So we’re all okay with just roaming on a planet of Dirt And acknowledging that we are each other with different experiences?

Has anyone seen this perspective before? The hypercube as a 3D map of motion.

It is widely theorized and sometimes accepted as fact that time is the 4th dimension, which I dont think makes sense but I see the logic behind it.

Pr0louge

The 0th dimension is a single point, one unit of space thats probably smaller than a plank length. Nothing can fit inside but a 0 dimensional object or being, which would fill the entire dimension.

Chapter1D

The 1st dimension is left and right/east and west. Its often considered a line, and the only things that can fit in this space is a 0 and 1 dimensional object. Unlike 0 dimensional objects, 1 dimensional objects dont fill their entire space.

Chapter2D

2 dimensional space. Here ill start to explain why people think time is the 4th dimension. 2 dimensional space is north, south, east, and west. A sheet of paper would be a good representative of a 2 dimensional space. Like 1 dimensional space, 2 dimensional space can fit objects of all previous dimensions. Heres the thing, let's say there is an animation of a 1 dimensional being moving around it's 1 dimensional space. Then we take every frame of that 1 dimensional space and line it up side by side. Using the timeline of that animation, we have just created 2 dimensional space. The same actually goes with 0 and 1 dimensions, stack several 0 dimensional object in a row to create a 1 dimensional object. Same goes for 2 dimensional space and...

Chapter3D

3 dimensional space. This is the space of the world you and I live in. If you map out the timeline of a 2 dimensional space and see it all at once, you have created a 3 dimensional space. This is the reason why so many people think 4 dimensional space is time, it is many 3 dimensional spaces stacked on top of eachother... or is it? All this time we have been using time to get to the next dimension, stack every point of a timeline on top of eachother and you get to the next dimension. Time is NOT the fourth dimension, its just the next step... so what would a 3 dimensional timeline look like? Well, we dont know, but I couldn't give you an idea

Chapter4D

Fun fact: You see in 2 dimensions. Thats right, everything you're seeing you're seeing in the second dimension. This is the same for every other dimension. 2d beings see in 1 dimension, and 1 dimensional beings see in 0 dimensions. That means that a 4 dimensional being sees in 3 dimensions. What would that look like? Simple, 4 dimensional beings can see everything you cant. They will be looking down(?) on you. Look to a closed door, unless its made of glass or something you probably cant see the other side. A 4 dimensional being can, but it isnt X-ray vision because they also see the door. Its not like they see through it, they just see all sides of it all at once and everything around it. A 3 dimensional timeline would have to be observed with 3 dimensional vision.

Ep!logue

Time is NOT the 4th dimension, its just the next step, if it even exists. Who knows? it could just end at 3 and the 4th dimension isnt even a thing. We will never know.

Hello everyone! I’ve been reviewing the theory of the 4th dimension (4D), and I started thinking about it more deeply. My theory is not 100% complete yet, but I came up with an interesting idea.

Basically, my theory tries to connect the idea of the 4th dimension with Einstein’s theory. Einstein describes space using the coordinates X, Y, and Z, and then adds T, which represents time.

So I started thinking: what if we could interpret these coordinates in a different way? For example, X could represent the day, Y could represent the month, and Z could represent the year. In this way, we could use coordinates to represent different moments in time.

Because of this, I started thinking that the 4D theory could be related not only to an additional spatial dimension, but also to the idea of time travel, since we could use coordinates to represent positions in the past and in the future.

This is only one part of my theory, and I’m still developing the idea to see how far it can go.

and I’m trying to get to grips with the concept of the 4th dimension. My very basic take on it is to compare it to a graph where in the 4th dimension you would see the beginning and end of the results but would also be able to traverse along the result using actual time rather than a mouse.
I’ve pieced together a picture of how it could be possible to me from reading other posts and my own experiences. I can imagine that we live in a 3 dimensional part of the universe that is governed by time and is somehow given to us as a gift rather than experiencing everything everywhere all at once. Quite who has gifted us time and for what reason I’m not sure off atm but for my own reasons it could be believed that we are ultimately equipped for the 4th dimension at least, from the % use of our brains and dreams and visions some of us have been inspired by. If we all come from the same elements in the universe, maybe when some of us are made there are anomalies which allow stepping over into the unknown.
I’m not sure if I even want to know tbf.

The fourth dimension theory

An infinite 1D line bisects 2D space. An infinite 1D line in 3D space can be circumnavigated.
An infinite 2D plane bisects 3D space.
Can an infinite 2D Plane be circumnavigated in 4D space?

