Explanation of Four-Dimensional Physics

[Lord Loss]

I'm thinking of writing a novel in which an architect is asked to create plans for a four dimensional building (that's not all the story would be about but it's an important part). However, I can't quite wrap my head around how they would work. If anyone could explain them to me, that would be awesome. Be as in depth or brief as you'd like. Thanks ever so much!

[Amidus Drexel]

Oooh, interesting concept.

This (https://www.youtube.com/watch?v=0ca4miMMaCE) immediately sprang to mind; it probably goes farther in-depth than you need, but it's a reasonably good analysis of dimensional theory (at least until it gets to the 7th dimension; that's where I lose it).

As far as otherworldly architecture goes.... Perhaps you could design this building with non-euclidean geometry, Lovecraftian-style? Imagine having to make five 90 degree turns to get back to your starting point, or have seemingly parallel hallways that don't actually lead where they appear to.

(This paragraph is only assumptions and suggestions based on them. Feel free to ignore it if the assumptions are wrong.)
If you want the fourth dimension to be time (or something of that nature), you'll have to decide how time travel works in your novel's setting, or just have your characters not use the fourth dimension for much (which doesn't seem like what you're trying to do). I particularly like Orson Scott Card's view of time travel (a la the Pathfinder series), as there are no physical or temporal paradoxes (just logical ones) because the changed time stream is assumed to be the correct one.

[nedz]

The fourth dimension is normally taken to be time.

There is another interpretation in that you just need to have another meaningful dimension e.g. brick size. The example usually given is of palaeontologists making a number of measurements, 18 say, of skulls they have found. Mathematically this gives you an 18 dimensional model upon which you can do cluster analysis — so that when they dig up a new skull they can quickly categorise it.

But I guess you want a geometric description ?

A Line has two sides (ends) which are Points.
A Square has four sides which are Lines.
A Cube has six sides which are Squares.
A 4-Cube has eight sides which are Cubes.
...
etc.

[A Rainy Knight]

(I'm not really an expert on this, so someone please correct me if I'm off base here.) I guess the best way I could think of to try to explain a fourth spatial dimension would be by analogy to the lower dimensions:

We start with zero dimensions. That is, we have a point with no thickness in any direction. If we want to go up to one dimension, we simply lay a infinite number of our fundamental unit of space (a point) next to each other in a single direction, and we end up with a line. The line is basically an infinite collection of points in a single additional direction. If we want to go up to two dimensions, we lay an infinite number of our fundamental unit of space (a line) in a direction orthogonal to how we did it before. So we lay a bunch of lines next to each other in a direction perpendicular to the length of the lines and get a plane, an infinite collection of lines in an additional direction orthogonal to the dimension of the lines. To go up to three dimensions, we lay a bunch of planes next to each other in a direction orthogonal to both of our existing directions (length and width), so we stack them up in the 'height' direction and get a space, a infinite collection of planes in an additional direction orthogonal to the dimensions of the planes.

Each dimension can basically be expressed as being composed of an infinite number of "slices" from the dimension below it, so you might think of a fourth dimension as being an infinite collection of spaces overlaid on each other such that in any point in 4-D space, you're in a typical 3-D space but also have the ability to move into different 3-D spaces 'above' or 'below' you in the 'stack' of spaces. I guess you could say that imagining the fourth dimension as being time explains the change in things over time as being passing through this stack of different 3-D spaces where each space is slightly different than the one before it in a manner consistent with what we would consider the passage of time.

...sorry, I'm just worried that I pushed an analogy beyond where it's appropriate and just spent all this time rambling like a madman. :smalltongue:

[Amidus Drexel]

-snip-
...sorry, I'm just worried that I pushed an analogy beyond where it's appropriate and just spent all this time rambling like a madman. :smalltongue:

That's a really good explanation, actually. With that line (heh) of thinking, we normally move through time in a line, from point A to point B. Your 4D architecture might allow your characters to move through time in a different manner.

If you wanted to design a building that utilizes the fourth dimension, but doesn't involve time-travel, imagine that the universe co-exists with infinitely many alternate universes that are almost identical to it. You could have a one-room house in one universe, but have the same house in three different universes, and thus have a three-room house (this would be an excellent solution to over-population problems. Too many people? Move them to another universe).

[Elemental]

...sorry, I'm just worried that I pushed an analogy beyond where it's appropriate and just spent all this time rambling like a madman. :smalltongue:

Rambling like a madman is the only way to explain these sorts of things.
My suggestion is to consider the reasons why the architect is being asked to design this building and what the buildings purpose is.
Then see if it is actually necessary to describe the fourth dimensional aspect, which will likely be cut to save on the budget.

However, if it's absolutely necessary to describe what it looks like or anything like that, then I can't help you.

[Jimorian]

Another way to look at it architecturally is that while our buildings are 3-dimensional, 1 of the dimensions is NOT identical to the other 2 because of the existence of gravity (at least on a planetary surface). So while moving forward and backward is functionally no different than left/right, moving up/down requires working with/against gravity. So perhaps moving in that 4th dimension requires working against/with <handwavium> and thus that gives you a characteristic you can work with.

[shawnhcorey]

Our universe has three dimensions because electromagnetic force can only be expressed in 3. If there is a 4th, it involves gravity. In other words, you can just make it up. It wouldn't be wrong or right, since nobody knows what would be right. :smallsmile:

[Shishnarfne]

I'm thinking of writing a novel in which an architect is asked to create plans for a four dimensional building (that's not all the story would be about but it's an important part). However, I can't quite wrap my head around how they would work. If anyone could explain them to me, that would be awesome. Be as in depth or brief as you'd like. Thanks ever so much!

Well, there's actually a short story addressing some of this, which may or may not be of use to you: "And He Built a Crooked House" by Robert Heinlein (1941).

I guess that this would come down to how you would define four dimensions... As the conventional physics definition of the fourth dimension is time, which flows in only one direction, and behaves far differently than the spacial dimensions.

[Lord Loss]

Thanks for all the advice so far, it's very helpful. Any ideas how I would go about designing/understanding something with 4 special dimensions, without using time travel?

[tensai_oni]

Another way to look at it architecturally is that while our buildings are 3-dimensional, 1 of the dimensions is NOT identical to the other 2 because of the existence of gravity (at least on a planetary surface). So while moving forward and backward is functionally no different than left/right, moving up/down requires working with/against gravity. So perhaps moving in that 4th dimension requires working against/with <handwavium> and thus that gives you a characteristic you can work with.

