Flatland: A Romance of Many Dimensions is an 1884 satirical novella
by the English schoolmaster Edwin Abbott Abbott. Writing pseudonymously
as "A Square", the book used the fictional two-dimensional world of
Flatland to comment on the hierarchy of Victorian culture; but the
novella's more enduring contribution is its examination of dimensions.
'In a tribute to Edwin Abbott's Flatland, a classic mathematical fantasy about a 2-dimensional being (A. Square) who receives a surprise visit from a higher-dimensional sphere, Rudy Rucker's Spaceland describes the life of Joe Cube, an average, modern-day Silicon Valley hotshot who one day discovers the fourth dimension from an unexpected visitation. Spaceland contains scenes that are violent and sexual in nature as well as suggestive illustrations.'
For simplicity, my rendering engine is a dead-simple raytracer which doesn't even bother with reflections- just cast rays and record the first surface they run into. Handling rotations and projections is really easy, but there are two problems I have found:
1. It's just really frickin' slow. Raytracing just ain't fast enough, though I may be able to find some additional optimizations to make it better.
2. In terms of gameplay, navigating the space is really, really hard. It is so easy to get completely lost regarding which direction you're facing and what hyperplane you're on when you can make arbitrary rotations in all four dimensions. It might be something I could get used to, but so far I feel like it's practically necessary to have some mechanism that will snap you back into alignment with some set of gridlines.
EX: walls in the way. <Set bomb off> Walls gone but cave collapses. <walk though wall> <go back in time> <keep walking>.
Or simply let you flip times direction. Going vary slow or backward prevents changing things, but you get to move. So, you might be able to for example walk on water when moving backward in time etc.
It's a different concept than true 4D though.
My favorite 2048 variation was the 4D version. It was trippy but I felt like I got my head around that. I think it was because the game rules were so simple that instead of trying to visualize what was going on, my brain just accepted the patterns.
We see in 2 dimensions and we infer the third from various cues. (The quote that we are "dimly aware of a fourth", which you may have heard, refers to time and is a different issue than a fourth spatial dimension.)
We have three dimensions, all orthogonal to each other. We can translate, rotate, and project things in between them.
So all we can do is apply those same principles and see what comes out - we shouldn't expect it to match anything recognizeable though.
xy, xz, etc. are not planes in 4d space - they are 3d-hyperplanes, and perpendicular to them are planes, not axes. Imagine this: you have a 4d vector and you hold x and y constant. You still have 2 degrees of freedom: a plane, not a line.
There are **infinitely** many 3D worlds stacked on top of
each other, even if in the Wall level the ground texture
makes it seem like there are only two.
Needless to say, it is confusing to the point of unplayability past a certain point, but utterly fascinating.
You can grab a copy from your Ubuntu, Fedora, or Arch repos, and it is certainly worth trying to wrap your head around for an hour or two, if you are into that sort of thing.
But when he got to the 4th dimension it didn't make much sense as an explanation (rubble from 3rd dimension showing up in the 4th).
However, if the 4th dimension was time, then you would walk back (or forward) in time to when the wall wasn't there (isn't there anymore cause it is now rubble), move "past the wall", and then walk forward/backward to the original time.
4th dimension is still time. 'The button' takes you to your character's view of moving across a 3rd dimensional plane. I'm assuming the two different textures on the ground represent the change in the 4th dimension (time).
So when you cross to that other side and hit the button again, you're back in the 3rd dimension across a different plane (time). So the desert area is either in the past or in the future (when the wall fell or was being built).
Then he goes through the wall and hits the button again and walks back to his original 3rd dimension.
That's what I took from it anyway. Seems really neat.
No, time is actually a 5th dimension in this 4D game projection.
The developer has actually done the proper 4 to 3D projections, like he has done for the 2/3D that he shows in the beginning.
In the 2D to 3D you can definitely see that he's not moving through "time", because you can see the 3rd dimension.
The problem is just that we can't intuitively visualize a 4th spatial dimension that makes this difficult.
But he's definitely not moving through "time" or in some "past" when the "wall wasn't there". And of course moving through time has different properties than moving through a 4th spatial dimension, so it's not really comparable.
E.g if we had a gradual rise in temperature from 0oF to 100oF in the time-dimension, then if you could move through the time-axis you'd experienced different temperature at will, whereas moving through any spatial axis would you'd only feel a partial rise in temperature.
Granted, you had me at “This game isn't real life!”
We could also have multi-dimension time dimensions as well. The idea of parallel universes where at least one decision is made differently from our own could instead be different dimensions of time. Move to the left or right in time and experience different choices as opposed to only going forward as I assume most of us do now. :D
Time is only called "fourth" because we just add it as an extra to the 3 spatial dimensions we perceive intuitively. Not because there's some specific order.
There can be an arbitrary number of special dimensions in mathematics (hence hypercubes, etc).
And according to some (quite prevalent) physics theories, there are actually more than 3 spatial dimensions in the actual reality -- string theory calculations give 10 spatial dimensions.
If I write an equation, and graph it, it has as many dimensions as variables. Those variables might have nothing to do with time OR space.
No. Only in science fiction novels.
It'd need to be measured in meters to make sense as a real 4th dimension.
In the 3D/4D world, the rubble fell off the wall and landed next to it.
