Gaming in the 4th Dimension 303
Wolf pointed me to a video clip demonstrating this game:
"Miegakure is a platform game where you explore the fourth dimension to solve puzzles. There is no trick; the game is entirely designed and programmed in 4D." Nothing to download yet.
xkcd (Score:1, Informative)
Wow, Randall must have some timing
http://xkcd.org/ [xkcd.org]
Re:So Many Questions (Score:5, Informative)
Time is not "the fourth dimension." It is very much like a spacial dimension, speaking as a physicist; however, it is also very different. This is clear both from experience (ever try to move back and forth in time?) and mathematically (via the signature of the metric of spacetime).
In this game, the fourth dimension is simply an extra spacial dimension. Consider the analog of "linking two rings" in a 2-D world: put one circle inside another. Well, if you're stuck in a plane, it cannot be done -- simply move outside of that plane into 3-D, and it's simple. In Miegakure there is a 4th spacial dimension. You can move in this fourth dimension without moving in any of the other three.
Yeah, it's weird. I'm not entriely clear as to what the shadows represent (except, maybe, for a helpful reminder as to what is "next" to you.)
Re:So Many Questions (Score:5, Informative)
Miegakure suggests that there is a fourth spatial dimention, just like the three you are used to seeing.
Take a read through Flatland, its a short story based on a square who lives on a 2 dimentional plane. Basically how he can only see things in 1 Dimension (a line) because him and his world are on a single plane. Now, imagine his world lives within our 3d Realm. His life doesn't change much, until we choose to interfere. Imagine if you slid a ball through his 2d plane. He would at first see nothing, then a dot, then that dot grow into a line, then it shrink, into a dot, and disappear.
Basically someone took this idea, and imagined what it would be like if there were a 4th spatial dimension we were unaware of (physics has however shown us that there isn't one). If someone pushed a 4d Cube (or hypercube) through our 3d plane, what would we see? Nothing at first, then a cube show up, then it grows into its full size, then shrink back down, and disappear.
Now someone has taken that idea and put it in a game. The programming is actually simpler than it seems. Instead of testing XYZ co-ordinates you are testing WXYZ co-ordinates.
Re:So Many Questions (Score:0, Informative)
If someone pushed a 4d Cube (or hypercube) through our 3d plane, what would we see? Nothing at first, then a cube show up, then it grows into its full size, then shrink back down, and disappear.
No, if someone pushed a 4d cube through our 3d plane, we'd see nothing, then a cube for a while, then nothing (no growing or shrinking). To get what you described, the object would need to be round in the fourth dimension.
Re:So Many Questions (Score:3, Informative)
You're only considering the trivial case. What if the 4d cube intersects our plane point-first?
Re:So Many Questions (Score:5, Informative)
Take a read through Flatland, its a short story based on a square who lives on a 2 dimentional plane. Basically how he can only see things in 1 Dimension (a line) because him and his world are on a single plane.
The XKCD alt-text contains a nice in-joke about flatland (IIRC) - all women are straight lines, and the more important a member of society, the more sides he has - a priest would be almost a circle, as he has so many sides he looks circular. The alt-text goes: "Also, I apologize for the time I climbed down into your world and everyone freaked out about the lesbian orgy overseen by a priest." Which is what the flatlanders would see when a stick-man enters their world :)
Re:So Many Questions (Score:5, Informative)
Imagining the Tenth Dimension, Part 1 [youtube.com]
Imagining the Tenth Dimension, Part 2 [youtube.com]
Re:So Many Questions (Score:3, Informative)
Re:So Many Questions (Score:5, Informative)
Think about it this way:
You put a box inside a safe. That safe has no doors. How do you get the box outside the safe? You slide it through the fourth dimension - so that the walls of the safe are no longer in the way. You change its XYZ co-ordinates, slide it back through the fourth dimension so its about where it began. The box is now outside the safe.
If thats still a little tricky to understand, we'll explain it flatland style.
You draw a circle inside of a square on a piece of paper. How do you get the circle outside of the square (assuming you can't move the lines through each other). Well, if you had the ability to take the circle off the paper, move it a few inches, and place it back on the paper, you would have moved it outside of the square with no intersection taking place.
The same thing is happening here, you are taking two rings, sliding them among a dimension that they do not occupy (thus removing any chance for collision) and then putting them back. Its tough to wrap your mind around, I know.