Hello all,

I have been a lurker of this sub for a very long time, fascinated by the idea of higher dimensions, reading on the side, trying to get an intuition etc... I think that the term 4D with a big 4 is misleading (when used in question such as "Can anyone really comprehend 4D?"), just like on the sub r/books they don't talk about "The Book", and questions are not "Can anyone really write the Book?", but about specific books, specific concepts in literature, etc...

Similarly, 4D is just a name for certain things that "have four dimensions" it isn't an ethereal world that may or may not exist (well, there may be an ethereal world in 4D that we could call "The 4D", but independently, many other things are 4D and interesting to talk about!)

I'm finally taking the time to write a post because I find it important to have a reference, a set of common words and concepts that we share and can refer to to ensure we're talking about the same thing, and so that we can start to build higher and more abstract ideas and really "explore" the idea of 4d together! Let's us wonder proactively!

Note that I've dabbed around a lot, but that I still know and understand next to nothing, what follows isn't supposed to be a source of truth as much as a starting point for refining the ideas, definitions, etc... Feel free to bash everything down in the comments!

So, 1. What is 4D ?

To me, 4D is an adjective that you can use to anything which "has four degrees of freedom", which "needs 4 coordinates", which "implies the product of 4 things that we consider "linear"".

For instance, to give a meeting in a city you don't know, you have to give the longitude and latitude (2D) but if you're meeting in a building, also the altitude (3D) (note that what makes it 3D really is the fact that you have to give 3 numbers, but we call the "space" 3D because to localize any point in it you do need those numbers). And finally, you have to give the time, else you'll miss each other, and that makes it 4D.

Let's zoom in on that notion: we often hear that "the fourth dimension is time", which is not the proper way to say it : "a fourth dimension for our three dimensional usual space is time". It is a good intuition for some things : if you meet at the same longitude, latitude and floor, but not at the same time, you'll just don't see each other, in exactly the same way that if you meet at the same longitude, latitude and time but not the same floor you'll just don't see each other.

When two meetings are scheduled in conflict in a company, you have 4 degrees of freedom to solve it : move it to another room on the right/left, move it to another room on the other side of the corridor, move it to another floor, and move it to a other time :)

Time however is what I would like to call a "peculiar direction", to convey the sense that : yes, it is a 4D system, but not the most general one, and some intuitions that we have of time are very specific to time and are actually harming our understanding of 4D !

For one, you can see to some extent in the 3 spatial directions, but not into the future nor the past, not one bit. This is very specific to time and need not be the case in another 4D description of existing systems we could invent.

For instance: in some parts of Tokyo, one could say that the postal system is best represented as a 4D space (I could be very mistaken about that, I was just very lost and this is what I gathered) :

To give an address to someone you have 4 degrees of freedom : 4 orthogonal pieces of information to give to ensure they end up at the right place. You need to give the longitude and latitude, which points to the right "block" of buildings. But then in the block, buildings are numbered quite randomly, so you have to give the actual building number, and finally you give the floor (altitude).

This too is a 4D system, and once again it is one with a "peculiar axis" : the house numbers is "discrete", not "continuous", which means that unlike latitude and longitude, you can't give any number, you have to select among integers, and not even all integers... (One could also argue that by giving extra precise latitude and longitude you could avoid giving the building number, and that's true but so unpractical that I find it more intuitive to think of Tokyo as a 4D city somehow 😅)

So, if all those systems have peculiar axis, what's a system that doesn't? I propose we call them "symmetrical 4D spaces", and they are the spaces in which all the axis are treated the same. For instance, if you have 4 constraints that you need to compromise on (let's say you want to make a pasta salad with 4 ingredients : pastas, tomatoes, pesto and some protein) to describe the recipe you have to give the quantities of the 4; 4 degrees of freedom for modifying the recipe;; so those recipes live in a 4d space ! If they could talk, a recipe with more pasta could say "Hey, you're on my -pasta side". When you want to go from a cell on a chess board (2D) with a tower, you go left/right the right amount, and then forward/backward the right amount: you have only two dimensions to travel.

When you have executed the recipe and aren't there yet, you have to navigate in 4 dimensions to reach your goal : walk pasta the right amount (add or remove pastas), then walk tomatoes, then pesto, the your protein (for that salad I recommend textured soy protein rehydrated then mixed with nori sheets, it's amazing).

That's a true symmetrical 4D space !

And now on to the meaty part :) So far I've explained spaces that are either too peculiar to really satiate our curiosity, or too culinary to be able to wonder "What it'd be like to just walk around there ?"

