Matter and Movement in Four (or more) Dimensions

These days, it only takes a little curiosity, access to the Internet, and a bit of patience to find explanations of progressive spatial dimensions or examples of four dimensional geometry, such as the old favorite the hyper-square. Some of the things you will find use analogies like Flatland, or animations which is a way of using time and motion to reveal a higher dimensional object using a lower dimensional cross section — the advantage of this kind of intersection or interface is the ability to scan through what is too dense to actually see through. In this way, we can emulate the ability to observe, say, the details of the internal structure of a three dimensional body in a manner similar to seeing it directly from the fourth dimension. Of course, we did not have to wait for the invention of magnetic resonance imaging to be able to perceive the insides of our bodies; our sense of touch gives us the closest thing to a physically four-dimensional perception. Our kinesthetic or spatial sense is annexed to our visual perception to give us an integrated sense of physical reality. In addition, we supplement our active field of vision with the memory of what we have previously seen, and studies on perception have revealed that we often rely more on our visual memory than our active sight in familiar settings. This ability to fill in the blanks around us is one that we can use to “see” into higher dimensions.

In the mind, it is possible to construct things in four or more dimensions, but that does not tell us if there are any objects in the universe that are constructed in four or more dimensions. Taking the example I gave of eight-dimensional time-space, we could surmise that the universe has height, width and depth in a kind of cellular structure in which every moment in time exists in strands of continuity along branches of probability in a network of possibility where multiple event paths lead to and away from any give moment. The instant is where-ever you happen to be focused on eternity. Time-travel would be non-paradoxical because time itself would be process based, a product of attention. The event you experience would largely be determined by the state of mind you are in as you approach the moment, so causal time would probably be the norm; that is the path of least resistance. The real challenge to time travel would be presented by the body and its influence on attention. As a three-dimensional spatial construct, the body predisposes us to move through time as a byproduct of moving through space. To arrive at a specific point in space and time, without transiting the intermediary space and time, would break the perceived continuity of events unless one could perceive space four dimensionally–in which case the intervening space was bypassed in an instant of time. The mind can conceive of four-dimensions internally, but the real question is, how would you move the body through a fourth-dimension externally?

A question like this is a question about matter as it relates to space. Among the things physicists know, matter occupies very little space and is distinguishable from energy only by structure. Attempts to understand the structure of matter has led to the identification of elemental atoms, primary particles and fundamental quarks; the last taking us down into the realm of quantum mechanics. In the process of getting down to the quantum level, physics has also run into fundamental forces, the electric and magnetic forces, gravity, the strong nuclear force and the weak nuclear force. These are all things that can be observed or inferred to exist based upon experimental observation, and for all that is known about them, there is much that is still not understood. The one aspect of matter that has captured my interest most often is the characteristic of mass and its association with gravity. A particle with mass is infinitesimally small and produces (or focuses) a force that has infinite range (though the strength of the effect diminishes over distance in a known, inverse-square ratio). Unlike electric and magnetic forces which are polarized, or both attract and repel, gravity seems only to attract and does so in a “like to like” fashion.

The “dent in space” model of gravity gets me thinking, as anyone who read my post on Gravity in a distributed, process driven, information-based Universe could tell. Einstein gave us the equation summarizing the relationship between matter and energy, but by itself, the equation does not explain what is really happening when energy is concentrated into mass. We have to ask, what is happening to the energy, and part of the answer lies in understanding how a point of mass is focused into a stable object and why that deforms the space around it. The answer is further complicated by the specific structure and electromagnetic properties of a given particle. Particle physics is a whole field of study unto itself, and if the great minds devoted to it will pardon me, outside the complexities that might be explored, the simple observation is that structure holds the answer. Energy is concentrated and structured into a more complex and dynamic state in which we find a focal point in three-dimensional reference and forces that produce one-dimensional (polarity), two-dimensional (surface tension, surface area), three-dimensional (height, width, depth) and four-dimensional (mass, gravity, inertia, vector) effects. There is so much going on, all of it debatable, but I always come back to the four-dimensional view of matter.

