The same analogy can be put forward to dimensions higher than three.

The original configuration cannot be restored unless it is again placed in a higher dimension space, three-dimensional space in this case. If we ‘pick’ it up from the 2D sheet, invert it and place it again in the plane. Suppose a shape exists in this fictional plane in a specific orientation. Another interesting property that needs consideration when discussing dimensions is inversion. A being of the fourth dimension can see in and out of our three-dimensional universe. If a 4D object moves through our space, we will see an eclipsing 3D object similarly, as we can see in and out of what is happening in this fictional flat plane. Moving forward with the same analogy, we cannot properly perceive the 4D objects due to the restrictions of our universe. As an effect of this, the sphere grows and shrinks in size. Sphere goes up and down the flat world in the hidden dimension which the flat world does not have. However, the sphere says there’s more to it than meets the eye. Sphere is a creature from the 3D world and we simply see it as a circle, because, well, we’re flat. Square is our wonderful friend guiding us through our now flat world, when we’re visited by this vile sphere. Thus, to understand the workings of dimensions higher than 4, we can take the help of an analogy from “Flatland” by Edwin Abbott. Movies like Interstellar make us think about what higher dimensions might feel like to us! Our minds cannot perceive objects intuitively in dimensions higher than 3. Many movies and novels have romanticized this idea in various ways. Mathematics seems to definitely hint at it, but as mentioned earlier, no experimental proof exists. And this is how the speculations of hyperspace came into being. Nevertheless, this signifies the possibilities of higher dimensions, i.e. Had the theory been complete, we may have been a step closer to the formulation of the grand unified theory. This is an incomplete theory because it fails at very high speeds or short distances. However, this theory required a 5D space. Kaluza-Klein theory attempted to unify Gravity and Electromagnetic force (two of the four Fundamental Forces of Nature). And this added set of equations were actually Maxwell’s Equations! Quite a coincidence! This went on to become the famous Kaluza-Klein theory. Solving these equations gave a spell binding result! The results were the usual Einstein’s Field equations and one extra set of equations (corresponding to the added dimension). The additional dimension involved what is known as the “Electromagnetic Vector Potentials” and scalar constants. This matrix represented four dimensions the same as which Einstein had used. He solved the same set of equations but this time using a 5x5 matrix. German mathematician and physicist, Theodore Kaluza wished to find out the electromagnetic equations using the same methods Einstein used. The metric tensors used in the equations have a 4x4 matrix, representing the three spatial dimensions and time. The famous Einstein’s Field Equations encapsulate all this and beautifully describe space-time and its curvature. According to Einstein, gravity results from the “curvature” of spacetime. Nonetheless, these ideas are essential to understand the theories put forward to explain this weird reality of ours.ĭon’t worry you don’t need a PG in Physics to understand this article, 1Ī 3-D variant of a 4-D object called Tesseract, 2Įinstein’s General Theory of Relativity gained prominence and was accepted around the 1920s, right after Arthur Stanley Eddington managed to experimentally show that relativity works in the famous eclipse observation in 1919. It can all possibly turn out to be utter nonsense if experiments show findings against these theories. Topology Appl.Reader’s caution: Ideas written in this article have been put forward by near-crazy physicists and have no experimental basis to them.

Zaragoza, Symmetric products of Erdős space and complete Erdős space. Dimension theory: an introduction with exercises. North-Holland Publishing Co., Amsterdam, 2001.

The Infinite-Dimensional Topology of Function Spaces. Van Mill, J., Pol, R.: On spaces without non-trivial subcontinua and the dimension of their producs. Michael, E.: Topologies on spaces of subsets. Kawamura, K., Oversteegen, L., Tymchatyn, E.D.: On homogeneous totally disconnected 1-dimensional spaces. Soc 208, 979 (2010)Įrdős, P.: The dimension of the rational points in Hilbert space. Dijkstra, J.J., van Mill, J.: Erdős space and homeomorphism groups of manifolds.

Hyperspaces dimensions