I'm not sure how truly 4D this world is, but it appears to let you switch between a fixed set of different 4 dimensional positions, each of which has a different 3D representation. Just as a plane in a 3D environment is a 2D slice, a plane in a 4D environment is a 3D slice. You could effectively fake this by imagining a triangular prism (like a cylinder, but triangular instead of round). Each face of the prism contains a fully defined 3D world. Switching to the alternate face of the prism is effectively doing the swap to the other 4th dimension, where you can walk along the alternate 3D environment to avoid the obstacle, then switch back to the original 3D environment.
> That's not quite what a 4th dimension is like.
"Flipping through dimensions is remarkably intuitive- [...] I shifted dimensions, messing about with this strange toy until I quickly understood most of the problems that I faced."
Have you read stories about people who implant magnets? After a while they develop a sense of direction. Brain adapts to new signals and starts to interpret them.
Different example, I remember reading about experiment where people had to wear glasses that flip the picture upside down. After not too long time they adapted and saw things normally. And everything would be upside down when taking the glasses off.
Yet another example is asking blind people what they see. They don't see black or grey, the sense of vision simply isn't there. Like our sense of 4th dimension isn't there.
So, one thing to try would be to give us sense of rotation and acceleration in 4th dimension and see how it goes. Next, maybe, a new "color channel" for our vision, and let the brain figure out how to represent it "internally".
Basically, they're not just 'hearing' in the traditional sense, though that happens as well; they're also 'seeing' the sound that bounces back. Kind of crazy
This is another vid trying to explain the same thing - https://www.youtube.com/watch?v=UnURElCzGc0
I really want to believe this is possible and this is how we'll be able to travel far into space. Like how we have to spend time walking around a very long wall when a bird can just fly over it in a fraction of the time, we wouldn't have to think about traveling light-years because there would something else we can do that's faster than a straight line.
You could make a shortcut in space, which is called a wormhole. You can either make one using extra dimensions, or in 3 dimensions with negative energy to stabilize it, but neither of those seem to exist. Edit: link https://en.wikipedia.org/wiki/Wormhole#Traversable_wormholes
The simplest example is about time - we (humans) have notion of time "entirely" due to the certain properties of our environment in which we have evolved - that there is day/night, Moon phases, seasons, periodical changes (due to rotation of the planet and its motion around the Sun, of course, but this is a very recent discovery).
Now imagine that you are somehow "suspended" in the outer space without any motion relatively to the Sun. What would be your notion of time?
The time of a certain process (a mass in motion) has nothing to do with time of another, completely different process (like radioactive decay) and the notion of some "common, universal time" is just a "creation of the mind" which is very handy and useful but "does not exist in reality".
Ancient Buddhist notions of "emptiness" or "void", and pre-Buddhist (Upanishadic) notions of "everything is mind" (which is wrong, but very close and accurate) are insights to the same "truths".
Your "dimensions" are "primitive concepts" of the same kind. Any coordinate system imposed on so-called "reality" is nothing but a "concept of the mind".)
That sounds very philosophical and all, but it seems to me that we have an internal perception of time based on the rate that electrical impulses propagate throughout our brains. Perhaps it would be distorted based on the lack of external stimulus, but I believe we would feel the passage of time all the same.
In the meanwhile, can anyone help me out?
In the 2D->3D example, you have one shared axis (Z -- vertical), and an alternating pair for the second axis (X and Y -- horizontal). In effect, from the 2D character's point of view, 'jumping' into the third dimension is just swapping your horizontal axis. Your previous horizontal axis is a vertical section through your current one, and vice versa. As such, when swapping axes, you would expect one 1D line (ie. a 1-pixel-wide vertical band) to be the same before and after the swap.
When going 3D-> 4D, you have 2 shared axes. Your third axis alternates, as before. When switching between your 'third' axes, then, you would expect one entire 2D plane of your perceived world-view to remain the same. This doesn't seem to be the case.
What am I missing?
 EDIT: This plane is likely to be a section through some concrete objects, so you won't necessarily have 'seen' it before, though it will have been there.
You can see when the 4D rotation occurs there, that in that plane, everything stays constant (e.g. rocks stay there, trees, etc.) You just look at the objects from different angles as it rotates.
Edit: Link to the relevant point in the video - https://www.youtube.com/watch?v=9yW--eQaA2I#t=148
So, in the video. The Z axis doesn't change (up and down) so that's one axis. The other one that doesn't change is at a 45 degree angle from lower left to upper right. Watch the tree: it is just as wide along this axis as it was before. Everything else sort of smoooshes around but that plane stays the same.
I suggest interested people check out adanaxis, a 4D space shooter. It's not particularly playable, but it is true four-dimensional space with four-dimensional spaceships zipping around.
For the second case, maybe it's the ground plane that's the same; it certainly has some of the initial texture in it, but it's been rotated and it's now seen from a different angle. But now we can tell the different because it varies along the dimensions it rotated around.
Or maybe I just can't visualize the rotation through the fourth dimension... I'm not sure.
The top comment on this stack exchange thread has more: http://physics.stackexchange.com/questions/55824/is-imaginin...
Maybe they will implement some more levels to make it look seamless. But there is simply too much work to design the world in 4d as a single piece of land holds a lot more information.
Einstein proposed a test to find out. I'm hoping this test will eventually be Gravity Probe D (Probe C will be a repeat of the failed Probe B).
And the game world has some super weird discrete geometry anyway.