Why our world is in 3D?

Our world has only 3 dimensions. This is a very low number: why only 3 and not 10000? How come it’s such a low number? The anthropic principle can be used as a beginning of explanation: life is not possible with less than 3 dimensions, and would be difficult with more. Let’s try to give some criteria to define life. A living organism should:

  1. self-replicate
  2. define a frontier between what is inside and what is outside
  3. have a metabolism (some exchange of matter and energy between ouside/inside)

Life in less than 3 dimensions

In two dimensions, it will be difficult to have point 2. and 3. to hold. Here is a two dimensional dog eating a bone:

A two-dimensional dog*

A two-dimensional dog*

Every food that our 2-dimensional dog will eat will cut him in 2. Not very practical to maintain an inside and an outside… So life in two dimensions or less seems difficult.

Life in more than 3 dimensions

To understand why life gets more complicated in more than 3 dimensions, we have to ask: what is the role of space? Well the primary role of space, in my opinion, is to order things. Like when you tidy your room: space is used to organize things. In Africa, there are extremely dangerous tigers that could eat you in seconds. But do you really care? No, because they are far. The farthest something is, the less it is important to us.

Me and a dangerous tiger

Me and a dangerous tiger

If you live in a building in 3 dimensions, you could have up to 6 neighboors: one above, one below, one on the right, one of the left, one in front of you and one behind you. That’s already quite a mess to deal with at times. But if your building had 4 dimensions, you could have up to 8 neighboors: even worse! In higher dimensions, you have more neighboors, so more trouble. In fact, with a lot of dimensions, everything could be in the same place: you, the tiger, everything! And how life would be with a tiger as a neighboor? In higher dimensions there is a lot more connections between things, so less order. However, life is about organizing things: a lot of dimensions doesn’t seem to be suitable for life.

* Image from S. Hawking book.