Continuum (measurement)

Continuum theories or models explain variation as involving gradual quantitative transitions without abrupt changes or discontinuities. In contrast, categorical theories or models explain variation using qualitatively different states.

In physics

In physics, for example, the space-time continuum model describes space and time as part of the same continuum rather than as separate entities. A spectrum in physics, such as the electromagnetic spectrum, is often termed as either continuous (with energy at all wavelengths) or discrete (energy at only certain wavelengths).

In contrast, quantum mechanics uses quanta, certain defined amounts (i.e. categorical amounts) 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".

The Continuum

The Continuum was an online strategy game that combines turn-based war gaming with role-playing game-like character development and the collectability of a tabletop miniatures game. It takes place in the Crossworld, a new reality formed from the collapse of several formerly separate worlds that became unhinged in the space/time continuum. The game was developed by Seven Lights and launched on June 25, 2008. It has been discontinued as of 2011.

Gameplay

One starts by signing up,and receiving free units to build a squad that you will use to battle other players and find usable equipment on the battlefield.(more on that later)You can also purchase units with real money, whether in starter packs of 40, booster packs of 15, or individually. The developers have indicated that everyone may play for free, receiving one free booster pack upon registration. Once you have purchased your units, you may begin spending their "ability points" to improve the units. Common units have one ability point to spend, Uncommon units have two, Rare units begin with three and Heroic units have four. As you spend these ability points, you choose what abilities your units will have in combat. Each choice becomes important, though you gain additional ability points as your units level up, depending on their rarity.

Continuum (topology)

In the mathematical field of point-set topology, a continuum (plural: "continua") is a nonempty compact connected metric space, or, less frequently, a compact connected Hausdorff space. Continuum theory is the branch of topology devoted to the study of continua.

Definitions

Continuum

Continuum may refer to:

Companies and organizations

Games

Theory

Theory is a contemplative and rational type of abstract or generalizing thinking, or the results of such thinking. Depending on the context, the results might for example include generalized explanations of how nature works. The word has its roots in ancient Greek, but in modern use it has taken on several different related meanings. A theory is not the same as a hypothesis. A theory provides an explanatory framework for some observation, and from the assumptions of the explanation follows a number of possible hypotheses that can be tested in order to provide support for, or challenge, the theory.

A theory can be normative (or prescriptive), meaning a postulation about what ought to be. It provides "goals, norms, and standards". A theory can be a body of knowledge, which may or may not be associated with particular explanatory models. To theorize is to develop this body of knowledge.

As already in Aristotle's definitions, theory is very often contrasted to "practice" (from Greek praxis, πρᾶξις) a Greek term for "doing", which is opposed to theory because pure theory involves no doing apart from itself. A classical example of the distinction between "theoretical" and "practical" uses the discipline of medicine: medical theory involves trying to understand the causes and nature of health and sickness, while the practical side of medicine is trying to make people healthy. These two things are related but can be independent, because it is possible to research health and sickness without curing specific patients, and it is possible to cure a patient without knowing how the cure worked.