Still: Infinitude by Canadian filmmaker Scott PortingaleIn Infinitude, abstract, geometrical shapes condense into stars, which explode into supernovae, sending an asteroid careening through space towards a nascent Earth.
|
|
It was the opposite: his being held together by an infinitude of minute forces.
|
|
"The Soft Edges of Time" (1976-82) further exemplifies Pousette-Dart's aim to communicate infinitude.
|
|
Instead, a seeming infinitude of variables influence what each of us eats and how the body responds.
|
|
The infinitude of narrative possibility in a given story of word is a persistent theme in Cesarco's work.
|
|
And while entrenched in a ghostly milieu, she explored a sonic palette that examined the infinitude of sound.
|
|
It became the doorway to the infinitude of the soul, and expressed humanity's collective longing for freedom and brotherhood.
|
|
"The critical point is the concentration used on our skin," says Dr. Mirela Mitan, CEO and founder of MMXV INFINITUDE.
|
|
She had an infinitude of choices; she had worldwide recognition and new friends like her fellow teen conquistadora, Taylor Swift.
|
|
It's a ring but also a symbol of infinitude and a symbol of two opposite things uniting in an infinite form.
|
|
He's captivated by its infinitude, at the range of possibility that exists in the space between its expected and actual outcomes.
|
|
Advertise on Hyperallergic with Nectar Ads High above the trees of Central Park, Alicja Kwade has created a celestial ode to infinitude.
|
|
The internet has given me Google Classroom, an infinitude of teaching resources that would have previously taken me several lifetimes to access.
|
|
Try to capture the infinitude of space and this is what you get: a fall from grace, a descent from the heavens to earth.
|
|
The difference between being alive and dead is, on this measure, easy to express: Death represents the end of QALYs, a zero stretching out into infinitude.
|
|
The work was more about a certain type of infinitude that is not at the end of time, or after death, but constantly circulating among us.
|
|
And given the infinitude of African-American music old and new, it could lead to additional concerts in many formats as the Shed welcomes culture without tuxedos.
|
|
The founding idea of this place is infinitude — mile after endless mile of cute houses connected by freeways and uninsulated power lines stretching out far into the forested hills.
|
|
I am a huge, receptive visual instrument with a flexible lens, and I'm taking in the infinitude of all space and time and dragonflies and owls and life and roadkill and hydrogen gas.
|
|
The patience required to bear the infinitude of the small indignities visited on Puerto Ricans by institutions is partly a reflection not of docility or of moral conformity, but of acquiescence to powerlessness.
|
|
The trick Sjon is struggling with here, it seems to me, is the one central to most long novels: how to squeeze the animating sense of life's infinitude into a finite number of pages.
|
|
Uncle Tito was a wise man, containing within him an infinitude of ancient Hawaiian wisdom and stereotypes, ready to drop science on So Cal skater kids whenever the episode requires a magical colored person.
|
|
But consider the limits of technology, and the limitless invention of the human mind — to say nothing of the infinitude of situations, positions, motions and so on that may feed into this engine of impalement.
|
|
The infinitude of strategic options and tactical decisions makes for a fascinating and intricate game of both planning and moment-to-moment reactions, all in the context of gorgeously rendered environments and massively chaotic, constantly shifting battle scenarios.
|
|
In the press release, he bloviates an infinitude of options for the queer artist: decontextualization, romanticization, aestheticization, collage, cartooning, the gritty, the glittery, the decadent, the outmoded, the extravagant, the degenerate, the outré, the déclassé, and (ironically) the indecipherable.
|
|
And for the ruling class, too, caught up in "the great game of dynastic advancement" that was played out with conspiracies, secret alliances and mortality dispensed in an infinitude of ways — by poison, exile, starvation, false accusations and arranged accidents.
|
|
The land is of course beautiful without the installation, but with it, the infinitude of the beauty is brought into focus: how vast it is and how each individual fairy chimney has a story and a history unknown to us.
|
|
In this, I think, the casting has given us an ideal representative; for we, too, would be facially immobile at the prospect of forever defending a prop wall against an infinitude of implacable digital effects with no letup in the lack of interest.
|
|
Though there are a near infinitude of ways both explicit and subtle to experience challenges in life, the adversity index will restrict itself to just three categories: neighborhood environment (including factors like crime and poverty rates and housing values); family environment (the income, education and marriage status of parents in that neighborhood); and high school environment (aspects like the free lunch rate and rigor of the curriculum).
|
|
Their infinitude has been proved several times, by Subbarao, Erdős, and Hardy & Subbarao.
|
|
There are an infinitude of other curved shapes in two dimensions, notably including the conic sections: the ellipse, the parabola, and the hyperbola.
|
|
Ralph Waldo Emerson: The Infinitude of the Private Man. Wrightwood Press, 2008: 74. In 1835, he purchased a home on the Cambridge and Concord TurnpikeWilson, Susan. Literary Trail of Greater Boston. Boston: Houghton Mifflin Company, 2000: 127.
|
|
The intention behind this distinction is to help men maintain a state of sobriety, reserve, concentration, and spiritual poverty (the "perfections of the centre"). Conversely, women, who symbolise unfolding, infinitude and manifestation, are not bound by the same constraints.
|
|
When M < N the system is underdetermined and there are always an infinitude of further solutions. In fact the dimension of the space of solutions is always at least N − M. For M ≥ N, there may be no solution other than all values being 0. There will be an infinitude of other solutions only when the system of equations has enough dependencies (linearly dependent equations) that the number of independent equations is at most N − 1\. But with M ≥ N the number of independent equations could be as high as N, in which case the trivial solution is the only one.
|
|
For example, he proved the infinitude of primes using the divergence of the harmonic series, and he used analytic methods to gain some understanding of the way prime numbers are distributed. Euler's work in this area led to the development of the prime number theorem.
|
|
For example, he proved the infinitude of primes using the divergence of the harmonic series, and used analytic methods to gain some understanding of the way prime numbers are distributed. Euler's work in this area led to the development of the prime number theorem.
|
|
Three given angles form a non- degenerate triangle (and indeed an infinitude of them) if and only if both of these conditions hold: (a) each of the angles is positive, and (b) the angles sum to 180°. If degenerate triangles are permitted, angles of 0° are permitted.
