I have said we could conceive, living in our world, thinking beings whose table of distribution would be four-dimensional and who consequently would think in hyperspace.
Here there is nothing unpicturable, and yet these sensations are precisely those which would be felt by a being possessed of a two-dimensional retina who could move in space of four dimensions.
We can represent to ourselves a four-dimensional world just as well as a non-Euclidean.
If therefore the possibility of motion is admitted, there can be invented only a finite (and even a rather small) number of three-dimensional geometries.
It would be easy to extend Beltrami's reasoning to three-dimensional geometries.
So vanishes the objection so far as two-dimensional geometries are concerned.
The two-dimensional geometries of Riemann and Lobachevski are thus correlated to the Euclidean geometry.
The images of external objects are painted on the retina, which is a two-dimensional canvas; they are perspectives.
Let us now see how this notion has been generalized and how from it has come the concept of many-dimensional continua.
Beltrami, in correlating likewise Lobachevski's two-dimensional geometry with a branch of ordinary geometry, has equally refuted the objection so far as it is concerned.
A tri-dimensional perception, like this sense of color, requires skilful training, and each lesson must be simplified to the last point practicable.
To illustrate the tri-dimensional nature of colors.
Only, we must not attempt to represent to ourselves four-dimensional space in three-dimensional space, especially not without a knowledge of its properties.
Therefore, despite the oft-repeated statements to the contrary, it is not impossible to imagine four-dimensional space.
Musical scale, a species of one-dimensional space, 105.
By taking two photographs of the same object from two different points, corresponding to the two eyes, a very clear three-dimensional picture of distant places or buildings can be produced by the stereoscope.
Three-dimensional systems of such coordinates have important applications in mathematical physics.
Then we shall have a vivid representation of three-dimensional spherical space, or, rather of three-dimensional spherical geometry.
Can we picture to ourselves a three-dimensional universe which is finite, yet unbounded?
The representation given above of spherical geometry on the plane is important for us, because it readily allows itself to be transferred to the three-dimensional case.
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.
For this purpose we will first give our attention once more to the geometry of two-dimensional spherical surfaces.
This is intelligible without calculation--but only for the two-dimensional case--if we revert once more to the case of the disc on the surface of the sphere.
Now we take an example of a two-dimensional continuum which is finite, but unbounded.
At once they were looking at the three dimensional image of the mail-room aboard the air liner.
The entire solar system was thus marked off as had been the planets long ages before, into a system of three dimensional latitude and longitude.
Space had been marked off into a great three-dimensional map, and each ship carried a small replica, the planets moving as they did in their orbits.
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 rods were movable; they formed a keyboard unimaginably complex; a keyboard whose infinite combinations were like a Fourth Dimensional chess game.
A drawing, like labeling the axes of a three-dimensional space.
The words “Autonomous activities” are important because they hint at the dimensional differences of these energies.
Metaphysics used words and conceptions of multi-dimensional meanings which of necessity resulted in hopeless confusion, in “a talking” about words, in mere verbalism.
But a better word should be found to define the dimensional differences between the activities found in inorganic chemistry and those found in organic chemistry.
The significance of attitude and gesture then were clear to me; the translation of this three-dimensional language I have lost again.
Action--a three-dimensional language--alone could be their vehicle.
The heat and pressure were restrained by the tight space warp for a while, until inter-dimensional barriers ripped wide open.
Being projected in the air before them was a three-dimensional moving, talking picture--the report of the sole survivor of the warship that had attacked the Skylark II.
At one end of the room, as upon a three-dimensional screen, the four Terrestrials saw themselves seated in the control-room of the Skylark.
The headsets are stereoscopic transmitters, taking or receiving a three-dimensional view.
They refer to it as a chart, but it's three-dimensional and almost incredible.
This three-dimensional model, or view, or whatever you want to call it, is converted into electricity in the headsets, and the resulting modulated wave goes back to the educator.
You'll see simply three-dimensional talking pictures of ourselves, transmitted by radio.
Crane and Dunark scarcely breathed as the three-dimensional picture in the visualizer varied from a blank to the hazy outlines of a giant space-cruiser.
Attempts have been made to construct drawings and models showing a four-dimensional body.
There is much, apparently, to suggest that the consciousness attained to by the Indian gnanis in their degree, and by hypnotic subjects in theirs, is of this fourth dimensional order.
