The Simple Contains the Complex
Why we should flip our mental model of dimensions
In high school mathematics, I was taught that the zero dimension was infinitesimally small. A point. Smaller than the tiniest dot I could make with my pen. The first dimension was a line, thinner than the width of a hair, connecting two of these vanishing points. The second dimension was unimaginably flat, like the geometric designs in my workbook.
The third dimension — well that was where I was. Reality. Solidity. “Thingness”. Later I learned about time as the fourth dimension and came to think about “reality” as I experience it, being four dimensions.
The other dimensions were smaller than 4D. Smaller than “reality”. That made intuitive sense. They were, after all, things I could hold in my hand or look at on a page, or even smaller than what I could see.
This mental model of dimensions as being “smaller” the simpler they become is reinforced in almost all conversations we have about them. We talk about the zero to third dimensions as being “lower” than the fourth. If you move in spiritual circles you will hear people talk about “ascending” to 5D.
But the way we were taught to think about dimensions in high school is backwards.
The simple contains the complex.
What does this mean?
Let’s start from the beginning, at the Big Bang. The singularity from which everything supposedly originated.
The way we usually imagine the Big Bang, is the singularity exploding outwards. Breaking apart into quarks, electrons, atoms…
This image assumes that everything became separated from each other. “The first scattering” is what cosmologists use to name the first point at which light became visible. We imagine something extremely compressed becoming more disconnected as time moves on.
But this doesn’t make sense. Existence has to have imploded.
When the singularity became duality (the first dimension), it became differentiated inside itself. How could it have done otherwise? If the singularity contained everything that would become reality as we know it, it couldn’t have exploded outward into unreality, but inward, further into existence.
Everything that exists now, is contained within the zero dimension. We are still inside the singularity. There is still no separation. Nonduality contains duality.
Let’s go further.
“The universe is the interplay of difference, and the primordial difference is between up and down, back and front, black and white, is and isn’t, male and female, positive and negative.” — Alan Watts, Way Beyond Seeking
As Alan Watts says, everything in existence can be described in terms of a binary system. “Is you is, or is you ain’t?”
Quantum physicists, observing particles — are they “here” or not? Existence or nonexistence? Yes or no?
We ask, is Schrodinger’s cat alive or dead?
This is what it’s like, being a four dimensional being contained within the first dimension (contained within the singularity). We are made up of binaries. Neurons firing — on and off. All experience the interplay between “self” and “not-self”.
But these binaries are not separate, but dipole. They are always two sides of the same process. They imply the existence of each other. One cannot be without the other.
It goes on like this. Two dimensionality is contained within one dimensionality.
The second dimension is not a picture on paper in a geometry textbook. It is not merely “length and width”. That is how it is described in mathematical (geometric) terms.
More broadly, the second dimension is relationship between two dipoles. In geometry we talk about length and width. However the second dimension can be observed in the “real world” as well. When statisticians measure the relationship between two variables they plot their graphs on the “x axis” and “y axis”. The “x” and “y” can stand for anything.
As you can see in this humorous example above, each axis is drawn as a line between two points. Number of legs: from none to many. Cuteness factor: from not at all, to extremely. These are the dipoles of the first dimension, interacting with each other. The relationship between these dipoles is depicted as a graph (a two dimensional shape) although in reality this relationship does not manifest as a visual shape.
The second dimension therefore, is found in the relationship between two dipoles, or binaries, which may be visualised as lines and shapes (although we should not be tempted to reify the shapes and lines as being the same thing as the first and second dimension). So the second dimension is contained within the first dimension. The simple contains the complex.
Continuing on — three dimensionality is contained by two dimensionality. In non-geometric terms, the third dimension is the relationship between the relationship between dipoles.
When three dimensions become four dimensions, it’s because the three dimensions interact with each other, passing through each other, creating change. This is experienced as time, which is why we call time the fourth dimension.
From here it becomes difficult to visualise. The more dimensions, the more complex the web of relationship. Everything is contained within the dipoles of start and end, yes and no, on and off which are themselves contained within the singularity, which is contained within nonduality (which Buddhists call, “the void”).
After all, there is nothing simpler (more undifferentiated) than the void from which existence springs.
“Form is emptiness, emptiness is form.” — The Heart Sutra, Mahayana Buddhism