The Dimensions

What we can understand depends on how many dimensions we have to perceive something.

Consider a sphere. How the sphere appears depends on the number of dimensions we have to perceive it.

If we take any line drawn in the sphere we have a one dimensional world.

In a one dimensional world, we can perceive only points. If we move along a line (our one dimensional world) we see only the points. I suppose that in such a world, it is impossible to get any idea about shape. There is just the oneness of mathematical points.


In the two dimensional world we can perceive lines. If we take any flat section from the sphere, we would get a circle. This would be one possible 2 dimensional world.

In this world, an inhabitant would notice lines. Using memory and imagination, the being could note the different lines. It is possible to get an idea of a circle in such a world from studying the lines. The lines could be described and a mathematical relationship deduced.

Wise beings in this world could get an idea of circles and triangles and other shapes in this 2 dimensional world. They could not actually 'see' them, but they could have an understanding of them.

The beings in the 2 dimensional world would not have even an idea of the sphere because much of the sphere simply doesn't exist in there particular flat section the sphere. The sphere exists (to us) but does not exist in the 2 dimensional world. We have a case of the sphere both existing and not existing!

If their minds were like our minds, then they could theorise on the existence of spheres, but they could never prove their theories. They could never visualise a sphere, and never see one.


In a three dimensional world, the beings can see shapes. They can see circles which are part of the sphere. Just as in the 2 dimensional world, they beings can 'put together' their perceptions in their minds to produce a shape, in the 3 dimensional world, the beings can put together the shapes to imagine a sphere. In the 3 dimensional world, they cannot actually 'see' a sphere, but they are only one step away from actually seeing it. They can actually see the various circles and can, if they are wise, put these images together to make the sphere.

In the 3 dimensional world, the inhabitants can see the lines (which are sections of the circle) and the circle at the same time. They can actually see that the lines are the same as the circle. They can in one perception see the lines AND the circle. Whereas, the inhabitants of the 2 dimensional world can 'see' only the lines and have to make a mental effort to deduce the circle. They cannot 'see' the circle directly.

They can also theorise, as their colleagues did in the 2 dimensional world that there could be other bodies, of which the imagined or 'sensed' sphere was only a section. But they could never prove the existence of this new body, or even imagine it.


In a 4 dimensional world, the inhabitants can actually see the sphere. They can see how a number of cross sections of the sphere come together to make the sphere. In the 3 dimensional world there could be arguments over, say the colour of the sphere. Because no one in this world can actually see a sphere, there is some possibility of arguing over, say, its colour or its smoothness. Does it have the same temperature over the whole surface, or not. Because they do not have direct experience, there is always the possibility of disagreement.

In the 4 dimensional world, they can theorise that the sphere which they perceive is only a section of some other sphere. They cannot see this other sphere, but could theorise that all spheres are examples or sections of a greater sphere which exists in 4 dimensions.

In the 3 dimensional world, the inhabitants could notice a circle that changes. They can actually see the circle, and using memory of the past, they can be aware that the circle is changing in size, say, growing.

If a sphere moves through a 3 dimensional world, it would be perceived as a number of circles. If we took a number of sections of a sphere and flipped through these sections we would apparently see a circle that comes into existence, grows, wanes, and finally becomes a spot and disappears.

To the viewers this could be circle that grows and wanes, or a sphere that does not change, but moves through the 3 dimensional world.

It may be impossible for them to determine which of the two cases is true. It could be sphere that does not change OR a circle that does change.


In the same way, they may notice themselves and others in the world growing and ageing. They could ask is this one person who changes by growing old, or is it one object which does not change but moves through the world?