If you paid attention in Iron Man 2, Howard Stark’s notebook with a drawing of a “hypercube”(or a Tesseract), was found among his research and examined by his son Tony Stark.
During my robotics study I came across hypercomplex numbers (Quaternions), hypercube and hypersphere. Humans cannot perceive dimensions which are higher than 3 as it is a 3 dimensional world. Understanding 4D will therefore be difficult as it is abstract and intangible. I will try to make it very simple and straightforward.
To understand 4D we must emphasize on projections and cross-sections.
Projections (bottom to top approach):
- Project a point on a plane perpendicular to it. You will get a line (1D).
- Project a line to a plane perpendicular to it. You will get a square(2D).
- Project a square to a plane perpendicular to it. You will get a cube (3D).
- Now, if you project a cube on a perpendicular plane (each side), you get a tesseract (or also called as a hyper-cube).
Cross-sections (top to bottom approach). Consider a 3D object such as a sphere. Its cross-section (on a 2D plane) is a point that grows into a circle. Similarly, the cross-section of a tesseract or a hypersphere on a 3D frame will be a cube or a sphere respectively.
Let’s try and visualize each of these now. You can see a cube inside a cube in the tesseract. When it is rotated you can see that the cubes swap places. Similarly, the inner sphere covering the outer sphere in the hypersphere.
So this is called lie groups and lie algebra in physics. So tesseract is not something we can hold in our hand.
A tesseract is shown with the capability of teleportation and source of energy (as on Marvel’s Avengers). It is presented as if it is simply a cube surrounded by a cube (that is a view when its rotated about a single axis). I wonder how did Loki get hold of a 4D object in Avengers ;)
It is also shown that, when a tesseract extends into space and time, it is considered to be a 5-Dimensional one. This kind of tesseract is seen in Interstellar. In Interstellar, the tesseract is a three dimensional representation of their four dimensional reality (which is 3 physical dimensions and time). This four dimensional reality was inside a 5th dimension (four dimensions and time) also known as hyperspace. Hence the reason, we were able to see 2 time frames in the movie.
Probably this post will help people in understanding the movie :D
