| 单词 | four-dimensional |
| 例句 | In general relativity, bodies always follow straight lines in four-dimensional space-time, but they nevertheless appear to us to move along curved paths in our three- dimensional space. A Brief History of Time: And Other Essays 1988-01-01T00:00:00Z Increase all dimensions by one, and you have the situation that may apply to us: the universe as a four-dimensional hypersphere with no center and no edge, and nothing beyond. Cosmos 1980-01-01T00:00:00Z The mass of the sun curves space-time in such a way that although the earth follows a straight path in four-dimensional space-time, it appears to us to move along a circular orbit in three-dimensional space. A Brief History of Time: And Other Essays 1988-01-01T00:00:00Z “I paid, like, twenty-eight dollars for this stupid cream that was supposed to boost my radiance. What did I get for it? A four-dimensional zit!” Goodbye Stranger 2015-08-04T00:00:00Z In such a case, we would have generated a four-dimensional hypercube, also called a tesseract. Cosmos 1980-01-01T00:00:00Z It is often helpful to think of the four coordinates of an event as specifying its position in a four-dimensional space called space-time. A Brief History of Time: And Other Essays 1988-01-01T00:00:00Z It is impossible to imagine a four-dimensional space. A Brief History of Time: And Other Essays 1988-01-01T00:00:00Z The hypersphere is expanding from a point, like a four-dimensional balloon being inflated, creating in every instant more space in the universe. Cosmos 1980-01-01T00:00:00Z And instead of reality being this impossible four-dimensional rush, it gets distilled, slowed down and packaged into these steady, consistent short pulses – these packets of information, rather like a tweet. David Mitchell is over the genre wars: “Confining an entire genre as being unworthy of your attention is a bizarre act of self-harm” 2015-10-25T04:00:00Z It’s an ingenious solution, one that turns the game into something like a treasure hunt; the viewer is invited to seek out each pathway and build a four-dimensional picture of the plot’s narrative possibilities. “Black Mirror” ’s “Bandersnatch” and the Pitfalls of Interactive Fiction 2019-01-03T05:00:00Z Instead, we reduce impossibly complicated, four-dimensional issues to binary yes and no responses. “Maya” in my America: Illusions of truth about art, culture and immigrant anger 2016-11-15T05:00:00Z Rules of geometry govern how these elements can fit together, and participants will learn about some of these principles, including recent revelations about four-dimensional space. Spare Times Listings for Kids for Oct. 10-16 2014-10-09T04:00:00Z Alexander Cary, a writer and executive producer on “Homeland,” wrote this six-episode spy thriller as a leisurely, literate, three- or four-dimensional game of chess. British Spies, Japanese Teens and a German Cop’s Wild Ride 2023-05-10T04:00:00Z While many TV episodes these days play with four-dimensional narratives and unreliable perceptions, “The Queen” stayed heartbreakingly grounded in character by anchoring itself in Ruth’s point-of-view. The Most Memorable TV Episodes of 2018 2018-12-24T05:00:00Z And—arguably—a threshold in human affairs was crossed, as many of us began to live four-dimensional lives. Apple at Forty: Steve Jobs Led Us to the Fourth Dimension 2016-04-01T04:00:00Z It is a half-hour mystical work with a mathematical title that has something to do with complex numbers and four-dimensional space. Music ensembles Hocket and Sakura bathe Monk Space in an acoustical glow 2015-10-15T04:00:00Z We are thick here in the art of intensive combinations of plants, where forms, textures and stages of growth form a four-dimensional canvas. It’s time to plan the new season’s garden, and it pays to be picky 2020-03-10T04:00:00Z He appeared capable of playing four-dimensional mental chess while carrying on a dinner conversation with lesser mortal beings. An Appreciation: Lorin Maazel conducted himself inimitably 2014-07-14T04:00:00Z He then arranges these with the help of digital technology into sequences that suggest immersive, three-dimensional and even four-dimensional space and movement. Dancing for Many Cameras, in the Round: ‘It’s Muybridge on Steroids’ 2021-01-26T05:00:00Z The music has something to do with a generously lush four-dimensional cello sound. Music ensembles Hocket and Sakura bathe Monk Space in an acoustical glow 2015-10-15T04:00:00Z He plays four-dimensional chess while his current analogue often seems to play Whac-a-Mole. The Trump Administration Shakes ‘House of Cards’ Hard 2017-06-06T04:00:00Z You become a kind of vanishing point, the focus of its four-dimensional perspective. 