# HOW TO VISUALIZE 4D SPACE

Evilember

IM ON A MISSION SCI

LISTEN UP:
THE FOURTH DIMENSION

IF YOU DONT ALREADY KNOW WHAT A HYPERCUBE IS GTFO

NO BRAINLETS ALLOWED, Of course I can't enforce that so the criteria I'm specifying is just at least have basic understanding of what 4D space is and how it works. I don't want this thread clogged up with spoonfeeding about basic brainlet shit.

Now, my mission. I want to visualize in 4D. I want to get my internal imagination to actually understand what an axis perpendicular to x/y/z actually is on an intuitive level. I already can understand the basic idea of course, but I feel like a 2D creature reasoning about cubes, but only able to imagine lines.

So far I think my best bet at gaining this intuition is examining how 3D cubes rotate in 4D space. It seems this should come far easier than jumping to hypercubes right away. While we are pretty good at visualizing 3D from 2D projections..attempting to visualize 4D from 2D projections is kinda absurd. Luckily many apps for examining 4D objects allow stereoscopic views. Unfortunately I haven't found any app which has just a 3D cube in 4D space, instead they're all 4D hypercubes. Cool to look at and help understand the basic idea, not as useful for trying to actually give yourself a new perception.

Pic related, its a 3D cube rotating on XW axis in 4D space. I fucking hate how simple it is, ffs...its so obvious, when its getting 'smaller' its actually just getting farther away in 4D space, however I just can't seem to perceive what that really means. It still looks like a 3D cube turning inside out. I want to REALLY SEE what its actually doing

SniperWish

Does anyone have a visualization of a 2D plane rotating in 4D space...I think that may help.

Dreamworx

IT HAS TO BE POSSIBLE

SCI HELP ME

Lunatick

I hate how I'm so fucking close but just can't quite get it.

I totally get how it works and all but I don't ///get/// it. I keep watching the gif but it just looks like a 3D cube being deformed, I can't seem to actually 'see' the smaller face as not smaller but 'farther away'

Crazy_Nice

You're FREAKING OUT MAN
4D is nothing interesting. It's simply the way in which the universe or any other body of space is wrapped around itself. There are no outer edges of the universe. You can go in any direction you want and what is behind you wraps around in all directions such that you would return to the same spot if you were to travel far enough.
Smoke a ton of weed or take edibles n you'll understand

@Crazy_Nice
I know what it IS, I know HOW it works, but I can't SEE it. I want to perceive it. Look at the 2D plane rotating in 3D space. You can switch back and forth from seeing it as what it is, a square rotating in 3D space, or what the image is, a square deformed into a trapezoid, going through itself and becoming a square again.

I know the 3D cube in 4D is the same thing but I just can't seem to make the perceptual 'pop' into 4D space.

MPmaster

@Crazy_Nice
also that's incorrect, you're talking about hyperbolic space, not 4D

Spamalot

Wait so what do you see in the op picture? Cuz I see it moving inside itself on the left and then wrapping around on the right

cum2soon

@Spamalot
yes, but thats not what actually is happening, its actually not being deformed at all. You are seeing a deformed 3D cube, but that is a projection of its 4D position. one face stays stationary, just as one side stays stationary with the 2D square rotating in 3D.

I thought I said no fucking brainlets. this is exactly the kind of basic shit I'm already long past.

Playboyize

@Evilember
Thinking in terms of a heat map can get the job done.

You can already visualize 3D space.

A heat map would ascribe a color (from a 1D gradient) to each point of this 3D space (functions from R^3 to R do this).
Note: This method is deficient for arbitrary 4D configurations (think vertical line test)

Now for arbitrary 4D configurations, it would not be just one color ascribed to each point in R^3, but instead, an entire set of colors assigned to each point of R^3.

Every rotation in 2D fixes a 0D point
Every rotation in 3D fixes a 1D line
Every rotation in 4D fixes a 2D plane

If your fixed plane of the 4D rotation is parallel to the "color axis" you will see no change of the colors.
These types of rotations would look like ordinary rotations of the heat map in 3D.

Now If your fixed plane of the 4D rotation is not parallel to the "color axis" you will see change of the colors through the rotation and the heat map will rotate elliptically in 3D (or just linearly oscillate if the "color axis" is perpendicular to the fixed plane).
You can understand the elliptical rotation if you imagine a tilted circle in 3D projected orthogonally to a plane.

I encourage you to try the same heat map technique in 2D to try to represent the familiar 3D rotations.

It also might help if you discretize the space using lattice points so you can see what is going on better.

Gigastrength

@Evilember
The distortions arise from the perspective projection. If you were to orthogonal projections (perspective at infinity) the distortions would go away.

They happen when a portion of the object "goes behind" the projection point.

