Kieran France Kieran France is a programmer for IDRSolutions in charge of there internal test suite. In his spare time he enjoys tinkering with gadgets and code.

# Abstract thought, or What I learnt in Flatland.

I recently had the joy of reading a novella Flatland: A Romance of Many Dimensions written by Edwin A. Abbott. It is an interesting story told in the perspective of the main character telling the reading about his experiences. The main character is a square (literally 4 sides, 4 corners, no depth. A square) living in a 2 dimensional world.

The start of the novella explains his world and the different castes found there, with line segments being the lowest caste and with each additional side the caste had more power with the highest past having so many sides that is appears to be a circle. This first section is a satirical look at Victorian culture. This part of the book is an interesting read but I think would have been more entertaining if I have greater knowledge of Victorian culture. Although that doesn’t mean it wasn’t entertaining.

After this we begin to stray into some more abstract concepts that is the reason for my article. The main character ends up exploring the idea of…

• Pointland – A place where there is a point and nothing else. It is the only inhabitant, the world and the whole universe.
• Lineland – A 1 dimensional world contained within a single line and inhabited by points.
• Flatland – A 2 dimensional world contained on a plain and inhabited by geometric 2D shapes such as lines, triangle, squares…
• Spaceland – A 3 dimensional world inhabited by geometric 3D shapes such as spheres.
• And above – The Square tried to convince a Sphere of the theoretical existence of a 4th dimension or higher.

In this later part of the book we find some interesting ideas. Admittedly many of these ideas may not directly cross over into your live but they can help when attempting to describe abstract ideas. When you have ideas that you can’t find a real world correlation for you need to find other ways to describe it. In Flatland, Spaceland is described quite simple to us as we already under stand it, depth is the direction at a right angle to the inside of the square. Imagine trying to do something similar for a Tesseract (they attempt it in the book).

So what does this book have to do with abstract thought. Well for one, it is full of it. With the lower dimensions it is easy to understand the concepts described, nearing the end it gets more complex. It also shows you a very nice way to describing abstract and complex ideas. Do it in small chunks. If you can find something that can be used to help visual the concept, even if it is not wholly accurate, so that the recipient has a base that they can start with and can correct the inaccuracies later.

I could go on more but it is only a short novella and I don’t want to ruin too much of the story. I can highly recommend reading this.

## Are you a Developer working with PDF files?

Kieran France Kieran France is a programmer for IDRSolutions in charge of there internal test suite. In his spare time he enjoys tinkering with gadgets and code.