What, no. Gravity is not an intrinsic quality of the third dimension nor does it affect the third dimension only. Any and all objects generate gravity. As you read this, your computer screen is trying to draw you in with its gravity field, and you are trying to draw in the computer screen. These forces are way, WAY too weak to notice in any meaningful way, but they're there.

The best way to explain a fourth dimension is by analogy - imagine if we had a sentient race of two-dimensional beings. They are flat and live on flat surfaces, such as pieces of paper. We can witness them, but they cannot witness us - unless we make a conscious attempt to be visible, by touching the paper they inhabit with a finger for example. But even then, they only perceive a tiny fraction of your whole being, the small section of a finger. Likewise, you can move such a flat creature from one place of living to another, but it will be totally confused as you move it through space, surroundings changing shape rapidly and chaotically from its primitive two-dimensional POV.

Two-dimensional beings are to us what we would be to four-dimensional ones. Anything that can perceive and act in four dimensions would be like a race of gods, invisible but always watching and being able to change your environment in ways you are not possible to perceive fully.

[Jimorian]

What, no. Gravity is not an intrinsic quality of the third dimension nor does it affect the third dimension only. Any and all objects generate gravity. As you read this, your computer screen is trying to draw you in with its gravity field, and you are trying to draw in the computer screen. These forces are way, WAY too weak to notice in any meaningful way, but they're there.

You're missing the point. Gravity affects our perceptions of that 3rd dimension when it exists. A wall is a wall is a wall, but a floor and ceiling, while still made of a flat surface perpendicular to the other surfaces, each have a characteristic that is solely defined by the fact that gravity pulls us away from one and towards the other.

In fact there's a weird phenomenon that is rarely discussed that distorts our perception of height by orders of magnitude. We think of the Himalayas as these huge outcroppings out of the Earth's surface, or the oceans as great depths, but if the Earth were the size of a bowling ball, we'd barely be able to feel either on its surface.

So if the OP instead of trying to describe the physical aspect of a 4th dimension instead concentrates on just the aspects of perception (much like the rest of your post does, but even more subjectively), it might not only be easier to get across, but create its own story possibilities.

[Tebryn]

Here. This should help. (http://www.youtube.com/watch?v=M9sbdrPVfOQ)

[nedz]

A good book to read on this is called Flatland (http://www.geom.uiuc.edu/~banchoff/Flatland/).

Ignore the literary criticism you might find in Wikipedia BTW — that article has to be the most inaccurate in the whole Wikiverse.:smallsigh:

[Morph Bark]

Oooh, interesting concept.

This (https://www.youtube.com/watch?v=0ca4miMMaCE) immediately sprang to mind; it probably goes farther in-depth than you need, but it's a reasonably good analysis of dimensional theory (at least until it gets to the 7th dimension; that's where I lose it).

I had been wondering about how all the stuff with 11 and 13 dimensions and such was supposed to work with theoretical physics. I guess I now know what's up with things up until the 9th dimension. I guess now we have to figure out how to travel through time and figure out ways to percieve beyond what we can now so we can see if there is something beyond the 10th dimension.

[noparlpf]

I'm thinking of writing a novel in which an architect is asked to create plans for a four dimensional building (that's not all the story would be about but it's an important part). However, I can't quite wrap my head around how they would work. If anyone could explain them to me, that would be awesome. Be as in depth or brief as you'd like. Thanks ever so much!

Sounds kind of familiar (http://www.math.union.edu/~dpvc/courses/2010-11/mth053-fa10/assignments/crooked-house.pdf).

[Astral Avenger]

another way to describe it:
one dimensional space
(x)
two dimensional space
(x,y)
three dimensional space
(x,y,z)
four dimensional space
(x,y,z,α)
five dimensional space
(x,y,z,α, β)
etc.

a line is
(0),(1)
so a square is defined by points
(0,0),(0,1),(1,0),(1,1)
a cube would then be
(0,0,0),(0,1,0),(1,0,0),(1,1,0),(0,0,1),(0,1,1),(1 ,0,1),(1,1,1)
a hypercube (4 dimensional)
(0,0,0,0),(0,1,0,0),(1,0,0,0),(1,1,0,0),(0,0,1,0), (0,1,1,0),(1,0,1,0),(1,1,1,0),(0,0,0,1),(0,1,0,1), (1,0,0,1),(1,1,0,1),(0,0,1,1),(0,1,1,1),(1,0,1,1), (1,1,1,1)
etc. (intresting corelation with this is to define a square equivalent in n dimensions you need 2^n points.

Not necessarily so useful as other people's discussion, but worth pointing out.

[Urpriest]

Thanks for all the advice so far, it's very helpful. Any ideas how I would go about designing/understanding something with 4 special dimensions, without using time travel?

One thing to keep in mind is that most of what an Architect does now involves computer drawing programs. So presumably designing something in the fourth dimension is as easy as adding another coordinate: instead of each point having three coordinates (x,y,z) it will have four (x,y,z,w). Presumably in a world where architects routinely design four-d buildings, this will be automatically part of the software.

Beyond that, you just need an appreciation for a 4d building's appearance, and that will mostly boil down to the idea that while a 3d building is seen from various 2d views, a 4d building will be seen from 3d views. So maybe your building looks like a gazebo when seen from one angle, and like the parthenon from another.

In general, having your architect design a 4d building is as easy as saying he does. You'd need a specific aspect you want to describe in order to actually have difficulty with it.

[Kelb_Panthera]

The simplest expression of this concept that springs into my mind is the classic building that's larger on the inside than it is on the outside; physically impossible in only 3 dimensions, but perfectly acceptable in 4.

Avoid time-travel like it's got the plague for any kind of gaming purpose. Time travel can create useful and interesting plot-points as long as it remains fairly rare, but as a freely useable ability it will make your head hurt just trying to understand it unless you limit it to the fairly immediate past and future.

Edit; forgot you said writing a novel, not planning a game. The above statement is still decent advice IMO. Paradoxes rarely make good story telling.

[Icewalker]

I think about this a lot, and do mental construction shenanigans with four spacial dimensions.

First, I just want to say:
Time CAN BE seen as a "fourth dimension" but it doesn't progress like we think of time progressing any more than a straight line can be said to progress (the whole thing is already there, if it's just a spacial dimension).

In terms of having four spacial dimensions to build with and walk around in, here is I think the best way to analogize it:

EDIT: This turned into everything I've ever considered about 4-dimensional spacial architecture, in more understandable terms and presentation as I have ever thought about it before. And I've thought about it a lot. So what follows is the (very beginning of) my own personal tutorial on 4-Dimensional Architecture. I apologize for the length, and the current lack of a proper conclusion.

