Three Dimensions In Flatland

We as humans live in a three dimensional world every day of our lives, and we take for granted the ability to visualize in the third dimension. However when asked to visualize a fourth dimensional shape; nearly all of us fail. If we can perfectly imagine dimensions from the 0th, being a single point in space, to the 3rd dimension; how is it that going one dimension beyond that is impossible? Well while we can’t create a new place to view a fourth dimensional object, there are tactics we can use to view them. In each transition from different dimensions we use one or sets of numbers to define the point in space. Or in the case of the 0th dimension we would see only a point, with no ability to move in any direction from that point. On a line …show more content…
The problem in the story is that he, the square, comes into contact with a third dimension. While he goes about learning all that he can about the third dimension, we see examples of how we can now imagine a higher dimension. In ”Flatland” the square is talking to a sphere, but in the beginning he can't see the sphere because he is below the sphere in his own two dimensional world. For the square to see the sphere it would have to be on the same plane that the square resides in. When the sphere comes into contact with the two dimensional plane he appears to be only a circle. As he continues to intersect the plane he becomes bigger in diameter, then he again shrinks smaller until he exits the plane. (Abbott) When finally the square understands that there are a new set of directions that he had never considered, he then sees that there exists more than merely two dimensions. So what we can learn from this is a new perspective to imagine the relationship between the third and fourth …show more content…
In a system of equations there would be four variables and four equations. The math would work the same way any other system of equations would, using substitution to solve for all of the variables to define a point or other object in four dimensional spaces. Other than solving the variables in a system of equations; a point in four dimensions would be defined with four numbers such as (1,2,1,2) this would be a point located 1 unit in the x, 2 in the y, 1 in the z, and 2 units in the new w direction. (Annenberg Foundation) There are many different ideas about the space we live in and one of the ideas is that; “They assumed that our space-time is a four-dimensional surface in ten-dimensional Minkowski space R1,9 with one timelike and nine spacelike dimensions”. (Paston and Semenova 1