Minimal Dictionary

I've always wanted to communicate my general thoughts about the world but didn't want to write a book for a few reasons. First, I have limited talent for writing and I'm not particularly interested in the art of storytelling. Second, my thoughts change and by the time I would be done writing a chapter, I would have changed my mind about it and would have to rewrite the whole chapter, if not the rest of the book. Third, concepts don't follow a particular order like a good story. Some terms are defined independently from each other and the reader should not have to read one before the other, nor should they have to work hard to guess which chapters can be safely skipped. This is why instead of a book made of chapters and paragraphs, I've decided to use a dictionary format, with the additional constraint that there be no cyclic definitions.

The avoidance of mutually-dependent definitions results in an acyclic dependency graph shown at the bottom of this page. It gives the reader a quick view of which concepts are more foundational than others.

This dictionary is an attempt to define or clarify various terms I consider important and unambiguous in my view of the world. Emphasis is placed on simplicity, consistency, and approachability. If I deem the approach successful, the document will grow and evolve over time.

abstract, action, activity, algorithm, art, artificial, cognition, communication, computation, computer, concept, concrete, creation, decision, engineering, environment, explicit model, feedback, formal language, identity, imagination, implicit model, individual, informal language, intuition, language, logic, mathematics, mind, model, mutable, nature, optimization, parameter, perception, program, reaction, reasoning, rule, science, sensing, sentence, set, society, state, symbol, system, taboo, time, tool, understanding, world

world: A subject of study plus everything that interacts with it directly or indirectly. It is normally referred to as "the" world because it is everything that exists from the subject's perspective. An interaction can be modeled as a flow of information, for some definition of information to be specified. A world is isolated from everything else, and therefore anything modeled within the world cannot learn anything about the existence or the nature of other worlds.

model: An unambiguous representation of the world. As such, a model can in principle, given sufficient technology, be translated into another language and recovered back without loss. A model is necessarily simpler than the world in which it can be expressed. An example of a simple model is the representation of the sun and the earth as points in a 2-dimensional Euclidean space, with the sun being immobile and the earth rotating in a circular orbit over a one-year period. Elementary mathematical knowledge is sufficient to read and copy this model without mistakes. Our definition of a model includes any arrangement of information that is believed to form a world model but may not be accessed or copied in its entirety. For example, a human body, mostly in its brain, holds world model, some of which was learned by interacting with it since birth. While we may not have the technology to copy correctly and completely the relevant information from a human brain, we assume it's all in there. Such world model that's a necessary part of any human mind shall not be confused with whatever explicit models a thinker or scientist can construct and publish.

time: An ordering over the states of a model. Time is the breakdown of a model into a sequence of objects called states with constraints over those states. A more specific definition of time is part of each model, if the model relies on such notion of time or successive states. Unless otherwise specified, the stepwise execution of computer programs uses a discrete, nonnegative index t to reference the successive steps of a computation. An ideal scenario is a computation of discrete states starting from an initial state t = 0 and a transition function. The transition function computes the next state from the previous one. Such computations are called simulations. More generally however, when there is no need for computing successive states, time is usually modeled as the real line.

system: A system refers to a partial model. It can be obtained by taking some elements of a world model and ignoring all interactions with the rest of the world, or by modeling the rest of the world in a simpler manner than in the original model. For example, modeling a car could consist in retaining a model of the car components as well as a model of a road and how the car interacts with the road, discarding all other elements of the world such as buildings and trees. In this example, the car is the system and the road is the rest of the world.

environment: In a model comprising systems, the environment refers to everything in the model that's not part of the system under consideration.

sensing: The acquisition of raw data by a system from the environment. This is usually done by special-purpose parts of the system, which are called sensors.

parameter: A parameter of a model is any property of this model that is left unspecified, defining a function in the usual mathematical sense. In general, a model can have any number of parameters.

state: A particular instantiation of the parameters of a model.

