Question: What is straight (nearly) and goes in every direction?
Answer: A place called space, which would be gone forever were it not for an eternal constancy called time."
The Dimensions of Nature
(What a Dimension Is and What a Dimension Is Not)
Imagine the term "parallel dimension." It is utilized frequently in fiction as a literary convenience for stories requiring metaphysical or extra-natural explanations for events occurring in the story. Indeed, anyone who has ever watched television has at very least, heard the term mentioned before. It has been utilized so frequently that many might find it a perfectly meaningful convention for specifying some sort of alternate "plane of existence" (many even to the point of embracing this purely fictional invention as being an actual physical possibility).
Though the notion of other distinct physical realities besides our seemingly single shared one existing alongside ours may be a great literary convenience for the sake of expressing the vague notions that fictional writing may necessarily require, associating the term 'parallel' as an adjective for the mathematical and/or scientific term 'dimension' is never – nor can it ever be – anything more than a 'fictional' tool. It serves the needs of the writer at the time, but nonetheless remains a stark contradiction to what a dimension really is.
In the mathematical terms that science uses, 'shapes', like one-dimensional lines, two-dimensional surfaces, and even actual three-dimensional spaces in a four-dimensional reality (like our reality is) can in fact be parallel. However, 'shapes' being parallel is one thing, does not mean that dimensions can be. They cannot. (It should be noted that this restriction excludes and therefore does not apply to parallel actual realities of the omni-verse or multi-verse, which are simply very complex shapes, both existing in “parallel” in a matter of speaking, as 'shapes' – but again not dimensions – do.)
Instead of parallel, dimensions are what is the exact opposite of parallel and best described, for the sake of this discussion, by use of the term 'perpendicular@. (In more precise scientific terms, the designation ‘orthogonal’ applies, of which perpendicular is just a single, unique case, among an infinity of other orientations.
One line intersecting another is an example of orthogonal; there is only a single orientation at which two lines can intersect perpendicularly, many in which two lines can intersect and be orthogonal. Two orthogonal lines crossing at a single point create a plane. A third line is orthogonal to these two orthogonal lines when it intersects at a single point the plane created by two orthogonal lines. A fourth line is orthogonal to three orthogonal lines when it intersects at a single point the three-dimensional space created by the three orthogonal lines. This last idea is critical to start understanding, however vague that understanding might be, that is, that a line can intersect a space at a single point.
The number of dimensions is always a whole, positive number. This number corresponds to the number of perpendicular lines that there can be.
What do dimensions "do"? Answer: provide more "room," infinitely more, with each additional dimension that there is. The room provided allows all 'lying' within such room to be distinguished, each individual anything from anything else, by means of unique location. Any dimension is the same as any other. As relativity reveals, time, in this sense then, is no different from space – each is a manifestation of the same 'thing' – a thing that we call dimension.
Dimensions in nature can be described precisely, in mathematical terms, but, because we are utilizing descriptions exclusive of any such terms as much as is possible, we only describe dimensions in conceptual ones. This is what dimensions are for us.
In every direction, a single dimension is a straight line that is perpendicular to all other dimensions, as straight lines. Any direction, as a straight line, in the three-dimensional space we see around us, is always perpendicular to two other lines (directions) in space, meaning that three perpendicular lines, each of which is perpendicular to the other two, like the three lines forming the corner of a room (like your jail or prison cell, or classroom), define three-dimensional space.
Time, which relativity assumes to be a dimension no different from space, is therefore, a line perpendicular to any three perpendicular lines in three-dimensional space. This means that time is a line perpendicular to each of the three spatial dimensions (ignoring how difficult such a notion might be to truly imagine). The dimension of time, therefore, in four dimensions, is a fourth line perpendicular to anything (any point) in three-dimensional space.
Although time and space may appear, due to the nature of our existence, to be two completely different things (the former being motion, the latter being spatial distance), as relativity considers them, they are not two different things, but the identical thing. In other words, any distance in space that you might imagine, is as much a distance in time as it is a distance in space. To be very precise, what is purely our space in every direction at any distance becomes in part -- however small that part might be -- time instead of space for something moving, as odd or unfamiliar as the idea of space being time can seem. It is what space and time are: the very same thing, inseparable and identical.
Gaining an understanding of what a physical dimension is and equally important, what a physical dimension is not nor can ever be -- parallel -- is the foundation upon which an extremely useful tool for understanding and explaining nature is based. It is a tool that is absolutely essential to accurately understanding how the world works, and in particular, appreciating the richness of its space and time by accurately modeling the marvels of its energy. The amazing tool that does all this is a tool called 'geometry'; a tool that we use all the time, albeit unknowingly, even in our dreams.
Although we may not be aware of it, we can't help but use geometry constantly in our thoughts, for the simple reason that either we ourselves move, everything around us moves, or both. This means that we always use geometry, albeit unknowingly, in the contemplation of our own motions and of those occurring around us. Geometry is inescapable; inseparable from normal human experience. And, not only do we use it, but so does nature too, in everything.
The geometry that nature uses has a formal expression in the language of science. We are using only the conceptual expression of that formal description here, not the mathematical one. This is why all we need to know to understand dimensions for our purposes is the concept of 'perpendicular', and how to count one by one the number of perpendicular lines possible at a single point. The number of perpendicular lines possible at a single point is the number of dimensions for the geometry.
Understanding what a dimension is is essential for grasping geometry conceptually, as we must do to understand science's best description of nature, the Theory of Relativity (for space and time) and the Theory of Quantum Mechanics (for energy). Moreover, we must begin by imagining geometry in four dimensions, instead of the usual three to which we are ordinarily so accustomed. However, this is not as difficult as it might at first seem, because we can "trim" the number of dimensions while maintaining the character of the geometric properties through analogy.
As the prior science articles have revealed, there are geometric "tricks" for simplifying the complicated – for example, analogizing the rising surface of a pond to time's constant passage in the article “Relativity in Ten Minutes,” or complicating the 'tilting' of the rising surfaces from this article into the 'bending' surfaces described in the article "Bending Space-Time and Gravity." These tricks can make the intangibly abstract clear and easy to grasp.
We have and will continue to use geometric "tricks" like these (i.e. analogies), as there are many such tricks that we can use to great effect. We shall use them whenever we can in the articles that follow. Hopefully, the reader will develop a more accurate understanding of nature than would ordinarily be available to him or her, by a most unlikely means: through a homeless newspaper.