The simplest, most elemental dimension of space is the point, a theoretical dimension without length, width or height, a zero dimension, sometimes called a singularity. Trying to imagine a theoretical point is as difficult as trying to imagine space or time continuing on for ever, without end.
String an infinite number of points together, end to end, and you have a one dimensional line. Now we can all relate to a line, something to hang the clothes on. But a theoretical line cannot be observed, since it has only length, no width or height. To the naked eye, it would be invisible.
Stack a heap of lines on top of each other and we have a two dimensional plane. This we can easily imagine, it looks like a wall, or a flat screen, but again, these everyday examples are an illusion, an imagining, since we know that all examples of planes are actually surfaces of “three dimensional” objects. A theoretical plane, having only width and height but no depth, would be invisible.
So far, we’ve identified three dimensions of space; the point, the line and the plane, which means the next dimension, the one called “three dimensional space”, is actually the fourth dimension of space, since it contains all of the three simpler dimensions, point, line and plane.
Now we can be sure that “three dimensional space” really does exist, it’s not just theoretical, it’s not an illusion, we know three dimensional space exists because we can walk around in the room and feel it. But what if that space existed for no time at all, could we say it really existed? Can there be existence without duration? Can space really exist without time? We know it always takes time to move through space, but apart from that, there is no obvious connection between the four dimensions of space and the fifth dimension of time. Whereas the four dimensions of space are bound together in a theoretical hierarchy, from the simple point, through line, plane to volume, time is an entirely different concept, yet in a way, essential to our observation and understanding of space. Notice this curious interdependence between the various dimensions, each one seems to rely on the others and/or human imagination to exist.
To this point, we have described an observable, multi-dimensional environment which we call the Universe. We can all agree that this environment exists, because we live in it, we experience it. But would it exist if there was nothing to observe it? If we could not imagine the first three theoretical dimensions of space - the point, the line and the plane - would we be aware of space? Would it exist? This is a question that continues to puzzle philosophers and theoretical physicists. The science of quantum mechanics recognises the integral role of the observer in constructing theories and modelling sub-atomic events. Maybe the human imagination, or the experience of mind, is yet another dimension of reality, interdependent with the others.
A theoretical point doesn’t really exist, but is contained within a theoretical line, which doesn’t really exist either, but is contained within a theoretical plane, which likewise doesn’t really exist but is contained within a theoretical volume which doesn’t really exist except that it is contained within time, and since we can observe it over time, we can be sure it exists. So has the Universe created us to observe and imagine itself, or have we created the Universe through our observations and imaginings?
Just wondering.
