FIELD GUIDE

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

Approximate Number System

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

Arithmetic

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

ArtificialNeuralNetwork

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

Biological Neural Network

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

Cardinality

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.

Category Theory

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

Cell

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.

Classical Physics

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

Classification

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.

Collective Computation

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

Complex System

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

Computational Universe

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

Comnnectonism

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.

Countable Set

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

Determinism

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.

Downward Causation

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

Dynamical System

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

Dyscalculia

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).

Embodied Cognition

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

Emergentism

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

Enculturation

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

Ethnography

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

Evolution

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

Extended Mind

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.

Field

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

Indeterminsm

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

Information Theory

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.

Integer Numbers

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.

Intuitionism

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

Linguistics

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

Logicism

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

Metamathematics

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.

Natural Numbers

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

Neuroplasticity

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...

Numerals

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

Numerical Cognition

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.

Numerosity

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.

Ontogeny

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.

Ordinals

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

Quantical Cognition

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.

Quantum Physics

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

Rational Numbers

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

Real Numbers

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

Relativity Theory

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

Semiotics

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

Statistical Physics

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

Subitizing

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

Theorem Prover

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

Theoretical Biology

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

Wolfram Physics Project