|
|
Partch, Harry. Grove Music Online. The first of Partch's "four concepts" is "The scale of musical intervals begins with absolute consonance (1 to 1) and gradually progresses into an infinitude of dissonance, the consonance of the intervals decreasing as the odd numbers of their ratios increase."Partch 1974, 87.
|
|
In 2010, he and a few young musicians formed the Asian Contemporary Ensemble to champion Singaporean and Asian composers. In 2016, he co-founded Project Infinitude to bring music to children with Ms Marina Mahler, the granddaughter of Gustav Mahler, as part of a global music education initiative with the Mahler Foundation she founded.
|
|
Among his most notable contributions to the logical foundations of mathematics are his work on typical geometries, on the problem of the infinitude of space, the three-body problem, on difference quotients, and on mathematical induction. In psychology, he developed theories about the observation of the transparent and on the depth and observation of compound colours.
|
|
This is a list of articles about numbers. Due to the infinitude of many sets of numbers, this list will invariably be incomplete. Hence , only particularly notable numbers will be included. Numbers may be included in the list based on their mathematical, historical or cultural notability, but all numbers have qualities which could arguably make them notable.
|
|
In general topology, a branch of mathematics, the evenly spaced integer topology is the topology on the set of integers } generated by the family of all arithmetic progressions. It is a special case of the profinite topology on a group. This particular topological space was introduced by where it was used to prove the infinitude of primes.
|
|
In chapter three, Lewis considers various views that he calls "ersatz modal realism." These views are attempts to develop a theory that provides the explanatory power Lewis notes in chapter one without modal realism's ontological commitment to an infinitude of concrete possible worlds. Lewis argues that all of these attempts fail but that each fails for different reasons.
|
|
However, the possibility of blending in Erie does not open up an infinitude of possibilities. In both Gasperini and Semtek, the common thread is that the blending is done in a way that is calculated to advance the aims of Erie (and York): non-discrimination between litigants, and discouragement of forum shopping.Allan Ides & Christopher May, Civil Procedure, 3d Edition.
|
|
In 2016, the college's F1 in Schools team, Infinitude, set the World Record at the World Finals in Austin, Texas, in collaboration with Brighton Secondary School, Adelaide. Also in this same year, a team of students successfully won the Australian STEM Video Game Challenge in the Year 9-12 Gamemaker/Gamestar Mechanic category with their game Spectrum.
|
|
He died at 65, after suffering from a brain tumor. With Andrew Granville and Carl Pomerance, he proved the infinitude of Carmichael numbers in 1994 based on a conjecture given by Paul Erdős. Although MathSciNet credits him with only eleven publications, two were in Annals of Mathematics, the most prestigious mathematical journal -- the Carmichael numbers paper, and a 1970 paper in knot theory.
|
|
The Gramsci Monument (The Bronx, New York, 2013) was the fourth and last monument, tribute to the Italian political theorist and Marxist Antonio Gramsci (1891–1937). These works are based on Hirschhorn's will “to establish a definition of monument,’ to provoke encounters, to create an event. [...] My love for Antonio Gramsci is the love of philosophy, the love of the infinitude of thought.
|
|
He earned his doctorate from Erlangen on 25 July 1828 with his thesis De infinitate, unitate, atque, communitate, rationis (On the Infinitude, Unity, and Universality of Reason), while he habilitated there in November 1828 with his thesis De ratione una, universali, infinita (The One, Universal, and Infinite Reason).Francesco Tomasoni, Ludwig Feuerbach: Entstehung, Entwicklung und Bedeutung seines Werks, Waxmann Verlag, 2015, p. 58.
|
|
There are no definitions of the Universal Mind, but two authors within the New Thought movement offer vague descriptions in superlatives such as omnipotence and infinitude. Ernest Holmes, the founder of the Science of Mind movement: New Thought author Charles Haanel said of the universal mind and its relationship to humans: The nature of the universal mind is said to be omniscient, omnipotent, and omnipresent.
|
|
Prime gaps can be generalized to prime k-tuples, patterns in the differences between more than two prime numbers. Their infinitude and density are the subject of the first Hardy–Littlewood conjecture, which can be motivated by the heuristic that the prime numbers behave similarly to a random sequence of numbers with density given by the prime number theorem., Prime k-tuples conjecture, pp. 201–202.
|
|
Giving things-in-themselves a theoretical meaning limits the capacity for humans to know it, but practical reason validates its value and infinitude. Thus, when the human mind becomes infinite in Confucian terms, all beings are given as things-in-themselves. For Mou, the precarious basis of the distinction between noumena and phenomena can be solved through the Confucian perception of man having the ability to transcend himself though moral transformation.
|
|
" He attended Marsha Stern Talmudical Academy and then Yeshiva University, where he concluded his BA and MSc studies at the age of 20 in 1955. Furstenberg published several papers as an undergraduate, including "Note on one type of indeterminate form" (1953) and "On the infinitude of primes" (1955). Both appeared in the "American Mathematical Monthly, the latter provided a topological proof of Euclid's famous theorem that there are infinitely many primes.
|
|
If the number of sides n is odd, then for any given set of sidelengths a_1, \dots , a_n satisfying the existence criterion above there is only one tangential polygon. But if n is even there are an infinitude of them.. For example, in the quadrilateral case where all sides are equal we can have a rhombus with any value of the acute angles, and all rhombi are tangential to an incircle.
|
|
In relation to God's essence, creation affects no change or withdrawal in the divine. "There is nothing but God". The ability to create can only come from the divine atzmut(essence), whose power of infinitude is described by the Tetragrammaton (name of God). However, "It is not the essence of the Divine to create Worlds and sustain them", as this ability is only external to the infinite essence.
|
|
Granville received his Bachelor of Arts (Honours) (1983) and his Certificate of Advanced Studies (Distinction) (1984) from Trinity College, Cambridge University. He received his Ph.D. from Queen's University in 1987 and was inducted into the Royal Society of Canada in 2006. Granville's work is mainly in number theory, in particular analytic number theory. Along with Carl Pomerance and W. R. (Red) Alford he proved the infinitude of Carmichael numbers in 1994.
