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or even Q-Gorenstein. Log terminal singularities are rational. An example of a rational singularity is the singular point of the quadric cone x 2 + y 2
Rational_singularity
Singularities of algebraic varieties
(1985) and Reid. In particular, a terminal 3-fold singularity is the quotient of a hypersurface singularity with multiplicity 2 by a finite cyclic group.
Canonical_singularity
Mathematical concept describing isolated singularity of an algebraic surface
a Du Val singularity, also called simple surface singularity, Kleinian singularity, or rational double point, is an isolated singularity of a complex
Du_Val_singularity
Topics referred to by the same term
Look up Singularity or singularity in Wiktionary, the free dictionary. Singularity or singular point may refer to: Mathematical singularity, a point at
Singularity
Curve defined as zeros of polynomials
equations of the branches. For describing a singularity, it is worth to translate the curve for having the singularity at the origin. This consists of a change
Algebraic_curve
Hypothetical event
The technological singularity, often simply called the singularity, is a hypothetical event in which technological growth accelerates beyond human control
Technological_singularity
Location around which a function displays irregular behavior
essential singularity of a function is a "severe" singularity near which the function exhibits striking behavior. The category essential singularity is a "left-over"
Essential_singularity
Concept in algebraic geometry
resolution of the conical singularity factorizes through the minimal resolution given by blowing up the singular point. However the rational map from the XY-plane
Resolution_of_singularities
American mathematician (born 1934)
contributed to the theory of surface singularities which are both fundamental and seminal. The rational singularity and fundamental cycles, which are used
Michael_Artin
Ratio of polynomial functions
removable singularity. The sum, product, or quotient (excepting division by the zero polynomial) of two rational functions is itself a rational function
Rational_function
Type of commutative ring in mathematics
singularities; in characteristic zero, these are rational singularities and hence are Cohen–Macaulay, One successful analog of rational singularities
Cohen–Macaulay_ring
Polynomial equation whose integer solutions are sought
non-rational coefficients), then it defines two hyperplanes. The intersection of these hyperplanes is a rational flat, and contains rational singular points
Diophantine_equation
Surface in algebraic geometry
investigated. Every non-singular rational surface can be obtained by repeatedly blowing up a minimal rational surface. The minimal rational surfaces are the
Rational_surface
American AI researcher and writer (born 1979)
(2012). Singularity Rising. BenBella Books, Inc. ISBN 978-1936661657. Miller, James (July 28, 2011). "You Can Learn How To Become More Rational". Business
Eliezer_Yudkowsky
Rationality-focused community blog
"Reflections on the Singularity Journey". In Callaghan, V.; Miller, J.; Yampolskiy, R.; Armstrong, S. (eds.). The Technological Singularity. The Frontiers
LessWrong
Theorem
theorem on rationality for surfaces is a classical result of Max Noether on complex algebraic surfaces, giving a criterion for a rational surface. Let
Noether's theorem on rationality for surfaces
Noether's_theorem_on_rationality_for_surfaces
several closely related notions such as nc divisor, nc singularity, snc divisor, and snc singularity. See normal crossings. normally generated A line bundle
Glossary of algebraic geometry
Glossary_of_algebraic_geometry
Theorem in ring theory
Boutot proved that if a variety over a field of characteristic 0 has rational singularities then so does its quotient by the action of a reductive group; this
Hochster–Roberts_theorem
Type of surface singularity used in algebraic geometry
algebraic geometry, an elliptic singularity of a surface, introduced by Philip Wagreich in 1970, is a surface singularity such that the arithmetic genus
Elliptic_singularity
AI thought experiment
capable of such an act), which increases the chance of a technological singularity. Roko went on to state that reading his post would cause the reader to
Roko's_basilisk