Re:So Many Questions (Score:3, Informative)
Re:So Many Questions (Score:5, Informative)
I don't see how adding another dimension can magically allow two objects to become linked when they were unable to be linked in a lower dimension. Two circles on a piece of paper cannot physically merge with each other if you assume their boundaries are solid and cannot pass through each other.
Say we've got two circles drawn on a 2D plane - a sheet of paper. Assume their edges are physical boundaries - if you push them together they'll bump into each-other, not merge or join.
Now, pick one of those 2D circles up off of the page. It no longer occupies the same 2D space that the other circle does. You can move it back and forth without it bumping into anything, because the other circle is stuck down on the piece of paper.
If you move the two circles so that they're overlapping a bit, like a Venn diagram... And then drop that circle back onto the 2D plane of the paper, they're now overlapping or linked. Even though that would have been impossible to do in just two dimensions.
Re:I see what he did there... (Score:2, Informative)
when you are manipulating the objects, it's not like the shadow world in zelda where a door might simply not be there. that shadow world is like a parallel world in the same dimensions. This game is all about one world in 4 dimensions. You have to hold in your head, a 4 dimensional image of what the volume of the object actually looks like. Often the puzzles involve manipulating the objects through many dimensions.
It bears a lot of similarity to the paper mario games, except it's easy to imagine and hold a 3 dimensional model of the world in your head. the 4th dimension is (for most people) hard to visualize.
try imagining a cube in x,y,z, then imagine that it has some planes extending out in the z,w and x,w planes. wtf does that look like? Where do you need to be in x,y,w to be standing on the right plane in x,z,w?
Re:So Many Questions (Score:3, Informative)
Topologically, the torus can be identified with something called S1xS1 (the cartesian product of two "one-spheres", aka circles).
Likewise, the n-dimensional torus is the cartesian product of n copies of the circle.
This means that the one-dimenstional torus is just the plain old circle. In one dimension, the torus and sphere are the same thing.
Re:Another 4d game (Score:2, Informative)
There's also a 4d space shooter, adanaxisgpl: http://www.mushware.com/ [mushware.com]
Re:So Many Questions (Score:3, Informative)
Project Gutenberg also has it: http://www.gutenberg.org/etext/201 [gutenberg.org]
Re:xkcd (Score:3, Informative)
There were playable demos at both GDC and PAX. I presume he was at one of those, possibly both.
Re:So Many Questions (Score:3, Informative)
No, that's the zeroth. A point has no dimension.
Re:So Many Questions (Score:3, Informative)
How is it different? why not just consider it indeed being the same as any other spacial dimension?
You can consider it however you like, if it's helpful. You have to be very careful in conversations like these to restrict your hypotheses to ones which have real observable consequences. Otherwise you wander away from science into philosophy, which is a fine conversation to have, but not one that scientists would enjoy having with you =P
General Relativity, being the most accurate model to-date of time and space themselves, treats time as a dimension, but one with slightly different mathematical properties. In taking the magnitude of a 4-vector, you *subtract* the square of the time component. This makes it possible to get negative distances, which is what "light-cones" attempt to visualize: in the interior of the cone are "time-like" points, where they are separated from the origin by a negative distance (under this sign convention), and are capable of influencing each other causally. The opposite would be "space-like" (nothing I do on Earth now can affect what someone on Alpha Centauri does now, and vice versa), and the boundary on the cone itself is "light-like".
That "explanation" is a load of made up nonsense (Score:2, Informative)
I've seen that video before, and sorry, but it's a load of rubbish - there is no mathematical or scientific basis to what he talks about above 4 dimensions.
The many worlds interpretation of quantum mechanics is just an interpretation - quantum theory does not tell us that it is true. But even if it was true, it makes no sense to call this the 5th dimension. Yes, colloquially in sci-fis, we call in "travelling to another dimension" when people travel to parallel universes, but mathematically it makes no sense to call it a dimension (which implies a continuum - if the universe splits into two, what's the universe halfway between them in this 5th dimension?)
To then say that the 6th dimension is simply magically jumping through this 5th dimension makes no sense at all. From this point onwards, there isn't even any vague relevance to science - he's just making it up as he goes along.
And lastly, this has nothing to do with the dimensions of string theory - if these exist, these would be additional spatial dimensions, not the nonsense that he's made up.
The frustrating thing is that the video is presented in a friendly way that makes it seem convincing - no doubt the reason why it's been propagated around the web, and you got modded up for it.