I would have to have a great deal of time and a decent amount of resources to formulate something more substantial from this speculation. I am sure there is a great deal more information available that could affect the assumptions I have about pervasive energy, pervasive space, particular matter in infinitesimal space, concentrated energy, mass, structure, gravity, spatial displacement, fields, force, electron shells, magnetic shells, and light. I have the interest and the fascination to keep probing and a desire for more reliable speculation, but until I find an opportunity to devote myself to it, I can only work with the insights I have now. The implication of four-dimensional structure in matter, or the idea of atoms as four-dimensional objects, does not make our world any less a three-dimensional environment. That is, matter may only be possible at the three-dimensional surface of a four-dimensional substrate of energy and space. There are particles that seem to spontaneously pop in and out of existence, if some of the reading I’ve done on particle and quantum physics is correct, and that might be an indication of structure transecting our three-dimensional “plane” but most atoms seem to be pretty well stitched into place.

I am not as confident in speculating on how energy and structure “bind” but that is what I see as a likely basis for fundamental forces. The forces seem difficult to understand or explain, but part of that is because the concept presents us with an inherent mental block. A concept allows us to hold onto an idea about an observed phenomenon, but in the act of grasping an aspect of reality in that way, we focus on the effect and become unable to see the cause. Stepping back and looking again, we might be able to see that what we call a force is simply a particular way the balance of energy in a structured system must behave to achieve stability. Seeing that way, we can begin to ask what imposes structure and how does it persist either as part of or apart from energy. The question brings me back to a notion I had about the nature of limits and how that impacted the perception of substance and solidity. If matter is mostly empty space, what keeps things from constantly falling through each other? The substance of matter is not in the mass, but in the repulsive forces of the electron shells of atoms. The thing that makes the world seem solid to our touch is the existence of forces associated with particles that prevent them from actually touching.

There is a great deal more needed in a comprehensive analysis of matter, but this is enough to return to the question of moving a body through four-dimensional space. A common observation is that an infinite number of objects of a given dimension can exist in an object of the dimension above it, being in effect an image of itself, but it would take the action of an entity acting in the higher dimension to manipulate or move the object through that hyper-space. In my example of a person attempting to jump from one position in space-time to another position in space-time without transiting the intervening space, either an outside agent would have to be involved, native to the higher dimensions, or the person would have to be constructed in four- to eight-dimensions to begin with. Not really a problem for the mind, assuming the mind is not exclusively internal to the body. The hard part, for a mind rooted in a physical body in a world such as ours would be figuring out that it did exist in more dimensions and that this enabled it to move through space and time in ways that transcend the physical limits of the body. No tool or technology grounded in the physical world would be of much use in discovering or exploiting this fact. Not that you could not discover it by accident if the mind should happen to wander; though you would have a hard time distinguishing random moments scattered over infinite probability from dreaming.

A Glimpse into the Eye of Paradox

On any given day, a small handful of people find their way to the eye of paradox. Some of them probably just glance at an article to see if it’s relevant to the search that brought them here. One or two might actually read something. Once in a blue moon, someone leaves a short comment. Taken all together, I do not see anything to indicate that my words mean much. Is that frustrating? A little. I think it only bothers me because I have so much on my mind all the time, and there seems to be little or nothing I can do with it. I have to ask myself, what am I really accomplishing here? I’ve said it before, I tend to write in the hope of provoking a little thought, usually because the inspiration to write is interesting in itself. I do not expect anyone else to find the result as interesting; partly because it is hard to capture a thought perfectly in words. I am not a thousand-word-a-minute typist and yet I seem to think a million miles a minute. I am not a linear thinker. My thoughts are more like a library in a hurricane. I have never really been able to explain it, but it’s what I mean when I talk about higher-dimensions of thought. The problem with that terminology is that we would all probably assign the dimensions differently, based on the way we think. I suspect that a lot of us think things out in words as a general rule, that good old internal dialogue. I have one, but it’s only one part of how I process information.

I think that most of what I think cannot really be put into words. Seriously, I find it easier to think in worlds. Every instant my brain is processing sensory data to assemble an endless stream of consciousness that ties what I perceive in the moment with things I have perceived in the past, things I imagine, things I have conceptualized, things I have analyzed, things I have articulated, things I intuit and things I have only imagined. I have this notion that I ought to be an author because stories come to me in bursts of instantaneous thought. The problem is that it takes so long to fully articulate one I will have conceived of a thousand variations in the time it takes to block out the basics of the one I started with. The sheer number of options and variations overwhelms me. I don’t find it surprising, however. This is what our brains evolve to do; in life we only get one chance to get anything right, and there are a lot of times when a mistake will cost you your life. When faced with a challenge, we automatically engage the imagination and run through as many simulations as our intelligence and attention allow. A good view of the future requires at least seven dimensions of thought. Our base line of reference is four dimensional (working in three spatial dimensions and one temporal dimension) and we have to be able to project that image forward to assess the consequences of our actions through to positive, neutral and negative outcomes.