General relativity model near spacetime singularities
relativity has a page on the topic of: BKL singularity A Belinski–Khalatnikov–Lifshitz (BKL) singularity is a model of the dynamic evolution of the universe
BKL_singularity
Power series with negative powers
f(x)} for all x ∈ C {\displaystyle x\in \mathbb {C} } except at the singularity x = 0 {\displaystyle x=0} . The graph on the right shows f ( x ) {\displaystyle
Laurent_series
Curves of genus > 1 over the rationals have only finitely many rational points
non-singular algebraic curve of genus greater than 1 over the field Q {\displaystyle \mathbb {Q} } of rational numbers has only finitely many rational points
Faltings'_theorem
Type of integral domain
2307/2315529. ISSN 0002-9890. JSTOR 2315529. Lipman, Joseph (1969). "Rational singularities with applications to algebraic surfaces and unique factorization"
Unique_factorization_domain
Kind of partial function between algebraic varieties
mathematics, in particular the subfield of algebraic geometry, a rational map or rational mapping is a kind of partial function between algebraic varieties
Rational_mapping
Fan fiction by Eliezer Yudkowsky
Harry Potter and the Methods of Rationality Miller, James D. (16 October 2012). "A Friendly Explosion". Singularity Rising: Surviving and Thriving in
Harry Potter and the Methods of Rationality
Harry_Potter_and_the_Methods_of_Rationality
Algebraic surface defined by a cubic polynomial
contains at least one A 1 {\displaystyle A_{1}} singularity, it will have an A 1 {\displaystyle A_{1}} singularity at [ 0 : 0 : 0 : 1 ] {\displaystyle [0:0:0:1]}
Cubic_surface
Class of mathematical function
singularity. The function f ( z ) = sin 1 z {\displaystyle f(z)=\sin {\frac {1}{z}}} is not meromorphic either, as it has an essential singularity at
Meromorphic_function
Concept in complex analysis
certain type of singularity of a complex-valued function of a complex variable. It is the simplest type of non-removable singularity of such a function
Zeros_and_poles
List of interlinear glossing abbreviations
abbreviated to 3ns, rather than to *3nsg, to avoid confusion with 3nsg (3 non-singular). Alexandra Aikhenvald & RMW Dixon (2017) The Cambridge Handbook of Linguistic
List of glossing abbreviations
List_of_glossing_abbreviations
American mathematician and businessman
2307/2374025, ISSN 0002-9327, JSTOR 2374025 Laufer, Henry B. (1972), "On rational singularities", American Journal of Mathematics, 94 (2): 597–608, doi:10.2307/2374639
Henry_Laufer
Ideologies of change via capitalism and technology
self-revolutionizing capitalism that would culminate in a technological singularity, resulting in artificial intelligence surpassing and eliminating humanity
Accelerationism
Algebraic variety
In mathematics, a rational variety is an algebraic variety, over a given field K, which is birationally equivalent to a projective space of some dimension
Rational_variety
Nonprofit AI safety organization
Retrieved August 28, 2018. "Press release: Singularity University Acquires the Singularity Summitt". Singularity University. 9 December 2012. Archived from
Machine Intelligence Research Institute
Machine_Intelligence_Research_Institute
Fraction with denominator a power of two
In mathematics, a dyadic rational or binary rational is a number that can be expressed as a fraction whose denominator is a power of two. For example
Dyadic_rational
Branch of mathematics
such as the field of rational numbers, number fields, finite fields, function fields, and p-adic fields. A large part of singularity theory is devoted to
Algebraic_geometry
American rationality writer and speaker (born 1983)
speaker and co-founder of the Center for Applied Rationality. From 2010 to 2021, she hosted Rationally Speaking, the official podcast of New York City
Julia_Galef
Components of the Fatou set
"domains on which the iterates tend to an essential singularity (not possible for polynomials and rational functions)" one example of such a function is: f
Classification of Fatou components
Classification_of_Fatou_components
Hypothetical agent surpassing human intelligence
or may not result from an intelligence explosion or a technological singularity. Some researchers believe that superintelligence will likely follow shortly
Superintelligence
Mathematical idealization of the surface of a body
