENCE	Invariants of a transformationSTRUCTURAL CORRESPONDENCEAlso described as: invariant properties	Graph-level (non-local) propertiesSTRUCTURAL CORRESPONDENCEAlso described as: graph/system properties	Why- and where-provenance; provenance semiringsSTRUCTURAL CORRESPONDENCE	Closed-loop systemsSTRUCTURAL CORRESPONDENCE	Higher-order functions (functions that return functions)STRUCTURAL CORRESPONDENCEAlso described as: functions producing/altering methods	No documented correspondence; nothing is drawn	No documented correspondence; nothing is drawn
Psychology & cognitive science	Assimilation and accommodation; conceptual changeSTRUCTURAL CORRESPONDENCEAlso described as: schema revision	Schemas; associative (semantic) networksSTRUCTURAL CORRESPONDENCE	Metacognition: monitoring and control of one's own cognitionSTRUCTURAL CORRESPONDENCE	Conservation (quantity invariant under perceptual change)EXPLORATORY HYPOTHESISAlso described as: continuity / reality constraints	Gestalt organization of perceptionEXPLORATORY HYPOTHESISAlso described as: pattern recognition	Source monitoring (attributing a memory or belief to its origin)STRUCTURAL CORRESPONDENCE	The TOTE unit (Test–Operate–Test–Exit)STRUCTURAL CORRESPONDENCE	Metacognitive controlSTRUCTURAL CORRESPONDENCEAlso described as: metacognition	Autonomy (self-determination theory)STRUCTURAL CORRESPONDENCEAlso described as: autonomy	The Barnum (Forer) effectSTRUCTURAL CORRESPONDENCE
Epistemology & philosophy of science	Belief revision; Bayesian conditioningSTRUCTURAL CORRESPONDENCEAlso described as: belief revision	Evidential support and attack graphsSTRUCTURAL CORRESPONDENCE	Mutual adjustment of rules and inferences (Goodman), later named reflective equilibrium (Rawls)EXPLORATORY HYPOTHESIS	Source ≠ evidence; context of discovery versus justificationSTRUCTURAL CORRESPONDENCEAlso described as: source/evidence distinctions	Inference to the best explanation (synthesized hypotheses)EXPLORATORY HYPOTHESISAlso described as: synthesized hypotheses	Testimony and its sourcesSTRUCTURAL CORRESPONDENCE	Conjecture and refutationSTRUCTURAL CORRESPONDENCE	Higher-order evidence; revision of methods and aimsSTRUCTURAL CORRESPONDENCEAlso described as: standards of justification	Epistemic authority and autonomyEXPLORATORY HYPOTHESISAlso described as: epistemic authority	Intellectual humility; fallibilismSTRUCTURAL CORRESPONDENCE
Hermeneutics & literary theory	Reinterpretation; fusion of horizonsSTRUCTURAL CORRESPONDENCEAlso described as: reinterpretation	IntertextualitySTRUCTURAL CORRESPONDENCE	The hermeneutic circleSTRUCTURAL CORRESPONDENCE	The fixity of the written text (distanciation)STRUCTURAL CORRESPONDENCEAlso described as: text/source continuity	Meaning of the wholeEXPLORATORY HYPOTHESISAlso described as: whole-context meaning	Textual criticism and stemmaticsSTRUCTURAL CORRESPONDENCE	Horizon of expectations; receptionEXPLORATORY HYPOTHESIS	Interpretation of interpretationsEXPLORATORY HYPOTHESISAlso described as: interpretation of interpretation	The reader's role in constituting meaningSTRUCTURAL CORRESPONDENCEAlso described as: reader participation	The open workEXPLORATORY HYPOTHESIS
Library & information science	Record revision; entity persistenceEXPLORATORY HYPOTHESISAlso described as: metadata/history revision	Bibliographic relationshipsSTRUCTURAL CORRESPONDENCE	No documented correspondence; nothing is drawn	Work–Expression–Manifestation–Item identitySTRUCTURAL CORRESPONDENCEAlso described as: item identity & provenance	Citation and co-citation structureSTRUCTURAL CORRESPONDENCEAlso described as: collection patterns	Copy-specific provenanceSTRUCTURAL CORRESPONDENCE	Berrypicking: evolving searchSTRUCTURAL CORRESPONDENCE	Reusable search strategiesEXPLORATORY HYPOTHESISAlso described as: reusable organization/inquiry	Reader privacy and controlSTRUCTURAL CORRESPONDENCEAlso described as: reader ownership/control	No documented correspondence; nothing is drawn
Complex systems	Dynamical systems (stocks, flows, states)STRUCTURAL CORRESPONDENCE	NetworksSTRUCTURAL CORRESPONDENCE	No documented correspondence; nothing is drawn	No documented correspondence; nothing is drawn	Emergence as failure of aggregativitySTRUCTURAL CORRESPONDENCE	No documented correspondence; nothing is drawn	Feedback loopsSTRUCTURAL CORRESPONDENCE	Adaptive agents that revise their rulesEXPLORATORY HYPOTHESIS	No documented correspondence; nothing is drawn	No documented correspondence; nothing is drawn
