How can there actually be more than 3 spatial dimensions?

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I’ve heard about this idea a lot, but on the flip side it doesn’t seem to make sense. Us as 3D beings can’t naturally encounter 2D things, just representations of them (drawings etc), but nothing in the real world that has just 2 dimensions. So how could it be possible for there to be 4 (or more) dimensions?

In: 3

Here’s how I understand it.
Consider a piece of paper. Because you are huge, you can only move forward/backward and left/right if you walk on it, effectively making it two-dimensional in space for you, with the third dimension being squeezed in space to the extent that it’s negligible.
Unless you’re a tiny flea. Now you can perceive the extra dimension of the paper and you can climb up or down it’s edge. Only if you are, yourself, comparably sized on that tiny scale.

That’s where the extra spatial dimensions are. We can perceive 3 because we are huge within the scales of those dimensions. The additional dimensions are squeezed into tiny spaces within the fabric of the universe (think plancks length… 1.6×10^-35 m) and we can’t perceive them unless we shrink down to that size.

Like Ant man does.

Edit… How small is plancks length? An electron is 2×10^-10 m. So its 10 million billion *billion* times smaller. Than a fxxxing *ELECTRON*. Hence even electrons are only capable of moving in 3 dimensions…

We don’t know if there are more than 3 spatial dimensions in this universe. From a physics standpoint, one of the major theoretical exploration is the idea that fundamental “particles” in our universe are built out of smaller bits. One way to make this explanation work (ie that it would result in something like our universe) is there are additional spatial dimensions (7 or 8 additional depending on theory)

The idea is that these are very, very small (much smaller than the smallest things like electrons) and sort of “rolled up”. So humans would not ever experience them directly.

Bear in mind, these are advanced theories and, so far, there is no way to verify the existence of these dimensions.

If there are other universes in existence (again no evidence to suggest this), there is also no reason to expect that 3 spatial dimensions is somehow “correct”.

You are discounting pretty quickly our ability to encounter 2D things. A drawing of a ball is a representation of a 3D object. That representation is not however 3D. We can create an illusion where it appears to be 3D, but it isn’t. Its a drawing on paper, and that drawing has no actual depth. It being a drawing doesn’t make it any less 2D. However our ability to create an illusion of being 3D is only possible because we understand that there is a 3rd dimension, and can observe it. You can look up “Lego Army” by Leon Keer for an example of this. When we move from the forced perspective, the illusion of a 3D army marching down the street is lost. A 2D person in a 2D universe could never see both perspectives.

Now as for higher spatial dimensions. We aren’t 4th dimensional beings and so while we can certainly describe the idea of a 4th dimensional object, they would have properties that are impossible. The tesseract for example is a 4th dimensional cube. If you imagine a regular cube, you can unfold it into 6 squares, a net, that can then be folded back up to make a cube. If you replaced each of those squares with a cube, and then folded them together, you’d have a tesseract. The problem, of course, is this is impossible. Each cube already inhabits three spatial dimensions, unlike the square net’s two. With the square net we can force it to inhabit a third dimension to form a cube. We can’t force the cube net to form a tesseract. If a tesseract actually existed, from one angle it would appear to be a perfectly normal cube. But the second we moved, its shape would change in the same way that walking around “Lego Army” changes how we perceive it.

So if we don’t have the capacity to perceive 4 dimensions, and we don’t live in a universe where its possible, as far as we know, for there to be 4 dimensions, why bother? Well, the answer as always is Math. Imagine we are a store owner who wants to maximize profit of a particular product. He discovers that there are 4 factors that affect the profit of the product. The price, the time of year, the location in the store, and the time of day. He also figures out how much each variable affects the profit. If he then wants to model this, we quickly run into a problem. This math problem is 4th dimensional. It has 4 axis that any point could be, and so can’t be traditionally graphed. But the math to maximize this problem is very possible without graphing.

This idea of a simple math problem that can’t be physically represented in its purest form led people to want to try to do so and 4th dimensional geometry was born. Just like a 2D person could never see all of the drawing there in the same way we can, we can’t observe a 4D object. But we can imagine and create some very cool ideas.

This won’t answer your question directly, but imagine you’re a stick figure on a piece of paper living in 2 dimensions. You can look up, down, forward, or backward. To an observer like us, theres a third dimension to the left and right, but the 2 dimensional being can’t perceive it. Technically he’s still moving in a dimension of 3 dimensional space, but doesn’t have access to the 3rd.

The analogy would have to fit for a 3rd dimensional being in 4th dimensional space. Theres space in a direction outside of your perception.

Some things may be not only just so complicated you don’t understand them; they may be so complicated you *can’t* understand them.

The human brain has certain capabilities and limitations. Unfortunately those limitations may prevent us from understanding everything. We won’t be able to understand them without an enormous amount of work, or maybe at all.

I’m not saying you’re too stupid to comprehend this. I’m just saying you might not want to put in the work. I mean there are some things we understand intuitively, some things we only understand through experience, some things that are counterintuitive and seem to go against experience but are nevertheless true, and some things that we will just never be able to understand, at least the way we are now.