'Sculpture in the Age of Donatello' shows artist's competitive spirit 2015-05-08T04:00:00Z Senator Roger Marshall, Republican of Kansas, described Mr. McConnell as “large and in charge of our lunches: He’s still playing four-dimensional chess up here when it comes to politics.” As McConnell Tries to Convey Business as Usual, His Future Is in Doubt 2023-07-27T04:00:00Z So what does the optimal packing of n four-dimensional balls in four-dimensional space look like? Gift Wrapping Five Oranges Has Outwitted the Best Minds in Mathematics for Generations 2023-06-06T04:00:00Z One demonstration in the study involved increasing the intensity of the smell generated as a woman in a four-dimensional movie brought a rose up to her nose. Virtual Reality System Lets You Stop and Smell the Roses 2023-05-09T04:00:00Z As it sprawls out, it encompasses a dizzying array of topics, from the mysterious Voynich manuscript to the way four-dimensional objects would appear to three-dimensional observers. The best books from 2022 that we’ve read in 2023 2023-03-02T05:00:00Z Castile and Leon’s conservative president, Alfonso Fernández Mañueco, said Monday that the central Spanish region would allow women seeking an abortion to request those procedures, including four-dimensional ultrasound scans or psychological counseling. Spain: Region drops order to offer heartbeat before abortion 2023-01-16T05:00:00Z But this process can be seen only from a four-dimensional perspective, outside of most people's—likely anyone's—reach. How Squishy Math Is Revealing Doughnuts in the Brain 2022-09-26T04:00:00Z As you might expect, to calculate the dot product of four-dimensional vectors, we simply add the products of the components as before, but the sum has four terms instead of three. Calculus, Volume 3 2016-03-30T00:00:00Z Other mathematicians subsequently showed that the conjecture was not true for many four-dimensional manifolds. Abel Prize for 2022 Goes to New York Mathematician 2022-03-23T04:00:00Z And despite that foam being limited to two dimensions, it gives rise to our four-dimensional world, with three dimensions of space and one of time. What Is Spacetime Really Made Of? 2022-01-18T05:00:00Z One participant likened the job to playing four-dimensional chess with spaghetti. Climate change: Five dealmakers who will influence the outcome at COP26 2021-11-01T04:00:00Z According to Albert Einstein’s epic discovery, we live in four-dimensional “spacetime.” Star Trek ’s Warp Drive Leads to New Physics 2021-07-13T04:00:00Z In that case, he would want to use four-dimensional quantity and price vectors to represent the number of apples, bananas, oranges, and grapefruit sold, and their unit prices. Calculus, Volume 3 2016-03-30T00:00:00Z Or, conversely, it was Guardiola distilling his beliefs down to their purest essence, trying to use the grandest stage of all to showcase his latest idea, the four-dimensional chess move of the boss-level supercoach. N’Golo Kanté, Chelsea and Beating the System 2021-05-30T04:00:00Z Fiction is not a blueprint, but it can be a gilded mirror, or a four-dimensional map. In Nikita Lalwani’s ‘You People,’ people and perspectives collide in a London pizzeria 2021-05-14T04:00:00Z They can act and improvise with humans in four-dimensional space-time. TV hasn't forgotten the Muppets. And it never should 2021-02-19T05:00:00Z On closer inspection, however, this limit only applies within the four-dimensional spacetime comprising the universe. Star Trek ’s Warp Drive Leads to New Physics 2021-07-13T04:00:00Z Therefore the “graph” of a vector field in ℝ2 lives in four-dimensional space. Calculus, Volume 3 2016-03-30T00:00:00Z “His die-hard supporters will tell you he’s playing four-dimensional chess,” Scaramucci said, “but all of us really know he’s eating the chess pieces; he’s munching on the chess pieces.” Analysis | The ending of Trump’s presidency echoes the beginning — with a lie 2020-11-15T05:00:00Z Their study isn’t limited to one dimension, either: Mathematicians also consider how knots made of two-dimensional spheres behave in four-dimensional space. Graduate student untangles nature of Conway knot 2020-05-22T04:00:00Z And following an unpopular president down a very strange rabbit hole is just another move in a game of four-dimensional chess. Opinion | Senate Republicans are staking their political future on lies and conspiracy theories 2020-05-21T04:00:00Z Dealing with a dynamic, four-dimensional