New Trailer: How to walk through walls using the 4th Dimension

An explanation of how walking through walls would actually look like if you could move in 4D.

This doubles as an explanation of how Miegakure works (finally! Also SPOILER ALERT) and what the fourth dimension is.

Ever since people discovered the concept of a fourth dimension of space around a century and a half ago, they have tried to come up with what would be possible if space was actually four-dimensional. Walking "though" walls would be one of the simplest consequences of being able to move in 4D space. But what would it actually look like? It's not often that watching a video-game trailer actually teaches you about real math.

Of course, if you have watched the video, you know that it is not "through," but rather "around" walls, despite what this movie poster or this comic book character, for example, would lead you to believe.

Additional Notes:

  • From the perspective of a regular 3D observer standing next to the wall the player character would suddenly disappear, and a few moments later reappear on the other side of the wall (assuming the player character is very thin along the fourth dimension).
  • 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. A more complex example is the shape at the beginning of the trailer, which is a true 4D shape called the 120 Cell, as explained here.
  • Yup, the 2D/3D section is part of the game. There are more 2D levels. Not going to spoil how you get access to them.
  • The 2D/3D section has been part of the game since I first showed it at the Experimental Gameplay Workshop 2009 a couple months after making the prototype. At first I made it in order to explain the game, but it seemed like a good idea to make it part of the game itself.
    I took inspiration from Flatland (of course) and Super Paper Mario for the aesthetic. I couldn't resist having the game contain its own Demake ;)
  • Fun anecdote: the code that handles movement in 2D/3D is the same as the code that handles movement in 3D/4D, but one axis is ignored ;) The display code is of course different, but it reuses a bunch of stuff.

This trailer took a long time to make! It will be the basis for talking about the game more.
The pixel art was done by G.P. Lackey and the music by Disasterpeace & Mateo Lugo. I love how it turned out!

Big thanks to Vi Hart [Youtube Channel], Chris Hecker [SpyParty], Brady Haran and others for their suggestions on how to improve this video.

Oh I forgot to post here that we will be showing the game at PAX Prime, as part of the Indie MEGABOOTH.

53 Responses to “New Trailer: How to walk through walls using the 4th Dimension”

  1. Hemlock Drew says:

    Ohhhhh, I'm slowly starting to get it! 🙂

  2. Steve Sybesma says:

    Hello Mark,

    Let me know where the trailer is so I can view it.

    Link was not in the email.

    Thank you!

  3. Aaron Holman says:

    I have wanted to play a game like this since I read flatland in high school. On the gameplay side, what about making movement in the 4th dimension a little more natural by tying movement along its axis to a slide control or two keys?

    • marc says:

      The problem with straight 4D movement is that you can't see where you are going, so you bump into invisible things.

      • Anon says:

        The part that confused me is:

        If in 2D (Mario world), we're seeing a projection of a 3D world, then our character exists in 3D. By rotating the view into the third dimension, we expect to see a different projection of this character: his front, rather than his side. (In this video, you kind of cheat by showing a "3/4 view" in both cases, which is fine, and not relevant to my point.)

        So in 3D, we're seeing a projection of a 4D character, but when I rotate the view to show the 4th dimension, that means I expect to see a different projection of my character. As a character, I've got height and width and depth, and in 3D those dimensions of my character occupy the three orthogonal axes I'm used to. When I rotate the view to walk through the 4th dimension, suddenly my width or depth (pick one) is extending into the 4th dimension. The new axis is showing both the 4th dimension (in space), and also the 2nd or 3rd one (in my size).

        (My first thought was that maybe the character just happens to look identical in both the 3rd and 4th dimensions, but that can't be the case, because he can turn around in the 4th dimension view.)

        That's the main argument I see for straight 4D movement: it doesn't display the 4th dimension in counterintuitive ways. Of course, the downside is that you can bump into things you can't see. If *I* were designing such a game 🙂 I would be OK with that, because I've played lots of old games where you can bump into things which you couldn't yet see. Consider a 2D adventure game of screen-sized rooms, where there's an opening (door) in this room but the next room is blocked.

  4. Steve Sybesma says:

    Yep, figured that out right after I left the post...thanks.

    Extremely interesting stuff. It would be like a 2-dimensional character getting across a line by jumping over it into 3-dimensional space, going a short distance and dropping back into the same 2-dimensional world he started from.

  5. Sebastien Binet says:

    Very-very good way to explain the 4D.
    Very professional video.

  6. Molkavi says:

    I loved the video! Idk why but it made me think of an isometric Shenmue. Still, overall kind of a tough concept to wrap one's head around, no?

    Considering this, could I offer a slight suggestion on how to improve the occurring phenomenon's explanation? It may not be precise, but given the accompanying footage it could fly and do a solid job. Something along the lines of:

    "...you just need to find a time in which the wall is not an obstruction".

