Explaining the different dimensions

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.


7 thoughts on “Explaining the different dimensions

  1. i was doing a bit of thinking recently about this, now i’m only in college at the moment studying graphic design, but my research lead to this page and i started thinking about the different dimensions particularly the 4th dimension time. I was trying to create a visual experience exploring the 4th dimension. This may be a more difficult task than i had originally imagined but i enjoy thinking about this sort of thing anyway. i had a few theories of my own about time and the dimensions, I doubt any of them are plausible as Im not educated enough to prove or really comprehend these, they are just ideas.

    But if the 10th Dimension is the limit of all other dimensions then there can’t possibly be an infinite amount of various timelines and ‘parallel universes’, also time is different in different places in the universe (can’t remember where I found this out) and round a black hole time goes more slowly and so time is effected by gravity and such. But also time could be personal to individual atoms and element ect, which means that there is no universal timeline, but a certain timeline for every atom in the universe that overlap and interlock with each other.

    I don’t really know what i’m talking about here they are just different theories that i was thinking through in class.

    1. College is about when most people seem to run into the concept of dimensions as a topic of significance. When I ran into my first real discussion about it, I had already developed a concept of space in four or more dimensions, so I was not inclined to endorse the view of time as the fourth dimension. I do acknowledge that you can represent a three-dimensional object over time in four-dimensions; that is a three-dimensional time-line. In a four-dimensional environment, you would need five-dimensions to represent a time-line. In both cases, the state of the object-environment encompasses all of the space in the referenced dimensions, so you need to represent the changes in state in a sequence of static “frames” with a frame-rate equal to the smallest degree of change possible between states. Time, as we experience it, is zero-dimensional; we exist in a point of time, the moment we refer to as now. “Now” is an eternal instant, constantly ending and beginning while doing neither. This could be an entirely subjective fact dependent on how we perceive reality, a “process” based form of time, in which case we might exist in a universe where there are different points in time relative to each other, and where there needs to be a discrete space for every moment in the universe. Thus, in a universe with three-dimensional objects, four-dimensions would allow you to move forward and back in time (though the mechanics of memory–which is process based–would probably only allow you to perceive movement toward the future). However, if moments in time are equivalent to positions in space, more dimensions would allow for more exotic positions in time-space. As soon as you have more than one dimension of time, more than one axis of change, the range of probability opens up towards infinity.

      I do not honestly believe that there is a limit to the number of dimensions, just a limit to the number of dimensions we can make sense of. In the year or two that I was focusing on dimensional theory, I was able to come up with a model of the universe that required ten dimensions to exist, and in that model the world as we know it operated within four of them. One dimension of time, three dimensions of space and four dimensions of mind. At four dimensions, the mind is complex enough to grasp reality, but the mind is usually operating in more dimensions projecting possible outcomes of present and future events. Dimensions are really just a way to measure relative complexity, and each dimension can contain an infinite number of objects of one less dimension. So, in a time-plane, there is room for an infinite number of time-lines. More importantly, in two-dimensions, time would be able to loop back on itself, spiral, intersect, and so on. To have a realistic idea of how many dimensions of time we might really exist in would be to create a coordinate system that could account for all of the options available for things to change in at any given instant. That is, for every object in the universe, you have to account for each “choice” available to it from one moment to the next. Since in many cases the options an object in this universe has can be entirely contextual and relative, the coordinate required to map the possible outcomes would have to approach infinite dimensions.

      A simple if overwhelming example would be a graphic model of every variation or permutation of a game of chess possible.

      1. Thank you for the comment, really insightful. I chose to make a website in Flash in the end, exploring time perception instead but this all sort of links to my new project too, studying dreams and perception of reality.

  2. Dimensional characteristics are subject to the natural laws of the universe they are contained in. The practicalities of this way of thinking are tied into the nature of the subject. The logical means in which materials behave within the natural laws of the universe they are contained in only apply to that universe. This is the reality and the law of dimensions because this natural law applies to all of them. Only nature decides what the common materials are when it comes to the building blocks of matter in that dimension.

