Continuum (theory)

For other uses, see Continuum (disambiguation).

Continuum theories or models explain variation as involving a gradual quantitative transition without abrupt changes or discontinuities. It can be contrasted with 'categorical' models which propose qualitatively different states.

In physics

In physics, for example, the space-time continuum model explains space and time as part of the same continuum rather than as separate entities. A spectrum in physics (e.g. of light) is often termed either a 'continuous spectrum' (energy at all wavelengths) or 'discrete spectrum' (energy at only certain wavelengths).

In contrast, quantum mechanics includes quanta, which are distinguished from continuous amounts.

In mathematics and philosophy

A good introduction to the philosophical issues involved is John Lane Bell's essay in the Stanford Encyclopedia of Philosophy. A significant divide is provided by the law of excluded middle. It determines the divide between intuitionistic continua such as Brouwer's and Lawvere's, and classical ones such as Stevin's and Robinson's. Bell isolates two distinct historical conceptions of infinitesimal, one by Leibniz and one by Nieuwentijdt, and argues that Leibniz's conception was implemented in Robinson's hyperreal continuum, whereas Nieuwentijdt's, in Lawvere's smooth infinitesimal analysis, characterized by the presence of nilsquare infinitesimals: "It may be said that Leibniz recognized the need for the first, but not the second type of infinitesimal and Nieuwentijdt, vice-versa. It is of interest to note that Leibnizian infinitesimals (differentials) are realized in nonstandard analysis, and nilsquare infinitesimals in smooth infinitesimal analysis".

In psychology

In psychology, theories of mental phenomena can propose discrete differences between individuals (e.g. everyone has certain personality traits and not others) or a continuum (e.g. everyone lies somewhere on a particular personality dimension). This can also apply to fields such as law or sociology or ethics in explaining or judging variation in human behavior.

In clinical psychology or psychiatry, categorical models seek to distinguish and define particular mental disorders or illnesses, whilst continuum or dimensional models propose that some people are more extreme than others on particular dimensions.

See also

• Categories (Aristotle)

External links

• John Bell, Stanford Encyclopedia of Philosophy, Continuity and infinitesimals

This science article is a stub. You can help Wikipedia by expanding it.v · Categories: Theories Science stubs Wikimedia Foundation. 2010. Игры ⚽ Поможем написать курсовую Jesper Knudsen Horsehead crossing Look at other dictionaries: Continuum mechanics — Continuum mechanics …   Wikipedia Continuum — may refer to: Continuum (theory), anything that goes through a gradual transition from one condition, to a different condition, without any abrupt changes Contents 1 Linguistics 2 Mathematics …   Wikipedia leadership continuum theory — See Tannenbaum Schmidt continuum …   Big dictionary of business and management Continuum (topology) — In the mathematical field of point set topology, a continuum (pl continua) is a nonempty compact connected metric space, or less frequently, a compact connected Hausdorff topological space. Continuum theory is the branch of topology devoted to… …   Wikipedia Continuum (mathematics) — In mathematics, the word continuum has at least two distinct meanings, outlined in the sections below. For other uses see Continuum.Ordered setThe term the continuum sometimes denotes the real line. Somewhat more generally a continuum is a… …   Wikipedia continuum — noun /kənˈtɪnjuəm/ a) A continuous series or whole, no part of which is noticeably different from its adjacent parts, although the ends or extremes of it are very different from each other. b) The set of all real numbers and, more generally, a… …   Wiktionary Theory of mind — is the ability to attribute mental states beliefs, intents, desires, pretending, knowledge, etc. to oneself and others and to understand that others have beliefs, desires and intentions that are different from one s own.[1] Though there are… …   Wikipedia Theory X and theory Y — are theories of human motivation created and developed by Douglas McGregor at the MIT Sloan School of Management in the 1960s that have been used in human resource management, organizational behavior, and organizational development. They describe …   Wikipedia Continuum hypothesis — This article is about the hypothesis in set theory. For the assumption in fluid mechanics, see Fluid mechanics. In mathematics, the continuum hypothesis (abbreviated CH) is a hypothesis, advanced by Georg Cantor in 1877[citation needed], about… …   Wikipedia continuum hypothesis — Math. a conjecture of set theory that the first infinite cardinal number greater than the cardinal number of the set of all positive integers is the cardinal number of the set of all real numbers. [1935 40] * * * ▪ mathematics       statement of… …   Universalium 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”