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Kata/Ana Alter-Dimension Games

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I was thinking about dimension, specifically, Kata and Ana directions in 4D.

According to theory, what we see in 3d are protrusions of 4D objects in the 3D plane. And as you move about ana and kata (4th dimension direction) the protrusions into 3D change, in our perspective, because the objects have been moved slightly in the fourth dimension direction.

Let me borrow an example from a book.

Imagine a 2D plane, with 2D people. Now, stick your hand through the plane slightly, so that your fingers go through, but not your palm. A flatlander (2d person) would see 5 circles. Then move your hand so that the palm goes through.

The flatlander would see the "circles" change shape, and merge into something else. But in reality, the hand just moved in a dimension that the flatlander couldnt, and the poor guy just couldnt see it.

Apply this to a 3D game, in which the character can move ana and kata (4D directions) slightly, and have the landscape change when he moves so.

Say the character is standing on a hyper-sphere to him it is a sphere. He moves a bit Kata, and the sphere shrinks. He moves a bit further, and it vanishes (like removing the hand completely).

This would make a good basis for a platformer/adventurer. The landscape would shift every time you moved ana/kata, and you would have new ways to get across gaps! (Pssst! Move kata! A bridge then protrudes into this dimension! But you'd better jump! Your platform disappears!)

Enemies could be complicated, but you could have 3D and 4D enemies. I'd imagine that the character would have some sort of glasses which let him see where the enemy would be if they shared the same ana/kata plane as him.

Going through a 4D world seen as 3D displayed on a 2D screen.

DesertFox, Dec 20 2005

Adenaxis by Mushware http://www.mushware.com/
4D space shooter. In development but available as a playable demo. [st3f, Sep 23 2006]

Very Large Numbers http://www.search.c...ge_numerals?redir=1
and their names [DesertFox, Sep 24 2006]

(?) Nintendo Wii (don't laugh) http://wii.nintendo.com/controllers.html
Wave it like you just don't care. [Veho, Sep 25 2006]

(???) Rotational Axis' in a 4D object http://www.madsci.o...159202681.Ph.r.html
I asked the "Madsci" website [apocalyps956, Sep 26 2006]

(???) 4DTRIS (tetris in 4 dimension) http://www.illusions/4dtris
Hello, i've just rewritten one of my old pascal game. It is a 4 dimensional tetris. [Simzer, Jan 19 2008]

Miegakure http://marctenbosch.com/miegakure/
4d puzzle platformer under development [iaoth, Jun 14 2011]

Shadowmatic http://www.appunwra...-walkthrough-guide/
Rotate 3d objects to produce 2d shadow [bungston, Nov 17 2015]

YouTube: Designing a 4D World : Miegakure https://www.youtube...watch?v=vZp0ETdD37E
[zen_tom, Aug 04 2017]


       Since 3D TV is finally being trialled early next year, will we soon be moving on to 5D games displayed as 4D on a 3D screen? Coz I think I might melt. +
moomintroll, Dec 20 2005

       Hah! Im having a hard time visualizing something displayed as 4D on a 3D screen in the first place, much less 4D representation of a 5D world! My head is melting, too.
DesertFox, Dec 21 2005

       [+] I'd never heard of Kata and Ana before.
zen_tom, May 05 2006

       Have you read Spaceland, by Rudy Rucker? Good stuff. (+)
GutPunchLullabies, May 05 2006

       I've not read Spaceland, but I have a copy of Flatland by Edwin A. Abbott, a Square. And really enjoyed that.
zen_tom, May 05 2006

       The sci-fi adventure "The Dig" used this for a bit (although not very explicitly) - quite a bit of the technology was based on objects that appeared or disappeared when shifted in this 4th dimension.   

       There are some problems with a game where you could freely travel in this 4th dimension. It would be very hard to provide "borders", and limit the player (see also: Klein bottle). And what would happen if while travelling kata for a bit the player encounters an object appearing in the middle of his head? Bet you didn't see that coming! And finally, there'd be the choice between fully visualizing this 4th dimension in a 3D game on a 2D screen (which would be extremely confusing) or simply presenting a 3D world that would change when pressing one of two buttons (which would reduce travel in the 4th dimension to a kind of magic, or worse, "turning objects on or off").
Forthur, May 22 2006

       That's an interesting point - we can see a 3d representation 'projected' onto a 2D surface using apparent perspective, where things converge toward one (or more) vanishing points as they go off into the distance. How would you show this perspective effect if you were tryng to project a 4D situation into a 3D space - you still ought to be able to see in that 4th dimension, or at least, some kind of projection of it.
zen_tom, May 22 2006

       //some kind of projection of it.//   

       In what direction are you looking at your screen? Kata or ana? Kata always gives me headaches...   

       Is there a name for "normal 3D", which is a zero movement in the 4th dimension?
Forthur, May 22 2006

       Oh yes, that's a good point. In a 2D projection, it is our position in relation to the screen that actually does all the projecting. I forgot about that.   