structure like spacetime is extremely complicated, however. Star Trek ’s Warp Drive Leads to New Physics 2021-07-13T04:00:00Z When we felt the effect of that in tandem with what our clients were already feeling with market volatility, it became a three- and four-dimensional problem. ‘It’s Going to Be a Bit of a Bumpy Ride’: Financiers Weigh In on the Crisis 2020-05-08T04:00:00Z Therefore, to determine a three-dimensional curve, the mind would need to picture the four-dimensional object. How Mere Humans Manage to Comprehend the Vastness of the Universe 2019-10-11T04:00:00Z To complete the picture, Das et al. used a technique known as four-dimensional scanning transmission electron microscopy to probe the swirling in-plane dipoles around the equator of a bubble that determine the bubble’s chirality. Electrifying skyrmion bubbles 2019-04-16T04:00:00Z Psaltis described a black hole as “an extreme warp in spacetime,” a term referring to the three dimensions of space and the one dimension of time joined into a single four-dimensional continuum. In astrophysics milestone, first photo of black hole expected 2019-04-06T04:00:00Z This allows the five dates to be edited into one four-dimensional hyperdate. A Dating Show Made for the Age of Apps 2019-03-14T04:00:00Z The data set is likewise hand-engineered in such a way that it is simple to analyse in this four-dimensional space. Machine learning in quantum spaces 2019-03-12T04:00:00Z For the former, the task is to conceptualize a three-dimensional universe that exists in a loop—an impossible visualization, for connecting every dimension would create a four-dimensional object. How Mere Humans Manage to Comprehend the Vastness of the Universe 2019-10-11T04:00:00Z According to Ms. Looker, the fit took three years and multiple four-dimensional body mapping sessions of professional athletes to adjust. Women Finally Get Their Own World Cup Soccer Style 2019-03-11T04:00:00Z Einstein’s general theory of relativity beautifully weaves space and time together into a four-dimensional fabric, known as space-time, and equates gravity with warps in that fabric. A Different Kind of Theory of Everything 2019-02-19T05:00:00Z What does life in a four-dimensional universe look like? How a fan fiction for Cixin Liu’s Three-Body Problem became an official novel 2018-10-19T04:00:00Z One of the main difficulties with stability proofs has to do with keeping track of what is going on in four-dimensional space-time as the solution evolves. To Test Einstein's Equations, Poke a Black Hole 2018-08-27T04:00:00Z Similarly, when considering the four-dimensional universe, mathematical measurements provide astrophysicists with an invaluable means of navigating the obscure. How Mere Humans Manage to Comprehend the Vastness of the Universe 2019-10-11T04:00:00Z The four-dimensional, analog world she loved has been flattened and digitized. ‘I’m ashamed’: Americans blame Trump after mom’s deportation 2018-07-23T04:00:00Z “With a closed primary, it’s a little bit of chess. With a jungle primary, it’s more like three- or four-dimensional chess,” said Jim Brulte, chairman of the California Republican Party. California’s ‘jungle primary’ sets off party scrambling 2018-06-01T04:00:00Z For our purposes, picture the Tesseract as a very strong, and four-dimensional, crystalline cube. A scientist calculated the ludicrous strength of Marvel villain Thanos 2018-05-18T04:00:00Z Rather than accepting the geometry of space and time as fixed, Einstein explained that we actually inhabit a four-dimensional reality called space-time whose form fluctuates in response to matter and energy. To Test Einstein's Equations, Poke a Black Hole 2018-08-27T04:00:00Z There are also giraffe sculptures, a defunct sensory deprivation tank, a four-dimensional hypercube called a tesseract and a fake particle accelerator made of gold-painted junk. In a forgotten town by the Salton Sea, newcomers build a bohemian dream 2018-04-23T04:00:00Z Along with his many achievements, Stephen Hawking also contributed to the widespread misunderstanding of physics by insisting that space-time is four-dimensional. Opinion | How will we remember Stephen Hawking? 