Higher-dimensional space in the context of "Hyperspace"

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⭐ Core Definition: Higher-dimensional space

In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coordinate is needed to specify a point on it – for example, the point at 5 on a number line. A surface, such as the boundary of a cylinder or sphere, has a dimension of two (2D) because two coordinates are needed to specify a point on it – for example, both a latitude and longitude are required to locate a point on the surface of a sphere. A two-dimensional Euclidean space is a two-dimensional space on the plane. The inside of a cube, a cylinder or a sphere is three-dimensional (3D) because three coordinates are needed to locate a point within these spaces.

In classical mechanics, space and time are different categories and refer to absolute space and time. That conception of the world is a four-dimensional space but not the one that was found necessary to describe electromagnetism. The four dimensions (4D) of spacetime consist of events that are not absolutely defined spatially and temporally, but rather are known relative to the motion of an observer. Minkowski space first approximates the universe without gravity; the pseudo-Riemannian manifolds of general relativity describe spacetime with matter and gravity. 10 dimensions are used to describe superstring theory (6D hyperspace + 4D), 11 dimensions can describe supergravity and M-theory (7D hyperspace + 4D), and the state-space of quantum mechanics is an infinite-dimensional function space.

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👉 Higher-dimensional space in the context of Hyperspace

In science fiction, hyperspace (also known as nulspace, subspace, overspace, jumpspace and similar terms) is a concept relating to higher dimensions as well as parallel universes and a faster-than-light (FTL) method of interstellar travel. In its original meaning, the term hyperspace was simply a synonym for higher-dimensional space. This usage was most common in 19th-century textbooks and is still occasionally found in academic and popular science texts, for example, Hyperspace (1994). Its science fiction usage originated in the magazine Amazing Stories Quarterly in 1931 and within several decades it became one of the most popular tropes of science fiction, popularized by its use in the works of authors such as Isaac Asimov and E. C. Tubb, and media franchises such as Star Wars.

One of the main reasons for the concept's popularity in science fiction is the impossibility of faster-than-light travel in ordinary physical space, which hyperspace allows writers to bypass. In most works, hyperspace is described as a higher dimension through which the shape of three-dimensional space can be distorted to bring distant points close to each other, similar to the concept of a wormhole; or a shortcut-enabling parallel universe that can be travelled through. Usually it can be traversed – the process often known as "jumping" – through a gadget known as a "hyperdrive"; rubber science is sometimes used to explain it. Many works rely on hyperspace as a convenient background tool enabling FTL travel necessary for the plot, with a small minority making it a central element in their storytelling. While most often used in the context of interstellar travel, a minority of works focus on other plot points, such as the inhabitants of hyperspace, hyperspace as an energy source, or even hyperspace as the afterlife.

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Higher-dimensional space in the context of Multilinear algebra

Multilinear algebra is the study of functions with multiple vector-valued arguments, with the functions being linear maps with respect to each argument. It involves concepts such as matrices, tensors, multivectors, systems of linear equations, higher-dimensional spaces, determinants, inner and outer products, and dual spaces. It is a mathematical tool used in engineering, machine learning, physics, and mathematics.

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Higher-dimensional space in the context of Jordan curve theorem

In topology, the Jordan curve theorem (JCT), formulated by Camille Jordan in 1887, asserts that every Jordan curve (a plane simple closed curve) divides the plane into two regions: the interior, bounded by the curve, and an unbounded exterior, containing all of the nearby and far away exterior points. Every continuous path connecting a point of one region to a point of the other intersects with the curve somewhere.

While the theorem seems intuitively obvious, it takes some ingenuity to prove it by elementary means. "Although the JCT is one of the best known topological theorems, there are many, even among professional mathematicians, who have never read a proof of it." (Tverberg (1980, Introduction)). More transparent proofs rely on the mathematical machinery of algebraic topology, and these lead to generalizations to higher-dimensional spaces.

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LINKED FROM (PARENTS)
← Hyperspace ← Multilinear algebra ← Jordan curve theorem
LINKS TO (CHILDREN)
Square (geometry) → Cube → Tesseract → Line segment → Square → Physics → Mathematics → Space (mathematics) → Mathematical object → Coordinates → Point (geometry) → Line (geometry) → One-dimensional space → Surface (mathematics) → Boundary (mathematics) → Cylinder (geometry) → Sphere → Two-dimensional space → Latitude → Longitude → Two-dimensional Euclidean space → Euclidean plane → Three-dimensional → Classical mechanics → Space → Time → Absolute space and time → Four-dimensional space → Electromagnetism → Spacetime → Event (relativity) → Observer (special relativity) → Minkowski space → Gravity → Pseudo-Riemannian manifold → General relativity → Superstring theory → Hyperspace → Supergravity → M-theory → Quantum mechanics → Function space →