The Klein bottle on the previous page is an example of a 4-dimensional model – well, a 3-dimensional model of a 4-dimensional shape, but what does that actually mean?
A shape with no dimensions looks like this … … well, like nothing, really. 0-dimensional shapes occupy no space, so there’s nothing to see.
The First Three Dimensions
One-dimensional shapes can’t really be seen either, as they are just lines with no thickness. However, in mathematics, it’s normal to imagine that lines are just thick enough to allow them to be drawn. So, here is a one-dimensional shape:
By extending it sideways, you can make a 2-dimensional shape. Here it is as diamond, or rhombus:
If you add some vertical lines and another rhombus, it becomes a representation of a 3-dimensional shape – a rhomboid.
What about the fourth dimension – how would that look?
To look at the fourth dimension and beyond, imagine a square. A 2-dimensional square is made with four lines – a 3-dimensional cube is made with 12 lines. The next square shape – in the fourth dimension – has 32 lines and is known as a tesseract, or hypercube.
The best way to think of a tesseract is to imagine two 3-dimensional cubes attached to each other, so that every face of the cube becomes a 3-dimensional shape, like this:
Did You Know?
Time is also a dimension. You travel from morning to night, just as you travel to and from school. Although, of course, reversing, turning and stopping in time isn’t possible – yet!
Spacetime
Time and space are always linked – they are known as spacetime. The most well-known scientist to work with spacetime was Albert Einstein. He discovered that when things travel very quickly, they change shape.
Imagine that there was a big bomb travelling through space. Einstein proved that if it was going fast enough, it would change shape, like this:
How Special!
Another part of Einstein’s spacetime theories said that time passes at different rates depending on how the person measuring it is moving. If you were unfortunate enough to be on the bomb, you might measure the time for its fuse to burn down as a minute. If someone on the ground watched you whiz past and timed the fuse, too, they might measure it as taking two minutes. To look at it another way, imagine a spaceship travelling at nearly the speed of light. If the astronauts on board travelled for what they measured as a year, they would find that far longer had passed on Earth when they returned to it – perhaps thousands of years.
Does the world really just have four dimensions? Of course not, that would be silly. In reality scientists think it has 11!
‘M-theory’ – the idea of 11 dimensions – suggests that ten dimensions are of space and one is time.
How come no one has ever noticed all these extra dimensions though? The answer is that they are scrunched up too small to see, or compactified. Perhaps this is just as well – a 10-dimensional equivalent of a cube, called a dekeract, is made up of 5,120 lines – imagine that!
Did you Know?
Einstein’s theories also say that the speed of light is the fastest thing possible. Until very recently, everyone was still certain that was true. However, scientists in Switzerland, at the European Organization for Nuclear Research, or CERN for short, discovered that it might be possible for tiny particles, called neutrinos, to move faster.