       How about some kind of shimmery effect around all objects, that permeates into all directions/views etc, in order to give some clues as to what's off stage ana/kata.
zen_tom, May 22 2006

       I'm not so sure about Forthur's point regarding the difficulty of delimiting the environment as the characters are still only moving in the standard 3 dimensions.

If the 4th dimension can be expressed mathematically then a PC shouldn't have too much trouble rendering it. However, the person who designs this world will probably have to spend months in therapy afterwards and I don't envy anyone who sits on the game's support desk.
DrBob, May 22 2006

       //characters are still only moving in the standard 3 dimensions// I understood they were to be free in the 4th dimension too, which means they could pass walls at that place in the 4th dimension where the walls wouldn't be there, or differently shaped.   

       //If the 4th dimension can be expressed mathematically then a PC shouldn't have too much trouble rendering it.// Not too much trouble *calculating* it, you mean. Rendering is quite something different. Although... Maybe kata should be a kind of fading overlay of the object in one color (say green), and ana in another color (say red). This would limit how far you could "look" in those directions, just as much as your 3D eye is limited. Shimmering would be optional.
Forthur, May 22 2006

       If an enemy is 3D, does it have to be the standard three dimensions? Or could it be 3D (1, 3, and 4) without 2, so that moving up or down would remove the enemy from play?
phundug, May 22 2006

       Drat. I was hoping this would be a game that could be used to train the mind to 'see' in the fourth, like in that Greg Bear story [Goes off to find 'Tangents'] 'Tangents'.
stilgar, May 22 2006

       A game like this would be training the mind as much as participating in a NASCAR race would be training for your drivers license.
Forthur, May 22 2006

       Very slick. I do not think that such a game would be best suited for a primary fighting game, but rather one of those puzzle solving games.   

       [Forthur]'s comment (does the 's go inside or outside brackets?) about an object appearing inside your head is pretty nifty too. I think that there should be a limited set of 4D objects - maybe 40 or 50. Players will get a feel for where these things are in 4D space by their 3D appearance, and understand which ones have projections liable to appear at head level after this happens a few times. Unlike the real hapless 3d adventurer who would learn very little after having his cerebrum share space with a shifting 4D object, the gamer would note what happened and learn from it.   

       3D simulations are so good in video games I do not think this would be so hard to do.   

       I do not think boundaries would be so hard either - just make it wrap in 4D.   

       I am wondering about the mass of a 4D object. Is it determined by the aspect projecting into 3D space, or is it the mass of the whole object?
bungston, May 22 2006

       [bungston], are you planning to write a physics engine for the 4D game? Better buy a lot of aspirin first. ;-)   

       I would think the "mass" as we know it for a 4D object would be the mass of its current 3D projection. It may help to see the 4th dimension as "time": an object may increase or decrease its mass over time, but its current mass is, well, the mass it has *right now* (which is the current location in the 4th dimension in our game).
Forthur, May 23 2006

       [bungston], I also like your idea of not having too much 4D objects. The (cliche) plot for the game could be something like: The first warpdrive powered manned probe to another galaxy fails; the lone survivor (surprise! It's you) ends up in an empty cave on a barren planet. Here he discovers the remains of an alien with a curious amulet, which enables him to travel in the 4th dimension, which he uses to pass some rocks that blocked off the deep end of the cave. Behind them, he discovers a city with friendly aliens, that are desperate for his help since their planet is destroyed by <generic catastrophe> and they're running out of <generic resource>. They're simple 3D, but have some 4D artifacts that they don't know how to use. There's a task for you...   

       If we assume there to be 4 dimensions, then *everything* is 4D, not just specific objects. Maybe we should make a distinction between objects that change when going kata or ana, and objects that do not. But how would the player himself change when going kata or ana? Do objects at different locations in the 4th dimension affect the player? What would a NPC alien see when the player moves past him in the kata direction? would the player "appear" and then "disappear"?
Forthur, May 23 2006

       // I understood they were to be free in the 4th dimension too//

<re-reads idea properly>
Ah, yes. So it does. You're right.
DrBob, May 23 2006

       /If we assume there to be 4 dimensions, then *everything* is 4D, not just specific objects./   

       Not necessarily. A 2D creature could move about on flat surfaces in a 3D world. I would propose that the player remain 3D.   

       One job in the game could be to manipulate 4D objects from 1 3D vantagepoint. I think players could catch on to this fairly quickly - manipulating an object through shapeshifts is standard stuff.   

       Consider, though, a 4D object. One might give it a push so that a different 3D aspect appears in your current 3D plane. That different aspect might not appear in front of you. It may be thousands of miles away. If I pick up a 3D manifestation of a 4D object and carry it with me, or if the object falls toward a gravitational body, does the rest of the 4D object appear to move from the perspective of other 3D viewers at different 3D vantagepoints? It might, or it might not, or it might rotate in 4D. This would be more advanced stuff, needless to say.   

