We live in a three-dimensional world. This means that any location in the space can be accurately defined using three coordinates, usually expressed as x,y and z (for example x=width, y=height and z=depth). Each object also has three dimensions; width, height and depth/thickness. Sometimes time is considered to be a fourth dimension. However, time is clearly different from the other dimensions that define space. In addition at least we human beings are not able to move freely in time, which we can do in space.

Often when we speculate with so called parallel worlds, we call them other dimensions. Yet this doesn't usually refer to a fourth a fifth dimension in the sense we know our familiar three spatial dimensions. Instead we talk about worlds that exist on a different level from ours, normally invisible and not understandable to us. Since our perception is almost totally based on vibration (light and sound are vibration, different states of matter are based on variable vibrations of the atoms), it is often talked about higher "frequencies"; worlds that exist on different frequency levels. Also the term "density" is used to describe parallel worlds.

Nevertheless, the purpose of this article is specificly to concentrate on the spatial dimensions. Is it possible that there can be a four-dimentional space? How would four-dimensional object seem to us living in the 3-dimensional world and how would our world appear seen from the fourth dimension?

Since both our perception and thinking is tied to 3 dimensions, it is impossible for us to concretelly figure out 4-dimensionality. Instead we can somehow imagine one- or two-dimensional worlds and compare them to the 3-dimensional. As we observe the changes that occur when moving from 1-dimensional to 2-dimensional and further to 3-dimensional space, we can "extrapolate"; continue the process to a hypothetical fourth dimension.

ONE-DIMENSIONAL WORLD

From our point of view a one-dimensional world is just a line with only length. Beings or objects in such a world can only move forwards and backwards. Assuming they can not go through each other, the can not pass each other either. To do this they should be able to go round an obstacle, but in a world that has no height or width this is not possible!

If a one-dimensional entity can see, it sees a zero-dimensional projection (just a dot of colour) of the one-dimensional object in front of it or behind. The "form" of an object is limited to its length and the "colour" or some other such feature varying along its length. Nobody living in this world could see any of this however. Neither could one see more than two objects, the one in front and the one behind.

To us a two-dimensional world is a plain that has a width and a length. Two-dimensional beings have much more freedom of movement than onedimensional. They can go round each other and move around freely from one spot to another. An occupant of this world sees everything as a one-dimensional projection. Though the objects can be of various forms; circles, rectangles, triangles etc. they would always be observed as lines (or projections with data only in one dimension). The shape of the object could only be visualized by looking at it from different angles. If the two-dimensional creature has two eyes, it can posess a stereoscopic sight, being able to see everything from two angles simultaneously (like we can) and this observe the two dimensions better.

Seen from the second dimension, a one-dimensional world can be seen totally at one glimpse, only restricted by the field of vision. All linear objects and beings with all their details can be seen from one direction. In the two-dimensional plane, objects behind others could naturally not be seen.

Now we are in a familiar place. We can move forward/backwards, left/right, down/up. Objects can have many different shapes and seem different from every angle. Yet we also see our world as a two-dimensional projection - actually two of them since we have two eyes. We can observe the three dimensions with the help of this stereoscopic sight (and hearing!), as well as movement and perspective.

Seen from the third dimension (lets say from above) a two-dimensional world is visible with all its details, like the one-dimensional world was from the second dimension. All flat object, no matter how they are positioned, are visible at the same time. And we can not just see their outlines but their insides as well. But again, of course we can't see an object behing a three-dimensional obstacle unless it's transparent. Nor can we see inside the object.

FOUR-DIMENSIONAL WORLD

Based on the previous, we can go on to the next dimension. In a four-dimensional world, yet an additional dimension is available for shapes and movement. This means that objects are far more complex and variable. Let's think about the two-dimensionla counterpart of a ball, a circle. In a two-dimensional world it is seen as a solid line from all directions, not changing in length. But to us it seem to be a circle seen from above (or from the third dimension), but as a line seen from the side.

A three-dimensional ball is visible to us as a similar circle from all directions. Seen directly from the fourth dimension, a viewer would see it as a three-dimensional ball, but seen from the "side" (directly from any other three dimensions, also above) as a circle.