    The laws that have to be obeyed, the physics applied all follow logically. The only way to truly know how these laws interact is to have knowledge of that dimensional space and to exist in that universe, everything else is just hypothesis or speculation of how that natural logic applies 😉 My name is Kevin Duke, welcome to the new age of unlocking God’s secrets, but be careful, the only gifts we are given are the ones we are allowed to figure out. What we cannot figure out we have no right to reveal. In time our wisdom will reveal these things and then we can be given the gifts God is willing to show us. Until then we stare out into space and dream like the mutant simians we have evolved to be.

    1. One could argue about how one might be able to test–or even make–a hypothesis about the objective truth of subjective truth, but that would still leave us in the position of being unable to do anything about it. To keep myself from going crazy, I try to deal with things on the conceptual level, in which case my thoughts and observations are limited to a specific context. In the case of dimension, I work on the assumption that the topic is bounded by the definition of the subject that is used. In considering dimensions, I find that the concept is meaningful only in the context of a particular medium. Hence, I argue against the idea of time as the fourth dimension in a dimensional breakdown of space. The problem I see with the approach theoretical physicists take is in failing to make clear that by grouping time and space they’re really saying that both time and space are merely aspects of a universe that is at once static and dynamic.

      In this respect, we are both making a similar point: the nature of reality is subject to interpretation. How you engage reality matters. Although there may be questions about the specific means and methods required to interface with a given reality, there should be no question that there is an interface–a determining context in which things can occur. That context is what makes the particular construct–the unique and particular laws governing a given reality–valid. Our experience is with a seemingly rational universe. Or, perhaps more accurately, when rational people look for rational explanations, the universe we live in is able to provide us with rational processes. Unfortunately, that does not really mean that the truth–and reality–must ultimately be rational. As physicists have observed, if certain constants are changed, reality as we know it would not be possible. I suspect that existence is less governed by laws that must be obeyed and more maintained in a constant state of dynamic equilibrium, trying to constantly balance infinite possibilities with the probability of their expression.

      In order for there to be actual Laws, there must be a power and authority actively defining, supporting, sustaining and enforcing them. Implicitly, God, but again the problems of definitions and interpretation arise. When we say “God” we’re referencing something that is, by definition, virtually indefinable. Ultimately, the only possible definition of God is self manifest–a being encompassing everything, capable of doing anything, and requiring nothing; thus, having no limits, the only possible, true definition of God is God. In God, definition is a simple consequence of expression. What God wills, God is. To us, that’s paradoxical, but the same paradox is part of our heritage. We find it in the nature of our own awareness. For all we focus on objective reality and objective truth, observation is a subjective process. We exist in our own awareness, effortlessly supported by a complexity that baffles and awes us. We are aware of our absence in all manner of times and places, the absence of our presence–but we can only be aware of our absence while we are present in our awareness. Action provides evidence of awareness in others, but the only proof we can have of our own awareness is us us being aware of it.

      We are the object of our existence. Space and time and matter and energy, forces and dimensions, all of the structure and material in the universe is made real to us in our minds, a rendering of information provided to us in a fashion that literally incorporates us into itself. This thing we call the universe–however it manifests itself–is really just a small corner of the mind of God. The manifestation of reality is simply part of the process by which information is transmitted from one mind to another. It’s an interface. How many dimensions does the interface have? Ask instead, how many dimensions are needed to express the idea of our existence? The universe is here because God is trying to tell us everything. Nothing is hidden. We understand what we understand; we all get what we allow ourselves to receive. We’re limited only by being limited; by existing entirely within the limits of what we choose to understand. The gift of existence is not for God to give, but for us to accept. It’s pretty hard to do that if we’re so busy looking for something from someone somewhere else, we fail to understand what we already have.

      It’s been a while since I stopped and thought about it, but once I do it’s usually pretty obvious. I just have to let myself see it.

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