the classification of the singular points is singularity theory. A singular point is isolated if there is no other singular point in a neighborhood of
Surface_(mathematics)
Field of combinatorics using complex analysis
for a similar theorem dealing with multiple singularities. If f ( z ) {\displaystyle f(z)} has a singularity at ζ {\displaystyle \zeta } and f ( z ) ∼ (
Analytic_combinatorics
Manifold or algebraic variety of dimension n in a space of dimension n+1
is defined over the rational numbers. It has no rational point, but has many points that are rational over the Gaussian rationals. A projective (algebraic)
Hypersurface
Used to count, measure, and label
centuries to include zero (0), negative numbers such as negative one (−1), rational numbers such as one half ( 1 2 ) {\displaystyle \left({\tfrac {1}{2}}\right)}
Number
Victorian era design movement favouring practical women's clothing
an objective of the Victorian dress reform movement (also known as the rational dress movement) of the middle and late Victorian era, led by various reformers
Victorian_dress_reform
AG]. Singh, Anurag K. (2002-08-28). "Cyclic covers of rings with rational singularities". arXiv:math/0208226. "what is the cyclic cover trick?". MathOverflow
Cyclic_cover
French mathematician
dissertation on Singularites rationnelles et groupes algebriques (Rational singularities and algebraic groups) under the direction of Lê Dũng Tráng. She
Hélène_Esnault
Asymptotically stable in the sense of geometric invariant theory
the condition that it is not of arithmetic genus one and every non-singular rational component meets the other components in at least 3 points (Deligne
Stable_curve
Physical theory of the cosmos
measurements of the expansion rate of the universe place the initial singularity at an estimated 13.787±0.02 billion years ago, which is considered the
Big_Bang
Point of interest for complex multi-valued functions
a multiple-valued function has nontrivial monodromy and an essential singularity. In geometric function theory, unqualified use of the term branch point
Branch_point
Algebraic structure in homological algebra
American mathematician Dennis Sullivan developed a DGA to encode the rational homotopy type of topological spaces. Let A ∙ = ⨁ i ∈ Z A i {\displaystyle
Differential_graded_algebra
Concept in mathematics
Chen, Suqin; Wu, Xionghua (2010). "A rational spectral collocation method for solving a class of parameterized singular perturbation problems". Journal of
Singular_perturbation
'Best' approximation of a function by a rational function of given order
theory—typically replace them. Since a Padé approximant is a rational function, an artificial singular point may occur as an approximation, but this can be avoided
Padé_approximant
{w}}}=0,\,i\geq 1.} In other words, X w {\displaystyle X_{w}} has rational singularities. There are also some other constructions; see, for example, Vakil
Bott–Samelson_resolution
Concept in algebraic geometry
applications in geometry and number theory, because they typically admit rational points, an elementary case of which is the Chevalley–Warning theorem. Fano
Fano_variety
Seven mathematical problems with a US$1 million prize for each solution
conjecture is: Let X be a non-singular complex projective variety. Then every Hodge class on X is a linear combination with rational coefficients of the cohomology
Millennium_Prize_Problems
Concept in special relativity
Bang, for example, appears as a singularity in ordinary time but, when modelled with imaginary time, the singularity can be removed and the Big Bang functions
Imaginary_time
Algebraic curve in mathematics
(except for a finite number of primes p, where the reduced curve has a singularity and thus fails to be elliptic, in which case E is said to be of bad reduction
Elliptic_curve
apply the Cholesky decomposition to a rational polynomial matrix and modify it to remove lower half plane singularities. That is, given P ( t ) = [ p 11 (
Polynomial matrix spectral factorization
Polynomial_matrix_spectral_factorization
Hypothesis about intelligent agents
with the Singularity Paradox?". Philosophy and Theory of Artificial Intelligence. Studies in Applied Philosophy, Epistemology and Rational Ethics. Vol
Instrumental_convergence
Indian mathematician
collaboration with Kapil Paranjape) and the characterization of rational singularities (in collaboration with Vikram Mehta). Srinivas's book on "Algebraic
