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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.

50 of 303 comments (clear)

  1. So Many Questions by eldavojohn · · Score: 5, Interesting

    So I've traditionally known "the fourth dimension" to be something like time. Although you can call it space-time or the relationship that our three dimensional world has with our concept of time. And in games like Braid (which is like an interesting two dimensional scrolling platform with four dimensional control), you get to have fun manipulating this time so that you can predict where your little character is when you slide back in time. It's where you were before.

    In Miegakure, it appears that the player is controlling a fourth dimension except it's not too clear what fourth dimension actually represents to me. If Miegakure's fourth dimension was time, we would see some indication of natural decay of the environment to give us visual cues that it's aging. For example, if one ring were made of steel and the other of wood, the wood one would decay as we go to the future and then we would make some action that is "special" (meaning that it is not subjected to our time control) and then move the steel ring into the wood ring and blast back to when the wood ring existed. Our special action could not be undone otherwise you wouldn't get anywhere with being able to control time.

    Miegakure seemed to invent non-natural transposed states of the environment that I, for the life of me, could not understand. How did I know which blocks would appear and disappear leaving only shadows? How do I know how far to go in a fourth dimensional direction? Must the player explore the available transposed states before planning their movements along all four dimensions? So that they can construct an interleaved solution?

    And what happens with a now block exists in a shadow space and you try to transposition yourself to the point when the shadow space is occupied by another block? Does the game block you from making that transposition? What if you want to transpose to a point beyond that when it is a shadow space again? Is this a blocking mechanism that will add to the difficulty of the puzzle?

    As someone ravaged by the Adventures of Lolo series on the NES, I could see a potentially high level of addiction here.

    --
    My work here is dung.
    1. Re:So Many Questions by pushing-robot · · Score: 4, Interesting

      Today's XKCD might help a bit. It's a world that has four spatial dimensions, like a hypercube.

      We haven't been able to find any evidence of "real" higher spatial dimensions (though theories abound), but thinking in an extra dimension is an interesting mental exercise nonetheless.

      --
      How can I believe you when you tell me what I don't want to hear?
    2. Re:So Many Questions by slim · · Score: 2, Insightful

      We haven't been able to find any evidence of "real" higher spatial dimensions

      Though superstring theory requires 10 or 11 dimensions of space (from what little I understand), so serious physicists really believe those dimensions might exist.

    3. Re:So Many Questions by Anonymous Coward · · 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.)

    4. Re:So Many Questions by Monkeedude1212 · · 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.

    5. Re:So Many Questions by Monkeedude1212 · · Score: 3, Interesting

      Well it depends on its rotation as well. For example a cube entering flatland would either pop up, stay the same, disappear, or dot-grow-shrink, depending on whether you are introducing the cube with one of the sides in parallel with the plane, or whether you to so with a vertice entering first.

    6. Re:So Many Questions by Anonymous Coward · · Score: 2, Funny

      (ever try to move back and forth in time?)

      I move forth in time every day, you insensitive clod!

    7. Re:So Many Questions by somersault · · Score: 5, Interesting

      This doesn't seem so much like a "fourth dimension" as a form of "subspace" or an alternate 3D reality (then again I haven't played the game and maybe am picking things up wrong from the video).

      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. Neither can 2 rings lain on a table, or two cylinders or two spheres be overlapped without breaking them somewhere. So how would adding another dimension allow you to join two 3D objects with a hole in the middle, even if you only moved one of them into this higher dimension?

      --
      which is totally what she said
    8. Re:So Many Questions by geekboy642 · · Score: 2, Informative

      You're only considering the trivial case. What if the 4d cube intersects our plane point-first?

      --
      Just another "DOJ fascist authoritarian totalitarian bootlicker" -- Zeio
    9. Re:So Many Questions by pushing-robot · · Score: 4, Interesting

      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.)

      I think that's the idea. It's hard to tell from the short video, but the blocky nature of the world implies to me that the game limits you to arbitrary "jumps" in each dimension. Just like the world could be divided into fixed-width planes in the X, Y, and Z dimensions, it looks like the W dimension is composed of distinct layers. Which would explain the shadows; they represent what would appear if you jumped to the next adjacent "slice" of 4d-space.

      --
      How can I believe you when you tell me what I don't want to hear?
    10. Re:So Many Questions by Garble+Snarky · · Score: 4, Interesting

      Here's one way to think about it: You have two concentric circles in a plane, they can't pass through each other in two dimensions. In three dimensions, the concept of "passing through each other" is no longer necessary for getting them "unlinked".

