Quotes about vector

A collection of quotes on the topic of vector, general, generation, generator.

Quotes about vector

“In 1917 Levi-Civita discovered his celebrated parallelism which is an infinitesimal transportation of tangent vectors preserving the scalar product and is the first example of a connection. The salient fact about the Levi-Civita parallelism is the result that it is the parallelism, and not the Riemannian metric, which accounts for most of the properties concerning curvature.”

Shiing-Shen Chern (1911–2004) mathematician (1911–2004), born in China and later acquiring U.S. citizenship; made fundamental contributio…

[Differential Manifolds (Classroom Notes) Math 352A, Spring 1952, Department of Mathematics, University of Chicago, http://mathunion.org/ICM/ICM1950.2/Main/icm1950.2.0397.0411.ocr.pdf]

“To know the quantum mechanical state of a system implies, in general, only statistical restrictions on the results of measurements. It seems interesting to ask if this statistical element be thought of as arising, as in classical statistical mechanics, because the states in question are averages over better defined states for which individually the results would be quite determined. These hypothetical 'dispersion free' states would be specified not only by the quantum mechanical state vector but also by additional 'hidden variables' - 'hidden' because if states with prescribed values of these variables could actually be prepared, quantum mechanics would be observably inadequate.”

John S. Bell (1928–1990) Northern Irish physicist

On the problem of hidden variables in quantum mechanics (1966)

Question

“While I was pursuing the concept of geometrical product, as this idea was established by my father… I concluded that not only rectangles, but also parallelograms, may be viewed as products of two adjacent sides, provided that the sides are viewed not merely as lengths, but rather as directed magnitudes. When I joined this concept of geometrical product with the previously established idea of geometrical sum the most striking harmony resulted. Thus when I multiplied the sum of two vectors by a third coplaner vector, the result coincided (and must always coincide) with the result obtained by multiplying separately each of the two original vectors by the third… and adding together (with due attention to positive and negative values) the two products. [Thus A(B + C) = AB + AC. ]
From this harmony I came to see a whole new area of analysis was opening up which could lead to important results.”

Hermann Grassmann (1809–1877) German polymath, linguist and mathematician

Ausdehnungslehre (1844)

Idea

“By generalization of methods developed by Kamefuchi, O'Raifeartaigh, and Salam, conditions for renormalizability of general gauge theories of massive vector mesons are derived. … It is shown that all theories based on simple Lie groups (with the one exception of the neutral vector meson theory in interaction with a conserved current) are unrenormalizable.”

Abdus Salam (1926–1996) theoretical physicist, and Nobel Prize in Physics recipient

[Renormalizability of Gauge Theories, Phys. Rev., 127, 331, 1 July 1962, https://doi.org/10.1103/PhysRev.127.331]

Lie, Gauge

“Happiness is not a state of being. Happiness is a vector, it is movement.”

Neal Shusterman (1962) American novelist

Source: Bruiser

Happiness

“What surprised me, which Google was part of, is that superficial search techniques over large bodies of stuff could get you what you wanted. I grew up in the AI tradition, where you have a complete conceptual model, and the information retrieval tradition, where you have complex vectors of key terms and Boolean queries. The idea that you can index billions of pages and look for a word and get what you want is quite a trick. To put it in more abstract terms, it's the power of using simple techniques over very large numbers versus doing carefully constructed systematic analysis.”

Terry Winograd (1946) American computer scientist

"Talking with Terry Winograd" http://www.acm.org/ubiquity/interviews/t_winograd_1.html, Ubiquity 3 (23), 29 July 2002.

Search, Idea, Parting

“The triplet of specifications - the product-market scope, the growth vector and the competitive advantage - describes the firm's product-market path in the external environment.”

Igor Ansoff (1918–2001) American mathematician

Source: Corporate Strategy, 1965, p. 110

“In the psychological fields most fundamental to the whole behavior of living things the transition seems inevitable to a Galileian view of dynamics, which derives all its vectors not from single isolated objects, but from the mutual relations of the factors in the concrete whole situation, that is, essentially, from the momentary condition of the individual and the structure of the psychological situation. The dynamics of the processes is always to be derived from the relation of the concrete individual to the concrete situation, and, so far as internal forces are concerned, from the mutual relations of the various functional systems that make up the individual.”

Kurt Lewin (1890–1947) German-American psychologist

Source: 1930s, A Dynamic Theory of Personality, 1935, p. 41; partly cited in: Kay Deaux, Mark Snyder (2012) The Oxford Handbook of Personality and Social Psychology. p. 74

Behavior

“In a previous paper we showed that a static (nonrotating) black hole cannot be endowed with exterior scalar-meson or massive vector-meson fields. Here we show that the same is true for massive spin-2 meson fields. We also extend the above results to the case of a rotating stationary black hole. We conclude from our results that a black hole in its final (static or stationary) state cannot interact with the exterior world via the strong interactions which are mediated by meson fields such as the π (scalar), ρ (vector), and ƒ (spin-2). A direct consequence of this is the impossibility of determining the baryon number of the black hole by means of exterior measurements alone. This results in the transcendence of the law of baryon-number conservation as originally predicted by Wheeler.”