|
|
E.B. Speirs and J. Burdon > Sanderson as Lectures on the Philosophy of Religion, New York: Humanities > Press, 1974. pp. 56-58 . > Spirit is immortal; it is eternal; and it is immortal and eternal in virtue > of the fact that it is infinite, that it has no such spatial finitude as we > associate with the body; when we speak of it being five feet in height, two > feet in breadth and thickness, that it is not the Now of time, that the > content of its knowledge does not consist of these countless midges, that > its volition and freedom have not to do with the infinite mass of existing > obstacles, nor of the aims and activities which such resisting obstacles and > hindrances have to encounter. The infinitude of spirit is its inwardness, in > an abstract sense its pure inwardness, and this is its thought, and this > abstract thought is a real present infinitude, while its concrete inwardness > consists in the fact that this thought is Spirit.
|
|
That is, it is the only matrix such that: # When multiplied by itself, the result is itself # All of its rows and columns are linearly independent. The principal square root of an identity matrix is itself, and this is its only positive-definite square root. However, every identity matrix with at least two rows and columns has an infinitude of symmetric square roots.Mitchell, Douglas W. "Using Pythagorean triples to generate square roots of I2".
|
|
Catharine Trotter Cockburn (16 August 1679 – 11 May 1749) was an English novelist, dramatist, and philosopher. She wrote on moral philosophy, theological tracts, and had a voluminous correspondence. Trotter's work addresses a range of issues including necessity, the infinitude of space, and the substance, but she focuses on moral issues. She thought that moral principles are not innate, but discoverable by each individual through the use of the faculty of reason endowed by God.
|
|
The theorem provides conditions on the lattice under which perfect reconstruction is possible. As with the Nyquist–Shannon sampling theorem, this theorem also assumes an idealization of any real-world situation, as it only applies to functions that are sampled over an infinitude of points. Perfect reconstruction is mathematically possible for the idealized model but only an approximation for real-world functions and sampling techniques, albeit in practice often a very good one.
|
|
God's unbounded essence is revealed in both complementary infinitude (infinite light) and finitude (finite light). The withdrawal was only the illusion of concealment of the infinite light into the essence of God, to allow the latent potentially finite light to emerge apparent to creation after the tzimtzum. God himself remains unaffected ("For I, the Lord, I have not changed" Malachi 3:6). His essence was one, alone, before creation, and still one, alone, after creation, without any change.
|
|
In mathematics, particularly in number theory, Hillel Furstenberg's proof of the infinitude of primes is a topological proof that the integers contain infinitely many prime numbers. When examined closely, the proof is less a statement about topology than a statement about certain properties of arithmetic sequences. Unlike Euclid's classical proof, Furstenberg's proof is a proof by contradiction. The proof was published in 1955 in the American Mathematical Monthly while Furstenberg was still an undergraduate student at Yeshiva University.
|
|
The alt=The Rhind Mathematical Papyrus The Rhind Mathematical Papyrus, from around 1550 BC, has Egyptian fraction expansions of different forms for prime and composite numbers.Bruins, Evert Marie, review in Mathematical Reviews of However, the earliest surviving records of the explicit study of prime numbers come from ancient Greek mathematics. Euclid's Elements (c. 300 BC) proves the infinitude of primes and the fundamental theorem of arithmetic, and shows how to construct a perfect number from a Mersenne prime.
|
|
Many fundamental questions about Mersenne primes remain unresolved. It is not even known whether the set of Mersenne primes is finite or infinite. The Lenstra–Pomerance–Wagstaff conjecture asserts that there are infinitely many Mersenne primes and predicts their order of growth. It is also not known whether infinitely many Mersenne numbers with prime exponents are composite, although this would follow from widely believed conjectures about prime numbers, for example, the infinitude of Sophie Germain primes congruent to 3 (mod 4).
|
|
The infinitude of prime numbers is proved. Books XI–XIII concern solid geometry. A typical result is the 1:3 ratio between the volume of a cone and a cylinder with the same height and base. The parallel postulate: If two lines intersect a third in such a way that the sum of the inner angles on one side is less than two right angles, then the two lines inevitably must intersect each other on that side if extended far enough.
|
|
The same term can also be used more informally to refer to something "standard" or "classic". For example, one might say that Euclid's proof is the "canonical proof" of the infinitude of primes. ; deep:A result is called "deep" if its proof requires concepts and methods that are advanced beyond the concepts needed to formulate the result. For example, the prime number theorem — originally proved using techniques of complex analysis — was once thought to be a deep result until elementary proofs were found.
|
|
Prime numbers have been studied throughout recorded history. Euclid devoted one book of the Elements to the theory of primes; in it he proved the infinitude of the primes and the fundamental theorem of arithmetic, and presented the Euclidean algorithm for finding the greatest common divisor of two numbers. In 240 BC, Eratosthenes used the Sieve of Eratosthenes to quickly isolate prime numbers. But most further development of the theory of primes in Europe dates to the Renaissance and later eras.
|
|
To Hasidism and Schneur Zalman, it is unthinkable for the "withdrawal" of God that "makes possible" Creation, to be taken literally. The paradox of Tzimtzum only relates to the Ohr Ein Sof ("Infinite Light"), not the Ein Sof (Divine essence) itself. God's infinity is revealed in both complementary infinitude (infinite light) and finitude (finite light). The "withdrawal" was only a concealment of the Infinite Light into the essence of God, to allow the latent potentially finite light to emerge after the God limiting tzimtzum.
|
|
Carlos Mastronardi (1901 – June 5, 1976) was an Argentine journalist, poet, and translator. His works included Luz de provincia, Tierra amanecida (1926), Conocimiento de la noche (1937), and Tratado de la pena. His non-fiction Valéry o la infinitud del método (Valéry, or the infinitude of method) won the Buenos Aires Municipal Prize for Literature (1955). Other important works of non-fiction included Formas de la realidad nacional (Forms of the National Reality, 1961) and Memorias de un Provinciano (Memoirs of a Man from the Provinces, 1967).
