Dimensions (2) Flatland

When I shared my thoughts on linear algebra with a friend who is an engineer and knows more maths than I have forgotten, he lent me a copy of a book called Flatland: A Romance of Many Dimensions. This book was written by Edwin A Abbot, who lived from 1838 to 1926. As the subtitle indicates, the purpose book is to explain the way that dimensions function. Abbot describes a two-dimensional world, where everything is flat. This world has length and width, but no height. The characters in book are circles triangles, squares and various polygons. When I read this book, I was fascinated by the parallels with what I had learned in linear algebra. Three things stuck me.

The first was the issue of perception.

In a three-dimensional world, sight is our best sense. We use sight to recognise other people and objects. People generally believe what they can see. Touch is also useful, but it is limited, because we can only touch things that are close to use. On the other hand, Thomas thought that he could prove Jesus was real, if he could touch his hands and side.

In a two-dimensional world, sight still works, but it is much less useful. Although the characters in Flatland were different shapes, they all looked the same to an observer. In a two-dimensional world, a circle a square and triangle, all look like a straight line. Skilled people could recognise the size of a person, by assessing the way the length of that line changed as the person came closer, but it was not possible to distinguish the type of person, by looking at them. In Flatland, they mostly relied on touch to recognise the type of characters they were dealing with. When a person came up against another, they could recognise their shape by touch.

Touch is the most useful sense in a two-dimensional world, but it is less useful in a three-dimensional world. Sight is less useful in a two-dimensional world, but is the best sense in a three-dimensional world. It follows that sight will not do that well in a four-dimensional world. Although we live a three-dimensional world, there is an additional spiritual dimension that it is an important aspect of reality. Our sight does not handle that dimension very well.

We need spiritual insight to understand what is happening in the spiritual dimension. That is why Paul prayed that they “eyes our hearts may be enlightened’ (Eph 1:18).