The fifth dimension made me do it.

I started writing this in 2018 and got sidetracked. I never returned to it. Now, at the very end of 2020, I’m setting it free. Not because I think it’s complete. It isn’t. Maybe there’s more. Only time will tell.

I want to start this piece with a very clear disclaimer: I have no clue what I’m talking about. And by that, I mean I don’t have formal training in what I’m about to get into — just passion and an unrelenting sense of fascination about the world and our understanding of it. So, if you’re reading this, I’d ask you to take it in the same light as a theoretical exploration of chemistry or magnetism undertaken by a 19th-century gentleman with far too much money and time. I’m a little short on both of those, but I think what I’m about to write is every bit as fanciful and far-flung.

When theoretical physicists write about multidimensional spaces (beyond the third dimension in the physical world — time being the fourth dimension), my eyes cross. As much as I want to wrap my mind around the concept of five, six, seven, or even twenty-two dimensions, I can’t. Multidimensional space is such a foreign concept that (in my opinion) we can’t even really diagram it without resorting to visual shorthand that almost makes things even more confusing. Sometimes, these new dimensions are depicted as being folded or deformed inside more familiar three-dimensional shapes (which always makes me wonder, why then aren’t they simply considered convolutions in the surface or volume of a three-dimensional shape?)

But other than my general discomfort with the mechanics of it, there’s something else that has always bothered me about the concept multidimensional space: why are all these additional dimensions inevitably physical ones? Are there additional dimensions of time? What would that even look like?

You know what — let’s just start at the beginning.

A point in space, sitting by itself without measurement or position, carries no dimensional information. But it soon will, so let’s give him an appearance: He’ll be purple, because I like purple.

Now, if you trace that same point along a single axis (I’ll go with “x” as a label, because tradition exists and this is going to get messy enough that there’s no reason to reinvent the simple stuff). Here, we’ve got a single dimension that our friend can exist along (left/right).

If we allow that same point to move not only left/right but also up/down, we’ve added a second dimension. The point now resides in a grid of sorts. Our friend could be a pixel on a computer monitor or television, a spot of ink on a printed page, or a pencil point in a drawing. This second dimension will get the label “y”, also for tradition’s sake:

Wrapping up the familiar physical dimensions, if we allow our friend the purple point to move backwards/forwards in “depth”, we’ve added our third dimension. (It’ll be labeled “z”). Nothing crazy here, yet:

Three-dimensional space is interesting to me because each of the three dimensions is effectively interchangeable. What I mean by that is, if you come at a rendering of a shape with none of the axes (X,Y,Z) labeled, no matter where you assign them, you change nothing about the shape. You need to be consistent in how you apply labels if you’re going to perform calculations on the shape, or share data about the shape with others — but that’s really it.

But time, on the other hand, is different.

From this point forward, to keep things simple, let’s think of our 3-dimensional purple friend (and all of his potential movement in that 3-dimensional space) as a single point. What I mean is, we’re no longer thinking about the directions he can move, or his current position — we’re just aware that the model allows him to move in three dimensions and representing it as such:

Because we live in a world where time exists, purple point is going to move through it. He’s doing it continually, even when his physical position isn’t changing . Let’s indicate the passage of time — the fourth dimension — like this:

So far, that’s all pretty straightforward. Although I created the above illustrations from scratch for the purposes of this article, you’ve likely seen very similar (if not practically identical) ones in a hundred places previously: textbooks, blogs, documentaries, and even children’s cartoons. Three physical dimensions with time as the fourth dimension, in 2019, is easy for me to get my head around.

It’s what comes after it — the theoretical “fifth dimension” and onward — that start to get really interesting (and really confusing) to me.

If we think of “standard time” (the linear movement through time that we all experience) as the “x-coordinate” of time, it follows that what we need to establish next is the “y-coordinate” of time:

When I was first planning this out, I was going to label the fifth dimension as “l” for “line”, as in timeline. Science fiction has gotten me pretty used to the concept of simultaneous timelines, each with variations on our world and the events occuring in it. But as you’ll see above, I labeled the axis “p” instead. What gives?

The more I thought about it, the more the notion of timelines as the fifth dimension felt at odds with the rest of the model up until this point. It just didn’t feel right. When we look at the standard XYZ coordinate model for physical space, the X and Y components effectively indicate our purple point’s position within a grid. A different “timeline” (at least in our current conception of one) carries a degree of separation that feels too far removed from the 4th dimension, to me. (I know, I know — this is completely subjective and kind of arbitrary. Remember, 19th-century gentleman.)