|
|
There are infinitely many prime numbers. Another way of saying this is that the sequence :2, 3, 5, 7, 11, 13, ... of prime numbers never ends. This statement is referred to as Euclid's theorem in honor of the ancient Greek mathematician Euclid, since the first known proof for this statement is attributed to him. Many more proofs of the infinitude of primes are known, including an analytical proof by Euler, Goldbach's proof based on Fermat numbers,Letter in Latin from Goldbach to Euler, July 1730.
|
|
The Jacobi–Madden equation is a Diophantine equation : a^4 + b^4 + c^4 + d^4 = (a + b + c + d)^4 \, proposed by the physicist Lee W. Jacobi and the mathematician Daniel J. Madden in 2008.Mathematicians find new solutions to an ancient puzzle The variables a, b, c, and d can be any integers, positive, negative or 0.In fact, any nontrivial solution must include both a positive and negative value. Jacobi and Madden showed that there are an infinitude of solutions of this equation with all variables non-zero.
|
|
In "The Garden of Forking Paths", Borges describes a novel by the fictional Chinese scholar Ts'ui Pên, whose plot bifurcates at every point in time. The idea of the flow of time branching can be compared to the many-worlds interpretation of quantum mechanics and the notion of multiverses present in some versions of string theory. Similarly, the infinitude of diverging, infinite universes in mathematical cosmology is reflected Borges' rejection of linear, absolute time. Borges' writings address the nature of entity and the possibility of infinite "realities", as in his essay "New Time Refutations" (1946).
|
|
Therefore, the Form drive's autonomy and intensity are maximized as a response to the maximization of the sense drive. "Where both these aptitudes are conjoined, man will combine the greatest fullness of existence with the highest autonomy and freedom and instead of losing himself to the world, will rather draw the latter into himself in all its infinitude of phenomena, and subject it to the unity of his reason"Schiller, p.123 This "conjoining" of the two faculties, are actually a mediation by the third fundamental drive, the play drive.
|
|
There are an infinitude of lines that bisect the area of a triangle. Three of them are the medians of the triangle (which connect the sides' midpoints with the opposite vertices), and these are concurrent at the triangle's centroid; indeed, they are the only area bisectors that go through the centroid. Any line through a triangle that splits both the triangle's area and its perimeter in half goes through the triangle's incenter (the center of its incircle). There are either one, two, or three of these for any given triangle.
|
|
If the linear system :A x = b has any solutions, they are all given by :x = A^+ b + \left[I - A^+ A\right]w for arbitrary vector . Solution(s) exist if and only if AA^+ b = b. If the latter holds, then the solution is unique if and only if has full column rank, in which case is a zero matrix. If solutions exist but does not have full column rank, then we have an indeterminate system, all of whose infinitude of solutions are given by this last equation.
|
|
Into the vacuum then shone a new light, the Kav ("Ray/Line"), a "thin" diminished extension from the original Infinite Light, which became the fountainhead for all subsequent Creation. While still infinite, this new vitality was radically different from the original Infinite Light, as it was now potentially tailored to the limited perspective of Creation. As the Ein Sof perfection encompassed both infinitude and finitude, so the Infinite Light possessed concealed-latent finite qualities. The Tzimtum allowed infinite qualities to retire into the Ein Sof, and potentially finite qualities to emerge.
|
|
In Hindu traditions, the "crossing or coming down" is symbolism, states Daniel Bassuk, of the divine descent from "eternity into the temporal realm, from unconditioned to the conditioned, from infinitude to finitude". An avatar, states Justin Edwards Abbott, is a saguna (with form, attributes) embodiment of the nirguna Brahman or Atman (soul). Neither the Vedas nor the Principal Upanishads ever mentions the word avatar as a noun. The verb roots and form, such as avatarana, do appear in ancient post-Vedic Hindu texts, but as "action of descending", but not as an incarnated person (avatara).
|
|
Otherwise the general solution has k free parameters where k is the difference between the number of variables and the rank; hence in such a case there are an infinitude of solutions. The rank of a system of equations (i.e. the rank of the augmented matrix) can never be higher than [the number of variables] + 1, which means that a system with any number of equations can always be reduced to a system that has a number of independent equations that is at most equal to [the number of variables] + 1.
|
|
If they are in the same plane there are three possibilities: if they coincide (are not distinct lines) they have an infinitude of points in common (namely all of the points on either of them); if they are distinct but have the same slope they are said to be parallel and have no points in common; otherwise they have a single point of intersection. The distinguishing features of non-Euclidean geometry are the number and locations of possible intersections between two lines and the number of possible lines with no intersections (parallel lines) with a given line.
|
|
The mathematical problem represented is typically ill-posed because it has an infinitude of solutions. In fact, in any three-dimensional solid body one may have infinitely many (and infinitely complicated) non-zero stress tensor fields that are in stable equilibrium even in the absence of external forces. These stress fields are often termed hyperstatic stress fields and they co- exist with the stress fields that balance the external forces. In linear elasticity, their presence is required to satisfy the strain/displacement compatibility requirements and in limit analysis their presence is required to maximise the load carrying capacity of the structure or component.
|
|
Asterion explains how he spends his days in solitude: running through the corridors; pretending to sleep; and sometimes pretending that "the other Asterion" has come to visit, and giving him a tour of the house. Asterion goes into detail about the infinitude of his house, comparing it to the universe. He also suggests that perhaps he created the world and has forgotten about it. Finally he makes mention of other people, nine men, who come every nine years "so that I may deliver them from evil", and whose bodies he leaves in the empty rooms to distinguish one from another.
|
|
Proclus provides the only reference ascribing the Elements to Euclid. Although best known for its geometric results, the Elements also includes number theory. It considers the connection between perfect numbers and Mersenne primes (known as the Euclid–Euler theorem), the infinitude of prime numbers, Euclid's lemma on factorization (which leads to the fundamental theorem of arithmetic on uniqueness of prime factorizations), and the Euclidean algorithm for finding the greatest common divisor of two numbers. The geometrical system described in the Elements was long known simply as geometry, and was considered to be the only geometry possible.
