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**APPROXIMATE NUMBER SYSTEM**

Cognitive ability to estimate the quantity of a collection of objects without relying on language or symbols.

**ARITHMETIC**

Processing of numerical information by means of the standard operations of addition, subtraction, multiplication, division and exponentiation.

**ARTIFICIAL NEURAL NETWORK**

Computational system vaguely inspired by biological neural networks that operates a large network of relatively simple computing nodes.

**BIOLOGICAL NEURAL NETWORK**

Physiological tissue composed by neurons and other specialized cells; linked to higher cognitive functions in some animals.

**CARDINALITY**

Measure of the size of a set; for finite sets this corresponds to the amount of elements in the set.

**CATEGORY THEORY**

Mathematical theory that puts emphasis on the relational structure within families of mathematical objects rather than their particular nature. A lingua franca between different branches of mathematics.

**CELL**

Minimal observed unit of conventionally attributed full biological function. Typically, a complex assembly of microscopic molecular machinery.

**CLASSICAL PHYSICS**

Collection of models and theories that describe phenomena at the macroscopic and astrophysical scales; historically, the physical theories predating the discovery of quantum phenomena.

**CLASSIFICATION**

General problem of determining and assigning categories in a group of individuals sharing traits and behaviour. Known as taxonomy for living organisms.

**COLLECTIVE COMPUTATION**

The phenomenon of information processing by a large group of individuals in interaction, each of which processes information individually and communicates with other individuals.

**COMPLEX SYSTEM**

Physical system with a large amount of components that interact to generate intricate emergent dynamics, self-organization, or chaotic behaviour.

**COMPUTATIONAL UNIVERSE**

The abstract space of all possible programs that can be executed by a computer following finite sets of instructions.

**CONNECTIONISM**

Approach in cognitive science which assumes that most of the relevant physical substrate of the mind can be modelled by a network.

**COUNTABLE SET**

Set with the same cardinality as some subset of the standard natural numbers. A countable set can be labelled by a (possibly infinite) sequence of natural numbers.

**DETERMINISM**

Philosophical view which posits that events are completely determined by the past or preexisting causes.

**DOWNWARD CAUSATION**

The idea that higher-level features of a system can be a cause of behaviour by lower-level components, such as a mind controlling a body or law regulating society.

**DYNAMICAL SYSTEM**

Mathematical model of a physical system that describes its time evolution, typically as a function of its present or past states.

**DYSCALCULIA**

Cognitive condition that greatly affects a person’s ability to learn mathematical skills, particularly in the manipulation of numbers and quantities.

**EMBODIED COGNITION**

Theory which posits that cognitive systems should be considered in all their extension (body), not just in the centers of information processing (brain).

**EMERGENTISM**

Philosophical view which posits that collectives can exhibit behaviour that cannot be inferred from knowledge of the individuals.

**ENCULTURATION**

Process by which individuals learn the dynamics of their surrounding culture and acquire behaviours appropriate to that culture.

**ETHNOGRAPHY**

Discipline dedicated to the study of human cultural manifestations, typically with a holistic view including history, habitat and human biology.

**EVOLUTION**

Process by which a population of individuals changes over time through mechanisms such as reproduction, inheritance, mutation and selection.

**EXTENDED MIND**

The idea that contents of the mind appear and are articulated in the world. Examples are written languages, cities or technology.

**FIELD**

Mathematical object generalizing the algebraic properties of ordinary numbers. Fields are part of commutative algebra, the natural ground for the abstract algebraic study of numbers.

**INDETERMINISM**

Philosophical view which posits that not all events are determined by the past or preexisting causes, either due to randomness or other mechanisms.

**INFORMATION THEORY**

Discipline dedicated to the scientific study of the quantification, storage, and communication of digital information.

**INTEGER NUMBERS**

Mathematical object capturing ordinary subtraction and the notion of negative numbers. Prime example of what is known as an (abelian) group in abstract algebra.

**INTUITIONISM**

Philosophical view which posits that mathematics is the result of the constructive mental activity of humans rather than the discovery of fundamental principles claimed to exist in an objective reality.

**LINGUISTICS**

Discipline dedicated to the study of languages. For human populations it entails the study of phonology, morphology, syntax and semantics.

**LOGICISM**

Philosophical view which posits that mathematics is an extension of or can be successfully modelled by formal logic.

**METAMATHEMATICS**

The systematic study of mathematics, its underlying assumptions and methodology. The *mathematics of mathematics.*

**NATURAL NUMBERS**

Mathematical object capturing the formal structure of the ordinary counting and ordering numbers. This object is at the foundation of most mathematics used in science and engineering.

**NEUROPLASTICITY**

Process by which biological neural networks rearrange and reorganize themselves leading to adaptation and change of learned behaviours.

**NUMERALS**

Symbol system used to capture numerosity. Examples in humans are the Hindu-Arabic 1, 2, 3, 4… and the Roman I, II, III, IV...

**NUMERICAL COGNITION**

The processing of exact and/or symbolic numerical information by a cognitive system. Almost exclusively observed in encultured humans.

**NUMEROSITY**

The property of a stimulus that makes it comparable to other discrete measurements such as counts or orderings. Abstracted as natural numbers in humans.

**ONTOGENY**

Process by which an individual is formed. In pluricellular organisms, the process from the fertilization of an egg to the formation of an adult.

**ORDINALS**

System of labels used to identify elements in a definite order; for finite sets ordinals correspond to labelling elements of the set with the standard natural numbers.

**QUANTICAL COGNITION**

The processing of quantitative information, possibly approximate, by a cognitive system. Observed in many non-human animals and some plants.

**QUANTUM PHYSICS**

Collection of models and theories that describe phenomena at the near-atomic and subatomic levels; characteristic quantum phenomena may present state entanglement and observational indeterminacy.

**RATIONAL NUMBERS**

Mathematical object capturing the formal structure of fractions. Prime example of what is known as a field in abstract algebra.

**REAL NUMBERS**

Mathematical object capturing the formal structure of geometric distances and approximating sequences; typically considered as the mathematical model of physical quantities.

**RELATIVITY THEORY**

Physical theory that provides the most accurate, compact and mathematically elegant model to date for the relation between observers of classical phenomena.

**SEMIOTICS**

Discipline dedicated to the study of signs, symbols and their meaning among populations of individuals.

**STATISTICAL PHYSICS**

Collection of models and theories that describe phenomena involving large amounts of constituents interacting according to known, relatively simple, physical laws.

**SUBITIZING**

Ability to quickly determine the exact quantity of a (small) collection of objects upon perception.

**THEOREM PROVER**

A computational system that automatizes the process of deriving logically consistent statements from a given set of axioms.

**THEORETICAL BIOLOGY**

Discipline dedicated to the formal modelling of biological systems by developing mathematical and philosophical frameworks.

**WOLFRAM PHYSICS PROJECT**

Broad research project aimed at reinterpreting the fundamental laws of physics as emergent phenomena from simple computational rules.