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69-1241: For the Dutch sequel to Flatland , see Sphereland . Bolland is a surname. Notable people with the surname include: Adrienne Bolland (1896–1975), French test pilot; first woman to fly over the Andes Brian Bolland (born 1951), British comics artist C. J. Bolland (born 1971), English electronic-music producer Charlotte Bolland , British art historian and curator David Bolland (born 1986), Canadian professional ice hockey player Gerardus Johannes Petrus Josephus Bolland (1854–1922), Dutch philosopher, scholar, and linguist Gordon Bolland (born 1943), English professional football player and manager Janice Bolland (born 1966), American cyclist Jasper Bolland (born 1986), Dutch professional football player Jean Bolland (1596–1665), Belgian Jesuit priest and hagiographer Kevin Bolland (born 1959), American race car driver Marc Bolland (born 1959), Dutch businessman, former CEO of Marks & Spencer Mark William Bolland (born 1966), Deputy Private Secretary to

138-450: A UV completion , of the kind that string theory is intended to provide. In particular, superstring theory requires six compact dimensions (6D hyperspace) forming a Calabi–Yau manifold . Thus Kaluza-Klein theory may be considered either as an incomplete description on its own, or as a subset of string theory model building. In addition to small and curled up extra dimensions, there may be extra dimensions that instead are not apparent because

207-417: A discrete set of points (such as a finite collection of points) to be 0-dimensional. By dragging a 0-dimensional object in some direction, one obtains a 1-dimensional object. By dragging a 1-dimensional object in a new direction , one obtains a 2-dimensional object. In general, one obtains an ( n + 1 )-dimensional object by dragging an n -dimensional object in a new direction. The inductive dimension of

276-441: A line is one, as a point can move on a line in only one direction (or its opposite); the dimension of a plane is two etc. The dimension is an intrinsic property of an object, in the sense that it is independent of the dimension of the space in which the object is or can be embedded. For example, a curve , such as a circle , is of dimension one, because the position of a point on a curve is determined by its signed distance along

345-399: A two-dimensional world inhabited by geometric figures (flatlanders ); women are line segments , while men are polygons with various numbers of sides. The narrator is a square , a member of the caste of gentlemen and professionals, who guides the readers through some of the implications of life in two dimensions. The first half of the story goes through the practicalities of existing in

414-439: A Circle considered the "perfect" shape. Women are lines, quite fragile but also dangerous, as they can disappear from view and possibly stab someone. To prevent this, they are required by law to sound a "peace-cry" while moving about and to use separate doors from men. In the world of Flatland, classes are distinguished by the "Art of Hearing", the "Art of Feeling", and the "Art of Sight Recognition". Classes can be distinguished by

483-414: A conceptual model of the cities as points, while giving directions involving travel "up," "down," or "along" a road imply a one-dimensional conceptual model. This is frequently done for purposes of data efficiency, visual simplicity, or cognitive efficiency, and is acceptable if the distinction between the representation and the represented is understood but can cause confusion if information users assume that

552-658: A dream in which the Sphere revisits him, this time to introduce him to a zero-dimensional space , Pointland, of whom the Point (sole inhabitant, monarch, and universe in one) perceives any communication as a thought originating in his own mind (cf. Solipsism ): "You see," said my Teacher, "how little your words have done. So far as the Monarch understands them at all, he accepts them as his own – for he cannot conceive of any other except himself – and plumes himself upon

621-416: A manifold depends on the base field with respect to which Euclidean space is defined. While analysis usually assumes a manifold to be over the real numbers , it is sometimes useful in the study of complex manifolds and algebraic varieties to work over the complex numbers instead. A complex number ( x + iy ) has a real part x and an imaginary part y , in which x and y are both real numbers; hence,

690-570: A particular space have the same cardinality . This cardinality is called the dimension of the Hilbert space. This dimension is finite if and only if the space's Hamel dimension is finite, and in this case the two dimensions coincide. Classical physics theories describe three physical dimensions : from a particular point in space , the basic directions in which we can move are up/down, left/right, and forward/backward. Movement in any other direction can be expressed in terms of just these three. Moving down