       The top level would be the one in which the player actually moved through the 4th dimension. If gravity only works on the aspect of an object currently in your own dimension, that means mass is not a fixed number for the object. It also means that the forces on the object as a whole determining its motion in 4D must be the vector addition of all the different 3D gravities. It might be possible to push an object through 3D planes into one which contains a very massive 3D object, which gravitationally seizes the 3D manifestation of the object and whisks it away.   

       I think that in the game, the 4D objects should be rare, to keep it simple. Maybe of a given color to help identify them. I am sure the aliens would know which things they were. Moving through 4D early on in the game should find fairly barren and empty dimensions - no gravity, no inhabitants, and only the other 3D maifestations of the current 4D objects. Later, these other 3D planes might have things in them important for solving the puzzle - gravitational masses, other 3D objects, or even other NPCs..
bungston, May 23 2006

       I think that an excellent adaptation of this concept would be 4D Tetris. Just as there are a limited number of blocks in tetris, so would there be a limited number of 4D puzzle shapes. One could peruse these in advance in a learners mode.
bungston, May 23 2006

       4D Tetris! Brilliant! I get dizzy thinking about it - I know a few people who hated Blockout since they couldn't think 3D.   

       The target of 4D Tetris would have to be to create 3D cubes, which then disappear, after which all blocks ana to the cube would fall a ways kata.   

       Could someone create a concept screenshot of 4D tetris? I'm very curious.   

       Maybe we could use a 3D representation of a series of cubes (each consisting of 6 x 6 x 6 cells), a bit diagonally from eachother (in all 3 dimensions), and each a distinctive color. "Filled" cells would be nearly opaque, empty cells would be nearly transparant. Blocks falling through the 4th dimension would change color on each step, and move diagonally a little. As soon as one of the cubes of a certain color is filled completely, the cells in it are emptied again, after which every cube shifts its contents to the next one.   

       In 2D Tetris there was one rotational axis. In 3D, three. How much for 4D? Does anyone know?   

       And would the blocks be 3D or 4D? In the 3D Tetris variant "Blockout" you could choose from a few block sets, of which one was classic 2D. Maybe we could do something like that here too.
Forthur, May 24 2006

       I propose that as soon as we have 4D Tetris coded, we start working on a 4D Arkanoid clone.
Forthur, May 24 2006

       A simple 4D adaptation would be to have simultaneous 3D tetris games on 4 screens. These would correspond to different 3D planes through which the 4D object extended. A turn would turn the block in all 4 views.   

       Initially one would remove the 5th dimension - time. The player would get used to the blocks. Then reintroduce the falling aspect at higher levels. Then reduce the number of screens at the highest level. One must remember the configuration of the sitting 4D blocks in order to properly place the currently falling one.
bungston, May 25 2006

       I wonder if it is possible to truly see in 4D. Imagine a 2D creature. It can only percieve the plane in front of it. Even if it learned to angle itself off its usual plane, it could still only see a new plane at a different angle, I suppose because its eyes would be 2D. We, with 3D eyes, probably can't see a 4th dimension, only 3D views of it, as previoiusly suggested for 4D Tetris.   

       Even if the 2D creature could bend itself so each eye was on a different plane, it'd be seeing two different planes, and probably unable to put them together into anything meaningful. I suppose we should consider what would happen if it bent itself at the eye, and if it might be able to learn to make sense of what it was seeing.
JoshM1217, Sep 23 2006

       I like the multiple-view 4d Tetris idea. I think another approach, perhaps more suited to an adventure, is to allow the player and objects to move ana or kata in discrete units. For the most part, the 3D sections of the game that exist in different spaces in the fourth dimension are seperated from each other by "walls". However, there are "holes" in these walls through which the player can put his or her self, objects, or maybe the business end of a 4D periscope. Some of the holes are doorways that can't be opened until certain conditions are met. 4D objects would have to be moved or rotated from one 3D space to make something attainable in another.
JoshM1217, Sep 23 2006

       Think of the controls for that game. Keyboard+mouse to move through 3D, and the scroll wheel on the mouse fot kata? Where would you put ana? I would suggest playing the game with two mice, both with scroll wheels, for precision dimension manipulaton.
Veho, Sep 23 2006

       Adenaxis (linked) is a playable demo of a 4D space shooter. I didn't find it particularly intuitive, but that probably says more about my spacial awareness in four dimensions than it does about the game.
st3f, Sep 23 2006

       I wonder how one could make a 5d game in which there is a 3d plane and two different kinds of time, rather than a 4d plane with normal time.   

