What is a dimension? The image the word brings to your mind might involve alternate worlds, aliens, and time travel. And while these are related to the subject of dimensions, it might not be in the way you thought.
At it's core, a dimension is simply a measurement. For instance, "The dimensions of this room are 14 feet by 12 feet." The different aspects of an object, place or person which you can measure, observe, or interact with. But how does this pertain to alternate realities and other sci-fi story elements?
The only way to explain is to start at the beginning, so without further adieu, buckle in for the 10 dimensions of our reality.
Length is a simple distance measurement. But what is a 1-dimensional object look like? A 1-dimensional object would be imperceptible to the human eye. Not just transparent, but unseeable, because it has no width or depth, and therefore, nothing to see. Traveling in the first dimension can only occur in two opposing directions. You can only move along a single line, so there is no turning, no changing course, no freedom other than moving forward along the line, or moving backward along the line. While the line is infinite in both directions, there is nowhere else to go, even if there's an obstacle in your way.
As we enter the 2nd Dimension, we discover width. This provides us with a bit more freedom of movement and perception, and also gives me a chance to introduce Dimension Dave, a brave little stick man illustrating what it's like existing in the next several dimensions. Above, you'll see him scratching his head and contemplating his existence. Instead of moving along an infinite line, as a 2-dimensional being, Dave can now move in all cardinal directions along an infinite plane, like a flat and perfectly straight sheet of paper spreading out forever in all directions. If an obstacle presents itself to Dave now, he can utilize both the dimensions of length and width and simply walk around it.
Getting used to his 2D freedom, Dave decides he wants more, and becomes aware of a 3rd Dimension: Depth. As a 3-dimensional being, Dave can now move up and down in addition to forward, back, left, and right. If Dave came across a short wall in the 3rd Dimension, he could easily hop over it, or dig a tunnel under it because of his newfound vertical freedom. In the 2nd Dimension, Dave could only get past a similar obstacle by going around it because the only alternative would be to pass through a solid wall. Perceived from a 2-dimensional vantage point, this would seem like Dave spontaneously disappeared on one side of the wall and a moment later reappeared on the other side.
Here's where things get interesting. With the fourth dimension of time it may be tempting to conceive of time the way our human brains perceive it: the past is gone, never to be seen again, the present is the continuously rolling moment of now that we are constantly experiencing, and the future has yet to happen. But when thinking about dimensions, it's more helpful to think of time much like we do length, width and depth. That is, that every point along the line of time exists. The "you" of 2 hours ago still exists, just as much as the you reading these words. If we think about time like a line, we can see that if we zoom in, we can find infinite points along that line. Each of these points exists at the same moment, and each of them together make up what we see as the line.
Following that train of logic, if we could see time the way we see the first three dimensions, we would see each person and object at every point in their existence from beginning to end all at once. If we were to look at one person in four dimensions, they would look like a long, swirling, lumpy snake. This snake would be thin at one end, representing our conception and birth, growing and thickening as we get older before thinning out and dispersing at the time of our death and decay. What we see in the real life present is merely a cross-section of this time-snake-person.
Notice in the image above how "Present Dave" stands at the front of a procession of his former selves. This image is a short slice of Dave's 4-dimensional self, from several seconds before, ending with his present moment.
5. Probability (Possible Universes)
Much like the way the 2nd Dimension adds an additional freedom of movement from what we have in the 1st Dimension, the 5th Dimension adds an additional freedom of lateral movement in time. Simply put, that means that the 5th dimension takes into account the element of chance, choice, randomness, and any way things could have played out differently than they did in the universe we experience right now.
Any time there is a chance that an event could play out in more than one way, it's theorized that an almost identical universe branches off from the original. Each break-off universe represents the timeline where things played out differently. If you ever made a decision at the flip of a coin, this created at least two timelines, one wear your flip came up heads, and the other where it got tails. If your buddy Jeff ever rolled a 6-sided die to see which of your friends should go outside to get the pizza?
And this effects more than just human acts and decisions. Think at an atomic level, the infinitely complex interactions that happen between particles. Imagine one of those physical or chemical reactions happening just a tiny bit differently, and this creates it's own timeline. Then consider the dizzying number of particles in the universe, and everything that could happen to them, and you quickly see the mind-blowing amount of alternate universes that this would imply.
Let's take it back down to the personal level again for a second. The 5th Dimension would, in effect, turn the 4-dimensional snake-person we explored in the 4th Dimension into a 5-dimensional, tendril-covered squid monster reaching out a new limb wherever a new possibility presents itself. Notice how in the above illustration that Dave is presented with the choice of either continuing forward, or turning right and approaching the camera, and both of these outcomes are represented. We as mortal humans can only perceive one of these universes, and that's the one we are currently experiencing. In the 5th Dimension, we cannot reach these other timelines because they do not have the same causal relationship to our own timeline. That is to say, the same series of events that happened in our world to produce what we see in this moment did not happen in the other universe to create the same outcomes, and vice-versa. Logically then, we are unable to be perceive that which did not happen in our own branch of reality. In order to have that freedom, we have to go up one level.