|
|
It is the origin of the Ohr Ein Sof, the "Infinite Light" of paradoxical divine self-knowledge, nullified within the Ein Sof prior to creation. In Lurianic Kabbalah, the first act of creation, the Tzimtzum self "withdrawal" of God to create an "empty space", takes place from there. In Hasidic Judaism, the Tzimtzum is only the illusionary concealment of the Ohr Ein Sof, giving rise to monistic panentheism. Consequently, Hasidism focuses on the Atzmus divine essence, rooted higher within the Godhead than the Ein Sof, which is limited to infinitude, and reflected in the essence (etzem) of the Torah and the soul.
|
|
A square root of a 2×2 matrix M is another 2×2 matrix R such that M = R2, where R2 stands for the matrix product of R with itself. In general, there can be zero, two, four, or even an infinitude of square-root matrices. In many cases, such a matrix R can be obtained by an explicit formula. Square roots that are not the all-zeros matrix come in pairs: if R is a square root of M, then −R is also a square root of M, since (−R)(−R) = (−1)(−1)(RR) = R2 = M. A 2×2 matrix with two distinct nonzero eigenvalues has four square roots.
|
|
František Kupka, Katedrála (The Cathedral), 1912-13, oil on canvas, 180 x 150 cm, Museum Kampa, Prague, Czech Republic The Orphists were rooted in Cubism but moved toward a pure lyrical abstraction, seeing painting as the bringing together of a sensation of pure colors. More concerned with the expression and significance of sensation, this movement began with recognizable subjects but was rapidly absorbed by increasingly abstract structures. Orphism aimed to dispense with recognizable subject matter and to rely on form and color to communicate meaning. The movement also aimed to express the ideals of Simultanism: the existence of an infinitude of interrelated states of being.
|
|
Solving Einstein's equations with his mathematical apparatus of chronometric invariants, Zelmanov obtained the total system of all cosmological models (scenarios of the Universe's evolution) which could be possible as derived from the equations. In particular, he had arrived at the possibility that infinitude may be relative. Later, in the 1950s, he enunciated the Infinite Relativity Principle: Most of his time was spent in scientific work, but he sometimes gave lectures on the General Theory of Relativity and relativistic cosmology as a science for the geometrical structure of the Universe. Because Zelmanov made scientific creation the main goal of his life, writing articles was a waste of time to him.
|
|
Especially important to Hellenistic science was the city of Alexandria in Egypt, which became a major center of scientific research in the 3rd century BC. Hellenistic scholars frequently employed the principles developed in earlier Greek thought: the application of mathematics and deliberate empirical research, in their scientific investigations.Lloyd (1973), p. 177. Hellenistic Geometers such as Archimedes (), Apollonius of Perga (), and Euclid (), whose Elements became the most important textbook in Western mathematics until the 19th century AD, built upon the work of the Hellenic-era Pythagoreans. Euclid developed proofs for the Pythagorean Theorem, for the infinitude of primes, and worked on the five Platonic solids.Bugh, p. 245.
|
|
One reason that the ancients treated the parallel postulate as less certain than the others is that verifying it physically would require us to inspect two lines to check that they never intersected, even at some very distant point, and this inspection could potentially take an infinite amount of time.For the assertion that this was the historical reason for the ancients considering the parallel postulate less obvious than the others, see Nagel and Newman 1958, p. 9. The modern formulation of proof by induction was not developed until the 17th century, but some later commentators consider it implicit in some of Euclid's proofs, e.g., the proof of the infinitude of primes.
|
|
Theaetetus was, like Plato, a disciple of Theodorus's; he worked on distinguishing different kinds of incommensurables, and was thus arguably a pioneer in the study of number systems. (Book X of Euclid's Elements is described by Pappus as being largely based on Theaetetus's work.) Euclid devoted part of his Elements to prime numbers and divisibility, topics that belong unambiguously to number theory and are basic to it (Books VII to IX of Euclid's Elements). In particular, he gave an algorithm for computing the greatest common divisor of two numbers (the Euclidean algorithm; Elements, Prop. VII.2) and the first known proof of the infinitude of primes (Elements, Prop. IX.20).
|
|
"If God is the ultimate ground of being out of which all arises, it must necessarily follow that God is not a person or persons as we customarily understand them." At the same time, Smoley contends, its very infinitude also includes the capacity to manifest in a personal form. "Whether or not God is ultimately personal in the sense that we humans understand it, the tradition suggests that we are persons, and God can address us in ways we can understand — that is, personally." Smoley's view of the Christian Father and Son resembles the "subordinationist" view found in such figures as Philo of Alexandria and Origen.
|
|
Ananta is a Sanskrit term which means 'endless' or 'limitless', also means 'eternal' or 'infinity', in other words, it also means infinitude or an unending expansion or without limit. It is one of the many names of Lord Vishnu. Ananta is the Shesha-naga, the celestial snake, on which Lord Vishnu reclines. In the Mahabharata, Ananta or Adi-sesa, is the son of Kasyapa, one of the Prajapatis, through Kadru as her eldest son. Kadru had asked her sons to stay suspended in the hair of Uchchaihshravas’s tail who on refusing to do so were cursed to die at the serpent-yajna of Janamejaya.
|
|
There are four aspects of cultivating the illusory-body: illusion in meditative equipoise; illusion in post-equipoise; illusion in dreams; and illusion in the intermediate state. # The stage of actual awakening, or the ultimate-truth luminous clarity; is "a path that brings about direct realization of the emptiness of innate great bliss" and its main function is "to vanquish the seeds of the emotional afflictions as well as their winds." # The stage of nondual pristine awareness, or the union of the two truths; This is the inseparable union of the great bliss that directly realizes the nature of reality; and the infinitude of pristine-awareness mandalas.
|
|
This conjecture includes as special cases the twin prime conjecture (when k = 2, and the two polynomials are x and x + 2) as well as the infinitude of prime quadruplets (when k = 4, and the four polynomials are x, x + 2, x + 6, and x + 8), sexy primes (when k = 2, and the two polynomials are x and x + 6), Sophie Germain primes (when k = 2, and the two polynomials are x and 2x + 1), and Polignac's conjecture (when k = 2, and the two polynomials are x and x + a, with a any even number). When all the polynomials have degree 1 this is Dickson's conjecture. In fact, this conjecture is equivalent to the Generalized Dickson conjecture.
