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Gaming in the 4th Dimension
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.
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.)
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.
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 :)
10 PRINT "SCUNTHORPE"(2 TO 5): GO TO 10
10 dimensions. There is a pretty easy to follow explanation on Youtube:
Imagining the Tenth Dimension, Part 1
Imagining the Tenth Dimension, Part 2
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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.
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.
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