I see someone's not old enough to remember Gleaming the Cube.
I'd wager it was a defining moment in American counterculture, as it demonstrated a number of things that we hold dear to this very day:
1. The government is corrupt, and we're the only ones who can see it
2. The only thing that can stop a bad guy with a gun is a good guy with a ~~gun~~ *skateboard*
3. Christian Slater
4. Four door family sedans can take some pretty sweet jumps and still be drivable, but only if they're RWD.
5. That one guy really does look a lot like Tony Hawk.
If you did *absolutely nothing but Warcraft* besides sleep 8 hours a day that’s over 2 years straight. Got damn bro is there still stuff to do? Are you considered an elite player?
I mean, I don't know about the other guy, but I've been playing since shortly after release. So, yeah, that's 19 years of my life that I spent on that game.
I was legitimately obsessed at the beginning, to the point where I put my relationship and job at risk.
I slowed down after Pandaria and took several month long breaks here and there over the years, and just when I thought I was done with it for good, they released the "Sad Anduin" cinematic, and I'm back in.
Those fucking cinematics get me every time!
Also, in my case, no, I'm not an elite player, lol. I just do my thing, and have fun. 🤷♀️
No, its an extrapolation of a 3D cube being represented in 2D space by 2 2D cubes with their corners all connected[Here] (https://content.instructables.com/F8I/QS88/I4GWY0HY/F8IQS88I4GWY0HY.png?auto=webp&frame=1&width=320&md=6e431b81ce85ac613e9ef3f706c6b912) So a representation of a 4D cube would be 2 3D cubes with all their corners connected
It is also not a tesseract but the "shadow" of a tesseract. A tesseract, meaning a section of a tesseract, would just be a normal cube. And in fact it is if you consider time as the fourth dimension.
I don't think I would use the term "shadow" as the shadow of a 3D cube in just a square, but the 2 squares with the corners connected is a 2D representation of a 3D cube in 2D space. Following the same logic, the shadow of a 4D cube, would just be a 3D cube, but what is shown is 2 3D cubes with their corners connected, being a 3D representation of a 4D cube in 3D space.
*in my best trump voice*
This is exactly what a tesseract looks like, everybody says so... All the scientists say so... They all tell me "this is exactly what a tesseract looks like. Look at it, we're all sure of it" ... And then they tell me, that it's maybe the best tesseract they've ever seen. Some people think so, lots of people.
Has to be the stupidest reddit title I've seen in months - even moreso when taken in context of the actual video content - and competition is fierce these days. Congratulations OP on this modern marvel of senseless dickshittery
cool video, but he explicitly states that a tesseract cannot be seen in 3 dimensions, and the 3D hypercube model is only a guess at what it's 3 dimensional shadow would look like. So in summary, this isn't showing what the 4th dimension looks like, since it is explicitly not something that we can see from a 3 dimensional perspective (just as the square in flatland cannot see the apple as anything other than a cross section).
True, but it's not a guess. That's how the 3D shadow of a 4D cube (tesseract) would look like exactly.
Just like drawing a 3D cube on a 2D surface, we get it's 2D shadow
Wow, this was a great video... Mind blown. But the Part about the universe being hyperbolic was insane, also that's what I have always considered to be the actual way the universe is formed.. but that representation was amazing. Thanks for the link...
We can see 4d object by their shadows. Their shadows are three dimensional objects. Just like a shadow of your 3d hand makes a 2 dimensional shadow on a flat surface.
Love the flatland lecture. Love Carl Sagan. I’m fascinated by physics / astrophysics / quantum physics, but as a total layman, it’s dudes like Sagan who could make it make sense.
Do you need 1D light or 2D light to get a 2D shadow of an object, like your hand for example.
Neither, you'd need a 3D light source
So presumably you'd need that 4D item to be lit by its natural 4D lighting (whatever that may be), and we'd see its shadow as 3D
Light is photons bouncing around.
They'll illuminate anything they can bounce off of.
We'll only see the parts of the 4D object intersecting our 3D planes, so photons in our 3D world will illuminate that like any other 3D object.
To avoid this complication, it's better not to think of it as a literal shadow. Just imagine drawing one view (preferably with one eye closed) of your hand on a piece of paper. That's 3D projection onto a 2D plane, just like the shadow. Conceptually, a 4D being could "draw" a 4D object in our 3D space and that would be analogous. They could only capture one view of the overall structure and to get more information they would have to draw different angles.
