A Quote by Marcel Duchamp

Since a three-dimensional object casts a two-dimensional shadow, we should be able to imagine the unknown four-dimensional object whose shadow we are. I for my part am fascinated by the search for a one-dimensional object that casts no shadow at all.
Since I found that one could make a case shadow from a three-dimensional thing, any object whatsoever - just as the projecting of the sun on the earth makes two dimensions - I thought that by simple intellectual analogy, the fourth dimension could project an object of three dimensions, or, to put it another way, any three-dimensional object, which we see dispassionately, is a projection of something four-dimensional, something we are not familiar with.
If a shadow is a two-dimensional projection of the three-dimensional world, then the three-dimensional world as we know it is the projection of the four-dimensional Universe.
There is a belief that there is a hyperobject called Overmind, or God, that casts a shadow into time. History is our group experience if this shadow. As one draws closer and closer to the source of the shadow, the paradoxes intensify, the rate of change intensifies. What is happening is that the hyperobject is beginning to ingress into three-dimensional space.
Most architects think in drawings, or did think in drawings; today, they think on the computer monitor. I always tried to think three dimensionally. The interior eye of the brain should be not flat but three dimensional so that everything is an object in space. We are not living in a two-dimensional world.
What is a body that casts no shadow? Nothing, a formlessness, two-dimensional, a comic-strip character. If I deny my own profound relationship with evil I deny my own reality. I cannot do, or make; I can only undo, unmake.
The peculiarity of sculpture is that it creates a three-dimensional object in space. Painting may strive to give on a two-dimensional plane, the illusion of space, but it is space itself as a perceived quantity that becomes the peculiar concern of the sculptor. We may say that for the painter space is a luxury; for the sculptor it is a necessity.
It is impossible to imagine a four-dimensional space. I personally find it hard enough to visualize a three-dimensional space!
We are actually fourth dimensional beings in a third dimensional body inhabiting a second dimensional world!
Genes are effectively one-dimensional. If you write down the sequence of A, C, G and T, that's kind of what you need to know about that gene. But proteins are three-dimensional. They have to be because we are three-dimensional, and we're made of those proteins. Otherwise we'd all sort of be linear, unimaginably weird creatures.
Painting does what we cannot do—it brings a three-dimensional world into a two-dimensional plane.
Painting does what we cannot do - it brings a three-dimensional world into a two-dimensional plane.
My fascination has been the space between cloth and the body, and using a two-dimensional element to clothe a three-dimensional form.
Essentially, I look for what is interesting to me, out there in the three-dimensional world, and translate or interpret so that it becomes visually pleasing in a two-dimensional photographic print. I search for subject matter with visual patterns, interesting abstractions and graphic compositions.
It was interesting to have humanoid villains that were rooted in our three-dimensional reality... or four dimensional reality, I'm not sure which!
I regret that it has been necessary for me in this lecture to administer a large dose of four-dimensional geometry. I do not apologize, because I am really not responsible for the fact that nature in its most fundamental aspect is four-dimensional. Things are what they are.
I like the idea of taking three-dimensional objects and making them two-dimensional so that they look like cartoons.
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