You are walking down a single hallway. At the moment, you are "effectively" traveling in one dimension: you have only one axis along which you can move. Let's call these two dimensions North and South.

You come to a point where the hallway becomes something of a crossroad, with a second hallway. You could turn left or right, and end up facing West or East. The layout is basically a + shape. You are now standing in what effectively serves as a two-dimensional space. You have two axes in which you can travel: North-South, and East-West.

What if that crossroad point you came to also had a tube with ladders which went Up and Down? You are now in three dimensional space. You can travel along any of three dimensions: North-South, East-West, or Up-Down.

What if this building has four spacial dimensions? Well, now you reach the crossroad point, and find that you can turn to face in any of four possible dimensions. North-South, East-West, Up-Down, and let's call our fourth axis directions "In" and "Out".

You are now standing at the center of this four-dimension crossroad space.
If you walked forward, which is North, you could walk down one dimension, the North-South axis.
If you turned to your right, you could walk East, down a second possible dimension, the East-West axis.
If you started climbing upward, you could travel through a third dimension, the Up-Down axis.

If you turned "In", you would travel in a fourth dimension, an "In-Out" axis.
Imagine turning 90 degrees to the side, and stepping into a hallway that wasn't visible before. It's hard for us to visualize, because we are not built to see four-dimensional spaces. You are not turning 90 degrees to your left or right, nor up or down, but instead in a new direction which doesn't exist to us normally. Still, other than what it feels like to turn in that direction, the concept of adding an additional axis down which you could travel isn't that crazy!


That's the simpler route to getting a feel for it. But, that only talks about theoretical perfectly-thin hallways, simple lines. Let's try to visualize things in what buildings are really built with: open rooms.

First though, you have the option here of making a BIG simplifying assumption. It's an assumption that would allow human minds and visuals to operate within this 4 dimensional space very easily. The 4th dimension would operate much like the 3rd dimension does in our buildings now. We can't just walk from a room into the room a floor above it or below it in the way we can walk from one side of a room to another. For us, a change in the 3rd dimension requires a distinct act of changing floors. You are on the 1st floor, then you travel to the 2nd floor. There is no in between. When it comes to our two other normal dimensions (North-South and East-West), you can be halfway across a room, and another few feet further that way, etc. But the third dimension (Up-Down) is sorted into distinct floors in our architecture, and you can't really ever be halfway between them. (You could be standing on a staircase, but shut up, you know what I mean. :smalltongue: )

Let's imagine a 4 dimensional building that operates in the same way.

You are standing in a big empty room. It's pretty simple. Kinda boring. There's a red wooden table in one corner. Nothing on it. The wooden floor paneling is red too. Lot of red in here.
You look forward (North). There's a door which opens into a bathroom, which has as toilet and sink but no shower. The bathroom is also painted red.
You look to your right (East). There is a door which opens into a bedroom. The bedsheets on the bunkbed are also in red.
You see the staircase that goes Up a floor, and you can see the door that opens into the attic, which is also painted red. Cool. Red everywhere.
Now you turn "In" and face in the fourth spacial direction. You are still standing in the middle of the big empty room, but when you face "In" there is a wall right in front of your face. It has a door on it. You open it and step through.

Now you are standing in the middle of another big empty room. It's simple. There is a blue standing lamp in one corner of the room. The carpet is blue. It's the same shape as the first room. Everything is blue.
You look North. There's a door which opens into a bathroom, which has a shower, but no toilet or sink.
You look to the East. There is a door which opens into a bedroom. There is a big double bed instead of the red bunkbeds that were in the other set of rooms. The sheets are all in blue. Everything in this second set of rooms is in blue, it looks like.
You see the staircase Up to the attic, which is also, unsurprisingly, blue. Boring. But at least it's consistent.

Let's stop for a second and compare our two sets of rooms, the Red Layer and the Blue Layer. They are the equivalent of two floors, a first floor and a second floor, which have identical floor plans.

In such a house with a 1st floor and 2nd floor with identical floor plans, the bedroom on the 1st floor would be directly underneath the bedroom on the 2nd floor. The rooms would be the same shape, even if they had, for example, different colored interiors. If you build a ladder between the 1st and 2nd floor bedrooms in that house, you could pass between them, and when you changed floors the room you were in would appear to remain the same size and shape, even though its interior might change: you would be in a different room. Imagine a building with a 1st floor bathroom which has only a toilet and a sink in it. There is a 2nd floor bathroom, located directly above the 1st floor bathroom, which has only a shower. Now, let's install a ladder between the two bathrooms. Easy enough to get between them, right? Instant functional bathroom (well, "functional"). In this 3D house, transitioning between spaces like this is just moving Up and Down. In our 4D house, it's exactly the same, except we're moving "In" and "Out" instead. Let's go back to the 4-dimensional house.

You are standing in the Blue Layer. It's like you're on a separate floor from your Red Layer, but with the same floor plan. You switched layers by passing through the "In" door from before, much like you would switch floors by climbing an Up staircase. And two separate floors can easily have multiple staircases between them, right?

You walk into the blue bathroom. The blue bathroom has a shower, but no toilet or sink. (The toilet and sink are in the red bathroom, remember.) Now, standing in the blue bathroom, you again turn to the 4th dimension. This time, you turn "Out" instead of "In".

(Going from the 1st floor to the 2nd floor requires you to face Up. Going from the 2nd floor to the 1st floor requires you to face the opposite direction, Down. Similarly, if going from the Red Layer to the Blue Layer required you to turn "In" and move in that direction, then going from the Blue Layer to the Red Layer should require you to turn "Out" and move that way. Think of "In" and "Out" as the dimensional-layer equivalents of what Up and Down are for separate floors in a building.)

So. You are standing in the blue bathroom, and you turn "Out". You see the door back into the Red Layer, and you step through it. You are now standing in the red bathroom, which has a toilet and a sink. How convenient. You step out of the red bathroom, to find yourself again standing in the red main room, the big empty one we started all these mind and space bending shenanigans in. Awesome.


So far, we have considered the analogy of having a Red Layer and a Blue Layer, taking the form of a 1st floor and a 2nd floor. We have two main rooms, two bathrooms, two bedrooms, and two attics, one in each layer. In a two-story building with identical floor plans for both floors, you would get exactly the same thing, except you couldn't have two attics! That's the beauty of putting in our extra dimension. A regular house has a collection of two-dimensional floors, connected by stairs in the Up-Down direction to make a three-dimensional building. Our house has a collection three-dimensional layers, connected by doors in the "In-Out" direction to make a four-dimensional building.