       Would all of the objects be constantly multiplying?
apocalyps956, Sep 23 2006

       Hm, if one of the dimesions represented time, you could introduce a living element. Like where you would need a herd of rabbits to accomplish a task, so you move to a future where an initial pair of bunnies has procreated enough to help you with your task. Or you have to move backwards in time to get enough dinosaurs (ad-libbing here) to solve some other puzzle. So living objects multiply or diminish depending on your movement through the time dimension(s).
Veho, Sep 23 2006

       //In 2D Tetris there was one rotational axis. In 3D, three. How much for 4D? Does anyone know?//   

       For two and three dimensions the number of rotational axis' can be expressed with the following function:   

       R(d)=(d-1)+(d-2) ... (d-d)   

       according to that formula, a four dimensional object would have six rotational axis'. I don't know if that formula is accurate, though.   

apocalyps956, Sep 23 2006

       Maybe it would be easier to fight enemies if you moved kata or ana a little bit so that they would be a little smaller and wouldn't be able to inflict as much damage.
apocalyps956, Sep 23 2006

       Perhaps you could make it ten-dimensional (11 including time) and one could gain the ability to move in more dimensions as he progress through the game. That would be really complicated. There would be 2048 posible locations if you only move to two different places in each dimension. If you could move to 100 different locations in each dimension, then there would be 10,000,000,000,000,000,000,000 (1e+22 or 10 sextillion) possible locations and with 1,000,000 posible locations in each dimension there would be 1,000,000,000,000,000, 000,000,000,000,000, 000,000,000,000,000, 000,000,000,000,000,000,000 (1e+66 or one unvigintillion) possible locations.
apocalyps956, Sep 23 2006

       / there would be 1,000,000,000,000,000, 000,000,000,000,000, 000,000,000,000,000, 000,000,000,000,000,000,000 (1e+66 or one vigentillion) possible locations./   

       Most of them would be boring, I bet.   

       Are there any fighting games where players manipulate swords or other weapons realistically? That is, the position of the sword in space really matters, and one can parry etc. A fighting game with some 3D and some 4D weapons might be cool. I can imagine a 4D sword or a 4D mace and chain.
bungston, Sep 24 2006

sp: vigintillion
And one vigintillion is equal to 10^63, not 10^66
See link

       *prepares for math feud*
DesertFox, Sep 24 2006

       //Are there any fighting games where players manipulate swords or other weapons realistically? That is, the position of the sword in space really matters, and one can parry etc.//

Oblivion does a reasonable job of this although it's an adventure game rather than a fighting game.
DrBob, Sep 25 2006

       //Are there any fighting games where players manipulate swords or other weapons realistically? That is, the position of the sword in space really matters, and one can parry etc.// Nintendo's new console, Wii (don't laugh), has a controller with solid-state motion and tilt sensors (gyroscopes), which gives the console feedback on the position and angle of the controller, as well as normal controllery feedback (buttons). This allows the movements of a sword in the game to follow the movements of the controller, which in this case emulates the sword hilt. See link.
Veho, Sep 25 2006

       //And one vigintillion is equal to 10^63, not 10^66// I guess it would be one unvigintillion then
apocalyps956, Sep 26 2006

       I was watching Adventure Time, and the hero Finn created a 4D bubble that had a tremendous gravitational pull. This did not seem right to me and I began thinking again of this thread. How does gravity behave in 4 dimensions?   

       /How about some kind of shimmery effect around all objects, that permeates into all directions/views etc, in order to give some clues as to what's off stage ana/kata./ — zen_tom, May 22 2006   

       It does not seem right that mass could change for a 4D object depending on what aspect what projecting across our 3D perspective - just as a Flatlander trying to move a circle along might find it inexplicably massive if it were actually a sphere.   

       A 4D object in our dimension would be more massive than it would appear to be because its gravity would be based on all of its 4D mass, much of which would not be apparent to a 3D viewer. Imagine this object were pushed out of our 3D plane. It then could not be seen or felt, but its gravity would continue to attract to the mass center. Thus an out of phase 4D object would simply appear as a gravitational attraction.   

       I wonder if this model could explain dark matter?
bungston, Jun 03 2011

       If you had a 4D object, the mass which was not in the same 3D plane as you would have no gravitational effect.   

       To take the 3D/2D analogy:   

       Imagine a dense 3D ball hovering above flatland. A flatman is standing underneath it, but he will feel no upwards pull, because he's constrained to the flat surface. (A pull has to create a displacement, and there is nowhere for him to be displaced to, if he's stuck on the plane.)   

       Now imagine that the sphere just dips into flatland, making a small circle, and imagine that the flatman is standing just to one side of this circle.   

       We (looking at it from a 3D viewpoint) would say that there is a large gravitational force pulling the flatman in a mostly upwards and slightly sideways direction (ie, the centre of mass of the sphere is above him and just slightly off to one side).   

       However, from the foregoing, it's clear that the vertical component of the force will have no effect on the flatman. Instead, he will only feel the very small sideways component of the vector, commensurate with the small circle next to him in flatland.   

       As the sphere sinks lower into flatland, it's "3D" force becomes angled more and more towards the horizontal until, when the sphere's equator intersects flatland, all of its gravitational pull is directed sideways, and the flatman feels all of the force.   

       As the sphere continues downward, its pull has a greater vertical component (now downwards) and a correspondingly smaller horizontal component (which is the only component felt by the flatman). At the same time, the circle in flatland becomes smaller and smaller.   