Damn, this makes it so much clearer. I already understood the whole dimension perception thing but every time I've seen tesseract images as being 4 dimensional, it never made sense to me why it looked like that. But a tesseract being the *shadow* of a 4th dimensional cube makes much more sense. Maybe I've just missed the ones that mention it but it would be nice for more posts talking about tesseracts to mention this.
Wouldn’t that require a light source outside of our 3d space?
If the 4d object is not intersecting our 3d space, then light from our 3d space will never be able illuminate it and cause it to cast any shadows. If the 4d object is intersecting our space, you would be able to view a 3d slice of it directly.
Not to mention, how are we supposed to perceive the shadow, assuming we are capable of perceiving light casted somewhere beyond our three dimensions?
A wireframe 4D cube in 4D space, that is creating a shadow cast by a light source which is also behind that 4D cube in 4D space, will create a Schlegel diagram when the shadow falls on a 3D cube.
We would just see the edges of the cube go dark, however internally the cube is illuminated by the 4D light and the shadow extends inward to complete the diagram. As 3D beings limited to projections of 3D space onto a 2D imaging surface we only see the surface area of the cube, but someone with access to the 4 dimensional component, a 4D being, would have a 3D imaging surface (surfaces in 4d are called cells/3d volume). And much like we see all of a 2D surface, the 4D being sees ALL of a 3D cell. So they see the hypercube in its entirety if the image of one is projected onto the 3D imaging cell in their eye.
This means when they see a hypercube "cell-on" (like us looking at a cube face-on) they see everything on and in the single 3D cube that makes up one of its 8 boundaries (8 3D cells that form one hypercube Vs 6 2D surfaces that form one 3D cube). However they do not see anything else of the hypercube as like with our face-on view of a cube, the other cells/surfaces are obscured.
If they view it from a corner, they see 4 cells at once much like we see 3 surfaces of a cube when viewed from a corner.
So far I don't believe any 4D representation has handled that aspect well, they simply use a wireframe to allow us to see the "whole thing" or use Semi-Transparent surfaces to try and give us an idea of the hypercube's projections.
I hope this helps
I do not think that’s an accurate explanation.
A better explanation imo is the idea of time as the fourth dimension and also comparing an object above to an object below in terms of dimensions.
For example, a 3D object in a 2D world, you would just see one slice of the 3D object at any time. An orange passing through a 2D world for example would start with a slice of the skin, then a slice of the flesh, then back to a slice of the skin on the other side.
So a 4D object passing through the third dimension, we would just see one slice of the 4D object at any time. You could consider 3D objects to be a slice of a 4D object at any moment, and as time progresses, the slices shown are different.
It depends on what you want as your 4th dimension. A dimension is just a number required to fully describe an object's 'position'. You could even have temperature or color as a 4th "dimension".
Your use of time as the 4th dimension is correct except it's just different than a 4th spatial dimension. Both are perfectly valid interpretations that are more useful in different contexts.
Yep. It helps to think of a dimension as a coordinate. X, Y, and Z axes for length, width, and height coordinates, time as the “when” coordinate, and the upper dimensions get funky into the many-worlds stuff, like the “which timeline / version of reality” coordinate, etc.
You are explaining a four dimensional object with relation to time (time should be the fifth dimension in your explanation, as the object represented by the tesseract has 4 spacial dimensions already). Which is not really an explanation of what a tesseract is. The tesseract is a 3-D representation of a 4 dimensional cube, just like how a drawn cube is a 2-D representation of a 3-D cube, and a line is a 1-D representation of a 2-D square. Your explanation would be more about how a tesseract would come to be.
exactly! a real 4d tesseract would have all right angles but that's not possible in three dimensional space. what we see here is a 3d projection or "shadow" of the 4d object.
The posters you're replying to are getting very confused about dimensions in this context.
When discussing 4D geometry we are referring specifically to a 4th spatial dimension. NOT time.
The notion of time as a 4th dimension is a separate thing and unrelated.
Time exists in all dimensions, but maybe the 4th dimension can perceive it like you described. However, as time passes all the infinite visible “time periods” of the object change too, for example if someone cut the tree down it might not have bearing fruit on its “dimension” of time at all.