...but who says floor plans have to be the same on every floor? Let's add a third layer: an equivalent to a 3rd floor, with a different floor plan. If our Red Layer is equivalent to a 1st floor, and our Blue Layer is equivalent to a 2nd floor, then to get to our third layer (the equivalent of a 3rd floor) we would need to go "In" (the equivalent of Up) past the Blue Layer to get there.

So, we're standing in the main room of the Red Layer. We turn "In", and open the door to the Blue Layer, and step through into its main room. Awesome. If we stopped and spun 180 degrees on the spot and faced in the opposite "Out" direction, which we just came from, we would see the door we just exited, back to the Red Layer. But, instead, let's keep going "In". Facing "In" from the Blue Layer (analogous to our 2nd floor) we can see a NEW door, which is equivalent to another flight of stairs continuing upward. Let's open it and step through.

Through this door (the equivalent of a 2nd to 3rd story staircase) we arrive in the Green Layer, which is our third layer, and equivalent to a third floor. This one doesn't have the same layout as the first two. It is in fact, a library, because why the hell not. I know I'd love to have an entire dimensional layer filled with books. We step out in the middle of the Green Layer. There are green-painted shelves of books all over the place. The walls aren't in the same places as they were in the main rooms of the first two layers, because this layer has a different floor plan. There are some side reading rooms along some walls. There are ladders in a few places up to a balcony floor above with more books, and ladders from that up to a series of pale green wrought-metal catwalks near the ceiling with even MORE shelves. The room is about 60 feet tall!

This is because, recall, in our 4-dimensional house, each of our dimensional layers can have entire 3D layouts, just like how in a 3-dimensional house, each of our floors can have two-dimensional layouts.

This Green Layer is like a 3rd floor. And it's pretty easy to have multiple staircases (or in our 4D house, doorways) between different floors (or layers, for us). Let's take a different route back to the Red Layer. So, in the Green Layer, our library, let's climb one of the ladders up to the balcony level. Now, let's find another and climb up again to the catwalk. Now we're about at the height and position that the attic was in our other two layers, just like how in a 3D house, you could be standing directly one floor above a particular room. From the catwalk, let's turn "Out", and head back. We have to find the door first (in a normal house you can't just turn Up and ascend a floor where there isn't a staircase!). We find the right spot, and turn "Out", finding the door back to the Blue Layer, and step through it, into the Blue Layer's attic. Awesome. Now let's climb back downstairs into the Blue Layer's main room. Easy-peasy. Turn "Out" one more time, and walk back through the door into the Red Layer's main room. Getting the hang of it?



That is the simple form of four spacial dimension architecture.

"If that's the simple form, what's the complex form?"


Well. This is where things get a bit harder. I haven't tried to lengthily describe anything like this before, so I'm kind of winging it. Let's see how understandable I can be.

In a normal, 3D building, two floors aren't always completely clear-cut distinct from one another. Sometimes, a room can span (http://floorplans.houseplansandmore.com/051D/051D-0258/051D-0258-balcony-8.jpg) multiple (http://www.architecture-buildings.com/images/2011/06/manhattan-balcony-indoor-view.jpg) stories (http://fc02.deviantart.net/fs70/f/2012/308/3/5/indoor_balcony_by_keldbach-d4qlxac.jpg).

What's the analogy for that? It starts to get difficult to visualize, and you also get some options on how you want to do the fictional perspective.

The way I have been describing things so far, which is the way I personally think about 4 spacial dimensions most of the time, is where you have your North-South, East-West, Up-Down, and "In-Out" dimensions. We, as humans, can only effectively comprehend three of these visually at a time. In the examples I've presented so far (and most of my personal thought experiments), the viewer is always comprehending North-South, East-West, Up-Down. The fourth "In-Out" dimension is always the oddity which exists down a direction we aren't looking, except in moments where we turn to step through a door.

However, it would be a bit more accurate to say that it just depends what direction you are facing. If you are facing one way, you are looking at North-South, East-West, Up-Down, and the odd imperceptible dimension is "In-Out". But if you turn to face another direction, then you can see and act in the North-South, Up-Down, and "In-Out" dimensions, and it's what used to be your East-West dimension which is now the super weird imperceptible one. Everything would look and feel like a normal room, just like it did in our three-layer house before, because East-West is no more or less normal than In-Out: we just aren't used to there being four axes.

To deal with this kind of thought, we have a continuous 4th dimension, instead of one split into distinct layers (our Red, Blue, and Green from before).

Let's try it.

If you were standing in the middle of a big empty warehouse, you could easily walk North, or South, or East, or West. If you could fly, (for the moment, let's assume you can!) you could also travel Up, and then Down. Hell, you can even walk NorthEast. Or SouthWest. Or fly UpNorth and then DownSouth back to where you started from. Diagonals will get very complicated later.

Now, because we need the extra storage space for our business, let's rent a 4-Dimensional warehouse.

In addition to being able to walk North, South, East, and West...
We can walk "In" and "Out". As we saw in our layered house, this would be like changing every aspect of the room, similar to how you could go up a floor in a building. But that doesn't really visualize right in my head, I don't know about you. And what's all that talk about 4-dimensional spaces being built out of cubes? Well, there's at least one mental jump at the end of that which even I have trouble with. But let's keep exploring this analogy together (I'm walking myself through this as much as I am any reader).

How can we visualize this more easily? Let's do the same thing we did before. Color. Check out the gradient on this wall (http://uncopy.net/wp-content/uploads/2012/08/doespiritosanto-anpassent5.jpg). This one runs from black to white. Let's use black and white in the 3D warehouse, shall we? So let's take our 3D warehouse: The East-most wall is painted solid black. The West-most wall is painted solid white. There is a gradient, much like the picture above, which runs from black to white as you move from East to West. You can tell where you are in the warehouse by how dark or light a grey the walls are! Cool. Can we do this to better visualize walking through 4 spacial dimensions?

Let's go back to our 4D warehouse. Remember how our layered house had a Red Layer and a Blue Layer, and they were each an entire distinct set of rooms? Well, what if, like these (http://floorplans.houseplansandmore.com/051D/051D-0258/051D-0258-balcony-8.jpg) mult-floor (http://www.architecture-buildings.com/images/2011/06/manhattan-balcony-indoor-view.jpg) open rooms (http://fc02.deviantart.net/fs70/f/2012/308/3/5/indoor_balcony_by_keldbach-d4qlxac.jpg) we saw before, they were open to each other, and you could move or look between them smoothly, rather than only in distinct layers like via doors or staircases?