       So, in a sort of a kind of a way, it all makes sense from both perspectives: we see a sphere whose gravitational pull is constant in magnitude but changing in direction. The flatman sees a circle which grows and then shrinks while its force on him increases and then declines.
MaxwellBuchanan, Jun 03 2011

       Could you escape the coils of the kataconda, sneaking up from be-underhind you, by anapulting yourself to safety?   

       Also, would you like to meet Anna and Katya, being the outmost and inmost shells of a four-dimensional matryoshka?
pertinax, Jun 05 2011

       Nice explanation Max. Vectors. It makes sense. But what force would act on the constrained flatman if he quickly affixed a set of flatlander tricycle handlebars (with a bell) to the 3d sphere and hung on to them? Since he is immune to that vector pulling the 3d sphere out of his plane, could he stop the motion of the entire 3d object? Could he slide it along, using only a force necessary to move the mass of the aspect in his plane?
bungston, Jun 05 2011

       Well, wouldn't the tricyclist be frustrated by the difficulty of finding a 2D fixative that could interfere in any way with movement in the third dimension? In other words, wouldn't 2D glue (or weld, or whatever) just slide off as the sphere moved away?
pertinax, Jun 05 2011

       //what force would act on the constrained flatman if he quickly affixed a set of flatlander tricycle handlebars (with a bell) to the 3d sphere and hung on to them?//   

       He couldn't do it. By definition, he can only attach something to the circle in his plane. If the sphere descends or climbs, the circle gets larger or smaller and "escapes" the knot he'd tied around it. I think.   

       My analogy isn't perfect, though. For instance, if the entire sphere is slightly above Flatland, but well off to the left of him, then its gravitational vector will still pull him strongly leftward even though there is nothing visible in Flatland.   

       (Which point, I suppose, harks back to a discussion elsewhere about "dark matter" - stuff which pulls but is not visible.)
MaxwellBuchanan, Jun 05 2011

       This would work much better as a VR game. Also this idea makes my head hurt [+]
Voice, Jun 05 2011

       Having considered this game I now permanently think in 4 dimensions. Thank you.
Voice, Jun 05 2011

       /harks back to a discussion elsewhere about "dark matter/   

       I was getting excited about thinking about this today. Imagine not some funky 4D sphere but normal 3D objects, each in their own 3D planes. OK, for illustration instead consider a series of flatland planes stacked like shelves. Objects on different planes at some 2D distance from each other attract each other because most of the vector is the 2d distance. Objects in different planes but at no 2D distance (right on top of each other) exert no gravity on each other. One could gravitationally detect extraplanar objects at a distance but not close. That is just like dark matter.   

       Now is where my physics gets sketchy. Gravity between planes would not obey the inverse square law because the extraplanar vector component is subtracted. Objects in various planes gravitationally attracting each other would still "orbit" one another but it is not clear to me how those orbits would behave: a stack of flatland shelves would be predictable, but what if some flatland planes are perpendicular to each other, or they wrinkle on 3D space. One could have one flatlander be in the same 2D location as two extraplanar others, who themselves were far distant from each other on their own plane which they perceive as flat but is actually very wrinkly in 3D.   

       It seems like 4D objects as dark matter should be modelable and testable.
bungston, Jun 06 2011

       Actually I have personal evidence of a kind of absolute Platic form dimension where things can be more or possibly less the amount of their actual absolute meaning of being.   

       Thus moving along that cline a cigar would go from just a cigar to an absolute essence of cigarness.   

       It does seem to have something to do with perception. how is it that a sky blue car differs from a white car, yet physically two white cars have similar meanings yet radically different masses. yet two of the identical versions of a make of car at different colors carry the greater perceived platonic amplitude difference.   

       Receptivity to those platonic like absolutes of form appears to adjustable. Ive seen those that can adjust the amount of activation be able to do things like teleportation or action at a distance which are the kind of activities some people that strive to appreciate higher dimensionality like.   

       Ive thought of some plausible reverifiable actions to test dimension of mind. Like if you have a radiant form then surround it with people each wearing a different shape of shield, can you then write up their perceptions, where a mathematical description would show that the shapes of the shields affected the received perception. Or, if you put something amazing at the center of a circle of persons, each wearing a different variety of tinfoil hat, could you show that the people that had (circle, square or wavy) similar gaps at their tinfoil hats of the same shape has similar impressions of the core radiant   

       I imagine the reactions to this as ranging from polite perplexity to enthusiasm that there is a way to test what Jung called synchronicity with the use of synchronicity gap filters   

       You could also use some of the amplifiers ive noticed to see if they could affect people perceptions as well.   