Vasudevan_Srinivas
Class of mathematical expression
arbitrarily large, and is said to "tend to infinity", a type of mathematical singularity. For example, the reciprocal function, f ( x ) = 1 x {\displaystyle
Division_by_zero
American mathematician
parameter ideals" (Inventiones Mathematicae 1994), "F-rational rings have rational singularities" (American J. Math. 1997, and, with Gennady Lyubeznik
Karen_E._Smith
Type of AI with wide-ranging abilities
intelligence and the possibility of a technological singularity: a reaction to Ray Kurzweil's The Singularity Is Near, and McDermott's critique of Kurzweil"
Artificial general intelligence
Artificial_general_intelligence
Type of function in mathematics
In mathematics, the Legendre rational functions are a sequence of orthogonal functions on [0, ∞). They are obtained by composing the Cayley transform with
Legendre_rational_functions
Function with unusual fractal properties
by Hermann Minkowski in 1904. It maps quadratic irrational numbers to rational numbers on the unit interval, via an expression relating the continued
Minkowski's question-mark function
Minkowski's_question-mark_function
English mathematician, mathematical physicist (born 1931)
only an apparent singularity, similar to the well-known apparent singularity at the event horizon of a black hole. The latter singularity can be removed
Roger_Penrose
Field of algebraic geometry
are given by rational functions rather than polynomials; the map may fail to be defined where the rational functions have poles. A rational map from one
Birational_geometry
Linguistic category of nouns
define noun classes include: animate vs. inanimate (as in Ojibwe) rational vs. non-rational (as in Tamil) human vs. non-human human vs. animal (zoic) vs.
Noun_class
Type of mathematical knot
bounds a self-intersecting disk with only ribbon singularities. Intuitively, this kind of singularity can be formed by cutting a slit in the disk and passing
Ribbon_knot
d\theta .}} When r equals 1, the integrand on the right hand side has a singularity at θ = 0. The truncated Hilbert transform is defined by H ε f ( φ ) =
Singular integral operators on closed curves
Singular_integral_operators_on_closed_curves
Solving integer equations from all modular solutions
the rationals in at least 14 variables. Restricting to non-singular forms, one can do better than this: Heath-Brown proved that every non-singular cubic
Hasse_principle
When there is a singularity in the function being integrated such that the antiderivative becomes undefined at some point (the singularity), then C does
Lists_of_integrals
Analogs of homology groups for algebraic varieties
{\displaystyle W} singular. For a scheme X {\displaystyle X} of finite type over k {\displaystyle k} , the group of i {\displaystyle i} -cycles rationally equivalent
Chow_group
Factors influencing economic decisions
theory. Behavioral economics is primarily concerned with the bounds of rationality of economic agents. Behavioral models typically integrate insights from
Behavioral_economics
fibration over the Riemann sphere; but with two qualifications about singularity. The first point comes up if we assume that V {\displaystyle V} is given
Lefschetz_pencil
Mathematical concept
factored through a "smaller" one; precisely, the singular fibers should contain no smooth rational curves with self-intersection number −1.) It gives:
Elliptic_surface
Proposed era of humanity after the Information Age
contrast, the main activities of the Information Age were analysis and rational thought). It has been proposed that new technologies like virtual reality
Imagination_Age
Measure of the coldness of a system
temperature, in which β is continuous as it crosses zero whereas T has a singularity. In addition, β has the advantage of being easier to understand causally:
Thermodynamic_beta
Algebraic variety defined within an affine space
that belong to kn are said k-rational or rational over k. In the common case where k is the field of real numbers, a k-rational point is called a real point
Affine_variety
In algebraic geometry, a crepant resolution of a singularity is a resolution that does not affect the canonical class of the manifold. The term "crepant"
Crepant_resolution
Algebraic surface with special triviality properties
