Yes, I do. To illustrate how it works, let’s think a little bit about dimensionality. We normally think in pure spatial terms, i.e. 3 vs. 2 dimensions. But there’s more to it than that, there’s dimensionality in between two and three. Here’s a matrix:
[math]|2, 3, 4|[/math]
[math]|5, 6, 7|[/math]
No idea how to make that look right. Anyway, here’s another way to represent that matrix, this might be familiar if you program computers:
- [[2, 3, 4], [5, 6, 7]]
What happened there? Did the two dimensional matrix just become one dimensional? If you didn’t know how the bracket operated, you’d be forgiven for thinking that. There’s a computing term for reducing the dimensionality of data down to ‘one’ dimension so that it can be easy transmitted, say, over a network, serializing. If I feed that 2D array into Ruby’s Marshal library, designed for just this, this is what it outputs:
- "\x04\b[\a[\bi\ai\bi\t[\bi\ni\vi\f"
All three of the above quoted things are representations of the same mathematical object, projected into various degrees of dimensionality. We can think about increasing the dimensionality of that particular object by, rather than bits on a screen, grouping actual objects. We can have one group of three groups of oranges, 2 in the first pile, 3 in the second pile, and 4 in the third. Then another one underneath with 5, 6, and 7 oranges respectively.
All representations of the same, 2 dimensional math object, projected into other shapes with different dimensionality. So far so good, I haven’t really demonstrated how things can exist as in between two and three dimensions yet, just projected from one shape to another.
So let’s represent a 3 dimensional shape:
- [[[1,2],[3,4]],[[5,6],[7,8]],[[9,0],[1,2]],[[3,4],[5,6]]
What makes this three dimensional is that there’s two ‘layers’ of brackets. See how adding a dimension makes it much much harder to see the grouping? Imagine removing the brackets, this is an operation we call ‘flattening’. By flattening the data structure, we make it easier to represent and understand what it is and what the relationship between the elements. But we’re removing critical information about the data that was embedded in that structure.
It’s like taking the atoms of the human body and stretching them out one by one in a line. It’s still the same human, technically. But good luck getting in your car and getting to work tomorrow!
But we don’t have to be destructive, we can also be additive. Let’s add dimension to a 2D data structure:
- {[a, b]{c, d}}
We just changed the shape of the data structure by adding a new type of relation between them, the relation denoted by the curly brackets. Note that we’re adding dimensionality but this data structure still isn’t quite 3 dimensional yet. Imagine going from black and white to color images. There’s more degrees of freedom, more ways to represent information other than just greyscale, but not quite enough to make it a 3D image.
Anything can be represented this way, any kind of rules we want to make, we can find a representation of those relations and so encode things and the rules by which they’re interacting into a giant data structure. The word we have for that in the computer world is ‘simulation’. We restrict the rules of interaction down to a subset so that it can be modeled as a computation. The state of the simulation exists in a giant data structure. It’s a lot of fun.
Our 3 dimensional reality, with the added non-spatial dimension of time, is impossibly, monumentally complicated, with not only an entire field of science studying the fundamentals of, physics, but also entire fields studying ‘little’ subfields like materials science, and even in materials science, there’s people studying specialties like steel alloys.
Think about all the ways we can complicate 2 dimensional data, and realize that there’s an order of magnitude more complications we can add to three. Complicating 2 dimensional data structures brings it ever closer to three true dimensions. Complicating 3 dimensional reality brings it ever closer to four dimensions.
It’s a bit silly to think that existence has to stop at three dimensions. Or that there has to be a limit to at which point it absolutely has to stop. Or that there’s a limit to the possibilities for complication. We can imagine complications on three dimensional reality and even do math on N-dimensional objects. Saying there’s no spiritual reality essentially draws a big line in the metaphorical sand across which nothing past can be ‘real’.