Another Dimension

It's not just a Beastie Boys lyric

The science fiction crowd loves to talk about dimensions — passing through dimensions, going into another dimension. The widely popular television series, Stranger Things, imagines creatures that can pass in and out of another dimension into our world. I have been listening to the podcast Blurry Creatures lately, one that is often far-fetched but always entertaining, and the “other dimensions” topic is a staple of conversation. A branch of theoretical physics called string theory explains the characteristics of the universe with a system that includes ten or eleven dimensions. With all of this talk about dimensions, it is good to have a concrete idea of what dimensions are and what they are not.

Colloquial use of the term “another dimension” has a sprawling conceptual footprint. Some people use it more or less correctly and other uses are all over the map. Some explainers say that something “jumped to another dimension,” using the term in a way no deeper than the sci-fi movies that engendered it. Others mix the dimension idea with the equally mysterious field of quantum mechanics leveraging one esoteric concept to enable the other. I will describe here the mathematical concept of different dimensions to give a more complete definition and help differentiate between what a dimension argument can and cannot legitimately do.

Mathematically, each dimension requires a single independent parameter to describe it. A point on the number line requires one real number to be completely defined. If the space has two dimensions, defining a position requires two numbers. Each additional dimension requires another independent number. The main key to a new dimension is the independence of the number. You cannot describe a new dimension with a combination of the existing dimensions. Independence is important because people often conflate moving “really far” in one dimension with a way to get to another dimension. This completely misses the point of dimensions. They are orthogonal to each other. Traveling in one dimension has nothing to do with traveling in any other dimensions. That is why defining a point in 3D space requires a north variable, an east variable, and an up variable. If we wanted to move in another dimension, it would require movement in a new direction that would need a separate number to describe it. The number of dimensions is equal to the number of independent variables that are necessary to describe a point in the space. Four dimensions would have to be described with north, east, up, and X.

We can only experience 3 dimensions in the physical world, so you run out of dimensions pretty quickly when you are trying to build up an understanding of what 4 or more dimensions might be like. Still, observing differences between 2 and 3 dimensions provides some good concepts for thinking about differences between our experience and that of higher dimensions.

There is always the person who will say something like, “There are actually 4 dimensions. You have to include time.” While this is correct in one sense, time is not really another dimension in our experience because we perceive only one moment of time at a time. (Advanced physics has found that space and time are intertwined at relativistic speeds, so the situation is more complicated. But we will confine our thought experiment to the classical scenario.) Still, time is a good way to visualize adding a spatial dimension to a system. For example, a point has zero dimensions, but moving a point in time creates a line which is a one-dimensional object. The line only exists if, as the point moves in space, it leaves a point behind at every moment in time. To create the line, all of the points that existed over time have to exist at the same time. Similarly, a line moving through time creates a 2-dimensional plane and a plane moving through time creates a 3-dimensional cube. We can conceive of adding a dimension as moving the current dimensional object in time and then thinking of all of the instances in time as existing at once.

Adding a dimension is like turning time into a spatial dimension, but it is still difficult for us to visualize. We are still trapped in the dimensions that we can experience. It is best to go back and forth between the 2 and 3 dimensions that we know. For example, consider a person constrained to a plane — a two dimensional man. If this person tried to visualize three dimensions and we told him to think about moving in time, he would think about motion in his plane of existence and conclude that 3 dimensions is like being all over his 2 dimensional plane at the same time. What we are really trying to get him to understand is dragging his plane through the third dimension over time, which he cannot visualize. Similarly, if we think about our third dimension progressing through time as a fourth dimension, it is correct, in a sense, but we cannot visualize it. We would need to be able to visualize our three dimensions moving through time in the fourth dimension and then think of the trail of points over the fourth dimension all existing simultaneously.

Mental Experiments

The analogy between going from 2 to 3 dimensions and going from 3 to 4 dimensions creates some evocative thought experiments for grasping qualities of a fourth dimension. Returning to the hypothetical 2-dimensional person, consider what it would be like to try to interact with this person. His eyes are confined in the plane, so he can only see two dimensional slices of an object in 3 dimensions. Do not imagine him seeing another 2-dimensional thing the way that we would as a 3-dimensional being. We could see the whole plane at once, or at least a large area of it. He could only see the “surface” of an object in 2 dimensions, i.e. a curve. If you wanted to present yourself to this person, you would have to put yourself into the plane. He would only see the slice of you that is currently in the plane and only see the surface of that slice. Imagine what it would look like to him as you stepped through the plane in which he exists. Your arm would enter first, and you would look like a circle of flesh, except he would not be able to see the whole circle at once, only the surface facing him. As your shoulder and torso enter, it would appear like you are changing shape. When you got your head into the plane, maybe you would resemble the man himself, assuming his shape is a two-dimensional projection of a 3-dimensional person. The whole process of entering and exiting the plane would seem to him like you had appeared out of nowhere, changed shape, and then disappeared. The third dimension would be completely foreign to his conception and invisible to him. The natural and obvious consequences of your movements would look like magic or supernatural phenomena to him.