    11. Re:So Many Questions by ZXDunny · · 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 :)

      --
      10 PRINT "SCUNTHORPE"(2 TO 5): GO TO 10
    12. Re:So Many Questions by Per+Wigren · · Score: 4, Informative

      10 dimensions. There is a pretty easy to follow explanation on Youtube:
      Imagining the Tenth Dimension, Part 1
      Imagining the Tenth Dimension, Part 2

      --
      My other account has a 3-digit UID.
    13. Re:So Many Questions by somersault · · Score: 3, Interesting

      Hmm... well that would similarly work for a sphere containing another sphere.. but a torus or any other object with a hole is surely a different class of object.. I'm not sure what the 2D representation of a torus would be..?

      --
      which is totally what she said
    14. Re:So Many Questions by francium+de+neobie · · Score: 2, Informative

      I don't really understand what you meant.. but there are no 4D toruses in the video - it's totally ok to have 3D, 2D, 1D and point objects in a mathematical 4D space. The point of allowing movements in a fourth dimension is to allow the toruses to be joined without breaking them.

    15. Re:So Many Questions by Monkeedude1212 · · 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.

    16. Re:So Many Questions by francium+de+neobie · · Score: 2, Informative

      You don't need to imagine the shape of the object in 4D space. It's really simple - a purely 3D object in 4D space occupies no "volume" in the 4D space because its height along the 4th dimension is zero. So when you lift a torus, or any 3D object up in the 4th dimension, the object effectively disappears from the original 3D space. Then, as long as you don't move the object back to its old coordinate along the 4th dimension, you can move it in any 3D way you want.

    17. Re:So Many Questions by Ephemeriis · · Score: 4, 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.

      --
      "Work is the curse of the drinking classes." -Oscar Wilde
    18. Re:So Many Questions by losfromla · · Score: 2, Insightful

      serious physicists really believe those dimensions might exist.

      Serious physicists work on testable, proveable concepts. String theory is little more than an exercise in imagination and really hairy mathematics. It requires far too many variables to close and new ones are added as they realize that they can't get anything that resembles reality despite the wonderfulness of the math. I've (as an informed layman) have lost interest in this black hole for research funding. Serious physicists have too. The ones still "working" on string theory are doing so because dropping it would invalidate their entire careers.

      --
      Only I can judge you.
    19. Re:So Many Questions by HungryHobo · · Score: 2, Interesting

      I've been thinking about trying to make something like this for so long but I've never been able to work out a sensible way of switching dimensions.
      Looks like these guys managed to make a decent game out of it.
      I've gotta try this this evening.

      Original thought was to try for 6 dimensions which you could rotate through but of course the number of points you need to keep track of going exponential- 4 points for a 2D square/rectangle, 8 points for a 3D cube, 16 for 4D, 32 for 5D, 64 for 6D....

      this is an area which could potentially make for some really unusual and head bending games

    20. Re:So Many Questions by SoVeryTired · · Score: 2, 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.

      --
      Slashdot: news for Apple. Stuff that Apple.
    21. Re:So Many Questions by nahdude812 · · Score: 2, Interesting

      A cube entering FlatLand at (45,45,45) degrees of rotation would appear at first as a dot, then grow into a triangle. Then the corners of the triangle would split into line segments which would grow while the original segments shrink until it becomes a triangle again, and eventually a dot and nothing.

      Interestingly at no point would it possess four sides, so to a flatlander, it would be very hard to conceptualize that this is a construct made up of squares (a concept they would understand).

    22. Re:So Many Questions by leonardluen · · Score: 2, Interesting

      It is very much like a spacial dimension, speaking as a physicist; however, it is also very different.

      How is it different? why not just consider it indeed being the same as any other spacial dimension? one in which we have a constant velocity that we currently don't, and maybe never will, know how to change. even if 2 objects in our universe have the same coordinates in 3d space they will still miss each other if their 4th dimension of time is different...ie many cars make it through an intersection because they go through at a different times...when their time is the same is when you have a crash...

      that we have a velocity, imparted on us by the big bang, in the time dimension that we don't know how to alter, does not mean it isn't a normal 2 way dimension like the other 3 standard spacial ones. at least to me, thinking of it as being the same as the other dimensions makes for a much simpler model of the universe...remember the earth also used to be the center of the universe back when we didn't know any better.

      maybe i am getting off base here, maybe Einstein already mentioned something like this, but my hypothesis is that the speed of light isn't just a speed limit, but also a constant. everything the sum of all velocity for every object in all spacial (plus time) dimensions in the universe is always the speed of light. ie assuming your are sitting still at a computer, we are currently moving at the speed of light in the time dimension. as we increase our speed in the 3 spacial dimensions, time moves slower for us (according to Relativity) thus we are reducing our velocity in the time dimension. so our velocity through time plus our velocity in all spacial dimensions equal some constant strongly related to the speed of light.