The future is not on a straight line. Neither is the past, really. An individual has no problem seeing history as a line running back through events, but there is such a line for every person and every object involved in every interaction. The past that we perceive is not the only past. For any given instant, there is a conceivable alternate path leading up to it, though usually the only people who are aware of this are people involved in reconstructing events. To a lesser degree, anyone who mulls over the days of their lives will notice the variable paths within the repeating cycle. You can stop, while walking down the street and suddenly put yourself on the other side of the street in some memory. It is one of the reasons we like routine. The more times we go through a sphere of activity, the better we understand the possibilities of acting in that sphere. We use it to maintain a hypersphere of potential activity. We use something similar in the mastery of our own bodies. At any given moment, there is only one position we can be in, but we are aware of all the positions we can move to just in the limits of our own bodies. In a sense, you could say that this is the real difference between the physical nature of something and the spiritual nature. We can only ever see one instance of an object, but that one instance contains the potential of every instance of that object. When you can look at an old man and see the little boy he once was, that is a very spiritual perception.

The funny thing is that we have run into this same thing in quantum physics, the notion that things have potential that exceeds what can be manifested at any given point. In the mind, we can hold onto everything at once, seeing nothing but aware of it all, and pull whatever we want into focus in an instant. I really don’t find it surprising that reality is pretty much the same way. We work constantly to bring the world into focus, we are in a constant process of realization, learning about changes in the world and updating our own internal representation accordingly. This is how we maintain our grip on the universe, and also how the universe maintains its grip on us. Or, this is how we maintain our grip on ourselves. This is a good spot to focus on if you take the question “who am I?” seriously enough. This is where I ended up after years of asking that question in an attempt to determine if it was who I am or what I am that makes me “me”. I came to the same conclusion the characters in the Matrix did, the body cannot live without the mind. Perhaps that is an indication of gestalt consciousness, an indication that the mind is more than the sum of the body’s parts? I am still thinking on that. In the meantime, while I find myself in the universe’s grip, there is an omniverse of information in my grip. I am holding the universe in a firm mental grip, but at the same time I am holding on to many, many more in my thoughts. Of course, I might just be apprehending the possibilities of the universe that would be found in higher dimensions.

What kind of sense organ would be able to perceive higher dimensions? I do it in my mind constantly, so I would be inclined to say the brain is that sense organ, as I rush along in the wake of intuition, chased by thoughts of perception being our key to acting in our environment. I grasp all of the implications of movement in higher dimensions of space and time and cannot keep up with the possibilities that seem to open themselves up. I am riding on an epiphany, a realization of a universe that contains infinite potential. What kind of words could begin to describe it? I struggle to find them, even now. I struggle to find the time to think things through enough to achieve a less dizzying perspective. This is my true field of study, and all I can do is stand at the threshold and stare into it longingly. The irony is, we’re all at this threshold. It’s kind of like the best kept secret, because it’s hidden in plain sight. I think the only reason I noticed it is because I am too.

Awakening

I have pointed out before that my struggle with gender dysphoria prompted me to search in all directions for a solution to being born in the wrong body, and the determination with which I pursued that goal in spite of all doubts and discouragements — even attempts to accept things the way they were, adapting to and adopting the identity imposed on me by circumstances — says a lot about me, and even about what I ultimately concluded. My existence may be supported by reality, the physical, chemical, biological and sociological fabric out of which we all seem to be spun, but none of these things are me. I exist in my mind and that is why the way I perceive myself in my own mind can not only contradict my physical form, but trump it in importance to my survival. I have heard the theories and arguments on nature versus nurture and taking my own experience into consideration I can say that there are elements in both that can help shape who you are, but only by presenting the options or stimulus necessary for you to determine who you are. I cannot tell you if this is a process of creation or revelation; it feels like both. I am the driving and defining force within my own mind; my mind is the structure and articulation of my soul.