2018-03-23T04:00:00Z In the real world, a tesseract is a four-dimensional cube. The physicist who melded the science and fiction of A Wrinkle in Time 2018-03-12T04:00:00Z The catch here is that the hypercubus in the painting’s title refers to a four-dimensional object. Salvador Dalí and the Hypercube 2018-03-08T05:00:00Z Two years later, he published The Tesseract, a story as structurally complex and interconnected as the titular four-dimensional cube. Alex Garland Stands by His Vision for ‘Annihilation’ 2018-02-15T05:00:00Z The eight large cubes forming the cross in Figure 18 are a three-dimensional net of a four-dimensional cube! Math at the Met 2017-11-16T05:00:00Z The four-dimensional notation is just a convenient way of handling the mathematical relationship between space evolution and time evolution. Opinion | How will we remember Stephen Hawking? 2018-03-23T04:00:00Z Space-time is the mind-bending, four-dimensional way astronomers see the universe. AP Explains: Why gravitational wave researchers won a Nobel 2017-10-03T04:00:00Z Finally, draw lines perpendicular to all faces of the cube, and you’ve got yourself a four-dimensional version of a cube, called a “hypercube.” Salvador Dalí and the Hypercube 2018-03-08T05:00:00Z He said mining space resources faces what he calls a “four-dimensional problem.” Space-mining may be only a decade away. Really. 2017-04-28T04:00:00Z Early in his book, Gleick explores one of the earliest conceptions of time travel, the Universe Rigid—a four-dimensional construct thought up by Wells. How to Build a Time Machine 2016-12-20T05:00:00Z We think in fragments, and in four-dimensional space. Novelist Connie Willis explains why telepathy is a terrible superpower 2016-10-13T04:00:00Z He is also credited with developing a new research field dubbed four-dimensional electron microscopy, which helps capture fleeting processes and turn them into a kind of digital film. First Arab Nobel science winner Ahmed Zewail dies - BBC News 2016-08-03T04:00:00Z Dalí and Banchoff discussed the nuances of four-dimensional geometry and other cutting-edge mathematics, and they continued to meet regularly until Dalí’s death in 1989. Salvador Dalí and the Hypercube 2018-03-08T05:00:00Z But Einstein's theory combined space and time together into one four-dimensional model called space-time. Scientists have finally proven Einstein’s century-old theory about gravitational waves 2016-02-11T05:00:00Z Gravitational waves are ripples in space-time — the four-dimensional concept in which time and space are combined into one continuum. Einstein’s theory about gravitational waves could be confirmed today 2016-02-11T05:00:00Z Thus do we reach the four-dimensional chess game. The Big Picture Take on Geopolitical Instability 2016-01-14T05:00:00Z The problem was that, in order to build a theory on this insight, Einstein needed to be able to create those descriptions in warped four-dimensional space-time. The most beautiful theory 2015-11-25T05:00:00Z It can be difficult to visualize transformations of the plane because the “graph” of such a transformation would live in four-dimensional space. Impossible Wallpaper and Mystery Curves: Exploring Symmetry in Mathematics and Art 2015-09-14T04:00:00Z The four-dimensional world of quantum mechanics may offer some guidance or, at the very least, a philosophical approach to strategic forecasting. Quantum Geopolitics 2015-07-31T04:00:00Z An important ingredient in some of the most promising candidates for such a geometry is a collection of four-dimensional shapes known as K3 surfaces. Mathematicians Chase Moonshine’s Shadow 2015-04-07T04:00:00Z Physicists often describe the fabric of the universe we inhabit as four-dimensional spacetime, comprising three dimensions of space and one of time. Sean Carroll Entangles Time and Entropy 2014-11-02T04:00:00Z The accomplishments of Dr. Donaldson include using a mathematical theory originally developed for particle physics to study and classify possible shapes of four-dimensional space. The Multimillion-Dollar Minds of 5 Mathematical Masters 2014-06-23T04:00:00Z They elevate it from a four-dimensional diagram used to record their experience into the kind of “real essence” that Bohr warned us not to seek. Physics: QBism puts the scientist back into science 2014-03-26T18:20:27.279Z Gravitational waves were a consequence of Einstein’s theory that Newton’s “force at a distance” was actually a curving of the four-dimensional fabric of space-time. Einstein's Gravitational Waves Discovered 2014-03-17T17:20:00Z The 23 new moonshines appear to be intertwined with some of the most central structures in string theory, four-dimensional objects known as K3 surfaces. Mathematicians Chase Moonshine’s Shadow 2015-04-07T04:00:00Z However, something remains invariant in the process: a unified, four-dimensional spacetime. Is It Solipsistic in Here, or Is It Just Me? 2014-03-12T17:22:25Z The space-time building blocks were simple hyper-pyramids — four-dimensional counterparts to three-dimensional tetrahedrons — and the simulation's gluing rules allowed them to combine freely. Theoretical physics: The origins of space and time 2013-08-28T17:20:26.740Z By identifying my abstract diagram with an objective reality, I fool myself into regarding that diagram as a four-dimensional arena in which my life is lived. Physics: QBism puts the scientist back into science 2014-03-26T18:20:27.279Z In the four-dimensional reality of Einstein’s relativity, other times — from the Big Bang to the Big Freeze — are as real as other places. Out There: Timeless Questions About the Universe 2013-07-01T20:36:55Z “It’s like a puzzle, but it’s in color and it’s four-dimensional because of the time element,” said a U.S. intelligence official monitoring the investigation. Boston blast investigators narrow focus on five-hour window 2013-04-18T01:24:38Z Each page slowly walks you through an understanding of spatial dimensions, and the animations, incredibly, will help you get a handle on how a four-dimensional space would work. Three Apps To Expand Your Mind Over The Holidays 2012-12-23T07:50:37Z Relativity portrays time as another dimension interwoven with the three dimensions of space, thereby creating a four-dimensional space-time fabric that comprises the Universe. Data teleportation: The quantum space race 2012-12-05T18:50:24.460Z Physicists represent all the events experienced by a single person as a line in four-dimensional space-time, called that person's 'world-line'. Physics: QBism puts the scientist back into science 2014-03-26T18:20:27.279Z This four-dimensional crystal would be similar to conventional 3D crystals, which are structures, like snowflakes and diamonds, whose atoms are arranged in repeating patterns. Eternal Clock Could Keep Time After Universe Dies 2012-09-25T22:15:00.270Z Gravity is the curvature of some four-dimensional mind stuff called space-time. ‘Einstein’s Jewish Science,’ by Steven Gimbel 2012-08-03T16:38:33Z Lawyers were poring over a dozen documents on Monday running to 1,000 pages outlining the mechanisms for an auction so complicated it was likened by one network source to "playing four-dimensional chess". Ofcom braced for legal action over 4G mobile phone internet auction 2012-07-24T17:56:00Z The view expanded to a four-dimensional kaleidoscope of scenes and senses. Perchance to bleam 2012-04-25T17:21:07.597Z The original three-dimensional spacetime becomes the boundary of a four-dimensional spacetime, with the new dimension representing the distance from this boundary. Where Do Space and Time Come From? New Theory Offers Answers, If Only Physicists Can Figure It Out 2012-04-12T21:15:02.897Z It's not just a three-dimensional material, it's four-dimensional because it changes with time as well. How jeans conquered the world 2012-02-28T09:39:23Z But in relativity theory, the two can be combined mathematically into something more fundamental: a four-dimensional abstraction called the space-time interval. ‘Einstein’s Jewish Science,’ by Steven Gimbel 2012-08-03T16:38:33Z HE negotiates with the Republican Senate leader, Dean G. Skelos, and the Democratic Assembly speaker, Sheldon Silver, in a sort of four-dimensional chess game. Gotham: Cuomo Smiles as Albany Nears Progressive Tax Deal 2011-12-08T03:40:05Z That was why Son was seeing quark–gluon equations in a string-theory calculation, Starinets explained: they were the three-dimensional equivalent of the gravitational fields that he and Policastro had been studying in the four-dimensional universe. A meeting of disciplines: String theory finds a bench mate 2011-10-19T17:20:28.410Z The universe is four-dimensional—three for space, one for time. What Do You Mean, The Universe Is Flat? (Part I) 2011-07-26T20:45:02.407Z Quaternions are a four-dimensional generalization of ordinary numbers and they show up in innumerable places in both math and physics. When Math(s) Turns Out To Be Useful 2011-07-19T11:15:04.210Z Attempts have been made to construct drawings and models showing a four-dimensional body. The Seven Follies of Science [2nd ed.] A popular account of the most famous scientific impossibilities and the attempts which have been made to solve them. 2011-06-30T02:00:34.290Z On the other hand, having the standardization of 0, 1, x, y available to us takes a four-dimensional problem, with four unknown numbers in the corners, and reduces it to just a two-dimensional problem. Wordplay: Numberplay: The Danger of Praise 2011-05-20T17:22:12Z They have also mapped the behaviour of four-dimensional black