Jacob Bekenstein (1947–2015) Mexican-Israeli physicist

[Nonexistence of baryon number for black holes. II, Physical Review D, 5, 10, 15 May 1972, 2403–2412, 10.1103/PhysRevD.5.2403]

World, Law, Strong

“Until always and forever. Now in 1944. After all the hours lived through. The vectors continue in their original direction. Nothing stops them. With no more knowledge than live emotion. With no other wish than to go on until they meet. Slowly. With great unease, but with the certainty that all is guided by the "golden section". There is cellular arrangement. There is movement. There is light. All centers are the same. Folly doesn’t exist. We are the same as we were and as we will be. Not counting on idiotic destiny.”

Frida Kahlo (1907–1954) Mexican painter

Quote of Frida Kahlo, from her letter to Diego Rivera (1944), as cited in The Diary of Frida Kahlo: An Intimate Self-Portrait; ed. Carlos Fuentes & C. Fuentes; Abrams, Harry N. Inc. 2005
1925 - 1945

Knowledge, Light

“By 1956, out of all the Cultural Avatars and Vectors available in 1950, THE GIRL had won. Authority. (And they had it, those girls; no one today has it.) They’d won the war, in a way.”

George W. S. Trow (1943–2006) American writer

My Pilgrim’s Progress (1999)

War, Way, Girl

“Helping people directly can be a noble thing. Forcing other people to do it with great inefficiency? Not so much. There isn’t a single thing that I would petition the federal government to add to its task list, and I would ask that it stop doing the majority of the things that it is currently doing. My vote is going to the candidates that at least vector in that direction.”

John D. Carmack (1970) American computer programmer, engineer, and businessman

Quoted in "John Carmack's Blog" http://media.armadilloaerospace.com/misc/government.htm

People, Help

“They based their extrapolations on numbers. That worked as long as money, which is easily measured numerically, was the principle motivating force in human affairs. But as time progressed, human actions became responsive instead to a multitude of incommensurable vectors.”

Gene Wolfe book Storeys from the Old Hotel

"The Marvelous Brass Chessplaying Automaton", Universe 7 (1977), ed. Terry Carr, Reprinted in Gene Wolfe, Storeys from the Old Hotel (1988), Reprinted in Gene Wolfe, The Best of Gene Wolfe (2009)
Fiction

Money, Motivation, Time

“If in two ellipses having a common major axis we take two such arcs that their chords are equal, and that also the sums of the radii vectores, drawn respectively from the foci to the extremities of these arcs, are equal to each other, then the sectors formed in each ellipse by the arc and the two radii vectores are to each other as the square roots of the parameters of the ellipses.”

Johann Heinrich Lambert (1728–1777) German mathematician, physicist and astronomer

Sect. 4, Lemma 26, Insigniores orbitae cometarum proprietates (1761) [Notable properties of comets' orbits] translated by Florian Cajori, A History of Mathematics https://books.google.com/books?id=kqQPAAAAYAAJ (1906) p. 259, from the German of Michel Chasles, Geschichte der Geometrie, haupsächlich mit Bezug auf die neuern Methoden https://books.google.com/books?id=NgYHAAAAcAAJ (1839) p. 183.

“Every person in your company is a vector. Your progress is determined by the sum of all vectors.”

Elon Musk (1971) South African-born American entrepreneur

What Elon Musk Taught Me About Growing A Business https://www.linkedin.com/pulse/what-elon-musk-taught-me-growing-business-dharmesh-shah/ (16 October 2017)

Personality

“Only by the concrete whole which comprises the object and the situation are the vectors which determine the dynamics of the event defined.”

Kurt Lewin (1890–1947) German-American psychologist

Source: 1930s, The conflict between Aristotelian and Galileian modes of thought in contemporary psychology, 1931, p. 165.

“Symmetrical equations are good in their place, but 'vector' is a useless survival, or offshoot from quaternions, and has never been of the slightest use to any creature.”

William Thomson (1824–1907) British physicist and engineer

Letter to G. F. FitzGerald (1896) as quoted in A History of Vector Analysis : The Evolution of the Idea of a Vectorial System (1994) by Michael J. Crowe, p. 120

“The universality, invariance, and elegance of principles governing the universe may be reflected in principles of the minds that have evolved in that universe - provided that the mental principles are formulated with respect to the abstract spaces appropriate for the representation of biologically significant objects and their properties. (1) Positions and motions of objects conserve their shapes in the geometrically fullest and simplest way when represented as points and connecting geodesic paths in the six-dimensional manifold jointly determined by the Euclidean group of three· dimensional space and the symmetry group of each object. (2) Colors of objects attain constancy when represented as points in a three-dimensional vector space in which each variation in natural illumination is cancelled by application of its inverse from the three-dimensional linear group of terrestrial transformations of the invariant solar source. (3) Kinds of objects support optimal generalization and categorization when represented, in an evolutionarily shaped space of possible objects, as connected regions with associated weights determined by Bayesian revision of maximum entropy priors”

Roger Shepard (1929) American psychologist

R. N. Shepard, (1994). "Perceptual-cognitive universals as reflections of the world." Psychonomic Bulletin and Review, 1, 2–28.