Burnblaze

@Evilember
haha funny how you don't want brainlets in the thread, being a massive brainlet yourself

SniperGod

@Burnblaze
damn i sure hope op had an insurance policy cause his shit just got REKT

TalkBomber

Dimensions don't exist, they're simply just products of the human imagination. Similar to maths and numbers.

JunkTop

@Evilember
I want to visualize in 4D
This is not physically possible. At best, you can intuit a 3D representation of a 4D object, but you can't actually visualize in 4D.

CodeBuns

@Playboyize
yea I've tried such an approach

@Gigastrength
the size distortions yes. I should be able to perceive it either way

@TalkBomber
stfu brainlet

calling others brainlets

New_Cliche

@Playboyize
I've tried such an approach but it only helps in understanding what 4D space IS, not seeing it. I fully understand how it works, I'm trying to actually see it. To be able to imagine actual 4D space. Without external input it's very difficult, I'm hoping that by using stereoscopic things, maybe even designing some sort of small game, I could gain this ability. I think the game may work because it would associate a reward with better understanding.

@JunkTop
Says you, brainlet.

There's absolutely no reason this can't be done. I am only worried its more difficult than I'm assuming.

I have a strong 3D representation intuition for it. I can visualize in 4D in some sense, but I don't think its accurate, if anything its probably some specific limited form.

Supergrass

@New_Cliche
There's absolutely no reason this can't be done.
You're being a retard.

A 2D plane is a collection of 1D lines. A 3D space is a collection of 2D planes. Ergo, a 4D hyperspace (I'm not sure what it would actually be called, but hyperspace sounds cool) would be a collection of 3D spaces. You would need an exponentially larger amount of brain power in order to process that much information at once.

Another way of thinking about it, is that you would need an exponential amount of the areas of the brain that process spatial awareness in order for you to see in actual four dimensions. You aren't going to compensate for that by concentrating on 4D properties.

Extrapolating from lesser dimensions, it should become readily apparent how absurd it would be: when looking at 2D things in 3D, you can see all sides contained within the 2D plane, so if you were looking at a 3D object in 4D, you would see every possible side of that object at once, something that you can't even imagine. It's like being blind, and trying to imagine the colour blue.

I'm going to hope, for your sake, that you're just posting bait and fishing for (You)s

Lord_Tryzalot

@Supergrass
You would need an exponentially larger amount of brain power in order to process that much information at once.
top fucking kek. its not 1:1 represented physically on your neurons you fucking tard. Even still, that just limits the complexity that can be achieved. A cube should still be ez.

so if you were looking at a 3D object in 4D, you would see every possible side of that object at once, something that you can't even imagine.
Uh, no shit, thats what I'm trying to accomplish. Look at the first gif, you can see all sides in that. The only reason you wouldn't be able to is because it's a 3d projection

takes2long

@Evilember
It's like a paper with a square and the square is rotating along an axis in 3-space parallel to the paper. Really if you have a 2x2 square then you can warp the paper a maximum height of 2 to make any points additionally 2+ away or sqrt(2^2+2^2+2^2) and easy to make it such that it doesn't even fit on a flat piece of paper and looks warped if you straighten the paper along with it.

Also a 4-plane divides 4-space into two but the thing in the middle is not a 2-surface but a 3-volume.

massdebater

@Lord_Tryzalot
top fucking kek. its not 1:1 represented physically on your neurons you fucking tard.
No shit it isn't a 1:1 relation, but it still has to store/process an exponentially larger amount of information, and you can't willpower that ability, end of discussion.
On a side note, it's clear you haven't studied much neuropsychology, so I'll point you to the wikipedia page for grid cells and hope you might get a better idea on why your goal is a fool's errand.
https://en.wikipedia.org/wiki/Grid_cell

idontknow

@MPmaster
Actually that would be elliptic space

Skullbone

@massdebater
you can't willpower that ability
I'm not trying to visualize a 4D girl or some shit, just a hypercube. Its just 8 cubes. I can visualize 8 cubes, I can visualize them rotating on whatever axis, I can visualize them as having a 4th dimension which is a vector (time) and stacking their movement. I still hold it's absolutely reasonable that a human brain can visualize relatively simple 4D geometry.

No I am not a neuropsychologist, but I don't see why that cell has any limiting function.

I am a machine learning researcher, however. If a set of bare level weights can add up to managing 3D models, then the billions of magic little shits in my head can visualize a simple 4D object.

Spamalot

@Evilember
@New_Cliche
Try the 4D rubik's cube.

http://superliminal.com/cube/cube.htm

(Mathologer explanation)

Poker_Star

@Evilember
no brainlets allowed he says
is trashed on by Veeky Forums
muh 4d "There's absolutely no reason this can't be done"
actually just kys

Spazyfool

farquit

@Evilember
something that will be of absolutely no interest to you op is that there is experiment where people who were previously blind but then have their vision restored were given 3D shapes that they were familiar with from feeling alone and asked if they could identify them by sight alone having never seen them before, no connection between the real physical touch object and the perceived image in 3d space.

it turns out they could not put the two together.

the point being that perhaps not being able to see and interact with a 4D physical object is hindering your ability to visualize it properly.

of course there is always the possibility that a 4th physical dimension does not exist just as neither do lower dimensions. what exists other than what we can perceive?