       Truly, get an equitalented group of people, then have them do a precision task while wearing variously G A or P letterized shirts each either Green, Blue or Red, then measure the effect on performance of rotating the shirts. I predict Blue G would always have greater precision than red A on average as the actual humans rotated through the platonic costumes. regardless of what I predict, its the isolation of platonic forms that creates new technological possibilities.   

       a reverifiable description of a dimension of mind that goes beyond Jung would be beneficial   

       here is another one: test the emotional visual reflex of persons to a scene made up of the phrase "sea squill squill" as well as a sphere plus a cube. see if persons that have different emotional reactions (if any) to that have absence or presence of reactions to phrases like "I know you dont see it" Regardless of what this means to readers these seperable groups of reactors could well have different reactions at the letterized color shirt test. The purpose being to find reproducible variations on dimension of mind.
beanangel, Jun 13 2011

       //If the sphere descends or climbs, the circle gets larger or smaller and "escapes" the knot he'd tied around it. I think//   

       For a sphere, yes, But imagine a 3D dumbell passing through 2D flatland. If Mr Flat runs round the small circle when the dumbbell is halfway though, and then ties a nice tight knot, has he not "caught" the 3D object?   

       Could we not similarly trap a 4D dumbbell in a box?
pocmloc, Jun 13 2011

       // imagine a 3D dumbell passing through 2D flatland. If Mr Flat runs round the small circle when the dumbbell is halfway though, and then ties a nice tight knot, has he not "caught" the 3D object?//   

       If the 3D-object's velocity is at an exact normal to the plane then it could be trapped by a *partially* pulled 2D-cord. Otherwise, if it was coming in at an angle or if the cord was pulled tight, it would just cut the object in half.   

       However an intelligently directed object could indeed be trapped by giving it the choice of staying put or being sliced.
FlyingToaster, Jun 14 2011

       You (mostly) seem to be treating the 4th dimension as special, but in a 4D world, ana/kata would be just like up/down, left/right and back/forward; ie. not special, just another diection to move.
<Flatland analogy>
If a flatlander were able to move in 3D (in a 3D world), he would still only see in 2D; a 'slice' of the 3D world, that he can re-orient (because he can move 3D). He doesn't 'lose' a particular direction (like 'up/down'), he can see a slice of 3D where-ever he looks. His viewplane can be in any direction, unconstrained.
Extend this into 4D - the 3D character can move in 4D, but only sees a 'slice' in 3D (projected in 2D on screen etc). His direction of view (and motion) is orientable among all 4 dimensions. It's up to you to understand the 4D world you're looking at (which would be very difficult) as you move and look.
(Aside: most videogame controllers have 2 joysticks - 4D control already built in!)
In the game, you would have to constantly shift your view direction, to make sense of where you were, and moving rapidly would be hazardous; so it would be a puzzle-type game, not fighting/combat or racing.
Hmm, this drivel may have confused me more than you, just by writing it...
neutrinos_shadow, Jun 14 2011

       Bean, why is Blue G the best? Also, the synchronicity gap filter, which I googled to no avail.
bungston, Jun 14 2011

       //it would just cut the object in half//   

       Aah - does an object that exists in (x) dimensions behave as a kind of ultimate knife when wielded in (x+1) dimensions?   

       Or is it all just about field of view?
pocmloc, Jun 14 2011

       //act as a knife in x+1 dimension//   

       Well, dealer's choice on the assumptions, but if a dim(x+1) object's x attributes are the same as a native dim(x) object, a solid would block it's passage, while a liquid or gas would be moved aside.   

       An x+1 hyper-needle, traversing a 3D scene might appear to the eye as a tiny globe that gets bigger then remains the same size for awhile.
FlyingToaster, Jun 14 2011

       Reading this one again after Inyuki posted 4D Tetris.   

       Braid is a videogame which does a nice job with 4D puzzles except the 4D is time. The linked video has an editor screen which I had no idea was part of the game. Time direction experienced by the character is depicted by speed/direction of musical accompaniment.   

       Max, are you there? Take a look at your analogy with the Flatlander that you posted. This part: /However, from the foregoing, it's clear that the vertical component of the force will have no effect on the flatman. Instead, he will only feel the very small sideways component of the vector, commensurate with the small circle next to him in flatland./   

       The Flatlander feels a sideways component when the 3D sphere intersects his plane. He feels nothing when the sphere is just above him, out of his plane because the out of plane vecotr does not count. But does he feel a sideways component when the sphere is out of his plane but to one side? It seems that he should, and this component should be weaker as he gets closer, and be zero when directly underneath.
bungston, Jun 06 2012

       I don't believe any of this more-than-3-spatial dimensions stuff. It sounds like nonsense. Analogies to imagined 2D people do not create a true understanding of something in reality. A vague idea of what some imagined thing may be like does not a valid scientific or mathematic idea create. Yeah, yeah, sure, MAYBE there are 10 dimensions or whatever, and we just can't "see" them. But such ideas will always be meaningless to humans, such maths cannot represent anything we actually know. Scientists need to accept that science itself is limited by human perception.
EdwinBakery, Jun 07 2012

       hmmmm..., OK, I came up with a good way to say what I'm trying to say.   

       Science is a kind of philosophy, a method, of answering questions/ describing phenomena. Implicit in "phenomena" is phenomena that humans OBSERVE.   