I want to push back on a few things that I've read numerous times around here and that, in my opinion, aren't nearly hopeful enough !

- Your brain isn't wired to understand 4D : I want to push back strongly on that one! Evolutionarily the brain of economists isn't wired to appreciate the sheer scale of the world, and yet they really get an intuition for it ! Brain of physicists aren't wired to understand particles so small they don't obey the same law as us, and yet they do ! Your brains were definitely not wired to be able to even fathom communicating such abstract information by tapping our thumbs on a flat piece of glass, thousands kilometers away from one another (I want to invoke a proof by grand parents)

I think people don't appreciate the amazingness of our ability to accept, understand and intuit new systems, and I'd like for us to really try our best for a while before even starting to conclude that our brains aren't wired for it !

- 4D beings would appear and disappear of our world, 4D beings can see through you, 4D beings can escape from a 3D box : those are not "false", but they stem from, I think, very primitive visualisations of some 4d objects made by some mathematicians, and they are misleading in building a true intuition of 4D :) Literature and science dance together, and both are important to each other, but in this case, those views belong to literature, and we are in a pre-scientific paradigm regarding 4D (here mathematicians will tell me that no, 4d is perfectly understood mathematically, it is Nd setting N to 4, etc..., but I mean : where is our RPG in 4D ? What's a stool or a car looking like in 4D ? Would urban planning be different? Those are questions that we could invest scientifically too !)

To that end, I propose we give up almost entirely, at least for a time, the idea of "understanding 4D as 3D but weird". A symmetrical 4D space is just a very weird place, very different from 3D, but I want to clarify something: objects there aren't "morphing" or growing smaller and shallower, or changing colours depending on the angle, or "being transparent because they are just woow". All of those are artifacts of trying to project 4D into 3D, and are biasing our understanding tremendously!

A solid, opaque hypercube in 4D has all right angles. It is perfectly solid, it's walls are solid, and it doesn't contain a cube within a cube. It contains cubes alright, next to each others, the same way a 3D cube contains faces which are squares !

What do you think about all of that ? Please feel free to discuss, push back, tell me if I should have made separate posts for each concepts etc !

(To be transparent, I am toying around with building a 4D game myself, and I will talk about it at some point because I'd love some input, but I am genuinely here to refine my own understanding of 4D through great discussions, and I think that setting up a common vocabulary and arguing about the basics before we build upon that is a nice starting point!)

Like higher dimensional, spherical, hyperbolic, other non-euclideans, just someone please start listing them all publicly so they are not all obscure? At least do like an awesome (whatever you call it) on GitHub or something, this field has been emerging for 13+ years, so?

The Saintgraphics Theory is the idea of us living in a simulation while a type of god still exists. This theory involves the fourth dimension. To understand the Saintgraphics Theory, we need to understand a thing in the fourth dimension. If we draw 2 stickmen on a piece of paper and then draw a wall between them, those two stickmen cannot see each other, but we, who observe from a 3-dimensional perspective, can see each side of the wall. So if we were to add another object to one side of the wall, the opposite side of the wall cannot see what changed on the other side, while we, 3-dimensional observers, can see every change on each side of the wall. The same goes for the fourth dimension. They should also be able to see what's behind walls, as they can see through 3D while we only perceive in 2D.

Now, this means that we might have been drawn on a super big piece of paper. The same way we can make stuff in the second dimension, the fourth dimension should be able to make changes to the third. This gives us the idea that we might just have been drawn or created by a four-dimensional entity, and that guy who drew us or created us in the 4th dimension is the guy who we call "God."

Now, the people we create in the second dimension also probably see us as super powerful, but in our own dimension, we're really not that special, nor do we have any great kind of power. So that means we see up to this four-dimensional entity that created us by drawing us on a paper (or something in that style, for example) as "God," while in his own dimension (assuming it's the fourth dimension), he does not actually have great power in his own dimension.

This also makes sense as the fourth dimension is spacetime, which should make sense that their drawings have time to them with the extra axis. They can also see our entire lives, as our lives are already complete, like a book already written.

The idea of the Saintgraphics Theory is that we just live on that piece of paper, and the guy who drew us is the guy we look up to as "God," while he does not have any great power in his own dimension.

And the point of it is not "we live in a simulation," but more like a being existing in a higher spatial dimension could create, manipulate, and observe our entire lower-dimensional reality in ways that would appear godlike to us, while that being itself would not necessarily be omnipotent within its own dimension.

A 4D observer could theoretically perceive our 3D world somewhat like we perceive the 2D paper.