|
|
This smaller map has the condition that if it can be colored with four colors, this also applies to the original map. This implies that if the original map cannot be colored with four colors the smaller map cannot either and so the original map is not minimal. Using mathematical rules and procedures based on properties of reducible configurations, Appel and Haken found an unavoidable set of reducible configurations, thus proving that a minimal counterexample to the four-color conjecture could not exist. Their proof reduced the infinitude of possible maps to 1,834 reducible configurations (later reduced to 1,482) which had to be checked one by one by computer and took over a thousand hours.
|
|
The infinite is present in the finite, while fully preserving its infinitude (and thus not through any "anderssein" or similar). God is simultaneously transcendent and an immanent ground for the finite world, and in so far as this world, qua finite, is undergoing a developmental process, he is the foundation, law and endpoint of this development, the creator and maintainer of the finite world, its providence and salvation. In relation to this, Boström develops a teodicé where he teaches that all imperfection and all evil depends entirely on finite beings, whereas God, as a perfect being, cannot be the ground of anything but the eternal life and salvation of these lesser beings.
|
|
The case n = −2 also has an infinitude of solutions, and these have a geometric interpretation in terms of right triangles with integer sides and an integer altitude to the hypotenuse. All primitive solutions to a^{-2} + b^{-2} = d^{-2} are given by : a = (v^2 - u^2)(v^2 + u^2), : b = 2uv(v^2 + u^2), : d = 2uv(v^2 - u^2), for coprime integers u, v with v > u. The geometric interpretation is that a and b are the integer legs of a right triangle and d is the integer altitude to the hypotenuse. Then the hypotenuse itself is the integer : c = (v^2 + u^2)^2, so (a, b, c) is a Pythagorean triple.
|
|
I understood why it is that here, > at the very hub of the wheel, one can embrace the most fantastic, the most > impossible theories, without finding them in the least strange; it is here > that one reads again the books of his youth and the enigmas take on new > meanings, one for every white hair. One walks the streets knowing that he is > mad, possessed, because it is only too obvious that these cold, indifferent > faces are the visages of one's keepers. Here all boundaries fade away and > the world reveals itself for the mad slaughterhouse that it is. The > treadmill stretches away to infinitude, the hatches are closed down tight, > logic runs rampant, with bloody cleaver flashing.
|
|
If points A and B are given, a wavefront expanding from A sweeps all possible ray paths radiating from A, whether they pass through B or not. If the wavefront reaches point B, it sweeps not only the ray path(s) from A to B, but also an infinitude of nearby paths with the same endpoints. Fermat's principle describes any ray that happens to reach point B; there is no implication that the ray "knew" the quickest path or "intended" to take that path. isotropic.) For the purpose of comparing traversal times, the time from one point to the next nominated point is taken as if the first point were a point- source.
|
|
A seeming paradox is that there are non- standard models of the theory of hereditarily finite sets which contain infinite sets, but these infinite sets look finite from within the model. (This can happen when the model lacks the sets or functions necessary to witness the infinitude of these sets.) On account of the incompleteness theorems, no first-order predicate, nor even any recursive scheme of first- order predicates, can characterize the standard part of all such models. So, at least from the point of view of first-order logic, one can only hope to describe finiteness approximately. More generally, informal notions like set, and particularly finite set, may receive interpretations across a range of formal systems varying in their axiomatics and logical apparatus.
|
|
Zhang's result set off a flurry of activity in the field, such as the Polymath8 project. If P(N) stands for the proposition that there is an infinitude of pairs of prime numbers (not necessarily consecutive primes) that differ by exactly N, then Zhang's result is equivalent to the statement that there exists at least one even integer k < 70,000,000 such that P(k) is true. The classical form of the twin prime conjecture is equivalent to P(2); and in fact it has been conjectured that P(k) holds for all even integers k. While these stronger conjectures remain unproven, a result due to James Maynard in November 2013, employing a different technique, showed that P(k) holds for some k ≤ 600.
|
|
Of Sanatan dharma, he says: > We know that in our books, a clear distinction is made between two sets of > truths. The one set is that which abides for ever, being built upon the > nature of man, the nature of the soul, the soul's relation to God, the > nature of God, perfection and so on; there are also the principles of > cosmology, of the infinitude of creation, or more correctly speaking, > projection, the wonderful law of cyclical procession, and so on; these are > eternal principles founded upon the universal laws of nature. Of Yuga dharma, he says: > The other set comprises the minor laws, which guide the working of our > everyday life. They belong more properly to the Puranas, to the Smrtis, and > not to the Sruti.
|
|
In the continuous time case, such systems translate into networks of conventional, idealized LCR networks. In discrete time, they conveniently translate into approximations thereof, using addition, multiplication, and unit delay. It can be shown that in both cases, system functions of rational form with increasing order can be used to efficiently approximate any other system function; thus even system functions lacking a rational form, and so possessing an infinitude of poles and/or zeroes, can in practice be implemented as efficiently as any other. In the context of causal, stable systems, we would in theory be free to choose whether the zeroes of the system function are outside of the stable range (to the right or outside) if the closure condition wasn't an issue.
|
|
These six lines are concurrent three at a time: in addition to the three medians being concurrent, any one median is concurrent with two of the side-parallel area bisectors. The envelope of the infinitude of area bisectors is a deltoid (broadly defined as a figure with three vertices connected by curves that are concave to the exterior of the deltoid, making the interior points a non-convex set). The vertices of the deltoid are at the midpoints of the medians; all points inside the deltoid are on three different area bisectors, while all points outside it are on just one. The sides of the deltoid are arcs of hyperbolas that are asymptotic to the extended sides of the triangle.
|
|
Gauss conjectured that this condition was also necessary, but he offered no proof of this fact, which was provided by Pierre Wantzel in 1837. The first few constructible regular polygons have the following numbers of sides: :3, 4, 5, 6, 8, 10, 12, 15, 16, 17, 20, 24, 30, 32, 34, 40, 48, 51, 60, 64, 68, 80, 85, 96, 102, 120, 128, 136, 160, 170, 192, 204, 240, 255, 256, 257, 272... There are known to be an infinitude of constructible regular polygons with an even number of sides (because if a regular n-gon is constructible, then so is a regular 2n-gon and hence a regular 4n-gon, 8n-gon, etc.). However, there are only 31 known constructible regular n-gons with an odd number of sides.