       It's oberve-> describe-> theorize-> test-> come up with theory. Along with of course, an assumption of the validity of deductive reasoning/pattern-forming (as in, it is entirely possible that every once in a while something falls UP and it's just that nobody's seen it, but that's doubtful and we assume it's not true and that the idea of gravity makes sense)   

       But that OBERSVE part is the kicker. It needs to be observable by humans. All ideas in the first place need to be within the scope of human perception/understanding, and our ability to understand things/ideas is limited by our perception. This is why we can only come up with weird, vague analogies for imagining more than 3 dimensions. In reality it's not something we observe.   

       Sure we can observe phenomena that these theories are meant to describe, but perhaps these theories are wrong and there are much simpler explanations. And the ideas that the theories are based on should eventually be directly testable/observable. And they sure as hell should actually make sense in terms of human perception.   

       things being drawn together by some force that just exists, that's imaginable. Electric fields creating magnetic fields creating Electric fields and thus make electrmagnetic waves makes sense, hell, we've all SEEN waves. All these things are within the scope of our sense and thus our imagination. But more than 3 spatial dimensions? What would that even mean? What the heck would that be?
EdwinBakery, Jun 07 2012

       //What the heck would that be?// Have you ever read Plato's Allegory of The Cave? It's a thought experiment over 2500 years old that covers just this thing. It doesn't provide any answers to your question, but it does (potentially) put it into context.
zen_tom, Jun 07 2012

       yeah, like I said, vague anaolgies to imagined 2-D only people/actors and what they would see in a 3-D world. I covered that. Something tells me people are going to keep bringing stuff like that up anyways in response to what I've said
EdwinBakery, Jun 07 2012

       Yes, you covered it, but you've missed the analogous point - that it is conceivable to see one thing and think it is true, when *in reality* it might just be a projection. Take proven (i.e. observed) wierdness in quantum dynamics, spooky action at a distance, apparent breaking of causality etc. Without recorse to theory, there's no real way to explain those observable phenomena. If you can theorise something, and provide the mathematics to prove it, and using that mathematics, be able to predict future applications and behaviours within acceptable tolerances - i.e. make your theory testable and refutable - then it may well be the case that the underlying model might be a better description of reality, despite what common sense might dictate.   

       Take radio for example, nobody can directly observe it, but the mathematics holds up - and pretty much all of us accept it to be true - despite there being some frankly unusual and unexplainable properties of radio waves; Inverse square law, speed of light, bending of waves around gravitational "lenses", dopplar shift being proportional to distance, suggesting the ability of "space" to change shape, self-interference of individual photons, quantum tunnelling...it all gets pretty far out
zen_tom, Jun 07 2012

       Now interestingly enough, there *is* a mathematical theory that might suggest that there are a limited number of dimensions, *and* which points towards that number being a sort of 3+1 configuration. There are the Real numbers, which are 1-dimensional, for which addition is the opposite of subtraction, division is the opposite of multiplication etc. Furthermore, if you multiply 5x4, you get the same number as if you multiplied 4x5, the order doesn't matter. There are other properties as well. Then there are the Imaginary numbers, for which all the above properties hold, which extend out into 2 dimensions. If you try to come up with an algebra with *only* 3 dimensions, it all goes a bit wrong. But with 4 (i.e. 3+1) you get back to a working number system - only with Quarternions (which is what this 3+1 system is called), 5x4 does not equal 4x5, i.e. it's noncommutative. If you take that and consider it as a physical model, it might have something to say about the arrow of time. Finally, you can sensibly continue to divide 20/4 and get 5. But why stop there? There's a wider system of numbers called the Octonions, which is sort of analogous to an 8-dimensional space (or perhaps a 7+1 dimensional space) at which point, division stops making sense. It just doesn't work any more. In fact, it's proven that you can only divide in 1, 2 or 4 dimensional systems. In fact, as you add more dimensions, more and more of the common rules of mathematics break down and stop making sense. That *might* prove fundamentally important in terms of describing physical systems - then again, it might not, but it is interesting all the same.
zen_tom, Jun 07 2012

       /All these things are within the scope of our sense and thus our imagination./ which itself is a product of our culture and place in history and biological phenotype.   

       The test of any model is whether it makes accurate predictions about what really happens. I revisited this 4D thing to speculate how gravity would interact with extraplanar objects and see if an additional spatial dimension could explain dark matter.   

       A separate issue is whether this would make a good video game.
bungston, Jun 07 2012

       hmmm... indeed with the accurate predictions thing, but there is also the element where the theory needs to make sense according to all the other theories, because in the long run if they don't match it can cause screw-ups when you're dealing with things that involve different kinds of science/engineering. All the classical physics work together perfectly well, but then quantum mechanics is all screwy, and negates a lot of rules created in the classical physics. Frankly, if quantum mechanics starts actually getting used more in engineering one day, they're going to run into problems. I can just imagine the scientists arguing about what elements of a machine are going to cause what effect because their own fields say different things about the world.   

