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.

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 be translated into another language and recovered back without loss. A model is necessarily simpler than the world in which it can be expressed.

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.

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

engineering: The activity of making tools.

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: 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.

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 order 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.

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.

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