    Can't wait to get a gnarly claw around this one!

    • Anon says:

      ...but the 4th dimension here isn't a time dimension, is it? Time still exists like normal. He hasn't done anything funky with that -- unlike, say, Braid.

      Bringing "time" into the explanation would just confuse things more.

  7. Steve Sybesma says:

    Was thinking some more...with the caveat that the line the two-dimensional being sees does not actually extend (as a plane) into the 3rd dimension, he would be able to cross it, otherwise he may have to jump into the 4th dimension.

    In our 3-dimensional world, as long as a door or wall does not extend into the 4th dimension, we could go around it as well by briefly jumping into 4D space.

    It's too bad we don't have a way to prove that 4D space actually exists...don't think anyone has ever observed anyone or anything travel into and out of our 3D world yet, but if they did and we never observed the actual entry or exit, it's possible we might never know anyway.

  8. Mark P says:

    Nice. Very explanatory

    I have to wonder what it would like if the camera kept the same position and orientation in 4-space when the character turns and walks along along 4-space.

  9. Sebastian says:

    This looks like it could be a lot of fun and the trailer helped me understand the concept.
    What I didn't understand, though, was how the player is supposed to know what to do on that 4th dimension line. The rubble helped knowing when the wall was crossed, but apart from that, it seemed the player would have to rely on trial and error.
    I'm sure you have seen crush3D, where players can "squash" the 3rd dimension onto a 2D plane. In that game, you'd have to try and understand what the resulting 2D plane would look like in advance, so as to know what move to make.

    Is there there a way for players to preempt what the 4th dimension looks like an how to use it here?

  10. Steve Sybesma says:

    just had another idea that flips the limitations of being in the 2nd (or 3rd) dimensional worlds on their head...never thought about this before:

    say you have a line in the 2nd dimension world that has a segment that can swing out (what is essentially a door for the 2-dimensional world)

    just because you have a door for the 2-dimensional world, given the line that (closed) door is a part of extends as a unbroken plane into the 3rd dimension, does not have to mean that the door in the 2nd dimension is necessarily part of a door in the 3rd, meaning that only 2nd dimensional beings can pass through it

    meaning you can have a door in the 3rd dimension (a door being essentially part of a wall that swings out) which is not necessarily part of a door in the 4th dimension and therefore could be an impediment to a 4th dimensional being

    what say you?

    • marc says:

      You mean that the door has two parts, one thin and the rest of it that extends in the orthogonal direction? And that the thin part could open independently from the rest?

  11. Steve Sybesma says:

    yes, that does not seem to violate anything about the object's potential existence in multiple dimensions (assuming a 3rd dimensional wall with a 3rd dimensional door which we can see and go through ourselves)

    so, assuming we have a door which exists in our 3rd dimension does not guarantee that if the wall the door is attached to extends into the 4th dimension that there will be a door for the 4th dimension person to go through; it could just be a solid wall to them

    let me know if I'm not thinking about this correctly

    that is, in a sense, taking what you described and flipping it on its head...a wall to us may not be an impediment to someone in the 4th dimension (unless it extends into it); so, a door to us may not be a door to them

    it is interesting to think about these possibilities

  12. Steve Sybesma says:

    the assumption I make that lies behind this idea is that if our world is merely an infinitesimally thin slice of 4th dimensional space, then the objects in that 4th dimensional space may not be consistently 'solid' or even exist at all points or look the same at all points...that would be pretty safe to say, as that is true in our own dimension (an example confined solely to our dimension would be a 'hole' in something where every place else on the object is solid)

    so taking the 2nd dimensional view, you can have a tree for instance in our 3rd dimension...we cannot pass through it obviously...but how do we know that a 2nd dimension being cannot? there may be a 2-dimensional slice (plane) intersecting the tree that we can see, but where no tree is observed in that same spot for the 2nd dimension (if it did, it would be a round, flat object that the 2nd dimension people could see and would normally have to walk around) so, it may not actually be there for them...they walk right through as if nothing were there

    whew! taking a risk there...hope I don't sound too silly

  13. Karen Newcombe says:

    Love the video, I'm more of an open worlder than a platformer but I'm very excited about this beautiful thing, very much looking forward to having my brain twisted into knots!

  14. […] Check out the developer’s full explanation of their game here. […]

  15. This is an amazing concept, and if you are thinking that it takes time to actually see something, then you could consider that you are in 4th dimension going to 5th 🙂

  16. Patrick Huizinga says:

    Looking at this demo, it seems the rotation only happens over one axis. Is this a deliberate limitation for gameplay purposes, or will you be able to rotate using different axes?