But by a rotation in four-dimensional space we could put ourselves so as exactly to coincide with our image.
There could be in four-dimensional space an infinite number of such solids, just as in three-dimensional space there could be an infinite number of infinite planes.
Why, then, should not the four-dimensional beings be ourselves, and our successive states the passing of them through the three-dimensional space to which our consciousness is confined?
The only shape which could exist in a one-dimensional existence of this kind would be a finite straight line.
The other alternative is that we have a four-dimensional existence.
Such a being would be able to make but a part of himself visible to us, for a cube would be apprehended by a two-dimensional being as the square in which it stood.
Another curious thing that could be effected with a two-dimensional being, is the following.
Now, if there are beings who live in a four-dimensional world, they must feel as habituated to it as we do to ours, and the conceptions which seem so impossible to us must be every-day matters to them.
And thus the assumptions which we have made as the basis of an electrical theory are justified on the assumption of a four-dimensional space, are untenable except on that supposition.
To justify this conclusion we have but to think of how a cube would appear to a two-dimensional being.
Having now passed in review some of the properties of four-dimensional figures, it remains to ask what relations beings in four dimensions, if they did exist, would have with us.
The gateway was vulnerable to third-dimensional weapons.
Perhaps as a man can cut finger or even throat on the edge of a near-two-dimensional piece of paper.
On Earth, dogs were said to be intellectually two-dimensional creatures.
They could be hurt, even killed by humans in a three-dimensional world.
As in all of this strange universe, excepting the dome-cages in which the captives were held, the training hall followed no rules of three-dimensional space.
He knew this even though no reason was apparent to his three-dimensional vision.
Tennant concentrated on the zone of strain at the point of dimensional contact, was there directly in front of it.
They seemed to live in a kind of fourth dimensional state, a realm comparable to that which we people with ghosts and spirits.
The equation of push equaling pull is fourth dimensional to the Attas.
It was a flat map instead of the three-dimensional space-model necessary for true distances, but it served as well as a Mercator Projection of the earth, which is a spherical body and far from flat.
Each completed link between star and star would improve the surveying of the galaxy and bring Neosol's dimensional error down and down through the banks of figures best stated by exponents of ten.
All these are evidently sections, as it were, Three-Dimensional representations of his Four-Dimensioned being, which is a fixed and unalterable thing.
Nobody knows what the stuff really is, and it cannot be explained or demonstrated by any model or concept in three-dimensional space.
The Panama-Pacific International Exposition is best seen in its fourth-dimensional aspect when approached through the Gateway of Memory.
Fourth-Dimensional Insight by Ormeida Curtis Harrison; and the illustrations are from etchings done by Gertrude Partington, and the Fourth Dimensional cover design by Julia Manchester Mackie.
A Fourteenth Century Legend Essay on the Fourth-Dimensional Reaches of the Exposition.
The Fourth-Dimensional Reaches of the Exposition San Francisco, 1915 By Cora Lenore Williams, M.
Consequently the mathematician holds the sole title to its knowledge unless we recognize the claims of the medium to a fourth-dimensional insight.
Here ends "The Fourth Dimensional Reaches of the Panama-Pacific International Exposition," written by Cora Lenore Williams, M.
So it is that the fear of being proclaimed a Brazenhead has restrained me until this eleventh hour from telling of my discoveries concerning the fourth-dimensional reaches of our Exposition.
From an etching by Gertrude Partington A Four-Dimensional Cover Design.
Life was not able to maintain itself on land until it had overcome this one-dimensional limitation.
In his first published work[624] Kant seeks to prove that the very existence of space is due to gravitational force, and that its three-dimensional character is a consequence of the specific manner in which gravity acts.
The permanent might still be apprehended as permanent, and therefore as yielding a possible basis for consciousness of sequence, even if it were apprehended in some four-dimensional form.
In three-dimensional space everything must have a right and a left side, and must therefore exhibit such inner differences as those just noted.
But three-dimensional scanning takes time, even at some hundreds of pulses per minute.
Diane handed over the transparent radar graph, to be fitted into the three-dimensional map in the making.
The three-dimensional map served as a matrix to control it.
The above list will hopefully give you a few useful examples demonstrating the appropriate usage of "dimensional" in a variety of sentences. We hope that you will now be able to make sentences using this word. Other words: cubic; cubical; flat; proportional; space; spherical; stereoscopic; superficial; surface
