- #1
wolfpax50
- 20
- 0
This question will probably make the most sense to those who have read Edwin Abbott Abbott's novel Flatland. But I'm sure many others know the answer.
To explain, I'll have to use some dimensional analogy.
Let's say you're a 2-dimensional being. You live in a two dimensional world and thus you are limited to 1-dimensional sight. If you were, for example, to look at the flat side of a square, and I was to draw your field of vision, it would be a line. Just as, if a 3-dimensional being (like a human) being were to look at the flat side of a cube, and I was to draw its field of vision, it would be a square.
Now if you, as a lowly 2-dimensional being, were to be gifted the power of 2-dimensional sight (like a human), and were lifted upward and rotated, you could see the square you had been looking at from above. Now, rather than just seeing a side, you would be seeing the entirety of the square at once. If I was to draw your field of vision, it would be square.
Now let's say you're a 3-dimensional being (like a human). As I stated prior, if you were to look at the flat side of a cube, and I was to draw your field of vision, it would be a square. Now if you, the 3-dimensional being, were to be gifted 3-dimensional sight (as the 2-dimensional being was gifted 2-dimensional sight) and were lifted into the fourth dimension and rotated, you could see the cube you had been looking at from a new direction. Now, rather than just seeing a square, you would be seeing the entirety of the cube at once. If I was to draw your field of vision, it would be cube.
Now that that's over with, here is my question. If I were to draw your field of view as a 3-dimensional being, staring at the corner (not the side) of a solid cube, and were to draw successive views as your view is lifted and rotated across the fourth dimension. What would these views look like? At the end would the cube still be solid? What about halfway through the transformation?
If the first view is of a 2-dimensional representation of a 3-dimensional cube and the last view is of a 3-dimensional representation a 3-dimensional cube, and I were to draw all of this on 2-dimensional paper, did anything change? Is it possible to represent this change?
My head hurts.
Any input is appreciated. Please include pictures if possible.
To explain, I'll have to use some dimensional analogy.
Let's say you're a 2-dimensional being. You live in a two dimensional world and thus you are limited to 1-dimensional sight. If you were, for example, to look at the flat side of a square, and I was to draw your field of vision, it would be a line. Just as, if a 3-dimensional being (like a human) being were to look at the flat side of a cube, and I was to draw its field of vision, it would be a square.
Now if you, as a lowly 2-dimensional being, were to be gifted the power of 2-dimensional sight (like a human), and were lifted upward and rotated, you could see the square you had been looking at from above. Now, rather than just seeing a side, you would be seeing the entirety of the square at once. If I was to draw your field of vision, it would be square.
Now let's say you're a 3-dimensional being (like a human). As I stated prior, if you were to look at the flat side of a cube, and I was to draw your field of vision, it would be a square. Now if you, the 3-dimensional being, were to be gifted 3-dimensional sight (as the 2-dimensional being was gifted 2-dimensional sight) and were lifted into the fourth dimension and rotated, you could see the cube you had been looking at from a new direction. Now, rather than just seeing a square, you would be seeing the entirety of the cube at once. If I was to draw your field of vision, it would be cube.
Now that that's over with, here is my question. If I were to draw your field of view as a 3-dimensional being, staring at the corner (not the side) of a solid cube, and were to draw successive views as your view is lifted and rotated across the fourth dimension. What would these views look like? At the end would the cube still be solid? What about halfway through the transformation?
If the first view is of a 2-dimensional representation of a 3-dimensional cube and the last view is of a 3-dimensional representation a 3-dimensional cube, and I were to draw all of this on 2-dimensional paper, did anything change? Is it possible to represent this change?
My head hurts.
Any input is appreciated. Please include pictures if possible.