       A good, simple example would be electrons "orbiting" around the atom. Numerous physics teachers will tell you different things, but the reality is we DON'T KNOW what's going on. All they know is the bubble/shape an electron might be in at any one time. They don't know if it's zipping around in there, or disappearing and reappearing here and there, or what. And if it IS orbiting, according to classical physics it should release electromagnetic radiation and lose its energy and slow down. There quite simply isn't an answer. Even Niels Bohr, writing his theory, when asked why the electron doesn't fall into the proton, simply said "It just doesn't". Even Schrodinger's cat was meant as an example of the practical ludicrousness of some aspect of quantum theory.   

       Frankly I think part of the problem is that all this stuff is on a much more smaller, more specialized scale that is just results from lab experiments. There isn't enough of these phenomena around and common enough that we could really see what's going on and be sure about our theories. With this kind of stuff, this theory or that theory COULD be true, or in 50 years it could turn out to be something completely different; some kind of theory that no one thought of.   

       I'm partial to some sort of theory like the one came up by Blacklight Power, basically a guy who came up with a completely different theory that most scientists are saying is wrong, and he claims he's invented a way to make power by utilizing some lower energy state of hydrogen lower than what we already know, and supposedly using a mix of Rainey nickel and a metal hydride can produce excess power. I don't know the details of the theory, but he claims that the electron orbits are not electrons orbiting, but the whole orbit is the charge. That it isn't a point charge/particle like we're used to describing. I'll bet the reality is it's something LIKE that.
EdwinBakery, Jun 07 2012

       // the reality is we DON'T KNOW what's going on. All they know is the bubble/shape an electron might be in at any one time.//   

       Actually we do know what's going on, it's just that we don't like it. We know what's going on with an electron much, much, much more precisely than we know what's going on in the turbulence behind and aeroplane, or what's going on in the economy. In fact we know what's going on orders of magnitude more precisely than we know the distance between London and New York.   

       What you mean is that we don't have an intuitive understanding of what's going on. Well, if what's actually going on does not lend itself to an intuitive understanding, that's our problem rather than reality's.
MaxwellBuchanan, Jun 07 2012

       I think of this concept occasionally. A nifty approach would be to adapt the Shadowmatic concept (see link) where floating 3d objects are rotated to produce a desired 2d shadow. I think 4d objects would be hard to render but you can render a 3d object and then rotate it thru 4 dimensions to produce desired 3d object.   

       Really that would not be too hard: it would be a 3d shape that morphs smoothly into other 3d shapes along a continuum as you rotate thru 4th dimension. Once you understood where each shape was along the continuum it would be doable. The trick would be to position the item in your dimension such that rotating it in 4d will produce the desired 3d shape(s) relative to shapes in your plane.   

       Early levels would have 3d shapes that change smoothly into other 3d shapes. But shapes that are irregular in the 4th dimension might have 3d aspects that pop into view at a distance.   

       5d objects would appear as a 3d shape with a different series of 3d shapes when rotated thru 4d, depending on its orientation in the 5d.   

       An dark Lovecraftian world of non-Euclidean geometry would be the setting for such a game. This game could be called Demention.
bungston, Nov 17 2015

       //5d objects would appear as 3d shapes// so... werewolves, vampires (that can change into bats and wolves), political campaign promises, et cetera.
FlyingToaster, Nov 17 2015

       Pondering this one again. 3d objects portrayed in 2d happen all the time on computer screens. Flipping the square depicting the 3d scenario such that it is now at 45 degrees to the viewer would be doable. It would portrayed as a page in a book, showing the object. One could then have a series of such pages with 3d depictions which would represent a 4 dimensional object.   

       5 dimensions is hard for me so far. Still thinking...
bungston, Dec 08 2016

       I have built (from scratch) a 3D wire-frame model display in Q-Basic (many moons ago). The conversion from the 3D co-ordinate system to the 2D (screen) co-ordinates was pretty simple; the hard part was keeping track of all the points and lines as they drew and re-drew.   

       I would suggest you do the same, only from 4D (space) to 3D ("character view") to 2D (screen). Create some simple 4D shape to wire-frame, and trust the equations (assuming you can figure them out...).
neutrinos_shadow, Dec 08 2016

       //Going through a 4D world seen as 3D displayed on a 2D screen.// using signals sent down a 1D wire carrying electrons which are, to all in tents and porpoises, zero-dimensional points.
MaxwellBuchanan, Dec 09 2016

       My imagining for a game of this type would be not to try and display the 4D shapes at all, stay in 3D with only the volumes to play with. The character in the game would be able to find 4D shape descriptions and then manipulate the volume, with Ana/Kata, once the intrusion volume is correctly orientated with shape description. This opens up different 4D shapes to teleport characters to closed rooms, crush enemies and turn on unreachable switches or physics cascades.   

       The whole principle would be to stimulate thought about the 3D volume changes with respect to chosen movement of a 4D shape.
wjt, Aug 05 2017


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