Where does variable collide?

In mathematics and logic, a variable is a symbol that stands for an unspecified or arbitrary element of a domain: it holds a place that a value can fill, and a quantifier can bind it so that it ranges over the whole domain rather than naming any one thing. A variable is called free when nothing in the expression fixes it and bound when a quantifier or operator captures it, and the same letter can be free in one formula and bound in another. Church's 1956 Introduction to Mathematical Logic set out the free and bound distinction and the rules for substituting into variables without collision. The referent is a syntactic placeholder in a formal language, not a measured attribute of study units, a cell of computer memory, or a star that changes brightness.[1]

Unit

A symbol occupying an argument place in a formula, free or bound

Recovery means

Not applicable

Measured by

Read off from the syntax: whether a quantifier or operator binds the symbol, and which domain it ranges over

In statistics, a variable is a measurable attribute that takes different values across the units of a study, such as height, income, or the outcome of a random trial. Variables are classified by how much structure their values carry, from unordered categories to ordered ranks to interval and ratio scales, and a variable whose values follow a probability distribution is a random variable. Stevens' 1946 On the theory of scales of measurement introduced the levels of measurement, nominal, ordinal, interval, and ratio, that govern which arithmetic and statistics a variable admits. The referent is a property that varies across observations and is recorded as data, not a symbol in a formula, a location in memory, or a fluctuating star.[2]

Unit

One measured attribute, scaled as nominal, ordinal, interval, or ratio

Recovery means

Not applicable

Measured by

Operationalised by assigning a value to each unit under a defined measurement procedure and scale

In computer science, a variable is a named location that holds a value a program can read and change while it runs: the name is bound to a place in storage, and assignment writes a new value into that place. A variable has a scope, the region of the program where its name is visible, and it may be mutable, so its value can be updated, or immutable, so once set it cannot change. Strachey's lectures, published in 2000 as Fundamental concepts in programming languages, drew the distinction between a variable as a storage cell, its L-value, and the value stored there, its R-value. The referent is a named container in a running machine, not a symbol in a proof, a measured attribute of a population, or a star of changing brightness.[3]

Unit

A named storage cell holding one value at a time

Recovery means

Not applicable

Measured by

Identified by its name, type, scope, and whether its stored value can be reassigned

In astronomy, a variable star is a star whose brightness as observed from Earth changes over time, whether because the star itself pulsates or erupts or because a companion periodically eclipses it. Some variables are prized as distance indicators: a Cepheid variable pulsates with a period tied to its true luminosity, so timing its cycle reveals how far away it lies. Leavitt and Pickering's 1912 Periods of 25 variable stars in the Small Magellanic Cloud reported the period to luminosity relation that made Cepheids the yardstick of cosmic distance. The referent is a physical star whose light varies, measured in magnitudes over days or years, not a symbol in a formula, an attribute of study units, or a cell of computer memory.[4]

Unit

One star, its brightness measured in magnitude over time

Recovery means

Many variables cycle, returning to a former brightness with a characteristic period

Measured by

Tracked by photometry as a light curve of magnitude versus time, and classified by period and amplitude