759-432: A representation of a real-world phenomenon may have a different (usually lower) dimension than the phenomenon being represented. For example, a city (a two-dimensional region) may be represented as a point, or a road (a three-dimensional volume of material) may be represented as a line. This dimensional generalization correlates with tendencies in spatial cognition. For example, asking the distance between two cities presumes

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828-455: A rule) one step in the scale of development and nobility. Thus the son of a Square is a Pentagon , the son of a Pentagon, a Hexagon ; and so on". This rule is not the case when dealing with Isosceles Triangles (Soldiers and Workmen) with only two congruent sides. The smallest angle of an Isosceles Triangle gains 30 arc minutes (half a degree ) each generation. Additionally, the rule does not seem to apply to many-sided Polygons. For example,

897-406: A topological space may refer to the small inductive dimension or the large inductive dimension , and is based on the analogy that, in the case of metric spaces, ( n + 1 )-dimensional balls have n -dimensional boundaries , permitting an inductive definition based on the dimension of the boundaries of open sets. Moreover, the boundary of a discrete set of points is the empty set, and therefore

966-448: A two-dimensional universe, as well as a history leading up to the year 1999 on the eve of the 3rd Millennium. On New Year's Eve, the Square dreams of a visit to a one-dimensional world , "Lineland", inhabited by men, consisting of lines, while the women consisted of "lustrous points". These points and lines are unable to see the Square as anything other than a set of points on a line. Thus,

1035-426: A two-dimensional world, a regular polygon can be identified by a single angle and/or vertex . To maintain social cohesion , irregularity is to be abhorred, with moral irregularity and criminality cited, "by some" (in the book), as inevitable additional deformities, a sentiment with which the Square concurs. If the error of deviation is above a stated amount, the irregular Polygon faces euthanasia ; if below, he becomes

1104-458: Is a dimension of time. Time is often referred to as the " fourth dimension " for this reason, but that is not to imply that it is a spatial dimension . A temporal dimension is one way to measure physical change. It is perceived differently from the three spatial dimensions in that there is only one of it, and that we cannot move freely in time but subjectively move in one direction . The equations used in physics to model reality do not treat time in

1173-578: Is an algebraic group of dimension n acting on V , then the quotient stack [ V / G ] has dimension m  −  n . The Krull dimension of a commutative ring is the maximal length of chains of prime ideals in it, a chain of length n being a sequence P 0 ⊊ P 1 ⊊ ⋯ ⊊ P n {\displaystyle {\mathcal {P}}_{0}\subsetneq {\mathcal {P}}_{1}\subsetneq \cdots \subsetneq {\mathcal {P}}_{n}} of prime ideals related by inclusion. It

1242-422: Is an example of a four-dimensional object. Whereas outside mathematics the use of the term "dimension" is as in: "A tesseract has four dimensions ", mathematicians usually express this as: "The tesseract has dimension 4 ", or: "The dimension of the tesseract is 4" or: 4D. Although the notion of higher dimensions goes back to René Descartes , substantial development of a higher-dimensional geometry only began in

1311-491: Is available to support the existence of these extra dimensions. If hyperspace exists, it must be hidden from us by some physical mechanism. One well-studied possibility is that the extra dimensions may be "curled up" at such tiny scales as to be effectively invisible to current experiments. In 1921, Kaluza–Klein theory presented 5D including an extra dimension of space. At the level of quantum field theory , Kaluza–Klein theory unifies gravity with gauge interactions, based on

1380-452: Is depicted, in a sense, as a prophet due to his intuition of the importance of time to explain certain phenomena: Some thirty or more years ago a little jeu d'esprit was written by Dr. Edwin Abbott entitled Flatland . At the time of its publication it did not attract as much attention as it deserved... If there is motion of our three-dimensional space relative to the fourth dimension, all

1449-522: Is different from Wikidata All set index articles Flatland Flatland: A Romance of Many Dimensions is a satirical novella by the English schoolmaster Edwin Abbott Abbott , first published in 1884 by Seeley & Co. of London. Written pseudonymously by "A Square", the book used the fictional two-dimensional world of Flatland to comment on the hierarchy of Victorian culture, but

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1518-428: Is imprisoned in the same facility. He cannot convince his brother, even after all they have both seen. Seven years after being imprisoned, A Square writes out the book Flatland as a memoir , hoping to keep it as posterity for a future generation that can see beyond their two-dimensional existence. Men are portrayed as polygons whose social status is determined by their regularity and the number of their sides, with