|
|
Furstenberg gained attention at an early stage in his career for producing an innovative topological proof of the infinitude of prime numbers in 1955. In a series of articles beginning in 1963 with A Poisson Formula for Semi-Simple Lie Groups, he continued to establish himself as a ground-breaking thinker. His work showing that the behavior of random walks on a group is intricately related to the structure of the group - which led to what is now called the Furstenberg boundary – has been hugely influential in the study of lattices and Lie groups. In his 1967 paper, Disjointness in ergodic theory, minimal sets, and a problem in Diophantine approximation, Furstenberg introduced the notion of ‘disjointness,’ a notion in ergodic systems that is analogous to coprimality for integers.
|
|
In an infinite distributed lag model, an infinite number of lag weights need to be estimated; clearly this can be done only if some structure is assumed for the relation between the various lag weights, with the entire infinitude of them expressible in terms of a finite number of assumed underlying parameters. In a finite distributed lag model, the parameters could be directly estimated by ordinary least squares (assuming the number of data points sufficiently exceeds the number of lag weights); nevertheless, such estimation may give very imprecise results due to extreme multicollinearity among the various lagged values of the independent variable, so again it may be necessary to assume some structure for the relation between the various lag weights. The concept of distributed lag models easily generalizes to the context of more than one right-side explanatory variable.
|
|
By the Rouché–Capelli theorem, the system of equations is inconsistent, meaning it has no solutions, if the rank of the augmented matrix (the coefficient matrix augmented with an additional column consisting of the vector b) is greater than the rank of the coefficient matrix. If, on the other hand, the ranks of these two matrices are equal, the system must have at least one solution. The solution is unique if and only if the rank r equals the number n of variables. Otherwise the general solution has n – r free parameters; hence in such a case there are an infinitude of solutions, which can be found by imposing arbitrary values on n – r of the variables and solving the resulting system for its unique solution; different choices of which variables to fix, and different fixed values of them, give different system solutions.
|
|
The overall winners of the National Finals are invited to compete at the World Finals, which are held at a different location each year, usually held in conjunction with a Formula One Grand Prix. In the UK competition there are 3 classes of entry: Professional Class aimed at 11-to-19-year olds; Development Class aimed at 11-to-19-year in their first year; and Entry Class aimed at 11-to-14-year olds. , the F1 in Schools World Champions are Evolve, UK. The F1 in Schools World Record was set in 2016 by the Australian team Infinitude and is 0.916 seconds. After safety issues concerning the use of extended canister chambers coupled with the Launch Energy Recovery System (LERS), the controversial device was banned globally from the 2017 World Finals season onwards, after being innovated in 2014 by Colossus F1.
|
|
More specifically, according to the Rouché–Capelli theorem, any system of linear equations (underdetermined or otherwise) is inconsistent if the rank of the augmented matrix is greater than the rank of the coefficient matrix. If, on the other hand, the ranks of these two matrices are equal, the system must have at least one solution; since in an underdetermined system this rank is necessarily less than the number of unknowns, there are indeed an infinitude of solutions, with the general solution having k free parameters where k is the difference between the number of variables and the rank. There are algorithms to decide whether an underdetermined system has solutions, and if it has any, to express all solutions as linear functions of k of the variables (same k as above). The simplest one is Gaussian elimination.
|
|
" Art critic Nancy Princenthal suggests that "these paintings evoke the flat farmland of Takenaga's childhood home, in Nebraska [...] There is that sense of limitless, un marked expanses in Takenaga's recent paintings, of matter-of-fact infinitude." The laborious, repetitive process involved to make her paintings suggests the passing of time in her work. Susan Cross writes: "Takenaga has likened her approach to art- making to both soap opera narratives in which essentially nothing happens over long stretches of time and to the myth of Odysseus's wife Penelope, who unraveled her weaving each night for three years to put off her unwanted suitors. In a similar fashion, Takenaga's process both marks time and slows it down, allowing it to move forwards and backwards much like the sense of space in her paintings, which takes us spinning deep into the cosmos or right back to the work's surface, evoking both beginnings and endings.
|
|
The system :x+y=3, :x+ 2y= 7, :4x+6y=20 has a solution, x = –1, y = 4, because the first two equations do not contradict each other and the third equation is redundant (since it contains the same information as can be obtained from the first two equations by multiplying each through by 2 and summing them). The system :x+2y=7, :3x+6y=21, :7x+14y=49 has an infinitude of solutions since all three equations give the same information as each other (as can be seen by multiplying through the first equation by either 3 or 7). Any value of y is part of a solution, with the corresponding value of x being 7–2y. The nonlinear system :x^2-1=0, :y^2-1=0, :(x-1)(y-1)=0 has the three solutions (x, y) = (1, –1), (–1, 1), and (1, 1).
|
|
The true Divine essence is above even Infinite-Finite relationship. God's essence can be equally manifest in finitude as in infinitude, as found in the Talmudic statement that the Ark of the Covenant in the First Temple took up no space. While it measured its own normal width and length, the measurements from each side to the walls of the Holy of Holies together totalled the full width and length of the sanctuary. Atzmus represents the core Divine essence itself, as it relates to the ultimate purpose of Creation in Hasidic thought that "God desired a dwelling place in the lower Realms",Schneur Zalman of Liadi Tanya I:36, further explained in later Habad thought (see Atzmut), defines this as the ultimate reason for Creation, taking the statement from Rabbinic Midrash Tanchuma: Nasso 16 which will be fulfilled in this physical, finite, lowest world, through performance of the Jewish observances.
|
|
This is a mere paralogism; we can never infer either absolute or infinite from relative or finite. The truth is that Cousin's doctrine of the spontaneous apperception of impersonal truth amounts to little more than a presentment in philosophical language of the ordinary convictions and beliefs of mankind. This is important as a preliminary stage, but philosophy properly begins when it attempts to coordinate or systematize those convictions in harmony, to conciliate apparent contradiction and opposition, as between the correlative notions of finite and infinite, the apparently conflicting notions of personality and infinitude, self and not-self; in a word, to reconcile the various sides of consciousness with each other. And whether the laws of our reason are the laws of all intelligence and being—whether and how we are to relate our fundamental, intellectual and moral conceptions to what is beyond our experience, or to an infinite being—are problems which Cousin cannot be regarded as having solved.
