Where does dimension collide?

In physics and cosmology, a dimension is one of the independent directions needed to locate an event, so ordinary spacetime is counted as four: three of space and one of time. Tegmark's 1997 On the dimensionality of spacetime asked why the observed world has exactly three large spatial directions and one of time, arguing that stable orbits and predictable physics depend on that count. Here the referent is a structural property of the physical universe, a whole number fixed by how many directions reality actually offers. That is not the count of columns in a data table, an axis of personality, or a contrast between national cultures.[1]

Unit

One independent direction of the physical world, counted as a whole number

Recovery means

Not applicable

Measured by

Inferred from physical law and observation, such as how forces fall off with distance

In statistics and data science, dimensionality is the number of variables, or features, recorded for each case, so a table with fifty measured columns is called fifty-dimensional. Jolliffe and Cadima's 2016 review Principal component analysis: a review and recent developments described how many correlated variables can be compressed into a few combined axes that keep most of the variation, a family of methods called dimension reduction. Bellman's 1957 Dynamic programming named the opposite problem the curse of dimensionality: as the count of variables grows, the data needed to fill the space grows explosively. The referent is a count of measured features in a dataset, not a direction of spacetime, a personality axis, or a cultural contrast.[2][3]

Unit

One measured variable per case; a dataset's dimensionality is its variable count

Recovery means

Not applicable

Measured by

Read off directly as the number of feature columns, and often reduced by methods such as principal component analysis

In personality psychology, a dimension is a continuous axis along which people differ by degree, such as how outgoing or how conscientious a person is, rather than a category they fall into. McCrae and John's 1992 An Introduction to the Five-Factor Model and Its Applications set out the five broad trait dimensions, often called the Big Five, on which each person sits somewhere between two poles. The referent is a graded axis of human individual difference, estimated from questionnaire responses. It shares only the word with a direction of spacetime, a variable count in data, or a contrast between whole societies.[4]

Unit

A person's standing on a continuous trait axis, between two poles

Recovery means

Not applicable

Measured by

Estimated from self-report or observer questionnaires and summarised by scale scores

In cross-cultural management, a cultural dimension is an axis along which national or group cultures can be compared, such as how strongly a society favours the individual over the collective. Hofstede's 2011 Dimensionalizing Cultures: The Hofstede Model in Context laid out several such dimensions, each scoring a country from surveys so that cultures can be placed relative to one another. The referent is a comparative axis describing aggregate societies, not a single person and not a physical or numerical count. It differs from the direction of spacetime, the variable count of a dataset, and the trait axis of one individual, even though all four are called a dimension.[5]

Unit

A country's score on a cultural comparison axis

Recovery means

Not applicable

Measured by

Computed from aggregated survey responses and expressed as national index scores