Phenomenology	No documented correspondence; nothing is drawn	Intentionality (consciousness is of something)STRUCTURAL CORRESPONDENCE	ReflectionEXPLORATORY HYPOTHESIS	Eidetic variationSTRUCTURAL CORRESPONDENCE	No documented correspondence; nothing is drawn	The biography of objects; lived spaceSTRUCTURAL CORRESPONDENCE	No documented correspondence; nothing is drawn	No documented correspondence; nothing is drawn	EmbodimentEXPLORATORY HYPOTHESIS	The epoché (bracketing assumptions)EXPLORATORY HYPOTHESIS
Learning science	Conceptual changeSTRUCTURAL CORRESPONDENCE	No documented correspondence; nothing is drawn	Inquiry as a cycleSTRUCTURAL CORRESPONDENCE	No documented correspondence; nothing is drawn	No documented correspondence; nothing is drawn	SourcingSTRUCTURAL CORRESPONDENCE	Formative feedbackSTRUCTURAL CORRESPONDENCE	Double-loop learning; transfer; objects-to-think-withSTRUCTURAL CORRESPONDENCE	Scaffolding and fading; the zone of proximal developmentSTRUCTURAL CORRESPONDENCE	No documented correspondence; nothing is drawn
Philosophy of mind	No documented correspondence; nothing is drawn	Coupled and distributed cognitionSTRUCTURAL CORRESPONDENCE	No documented correspondence; nothing is drawn	No documented correspondence; nothing is drawn	No documented correspondence; nothing is drawn	No documented correspondence; nothing is drawn	Epistemic actionsEXPLORATORY HYPOTHESIS	No documented correspondence; nothing is drawn	Endorsement conditions for extended beliefSTRUCTURAL CORRESPONDENCE	The bounds of cognition (critiques)STRUCTURAL CORRESPONDENCE
Semiotics	SemiosisSTRUCTURAL CORRESPONDENCE	The triadic sign relationSTRUCTURAL CORRESPONDENCE	Unlimited semiosisSTRUCTURAL CORRESPONDENCE	Use and mentionSTRUCTURAL CORRESPONDENCE	No documented correspondence; nothing is drawn	Annotation with targets and provenanceSTRUCTURAL CORRESPONDENCE	No documented correspondence; nothing is drawn	Second-order significationSTRUCTURAL CORRESPONDENCE	The model readerSTRUCTURAL CORRESPONDENCE	No documented correspondence; nothing is drawn
Historiography	Path dependenceSTRUCTURAL CORRESPONDENCE	No documented correspondence; nothing is drawn	Reception historyEXPLORATORY HYPOTHESIS	Source criticismSTRUCTURAL CORRESPONDENCE	No documented correspondence; nothing is drawn	Provenance and time in recordsSTRUCTURAL CORRESPONDENCE	No documented correspondence; nothing is drawn	The history of historical methodEXPLORATORY HYPOTHESIS	No documented correspondence; nothing is drawn	Contextualism in intellectual historySTRUCTURAL CORRESPONDENCE
Cybernetics	Transformation (operand, operator, transform)STRUCTURAL CORRESPONDENCEAlso described as: feedback update	Coupling of systemsEXPLORATORY HYPOTHESIS	Circular causalitySTRUCTURAL CORRESPONDENCE	Stability and invariant setsEXPLORATORY HYPOTHESISAlso described as: control constraints	Whole-system behaviour of coupled partsEXPLORATORY HYPOTHESISAlso described as: system behavior	No documented correspondence; nothing is drawn	Feedback and controlSTRUCTURAL CORRESPONDENCE	Second-order cybernetics; ultrastabilitySTRUCTURAL CORRESPONDENCEAlso described as: second-order control	Levels of automation; supervisory control; ironies of automationSTRUCTURAL CORRESPONDENCEAlso described as: human authority	No documented correspondence; nothing is drawn
Ethics & philosophy of technology	Correction as an obligationEXPLORATORY HYPOTHESISAlso described as: corrective revision	Contextual integritySTRUCTURAL CORRESPONDENCE	No documented correspondence; nothing is drawn	Norms that travel with informationSTRUCTURAL CORRESPONDENCEAlso described as: rights/permissions	Aggregation as a harmSTRUCTURAL CORRESPONDENCEAlso described as: avoiding overclaiming patterns	No documented correspondence; nothing is drawn	No documented correspondence; nothing is drawn	Reflection on design criteriaEXPLORATORY HYPOTHESISAlso described as: reflection on criteria	Autonomy and non-manipulationSTRUCTURAL CORRESPONDENCEAlso described as: agency & consent	Reasonable inferences; predictability ≠ permission; identity prejudiceSTRUCTURAL CORRESPONDENCE