Let's walk all the way "In" to our warehouse, until we can't walk any further "In". (We'll come back to exactly what the "In"most wall looks like later: it's some of how we'll try to understand why the walls are described as cubes.) For now, we'll just stop when we get all the way "In". Now, let's paint the walls, and floor, and ceiling, all bright blue, just like our "In"ward second Layer in the 4D house. Okay, awesome. Now, let's turn around, and start walking "Out". It takes exactly as long to walk from the "In"most edge of the warehouse to it's "Out"most edge as it would to walk from it's Northmost edge to it's Southmost edge: it's just another dimension. Now that we have reached the "Out"most edge, let's paint everything bright red, walls, floor, and ceiling. Now, our "Out"most edge of the warehouse is painted red, and our "In"most edge of the warehouse is painted blue.

Now, let's run a gradient between the two. With a snap of the fingers (we bought magic paint. I know a guy.) a gradient now runs from red, to reddish-purple, to purple, to bluish-purple, to blue, across all the walls and floor and ceiling, from "Out"most to "In"most.

Normally, in a 3D warehouse, we can look at the distance to the walls in front and behind us, and on either side, and to the ceiling, and we know where in the room North-South we are, and where in the room East-West we are, and where in the room Up-Down we are (usually the floor!).

In our 4D warehouse now, with our little trick, we can look around us at the walls in front ad behind us, and on either side, and the ceiling, and the color, and we can easily tel where we are in terms of North-South, East-West, and Up-Down as before, and now, by observing how red, purple, or blue the walls are, we can tell exactly how far "In" or "Out" we are! Awesome.

This is of course just a visualization tool. If we were used to 4 spacial dimensions, we wouldn't need it: we could just look "In" and "Out" in just the way we look North and South or East and West, and we would be able to see how far from the "In"most and "Out"most walls we were.

Let's try to understand the cube-for-walls thing. A cube has six walls, each made of a square. The 4-dimensional equivalent of a cube, called a tesseract, has eight walls, each made of a cube.

:smalleek:

First, let's try to understand and visualize what each of our cube-walls is in our 4D warehouse. Remember how I said we'd come back to the "In"most wall idea? Well, here we are.

Let's start, as always, with the 3 dimensional version: If you walk North, you will eventually hit the Northmost wall. Nice and easy. It doesn't matter where in the warehouse you start: you can take several steps to the East. You can float a dozen feet Up. You can change your starting position to any point along those two axes (which, together, make a 2D plane, a square, which you can move in: that's important). No matter where you start from in the East-West axis and the Up-Down axis, when you keep moving North, you WILL eventually hit the Northmost wall, right? That's because, like the limited East-West Up-Down square you are starting in, the Northmost wall is also a square which runs East-West and Up-Down.

Let's go 4 Dimensional. The same laws apply. If you walk "In", you will eventually plant your face on the "In"most wall, and probably get blue paint all over it and look like an idiot. Now, no matter where you are starting from, if you walk "In", you will hit the wall. Just like in the 3D warehouse. Except this time, the spot you are starting from is not anywhere in an East-West and Up-Down square: you are starting from anywhere in an East-West, North-South, and Up-Down space (a cube of empty warehouse). And no matter if you take a few more steps West, or move a little ways North, or fly Up a short distance before you start moving: regardless of where you are when you start, if you keep moving "In" you will hit the "In"most wall.

You can start anywhere in an East-West, North-South, and Up-Down cube. And, in just the same way, the "In"most wall runs North-South, East-West, and Up-Down. The "In"most wall is a solid cube.

Here's another angle (haha) to look at things from (sorry). Think about this. Standing in the 4D warehouse, we look North. There is a Northmost wall. If we walk North, we will walk into it. Here, take this paintball gun. Alright? Awesome. It's got bright yellow paint in it. Let's shoot the Northmost wall from where we're standing. There's a spot there. Okay cool.

Let's say we take a few steps to the East. There is still a Northmost wall. Fire another paintball. Now there is a second spot, a couple feet to the East of the first spot.

Let's fly a few feet Up. There is still a Northmost wall. Let's fire off another paintball. Now there is a third spot, a couple feet Up from the first two. You can see spatters of paint all of two dimensions of wall, both East-West and Up-Down.

Let's walk a few feet "In". There is still a Northmost wall. Fire another paintball. Now we have created a fourth spot on the Northmost wall. This spot is not to the East of the other spots. It is not Up from the other spots. This spot is "In" from the other spots, but it is still undeniably on the Northmost wall. It is along the "In-Out" axis from the other spots, on the Northmost wall. See now, how the Northmost wall has an East-West axis, an Up-Down axis, and an "In-Out" axis? It is three dimensions of solid object, just like how a wall in our 3D warehouse had East-West and Up-Down axes, making it two dimensions of solid object.


Geez, we're getting paint freaking everywhere. Let's look again at the overall picture.

In our 3 dimensional warehouse, we painted the East square wall black and the West square wall white. The other four surfaces (the two walls, and the floor and ceiling) were all coated in a gradient running through shades of grey (no, there are not 50 of them. Sod off.) Let's consider the North wall. It has two dimensions: Up-Down, and East-West. If you look along the East-West axis, it has a gradient from black to white, regardless of where in the Up-Down axis you are. If you look along the Up-Down axis, the color is constant, always a single color of grey: exactly what grey it is depends on where in the East-West axis we are.

In our 4 dimensional warehouse, we painted our "Out"most cube-wall red, and our "In"most cube-wall blue. Let's take a look at the Northmost wall, shall we? Our Northmost wall is a cube. It has three axes: East-West, Up-Down, and "In-Out". To imagine looking along an axis in a cube, imagine gradually stripping one micro-thin layer after another off of one side, cutting off perfectly thin squares over and over, down the length of the cube.

If we look through the "In-Out" axis, each successive square we cut off is gradually shifting from blue to red, each one is the next shade of purple. Cool.

If we look through the East-West axis, each successive square is still the same color, one specific shade of purple. Exactly what shade depends on where in the...is this right?

Gods. I want to keep going. This is so much fun. :smallsigh: I really need to study for neuroscience finals tomorrow though. I've already spent hours on this and at an organ concert today. Instead of trying to wrap my head further around the 8 cube-walls, I'm afraid I'm going to have to cut off here. I may come back to this and continue after finals are over with.

[GnomeFighter]

The simplest expression of this concept that springs into my mind is the classic building that's larger on the inside than it is on the outside; physically impossible in only 3 dimensions, but perfectly acceptable in 4.

Avoid time-travel like it's got the plague for any kind of gaming purpose. Time travel can create useful and interesting plot-points as long as it remains fairly rare, but as a freely useable ability it will make your head hurt just trying to understand it unless you limit it to the fairly immediate past and future.