holes in string theory to the conditions at which many materials will change phase into states other than the familiar solid, liquid and gas. A meeting of disciplines: String theory finds a bench mate 2011-10-19T17:20:28.410Z The universe is four-dimensional—three for space, one for time. What Do You Mean, The Universe Is Flat? (Part I) 2011-07-26T20:45:02.407Z The dichotomy has led to decades of research in mathematics and physics, including the discovery of “fake” four-dimensional spaces by Simon Donaldson in 1984. Pioneer of High-Dimensional Spaces Wins Abel Prize 2011-03-23T23:05:21Z It is difficult to conceive of a curved three-dimensional space, let alone a curved four-dimensional space-time, but some idea of what it means can be gained from an analogy with two-dimensional surfaces. Gravity, by George Gamow [Special Archive Article] 2011-03-04T13:45:00.433Z By using short pulses of light, a four-dimensional view can be obtained and provide snapshots of dynamic processes. This Week in Science 2011-01-06T19:25:00.633Z The Alaskan senator was so awe-struck by the industry's four-dimensional seismic imaging that she proclaimed deep-sea drilling to have reached the very height of controlled artificiality. Gulf oil spill: A hole in the world 2010-06-18T23:01:00Z About 160,000 babies were born at the hospital, which helped pioneer the use of innovations such as four-dimensional "real time" ultrasound scans. 2010-01-13T00:37:00Z I could pose myself a problem in, say, four-dimensional vector analysis and see the solution immediately, like a flash of intuition. Last Resort Here we are speaking of geodesics in the four-dimensional space-time continuum. Gravity, by George Gamow [Special Archive Article] 2011-03-04T13:45:00.433Z That gate is the one through the fourth dimension, for Xoran and your planet in a four-dimensional universe are almost touching each other in spite of the great distance separating them in a three-dimensional universe. Astounding Stories of Super-Science January 1931 The field of this meteorite bends light through space-time, through the four-dimensional continuum. Astounding Stories, March, 1931 The four-dimensional mode of consideration of the "world" is natural on the theory of relativity, since according to this theory time is robbed of its independence. Relativity: The Special and General Theory I'm going to convince you of the reality of four-dimensional space as you would not be convinced in the old days. Astounding Stories of Super-Science, May, 1930 Admitting that individual self-consciousness persists beyond the change called death, it only means that such consciousness is being exercised along another plane; from a three-dimensional it has entered a four-dimensional world. The New Theology We of Xoran, being three-dimensional creatures like you Earthlings, can not even exist on a four-dimensional plane. Astounding Stories of Super-Science January 1931 Our material universe is merely the intersection of tangled world lines of geodesics in a four-dimensional continuum. Astounding Stories, March, 1931 We refer the four-dimensional space-time continuum in an arbitrary manner to Gauss co-ordinates. Relativity: The Special and General Theory He can't hold that boat steady in four-dimensional space, as he pretends he can. Astounding Stories of Super-Science, May, 1930 Out beyond the dense space that surrounds all stars, the long ship probed the ever-shifting currents in the four-dimensional universe. General Max Shorter They could use their minds; they could rationalize correctly; they could use their curious four-dimensional knowledge to bring them to answers no three-dimensional man could reach. The Dark Door We are able to see what we do because the field of the meteor bends light through the four-dimensional continuum. Astounding Stories, March, 1931 From a "happening" in three-dimensional space, physics becomes, as it were, an "existence" in the four-dimensional "world." Relativity: The Special and General Theory Instead, it was partially a four-dimensional pseudo-manifold superimposed on normal space. Pagan Passions The suggestion appeared to be that, in exactly a similar way, events which to the three-dimensional man can only be perceived normally in sequence, would co-exist for a four-dimensional being. Seen and Unseen It would be easy for such four-dimensional pieces to fall into burlesque, but in at least two cases, to wit, in "The Blue Sphere" and "In the Dark," they go off with an air. A Book of Prefaces The totality of event-particles will form a four-dimensional manifold, the