SomethingNew

@Supergrass
The problems you descibe are insurmountable for humans, especicially considering our vision is in 2D (retina) with a perspective trick in our brains with two eyes to get a 3d perception of depth in our world.

We can see every aspect of a 2D flatlanders world at a given moment of his depth/time, with nothing ever being blocked/obstructed from our view. A 4D beings perspective of our world would be "total" 360 every angle at once, nothing hiden, but only for a given moment our time/4d/his Tdepth .

Bidwell

@Evilember
Like how it was said in @SomethingNew
, you'd have to process a 3D "spatial" vision to see in 4D, OP. Kinda like fusing all the cross-sections 2D visions of one object into one single vision. Try to imagine seeing the outside and inside of a cube at once and you'll be on the right track.

Sharpcharm

@Evilember
Have you tried 4D maze? It migh help somewhat.

I tried to install the 4D train, but I'm too stupid to follow the instructions properly.

RumChicken

@Sharpcharm
The creator of that game tried what you are trying, to limited sucess. Or maybe he failed.

If you see the 2d projection of a 3d cube, it sure looks like 2 squares (one big, one small inside) with 4 lines connecting them. But then it clicks, and it is a 3D cube. You have already described that process.

My question then, what makes you think that that "clicking" is not a brain in-build feature that no amount of training can replicate? I sure hope virtual reality headgear can allow science to answer that question some day.

BinaryMan

@RumChicken
With the amount of neurons we have, 4 digit multiplications without using paper should be trivial, yet here we are...

I encourage you to try the 4D maze thingie (it is not a 3d cut of a 4d space, it is a proper projection), but I'm not as optimistic as you are.

@Evilember
Your brain cant intuitively comprehend 4D space, not without lots of math in between anyway.

haveahappyday

Just try to visualize multiple discrete 3D slices of your 4D space. Then mentally take the continuum limit. If you train this to perfection, you should arrive at the limit of 4D visualization which is possible for you.

Skullbone

@Evilember
Have you tried watching Flatland?

Or the weeaboo version?
https://i.4cdn.org/wsg/1502551878634.webm

SniperGod

@Evilember
Play ya some Miegakure!

StrangeWizard

@Evilember
There are a few ways to do it, one is the embedding picture where you try to take 3-d slices of the object and embed it into our 3-d space, another is the stereo-graphic projection of objects from 4-d to 3-d (like how you can shine a light on a cube and get the shadow on a 2-d surface). You can also try using complex numbers to do it, as the complex line is actually 2 dimensional, which is why we call it the complex plane even though it's technically a line. Taking the two complex number together gives you an identification with 4-d, so there you go. There are many other tricks as well, but I'd suggest watching these videos first.
@Crazy_Nice
4D is nothing interesting
4-manifolds are some of the most interesting objects in all of modern geometry

A flatlander could make a 3d cube by holding a square and waiting in his Ztime for the depth to occur in our dimension. Like fast forwarding a movie and connecting the corners through time or stacking the frames upon each other..

kizzmybutt

@Skullbone
I am a machine learning researcher
high school, mate. you're in high school. and that's being generous.
If a set of bare level weights can add up to managing 3D models, then the billions of magic little shits in my head can visualize a simple 4D object.
no they shouldn't. what's so hard to get? it's not even a matter of brainpower it's a qualitative difference. human brains can't see 4D. of course computers can manage 3D models. but they don't see anything. they use linear/bilinear algebra or some shit. they can also manage 3D, 5D, 8D models and so can you if you process things like they do. but you won't be able to see it. it won't be proper geometry anymore. wait until uni, you'll learn about all of that.
probably b8ing though

Boy_vs_Girl

I think you can define a set of principles and rules and categories eg what is a plane in all the dimemensions and how a triangle in 3space is a tetrahedron in 4space and this is the minimum to calculate a normal.vector to the 3tri or 4tet and that a 4tet in 3space is just a 4tet with one of the vertices emersed like a triangle in 1d is a line or a triangle with a point in the middle submerged and that a cross product in 3d requires two vectors and is analogous to a perpendicular vector in 2d and in 4d requires two vectors.probably and you can see this as if you try to use a single axis vector.for.a rotation in 4space you get a.sphere of possible answers analogous to a circle in 3d if you use an axis of rotation and so need two angles.or axes in 4d.

idontknow

@Boy_vs_Girl
Ehh... Brainless

King_Martha

@SniperGod
That's a 3d cut of the 4d hyperspace. Have you see a CAT scan? Even us 3D-understanding beings are unable to properly understand the proportions of things if shown in 2d slices.