1587-557: Is mainly concentrated in the first part of the book, "This World", which describes Flatland. The main points of interest are the Victorian concept of women's roles in the society and in the class-based hierarchy of men. Abbott has been accused of misogyny due to his portrayal of women in Flatland . In his Preface to the Second and Revised Edition, 1884, he answers such critics by emphasizing that

1656-403: Is probably the dimension of the tangent space at any Regular point of an algebraic variety . Another intuitive way is to define the dimension as the number of hyperplanes that are needed in order to have an intersection with the variety that is reduced to a finite number of points (dimension zero). This definition is based on the fact that the intersection of a variety with a hyperplane reduces

1725-416: Is said to be infinite, and one writes dim X = ∞ . Moreover, X has dimension −1, i.e. dim X = −1 if and only if X is empty. This definition of covering dimension can be extended from the class of normal spaces to all Tychonoff spaces merely by replacing the term "open" in the definition by the term " functionally open ". An inductive dimension may be defined inductively as follows. Consider

1794-455: Is strongly related to the dimension of an algebraic variety, because of the natural correspondence between sub-varieties and prime ideals of the ring of the polynomials on the variety. For an algebra over a field , the dimension as vector space is finite if and only if its Krull dimension is 0. For any normal topological space X , the Lebesgue covering dimension of X is defined to be

1863-680: Is the largest number of spatial dimensions in which strings can generically intersect. If initially there are many windings of strings around compact dimensions, space could only expand to macroscopic sizes once these windings are eliminated, which requires oppositely wound strings to find each other and annihilate. But strings can only find each other to annihilate at a meaningful rate in three dimensions, so it follows that only three dimensions of space are allowed to grow large given this kind of initial configuration. Extra dimensions are said to be universal if all fields are equally free to propagate within them. Several types of digital systems are based on

1932-410: Is the same as moving up a negative distance. Moving diagonally upward and forward is just as the name of the direction implies i.e. , moving in a linear combination of up and forward. In its simplest form: a line describes one dimension, a plane describes two dimensions, and a cube describes three dimensions. (See Space and Cartesian coordinate system .) A temporal dimension , or time dimension ,

2001-592: The brane by their endpoints, whereas the closed strings that mediate the gravitational interaction are free to propagate into the whole spacetime, or "the bulk". This could be related to why gravity is exponentially weaker than the other forces, as it effectively dilutes itself as it propagates into a higher-dimensional volume. Some aspects of brane physics have been applied to cosmology . For example, brane gas cosmology attempts to explain why there are three dimensions of space using topological and thermodynamic considerations. According to this idea it would be since three

2070-630: The force moving any object to change is time . In physics, three dimensions of space and one of time is the accepted norm. However, there are theories that attempt to unify the four fundamental forces by introducing extra dimensions / hyperspace . Most notably, superstring theory requires 10 spacetime dimensions, and originates from a more fundamental 11-dimensional theory tentatively called M-theory which subsumes five previously distinct superstring theories. Supergravity theory also promotes 11D spacetime = 7D hyperspace + 4 common dimensions. To date, no direct experimental or observational evidence

2139-410: The physical space . In mathematics , the dimension of an object is, roughly speaking, the number of degrees of freedom of a point that moves on this object. In other words, the dimension is the number of independent parameters or coordinates that are needed for defining the position of a point that is constrained to be on the object. For example, the dimension of a point is zero; the dimension of

Bolland - Misplaced Pages Continue

2208-411: The surname Bolland . If an internal link intending to refer to a specific person led you to this page, you may wish to change that link by adding the person's given name (s) to the link. Retrieved from " https://en.wikipedia.org/w/index.php?title=Bolland&oldid=1141561811 " Category : Surnames Hidden categories: Articles with short description Short description

2277-415: The 19th century, via the work of Arthur Cayley , William Rowan Hamilton , Ludwig Schläfli and Bernhard Riemann . Riemann's 1854 Habilitationsschrift , Schläfli's 1852 Theorie der vielfachen Kontinuität , and Hamilton's discovery of the quaternions and John T. Graves ' discovery of the octonions in 1843 marked the beginning of higher-dimensional geometry. The rest of this section examines some of