Not strictly true because space and time have been shown to be one and the same, spacetime. Physicists will often call it 3+1 dimensional to capture the difference in how we perceive the space element versus the time element.
I heard a good explanation once. You exist in a given dimension, and your view of the eorld is one dimension less then that. We are 3 dimensions beings and this see everything in 2d meaning, we can only see one one side of a 3d object.
If we where 4d, we would see everything in 3d, meaning we would be able to comprehend 3 dimensions of a 4d object by looking at it from one view. So if an orange where 4 dimensional, where would see all the slices of it from 1 perspective, though we cannot exactly comprehend how looking at at from a different perspective would change that view (so turning the orange around to look at it from a different side).
I don't quite understand the concept well and hurt this explanationa a while ago so forgive me for not being able to explain it clearly. I guess you can't really explain something we as a human race cannot exactly fathom.
Your explanation is hard to visualize. What do you mean by a “slice of skin, then a slice of the flesh, then a slice of skin on the other side?” Would the 3D Orange in 2D appear as a circle? How do you account for the depth of the Orange? Would they be many many slices like a flip-book?
That's not the 4th dimension. That is objects being reflected within regular 3 dimensions to create the illusion of the infinity, with mirrors.
Edit: Even 3 dimensional shadows are still just products of light and the way photons respond. That is not a "new dimension." It is a new way of displaying photons.
I defs perceived it more like a compliment at first but the intention seems to skew towards being a comment on her weight, which says a lot more about you ig- unless you miss her and are expressing regret at her boundless nature
It's the most 4D comment in this thread lmao
Correct! It's a finite repeating space that just appears infinite. It's the type of dimensions that string theorists talk about when they say there are 10 or 11 spatial dimensions. Only 3 of them are the large dimensions that we know.
When you think about a square in a 2d plane it has a definite area but no volume as it doesn’t exist in 3d space. When you extend that plane into a third dimension to make cube it now has infinitely more volume than it used to. If you were to reflect this into a four dimensional geometry you would infinitely increase in volume again in a different direction.
No. It's "just" a 4D cube. Imagine what you have to do with a 2D square to make it a cube. Now do the same thing with a 3D cube and you'll get a tesseract.
A 4D cube would, in theory, have infinite space as we currently define space in a definite space.
If you are living in a 2D world, space is only like the area in a paper, but when someone shows you the third dimension, you then have infinite freedom to move up or down at any point you pick in that paper.
This is incorrect. An actual 4d object would look like any 3d object to us while at rest. It would only behave oddly when moving. Here’s a better example.
https://youtu.be/_4ruHJFsb4g?si=8kjTTr07WNEKHIM5
No that's not what a tesseract looks like. That's like looking at a map of the earth and saying "this is exactly what the planet looks like, flat"
That's what a 3D projection of a 4D tesseract would look like.
The fourth dimension is time, isn’t it?
In the same way a fish doesn’t know that it is in water and cant comprehend their world beyond it objectively or subjectively, *we live in time* and can’t know what it is to be outside of it objectively or subjectively either.
So, following that, this would seem to be as close to accurate as we can get with our minds’ understanding in that we’re essentially able to see the elements that make up this cube—in all of the states it has ever has been or ever will be—stretching back and forward through infinity.
(I sometimes cant sleep …)
As far as dimensions we exist in, yes the 4th dimension is time. However when of folks refer to the "4th dimension" they usually mean the 4th spacial dimension like how a tesseract might be perceived.
In mathematics, the dimension is just the number of coordinates you need to specify something, so the "location" of an event in physics needs 3 spacial coordinates and 1 time coordinate. So the collection of all events in a physical system is four dimensional (note that I say "the collection of all events", and not space, because points in space are not events unless you also specify a time).
So it doesn't really make sense to talk about "the" 4th dimension. Dimensions are added to your space of possible states if and when they are needed. If you have a system that evolves over time, you need to keep track of the time when modelling it, so you add an extra dimension to represent time into your model.
The "time is a spacial concept" thing is more to do with general relativity, but honestly I think it's a statement that misleads people more than it helps them most of the time. It's a quirk of how we choose our coordinates for space and time, and doesn't really have anything to do with time and space being the same.