Adding a dimension expands the amount of space available in profound ways. If the 2-dimensional man truly had zero extent in the third dimension, then a parallel plane could exist infinitely close to the one in which the man lives, and he would not know it. You could have ten 2-dimensional “universes” all in an inch apart in the third dimension, and they would have no idea about the others’ existence. People like to talk about parallel universes to support some science fiction ideas. In a fourth dimension, there could be many parallel 3-dimensional universes all stacked next to each other like books on a bookshelf. The possibility of parallel universes does not imply their existence. The 4th dimension concept simply gives a framework of how and where they could exist. They would not take up any extent in the 4th dimension and could be infinitely close to each other, assuming that they had no 4th dimensional extent.

But what if they did have extent in the fourth dimension? Assume the 2-dimensional man is really 3-dimensional, but his motion and his sight are confined to the 2-dimensional plane. He would be 3 dimensional, but his 3rd dimensional component would be invisible to him and attached to his 2-dimensional body. For the sake of conceptualization and conversation, his extent in the 3rd dimension could be called his “spiritual” component. He could operate in the 2-dimensional plane not directly sensing anything about the spiritual dimension, but phenomena and effects in the spiritual dimension might affect him in his physical two dimensions because they are connected. A three dimensional being could touch the spiritual component of the man, and he would have feel the effects without having any “physical” explanation for it. If there were this kind of interaction in the spiritual dimension that affected the other dimensions, they would be scientifically measurable. So, it is not a completely inaccessible, mystical dimension. Because it is attached to the 2D man, it is part of him. You could imagine the 2-dimensional man occupying a 3-dimensional volume because of the spiritual component and this being his true whole self.

The fact that we can see everything in the 2-dimensional plane has interesting implications too. A 2-dimensional man might think that he can hide by going inside of a room. But the walls of his room do not cover the 3rd dimension. He can block off every direction in the plane, but we can see everything by looking at the plane from a perpendicular angle in the third dimension. In fact, it would probably seem silly to us for the 2-dimensional man to think that he is hiding from us by going inside his house or into a cave or something. We see it all. We even see inside his body because of course everything that functions inside of him and keeps him alive would be contained in the outline of his skin. Extrapolating to a 4-dimensional being looking at us, they would clearly be able to see everything in our world at any moment. Nothing can obscure anything else from the perspective of 4-dimensional sight. The same way that we see the whole plane, everything on a piece of paper for example, 4th dimension sight sees all of 3 dimensions — through our walls, through the earth, even through our bodies.

The idea and language of “jumping” dimensions has some difficulties to work through. At the very least, the language is imprecise. The term usually means passing from our universe to a completely different universe. Perhaps they mean moving from one parallel universe to another via the 4th dimension. This is not jumping to another dimension. It is jumping from one universe to another via an extra dimension that neither of the universes occupy. Maybe that’s what the term means, but that is not what the term sounds like. From what I can observe, jumping dimensions is all hypothesis and conjecture — a concept developed solely to explain creatures or objects that we think we see but for which we cannot find any evidence. If the two-dimensional man jumped literally to another dimension, that would mean that his plane of existence was, for example, the north-up plane and then he jumped to the east-up plane. That way, at least one of his dimensions of existence would be different and we could say that he jumped to another dimension. To support this idea, there would have to be an orthogonal plane of existence for him to jump to, and it becomes another flavor of the parallel universe idea. We would have to deal with the implications of the line where the universes intersect. The idea of jumping dimensions is interesting to think about, but completely hypothetical. More often than not, the idea is just a term used to explain the unexplainable in scientific sounding terms rather than a serious theory with a thorough foundation of thought.