extra dimension arising from time—in other words—arising from the points of a timeless space being each a class of event-particles. The Concept of Nature The Tarner Lectures Delivered in Trinity College, November 1919 "Well, as far as we know, we live in a four-dimensional universe," the colonel started. Crossroads of Destiny The turn of a four-dimensional world is near, but the puzzle of science will ever continue until their concepts reach the natural dimensions of visible and invisible space—in its septenary completeness. Five Years of Theosophy Will the psychology of the new dispensation find expression through some adaptation of four-dimensional geometry? Architecture and Democracy Behind such organic change—assumed to be four-dimensional—there is the determination of some will-to-live, which manifests itself to consciousness as thought and as desire. Four-Dimensional Vistas Since an event is four-dimensional, the boundary of an event is a three-dimensional manifold. The Concept of Nature The Tarner Lectures Delivered in Trinity College, November 1919 This is the ultimate foundation in fact which enables us to speak with meaning of the mensuration, in Riemann's sense of the word, of the four-dimensional continuum of space-time. Sidelights on Relativity Well," he resumed, after a moment's pause, "I procured the implements and the coloured blocks for practical experiment, and I followed the instructions carefully till I had arrived at a working conception of four-dimensional space. Three More John Silence Stories This regular solid of four-dimensional space consists of sixteen cells, each a regular tetrahedron, thirty-two triangular faces, twenty-four edges and eight vertices. Architecture and Democracy In four-dimensional space, however, the ten equal distances between any two of five points are geometrically independent, thus greatly augmenting the number and variety of possible arrangements of atoms. Four-Dimensional Vistas The two boundaries must have a common portion which is in fact a continuous three-dimensional locus of event-particles in the four-dimensional manifold. The Concept of Nature The Tarner Lectures Delivered in Trinity College, November 1919 From a "happening" in three-dimensional space, physics becomes, as it were, an " existence " in the four-dimensional " world." Relativity : the Special and General Theory I had attained to the state of continuous consciousness, for at night I regularly, with the first approaches of drowsiness, entered nolens volens the four-dimensional world. Three More John Silence Stories Now this coincides remarkably with the idea implicit in all higher-space speculation, that the figures of solid geometry are projections on a space of three dimensions, of corresponding four-dimensional forms. Architecture and Democracy If Hinton's hypothesis be the true explanation, the universality of electro-magnetic action would again point to the conclusion that our three-dimensional world is superficial—the surface, that is, of a four-dimensional universe. Four-Dimensional Vistas Their definition is simple enough when the four-dimensional manifold of event-particles has been more fully explored as to its properties. The Concept of Nature The Tarner Lectures Delivered in Trinity College, November 1919 But viewed from below, from the standpoint of normal physical experience, they are powers truly magical; as the powers natural to a four-dimensional being will appear magical to a three-dimensional being. The Yoga Sutras of Patanjali: the Book of the Spiritual Man I discovered, that is, that my ordinary three-dimensional body was but an expression—a projection—of my higher four-dimensional body! Three More John Silence Stories And because the more remote these are from the things of sense, from knowledge and experience, the projected figures of four-dimensional geometry would lend themselves to these uses with an especial grace. Architecture and Democracy Psychic phenomena indicate that occasionally, in some individuals, the will is capable of producing physical movements for whose geometrico-mathematical definition a four-dimensional system of co-ordinates is necessary. Four-Dimensional Vistas In looking to nature for evidence of absolute position it is of no use to recur to the four-dimensional manifold of event-particles. The Concept of Nature The Tarner Lectures Delivered in Trinity College, November 1919 Thus there are three types of parallelograms in the four-dimensional manifold of event-particles. The Concept of Nature The Tarner Lectures Delivered in Trinity