Written by Himangshu Saikia on 23 January 2021
In his book ‘Hyperspace’, Michio Kaku stresses on a single underlying concept : “Everything is simpler, in higher dimensions”. There can be multiple connotations to this. Kaku explains from a Physics standpoint, that several of the fundamental theorems of Physics appear to be specific forms of a general universal theorem in 5 or more dimensions (please refer to the Kaluza-Klein theory). The simplest way to look at it is this : a problem may or may not appear solvable, or even intelligible, when looked at from a limited perception — usually, with the perceptual abilities that created it — but with a little enhanced perception, the solution might appear obvious, even trivial.
Flatlanders
Kaku talks about flatlanders — creatures that live in a 2D spatial world and are limited to only 2D perceptual abilities — which is not a new concept in itself (first introduced in a Novel called ‘Flatland’ by Edwin Abbott Abbott in 1884), but by the mathematical technique of induction, it makes it easier to reason about unsurmountable, unbelievable, or unthinkable situations in a 2D world appearing trivial when seen from a 3D perspective. Imagine a circular shaped flatlander, living in its flat 2D world. The flatlander can be considered to be very intelligent, human-like even, and can question its existence and of the world that it lives in. However, its perception is restricted to its 2D spatial world only and can visually observe projections of its 2D world on a 1D line. Here are some observations :
- Any 3D creature (human) can always observe a flatlander inside-out, i.e., can see its inner organs, arteries, veins and all of what constitutes its body. To a flatlander this might seem unreal, magical even. But for the human, this is just an obvious fact.
- The flatlander cannot observe the human in their entirety. To them, only a single cross section of the human body is visible at any time, or none at all. This might look very weird to them, as the human may appear and disappear from their sight as if by magic. But for a human, it’s just natural that moving about in their 3d world may result in different cross sections of their body being visible on a 2D plane.
- The human can teleport objects or themselves, in flatland. This amounts to moving an object out of its plane of existence into the 3rd dimension and back at another place in the same plane. This effectively seems like teleportation to the flatlander, though this is just a normal 3D translation for the human. These observations seem pretty trivial, but underlie a very important point. What appears to be unthinkable or physically impossible in 2D, is extremely trivial in 3D. Hence, the phrase “Everything seems simpler in higher dimensions”, holds true as seen from this perspective.
Height as a perspective
In military parlance, having the high ground is seen as a strategic advantage. This is true in FPS games as well. This is because, from the ground (flatland) perspective, one does not get an overall idea of the entire battle, how groups of troops are moving with respect to each other, what effect the terrain has on the battlefield, how the battle evolves over time in certain fronts and so on. From a high ground, with the added perspective of height, one can observe all of this together, and can formulate an optimal strategy to gain an upper hand in the battle. Here, the height adds a 3rd dimension to the 2D battle field, and provides an additional layer of information over what an ordinary soldier fighting in the battle can perceive.
The whole is more than the sum of its parts
The 5 sense organs that we use to ascertain our entire existence — sight, hearing, touch, smell and taste — not just add up , but hugely complement each other. Losing one, means losing some complementary information in all of them. So an added dimension, a sensory dimension in this case, not only adds to what is already there, but expands the existing abilities exponentially. Imagine, the case of explaining the color ‘Red’ to a very intelligent man who has been blind all his life. No matter how hard one tries, it is seemingly impossible to explain this concept which is so abstract to this man. However, explaining the same concept to a child, whose intelligence, in all probability, is orders of magnitude lower than the blind man, is much simpler. Here, the added dimension of sight — a sensory dimension — makes an entirely abstract concept to an intelligent adult, quite trivial to understand to a child.
Why is it difficult to understand other people?
Intelligence has very little role to play, when perception is limited. This is why some conversations between two (groups of) very intelligent people can go on forever without any meaningful conclusion. If one does not understand or grasp the perception (point of view) of the other, it may be impossible to fathom the reasoning or cause of the problem they may find themselves in, let alone work on a solution. In Figure 1, we can observe the two orthogonal projections of a cylinder — a rectangle and a circle. Unless, one sees the entire cylinder as a whole, or both of its projections, it will be hard to reason for someone, just from a single 2D projection alone — that the object could have this specific shape in 3D. This becomes even more difficult for flatlanders, who can only perceive 2D. Imagine two flatlanders, each seeing either one of the two projections, and claiming that their version is true. They would end up in a never ending argument, unless they knew about the existence of 3D objects, or could observe each others’ versions with their own eyes. Similarly, in a real life situation, many times we are unaware of where the other person is coming from, either because we fail to see what they see, or because we are unaware of this higher dimension (reason) which may be causing this conflicting opinion. Both opinions could be truths, or partial truths, but to see the actual truth, one must be open to expanding their perceptions (listen, or sometimes just believe, in the other side, even though one’s intelligence disagrees).
Expanding perceptions in life
I believe, we are always able to expand our perceptions, listen more, trust more, suspend our egos and prejudices more and empty our minds a bit, so that we can understand the other perspective better. We must always know and realize that there may be (and indeed are) other angles of perception that we are not equipped with, and so, our convictions of what is absolutely right and absolutely wrong, might just be clouded by an inadequate sense of perception in spite of our heightened knowledge and intelligence.