Oh I have heard of this. I've never read them, though.

I don't know what the three body trilogy is but yeah. A 4-torus manifold is exactly that.

"Fourth dimension" describes a position. But that's a relativistic universe made useful to us. Time can be the first dimension if you want—and space can be second, third, and fourth. It's really about describing a tensor. For all the problems we want to solve, we first need to know where.

However, you're a 3D being, so you can move. You can experience the third dimension. But only by movement—a change in position. That's what a dimension is, really. Depth perception, proprioception. It's 2D + a third coordinate.

A 4D being would be able to see the front and back at the same time.

But let's say it's a thick piece of paper. Now it has three dimensions—length and width PLUS thickness, which gives it a front and back.

As a 3D being, you can't see the back of the paper and the front of the paper at the same time.

I love this. I agree with you about the bottles. That's probably why I drew one! But also it's a great compliment thank you.

And the goal of art, really any kind of visual art that aims for representative or figurative qualities, is to connect that bridge. When you draw form or shadow or sculpt depth, it's all 2D. We see it in 2D. But it reminds people that they exist in 3D, which is vital. Literally vitality. Moving.

And the reason I was able to do that is not because I turned 3 dimensions into 2.

It's because I turned 2 dimensions into 2. I mimicked how you perceive 3D space—you perceive it as 2.

And that's all realism is. It's understanding that a 3D being can only view 3D objects as 2D.

A 4D being would be able to see fully in 3D. Every side of every three dimensional object at once.

Just as we can see every side of something in 2D.

We know something is a sphere because we are 3D beings with 3D eyes spaced apart to see depth. We exist in 3D.

But we don't really see it. Not really. If we could really see in 3D, we would be able to see around and through every object at all times. We can do that in 2D, but not 3D. Not really.

Genuinely this is just like Jimmy Carter's note on Voyager 2. The whole "We cast this message into the cosmos" thing. Like almost a hundred years after the book. How cool is that.

This bit. It's so cute.

The scientists in Paperworld scramble to figure out the line. Eventually someone says, "Hey what about a 3rd dimension." They burn him at the 2D stake. BUT LISTEN.

I can recreate that. As a 3D being. Right now. I can move a 3D object and interact with 2D space. So surely a 4D being can do the same.

Like imagine you're a 2D person. You live on a flat piece of paper. Suddenly a 3D sphere arrives. Like a big ball. It passes through your world—through the paper.

From your POV, it would just be a line appearing out of nowhere. It would start out small, get big, then shrink and disappear.

Dr. Maggie Miller did an amazing breakdown on 4D pretty recently. If you watch this video where she describes manifold space to describe 4D and then watch the mirror guy, it's like "oh yeah that's it." www.youtube.com/watch?v=MURz...

Four dimensional space is so hard to wrap your head around for obvious reasons. You'll see "space across time" or tesseract animations or whatever. But this is an elegant way of demonstrating it topologically. Using the mirror as a surrogate for time is A+.

Here's my original image. And your photo of your computer screen with the added mirror.

Our eyes and brain expect some sort of flip or trick to be happening, but there isn't one. Your mirror is just a mirror reflecting at an angle of incidence same as the first mirror.