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.
Reminds me of a scene from Schild's Ladder by Greg Egan. This is a conversation between an embodied human and a person who grew up in a completely virtual environment:
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'm pretty sure our brains are hardwired to perceive euclidean 3D space as a perspective projection onto our 2D retinas. We can only understand 4D space in an intellectual, non-intuituve fashion.
I think you'd be surprised how much our perspective can change. I'm not sure we can understand 4D, but I'm definitely sure we can think we intuitively grasp 4D.
It isn't intuitive at all. Try thinking of 3D as 2D space + time. It is weird. You may recognize a moving slice of a CT scan for instance, because it is a mostly convex object you are familiar with, but on more complex shapes (ex: a cage), all you are going to see are dancing shapes. Mapping a 2D animation into a 3D shape is even weirder.
And then you have rotations, rotating space into time and vice versa is one of the most confusing things you can do with dimensions.
Personally, I don't agree with this. I can't grasp the concept of 3D by only thinking in 2D + time.
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.
How I use time to visualize the 4th dimension is this:
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.
For the sake of discussion let's try it for 2D->3D: At each instant in time, your body has a 2D position on the screen. So the 3D shape of your body between t0 and t1 is kind of like the path your body took across the screen. You can create a 2D 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.
> That doesn't help me understand 3D space. It helps me understand 2D changing over time.
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?
The “3d object that changes with a variable (like time)” metaphor helps a little bit, but doesn’t really help to e.g. understand how a rotation of a 4d object plays out.
4D in games is something that sounds funner then it is. In theory it's some braintwisting geometric/spatial effects. In practice it's just a lot of geometry clipping into and out of view that doesn't lend itself to interesting gameplay. Despite marc's best efforts.
Maybe it's not really optimized to be finished. More like a continuous project he works on occasionally, maybe with some occasional years long writer's block in between. It's a unique idea that facilitates perfectionism.
> In practice it's just a lot of geometry clipping into and out of view
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.
Could beings that are naturally able to perceive 4D be tricked into thinking they could only see 3D?
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…
We can make ourselves to believe we are seeing 2D, or that 2D somehow has depth. So I am sure a hypothetical 4D being could do the same.
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.
The way architecture influences thinking is really fascinating to think about.
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.
What did I just saw... brings some memories from reading 3-body problem. Not sure how 4D represented on two 2D screens in VR can be grokked by my tiny brain. Or just ordinary 2D screen
Always love to see updates from this project. Miegakure is the peak of game design: not merely a Skinner box or masturbatory fantasy, it's an honest exploration of what-if, so far outside the realm of our daily 3D experience that the process of modeling it has been something akin to fundamental research.
SIGGRAPH actually released a technical paper by Marc Ten Bosch a couple years back. [0] Developers like him who put a decade+ of work into a project just because they love the subject are a direly needed example of what hard work can mean instead of a 'grindset' mentality.
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.
I haven’t had the feeling that computers are awesome in quite a long time (probably since starting my career). The video in the landing page gave me the feeling that computers can be such an amazing thing!
Another way is to realize waves of different frequency are literally orthogonal vectors. Also, RGB colors form a literal color space. So at the cost of sacrificing normally colored objects, you can have rainbow banding in the 4th direction. Imagine along the 4th dimension there's a hallway with evenly spaced lightbulbs tinted in RGB such that looking down the hallway you see rainbows. If you are moving in the direction of the 4th dimension, these rainbows will appear to be moving like waves rushing towards you from the vanishing point. If you are moving perpendicular to it, the bands of rainbow colors will remain constant relative to your motion. In general, the apparent speed of the background color banding patterns will be proportional to the component of your motion in the direction of the 4th d. The rings of rainbows are easily spaced, so looking at the scene you can tell how far along the W axis it is by seeing how tightly the rings are bunched (must be approaching vanishing point if they seem close) and also by just eyeballing how often the rainbow has repeated between your position and the object, judging distance as if you were counting floor tiles.
That's actually how we visualize 3D with our 2D retinas and monitors. It is a perspective projection: objects that are far away (in 3D) appear smaller (in 2D).
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.
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.