Edit; forgot you said writing a novel, not planning a game. The above statement is still decent advice IMO. Paradoxes rarely make good story telling.

Well, I don't know about it becoming to complex. If the building was 4 dimensional and the 4th dimension was time, then the building would exist within constraints. Your time travel would be limited by the constraints of the building. I.e. you could not travel outside the life of the building any more than you could travel outside the area of the building.

You could also have forward travel limited to someone only being able to travel backwards and as far forwards as the time they are "from". This could either be a physical property of the building, that from the point of view of the person nothing forward of that point has been "built" yet, or that the risk is too great. Having a version of a "Danger no entry" sign up as you know what has happened in the past, but moving forward in time is just as dangerous as walking in to a building site without knowing your way around. You might take a wrong turn and walk down a corridor that dose not exist in the time you are going to.

You also have to deal with causality. Also, how would you book a room in a hotel with 4 dimensions? Would you be able to book 4 consecutive nights 3 weeks apart?

[Traab]

You know, talking about how each dimension is created by stacking an infinite number of the previous dimension, (infinite points equals a line, infinite lines equals a flat surface, infinite surfaces equals a cube, then infinite cubes = ???"

It all made me think of the book The Redemption of Althaus. In it, they have this building, its the house god slept in while making everything. But thats not important to the discussion. What IS important is that the house is literally, as one of the characters describes, Everywhere and Everywhen all at the same time. Its an infinite space that takes place in an infinite time. You cant comprehend it really, its just, every door leads somewhere, if you have the right frame of reference to understand this, and the house is an unknown, ( infinite ) size on the inside with what amounts to an endless supply of doors if you just go looking for it.

In other words, it seems to me that you couldnt really build a 4th dimensional house because a human doesnt have the frame of reference to comprehend how to build that, and another human wouldnt be able to comprehend what he is seeing if you did build it. Much like how all the characters in redemption saw nothing but a big house on the outside, and a house they couldnt find an end to on the inside, your mind would likely try to find a way to reduce it to something it could comprehend. We can understand the first second and third dimensions because we live in it, and our 3rd dimension is built upon the other 2.

The 4th dimension is beyond us. Its easy to say something like infinite cubes, but what does that even mean? The only thing my mind can think of when picturing that is one giant honking cube that stretches off into infinity which is nothing more than third dimension. At best its an infinite number of smaller cubes creating the giant omnicube filled with so many lines and intersections that it likely would appear to be a solid mass of lines when looked at from the outside. Does that mean that a 4th dimensional traveller would basically be able to move anywhere within our third dimensions concept of infinity at will? Would that mean there is a race of beings that exist in the 4th dimension, who are probably wondering if it is even possible for beings to exist in something as limited as a third dimension, like we might wonder about the second? Gah, its too early in the day and my head hurts.

[noparlpf]

You know, talking about how each dimension is created by stacking an infinite number of the previous dimension, (infinite points equals a line, infinite lines equals a flat surface, infinite surfaces equals a cube, then infinite cubes = ???"

It all made me think of the book The Redemption of Althaus. In it, they have this building, its the house god slept in while making everything. But thats not important to the discussion. What IS important is that the house is literally, as one of the characters describes, Everywhere and Everywhen all at the same time. Its an infinite space that takes place in an infinite time. You cant comprehend it really, its just, every door leads somewhere, if you have the right frame of reference to understand this, and the house is an unknown, ( infinite ) size on the inside with what amounts to an endless supply of doors if you just go looking for it.

In other words, it seems to me that you couldnt really build a 4th dimensional house because a human doesnt have the frame of reference to comprehend how to build that, and another human wouldnt be able to comprehend what he is seeing if you did build it. Much like how all the characters in redemption saw nothing but a big house on the outside, and a house they couldnt find an end to on the inside, your mind would likely try to find a way to reduce it to something it could comprehend. We can understand the first second and third dimensions because we live in it, and our 3rd dimension is built upon the other 2.

The 4th dimension is beyond us. Its easy to say something like infinite cubes, but what does that even mean? The only thing my mind can think of when picturing that is one giant honking cube that stretches off into infinity which is nothing more than third dimension. At best its an infinite number of smaller cubes creating the giant omnicube filled with so many lines and intersections that it likely would appear to be a solid mass of lines when looked at from the outside. Does that mean that a 4th dimensional traveller would basically be able to move anywhere within our third dimensions concept of infinity at will? Would that mean there is a race of beings that exist in the 4th dimension, who are probably wondering if it is even possible for beings to exist in something as limited as a third dimension, like we might wonder about the second? Gah, its too early in the day and my head hurts.

You know how you can visualise a cube on paper by drawing intersecting, skewed squares as if there were three dimensions? You can sort of do a similar perspective trick in three dimensions to represent a tesseract using intersecting, skewed cubes. Try that sometime.

[Traab]

You know how you can visualise a cube on paper by drawing intersecting, skewed squares as if there were three dimensions? You can sort of do a similar perspective trick in three dimensions to represent a tesseract using intersecting, skewed cubes. Try that sometime.

By skewed I assume you mean there are parts of the cubes inside each other? Its not like putting together building blocks where you slap a cube on each surface of the first cube, then slap more cubes on each surface of THAT ad infinitum? Oh sweet monkey jeebus thats even worse than I thought. Kill me now before my head explodes, that always leaves a big mess, so I try to avoid it.

[noparlpf]

By skewed I assume you mean there are parts of the cubes inside each other? Its not like putting together building blocks where you slap a cube on each surface of the first cube, then slap more cubes on each surface of THAT ad infinitum? Oh sweet monkey jeebus thats even worse than I thought. Kill me now before my head explodes, that always leaves a big mess, so I try to avoid it.

Well a tesseract (hypercube) has eight "faces" made of cubes, the way a cube has six faces made of squares.
So this is a cube represented in two dimensions:
http://upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Necker_cube.svg/400px-Necker_cube.svg.png
And here's a Wikipedia article on tesseracts (http://en.wikipedia.org/wiki/Tesseract). The image on the top right? Each of those vaguely trapezoidal chambers is also a cube, and the inner and outer cubes are the same size.

[Bulldog Psion]

This is fascinating. And makes me feel the edges of Lovecraftian madness brushing at my mind. Especially watching the moving projections of those tesseracts on Wikipedia -- because it makes a weird kind of sense. :smalleek: :smallcool:

[Weezer]

I'd actually recommend not getting caught up in the nitty gritty details of how a 4 dimensional building would work, unless those details are directly important for the story. Someone reading the book won't want to encounter a treatise how multi-dimensional architecture. Have the dimensionality of the building turn up more in how your characters see/are effected/are confused by them (see how lovecraft did it). A sufficiently effective visual description, coupled with suitable reactions from the characters should be plenty.