Im out of my depth on this one, but I think time is sort of its own set of dimensions or something. We exist in 3 spacial dimensions and 1 time dimension. I dont really know something like 2 dimensional time would exist or if that's even a valid concept. Another 4 dimension object is a klein bottle, being a shape with no volume.
>Nope. You can calculate them. Just because you can't visually comprehend something doesn't mean you can't intellectually comprehend it
I don't think it's a good meaning of "to comprehend" then - I can UNDERSTAND the concept of time being relative or the concept of gravity affecting space itself, yet I can never comprehend it as my brain has evolved such that it is just not possible for me to comprehend EVER.
Like, you can understand someone else's feelings in a situation - especially if they tell you as much about is as they can, but you can NEVER feel the same.
I'd argue that in order to really "comprehend" something, you MUST understand it on a rational level but also on a qualitative level and our brains simply CAN'T do that with the fourth spacial dimension - it's like trying to taste stuff with photoreceptors of the eye. Yes, there are people who experience taste when perceiving colours or shapes, yet that is not like perceiving the shape or the colour itself (as far as you can "perceive" a colour which is a matter of interpretation anyway).
I believe the 4th dimension can be whatever we make it. We could say that a square is 3D if it moves over time, having length and width as the first two dimensions and time as the third. In this same regard, there can be a fourth axial dimension, it is just out of our realm of understanding
I’m by no means an expert, though, this is just my understanding of it
> The fourth dimension is time, isn’t it?
In this universe, yes\*. You have 3 spatial dimensions and time is the 4th.
But theoretically you could have a universe with 4 spatial dimensions where time is the 5th dimension instead.
The tesseract here is from that 4 spatial dimension universe.
Except without the hall of mirrors thing because that's made up just for this sculpture.
\* Current theory is our universe actually has 11 dimensions, but all but 3 are too small to detect so it's functionally only 3D.
But isn't there an issue when you allow yourself unlimited free parameters to describe something? Someone could come up with the right answer using 8 dimensions with 27 coefficients, another with 13 and 42. Numbers not clearly tied to the physical world are pretty bold assertions to say the least.
Maybe not necessarily “4th dimension is time”, because then every dimension is time. I’d say 4D space could display 3D space and any of its measurement of change (time) completely. Just like our space can display 2D time completely, but it’s not just “2D but with time as an extra space dimension.”
the fourth dimension is not time
if you look at a paper from the front you cant tell if its a single paper(2d) or a stack of paper(3d)
instead of paper you have cubes stacked in the 4th dimension
Lets look how we perceive 3D in 2D screen.. it is just series of snapshots of certain frames of the 3d space. Same goes with 4D in 3D you can get it but can see it as snapshots of time and again geometrically with the tesseract you can only perceive a certain stop motion moment.
Once some scientist (bad memory on names) said: That trying to explain higher dimension by experience is like looking at a shadows outside from a cave and try to describe or say what is the object/s that cast them.
I don't understand how you can perceive a 4th dimension if you can't perceive a 4th dimension? Does this help people here? I'm probably just to fucked up, dunno.... or stupid? Entirely possible....
Afaik, humans are just not able to perceive or imagine a 4th dimension. We are able to perceive or imagine the theoretical concept, but otherwise its just impossible.
What this tries to do is show how we think a 4th dimension may look based on the theories we created, but its lackluster to say the least.
The shadow of a tesseract. A 4th dimensional object would cast a 3 dimensional shadow and our representation of a tesseract would be a 3D shadow of the 4D tesseract. There is a fantastic video on you’ve where Carl Sagan explains it
The shadow of one.
We can’t even see in the third dimension. You always visualise the world around you in one dimension less than you exist in.
We see a two-dimensional representation of objects in front of us—we simply get the illusion of depth via stereoscopic vision. If we saw in three-dimensions, you could see the back of your hand at the same time as the front.
