Understanding 1 dimensional space
Supersymmetry involves the concept of multidimensional space. In order to understand dimensional spaces higher than three, let’s start with the simplest 1D case, that of a 1D observer – a line. You might think, well that’s quite easy. In fact it is quite easy, but if you really understand it, you might use your knowledge to understand higher dimensions. The animation below shows the observer as a grey line, who is trying to percieve a reality (a 2D circle in this case) in his 1D limited mind. The animated blue line is what he perceives. Note that the reality, the circle, is not changing in time, its radius, colour and all other properties are a part of the reality. The observed thing is quite different from this, it is a blue line varying in length WITH TIME. For the observer, it remains a mystery as to what happened to the original full length of line, why and how it changes length and ‘pops in and out’ of his ‘observed reality’. Also, the 1D observer has no way to find out whether the oscillating line is due to observing a circle (2D), a sphere (3D) or hypersphere (D>3). Also, in order for an observation to take place, we need the grey line (1D) observer, to have a ‘thickness’. This thickness is very small, just enough for the observed image to be projected on, similar to a projector screen, but has to be greater than zero.
Understanding 2 dimensional space
Let’s now start analyzing a 2D case, that of the classic Flatland example, in which a person lives in a 2D universe and is only aware of two dimensions (shown as the blue grid), or plane, say in the x and y direction. Such a person can never conceive the meaning of height in the z direction, he cannot look up or down, and can see other 2D persons as shapes on the flat surface he lives in.
Now we know that 3D space exists, and can conceive that, because we see each other in 3D space. So, what does a 3D reality sphere look like into a 2D plane? The answer is again graphically shown in the animation, which shows a circle expanding and contracting depending on which slice of the sphere intersects the 2D observation plane. In the 2D plane, the thickness of the plane tends to zero, but again, cannot be absolute zero. There must be enough thickness for the circle to form and be observed. Thus, the 3D sphere is being differentiated with respect to one of its spatial dimensions (z in our case) across its diameter.
For the person that lives in 2D, the only way to recognize such a 3D structure is through integrating all the circles he sees, on top of each other. But here is the problem, he cannot imagine anything ‘on top of each other’. A clever 2D guy has just one simple way to refer to this z-axis, which is constantly differentiating the 3D object, and that is TIME.
Time is unity.
“It’ s obvious that from a 4D being point of view our 3D time is a still , unchanging variable. So everything we experience as 3D beings is just an illusion. The illusion of going through time. The 4D being sees everything that was and will be for a 3D being. And, of course a 4D being has no way of really understanding a 5D dimension.
The question is, how can we know how many dimensions is the universe made up from. All the arguments mentioned above can be applied to any dimension and would imply the possibility of an infinite dimension space. However other known things as the relationship between the gravitational constant and all the matter in the universe indicate that the universe is closed and limited. Even mathematics shows us that there are yet unknown reasons for which an ultimate dimension may be reached. One very interesting curve is the plot of surface area of hyper spheres of different dimensions, shown below. One would easily think that as we go higher in dimensions, the surface area of the n-sphere would increase at each stage, and yet, something very strange occurs, as a maxim in its surface area is reached at the 7th dimension. This could easily be the reason for the relentless way the energy always seeks the lowest energy levels. Could this indicate the real ultimate dimension of the universe?. Most probably yes.