Toot…

After reading the first article, A Practical Man’s Proof of God (of which I based on when I wrote the article A Practical Man’s Proof of God?), I decided to continue reading the following article. As you can surely guess, the article is A Help In Understanding What God Is, of which this article will be based on. If you have not read it, please do. It’s not a long article and and will only take you a few minutes to read it.

A Help In Understanding What God Is “borrows” the analogy from a famous book Flatland: A Romance of Many Dimensions by Edwin Abbot. When I was reading it, I came across a few confusing and misleading ideas which I want to point out here.

Firstly, you can notice a clear difference between Flatland and the analogy (to distinguish the book Flatland and the analogy used by the author of A Help in Understanding What God Is, I shall call the analogy Help in this paragraph.) used in that article of the main characters. In Flatland, the main character is a Square, while a Man (or assuming it is at least some sort of complex being, of which we will just call it Man) is the main character in the analogy. Both these characters live on the world a 2-dimensional world. I hope that you can pin point the biggest flaw in the analogy now. In a two dimensional world, a Square can exist, but a Man cannot. A Man, being a complex being, would most probably have a complex digestive system much like our own. If that is the case, the Man would simply fall apart, and hence cannot exist in a 2-dimensional world. You can argue that in Flatland, Square is seen as a living complex being, capable of logical analysis too. However, what you can notice in Help that the author is trying to compare our world (3-dimensional as we see it) to a 2-dimensional one. Complex beings in our world just simply can’t exist in 2-dimensional plane.

In Help, When the Man asked the Sphere “what it is like to be a sphere?”, the Sphere answer, “I’ll tell you what it’s like; draw a circle on your floor.” The first question which came into my mind is “A what on the what?” If the 2-dimensional Flatland is analogous to our 3-dimensional world, then logically, our 2-dimensional floor would be analogous to a 1-dimensional line in Flatland. I can only wonder how the author is going to draw a 1-dimensional circle.

If this is not weird enough, the author did mention Man’s “perception of a circle is a constantly curving line that returns to its origin, but he cannot see all of the circle at once”. Not exactly a circle on the floor, is it? Try imagining it in 3-dimensional. If you were to look at a face (other than the top and bottom) of a cylinder, you’d not be able to see the whole of its surface at the same time. Instead, you will see rectangle. I repeat, rectangle. I use a cylinder as an example because the cross section the cylinder is of constant area, which the cross section of a sphere is not. If we were to consider a case which is valid for all possible Flatlands, it is better to consider a circle which is of constant rather than one which is valid for only some Flatlands, as the circle would exist in only a finite number of Flatlands (Of course, a rectangle is not a valid comparison also, since the cylinder would be of infinite length. You can’t actually see a rectangle from that. However, for easier comparison, we will consider only a finite domain, hence a rectangle). If we reduce the rectangle by 1 dimension, it is a straight line of certain length. This means that a Man in Flatland will see a circle as a straight line, NOT a curving line. And if Man sees a curving line, of which I can’t imagine how he can, I assure you that it is certainly not a circle. Perhaps the author is trying to describe this: the Man will see an infinitely long line (remember that he is 2-dimensional) enclosing a finite area.

The author then says “People in Flatland commit suicide by drawing circles around themselves that they can never get out of.” That sounds quite logical at first. If the 2-dimensional Man is enclosed in a circle in a Flatland, “air”(which is 2-dimensional in Flatland also) cannot get through the circle. The Man would slowly suffocate to death. However, by closer inspection, you will notice that this is not a valid comparison to our 3-dimensional world. For the circle to be valid in every possible Flatland, I already pointed out that it must be a cylinder in a 3-dimensional world. In fact, the cylinder must be of infinite length. If you are enclosed in a cylinder of infinite length, that means the volume air in the cylinder is infinite also. You can never suffocate to death in this case. Secondly, a Man can never draw a circle in Flatland as it is analogous to you building a cylinder of infinite length. Another reason a Man can never DRAW a CIRCLE in Flatland because it is analogous to you creating matter out of nothing. That would be a violation of the Mass-Energy equivalence.

The story continues with the Man miraculously able to draw a circle (or in our 3-dimensional world, building a cylinder of infinite length and creating matter out of nothing), he is asked by the Sphere to “rotate the circle about its diameter producing a sphere”. We can do that in our 3-dimensional world. If we rotate the supposedly cylinder by the cross-sectional circle’s diameter, we would get something of an enclose space with infinite length and height but with finite width. You will notice that we are still rotating the circle in the world that we know - within the 3-dimension that we live in. If you were asked to rotate a circle to a 4th Space Dimension, you can never actually get a visible result. Compare this logic to a 2-dimensional Flatland. It makes little sense to ask the Man to “rotate the circle about its diameter”. Note that I used the phrase “can never actually get a visible result” and “little sense” rather than “can never do it” and “no sense”. This is because with our understanding of mathematics, we CAN do it. For example, trying to find the volume of a sphere by integration.

The purpose of the true story of Flatland: A Romance of Many Dimensions by Edwin Abbot is to raise our awareness about dimensions other than the 3 that we are used to. However, the author of the mentioned analogy says the only thing the Man “can understand is the world or dimension in which he lives.” Luckily, by mathematical means, we are able to understand and do calculations about the extra dimensions then the 3 we are used to. One great example would be Einstein’s 4-dimensional Space-Time in his theory of Relativity, where Time is of course an extra dimension. You can see that the “conclusion” which the Man has come to is in no way the same as what happened in the story of Flatland by Edwin Abbot, where Square’s mind is opened to the concept of extra dimensions.

In the last paragraph, the author said that God is of higher dimension than we are. The funny thing is that if Flatland does exist, by what the author implies, we would all be Gods to the Flatlanders. In addition, if we don’t see that matter is created out of nothing, our current description of the universe is good enough, though not perfect. However, if we do see that matter is created out of nothing, we would be able to investigate it further mathematically without involving the entity of which the author refers to as God. It is interesting that the author would attribute God with more-than-3-dimensions. If we were to look at the theory on quark(not 3-dimensional) as more of a fundamental element than the elements for an atom (the proton, neutron and electron), why not attribute God with less-than-3-dimensions? What about The String Theory? If it is true, we’d be attributing God with 1-dimension. Why not we don’t call it God, but call it Nature instead?