2346-659: The Prince of Wales 1998–2002 Martin Bolland (born 1956), British businessman Paul Bolland (born 1979), English professional football player Phil Bolland (born 1967), English professional football player Brothers Rob and Ferdi Bolland (born 1955 and 1956), composers and music producers, who recorded as "Bolland" and "Bolland & Bolland" William Bolland (1772–1840), lawyer and bibliophile William Procter Bolland (1815–1863), cricketer See also [ edit ] Boland (disambiguation) Bollandist [REDACTED] Surname list This page lists people with

2415-460: The Sphere's existence and prescribing the silencing. After this proclamation is made, many witnesses are massacred or imprisoned (according to caste), including the Square's brother. After the Square's mind is opened to new dimensions, he tries to convince the Sphere of the theoretical possibility of the existence of a fourth dimension and higher spatial dimensions. Still, the Sphere returns his student to Flatland in disgrace. The Square then has

2484-518: The Square attempts to convince the realm's monarch of a second dimension but cannot do so. In the end, the monarch of Lineland tries to kill the Square rather than tolerate him any further. Following this vision, the Square is visited by a sphere . Similar to the "points" in Lineland, he is unable to see the three-dimensional object as anything other than a circle (more precisely, a disk ). The Sphere then levitates up and down through Flatland, allowing

2553-477: The Square cannot convince anyone of Spaceland's existence, especially after official decrees are announced that anyone preaching the existence of three dimensions will be imprisoned (or executed, depending on caste). For example, he tries to convince his relative of the third dimension but cannot move a square "upward," as opposed to forward or sideways. Eventually, the Square himself is imprisoned for just this reason, with only occasional contact with his brother, who

2622-406: The Square to see the circle expand and contract between great circle and small circles. The Sphere then tries further to convince the Square of the third dimension by dimensional analogies (a point becomes a line, a line becomes a square). The Square is still unable to comprehend the third dimension, so the Sphere resorts to deeds: he gives info about the "insides" of the house, moves a cup through

2691-660: The changes we experience and assign to the flow of time will be due simply to this movement, the whole of the future as well as the past always existing in the fourth dimension. The Oxford Dictionary of National Biography subsequently revised his biography to state that [Abbott] "is most remembered as the author of Flatland: A Romance of Many Dimensions " . Numerous imitations or sequels to Flatland have been created. Examples include: Books and short stories inspired by Flatland include: Dimension In classical mechanics , space and time are different categories and refer to absolute space and time . That conception of

2760-448: The complex dimension is half the real dimension. Conversely, in algebraically unconstrained contexts, a single complex coordinate system may be applied to an object having two real dimensions. For example, an ordinary two-dimensional spherical surface , when given a complex metric, becomes a Riemann sphere of one complex dimension. The dimension of an algebraic variety may be defined in various equivalent ways. The most intuitive way

2829-461: The curve to a fixed point on the curve. This is independent from the fact that a curve cannot be embedded in a Euclidean space of dimension lower than two, unless it is a line. The dimension of Euclidean n -space E is n . When trying to generalize to other types of spaces, one is faced with the question "what makes E n -dimensional?" One answer is that to cover a fixed ball in E by small balls of radius ε , one needs on

Bolland - Misplaced Pages Continue

2898-558: The description of women was satirizing the viewpoints held, stating that the Square: was writing as a Historian, he has identified himself (perhaps too closely) with the views generally adopted by Flatland and (as he has been informed) even by Spaceland, Historians; in whose pages (until very recent times) the destinies of Women and of the masses of mankind have seldom been deemed worthy of mention and never of careful consideration. Flatland did not have much success when published, although it

2967-468: The dimension by one unless if the hyperplane contains the variety. An algebraic set being a finite union of algebraic varieties, its dimension is the maximum of the dimensions of its components. It is equal to the maximal length of the chains V 0 ⊊ V 1 ⊊ ⋯ ⊊ V d {\displaystyle V_{0}\subsetneq V_{1}\subsetneq \cdots \subsetneq V_{d}} of sub-varieties of

3036-450: The direction of increasing entropy ). The best-known treatment of time as a dimension is Poincaré and Einstein 's special relativity (and extended to general relativity ), which treats perceived space and time as components of a four-dimensional manifold , known as spacetime , and in the special, flat case as Minkowski space . Time is different from other spatial dimensions as time operates in all spatial dimensions. Time operates in