    23. Re:So Many Questions by theCoder · · Score: 2, Informative

      Project Gutenberg also has it: http://www.gutenberg.org/etext/201

      --
      "Save the whales, feed the hungry, free the mallocs" -- author unknown
    24. Re:So Many Questions by TerranFury · · Score: 2, Interesting

      Watching the video, it appears (1) that the objects are all cubes, and (2) that all movement (in all dimensions) is in cube-sized jumps (although these are animated smoothly). This makes me think that the underlying representation is as 4d voxels.

      If I'm counting cubes right, then the world shown is about 9x4x6 cube-units in the x,y,z-dimensions, and maybe 4 cube-units in the w-dimension. So you need a 9x4x6x4 voxel grid; that's 864 voxels, and can be represented as a bitfield with just 27 32-bit integers. Not bad at all.

      From reading the website, it seems that one can simply choose which three dimensions you see on the screen at any time. In the video, the ring they show lives in a 2d slice of the voxel grid. Then there are two axes which are orthogonal to this slice, and it appears that when in the video they "go into the fourth dimension" what they are doing is switching between which of these two dimensions they are appending to the two the rings lives in to get the three dimensions they display.

      I wonder if they enforce that you select dimensions in a way that is orientation-preserving (e.g., you can't go (x,y,z) ---[swap z/w]---> (x,y,w)--->[swap y/z]--->(x,z,w)--->[swap w/y]--->(x,z,y) )?

      Anyway, it seems that this "toggling dimensions" thing is not animated in any particularly tricky way. What would be absolutely awesome though is if they, as you suggested in your post, actually animated a continuous rotation between the two. Since each exchange only swaps two coordinates, each rotation is really a 2d rotation, and can be represented as a Givens rotation; all they need to do is interpolate the angle. The one issue though would be computing the intersection of your 4d cubes with your 3d subspace as you do this interpolation, since your intermediate shapes won't be cubes...

    25. Re:So Many Questions by spazdor · · Score: 2, Informative

      No, that's the zeroth. A point has no dimension.

      --
      DRM: Terminator crops for your mind!
    26. Re:So Many Questions by Late+Adopter · · Score: 2, 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".

    27. Re:So Many Questions by somersault · · Score: 3, Funny

      .

      (This is to get around the lameness filter)

      --
      which is totally what she said
    28. Re:So Many Questions by leonardluen · · Score: 2, Insightful

      So einstein is the last person that will ever make a scientific discovery?

      to be a constructive debate you could at least have the courtesy of saying what part of what i said doesn't really make sense, and provide examples why. or provide examples of why none of this is testable and thus doesn't meet the criteria of a proper scientific theory.

      much of what i said is already indeed supported in by relativity, i am merely taking a step further.

      yes there is an idiot in this thread, however it isn't me.

  2. Flatland by Kagura · · Score: 4, Funny

    This article was written by the most hideous of triangles.

  3. Re:xkcd by toastar · · Score: 5, Insightful

    Actually i think the poster stole it from him.

  4. Re:xkcd by somersault · · Score: 5, Funny

    Now I know what us 6 digit users must look like to the 5 digit users..

    --
    which is totally what she said
  5. Re:xkcd by Pteraspidomorphi · · Score: 3, Funny

    ...You insensitive clod!

  6. The Fourth Dimension? by jimicus · · Score: 2

    Didn't they get to number six with "Baby I Want your Love Thing"?

  7. Re:xkcd by A.+B3ttik · · Score: 2, Interesting

    If there's nothing to download, how did he play it?

  8. Spatial dimensions and geometric projections by valderost · · Score: 2, Insightful

    I haven't wtfv (watched the video), but 4-D can be represented in 3- and 2-D using projections, just like we regularly watch 3-D images projected into 2 dimensions (TV, video games).

