Foundations of Information Theory

Ontological Principle O1 (the Locality Principle)

• Empirically, information can be considered only for a system, called its receiver or recipient; conventional theories instead treat information as absolute.The section allows that absolute information may be mathematically modeled, but says this is not possible empirically.Source: §2 · p. 4
• Informativeness is relational to a recipient’s questions and background knowledge, not an inherent property of an object.The paper notes that claims about informativeness depend on knowledge and can turn out to be wrong.Source: §2 · p. 5
• O1 treats information as relative to a chosen system, not as absolute; this relativity is distinct from subjectivity.Information has objective but relativistic properties, alongside subjective estimates.Source: §2 · pp. 5–6
• Both objective and subjective estimates of information for a recipient can change with time, recipient-carrier interaction, and the recipient’s work.The paper says axiological principles (Burgin, 1995; 1997) show that information in a paper can objectively grow for a recipient.Source: §2 · p. 6
• O1 helps clarify the role of the observer in interpretations of quantum theory.Source: §2 · p. 6

2. Ontological Principles of Information Theory

• For people, a thing exists through information received about it; O1 and O4 explain this through generalized observation, which requires interaction but no special kind of observer.The observer need not be human or have any property beyond the possibility of interacting with what is observed.Source: §2 · pp. 7–8
• An electron’s existence is supported by information produced when it interacts with molecules in a Wilson cloud chamber, before a physicist views the recorded track.The passage describes a camera recording the track and a physicist examining the picture 30 days later.Source: §2 · p. 8
• Information need not involve a sender: a recipient can extract it from a carrier that does not send it, so the necessary input triad is information, carrier, and receiver.This input structure differs from the classical communication triad, which includes a sender.Source: §2 · pp. 8–9
• The input triad is complemented by an output triad, and their sequential composition forms the communication triad.The carrier in either triad may coincide with the sender.Source: §2 · p. 9
• O1 reconciles claims that information exists only in society with claims that it exists in any phenomenon: information for people exists in society, while more generally it exists in everything.The passage adds that the challenge in the general case is how to extract it.Source: §2 · pp. 9–10
• O2 defines information broadly as the capacity of material or abstract things to cause changes in other things.For a system R, information is a capacity to cause changes in that system.Source: §2 · p. 10

• O2 holds that information exists only as portions that can be separated from other information.Source: §2 · p. 11
• Information and transformation are functionally similar in changing systems, but information causes change while transformation is the change itself.Source: §2 · p. 12
• O2 links information’s influence on individuals and social groups to transformation, and says that influence grows as society develops.The passage also characterizes energy as a kind of information in a broad sense.Source: §2 · p. 12
• O2 enables distinctions among kinds of information, including information that affects different memory agencies and cognitive, affective, and effective information.Studying the information that changes different memory agencies may help explain stability and flexibility in mind and memory.Source: §2 · p. 13
• Because O2’s broad generalizations exceed common usage, the section introduces strict, system-relative information using an infological system as a free parameter.For an intelligent system, its knowledge system, or thesaurus, is offered as a model infological system.Source: §2 · pp. 13–14
• Information for a system R is the capacity of objects to produce changes in R’s infological system IF(R).Source: §2 · p. 14
• O2g generalizes O2 by allowing different infological systems to distinguish kinds of information that O2 treats alike.Source: §2 · pp. 14–15
• Energy is a specific kind of information that acts directly on material bodies, while other kinds act indirectly through energy.Source: §2 · p. 15
• Making the infological system a parameter lets researchers tune the definition’s scope and meaning to their goals and overcome limitations in information theory.Source: §2 · pp. 15–16
• The flexible definition can represent existing understandings and encompass both broad information and restricted concepts, while possessing univocity, analogy, and equivocity.Source: §2 · p. 16
• Any system may have one or more infological systems, making information relevant to both biotic and abiotic worlds and allowing complex systems to have different information types.Source: §2 · p. 17
• Infological systems can be dynamic: a system’s behavior can serve as one, reflecting information’s role in controlling action and operating organization.Source: §2 · p. 17