3105-409: The empty set can be taken to have dimension -1. Similarly, for the class of CW complexes , the dimension of an object is the largest n for which the n -skeleton is nontrivial. Intuitively, this can be described as follows: if the original space can be continuously deformed into a collection of higher-dimensional triangles joined at their faces with a complicated surface, then the dimension of

3174-408: The first, second and third as well as theoretical spatial dimensions such as a fourth spatial dimension . Time is not however present in a single point of absolute infinite singularity as defined as a geometric point , as an infinitely small point can have no change and therefore no time. Just as when an object moves through positions in space, it also moves through positions in time. In this sense

3243-428: The given algebraic set (the length of such a chain is the number of " ⊊ {\displaystyle \subsetneq } "). Each variety can be considered as an algebraic stack , and its dimension as variety agrees with its dimension as stack. There are however many stacks which do not correspond to varieties, and some of these have negative dimension. Specifically, if V is a variety of dimension m and G

3312-432: The lowest rank of civil servant . An irregular Polygon is not destroyed at birth, but allowed to develop to see if the irregularity can be "cured" or reduced. If the deformity remains, the irregular is "painlessly and mercifully consumed." In Flatland , Abbott describes a society rigidly divided into classes. Social ascent is the main aspiration of its inhabitants, apparently granted to everyone but strictly controlled by

3381-399: The lowest rank of nobility, all the way up to (near) Circles, who make up the priest class . The higher-order Polygons have much less of a chance of producing sons, preventing Flatland from being overcrowded with noblemen. Apart from Isosceles Triangles, only regular Polygons are considered until chapter seven of the book when the issue of irregularity, or physical deformity is brought up. In

3450-430: The matter associated with our visible universe is localized on a (3 + 1)-dimensional subspace. Thus, the extra dimensions need not be small and compact but may be large extra dimensions . D-branes are dynamical extended objects of various dimensionalities predicted by string theory that could play this role. They have the property that open string excitations, which are associated with gauge interactions, are confined to

3519-486: The more important mathematical definitions of dimension. The dimension of a vector space is the number of vectors in any basis for the space, i.e. the number of coordinates necessary to specify any vector. This notion of dimension (the cardinality of a basis) is often referred to as the Hamel dimension or algebraic dimension to distinguish it from other notions of dimension. For the non- free case, this generalizes to

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3588-428: The notion of the length of a module . The uniquely defined dimension of every connected topological manifold can be calculated. A connected topological manifold is locally homeomorphic to Euclidean n -space, in which the number n is the manifold's dimension. For connected differentiable manifolds , the dimension is also the dimension of the tangent vector space at any point. In geometric topology ,

3657-445: The novella's more enduring contribution is its examination of dimensions . A sequel, Sphereland , was written by Dionys Burger in 1957. Several films have been based on Flatland , including the feature film Flatland (2007). Other efforts have been short or experimental films, including one narrated by Dudley Moore and the short films Flatland: The Movie (2007) and Flatland 2: Sphereland (2012). The story describes

3726-601: The object is the dimension of those triangles. The Hausdorff dimension is useful for studying structurally complicated sets, especially fractals . The Hausdorff dimension is defined for all metric spaces and, unlike the dimensions considered above, can also have non-integer real values. The box dimension or Minkowski dimension is a variant of the same idea. In general, there exist more definitions of fractal dimensions that work for highly irregular sets and attain non-integer positive real values. Every Hilbert space admits an orthonormal basis , and any two such bases for

3795-504: The observer will fade more rapidly than polygons with more gradual angles. Colour of any kind was banned in Flatland after Isosceles workers painted themselves to impersonate noble Polygons. The Square describes these events, and the ensuing class war at length. The population of Flatland can " evolve " through the "Law of Nature", which states: "a male child shall have one more side than his father, so that each generation shall rise (as

3864-577: The order of ε such small balls. This observation leads to the definition of the Minkowski dimension and its more sophisticated variant, the Hausdorff dimension , but there are also other answers to that question. For example, the boundary of a ball in E looks locally like E and this leads to the notion of the inductive dimension . While these notions agree on E , they turn out to be different when one looks at more general spaces. A tesseract

