I normally avoid the first person when writing an article or essay, but in this case I need to begin with a personal story. A year into my studies at Humboldt State University a mutual acquaintance showed up at my friend’s apartment while I was visiting and regaled us with his synopsis of a lecture on dimensions he recently attended. I do not recall what the class was, and I’m not even sure I remember the student’s name, but I will never forget that conversation. Prior to that day, I had not given the concept of dimensions my full attention, even though I had previously encountered the topic in math, science and science-fiction.
The discussion we had that day about dimensions was not significantly different from the usual lecture on the first four dimensions, the point, the line, the plane, and the volume. The debate that followed was prompted by discussion of four-dimensionality. I got caught up initially in the numbering conflict; having just discussed four different dimensions, the “fourth dimension” being volume. Once the proper numbering of the dimensions was reestablished (0, a point; 1, a line; 2, a plane; 3, a volume) along with the accepted rule of progression (once an initial line is established, each new dimension lies outside of and perpendicular to the previous dimensions) we returned to addressing a four-dimensional object.
In specific, my acquaintance asserted that it was not possible to visualize a four-dimensional object. I conceded that it would be difficult to represent, graphically, but not impossible. Having an artistic background, I had thought immediately of the representation of depth in drawings (a two-dimensional environment.) I suggested that a representation of a four-dimensional object could be visualized in the mind. I suspect he took me too literally, because he objected, claiming, “The only way you could imagine four-dimensions is if your mind got warped into the fourth-dimension!” My immediate thought was, “Maybe it has.”
Since that day, I have given a lot of thought to the concept of dimensions, and the ways that dimensional concepts have been (or can be) applied. To date, the best example I have ever found for a four-dimensional object is the mind. The mind not only creates its own space (defines its own space, I should say), it contains the three-dimensional image we use to interface with reality. The mind’s ability to encompass dreams, memories and images of different times and places, real or imagined, and to jump between them or layer them one upon the other, reflects many of the examples given for the manipulation of lower dimensional constructs in a higher dimension.
This perception has left me in disagreement with the notion of Time as the fourth-dimension. Certainly, you need four-dimensions to represent the time-line of a three-dimensional universe, but this isn’t really a three-dimensional universe. By virtue of the way we are constructed, the image of the universe we construct is a three-dimensional cross-section of the universe. It can be argued, of course, but not in the space I have here, so I won’t press it. To get back to the point, Time is a dynamic medium, or a measure of change in a structure or system. Space is a static or graphic medium, in which the structure or state of a system is represented and subject to measure.
Time, as a process, can be attributed its own dimensions. We exist at a point in time, the present. Many points in time, related to each other sequentially, would give us linear time, a one-dimensional continuity. Many points in time distinguished from each other by different sequences would give us varying degrees of alternate time-lines, or the prospect of time at a different orientation like side-real time. The entire concept of time has to change when viewed as an operation upon space or physical systems. That’s another topic to explore in detail somewhere else.
Here, where explaining the different dimensions is what matters, the position I’ve taken and explored is the importance of associating dimensions with a specific media. Space, Time and the Mind all qualify as media, and all can be structured with greater complexity through increasing dimensions. In practical terms, the expression of a higher dimension normally does not occur until the possibilities available at a lower dimension are exhausted. However, the representation of higher dimensions can be intuited by remembering that lower dimensions are contained in and are directly accessible from higher dimensions. All dimensions can be constructed around a common zero-axis.
An infinite number of points can be contained in a line.
An infinite number of lines can be contained in a plane.
An infinite number of planes can be contained in a volume.
An infinite number of volumes can be contained in… a mind?
Obviously, the fourth-dimension is going to take a bit more work to understand, but for the moment, the mind you live in is the best place to begin working.
Originally posted on Helium.
Ammended on 2009/06/22 at 12:38am
My thoughts on dimension did not stop at the fourth dimension, and from the phrasing of the search queries that seem to lead people to this article, other people are curious about higher dimensions. I found the problem of examining higher dimensions lay in the absence of established terms for identifying and describing them. In my personal notes and journals, I adopted terms for my own convenience, but on reviewing them I realized they would probably confuse a prospective audience. For example, I referred to a four-dimensional object as a field or a fold; a four-dimensional object would effect (as a field) or contain (as a fold) more space than it appears to occupy. Any such terms are only useful if the concept they stand for can be communicated, however.
To that end, there is a mental exercise I used to build up a sense of higher dimensions that is easy enough to explain. It involves a challenging thought exercise based first on the description of the first four spatial dimensions, and then adding dimensions of time in space to illustrate up to eight dimensions in total. I am going to present the experiment in the manner I originally worked it out, which assumes that mass, fields of force and the curvature of space are all evidence of four-dimensional spatial structure. This means that the model presented here transitions from spatially derived dimensions to spatially and temporally derived dimensions at four dimensions of space and zero dimension of time. I have already described time as a point (the present), time as a line (the past), time as a plane (alternate time lines) and hinted at time as a volume. The third dimension of time (seven dimensions of space-time) presents some interesting conceptual challenges because the initial thought is to simply think of time lines parallel to parallel time lines.
In three dimensions, we’re not limited to just parallel lines in one plane. We can have parallel lines in different planes (360 degrees surrounding the primary line) or perpendicular to the primary line at any point. To us, in our own time line, all the time in a line perpendicular to us would pass in an instant. Even more fascinating, in three dimensions, a time line would not have to be straight. Neither would time planes. They could have peaks and valleys, curves and bends (spiraling or even closed loops of cyclic time), or even more complex planar topography.
In four dimensions (eight dimensions of space-time), time becomes even more strange. It would seem that all the possibilities of time are explored in three dimensions, but in four dimensions, all points in time become directly accessible to all other points in time. In my own notes I describe this as a time field (as opposed to a spatial field, which I neglected to mention previously). The interesting thing is, a four dimensional temporal universe would not only allow for time to progress in different relative directions (up, down, forward, back, right, left, what have you) it would also be possible to jump from any point in time to any other point in time instantaneously.
It is paradoxical, but that is what you get with order that is all encompassing. Instead of relying on cause and effect, you would have potentiality and probability in a constant feedback; all possibilities and permutations are implicit in the instant (eternity) resolving at all points simultaneously (infinity) each of which can be experienced discretely (and subjectively) by positioning attention at the relevant coordinates of causality.
As before with space, this kind of structure can be held in the mind, in its abstract form, and used by the mind in the thinking process to model endless variations on reality as part of the decision making process. This moves the mind from an object of four dimensions to an object of nine dimensions. Given the possibility of modeling information in even higher dimensions, though, the bounds of the mind should be said to exceed ten dimensions. This is based on the observation that a construct of one greater dimension is required to project an image of an object in a given dimension. A common example is viewing a two-dimensional image (obliquely) from the perspective of the third-dimension. By extension, a three-dimensional image is viewed obliquely from a four-dimensional perspective, and so on.