A four-dimensional being see the world as a three-dimensional projection. This is somethin totally uncomprehensable to us, since we can not see three-dimensionally, even though our brains estimate depth and distances based on the pair of two-dimensional images received through the eyes.

What is interesting, continuing the progress like before, that seen directly from the fourth dimension our three-dimensional world can be seen totally at once. This means for example that a person is seen simultaneously from front, behind, side and inside! Nothing is hidden from the four-dimensional observer.

This can be further explained by going back one dimension for a moment. In a two-dimensional world one can see an object from all sides only by going round it. Yet only the outer surface can be seen - not what is inside. Yet seen from the third dimension, all of it can be seen at once, including the inside.

In a three-dimensional world we also must go round the object, view it from front, behind, left, right, up and down and again we only see the outside. Seen from the fourth dimension all details outside and inside can be seen without having to move an inch. Imagine seeing a house from all directions, all the objects inside it, everything inside those objects, all at once!

PERCEIVING AN OBJECT COMING FROM A HIGHER DIMENSIONAL WORLD

How would we perceive a four-dimensional object passing our three-dimensional world?

Again we must first step back one or two dimensions. Lets choose again the simplest and most symmetrical object, a sphere. If a two-dimensional sphere, a circle, passes a one-dimensional world, the observer there sees a dot appearing from nowhere and then disappearing. Of course in reality the object appears as a growing and shrinking line, but the poor one-dimensional creature can not see this.

A sphere passing a two-dimensional plane appears from nowhere as a growing circle and the shrinks until it disappears again. The observers of course only sees a line that appears, grows in length, shortens and then vanishes without leaving a trace.

Accordingly a four-dimensional sphere (something we can't imagine) passing a three-dimensional world appears as a small three-dimensional ball, growing, shrinking and disappearing. We see it as a circle.

If a more complex object passes through a two-dimensional world, it is perceived as something appearing from nowhere, changing its two-dimensional shape until disappearing. Accordingly, a complex four-dimensional object passing through our space changes its three-dimensional shape!

Furthermore, as long as a three-dimensional object moves on the level of the two-dimensional plane, so not moving up or down, it stays visible. Yet if it rotates, the two-dimensional "slice" changes its shape constantly. Likewise a four-dimensional object when moving only along our three dimensions stays visible until it changes its location in the fourth dimension. It can move freely from one place to another in our world and appear to change its shape. If it bumps into something, the collision only occurs to the "slice" (a three-dimensional projection) that occupies our space at the moment. The object itself is not much harmed.

ABOUT THE LOCATION AND INTERFERENCE OF MULTIDIMENSIONAL WORLDS

Since a two-dimensional world has no thickness, we could have an infinite amount of them in our universe. In the same way, an infinite amount of three-dimensional universes would fit in a four-dimensional one.

But if we think about a 2D plain world splitting our space, we face a slight problem. It would be unavoidable that sometimes a 3D object (a star or a planet for example) would pass through it. What would happen then? If the the object passes the plain in a spot where no 2-dimensional celestial body exists (in other words, empty space), no damage is done. But if a collision occurs, the consequences can be dramatic. But how likely is it that this kind of collision occurs, when we think how scarcely the stars and planets are located after all?

Additionally we must remember that there is really no solid matter. What we observe as solid substance is made of atoms that according to our present knowledge are mostly "nothing". The deeper we go into the microscopic world, the more emptyness we are likely to find; there is no matter but just organized energy. If the energy is organized into apparent matter in various ways in different worlds, it is possible that there is no observable interaction between them unless the beings in the "higher" world can change their "frequency" or density so that they can "materialize" in the lower world.

Finally let us note that our idea of the perfect order of our three-dimensional universe is already breaking; scientists talk about the "curvature" of space and time. If a two-dimensional universe curves in the large scale, it actually becomes partially three-dimensional. Perhaps our universe curves in the "outer limits", becoming four-dimensional...

AND PERHAPS... TIME REALLY IS THE FOURTH DIMENSION!!

Martin Keitel, 1998