mutable: An entity is said mutable when it consists of time-indexed sequence of states. Such sequence of states is meant to represent successive transformation of an initial object within a model.

individual: In a model of the world, an individual is a mutable system which interacts with the rest of world, including other individuals. Each individual exists for some continuous period of time, usually in a binary fashion: at a given time, the individual either exists or doesn't exist.

artificial: The property of being created by individuals, as opposed to being imposed by the model of the world in which the individuals exist.

identity: The collection of properties associated with an individual.

set: A set as defined in mathematics by the axioms of set theory.

rule: An artificial constraint. Unlike a physical constraint which can apply to various portions of a model, an artificial constraint applies to individual members of a society, and said members can decide whether to follow it.

society: A set of individuals known as society members within a model of the world, and associated with rules.

nature: A model of the world without a society.

tool: A tool, in the very general sense that interests us, is an extension of what's normally considered the body of an individual and facilitates their interaction with the environment. This definition includes all machines, methods, and processes stored outside of the normal body of an individual. In the usual human world, this includes not just physical devices such as a hammer or a computer, but also all data stored outside the body such as books and other recordings. Therefore, other individuals can also be considered as tools according this definition.

activity: Collection of events involving individuals using specific tools or methods.

science: The activity consisting in creating and refining models of the world.

creation: Activity whose impact on the world is noticed and becomes associated with a new concept, in some model of interest.

engineering: The activity of creating tools.

art: The activity of creating anything that is not a tool.

mathematics: The study of the structure of unambiguous statements. Mathematics are useful for dealing with models in science, engineering, and other fields of study.

computer: A finite system that reads discrete instructions and carries them out predictably. A computer can be represented as a sequence of states comprising a mutable, discrete storage space. Turing machines are idealized representations of computers with unbounded storage or memory; they are used in theoretical studies for proving some properties of computers. This definition excludes hypercomputers, which would allow solving problems that Turing machines cannot, such as the halting problem.

logic: The mathematical subfield of logic. It is focused on the general properties of formal systems and characterizing what can and cannot be done with mathematics and computers.

computation: The successive states of a computer.

program: A computer program in the usual sense. A program consists of a finite collection of instructions that can be executed by a computer or by a Turing machine. A program may or may not take external input. In theoretical studies, the input is often baked into the program or into the initial state of the computer's memory. A program may or not terminate. Determining whether a program terminates is not always possible, which is known as the halting problem. A program can be viewed as a mathematical proof and vice-versa, which is known as the Curry-Howard correspondence, and offers a link between logic and computation.

algorithm: An algorithm is a program that terminates.

action: A change in two successive states of a system that determines a change elsewhere in the world model, possibly in the system itself.

decision: An action of a system onto itself, in particular when examining a small selection of possible actions that are mutually exclusive.

mind: (1) The components of a system that make it more durable independently from its other properties. This tentative definition is meant to incorporate the dualist notion that the mind is separate from the rest of the body and somewhat optional, while emphasizing that it's only a simplified model useful for studying decision processes. (2) A self-improving world model. In this equivalent view, the mind continuously gathers information about the environment around the system and uses it to make better decisions.

cognition: The properties of a mind.

concept: A binary state within a mind. A concept is generally considered to be turned on or off by the activity of the mind, including other concepts.

abstract: A concept is said more abstract than another when its full definition from elementary concepts is more complex.

concrete: The opposite of abstract. A concept is more concrete than another when it is less abstract. In a mind, the most concrete concepts are the states of sensors.

intuition: The activation of abstract concepts or ideas within a mind.

perception: A form of intuition involving concepts that form a model of the world as it is being sensed.

reaction: An action that is triggered within a mind by the presence of a particular concept.

optimization: An activity consisting in modifying a system so as to increase its fitness, which is a number, specifically an element taken from an ordered set. The goal function, objective function or fitness function is the function that maps a state of a system to the number referred to as fitness.