3933-450: The realization that gravity propagating in small, compact extra dimensions is equivalent to gauge interactions at long distances. In particular when the geometry of the extra dimensions is trivial, it reproduces electromagnetism . However, at sufficiently high energies or short distances, this setup still suffers from the same pathologies that famously obstruct direct attempts to describe quantum gravity . Therefore, these models still require

4002-406: The same way that humans commonly perceive it. The equations of classical mechanics are symmetric with respect to time , and equations of quantum mechanics are typically symmetric if both time and other quantities (such as charge and parity ) are reversed. In these models, the perception of time flowing in one direction is an artifact of the laws of thermodynamics (we perceive time as flowing in

4071-412: The smallest integer n for which the following holds: any open cover has an open refinement (a second open cover in which each element is a subset of an element in the first cover) such that no point is included in more than n + 1 elements. In this case dim X = n . For X a manifold, this coincides with the dimension mentioned above. If no such integer n exists, then the dimension of X

4140-432: The sons of several hundred-sided Polygons will often develop 50 or more sides more than their parents. Furthermore, the angle of an Isosceles Triangle or the number of sides of a (regular) Polygon may be altered during life by deeds or surgical adjustments . An Equilateral Triangle is a member of the craftsman class . Squares and Pentagons are the "gentlemen" class, as doctors, lawyers, and other professions. Hexagons are

4209-464: The sound of one's voice, but the lower classes have more developed vocal organs, enabling them to feign the voice of a Polygon or even a Circle. Feeling, practised by the lower classes and women, determines the configuration of a person by feeling one of its angles . The "Art of Sight Recognition", practised by the upper classes, is aided by "Fog", which allows an observer to determine the depth of an object. With this, polygons with sharp angles relative to

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4278-471: The state-space of quantum mechanics is an infinite-dimensional function space . The concept of dimension is not restricted to physical objects. High-dimensional space s frequently occur in mathematics and the sciences . They may be Euclidean spaces or more general parameter spaces or configuration spaces such as in Lagrangian or Hamiltonian mechanics ; these are abstract spaces , independent of

4347-424: The storage, analysis, and visualization of geometric shapes, including illustration software , Computer-aided design , and Geographic information systems . Different vector systems use a wide variety of data structures to represent shapes, but almost all are fundamentally based on a set of geometric primitives corresponding to the spatial dimensions: Frequently in these systems, especially GIS and Cartography ,

4416-478: The theory of manifolds is characterized by the way dimensions 1 and 2 are relatively elementary, the high-dimensional cases n > 4 are simplified by having extra space in which to "work"; and the cases n = 3 and 4 are in some senses the most difficult. This state of affairs was highly marked in the various cases of the Poincaré conjecture , in which four different proof methods are applied. The dimension of

4485-428: The third dimension, and even goes inside the Square for a bit. Still unable to comprehend 3D, the Sphere takes the Square to the third dimension, Spaceland. This Sphere visits Flatland at the turn of each millennium to introduce a new apostle to the idea of a third dimension in the hope of eventually educating the population of Flatland. From the safety of Spaceland, they can oversee the leaders of Flatland, acknowledging

4554-408: The top of the hierarchy. Freedom is despised and the laws are cruel. Innovators are imprisoned or suppressed. Members of lower classes who are intellectually valuable, and potential leaders of riots , are either killed or promoted to the higher classes. Every attempt for change is considered dangerous and harmful. This world is not prepared to receive "revelations from another world". The satirical part

4623-446: The variety of Its Thought as an instance of creative Power. Let us leave this god of Pointland to the ignorant fruition of his omnipresence and omniscience: nothing that you or I can do can rescue him from his self-satisfaction." The Square recognises the identity of the ignorance of the monarchs of Pointland and Lineland with his own (and the Sphere's) previous ignorance of the existence of higher dimensions. Once returned to Flatland,

4692-624: 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

4761-616: Was not entirely ignored. In the entry on Edwin Abbott in the Dictionary of National Biography for persons who died in the period of 1922 to 1930, Flatland was not even mentioned. The book was discovered again after Albert Einstein 's general theory of relativity was published, which brought to prominence the concept of a fourth dimension. Flatland was mentioned in a letter by William Garnett entitled "Euclid, Newton and Einstein" published in Nature on 12 February 1920. In this letter, Abbott

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