|
|
In the Biblical account, God descended on Mount Sinai to speak to the Israelites "Anochi Hashem Elokecha" ("I am God your Lord").Exodus 20:2. In this verse the names of God are translated opposite to their usual form ("I am the Lord your God"), as in Kabbalah the Tetragrammaton describes Divine Infinitude ("God", the Ein Sof power of Creation through the Sephirah Keter-Supreme Will, combining the words "was","is" and "will be" in one name), while Elokim describes God's concealing limitation to allow His lifeforce to immanently form the finite Worlds (becoming "Lord", the master relating to this world through the last sephirah Malkuth-Kingship, numerically equivalent to "HaTevah"-"Nature") This is explained in Hasidic thought to describe Atzmus, the Divine essence (Anochi-"I"), uniting the separate Kabbalistic manifestation realms of spirituality (Hashem-The Tetragrammaton name of Infinite transcendent emanation) and physicality (Elokecha-The name of God relating to finite immanent lifeforce of Creation). Before the Torah was given, physical objects could not become sanctified.
|
|
Spirit, as possessed of freedom, does not belong to the sphere of > things limited; it, as being what thinks and knows in an absolute way, has > the universal for its object; this is eternity, which is not simply > duration, as duration can be predicated of mountains, but knowledge. The > eternity of spirit is here brought into consciousness, and is found in this > reasoned knowledge, in this very separation, which has reached the > infinitude of being-for-self, and which is no longer entangled in what is > natural, contingent, and external. This eternity of Spirit in itself means > that Spirit is, to begin with, potential; but the next standpoint implies > that Spirit ought to be what it is in its essential and complete nature, in- > and-for-itself. Spirit must reflect upon itself, and in this way disunion > arises, it must not remain at the point at which it is seen not to be what > it is potentially, but must become adequate to its Concept, it must become > universal Spirit.
|
|
In 1976, Lebe purchased a townhouse in Philadelphia with space for living quarters, a darkroom, and a studio. He began making photograms using plants collected from his rooftop garden or from trips to the country or beach. He converted these negative prints into positives, occasionally adding a Sabattier effect during the printing process. Some prints he left black and white; for others, he hand-colored the negative and/or the positive, a unique process that "transformed the photograms into surreal painterly abstractions."Feigin, “A Photographer’s Infinite Infinitude.” Several distinct series emerged from this experimentation: Specimens, which features plants, bones, and other objects combined to create fantastic hybrid forms; Garden Series, images focused exclusively on plant material, often dissected and reassembled to create new “species”; and Landscapes, which places these hybrid forms in hand-painted (and often otherworldly) settings. Of these images, Lebe has said: “I was creating the gardens and landscapes I longed for. Along the way, other ideas got expressed.”Richard Kagan, “An Interview with David Lebe,” The Photo Review 18, no.
|
|
However, the Torah does narrate God speaking in the first person, most memorably the first word of the Ten Commandments, a reference without any description or name to the simple Divine essence (termed also Atzmus Ein Sof – Essence of the Infinite) beyond even the duality of Infinitude/Finitude. In contrast, the term Ein Sof describes the Godhead as Infinite lifeforce first cause, continuously keeping all Creation in existence. The Zohar reads the first words of Genesis, BeReishit Bara Elohim – In the beginning God created, as "With (the level of) Reishit (Beginning) (the Ein Sof) created Elohim (God's manifestation in creation)": The structure of emanations has been described in various ways: Sephirot (divine attributes) and Partzufim (divine "faces"), Ohr (spiritual light and flow), Names of God and the supernal Torah, Olamot (Spiritual Worlds), a Divine Tree and Archetypal Man, Angelic Chariot and Palaces, male and female, enclothed layers of reality, inwardly holy vitality and external Kelipot shells, 613 channels ("limbs" of the King) and the divine Souls of Man. These symbols are used to describe various levels and aspects of Divine manifestation, from the Pnimi (inner) dimensions to the Hitzoni (outer).
|
|
In that book, by a > multitude of arguments and experiences, the solar reflection from the earth > will be shown to be quite real-against those who argue that the earth must > be excluded from the dancing whirl of stars for the specific reason that it > is devoid of motion and of light. We shall prove the earth to be a wandering > body surpassing the moon in splendor, and not the sink of all dull refuse of > the universe; this we shall support by an infinitude of arguments drawn from > nature ' Galileo may have been trying to quietly introduce his more speculative ideas about the universe among the empirical observations made with his telescope, but these few sentences gave delle Colombe sufficient grounds to attack him at an apparent weak point, in an attempt to force him to defend the motion of the Earth specifically. In 1610, delle Colombe contested Galileo's views – though he did not mention Galileo by name – in his leaflet Contro il Moto della Terra (Against the Motion of the Earth). It was not printed, but circulated in manuscript form, mostly in Florence.
|
|
"Frye (1947: 345) Working along the same lines, Florence Sandler argues that in these texts Blake "set himself to the task of separating true religion from its perversions in his own age and in the Bible itself."Sandler (1990: 43) Also concentrating on the refutation of deism, Alicia Ostriker refers to the series as a "mockery of rationalism and an insistence on Man's potential infinitude."Ostriker (1977: 877) S. Foster Damon suggests that what Blake has done in All Religions are One is "dethroned reason from its ancient place as the supreme faculty of man, replacing it with the Imagination."Damon (1988: 343) Damon also argues that "Blake had completed his revolutionary theory of the nature of Man and proclaimed the unity of all true religions."Damon (1988: 16) Harold Bloom reaches much the same conclusion, suggesting that Blake is arguing for the "primacy of the poetic imagination over all metaphysical and moral systems."Harold Bloom, "Commentary" in Erdman (1982: 894) A similar conclusion is reached by Denise Vultee, who argues that "the two tractates are part of Blake's lifelong quarrel with the philosophy of Bacon, Newton, and Locke.
|
|