
Source: 1930s, On my Painting (1938), p. 16
Source: Flatland: A Romance of Many Dimensions (1884), PART II: OTHER WORLDS, Chapter 19. How, Though the Sphere Showed Me Other Mysteries of Spaceland, I Still Desired More; and What Came of It
Context: I despair not that, even here, in this region of Three Dimensions, your Lordship's art may make the Fourth Dimension visible to me; just as in the Land of Two Dimensions my Teacher's skill would fain have opened the eyes of his blind servant to the invisible presence of a Third Dimension, though I saw it not.Let me recall the past. Was I not taught below that when I saw a Line and inferred a Plane, I in reality saw a Third unrecognized Dimension, not the same as brightness, called "height"? And does it not now follow that, in this region, when I see a Plane and infer a Solid, I really see a Fourth unrecognized Dimension, not the same as colour, but existent, though infinitesimal and incapable of measurement?
Source: 1930s, On my Painting (1938), p. 16
Otto Dix quoted by Eva Karcher, in Otto Dix, New York: Crown Publishers, 1987, p. 41; as cited by Roy Forward, in 'Education resource material: beauty, truth and goodness in Dix's War' https://nga.gov.au/dix/edu.pdf, p. 9
“He saw that this process demanded a fourth dimension which he rejected”
"Why Physical Space has Three Dimensions," British Journal for the Philosophy of Science, 6 #21 (May 1955)
Context: Perhaps the first to approach the fourth dimension from the side of physics, was the Frenchman, Nicole Oresme, of the fourteenth century. In a manuscript treatise, he sought a graphic representation of the Aristotelian forms, such as heat, velocity, sweetness, by laying down a line as a basis designated longitudo, and taking one of the forms to be represented by lines (straight or circular) perpendicular to this either as a latitudo or an altitudo. The form was thus represented graphically by a surface. Oresme extended this process by taking a surface as the basis which, together with the latitudo, formed a solid. Proceeding still further, he took a solid as a basis and upon each point of this solid he entered the increment. He saw that this process demanded a fourth dimension which he rejected; he overcame the difficulty by dividing the solid into numberless planes and treating each plane in the same manner as the plane above, thereby obtaining an infinite number of solids which reached over each other. He uses the phrase "fourth dimension" (4am dimensionem).
"The Singularity," The New Humanists: Science at the Edge (2003)
“Love, Allie concluded, wasn't blind, it simply saw alternate dimensions.”
Source: Everfound
“Doing is thinking in the third dimension.”
Ron English's Fauxlosophy: Volume 2 (2022)
“Time is not a line but a dimension, like the dimensions of space.”
Cat's Eye (1988)
Leon M. Lederman, p.103 The God Particle: If the Universe is the Answer, what is the Question? (1993) https://books.google.hr/books?id=-v84Bp-LNNIC
Context: The phrase "ahead of his time" is overused. I'm going to use it anyway. I'm not referring to Galileo or Newton. Both were definitely right on time, neither late or early. Gravity, experimentation, measurement, mathematical proofs … all these things were in the air. Galileo, Kepler, Brahe, and Newton were accepted - heralded! - in their own time, because they came up with ideas that scientific community was ready to accept. Not everyone is so fortunate. Roger Jospeh Boscovich … speculated that this classical law must break down altogether at the atomic scale, where the forces of attraction are replaced by an oscillation between attractive and repulsive forces. An amazing thought for a scientist in the eighteenth century. Boscovich also struggled with the old action-at-a-distance problem. Being a geometer more than anything else, he came up with the idea of "fields of force" to explain how forces exert control over objects at a distance. But wait, there's more! Boscovich had this other idea, one that was real crazy for the eighteenth century (or perhaps any century). Matter is composed of invisible, indivisible a-toms, he said. Nothing particularly new there. Leucippus, Democritus, Galileo, Newton, and other would have agreed with him. Here's the good part: Boscovich said these particles had no size; that is, they were geometrical points … a point is just a place; it has no dimensions. And here's Boscovich putting forth the proposition that matter is composed of particles that have no dimensions! We found a particle just a couple of decades ago that fits a description. It's called a quark.
as quoted by K.C. Cole, "A Theory of Everything" New York Times Magazine (1987) Oct.18