The whole dimension aspect to the experience is perhaps one of the most intriguing and beloved to me. People usually start by instantly talking about the fourth and higher dimensions, but I'm gonna take a second to step back and go the other way first.
There was one day where my GVG had an abnormally large amount of DMT condensate in the U-neck. I decided that instead of cleaning it out, I would just try to super-heat the vaporizer to vape it all. Having known that it would be difficult to do, I had the idea (which I later found out wasn't original of course) to remove the top piece of the GVG with the ceramic filter and carefully lower the torch from above. The GVG instantly and effortlessly plumed with thick white vapor that cleared with extreme ease and no harshness at all. As I held my hit in, I began looking around my bedroom with my eyes open, only to discover that I had lost 100% depth perception. I was seeing the external world in complete 2D. Everything was completely flat, even and equal in relation to me. I decided I would try to take another hit, being the first one was so easy to take, and I was looking to push my limits to see how far I could get. The only problem is that when you're vision is in 2D, it can be remarkably hard to place the flame over the GVG. It was pretty much the only time where I felt it physically difficult to take another hit when I wanted to, though I eventually did manage.
As I was holding in my second hit, I was looking at my wall, and I noticed there was a spot that wasn't flat. Not only wasn't it flat, but it looked like I was seeing deep through my wall into another dimension through which 4D machinery was floating out. This was the first time I saw 4D objects with my eyes open (before only with eyes closed), though I can now see such phenomena with ease which makes me believe that it was thanks to this experience that I sort of unlocked that feature of the experience. I could go on with how that experience bizarrely proceeded, but I'll save that for elsewhere because it doesn't really pertain to dimensions.
Here's something that I ended up realizing about the 2D experience in retrospect. I was seeing in 2D but because I had the natural where-with-all to know that I really exist in 3 dimension, I was thus able to move in 3D, though my eyes wouldn't show me that. Point being that just because our nervous systems only allow us to normally see in 3 dimensions, doesn't mean that we're not constantly moving about in the upper dimensions (mostly unknowingly).
So I know when I'm experiencing the second and third dimensions. From there anything else is really sort of a guess, and I'll most often just chalk it up to the fourth or play it safe and describe it as "extra-dimensional, "inter-dimensional" or "multi-dimensional". Why those extra dimensions come into play in the DMT experience, I don't know, other than to say that I'm more likely to get it, the more efficiently I vaporize the DMT. I can rarely move about freely, though to be honest I don't really ever try much.
There was one time where I had a lesson by some entities where they demonstrated the mechanics of their inter-dimensional antics. They started off with the most basic example, making sure I could clearly see every detail that was going on, and a little "behind-the-scenes" view of things. They play off this sort of foreground/background technique. This is different than how we would think of foreground/background in a painting. In this scenario, the background is a "hidden background", that is to say when you're having your DMT experience, it is an area that you aren't supposed to see. Hyperspace material easily slides back and forth into this hidden dimension which gives the illusion of basic uni-dimensional movement. For example, imagine a hand moving from left to right in hyperspace. It all appears to take place on one plane, but in reality, the left part of it is slipping into the background as unseen matter slips into the right part of the foreground. This concept can then be (complexly) expanded into inter-dimensional movement. The same concept is at play with what we perceive as multi-dimensional objects/entities, except now we have a foreground and a real background in addition to the hidden background. Anyone who has ever seen layers slide through each other may have an idea as to what I'm talking about. I understand that the experience is different for everyone, so please understand this was how it was presented to me. Sometimes a "hiccup" in the experience can sort of derail it, allowing you to see some behind-the-scenes dimensions, though it can effectively ruin the experience to some extent.
"Science without religion is lame. Religion without science is blind" - Albert Einstein
"The Mighty One appears, the horizon shines. Atum appears on the smell of his censing, the Sunshine- god has risen in the sky, the Mansion of the pyramidion is in joy and all its inmates are assembled, a voice calls out within the shrine, shouting reverberates around the Netherworld." - Egyptian Book of the Dead
"Man fears time, but time fears the Pyramids" - 9th century Arab proverb