    Think of a cone, a 3 dimension shape. In the 3-to-2 dimension projection, that cone can look like a triangle, a circle, an ellipse, or an ellipse with a point, all depending on how you rotate it.

    Now imagine that there's a 4-D shape whose projection changes appearance as the shape is rotated about its fourth-dimensional axis. There's no reason you can't have one projection of it that shows a cube, and another of the same object that shows a sphere.

    It's tough to conceive of what this shape looks like since we can't see or experience it in four dimensions. But it's still possible to develop enough of a concept of the shape to recognize its various projections, learn how they're connected, and eventually be able to navigate it.

    Projecting a shape from 4 to the 2 dimensions of a screen will lose an awful lot of information, but we seem to be good at developing a 3-D concept based on motion and visual cues.

    Interesting stuff.

  9. Re:xkcd by Aladrin · · Score: 4, Funny

    You want to know how a character in a fictional cartoon universe played a game that doesn't exist yet?

    --
    "If you make people think they're thinking, they'll love you; But if you really make them think, they'll hate you." - DM
  10. abstrusegoose.com by iYk6 · · Score: 2, Interesting
  11. string theory by malp · · Score: 3, Insightful

    providing no unique, testable predictions for over 20 years...

    1. Re:string theory by Rogerborg · · Score: 4, Insightful

      providing continuous funding for non-disprovable theories for over 20 years...

      Fixed that for you. Try to focus on what's really important, will you?

      --
      If you were blocking sigs, you wouldn't have to read this.
  12. W-axis by AlpineR · · Score: 5, Funny

    Actually, there is a demo to download. You just have to move your mouse along the w-axis to reach the link.

    1. Re:W-axis by moonbender · · Score: 5, Funny

      I think there's an option in xorg.conf to make the mouse wheel do that.

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      Switch back to Slashdot's D1 system.
  13. Another 4d game by danhaas · · Score: 3, Interesting

    If you want to try another 4d game while Miegakure doesn't release, check http://harmen.vanderwal.eu/hypercube/ The objective of the game is to push the big ball towards the blue cross, then move the cursor to the square. You will then be outside the box and have to reach the green square again, while you avoid the small ball. Try it in 2d and 3d before going to 4d.

    1. Re:Another 4d game by dstech · · Score: 2, Informative

      There's also a 4d space shooter, adanaxisgpl: http://www.mushware.com/

  14. Re:I see what he did there... by shadowrat · · Score: 2, Informative

    It's more than a shadow dimension. Objects can extend into any of 4 dimensions, x,y,z,w. it's a game of visualizing how an object is shaped while only seeing 3 of those dimensions. The shadows are a hint of what's in the unseen dimension. At any point, that unseen dimension could be x,y, w, or z.

    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?

  15. Re:xkcd by Spy+der+Mann · · Score: 3, Insightful

    Has anyone of you noticed the pun behind A. Square's words?

    Guy: "Hey, A. Square, how's flatland?"
    A. Square: "Still flat. What's up?"

    Take a look at the picture, and notice that there is no "up" in flatland. So, was A. Square's question metaphorical, literal or philosophical?

  16. Re:xkcd by ZorbaTHut · · Score: 2, Informative

    There were playable demos at both GDC and PAX. I presume he was at one of those, possibly both.

    --
    Breaking Into the Industry - A development log about starting a game studio.
  17. Re:I Suspect String Theory is Just Wrong by node+3 · · Score: 2, Insightful

    That's why there are only five elements, Earth, Air, Fire, Water and Quintessence, instead of the hundreds those wrong-headed "scientists" seem to think must exist. They claim there exist so many that they have to lay them out in a table to even make any sense of them! What's worse, they don't even know how many more there can be.

    And Newtonian physics is far simpler than quantum theory, as well as simpler even than relativity. Aether is simpler than space-time. Creation is simpler than evolution. Homeopathy is simpler than medicine.

    And don't even get me started on chaos theory!

  18. OK, lets try this in 1D: by s-gen · · Score: 3, Interesting

    a line:
    ______________________

    a "ring" called "A":
    __A_____A_____________

    and another "ring" called "B":
    __A_____A___B_____B__

    lift "B" into the second dimension:
    _____________B_____B__
    __A_____A_____________

    slide "B" across:
    _____B_____B___________
    __A_____A_____________

    drop "B" back onto the line:
    __A__B__A__B_________

    "A" and "B" are now "linked" in the 1D universe.

  19. That "explanation" is a load of made up nonsense by mdwh2 · · 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.