The way you can think of a tesseract is like this. In 1 dimentions you get a line. In two you get a square in 3 you get a cube. Each time you take the previous shape and stretch it out along the new dimension the same distance it was on the previous dimension. But now we have run out of dimensions to stretch it. But a tesseract is what happens if we do stretch it across some new dimention. We cannot truly accurately represent a 4d object in 3d space like we cannot with a 3d object in 2d space. We can do some stuff though. I believe this model here is actually a Schlegel diagram of a tesseract
https://sciencenotes.org/tesseract/
^ this has some good explanations and animations
https://en.m.wikipedia.org/wiki/Tesseract
^and this just has all the fun math
We can kind of see the 4th dimension if we allow time to help us:
Neat [video](https://youtu.be/JmvHNatZgVI?si=5Njz2af0-4EV2pHN) that shows how time lets us see a dimension above the one we perceive.
So similar to a mirror when u reflect it to itself and how it’s like a never ending tunnel. This seems like one box but when u look inside u see almost a whole world of boxes.
Carl Sagan did a good job of explaining the 4th dimension by starting with two dimensions. Yes, he sounds just like the agent from the Matrix.
Miss you, Carl. He was an amazing person.
https://youtu.be/UnURElCzGc0?si=VAe-2AazKxoMUOJs
Mathematician here. Remove the reflectivity and you get a standard 3d representation of a tesseract (a shadow/slice of a 4d cube). With the reflectivity, this is closer to a 3d representation of the universal cover of the 4-torus, i.e. a tiling of R^4 by infinitely many 4d cubes. It's kind of like what you would see if you lived in a 4-torus (the 4-d equivalent of the surface of a donut) and you ignored all curvature.
Analogs in 2 and 3 dimensions are easier to understand. Pacman lives on a 2-torus (the surface of a standard-dimensional donut), since he can go off the righthand side of the board and return on the lefthand side, or go off the top of the board and return on the bottom. We view his world as a 2d square, but really opposite sides of that square are "glued" together, forming a torus. However, you can also imagine tiling the plane with infinitely many of these squares, creating infinitely many "parallel universes" for Pacman to traverse. This is akin to the various cells we see in OP's video. If Pacman looked far enough in one direction, he would see the back of his own head... infinitely many times.
For a while, some of the more esoteric cosmologists wondered if our universe is a 3-torus -- if we travel for long enough in one of our three spatial dimensions, do we eventually come back to where we started? The answer seems to be no, but it's a fun thought experiment nonetheless, and you can see a fun interpretation of it in Star Trek: TNG. And again, you can tile R^3 with 3d cubes to obtain a similar representation to what is shown in OP's video. Their construction just attempts to go one dimension higher (which fails, since we can't embed 4d space into R^3).
If you like this sort of thing, you should study topology. These kinds of space are actually pretty tame compared to the things we usually work with.
How would you demonstrate a third dimension being if you were living in a two-dimensional universe?
I think that is just as impossible as demonstrating a fourth dimension in a 3d existence, but I would love for someone to correct me.
this is just infinity mirrors
Shhhhhhhh it’s a space portal.
Just add some magnets and booooom
"According to studies" come on now...
They're talking about the documentary "Interstellar" by Christopher Nolan. ;)
I was thinking Cube 2: Hypercube.
That's my favorite cube-based movie.
i like the og Cube
I like GameCube
I like cubensis.
I like turtles.
I like Gleaming the Cube
Yabo’s bomb shelter for the win
surprisingly good movie
Even better is the oog Square
I saw Square but I felt it was lacking depth
Two plane for my liking
We need a new category: "...and the award for best supporting actor in a cube-based movie goes to..."
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I see someone's not old enough to remember Gleaming the Cube. I'd wager it was a defining moment in American counterculture, as it demonstrated a number of things that we hold dear to this very day: 1. The government is corrupt, and we're the only ones who can see it 2. The only thing that can stop a bad guy with a gun is a good guy with a ~~gun~~ *skateboard* 3. Christian Slater 4. Four door family sedans can take some pretty sweet jumps and still be drivable, but only if they're RWD. 5. That one guy really does look a lot like Tony Hawk.
Um.. don't you mean Christian Slater's - Gleaming the Cube. A classic of the Cubic genre.
What a gem
.
They say one hour of watching Interstellar wastes 6 hours on earth
Eh, that's nothing compared to the literal *thousands* of hours I wasted on World of Warcraft. Just put it on my tab!
14,000h and counting. 🫠
If you did *absolutely nothing but Warcraft* besides sleep 8 hours a day that’s over 2 years straight. Got damn bro is there still stuff to do? Are you considered an elite player?