Instead, I’m labeling our theoretical fifth-dimension “p” for “phase”. For this exploration, let’s assume that the phase coordinate of a point in space-time indicates whether or not it is able to be observed by (or to observe) other points in space-time. Consider it an “alignment” or “orientation” — perhaps similar to the polarization of light. Points with the same position in time and the same phase value can interact with each other. Points with the same position in time and different phase values cannot. To make things even more interesting, imagine that the degree of visibility/interaction isn’t binary, but a spectrum: close-but-not-quite-there phase values allowing partial interaction, distant values practically nothing. Perhaps all values exert an influence or some sort, even if vanishingly small.

Then, that leads us to the sixth dimension. This is where I would introduce the concept of “timeline” (labeled “l”): different “tracks” of contiguous time that our point can occupy, but that do not intersect in space-time:

You might expect that after writing about the first six dimensions, I’d want to get into what’s next: further dimensions. Honestly, though, I don’t. It’s not for lack of interest. Frankly, I don’t even know where I’d begin. I said at the beginning of this article that I was approaching this as a non-professional, untrained, simply eager to explore. I could sit and make up something about the seventh dimension, but my heart just isn’t in it. It’s too abstract for me to latch onto.

In fact, I don’t even really feel like discussing the sixth dimension at the moment (timelines are great theoretical fun and all, but the implications are far-reaching and could quickly overwhelm my will to actually finish writing this piece).

I’d rather drop back down and take another look at the fifth-dimension.

One of the reasons why I love the concept of the fifth-dimension being phase is that it opens up all sorts of interesting possible explanations for everyday phenomena. In this article, I want to focus on just one of those: Memory

Memory is at the heart of so much that we consider truly “human”:

• Memory allows us to learn new information, and to integrate it.
• Memory allows introspection. It’s the information that we use to provide context to — and to consider our progression through — life.
• Memory is strongly tied to emotion.
• Memory enhances visual recall and identification, and seamlessly integrates our experience of the here-and-now with our past knowledge. My go-to example here is the way we can spot a tiny speck of color on the side of the highway and immediately identify it as a crumpled pack of cigarettes. Along with that identification comes (if you’re familiar with the object) the crinkle of the cellophane wrapper over the paper box, the weight and the feel of the pack, the smell of the smoke — everything that connects to it. None of that had to be observed visually, but once you’ve made the connection, it all becomes accessible.

Maybe memories are so difficult to pin down (both conceptually and scientifically) because they aren’t stored in the structures of the brain at all. Maybe the experience of memory recall is created by initiating a phase alignment that allows you to access events with the same phase value at a different point on your current timeline. For all its complexity and bewildering (often unfathomably distant and numerous) connections, what if the entire “conscious” portion of the human brain is really just an apparatus for constructing sequences of phase values?

This would also mean that memories, rather than being a construction of an individual’s brain, are bits of actual events. Not a “recording” of those moments— but the events themselves.

But wait a minute — what about false memories, or the proven inaccuracy of memory in general? If the act of remembering literally creates a conduit to the original event, how could that memory be inaccurate (or even nonexistent)? But how do you know that a memory consists of a single “conduit” to a single moment in space-time? I’d actually argue that, in this theoretical model (or honestly, under any model, given my own experience with memory), it almost certainly wouldn’t.

I think that memories are “nested”. Individual elements within a memory can stand out in vivid detail, while others might be only a vague sense of recollection. This might be, in effect, because the recall event for a “master” memory (the broad frame for the event you’re recalling) initiates subsequent “secondary recalls” for elements within the memory. Your memory of your fifth birthday might contain separate recalls of the space (your childhood dining room / kitchen / house), the people in the scene (your family, friends), the food, the gifts, etc. Each of these recalls could initiate its own set of nested recalls, as well (your memory of a video game you received as a present could trigger recalls of memorable time spent playing it, friends you played it with, the space you played in, etc.). A single memory recall event could consist of dozens or even hundreds of phase recalls, each linking to a different moment in space-time.

With that concept in mind, the notion of false or flawed memories doesn’t seem problematic to me. The human brain is adept at stitching together information from different sources to create (in effect) a “fantasy” recall of something we’ve never actually seen/experienced (think of the popular public speaking tip to “picture everyone in the audience naked”). False memories could simply be well-practiced fantasies that are intentionally reinforced as true recall. Flawed memories could stem from a few crossed signals and incorrectly correlated moments (for example, that strong memory of your birthday might include a friend who was never actually there, but with whom you later played the game you’d received as a present, often in the same room where you gathered for the celebration)

December 11, 2020 Note: This is where my original writing stops. I haven’t added to this piece since I first wrote the above in 2018. I’m leaving this note simply to say, there was supposed to be more. Someday, I’ll pick this up. For now, I think it’s an interesting capture of the ideas I was trying to make sense of.