“Rotation through a fourth dimension can’t affect a three-dimensional figure any more than you can shake letters off a printed page.”

“The triangles that we can measure are not large enough… to detect the curvature. Fortunately, however, we are, in a way, able to communicate with the fourth dimension. The theory of relativity has given us an insight into the structure of the real universe: …a four-dimensional structure. The study of the way in which the three space-dimensions are interwoven with the time-dimension affords a kind of outside point of view of the three-dimensional space… from this outside point of view we might be able to perceive the curvature of the three-dimensional world.”

“Whereas the conception of space and time as a four-dimensional manifold has been very fruitful for mathematical physicists, its effect in the field of epistemology has been only to confuse the issue. Calling time the fourth dimension gives it an air of mystery. One might think that time can now be conceived as a kind of space and try in vain to add visually a fourth dimension to the three dimensions of space. It is essential to guard against such a misunderstanding of mathematical concepts. If we add time to space as a fourth dimension it does not lose any of its peculiar character as time. …Musical tones can be ordered according to volume and pitch and are thus brought into a two dimensional manifold. Similarly colors can be determined by the three basic colors red, green and blue… Such an ordering does not change either tones or colors; it is merely a mathematical expression of something that we have known and visualized for a long time. Our schematization of time as a fourth dimension therefore does not imply any changes in the conception of time. …the space of visualization is only one of many possible forms that add content to the conceptual frame. We would therefore not call the representation of the tone manifold by a plane the visual representation of the two dimensional tone manifold.”

“Nanoparticles constitute a major class of nanomaterials. Nanoparticles are zero-dimensional, possessing nonmetric dimensions in all three dimensions.”

“Most studies employing three-dimensional objects as stimuli have used simultaneous presentation whereas most studies employing two-dimensional objects have used comparison of a single visual stimulus with a memory presentation. We suspect that it is this procedural difference rather than the difference in dimensionality that is the principal determiner of rate of mental rotation.”

“We live in a three-dimensional world, and our brains are organized in three dimensions, so we might as well compute in three dimensions. …Right now, chips, even though they're very dense, are flat.”

“You can always edit a bad page. You can’t edit a blank page.”

“I already see things backwards! You see, in printmaking everything comes out backwards so printing is an absolute natural for me. It is difficult for a lot of artists to do prints because they draw one way and can’t imagine it the other way. I always had trouble reading as a child. Every few minutes my mind would shift and I would pick out all the o's, than all the letter a's on a page.”

“Which of us has not felt that the character we are reading in the printed page is more real than the person standing beside us?”

“Minkowski… supposed that this fourth dimension of time was not detached from and independent of the three dimensions of space. He introduced a new four-dimensional space to which ordinary space contributed three dimensions, and time one; we may call it 'space-time'…. The succession of positions which a particle occupied in ordinary space at a succession of instants of time would be represented by a line in space-time; this he called the 'world-line' of the particle…. Newton's absolute space and absolute time fell out of science, and they carried much with them in their fall. First to go was the concept of simultaneity…. It now became necessary to find a way of treating gravitation which should not involve simultaneity. Einstein found through the medium of his 'Principle of Equivalence'.”