4D Toys Update 8: Rotating the 3D Slice, 2D Faces Projections, Marble Scenes
marctenbosch.com
marctenbosch.com
He has been working in 4D for more than a decade (first mentions of Miegakure was in 2009), if it is ever possible to get an intuitive feeling of a 4D world, that should do it.
The alternative is to just throw away intuition and just do the maths with one extra vector coordinate, but that would be unfortunate for a game that is all about thinking in 4D.
Yann, sitting beside him, caught his eye. "You okay?"
Tchicaya nodded. "In the scapes you grew up in," he asked, "was there a vertical?"
"In what sense?"
"I know you said once that you didn't feel gravity...but was everything laid out and connected like it is on land? Or was it all isotropically three-dimensional--like a zero-gee space habitat, where everything can connect in any direction?"
Yann replied affably, "My earliest memories are of CP4--that's a Kähler manifold that looks locally like a vector space with four complex dimensions, though the global topology's quite different. But I didn't really grow up there; I was moved around a lot when I was young, to keep my perceptions flexible. I only used to spend time in anything remotely like this"--he motioned at the surrounding, more-or-less-Euclidean space--"for certain special kinds of physics problems. And even most Newtonian mechanics is easier to grasp in a symplectic manifold; having a separate, visible coordinate for the position and momentum of every degree of freedom makes things much clearer than when you cram everything together in a single, three-dimensional space."
So much for being a seasoned traveler. Tchicaya didn't envy Yann's upbringing, but it probably rendered the world behind the border less exotic to him than the notion of a jungle had been to Tchicaya as a child. It shook his confidence to be reminded that there were measures by which his millennia of experience had been laughably narrow.
I find a more effective attempt at imagining 4D space to consider what it would be like to only see in 1D projection of 2D space.
Imagine standing on a piece of paper with other pieces of paper sitting on top that create a maze - all you can see as you turn and move about in 2D space are where walls and hallways are. You have a concept of depth (in 2D). You can move about the maze.
Now imagine the sensation of that flat world expanding into 3D space and your senses expanding with it. Now it's a 3D maze and you can fly- able to navigate the 3D space.
That change you just imagined, try imagining that same expansion into a fourth spatial dimension and it being projected into a 3D space you can perceive.
Instead of being able to tell the 3D shape of something by observing shading and how light interacts with it, you'd be able to perceive the 4D shape of something, even though you can only see a 3D projection at any given time.
Imagine standing on one side of a room at t0 and walking across the room, reaching the other side at t1. At each instant in time, your body has a 3D position in the room. So the 4D shape of your body between t0 and t1 is kind of like the path your body took through the room. You can create a 3D slice at any point between t0 and t1 and get exactly where your body was at that moment in time.
That doesn't help me understand 3D space. It helps me understand 2D changing over time.
Think of all the implications that "depth" - that extra spacial dimension - has on the world. How dramatically it changes things, and how differently things work with it.
If you treat time as a dimension then you now understand 3D.
There is a book called Flatland that takes place in a 2D world occupied by 2D shapes. The shapes can only perceive two dimensions. One shape encounters a sphere, but to the shape, the sphere looks like a changing circle. It makes you realize that it's probably impossible to conceptualize a sphere if your only frame of reference is two dimensions. Similarly, in your maze example, you're placing one piece of paper over another one, meaning the paper already exists in 3 spatial dimensions. How can I place one 4D object "over" another one?
And then you have rotations, rotating space into time and vice versa is one of the most confusing things you can do with dimensions.
the slices of dimensions from one d dot to four d object make sense when you roll them around in your hands via game controls.
Space Dandy had an episode where the hero dates a four dimensional girlfriend. It's not 'magic', it makes sense.
The idea that our brains are hard wired for basic concepts is almost synonomous with a self-limiting belief.
There needs to be a lot of hard evidence/definitive causation, to make those claims about a biological organ and not accidently limit yourself.
F.A.Q.
When is the game coming out?
As soon as possible, we are very far along but haven't announced a release date yet.
I tink 4D toys allows you to view 4D and 3D objects on a 2D plane. It makes me wonder how much we can really perceive a 4D world in a 3D world on a 2D surface (screen). A 3D hammer could be appreciated in 2D, but could a 3D philips screwdriver? I am not so sure.
I remember reading something along the lines that human perception is extremely biased by the architecture we live within. Our edge detection gets much worse when it doesn’t follow similar lines of a room. Suggesting other cultures that live outside could perceive certain “illusions” that aren’t illusions at all. If that makes sense…
But can I work the other way? Can we ever have a true understanding of 4D?
I am not sure our edge detection gets worse in werid architecture. I visited a large scale surreal 3D art installation and had no problems with edge detection even if the scale of objects was designed to mess with my senses.
Peter Watts’ universe features vampires that get grand mal brain seizures when they perceive crosses (that is, intersecting lines at roughly right angles). The idea is that large right angles very rarely occur in nature, so vampires were able to flourish in antiquity, but as human architecture began wrapping civilization in boxes with walls, windows, roofs, etc, vampires would naturally stay away from cities and population centers, explaining their rarity.
In the story of course, humans developed drugs that inhibit that part of the vampiric visual cortex so we could subjugate them for study and free labor, but vampires are quite smart, so things predictably go off the rails…
“Echopraxia” by Peter Watts draws this idea further if you’re curious.
Uhhh let's at least wait until it's released. There's a lot of cool stuff out there already, we don't need to be declaring this development-hell game as the peak before it's even out.
Making a perspective projection from 4D to 3D, and then from 3D to 2D for display is simple mathematically, and it could be done in wireframe mode instead of what is currently, I think, a simple orthographic projection. In fact, it is very possible that the author tried it but didn't like it enough to include it.