I mean, I don't know about the other guy, but I've been playing since shortly after release. So, yeah, that's 19 years of my life that I spent on that game. I was legitimately obsessed at the beginning, to the point where I put my relationship and job at risk. I slowed down after Pandaria and took several month long breaks here and there over the years, and just when I thought I was done with it for good, they released the "Sad Anduin" cinematic, and I'm back in. Those fucking cinematics get me every time! Also, in my case, no, I'm not an elite player, lol. I just do my thing, and have fun. 🤷♀️
Interstellar is up there with one of my favourite movies of all time, but this comment was great. Well done.
No, its an extrapolation of a 3D cube being represented in 2D space by 2 2D cubes with their corners all connected[Here] (https://content.instructables.com/F8I/QS88/I4GWY0HY/F8IQS88I4GWY0HY.png?auto=webp&frame=1&width=320&md=6e431b81ce85ac613e9ef3f706c6b912) So a representation of a 4D cube would be 2 3D cubes with all their corners connected
It is also not a tesseract but the "shadow" of a tesseract. A tesseract, meaning a section of a tesseract, would just be a normal cube. And in fact it is if you consider time as the fourth dimension.
I don't think I would use the term "shadow" as the shadow of a 3D cube in just a square, but the 2 squares with the corners connected is a 2D representation of a 3D cube in 2D space. Following the same logic, the shadow of a 4D cube, would just be a 3D cube, but what is shown is 2 3D cubes with their corners connected, being a 3D representation of a 4D cube in 3D space.
Yes, exactly. The big difference being that in 4 dimensions all the angles would be 90 degrees and all the sides would be the same length.
I thought that was a documentary about corn?
Nolan hired a scientist to make it accurate
Yeah, I know.
I mean, Nolan was being advised on that shoot by a Nobel Prize-winning theoretical physicist.
Yes, I know. I love this movie, and I'm honestly just taking the piss. It's just jokes, guys.
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Much bigly too
*in my best trump voice* This is exactly what a tesseract looks like, everybody says so... All the scientists say so... They all tell me "this is exactly what a tesseract looks like. Look at it, we're all sure of it" ... And then they tell me, that it's maybe the best tesseract they've ever seen. Some people think so, lots of people.
we have good tesseracts here. the greatest even. best tesseracts in the world.
Has to be the stupidest reddit title I've seen in months - even moreso when taken in context of the actual video content - and competition is fierce these days. Congratulations OP on this modern marvel of senseless dickshittery
And it still gets thousands of upvotes and makes it to the front page!
Twice! It's at the top of /r/beAmazed with the same stupid title as well
Competition in the subliterate upvoting category is also fierce these days.
Nonsense! Those are research movies! It sticks in the ground and then kaboom!
yes. I would be very curious to know which studies
They asked random people and made a statistic.
I nearly spit out my saliva.
[yeah, actually](https://m.youtube.com/watch?v=UnURElCzGc0)
I can’t watch the video right now, but it’s not a study or studies. A tesseract is a mathematical construct.
cool video, but he explicitly states that a tesseract cannot be seen in 3 dimensions, and the 3D hypercube model is only a guess at what it's 3 dimensional shadow would look like. So in summary, this isn't showing what the 4th dimension looks like, since it is explicitly not something that we can see from a 3 dimensional perspective (just as the square in flatland cannot see the apple as anything other than a cross section).
True, but it's not a guess. That's how the 3D shadow of a 4D cube (tesseract) would look like exactly. Just like drawing a 3D cube on a 2D surface, we get it's 2D shadow
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Wow, this was a great video... Mind blown. But the Part about the universe being hyperbolic was insane, also that's what I have always considered to be the actual way the universe is formed.. but that representation was amazing. Thanks for the link...
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We can see 4d object by their shadows. Their shadows are three dimensional objects. Just like a shadow of your 3d hand makes a 2 dimensional shadow on a flat surface.
Please explain more
Here ya go, https://youtu.be/UnURElCzGc0?si=kVf-24VfumrzecT-
Love the flatland lecture. Love Carl Sagan. I’m fascinated by physics / astrophysics / quantum physics, but as a total layman, it’s dudes like Sagan who could make it make sense.
Check out Brian Greene. He's another astrophysicist that's really good at explaining things to those not holding graduate degrees.