    In your demo world you would then basically see a strip of 5x2, orientated roughly from top to bottom, where you would see a square of wall besides a square of rubble in the middle.

    And besides that, you can imagine even more ways to rotate the world. In the 2D world, for example, you could then rotate the world in such a way that the view would be from the top, where you would no longer be able to jump.

    • marc says:

      I will explain more in a blog post soon, but... Yes, it is deliberate that the rotation only happens on one plane. The reason is that it does not add enough to be worth making the game more complicated. Yep that's what you would see! And of course you don't really want to not be able to jump anymore.

  17. viewer says:

    I don't care for the 8-bit art style in the 3d demo much.
    I would much rather see it drawn in the same artistic fashion as the rest of the four-dimensional game. The whole 8-bit thing is a huge cliche among indie games that I wish would stop being used because it's getting quite stale.

    • Apromixately says:

      I thought that was common among indie games because it can often be done cheaply or even without an artist.

    • viewer says:

      Jesus christ, do the 2d sections have to be 8-bit? Why don't you at least try to make your game look like all the other indie shit out there right now.
      I'm bitterly disappointed that you didn't use a better art style for this section of the game.

      • marc says:

        Actually yeah, I should write a blog post detailing why we picked that style, but I will try to summarize it here. A big reason why we picked a pixel art style is that it allows us to edit the sprites by hand (each block is 16x16x16 pixels). If they were bigger than that, we would have to rely more on procedural generation, which is what we do for the main game. It felt like too much of a challenge to tackle making it look good, on top of the work we are doing for the main game. But mostly the reason is that we could edit them by hand, which felt much more interesting than trying to generate them. I also wanted to reflect the simplicity of the 2D section with the graphics. Anyway, worse case, the 2D section is totally optional!

  18. Dion says:

    That is so f*cking elegant. Both conceptually and the beautiful implementation make for an outstanding representation of how 4d space might be interpreted and interacted with.

    very cool
    D.

  19. Apromixately says:

    I think the main point to find this all a little more intuitive is to understand that all the objects extend along the fourth dimension as well.
    Very importantly that also includes the player and that is what determines how the player appears and disappears when he moves along the fourth dimension as seen by others.
    Basically if you imagine a 2D slice of 3D space into which you poke your finger. Then the 2D slice would look like an MRI of your finger and when you poke it in the finger magically appears in the middle. But because your finger is a 3D object with a 3D shape it doesn't just pop up but instead it starts very small (at the fingertipp) and then grows when you poke in further.
    Now if our 4D character has a 4D shape we could imagine him to be similar along that dimension. In this case he would always be visible and seem totally normal to 3D entities but he would be constrained by all objects along that dimension at once so he would only barely be able to move.
    If on the other hand the character would slowly fade away and disappear along the fourth dimension that would be what it would look like when the character travels along the fourth dimension.
    Another possibility would be that the character fades away to a blackish shape which has no collisions. In that case it would always be visible as some sort of ghost. 🙂

    Not sure why I wrote this, just amuses me to think about it. 😀

  20. […] watch this video and read the accompanying blog post for the low-down. I couldn’t possibly summarise it concisely and […]

  21. Vincent says:

    I still don't get it!
    It's easy to understand the 2D/3D example, because I can cleary see the 'connection' between the two 2D worlds ( e.g. the gravel ) while switching. I can understand why the gravel lies here and how this "new world" creates itself during the switch.
    BUT in the actual 3D/4D example I can not see the reason why it should be this way after the switch. Where are the connections? I feel a little angry that so many guys here think to understand the game. I really want to get my head around it, too.

  22. Jason says:

    I'm dumb. He's walking around in 3 dimensions still. I can only comprehend this as moving in 3d space while pausing time or continuing time as its experienced by the time-bound viewer. I'm just a simpleton and can't understand a tesseract as its depicted in 3d space. The 4th dimension to me is tied with space (space-time) so when moving in 3d space you would disappear and reappear at the same moment to the time-bounded viewer assuming you didn't change your 4th dimension.

  23. Thomas says:

    Hello Marc,

    I've followed your explanations and teaser videos since the xkcd reference (721) and tried to wrap my mind around the 4 dimensions game idea.

    Is it ok to mentally represent it as parallel 3D universes, or am I missing something ?

    Also, obviously at any given time, we're only seeing and moving along 3 directions, the 4th one having to be "switched" with one of the 2 "horizontal" (XY) ones - the vertical (Z) staying always the same - to be walkable. Is the one being exchanged (X or Y) always the same, or does it depend on where your avatar is facing ?

    Lastly, in most of your video examples, the "parallel" universes seem to be visually different (green/desert in the last video). While this is probably a game design choice as a hint to help understand what you're looking at (along with the background color change), this ruins the idea that the 3 "horizontal" directions are of the same nature, in favor of the "parallel universes" idea (2 directions actually horizontal, and one "sliding" one). Is this only true in the first tutorial levels, or is the "omitted direction preference" vanishing as you advance in the game ?

