By dimensional analogy, we know that the 3-D cube will cast a shadow of two-dimensional squares joined by vertices. Take a 3-D cube and project its shadow on a 2-D surface. projecting n-dimensional object in (n-1) dimensions and then inferring how (n+1) dimensional object would be projected in n dimensions. From our (3-D) perspective, a four-dimensional being would have God-like powers as it will have the ability to see everything that from a three-dimensional perspective is enclosed behind the walls.īut how this four-dimensional being will look like? Another useful application of dimensional analogy is in projections i.e. Taking this concept to (n+1) dimension i.e. Therefore, from a perspective of the 2-D square, a three-dimensional being has seemingly God-like powers as it has the ability to remove or place objects without being visible by standing a few inches away in third-dimension. However, a 3-D object can easily see what’s inside the house from ‘up’ of the house. A 2-D object like square cannot see anything inside the house until and unless he goes inside. In the 2-D world, there is no conception of ‘height’ and their houses are absolutely flat. On another hand, a 3-D cube is capable to move forward, backward, left, right, up and down. The square can move forward, backward, left and right, but cannot move up and down as it’s constrained to two-dimensions. In his book, he narrated a story of a 2-D square living in a two-dimensional world. This analogy was used by Edwin Abbott (Shakespeare scholar) in his book ‘Flatland’. they study how (n-1) dimensions are related to n dimensions and then inferring how n dimensions would relate to (n+1) dimensions. Therefore, scientists use dimensional analogy to understand the nature of higher-dimensional space i.e.

As I said earlier, it’s difficult to visualize a higher dimensional object with our brain. Tesseract is a four-dimensional version of the 3-D cube, similarly as cube is a three-dimensional version of the 2-D square. Therefore, we can say by looking at the above trend that a four-dimensional hypercube (or tesseract) is comprised of eight three-dimensional cubes. Similarly, a two-dimensional square is comprised of four one-dimensional lines and a three-dimensional cube is comprised of six two-dimensional squares. A point is dimensionless and a one-dimensional line is comprised of two dimensionless points. Mathematics is the tool which can help us to ‘visualize’ how higher-dimensional objects would look like. The retina sees a two-dimensional image and our neurotransmitters convert them to the 3-D image. This is since our neurotransmitters are aware of how a 3-D world looks like, however, unaware of how a 4-D world looks. Higher-dimensional objects are much more complex to visualize than a three-dimensional object. HOW DOES A FOUR-DIMENSIONAL OBJECT LOOKS LIKE?: Einstein’s 4-D spacetime uses Minkowski’s structure rather less complex Euclidean 4-D space.

4 d cube