I was born in a context in which everything and everyone seemed to deny my existence, in accordance with the belief that who I was was based upon what I was and where I came from. I was not encouraged to express myself in ways that were inconsistent with my appearance. I’ve described some of the ways I was discouraged in other writing, and how it affected me. The most important result of this situation was that it did make me conscious of the fact that there was more to me than just my body. I have long since realized that most people are not very clear on what a spirit or a soul really is, but I never really had a problem with that. It was difficult for me to understand the modern view of consciousness and things like mind, spirit and soul as mere epiphenomena. I eventually understood the limitations of scientific thinking responsible for promoting this view, as I understand the way it drives scientists to look for a physical mechanism for the origin of consciousness. On the other hand, I had no difficulty understanding that the mind was central to everything that really mattered about existence. Perhaps that is a result of being hyper-conscious of every thought and action I took as a consequence of being forced to override all of my natural instincts and impulses to conform to people’s expectations of me.

I spent my childhood engaged in a constant, intensive observation of myself and everyone around me. I analyzed the world and all my experiences in it as if my life depended on it, often discovering new ways in which it clearly did. In my day to day life I was as deliberate in the control of my thoughts and emotions as I was in the control of my body. I had to understand as much as possible about how my mind and body worked to achieve that degree of control, which included managing or bypassing a number of “hard wired” behaviors and responses. I was thinking hyper-dimensionally long before I learned that was the way to describe what I was doing, or how to explain the process to someone else. I think the first step in thinking hyper-dimensionally involved the unstated realization that everything in my existence occurred in my mind; the “outside” world distinguished from my “inner” world by my physical perspective in it and limited influence over it. In my “inner” world, I was everyone and everything, everywhere at once — all on the verge of being nowhere, nothing and nobody. My consciousness was an all encompassing point with unconscious depths in the shadow of oblivion.

I began to understand that there are many things you have to figure out for yourself, in order to know and understand them, and consciousness is one of those things. I suspect that the scientific study of consciousness will inevitably conclude that it is a complex form of a basic property of “awareness” inherent in energy as the combined medium of information structured in space, time and mind. It might arrive at that conclusion with more esoteric and granular terms, but that is pretty much what it will amount to. Any other proposition runs into the problem of spontaneous generation of the subjective state phenomenon that is the prerequisite for any observer of the objective state. The consequence of any reductive analysis is an increase in relative potential; which is to say that everything is implicit in nothing. The information potential of a singularity is infinite. The interesting thing is that I am not saying anything new here. The same observations have been made again and again in many different ways. None of them make any sense to people until they observe it for themselves. I have no idea what conclusions a scientifically valid description of it will lead to. The first steps in this direction were taken when science confronted the quantum paradox and the possibility of observer based reality.

For my purposes, this observation is not the end; it is just the beginning. To be perfectly frank, I find myself in an untenable position and this can only be corrected in a world where things we would think of as magical or miraculous can occur. In part, this is because any question of physical transformation runs into problems related to the preservation of the mind. I ran into this while contemplating the use of future nanotechnology to remodel a living body, picking this as the most scientifically plausible method of turning a man into a woman. Biological processes can and should be viewed as proof of the concept of nanotechnology, in which complex organisms are constructed on a molecular level. We know that some aspects of personality can be passed on biologically, but there is no indication that the subjective consciousness is transferable. If you were cloned, the clone would be his or her own person, with a unique subjective consciousness. He might be like you, and assuming your exact brain structure and chemical memory was copied precisely, think he was you, but you would not be him. Nothing we know of suggests that there is any continuity of consciousness in that kind of situation. In a transformational process, there is every chance that the thread of subjective consciousness would be broken as one form was broken down and another built up.

The possibility of transitional death forced me to focus on understanding the nature and survival requirements of the mind, and this is ultimately a question of significance for all of us in the face of the inevitability of death. Death is the inescapable paradox. It is reasonable to assume that it inspired the concepts of spirits and souls. The prospect of oblivion is something that drives us to truly assert ourselves, to dream of and strive for immortality. In our lives we experience oblivion in different ways. In a way, the singularity of our consciousness exists in a bubble of oblivion. It is not hard to argue that individual consciousness can only exist if it is shielded from universal consciousness. Until we actually die, we cannot know if death is the end of consciousness, the end of individuality, or the beginning of something else. All we can do is ask what the existence of the mind really depends on. One possibility is that the body and brain is the foundation on which the mind is built, while the other is that the body and brain are merely the scaffolding used in building a mind that can stand alone. We might as well be asking if the world is really what it appears to be. As it happens, it is not. The world as we know it exists only in our minds.