I doubt this is the right avenue.

PackManBrainlure

Skullbone

@Evilember
Try to imagine a fourth spatial dimension oh wait you cant since your brains imagination can only operate on:
Length
Height
Width

Evilember

Bumping to keep thread alive, som gud shit is in here

RavySnake

@Crazy_Nice
And the Earth had just been made and we're swimming in the water, didn't know then "was it a son, was it a daughter?", and it occurred to me that the animals are swimming around in the water in the oceans in our bodies. Another had been found, another ocean on the planet, given that our blood is just like the Atlantic. And how?

Well the universe is shaped exactly like the Earth, if you go straight along enough you'll end up where you were.

StonedTime

@Skullbone
Your brain is an abstraction engine, use it.

ZeroReborn

@Skullbone
Studied enough brain science to understand how human spacial visualization works and it's limitations.
Wow, that's really impressive, user!

PurpleCharger

@Skullbone
Ballsack.

Poker_Star

@Evilember
He just saw Flatland

AwesomeTucker

how can you visualize a dimension that you don't even exist in or interact with, let alone one that none of your senses can detect

baka

haveahappyday

@Dreamworx
It's not possible. There's a game called 4D Toys if you want to play around with them.
You'll never be able to visualize a 4D hypercube in its native dimension. Perhaps it would be possible somewhere down the line if you can augment your brain with a computer, but that hunk of cells in your skull won't cut it. The brain just doesn't have any system for 4D spatial analysis.

TreeEater

@Skullbone
Weight, density, color, texture, time, context, threat, importance, relation, interaction, synthesis, annoyance, level of bullshit, stupidity.... I think ya see where I'm going with this.

Supergrass

Do psychedelics OP

Trust me.

You will have no clue how to describe it, but you'll know it when you see it

Fried_Sushi

@Supergrass
Dont trust this dubious reddit fuck, he is a slave to substance, not mindfulness.

There's only one dimension of space; space.
The polar opposite of the dimension of space is counter space.
Look it up.

Sharpcharm

does that image preserve positive values of the moving rays? does the ultimate length of the bottom and top sections double or remain the same.

are there two sort of min=median/max values for side lengths that are not doing the rotating in this video.

also i suppose we could rotate this shape and lead to its 3D transformation via some 4D function no? or will the magnitude of the side lengths always be constant? or is there an oscillation occurring?

King_Martha

2D examples:
Imagine deleting a line from the plane. You're left with two infinite regions that are half planes, each pretty simple. You can shrink each one to a point.

If you delete a point from the plane, you're left with one region, but now it's not so simple. You've got a hole so you can't just shrink everything down to a point, but you can radially contract everything onto a circle centered at the removed point.

3D examples:
If you remove a line from 3-space, you can shrink everything onto an infinite cylinder surrounding the line, and then shrink the infinite cylinder to a circle.

If you remove a plane and a line which intersect at a single point, then the result space shrinks to two disjoint circles.

4D examples and exercises:
Remove a point from 4-space. You get a 3-sphere.

What if you remove a line? A plane? Two planes which intersect at a point? If you can figure these out you're well on your way to understanding 4D space, since you will have been forced to come up with ways to visualize it.

BunnyJinx

OP here
@Sharpcharm
its a 3D cube rotating along the XY axis in 4D space

I'm definitely getting closer. I can easily predict the 3D projection of different shapes in different rotations, fairly accurately. I feel like the 'pop' could happen any moment. I'm coding my own 4D vis toolkit to help as well. I think especially VR apps could help. If I could see in front of me in 3D several 3D forms rotating in 4D space, a plane, a cube, a sphere, a pyramid maybe, and then also their 4D forms rotating.

Its convenient how similar 4D rotation is to 3D compared to 2D. Looking at a cube and how the planes which comprise it rotate, become trapezoids folding in on themselves, makes it pretty obvious why the 4D hypercube looks as it does when rotating.

Supergrass

@BunnyJinx
hmm actually it seems just examining this gif and switching from 2D to 3D and examining how the switch occurs is helping. I can look at it in 2D and it just seems so fucking odd

oh also
@Supergrass
shut the fuck up, I've done acid 10 times now and seen some very interesting shit, fully rendered 3D fractals and shit. Not 4D though. Actually was aiming for it last trip but totally fucking forgot the entire time, the fractals are definitely pretty fucking cool tho.

Harmless_Venom

@Evilember
Implying the hypercube, represented heavily in popsci, is not already common knowledge, even among normies.
You're a brainlet, Op.

Just map the W axis to the time axis of 3d and use static 4d objects. This is how everyone else visualizes 4d and it works fine.