- A train is restricted to its track and can only move back and forth (along one direction). It moves along a length.
- A car has more freedom and can move back and forth as well as sideways (two directions). It can move over an area. While
- an airplane has no restrictions and can move back and forth, sideways as well as up and down (three directions). It can move inside a volume.
Why don’t we call these “directions” dimensions? One, two or three directions needed would then be called 1D (1-dimensional), 2D and 3D. Were no directions required, then 0D.
- A chunk of clay is 3D; let’s name such things bodies.
- A house façade is 2D; let’s call it a face (as in ‘surface’).
- A pencil stroke is 1D; let’s simply say a line.
- A dot is 0D; let’s call this a point.
Can you imagine a fourth dimension? It seems impossible. Maybe our world is in 3D only.
But that’s only because our minds are stuck on size and space now. Let’s consider time in the same way: With it’s past, present and future, time has a forward/backwards sense. We think of it as a timeline because time seems 1-dimensional.
All in all, the world seems to consist of
- 3 dimensions of space (3 spatial dimensions), and
- 1 dimension of time.
We could continue and also imagine quantity as its own dimension. Any independent property can be thought of as defining new dimensions.1
Note, that lines don’t have to be straight and faces to be flat – a curled string and a curled curtain still have 1D length and 2D area.