College, November 1919 Apparently sleep is unnecessary in the higher—the four-dimensional—body. Three More John Silence Stories The idea is far from absurd, by reason of the decorative quality inherent in many of the regular hypersolids of four-dimensional space when projected upon solid and plane space. Architecture and Democracy This reminds us of the segmentation of cell life observed under the microscope, as though a four-dimensional figure were registering its passage through our space. Four-Dimensional Vistas The other reason for failure arises from the four-dimensional extension of events so that there is no determinate route of transition of events in linear series. The Concept of Nature The Tarner Lectures Delivered in Trinity College, November 1919 Thus the life of a material particle is its adventure amid a track of event-particles strung out as a continuous series or path in the four-dimensional space-time manifold. The Concept of Nature The Tarner Lectures Delivered in Trinity College, November 1919 We have got to find the way of expressing the field of activity of events in the neighbourhood of some definite event-particle E of the four-dimensional manifold. The Concept of Nature The Tarner Lectures Delivered in Trinity College, November 1919 Now the flux of things corresponds to the four-dimensional aspect of the world, and with this the reason finds it impossible to deal. Four-Dimensional Vistas Then he conceives of what such a vortex would be in a four-dimensional medium of analogous properties. Four-Dimensional Vistas Thus in the four-dimensional geometry of all event-particles there is a two-dimensional locus which is the locus of all event-particles on points lying on the straight line r. The Concept of Nature The Tarner Lectures Delivered in Trinity College, November 1919 A four-dimensional being would experience no difficulty, under suitable conditions, in possessing itself of any part of the bodily mechanism of another. Four-Dimensional Vistas All unconsciously to himself, he has called into play four-dimensional mechanics. Four-Dimensional Vistas With the symmetry of solids, or symmetry with relation to an axial plane, no such simple movement as the foregoing suffices to produce or explain it, because symmetry about a plane implies four-dimensional movement. Four-Dimensional Vistas It is a reasonable inference that the fourth state of matter, the corpuscular, is affiliated to some four-dimensional manner of extension, and that there may be states beyond this, involving even higher development of space. Four-Dimensional Vistas I do not apologise, because I am really not responsible for the fact that nature in its most fundamental aspect is four-dimensional. The Concept of Nature The Tarner Lectures Delivered in Trinity College, November 1919 Now could it be shown that the two-dimensional symmetry observed in nature is the result of a three-dimensional movement, the right-and left-handed symmetry of solids would by analogy be the result of a four-dimensional movement. Four-Dimensional Vistas In the mirror image of a solid we have a representation of what would result from a four-dimensional revolution, the surface of the mirror being the plane about which the movement takes place. Four-Dimensional Vistas Every electron, in other words, must be the starting point of a pathway into—and a terminal point out of—four-dimensional space. Four-Dimensional Vistas Nature affords a sufficient number of representations of four-dimensional forms and movements to justify their consideration. Four-Dimensional Vistas These event-particles are the ultimate elements of the four-dimensional space-time manifold which the theory of relativity presupposes. The Concept of Nature The Tarner Lectures Delivered in Trinity College, November 1919 Such dreams belong to both worlds, partly to the three-dimensional and partly to the four-dimensional. Four-Dimensional Vistas Leadbeater in Clairvoyance specifically affirms that this higher power of sight is four-dimensional. Four-Dimensional Vistas This was suggested to the author by the endeavor of two friends whose interests were pre-eminently mathematical to discover what certain four-dimensional figures would look like in three-dimensional space. Four-Dimensional Vistas The helix of many helices would become four-dimensional, and superficial space would change to solid space: each tiny circle of intersection would become a sphere of the same diameter, describing, instead of loops, helices. Four-Dimensional Vistas |
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