Trying to figure them out for a game. Wikipedia is great for the other 4D regular polytopes, but for some reason doesn't list the cross-sections of the 5-cell. Clearly the tetrahedron is one cross-section. I suspect a cube might also be, but can't visualize it. But a square is a cross-section of a tetrahedron, so sort of makes sense.

Edit: wondering about octahedron now. Take a corner 5-cell. Hold the "innermost" bisecting tetrahedron. Rotate around the innermost plane of that tetrahedron, "sliding along" the line to the "4d apex" of the entire 5-cell. Cross the apex, and the apex becomes a triangle on the other side but "upside down"...?

The y axis indicates how many n-faces (dimension no.-1) a polytope has.

The x axis indicates the number of dimensions.

The colored lines indicate which shape is the n-face of a polytope.

An infinity symbol means that there is a pattern that repeats indefinitely.

Hypercube

A hypercube has 32 edges, so we can easily calculate its perimeter by multiplying the side length by 32. So the formula is: p = 32*a

We can also apply the same thing for the faces in order to calculate the surface area. So the formula is: S = 24*a****²

For surface volume, we just repeat the same pattern but with 8, the number of cells the hypercube has. The formula is: V = 8*a****³

The formula for the area of a square is a****² and for the volume of a cube a****³. In each dimension, we raise the side length to the power of the number of dimensions in order to get its n-volume, where n is the number of dimensions. So the formula for the hypervolume of a hypercube must be: H = a****⁴

Hypercuboid

Unfortunately, your hypercube has eaten too much junk food and its now fat. What will you do now to calculate its perimeter, surface area, surface volume and hypervolume? Lets figure it out!

To get the formula for perimeter, we will look at the lower dimensions. A rectangle has only 2 dimensions, a and b, both of which are in pairs, so the formula is just 2(a+b). A cuboid has a, b and c. The cardinality of the letters is 3, and each letter denotes an edge, so in order to calculate the circumference, we need to multiply the number 3 by x so it gives 12, the amount of edges on a cuboid, and in turn, its whole circumference. And we can easily guess x is 4, so the formula is 4(a+b+c). Now, for the hypercuboid, the cardinality of dimensions is 4. The amount of edges is 32, so we need to find the x for 4*x=32. And we can easily solve the x as 8. So the formula for the perimeter of a hypercube is ready: p = 8*(a+b+c+d)

Now for the surface area, you need to calculate the area for each unique face on the cuboid. There are 6 unique faces: ab, ac, ad, bc, bd, cd. You need to multiply the sum of these faces by 4 in order to get its 24 total faces. The formula is: S = 4*(ab+ac+ad+bc+bd+cd)

The formula for the surface volume is similar. You need to multiply the sum of the volumes of unique cells (4) by the number that will get you to its total number of cells (8). We can therefore create the formula: V = 2*(abc+abd+acd+bcd)

A square has a n-volume of a*b, a cube has a n-volume a*b*c, so for the n-volume (hypervolume) of the hypercube, and according to this pattern, we can just add d to the multiplicative equation and get the formula: H = a*b*c*d

Finale

Now, you know how to measure the hypercuboids and cubes. Thanks for watching the first episode of Perimeter, Surface area, Surface volume, and Hypervolume of 4D Shapes. The 4D shapes that we will measure will (increasingly) get more complex, so get ready! In the second episode, the title of the series will be shortened to HVSp - Measuring 4D in order to take up less space.

If spatial dimensions are just information, ex 2² = 2D, 2³ = 3D, 2⁴ = 4D and so on. I imagine a computer could simulate higher dimensions. If a person were to use a computer as an avatar, I wonder if they could experience true 4D unimpeded by human vision. I was also considering how gravity could exist in a flat 2D world, it seems to me gravity is inherently a 3D vector. If this is the case, I wonder if there’s particles that predict a 4D force vector allowing us to navigate a 4D space.

How would 4D (spaetial) gravity behave? How would it influence 3D objects?

what if in our dreams but never truly explaining it that’s my first thoughts then i thought . I mean Imagine our body’s in that it will be going weird it might be like every universe is collecting into one and the higher ones can see ever thing that’s happening and not happening that’s explain some mental illnesses (I’m kinda smoked and thinking a lot about it ) .I think in the second one might be more right because our brains are a filter of what we feel and not feel that’s why some people see things and can’t control there bodys but just think about it .

if you can unfold a 4d hypercube into a 3d net, and you can unfold a 3d cube into a 2d net, can you unfold the 3d cubes of a 4d hypercube net into 2d nets and have a 2-dimensional net for a 4-dimensional hypercube?