2. Ontological Principles of Information Theory

• The world of structures is presented as a recently discovered level of reality whose existence can be demonstrated through observation and experiment.Structures are said to form the world's structural level.Source: §2 · p. 19
• Structures determine the essence of systems and include knowledge and intellectual contents such as books, documents, and scientific theories represented in people's mentality.The account identifies Popper's World 3 with such knowledge structures (Burgin, 1997; 2004).Source: §2 · pp. 19–21
• The Existential Triad comprises physical reality, a mental world extending to social conscience, and a world of structures associated with ideas or forms.The mental world is broader than individual consciousness, while structures are associated with ideas or forms (Burgin, 1997; Burgin and Milov, 1999).Source: §2 · p. 20
• The three worlds are not separate realities but interact: mentality is based on the material brain, and no material thing exists without structure.The account also notes that knowledge of the physical world depends substantially on interaction between the mental and material worlds (von Baeyer, 2001).Source: §2 · p. 21

• A structural representation is an abstract image of an entity’s parts and their connections, and representations may be material, symbolic, or intrinsic.Each system has inherent structural representations, which may be revealed by representations situated in other systems.Source: §2 · p. 22
• A system’s structure depends on the level of structuring: distinguishing or grouping elements can give the same systems different structures.The passage illustrates this with functions over the natural and real numbers: treating those sets as the same kind of object yields a shared structure, while distinguishing them yields different structures.Source: §2 · p. 23
• Although explaining structures can seem subjective because it depends on which elements and ties are distinguished, the text treats structures as existing in reality.It says repeated observations and experiments help distinguish objective reality from illusions, while acknowledging that these methods are imperfect.Source: §2 · pp. 23–24
• Research into structural reality identifies the fundamental triad, also called the named set, as the most basic structure.Source: §2 · p. 25
• A named set X is defined as the triad (X, f, I), with X as support, I as the component of names, and f as the naming correspondence.Source: §2 · p. 25
• An infological system of a material system comprises material, symbolic, and structural components, with the symbolic component linking the other two.Source: §2 · pp. 25–26
• Many disciplines recognize the potential importance of semiotic paradigms but have not found a satisfying way to integrate them into their domains.Source: §2 · pp. 26–27
• Peirce’s sign is a relation among Name (Vehicle), Object, and Meaning, corresponding to structural, physical, and mental worlds, respectively.Source: §2 · pp. 27–28
• An icon signifies through likeness, allowing information about its object to be inferred; icons include images, diagrams, and metaphors.Source: §2 · p. 28
• An index has a causal or sequential relation to what it signifies, linking the two organically with little or no participation of the mind.Source: §2 · p. 29

Symbols

• A general symbol signifies both an abstract notion and the collection of things encompassed by that notion.The passage contrasts “a lover” as a general symbol with “love” as an abstract symbol.Source: §2 · p. 30

Infological systems

• The brain is the material component of a human infological system, while the mind is its symbolic component; data and knowledge systems correspond symbolically to memory.Source: §2 · pp. 30–31

Symbols

• A symbol can be stored as a process in a neural network, making the process itself a symbol.The passage describes a latch as one example of a process that stores a binary bit.Source: §2 · p. 31

Infological systems

• Selecting an infological subsystem in a system determines the type of information considered, and changing that choice changes the scope of information entities.Source: §2 · p. 32

2. Ontological Principles of Information Theory

• Cognitive information is a capacity to cause changes in a system’s cognitive infological system and is the source of changes in its knowledge.The cognitive infological system contains knowledge of the system to which it belongs.Source: §2 · p. 34
• Information in the strict sense is a capacity to change structural infological elements in a system’s infological system.Changes to a system’s structural features, and through them other system characteristics, are described as the essence of information in the strict sense.Source: §2 · p. 35
• The definition of information in the strict sense remains incomplete unless the concept of structure is understood.The paper frames this as a fundamental ontological question about how the world is organized.Source: §2 · p. 35
• The strict-sense principle distinguishes information from knowledge and data, which are structures.This distinction follows from defining information as a capacity to change structural infological elements.Source: §2 · pp. 35–36

