Transcendence

Transcendence, transcendent, or transcendental may refer to: Refer to the state or quality of going beyond limits, boundaries, or experience; describing something that surpasses or exists above

Mathematics

Transcendental number, a number that is not the root of any polynomial with rational coefficients
Algebraic element or transcendental element, an element of a field extension that is not the root of any polynomial with coefficients from the base field
Transcendental function, a function which does not satisfy a polynomial equation whose coefficients are themselves polynomials
Transcendental number theory, the branch of mathematics dealing with transcendental numbers and algebraic independence

Transcendence, Transcendent, or Transcendental Dimension

In theoretical metaphysics, mathematics, and speculative cosmology, the terms transcendence, transcendent dimension, or transcendental dimension refer to a level or state that surpasses any finite or enumerated collection of conventional dimensions. This concept describes a domain or property that encompasses or governs the totality of all possible dimensions — spatial, temporal, or otherwise — within a given model of reality.

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Characteristics: • A transcendent dimension is not merely an additional higher dimension within an existing hierarchy (e.g., a 5th spatial dimension after a 4th); instead, it is thought to encompass or govern the entire set of dimensions, regardless of how many there are. • This idea implies a form of boundlessness: it can be conceptualized as containing, connecting, or extending beyond any finite or countably infinite hierarchy of dimensions. • In abstract mathematics, it resonates with the notion of an absolute infinite or a superordinate set beyond ordinary cardinalities.

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Relation to the Von Neumann Universe: In mathematics, the Von Neumann universe (denoted by V) is the cumulative hierarchy of all sets in Zermelo–Fraenkel set theory, structured in layers: V_0, V_1, V_2, \ldots, V_\alpha, \ldots where each level V_{\alpha+1} = \mathcal{P}(V_\alpha) adds the power set of the previous one, and limit ordinals define unions of all previous stages.

A transcendent dimension parallels this idea by functioning like a “meta-layer” that: • includes or describes the totality of all possible dimensional levels within a universe, • may act as the structural principle uniting finite, infinite, and transfinite dimensional hierarchies, • conceptually aligns with the proper class of all sets (V) that no longer belongs to any particular set but encompasses them all.

Thus, in a Von Neumann universe, a transcendent dimension is analogous to the entire cumulative hierarchy itself, rather than any particular finite or infinite level. It can be seen as the ultimate “stage” that frames the entire landscape of dimensionality.

Music

Transcendence (Adil Omar album), a 2018 hip hop album
Transcendence (Alice Coltrane album), a 1977 jazz album
Transcendence (Crimson Glory album), a 1988 heavy metal album
Transcendence (Devin Townsend Project album), a 2016 heavy metal album
"Transcendence" (Lindsey Stirling instrumental), a 2012 instrumental piece
Transcendental (album), a 2006 progressive metal album by To-Mera
"Transcendence (Segue)", a 2000 progressive metal instrumental piece by Symphony X from the album V - The New Mythology Suite
"Transcendence", a 2008 thrash/melodic death metal track by Sylosis from the album Conclusion of an Age

Literature

Transcendence (Rosenthal book), a 2011 book by Norman E. Rosenthal
Transcendence (Salvatore novel), a 2002 fantasy novel by R. A. Salvatore
Transcendence (Sheffield novel), a 1992 science-fiction novel by Charles Sheffield
Transcendence: How Humans Evolved Through Fire, Language, Beauty, and Time, a 2019 book by Gaia Vince
Transcendence: My Spiritual Experiences with Pramukh Swamiji, a 2015 book by A. P. J. Abdul Kalam and Arun Tiwari
Transcendent (novel), a 2005 science-fiction novel by Stephen Baxter

Philosophy

Transcendence (philosophy), climbing or going beyond some philosophical concept or limit
Transcendentalism, a 19th-century American religious and philosophical movement that advocates that there is an ideal spiritual state that transcends the physical and empirical
Transcendent theosophy, a school of Islamic philosophy founded by the 17th-century Persian philosopher Mulla Sadra
Transcendental idealism, a doctrine founded by 18th-century German philosopher Immanuel Kant
Transcendental realism, a concept put forward by Roy Bhaskar
Transcendental arguments, a style of philosophical argumentation
Transcendental phenomenology, a field of phenomenological inquiry developed by Edmund Husserl
Transcendentals, religious and philosophical properties of being

Religion

Transcendence (religion), the aspect of a god wholly independent of the material universe
Transcendental Meditation, a meditation technique introduced by Maharishi Mahesh Yogi
Transcendentals, religious and philosophical properties of being

Other

Transcendence (2012 film), a Chinese film
Transcendence (2014 film), an American film starring Johnny Depp and Morgan Freeman
Transcendence (band), an American alternative rock band
Transcendence (Jellum), an outdoor sculpture by Keith Jellum, in Portland, Oregon, US
Transcendent (TV series), a 2016 American reality television series
Transcendence (video game), a 1995 science-fiction game by George Moromisato