    Again, thanks for that mind-bending fresh idea of a game. I sincerely hope you get the success you deserve for that.

    • Thomas says:

      Ok, thinking a bit more about it, I now have mixed feelings about the "parallel universes" representation for a 4D world.

      It implies the idea that each universe is discrete, separated from its neighbours and you "jump" from one to one, whereas a 4-dimensions world would have every dimension continuous, so the added "sliding" dimension must be continuous too, and you can walk it.

      Except of course that in the game you use tiles, and (at least in this video) have a visually different environment when you move along the 4th direction, so it's probably good enough.

      I get most objects in the game are defined in 4D and continuous along the 4th dimension, like the Polydodecahedron, and probably rocks and trees. But what about that wall and rubbles (and build structures in general) ? They don't seem so continuous, probably 3D only.

      Oh well, I'm probably overthinking this with no actual support to test ideas. Can't wait to see your piece of art released.

      • marc says:

        The layers on the ground are just a texture. The games uses layers to make it easier to understand, but it is not limited to them. Worlds can interact with each other but I don't want to spoil exactly how.

        The wall is built out of 4D tiles, and the rubble is a bunch of hypercubes randomly deformed and rotated.

        Built structures like the windmill are extruded 3D objects, for obvious reasons. There are some real 4D structures though.

  24. Vincent says:

    How do you build/edit the levels? Can you show us a screenshot?

  25. Tom says:

    RELEASE THE FUCKING GAME ALREADY

  26. Marko says:

    Waiting for the game since i heard of it a few years ago... great idea, and looks like a great realization.

  27. Chet says:

    This is a very interested concept. Its interesting to notice that the 4th dimension is binary. There are only two discrete states. What if the 4th dimension were continuous? That would leave an infinite amount of 3D existences.

  28. Felewin says:

    Use the 4th, Luke!

  29. Stevan Allen says:

    Dividing a 4d object with a 3d object

    How can we visualize the following progression of fully dividing a dimension in half by its next lower dimension?

    A 1d object (line) ____ is fully divided in half by a 0d object (point) __ __

    A 2d object (plane) is fully divided "in half" by a 2d object line

    A 3d object is fully divided "in half" by a 2d object (plane)

    How can we visualize a 4d object being fully divided "in half" by a 3d object?

  30. Stevan Allen says:

    Correction:

    A 2d object (plane) is fully divided in half by a *1d* object (line)

  31. Alejandro says:

    Stevan: It would be visualized as a Cube.

  32. Joe Fourdey says:

    The character on 'this side' of the wall is a four-dimensional being, with his physical body being the only portion of his being that is "exposed" in the 3 dimensional universe. In reality, if he wanted to get to the other side of the wall, he need only withdraw out of the third dimension and then re-enter the third dimension on the other side of the wall. Similar to a 3 dimensional being that touches a hot stove (a 2 dimensional surface), once he realizes the error of his ways and withdraws his skin off the burner, he has, in effect, disappeared from the 2 dimensional 'world' from the view of the hot burner plane. He is still very much intact in 3 dimensions and is free to interact with the 2 dimensional plane in any manner he chooses.

    Analogies between the 2nd dimension and 3rd dimension relationships are difficult to apply to the 3rd dimension/4th dimension relationship.

    I prefer to describe the latter, if I must use an analogy, as dipping one's toe in a pool of water. To a fish (3d creature) that has no concept of "above the water" (the 4d realm) the toe's appearance is sudden and unexplainable. When the toe is withdrawn from the water (3d universe) back to "above" (4d realm), to the fish the toe appears to have disappeared.

    The technology to make 3 dimensional objects "disappear" by sending them "back" to reside only in the 4th dimension was invented in the United States a few months ago. When the technology is used it is most astonishing to the casual (human/3d) observer, as it requires very little energy (9V battery will be all that is needed) to move most man-made objects to and from the 4th dimension. This technology is the "final" invention mankind will discover. This is because the 4th dimension is far different than most people can imagine, and the person(s) that control this technology will effectively be able to control the world. This technology makes all of the following (and much more) possible: invisibility of physical objects (both short term and indefinite duration); instantaneous 'secure' mental communication amongst two people (think encrypted IMs that only exist in the two people's minds); and the biggest bombshell of them all, communication with 4 dimensional intelligence that is omnipotent and far different from human -- think of a fish in an aquarium being able to communicate with the human observing it, if you must have an analogy.

    Good luck with your game though!

    😉

  33. J3 says:

    This is excellent - my son (4th grade) was trying to explain it in something he's writing for school and now knows how. Good stuff, sir.

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