Color, Way, Optimism, Support

“World War II changed the demography. For a while, high seriousness was a part (only a part) of the mix. No one likes to think that the vector that has carried him into the demography could get lost in the demography, but that is what happens. Rock and roll—or the generating spirit of rock and roll—could get lost there, easily. And just think of all the ideas—and changes—there were implicit in the hegemony of rock and roll. We could be left with... just some of the music.”

George W. S. Trow (1943–2006) American writer

Collapsing Dominant (1997)

War, World, Music, Idea

“The physicist who states a law of nature with the aid of a mathematical formula is abstracting a real feature of a real material world, even if he has to speak of numbers, vectors, tensors, state-functions, or whatever to make the abstraction.”

Hilary Putnam (1926–2016) American philosopher

in What is Mathematics, in [Hilary Putnam, Mathematics, matter, and method, Cambridge University Press, 1979, 0521295505, 60]

World, Law, Mathematics, Nature

“A new development began for relativity theory after 1925 with its absorption into quantum physics. The first great success was scored by Dirac's quantum mechanical equations of the electron, which introduced a new sort of quantities, the spinors, besides the vectors and tensors into our physical theories. …But difficulties of the gravest kind turned up when one passed from one electron or photon to the interaction among an indeterminate number of such particles. In spite of several advances a final solution of this problem is not yet in sight and may well require a deep modification of the foundation of quantum mechanics, such as would account in the same basic manner for the elementary electric charge e as relativity theory and our present quantum mechanics account for c and h.”

Hermann Weyl (1885–1955) German mathematician

Preface to the First American Printing (1950) Note: see Paul Dirac, The Principles of Quantum Mechanics (1947)
Space—Time—Matter (1952)

Problem, Success

“We can regard the vector ci as representing certain physical, social, and psychological attributes of player i himself in that it summarizes some crucial parameters of player i's own payoff function Ui as well as the main parameters of his beliefs about his social and physical environment… the rules of the game as such allow any given player i to belong to any one of a number of possible types, corresponding to the alternative values of his attribute vector c i could take… Each player is assumed to know his own actual type but to be in general ignorant about the other players' actual types.”

John Harsanyi (1920–2000) hungarian economist

Source: "Games with Incomplete Information Played by “Bayesian” Players," 1967, p. 171; As quoted in: Mertens, Jean-Francois, and Shmuel Zamir. " Formulation of Bayesian analysis for games with incomplete information http://jeremy-chen.org/sites/default/files/files/convexset/2013_01/formulation_of_bayesian_analysis_for_games_with_incomplete_information_mertens_and_zamir_1985.pdf." International Journal of Game Theory 14.1 (1985): p. 1-2

Game

“What did it matter, Babe Ruth or Jersey Joe Stripp? If vector analysis was beyond me, I could still watch a ball game.”

Roger Kahn (1927–2020) American baseball writer

Source: The Boys Of Summer, Chapter 1, The Trolley Car That Ran By Ebbets Field, p. 19

Game

“Z-relation, or rather, "that certain pitch-class collections share the same 'interval vector' even though they are neither transpositionally nor inversionally equivalent was first pointed out by Howard Hanson in Harmonic Materials of Modern Music (New York: Appleton-Century-Crofts, 1960), p. 22, and by David Lewin in "Re: The Intervallic Content of a Collection of Notes," Journal of Music Theory 4:1 (1960). For a general criticism of Forte's concepts of pitch-class set equivalence see Perle, "Pitch-Class Set Analysis: An Evaluation," Journal of Musicology 8:2”

George Perle (1915–2009) American composer

1990
Page 67, note 8
See: Musical set theory
The Listening Composer

Music

“Wherever there is a main issue the elimination of other things which are not essential will make for a stronger result. In the earlier static abstract sculptures I was most interested in space, vectoral quantities, and centers of differing densities.”

Alexander Calder (1898–1976) American artist

1930s, Statement from Modern Painting and Sculpture (1933)
Source: en.wikiquote.org - Alexander Calder / Quotes / 1930s / Statement from Modern Painting and Sculpture (1933)

Making love

“How can art be realized? Out of volumes, motion, spaces bounded by the great space, the universe. Out of different masses, tight, heavy, middling - indicated by variations of size or color - directional line - vectors which represent speeds, velocities, accelerations, forces, etc...”

Alexander Calder (1898–1976) American artist

these directions making between them meaningful angles, and senses, together defining one big conclusion or many. Spaces, volumes, suggested by the smallest means in contrast to their mass, or even including them, juxtaposed, pierced by vectors, crossed by speeds. Nothing at all of this is fixed. Each element able to move, to stir, to oscillate, to come and go in its relationships with the other elements in its universe. It must not be just a fleeting moment but a physical bond between the varying events in life. Not extractions, but abstractions. Abstractions that are like nothing in life except in their manner of reacting.
1930s, How Can Art Be Realized? (1932)

Universe, Color, Speed, Art