Ontological Principles of Information Theory

• Choosing different infological systems helps explain different information types, with each type corresponding to an infological-system type.The section also relates information to knowledge and data as energy relates to matter.Source: §2 · pp. 36, 38
• The general theory of information supports treating information as a property, and the section proceeds with information in this strict sense.It contrasts the property approach with treating information as a thing or a structure.Source: §2 · p. 38
• Ontological Principle O3 states that every portion of information has a carrier for the system receiving it.The principle is stated for information I and carrier C.Source: §2 · p. 38
• For materialists, OM3 strengthens embodiment by requiring that some substance contain every portion of information.The section calls this the Material Embodiment Principle.Source: §2 · p. 38
• Confusing information with its carrier leads to definitions equating information with messages, facts, data, or knowledge; the section instead argues that physical laws derive from information laws.It contrasts this position with Landauer (2002) and points to the title Physics from Fisher Information.Source: §2 · p. 39
• Information carriers fall into three classes: material, mental, and structural.The section uses a book to illustrate how the physical book, its meaningful text, and the represented knowledge serve as different carriers.Source: §2 · p. 39
• The same book can yield different information to different readers because its content depends on each reader’s means of information extraction.The material representation remains unchanged while the information available differs with the receiver.Source: §2 · p. 40
• Under O2, information is the same when it causes the same changes in an infological system, and the same information can use different carriers.Carriers may include different texts or carriers of different natures.Source: §2 · pp. 40–41
• An information representation always serves as a carrier, but a carrier need not represent the information it contains.The carrier is therefore the broader concept.Source: §2 · p. 41
• O4 states that every portion of information has a representation for a system.The principle identifies the representation as C and the system as R.Source: §2 · p. 41
• O5 requires interaction between carrier C and system R for an information transaction, but possession of the same information does not prove transmission.The second system might have created the information itself; a channel makes transmission possible but does not necessitate it.Source: §2 · p. 42
• Under O5a, a system receives information only when its carrier transmits it or the system extracts it.Transmission or extraction may be direct or may use a channel.Source: §2 · p. 42
• Transmission is passive for the receiver and active for the carrier, whereas extraction is active for the receiver and passive for the carrier.These are the two ways of information exchange identified in the section.Source: §2 · p. 43
• When the carrier is the receiving system itself, the operation is information processing, which includes transformation and production.The section attributes transformation and production to Burgin (1997b).Source: §2 · p. 43

• The educational implication is that teachers should help students acquire information and build knowledge, rather than merely supplying more subject material.Source: §2 · pp. 43–44
• O6 states that system R accepts information I only when its transmission or transition causes corresponding transformations.Source: §2 · p. 45
• The general theory of information can explain aspects of entertainment’s impact but does not solve every problem, so the text calls for interdisciplinary study.Source: §2 · p. 45
• O7 states that one carrier C can contain different information for the same recipient, as a person’s knowledge of Japanese changes what a book conveys.Source: §2 · p. 45
• To convey information efficiently, communicators should prepare audiences to accept it, a concern the text highlights for mass entertainment.Source: §2 · p. 45
• The theory refines common usage: information gives knowledge of a specific event or situation, while a collection of facts or data contains information (The American Heritage Dictionary, 1996).Source: §2 · p. 47

2. Ontological Principles of Information Theory

• The general theory does not essentially reverse conventional meaning; it makes that meaning more precise by separating information from its representation.Everyday speech usually does not distinguish the two, but that distinction can matter in science and communication when interpreting a message beyond its literal meaning.Source: §2 · p. 48
• The theory’s principles reflect basic properties of information, but mathematical structures are needed to achieve the necessary exactness.The principles are converted into postulates and axioms that provide an exact mathematical reflection of the main principles.Source: §2 · p. 48
• The general axiomatic theory is based on the theory of named sets, or fundamental triads, which are used to construct its mathematical part.Source: §2 · p. 48