feedback: Input of the fitness function of a system.

symbol: A conventional representation of a concept. It is a component of the world to which some members of a society will react in a similar manner and that does not provide benefits other than eliciting similar reactions in others. A special case of a symbol is one that's used only by a single individual. It suffices that the concept be identified as such by the individual to be considered a symbol. For example, "that feeling when I do X" shall be considered an internal symbol because it's a concept whose presence is clearly identified by the subject. The subject might then try to reproduce it with the aim of eliciting a particular reaction in their own mind.

reasoning: Any mental activity that makes heavy use of symbols.

sentence: A sentence is a compound symbol i.e. a symbol formed by combining multiple symbols into one.

language: A collection of symbols produced by combining other symbols. A combination of symbols that itself forms a symbol is referred to as a compound symbol or a sentence. One shall distinguish formal languages from informal languages.

informal language: An informal language is a language made of ambiguous symbols. A simple symbol or a compound symbol is ambiguous if it elicits different reactions in different people. For example, a simple English sentence like "the sky is blue" is ambiguous at least because different people have different notions of the color blue or whether this claim asserts that the sky is always blue. The missing details are usually called "context" but for an informal language, it is not possible to provide all the context for a sentence to become unambiguous. What prevents this is how each mind produces concepts and reacts to them as a function of its own state rather than just as a function of new external data.

formal language: A formal language is a language defined mathematically, or equivalently unambiguously. Most programming languages can be thought of as formal languages, even if in practice certain aspects of the language are left undefined. Another example of "almost formal" languages are mathematical proofs. While ordinary mathematical proofs are expressed in a natural language such as English, they are believed to be translatable into one or more equivalent proof-checking algorithms by different people. Since not everyone understands a given mathematical proof, the key is to convince the audience that they understand the proof only if they really do. As a shortcut, we might therefore allow ourselves to treat most mathematical discourse as using a formal language. This contrasts with everyday informal languages, which are not believed nor designed to be unambiguous.

imagination: A form of intuition, generally involving concepts for which symbols already exist.

implicit model: A model implemented by a mind. A mind makes decisions at least partially by relying on some internal structure in the system, without relying on a symbolism or language that makes it transferable to other individuals. This internal structure is considered an implicit world model.

explicit model: A model transferable by a system to another system using symbols forming a language.

understanding: (1) Some measure of how much a mind reproduces implicitly the essential features of some external model. It can be tested by placing the mind in an environment that requires quick decisions that benefit from identifying features of the model without much computation. (2) The properties of a mind that allow it to extend its implicit world model.

communication: Transfer of concepts from an individual to other individuals. A concept is the activation of a construct within a particular mind. In general and ideally, two individuals with similar experience and exposed to the same input will activate approximately equivalent concepts. For example, when seeing an apple, some kind of neuron may light up, corresponding to the approximately defined concept of "an apple being present in front of them". We distinguish concepts, which are internal to each mind, from symbols which are placeholders meant to activate, trigger, or elicit a particular concept. Communication may or may not rely on symbols. Language relies on symbols to represent concepts. An example of communication without symbols is teaching by example, such as an animal showing their offspring how to catch prey by just doing it.

taboo: A concept that is being avoided by one or more individuals. Keeping in mind that a concept is the activation of a particular state of the mind, avoiding a concept is a complex process. It takes the mind some training that consists in identifying situations that may lead to the concept, and favoring decisions that take the focus away from the taboo concept. It is important to distinguish a taboo from any undesirable situation. A taboo concept is not just about avoiding a specific situation but also avoiding thinking about it. For example, the concept "a tiger is attacking me" for most people is not taboo because we don't have a problem imagining this. The actual concept that we want to avoid is "the tiger is attacking me right now for real". A taboo is a concept that is completely avoided, possibly due to threats communicated by others or more generally due to fear caused by negative past experience involving co-occurring concepts.