6. All Possible Universes Branching from the Same Start Conditions
Remember how the 3rd Dimension introduced the ability for Dave to move jump, effectively disappearing from one point and reappearing in another when viewed from the 2nd Dimension? The 6th Dimension does something similar in it's expansion of the 5th. If the 4th dimension is comparable to a line, then the 5th is a plane and the 6th can be thought of as a "3-dimensional" space, where Dave can now "jump" from his current position to a position on another timeline. Viewed from the 5th Dimension, this would appear as Dave spontaneously disappearing from our universe, and reappearing in another.
The 6th Dimension takes into account all possibilities that could ever occur if we assume a single starting point (in our case, the Big Bang) with the same starting conditions (the laws of physics as we know them). Starting at the moment of the Big Bang, we see universes sprouting out from every probabilistic outcome, creating an infinite array of branching realities. This is often termed the "multiverse theory" or "many worlds theory".
From this level, if he so desires, Dave can leave our universe and find himself in a universe where hyper-intelligent dodos became the dominant species of Earth and Dave is viewed as a curious primitive ape by the nerdy birdies. Any number of adventures that follow our laws of physics are now open to him. But what if, when he gets to a new universe, Dave wants to practice dark magic, or perhaps be able to jump twice as high as he normally could? For that, we need to go up one more level (maybe two, depending on what he wants to do).
7. All Possible Spectrums of Universes with Different Start Conditions
In the 7th Dimension, the multiverse we live in exists on any number of spectrums where the laws of physics are dialed up or down. For instance, we can place our multiverse at one point on piece of paper and draw a straight line through it. If we want to visit a multiverse where the strength of gravity is weaker, we can move in one direction down that line. Each move along that line requires us to pass through each point that exists on that line (remember, that an infinite amount of points exists on any line). So in order to get to a multiverse with gravity at exactly half the strength of our home, we are forced to pass through every infinitesimally different universe in between.
But remember, moving 7-dimensionally means that we are only dialing one universal law up or down at a time. You cannot change two of these variables at once. At the 7th Dimension, you can't visit a universe where gravity is at half strength and the speed of light is also twice as fast. For that, you need to change the line to a plane, which, as you might have guessed, means you have to add another dimension.
8. A Plane of All Possible Universes, Different Start Conditions
The 8th Dimension allows us to change two variables at once. Any multiverses we visit exists on any number of intersecting planes, each plane representing the relative relationship of the two variables in question and the infinite range of values at which you could set each variable.
9. Direct Movement from One Multiverse to the Another Non-Adjacent Multiverse with Different Start Conditions
At the 9th Dimension, we gain an additional degree of freedom. Just as we gain the ability to "jump" in the 3rd and 6th Dimensions, we gain the same "vertical" freedom in the 9th Dimension. This time, the new freedom translates to the ability to disappear from one multiverse, and reappear in another with different multiverse with its own laws of physics and starting conditions.
10. Infinite Possibilities
At last, we reach the 10th Dimension. Throughout this entire process, the addition of each dimension has followed a pattern. The 1st, 4th, and 7th Dimensions are all represented by a line. 2nd, 5th, and 8th expand upon the dimensions before them by turning that line into a plane. And finally, the 3rd, 6th, and 9th dimensions turn that plane into something analogous to a "3D" shape or "solid". When we reach the 4th and 7th Dimensions, we're asked to condense all the data from the previous dimension and represent it as a single point, connecting that point to another similar point with a line, and the whole pattern begins again.
By the time we reach the 10th Dimension, we've condensed the 9th to a single point. But, hold on: Didn't the 9th Dimension express every possibility that could ever arise in any universe, with any physical laws, at any time, ever? What, then, is left to connect to a point that represents absolutely everything?
The answer is... nothing. There is no other dot we can connect to from here to create a line and measure something new. The 10th dimension is every event imaginable or unimaginable, with any start conditions and infinite variations that could ever or will ever occur under any circumstances condensed to a single point, with only nothingness extending beyond its reach.
Just like the famous theorem tells us how having infinite monkeys at infinite typewriters would eventually result in the complete works of Shakespeare, one could imagine that any story or scenario you could imagine has happened in a universe somewhere. Star Wars, Lord of the Rings, the Marvel Cinematic Universe; all of them could be reality in some universe. No matter how low the odds, they're still not zero. So in an infinite and expansive multiverse, they must exist somewhere.