To be more specific, we exist in our minds and the world we perceive is constructed in our minds based on information provided through our senses. What we can know about the universe is based on the information that can be derived through its structure. Perception is the conversion of structure into information, through the structure itself, into our minds. Our bodies, our physical senses and our brains are part of and can be found in that structure, but our minds cannot. Our minds possess structure, based on they way they use information, however; this gives us information and structure in both abstract and manifest states. The process of transition from a manifest state to an abstract state presents us with one dynamic. The constant transformation of structure in the universe and in the mind gives us another dynamic, in general terms “change” or in more specific resolution “time” which we derive from the continuity of perception. It is possible that consciousness emerges from the organization of awareness in the structures of perception through the interpretation of information derived from static interactions with dynamic structure in the universe. The interesting question, of course, is what does the existence of the universe depend on?

I am not sure anyone claims to know an answer to this question, but science has given us a lot of ideas derived from tested information about the universe. It does not give us an origin for the medium of space-time or energy, but it can tell us that all matter is derived from energy and structure. I am strongly inclined to look at space and time as part of the way energy is structured, viewing dimensionality as a component of structure along with size, scale, position, etc. If, as I suspect, awareness is a property of energy, then even the mind can be fully encompassed in the universe. Mostly, energy seems to be the most persistent and pervasive thing encountered along the spectrum of extrapolation or reduction. I would hope that anyone critical of my inclination to view awareness as an inherent potential of energy will understand that I simply find awareness too fundamental to our experience of existence not to be implicit in energy. I think that the obvious complexity of structure found in the human brain and perceptual processes is evidence enough of the difficulty of focusing potential awareness into coherent consciousness. I do not pretend to have a hypothesis for how the structure and organization works, or where in the process proto-awareness becomes awareness or proto-consciousness becomes consciousness. I just see it intuitively in life in the world around us.

I did not get to this point in my speculation following a straight and direct route, and some of the most interesting and useful things I spent time on were essential to getting me this far, such as a study of dimensionality, part of which I have elaborated on in explaining the different dimensions and part of which I only hinted at in this post — dimensions of mind. It is a lot to go over and again, too much to really explain inside another topic. We do not truly know what energy is, but it does seem to be pervasive and universal enough to be a base medium that, through structure in manifest, static, dynamic and abstract ways would give us space, time and mind, the three media that encompass existence as we know it. Information and structure both have intimate relationships with energy. Our bodies and our minds can easily be seen as structured energy. We are energy and information forged into a truly dynamic state. With all the universe to show us that energy sustains information, it seems absurd to think it would simply delete information like us. Most of all, I would think that energy organized to the point of self-awareness would somehow be self sustaining. If we could become more complex by one dimension of space-time-mind, I suspect that maybe we would. Of course, that’s just me commenting on a mountain of unshared speculation.

Divide by Zero

Is it possible to divide a number by zero? Conventional thinking in mathematics declares this to be impossible, but this answer is contingent on a point of view. The problem here lies in the normal interpretation of the value of the number zero; a representation of “nothing” zero is seen as more of a place holder, a number that has no value. By contrast, infinity is a value that has no number. In multiplication, the value of any number times zero is zero. It is like declaring a number in theory. It is like saying “no number” and when it comes to division by zero, one might as well be saying “no division” because use of the number zero declares no number of parts into which a value could be separated, including one, producing a value in no parts. The common assumption is that division by zero would equal infinity.

The question to ask here is, is there any other representation of zero that could allow for a different point of view, one from which a number can be divided by zero? The answer to this question is, surprisingly, yes. It can be done on any number line that includes positive and negative numbers. For simplicity’s sake, ten divided by zero is equal to five plus minus five; it is a line segment with an absolute value of ten and an effective value of zero – or zero to the power of one (indicating one bisection). It could also equal two-point-five-sub-x minus two-point-five-sub-x plus or minus two-point-five-sub-y minus two-point-five-sub-y; it is an intersection of vertical and horizontal line segments with an absolute value of ten and an effective value of zero – or zero to the power of two (indicating two bisections).

To be a bit more explicit, any number divided by zero is equal to a symmetrical, neutral “excluded” equation. As stated above, division by zero declares no number of parts into which a value can be separated, but it does not matter. Any rational number of parts that, in absolute value, cancels out the apparent value will suffice. A valid solution of ten divided by zero might be a circle with the circumference of ten at a radius perfectly perpendicular to the number line at zero. In application, a number divided by zero is effectively “displaced” from the working continuum; the segment of the number line bridging zero is effectively compressed into the singularity of the zero point. This could be represented by placing that segment across the zero point perpendicular to the base number line. It represents a number or value that still exists but is now external to or in a different dimension from the original system.

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.