Time Implications

A fourth dimension provides space to roll out a 3-dimensional reality’s timeline and view it all at once. This aspect of dimensional relations has deep implications for the concept of time in this 4th dimension. An attribute of God is that all of time is simultaneously the present for Him. Moses asks God for a name to give the people of Israel, and God tells him, “Say this to the people of Israel: ‘I AM has sent me to you,’” implying that a primary attribute of God is his perpetual being. In the New Testament, Jesus claims his deity to the Jews by saying, “Truly, truly, I say to you, before Abraham was, I am,” which is perhaps the most explicit statement in the Bible about how God’s present is at all times of our existence. It is possible to begin to see a way to understand that kind of a reality by imagining Him as a 4-dimensional being. (Of course, He would not have to be confined to 4, but restrict the argument to 4 for now.) If all of our 3-dimensional reality were laid out on a timeline in 4-dimensional space, God could visit any point in that timeline whenever He chose. All points in the line would be His own present time. Naturally, we still imagine him doing things in a separate time variable because it is impossible to imagine an existence that does not involve time. Maybe there would be another time dimension that you would roll out into a 5th dimension, completely independent of our time dimension. Regardless, a 4th dimensional being would not have to be confined to a point in time of our 3-dimensional universe. He could be at anytime he wanted, or in a sense be at all points of time at the same time.

Theologically, time seems to come up a lot. The argument about free will versus predestination hinges on time. It limits God to our experience of time and insists that either He has decided what will happen before it happens or that we have true agency in the world and the future is up to our choices. Opening up the question to a higher dimensional reality allows for the possibility that God knows what will happen in the future because He is experiencing it right now. He is at all times at the same time. Suddenly the question about whether or not God determined the future no longer makes sense. He is in the future, and He is now at the same time. He does not have to determine it and wait for it to happen. He’s already there. If He exists in a larger dimensional space than our 3, then it is no longer a logical inconsistency to say that all points in our timeline could be in His present. Similarly, there is a question that asks about people who lived before Jesus. How can they be saved if He did not die for them yet? If Jesus’ divine existence experiences all time at the same time, then there is no difficulty about when things might have happened. He only has to die once, and it can apply to all of time.

The Bible sometimes says things that seem to be nonsense, like “with the Lord one day is as a thousand years, and a thousand years as one day” (2 Peter 3:8) or “For a thousand years in your sight are but as yesterday when it is past, or as a watch in the night” (Psalm 90:4). The Psalm verse is amenable to the idea that God lives so long that 1,000 years to us seems like just a watch of the night to Him, but it also suggests that God is on a different timeline than us. The 2 Peter verse more overtly suggests an independent timeline for God. If one day is as a thousand years AND a thousand years is as a day, then his time passes both faster and slower than ours. The only reasonable explanation for that is a totally independent timeline which fits in a reality with additional dimensions.

Why We Need to Think About Dimensions

It is important for thinkers, and Christian thinkers in particular, to think about hard and abstruse questions like additional dimensions of reality and to continue to push the boundaries of knowledge and understanding, asking God to continue to open up more of it to us. Otherwise, we risk falling into the trap of the enlightenment. In the enlightenment, people began to be more organized with their knowledge and information and more rigorous about their investigation processes. They made advances and then looked down on the generations before them, mistaking a lack of good record keeping for an inferior ability to discover knowledge. In their pride they began to cast aside knowledge like 2 Peter, assuming that this description of time is a bit of nonsense from a people who did not know better. It obviously did not fit with the knowledge that they had developed about our 3-dimensional reality through math and physics. But a further expansion of mathematical and physical knowledge proves 2 Peter to be a more deeply profound understanding of God than the enlightenment could comprehend, rather than a bit of nonsense.

The Christians who capitulated to the atheistic humanists of the enlightenment in the realm of science and reason did mankind a great disservice. Rather than having the courage to persevere in their beliefs and search for a deeper understanding to explain them, they retreated to the refuge of dualistic thinking. Rather than holding the unresolved tension of their unexplained beliefs, they forfeited nearly all spheres of thinking to their opponents. The atheists can have science and secular society while the Christians occupy religious circles and never the two shall mix. This did not benefit either society or Christianity. It would have been a deep disappointment to the great Christian fathers who pioneered the expansion of knowledge, like Isaac Newton and James Clerk Maxwell, to see their scientific descendants divorce scientific inquiry from the religious beliefs that they deeply held. Society needs a tireless body of Christians in every sphere of knowledge continuing to strive for greater understanding and harmonizing it with the truths of the Bible. The consequences of the failure of the Christian community to occupy these positions is obvious in various fields of learning. We wind up with a psychological community that does not know the difference between healthy and pathological thought processes. We wind up with a scientific and healthcare community that publishes narratives rather than discoveries of truth. We wind up with an education system that seems to hold the practical education of students at the bottom of its priority list. Society needs a tireless Christian community staying abreast of the forefront of knowledge to be able to make the arguments and protect against the pitfalls that will otherwise arise. The fallacies that overtake each area of learning inevitably destroy the viability of these fields and turn them from benefits of society into its bane.