[Traab]

Yeah, their eyes crossing or refusing to focus if the people inside try to follow its lines, ending up in a place that doesnt make sense considering the direction they left in, the perspectives are all wrong, make it seem like the house follows a set of rules that arent very clear or easy to follow. There is a pattern, but its just out of everyones reach.

[Icewalker]

I'd actually recommend not getting caught up in the nitty gritty details of how a 4 dimensional building would work, unless those details are directly important for the story. Someone reading the book won't want to encounter a treatise how multi-dimensional architecture. Have the dimensionality of the building turn up more in how your characters see/are effected/are confused by them (see how lovecraft did it). A sufficiently effective visual description, coupled with suitable reactions from the characters should be plenty.

Agreed! This kind of thing often makes for a better story. At the same time, if you have entities who are perfectly comfortable with the 4D physics, it can be interesting to juxtapose the two, with these characters shrugging off the oddities and confusion as things they are familiar with. Lots of options!


Yeah, their eyes crossing or refusing to focus if the people inside try to follow its lines, ending up in a place that doesnt make sense considering the direction they left in, the perspectives are all wrong, make it seem like the house follows a set of rules that arent very clear or easy to follow. There is a pattern, but its just out of everyones reach.

Here's the thing, though: while you can do stuff like this, you might be describing some non-euclidian architecture, not necessarily an accurate 4D architecture. Of course, at the same time, because we can't comprehend 4D visuals, we can't really do a good job predicting how we would react to them, and what about them would confuse and disorient.

[Tengu_temp]

I'd actually recommend not getting caught up in the nitty gritty details of how a 4 dimensional building would work, unless those details are directly important for the story. Someone reading the book won't want to encounter a treatise how multi-dimensional architecture. Have the dimensionality of the building turn up more in how your characters see/are effected/are confused by them (see how lovecraft did it). A sufficiently effective visual description, coupled with suitable reactions from the characters should be plenty.

An author who wants to write a book that includes a specific topic doesn't need to include a treatise on this topic in the book, no. But at the same time, the author should do research on the topic, so knowledgable readers will know he's not talking out of his ass. The moment you realize the supposedly scientifically-accurate book you picked up is anything but, your immersion shatters.

[Fibinachi]

"I walked down the hallway
Meandering north
So that when I want to walk back
I have to go the same way - east

My kitchen's in tomorrow, my sink somewhere AD
(I forget where I keep the broom closet)
While maybe yesterday the possible mailman will deliver
through the ceiling-roof
a package
which will come through the door that isn't there and end up
on my stairway
tomorrow
where I will trip, coming down
from my basement room (3rd floor, good view)
yet land safely on the portrait hanging from the wall
You know, the knight and the dragon opposite the floor"

Alternatively, if the architect is asked to draw a 4th Dimensional building, would the person asking this be N. Arla from Thotep?

What's the use of the building, the reason behind its construction, the impetus that drives someone to want such an edifice to the spatially challenged?

[Urpriest]

An author who wants to write a book that includes a specific topic doesn't need to include a treatise on this topic in the book, no. But at the same time, the author should do research on the topic, so knowledgable readers will know he's not talking out of his ass. The moment you realize the supposedly scientifically-accurate book you picked up is anything but, your immersion shatters.

Yes, but in this particular situation the immersion-shattering detail sounds like whether or not the building is four-dimensional in the first place, not any particular details of the building itself, given that it sounds like no details of the building are necessary.

[Icewalker]

Yes, but in this particular situation the immersion-shattering detail sounds like whether or not the building is four-dimensional in the first place, not any particular details of the building itself, given that it sounds like no details of the building are necessary.

Not necessarily. Depends on what he's writing. I'm super in agreement with Tengu here.


"I walked down the hallway
Meandering north
So that when I want to walk back
I have to go the same way - east


For example if I saw this in a description, while I would understand it was a crazy and non-euclidean design, if I was told was a 4 dimensional house, I would be distracted because I'd recognize that the author didn't understand extra spacial dimensions, and it'd make it less immersive for me.

[Morph Bark]

In case of a fourth spatial dimension, is that simply things being bigger on the inside than on the outside, needing five or more turns around a "square" building to get back to your begin point, and/or the possibility of going through a tunnel and finding yourself on the other side of the planet?

[nedz]

We would likely perceive any four dimensional structure as a three dimensional hyper-plane. A hyper-plane is like taking a two-dimensional slice through a three dimensional object. So as we, and the structure, moved through the fourth dimension: we would experience the structure as morphing, in a linear manner.

Non-Euclidean geometry is an entirely different thing. You can have Non-Euclidean geometry in two dimensions, for example.

[Morph Bark]

If there is a simpler explanation, or rather one that builds up slowly to make it easier to understand, about a possible fourth spatial dimension (kind of like the video Amidus Drexel linked in the second post, except that one was about the fourth dimension being time-related), then I would much appreciate it.

For instance, I have little grasp on non-Euclidian geometry. In fact, I had to look up what it was exactly again just now, because the last time I saw people talking about things being non-Euclidian, it was someone claiming non-Euclidian objects cannot exist in our world, despite that simply referring to round objects.

Also, I could understand the bit about us likely experiencing "the structure as morphing", but I got immensely confused what you meant by "in a linear manner". (I sort of guess you mean that it would appear to be changing in more than one direction, even though we're only going forward?)

[GnomeFighter]

We would likely perceive any four dimensional structure as a three dimensional hyper-plane. A hyper-plane is like taking a two-dimensional slice through a three dimensional object. So as we, and the structure, moved through the fourth dimension: we would experience the structure as morphing, in a linear manner.

Non-Euclidean geometry is an entirely different thing. You can have Non-Euclidean geometry in two dimensions, for example.

And Euclidean geometry in four dimensions.

[A Rainy Knight]

Also, I could understand the bit about us likely experiencing "the structure as morphing", but I got immensely confused what you meant by "in a linear manner". (I sort of guess you mean that it would appear to be changing in more than one direction, even though we're only going forward?)

This is just my guess at what is meant:

If we wanted to make a 3D space something that could be experienced by someone who can only experience two dimensions, we could do it by sweeping this 2D person's plane of observation through the 3D world. It would appear to the 2D dweller that things were appearing, disappearing, and changing in his world whenever one planar cross-section contained something different from the one before it. Still, it can be called 'linear' because we can only sweep the plane up and down in one dimension. If we've been 'morphing' the contents of the plane by moving it continually upwards, our only options are to continue moving it upwards or to bring it back down along the same path, so there's essentially a single 'line' of morphing that is perceived in the plane. Then just kick everything up a dimension and it's sort of analogous.