Castelnuovo (1895) about whether a surface with q = pg = 0 is necessarily rational, though some of the Reye congruences introduced earlier by Reye (1882)
Enriques_surface
Monitoring and controlling the behavior of AI systems
with the Singularity Paradox?", Philosophy and Theory of Artificial Intelligence, Studies in Applied Philosophy, Epistemology and Rational Ethics, vol
AI_capability_control
Natural number
Arabic numeral. Linguistically, in English, "one" is a determiner for singular nouns and a gender-neutral pronoun. In mathematics, 1 is the multiplicative
1
Rational numbers with root 5 added
, where a {\displaystyle a} and b {\displaystyle b} are both rational numbers and 5 {\displaystyle {\sqrt {5}}} is the square root of 5,
Golden_field
The method can also be used to factorize specific matrices (non-rational, singular, large scale, depending on a parameter) which was not possible before
Gigla_Janashia
Mathematical theory of topological spaces
is a rational homotopy equivalence if and only if it induces an isomorphism on singular homology groups with rational coefficients. The rational homotopy
Rational_homotopy_theory
Individual being
ontological definition of the person as "an individual substance of a rational nature" (Boethius). The self-consciousness-based definition of the person
Person
Curve created by a geometric operation
if C is p-circular of degree n, and if the center of inversion is a singularity of order q on C, then the inverse curve will be an (n − p − q)-circular
Inverse_curve
Concept in algebraic geometry
projective surface and the fibers of f {\displaystyle f} do not contain rational curves of self-intersection − 1 {\displaystyle -1} , then the fibration
Canonical_bundle
Inputs for which a function's value is non-zero
is 0 {\displaystyle 0} on irrational numbers and 1 {\displaystyle 1} on rational numbers, and [ 0 , 1 ] {\displaystyle [0,1]} is equipped with Lebesgue
Support_(mathematics)
German social philosopher (1929–2026)
of critical theory and pragmatism. His work addressed communicative rationality and the public sphere. He held professorships at Heidelberg University
Jürgen_Habermas
Absence of belief in the existence of deities; the opposite of theism
limitation of human knowledge to singular objects, and asserted that the divine essence could not be intuitively or rationally apprehended by human intellect
Atheism
Domain of convergence of power series
At z = 0, there is in effect no singularity since the singularity is removable. The only non-removable singularities are therefore located at the other
Radius_of_convergence
In religion and philosophy, immaterial essence of a living being
composed of non-rational and rational elements. The non-rational dimension was subdivided into the vegetative and animal souls, while the rational aspect was
Soul
quadratic form over a ring that represents every element of the ring. A non-singular form over a field which represents zero non-trivially is universal. Over
Universal_quadratic_form
Longest-lived Biblical figure
"Methuselah dogs". The word "Methuselarity", a blend of Methuselah and singularity, was coined in 2010 by the biomedical gerontologist Aubrey de Grey to
Methuselah
Distinct figure or entity
liberty and rights of the individual, society as a social contract between rational individuals, and the beginnings of individualism as a doctrine. Georg Wilhelm
Individual
Branch of mathematics studying functions of a complex variable
applicable (see methods of contour integration). A "pole" (or isolated singularity) of a function is a point where the function's value becomes unbounded
Complex_analysis
Logical principles
logic who consider that logical laws can be regarded as constitutive of rational thought, they too reject the old view of logic as the "three laws". The
Law_of_thought
Legendary species of small animal in South American folklore
large and beautiful, and between them, in the middle of the forehead, a singular Stone like a hazelnut in the shape of a diamond point, which is covered
Carbuncle (legendary creature)
Carbuncle_(legendary_creature)
RATIONAL SINGULARITY
RATIONAL SINGULARITY
Girl/Female
Hindu, Indian
Rational
Boy/Male
Muslim
Talker, Speaker, Rational
Boy/Male
Arabic, Muslim
National Leader
Boy/Male
Hindu, Indian, Tamil
Revolving; Pearl
Boy/Male
English
National protector.