[nedz]

And Euclidean geometry in four dimensions.
Yes, in fact I was sticking to Euclidean Geometry to try and minimise confusion. I'm not sure I succeeded — but this stuff is hard to get your head around.

This is just my guess at what is meant:

If we wanted to make a 3D space something that could be experienced by someone who can only experience two dimensions, we could do it by sweeping this 2D person's plane of observation through the 3D world. It would appear to the 2D dweller that things were appearing, disappearing, and changing in his world whenever one planar cross-section contained something different from the one before it. Still, it can be called 'linear' because we can only sweep the plane up and down in one dimension. If we've been 'morphing' the contents of the plane by moving it continually upwards, our only options are to continue moving it upwards or to bring it back down along the same path, so there's essentially a single 'line' of morphing that is perceived in the plane. Then just kick everything up a dimension and it's sort of analogous.

Yes — exactly.

I linked to the text of Flatlands in post #14. This explains it very much better.

[Lord Loss]

Wow! You guys are just plain awesome!

Thanks for that long and detailed explanation Icewalker! You're a boss!

Also Flatland is proving to be really interesting.

I'm writing about a drunken, unemployed architect who's bordering on broke and shut himself away in a dying town in the middle of nowhere. Which is when he starts hearing clocks ticking away, voices who seem to know him too well and the barking of dogs. Other important characters are the barmaid Sonata who works at the local bar and a strange man called Byron who lives right next door from him.

It's the voices who force him to create a four dimensional buildings, for reasons he doesn't fully understand. Therefore I'd like both my character to slowly start to learn about and eventually be subjected to the workings of the fourth dimension.

[Kelb_Panthera]

Wow! You guys are just plain awesome!

Thanks for that long and detailed explanation Icewalker! You're a boss!

Also Flatland is proving to be really interesting.

I'm writing about a drunken, unemployed architect who's bordering on broke and shut himself away in a dying town in the middle of nowhere. Which is when he starts hearing clocks ticking away, voices who seem to know him too well and the barking of dogs. Other important characters are the barmaid Sonata who works at the local bar and a strange man called Byron who lives right next door from him.

It's the voices who force him to create a four dimensional buildings, for reasons he doesn't fully understand. Therefore I'd like both my character to slowly start to learn about and eventually be subjected to the workings of the fourth dimension.

Lovecraft would approve, I think. :smallcool:

[Lord Loss]

Thanks!! I'm a huge fan of lovecraft, despite not having read all that many of his works. The story started out with just the main character, then Sonata got thrown in there, then the clocks, then the idea of an architect making four dimensional buildings, and before I knew it it had turned lovecraftian!

[The Second]

Let me see if I've got a handle on this.

Suppose that 4d space could be expressed as a small cubical room. I am standing in the center of this room, halfway up a ladder that reaches floor to ceiling.

The room I am in now is connected to eight other rooms, each identical to the one I am standing in.

The room I am in now is at the center of the eight rooms.

To reach the north wall of the room, I must travel forward.

To reach the west wall of the room, I must travel left.

For the south and east walls, I simply have to travel along the inverse of the direction I used to travel to the north and west walls.

To reach the ceiling I must travel up, and to reach the floor, down.

If I travel inward-north, through 4D space, I will reach the inward-north room, standing halfway up a ladder that reaches floor to ceiling in this room. If I travel outward-south, I will reach the outward-south room and still be standing halfway up the ladder.

Lets then assume that there's also a 4D me.

3D me: I exist in only one of the identical rooms, 4D rooms. I can only travel in 3D, north south east west up and down, or any combination of the six.

4D me: my physical presence is within some, but not all of the rooms; my head takes up space in the up-center room, my torso is in the center room, and my feet are in the down-center room, left arm in the west-center, right arm in the east-center, so on and so forth. When I travel I must travel 4D, that is, I can travel in-north or out-north, but I cannot travel only north or in.

When I travel, I leave the 4D space I was once occupying and arrive at another 4D space.

My 3D self is in the center room and, if I could perceive a 4D reality, would
perceive my 4D self, but only the part of my 4D self that exists in the center room. If my 4D self were to take my 3D self by the hand and guide me to the up-center room, my 3D self would not perceive the room moving, but would notice that my body 4D self's body seems to move through 3D space. Once my 3D self is in the up-center room, my 3D self no longer perceives what was in the center room, but only what is in the up-center room, that is, my 4D self's head. Neither my 3D or 4D self have moved from the center of the room, but my 3D self has moved from the center of the center room to the center of the up-center room.

Now that that's done with, I'm never thinking about 4D spaces again. They make my head hurt.

[Icewalker]

Oof, yeah, trying to start envisioning existing yourself in 4 dimensional space gets especially confusing. And terminology is always a huge barrier.

Lord Loss, that sounds super cool. Short story, or something longer? Sounds like it'd be a fun read.

[Lord Loss]

Novel or novella length. Between 30 000 and 50 000 words. My ideas are all still really vague, it should take me a few weeks until I get to the writing, which I'll probably start over the Christmas break.

[killer_monk]

Don't think about anything said so far too hard, this stuff will fry you're brain like an egg...

[Lord Loss]

My friend and I now have headaches from overthinking 4D physics. My head. My poor, poor head. :smalltongue:

[Icewalker]

The best headaches.

[Slipperychicken]

Does it matter?


Supposing we're the "flatlanders", who exist entirely in our three or four dimensions, we can't suddenly thrust our influence into a 5th dimension, or bend it, or travel through it, or build into it, or whatever.

To us flatlanders, a "extra-dimensional" incursion or excursion (like a hole appearing in the "paper" flat-land) would be a truly bizarre event, with objects seeming to appear or disappear inexplicably. But do any such events (inexplicable disappearance or appearance) actually happen? I'm vaguely aware there's some rare insignificant particle which appears to do that... but is it actually enough for there to be any practical concern?

Does the fifth or sixth or seventh dimension actually mean anything to us living in the real world, or is it just some ethereal, indeterminate nonsense which has no effect outside our imaginations?

[Marillion]

Piers Anthony, in one of the later Xanth books, had his characters explore a series of increasingly hyper-dimensional worlds. The first, of course, was a tesseract, and when they figure that out they move on to a torus, and so on. It's been a very long time since I read it, but though I never quite got my head around it, he seemed to understand what he was talking about.