Boy/Male
Indian
Talker, Speaker, Rational
Boy/Male
Hindu, Indian
National Player
Girl/Female
Indian
Optional
Girl/Female
Christian, German, Greek, Hebrew
Noble; Kind; Rational; Great Happiness
Girl/Female
Hindu, Indian
Rational
Boy/Male
Hindu
Rational
Boy/Male
Tamil
Rational
Boy/Male
Hindu
Rational
Boy/Male
Tamil
Rational
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Animated; Rational
Boy/Male
Indian, Tamil
National Boy; Lord Krishna
Boy/Male
American, Anglo, British, English, Teutonic
National Protector; Wealthy Defender
Boy/Male
Gujarati, Hindu, Indian
Lord of Pleasure
Girl/Female
German, Greek
Noble; Kind; Rational
Boy/Male
Muslim/Islamic
Categorical (decision) talker, speaker, rational
RATIONAL SINGULARITY
RATIONAL SINGULARITY
Surname or Lastname
English
English : metonymic occupational name for a grower or seller of beans, from Old English bēan ‘beans’ (a collective singular). Occasionally it may have been applied as a nickname for a someone considered of little importance.English : nickname for a pleasant person, from Middle English bēne ‘friendly’, ‘amiable’ (of unknown origin; there is apparently no connection with Bain or Bon).Scottish : Anglicized form of the Gaelic personal name Beathán, a diminutive of beatha ‘life’.Translation of German Bohne, or an altered spelling of Biehn. See also Bihn.Mistranslation of French Lefevre. As the vocabulary word fèvre ‘smith’ was replaced by forgeron, the meaning of the old word became opaque, and the surname was reinterpreted as if it were La fève, from fève ‘(fava) bean’. Lefevre is the most common name in French Canada; great numbers of them migrated to the US, where many adopted the name Bean, in the belief that it was a translation of Lefèvre. See also Lafave.
Boy/Male
American, Anglo, British, English, French, German
Glory at Sea; Shining Sea
Girl/Female
American, Anglo, Australian, British, Chinese, Danish, Dutch, English, Finnish, French, German, Greek, Gujarati, Hebrew, Hindu, Indian, Jamaican, Portuguese, Russian
Light; Foreign; Beautiful Fairy Woman; True to All; Little Ash-girl; The Name of a Fairy-tale Heroine; All; Completely; Torch; Bright Light
Boy/Male
Indian
Prince
Boy/Male
Hindu, Indian, Sikh
Breve
Female
English
 Latin form of Greek Chloē, CHLOE means "green shoot." In mythology, this is a surname of the goddess Demeter. In the New Testament bible, this name is mentioned by Paul in 1 Corinthians 1:11.
Girl/Female
British, English, Greek
Light
Boy/Male
Arabic, Muslim
Servant of the Rightly Guided One
Female
Slavic
Variant spelling of Slavic Danica, DANIKA means "morning star."
Boy/Male
Arabic, Muslim
Heart; Mind; Soul
RATIONAL SINGULARITY
RATIONAL SINGULARITY
RATIONAL SINGULARITY
RATIONAL SINGULARITY
RATIONAL SINGULARITY
v. t.
To form a rational conception of.
n.
The state of being national; national attachment; nationality.
a.
Attached to one's own country or nation.
a.
Involving an option; depending on the exercise of an option; left to one's discretion or choice; not compulsory; as, optional studies; it is optional with you to go or stay.
a.
Expressing the type, structure, relations, and reactions of a compound; graphic; -- said of formulae. See under Formula.
a.
Involving surds; not capable of being expressed in rational numbers; radical; irrational; as, a surd expression or quantity; a surd number.
v. t.
To supply with rations, as a regiment.
a.
Fractional.
a.
Not rational; void of reason or understanding; as, brutes are irrational animals.
a.
An explanation or exposition of the principles of some opinion, action, hypothesis, phenomenon, or the like; also, the principles themselves.
a.
Agreeable to reason; not absurd, preposterous, extravagant, foolish, fanciful, or the like; wise; judicious; as, rational conduct; a rational man.
a.
Relating to the reason; not physical; mental.
a.
Given to foolish or visionary expectations; whimsical; fanciful; as, a notional man.
a.
Of or pertaining to fractions or a fraction; constituting a fraction; as, fractional numbers.
a.
Relatively small; inconsiderable; insignificant; as, a fractional part of the population.
n.
A rational being.
adv.
In a rational manner.
a.
Of or pertaining to a nation; common to a whole people or race; public; general; as, a national government, language, dress, custom, calamity, etc.
a.
Notional.
a.
Having reason, or the faculty of reasoning; endowed with reason or understanding; reasoning.