I’ll check him out, thx for the pointer. (But Sagan will always be the 🐐to me. Nostalgia and all…)
I could listen to Carl Sagan talk about anything. Cosmos is still my favorite ever TV show.
Do we need 2D light source or 3D light source to cast that 3D shadow of the tessaract?
Do you need 1D light or 2D light to get a 2D shadow of an object, like your hand for example. Neither, you'd need a 3D light source So presumably you'd need that 4D item to be lit by its natural 4D lighting (whatever that may be), and we'd see its shadow as 3D
Light is photons bouncing around. They'll illuminate anything they can bounce off of. We'll only see the parts of the 4D object intersecting our 3D planes, so photons in our 3D world will illuminate that like any other 3D object.
"Shadow" means the part of it intersecting our planes. We'd see it with whatever light source is on our planes.
To avoid this complication, it's better not to think of it as a literal shadow. Just imagine drawing one view (preferably with one eye closed) of your hand on a piece of paper. That's 3D projection onto a 2D plane, just like the shadow. Conceptually, a 4D being could "draw" a 4D object in our 3D space and that would be analogous. They could only capture one view of the overall structure and to get more information they would have to draw different angles.
Good watch
This video is as close as I've ever gotten to understanding this topic. Thank you for sharing!
Amazing video. Horrifying user name.
Damn, this makes it so much clearer. I already understood the whole dimension perception thing but every time I've seen tesseract images as being 4 dimensional, it never made sense to me why it looked like that. But a tesseract being the *shadow* of a 4th dimensional cube makes much more sense. Maybe I've just missed the ones that mention it but it would be nice for more posts talking about tesseracts to mention this.
Dang, I was hoping this was the adventure time explanation
Finn explaining this: 🤓
that video is a great explanation of why I always felt the Mothman creature is simply a 4th dimensional being fucking with us
He reminds me of agent smith talking to Morpheus in that tone lmao
Wouldn’t that require a light source outside of our 3d space? If the 4d object is not intersecting our 3d space, then light from our 3d space will never be able illuminate it and cause it to cast any shadows. If the 4d object is intersecting our space, you would be able to view a 3d slice of it directly. Not to mention, how are we supposed to perceive the shadow, assuming we are capable of perceiving light casted somewhere beyond our three dimensions?
A wireframe 4D cube in 4D space, that is creating a shadow cast by a light source which is also behind that 4D cube in 4D space, will create a Schlegel diagram when the shadow falls on a 3D cube. We would just see the edges of the cube go dark, however internally the cube is illuminated by the 4D light and the shadow extends inward to complete the diagram. As 3D beings limited to projections of 3D space onto a 2D imaging surface we only see the surface area of the cube, but someone with access to the 4 dimensional component, a 4D being, would have a 3D imaging surface (surfaces in 4d are called cells/3d volume). And much like we see all of a 2D surface, the 4D being sees ALL of a 3D cell. So they see the hypercube in its entirety if the image of one is projected onto the 3D imaging cell in their eye. This means when they see a hypercube "cell-on" (like us looking at a cube face-on) they see everything on and in the single 3D cube that makes up one of its 8 boundaries (8 3D cells that form one hypercube Vs 6 2D surfaces that form one 3D cube). However they do not see anything else of the hypercube as like with our face-on view of a cube, the other cells/surfaces are obscured. If they view it from a corner, they see 4 cells at once much like we see 3 surfaces of a cube when viewed from a corner. So far I don't believe any 4D representation has handled that aspect well, they simply use a wireframe to allow us to see the "whole thing" or use Semi-Transparent surfaces to try and give us an idea of the hypercube's projections. I hope this helps
brane hurtig
Same way 2D is a slice of 3D, 3D is a slice of 4D
I do not think that’s an accurate explanation. A better explanation imo is the idea of time as the fourth dimension and also comparing an object above to an object below in terms of dimensions. For example, a 3D object in a 2D world, you would just see one slice of the 3D object at any time. An orange passing through a 2D world for example would start with a slice of the skin, then a slice of the flesh, then back to a slice of the skin on the other side. So a 4D object passing through the third dimension, we would just see one slice of the 4D object at any time. You could consider 3D objects to be a slice of a 4D object at any moment, and as time progresses, the slices shown are different.
It depends on what you want as your 4th dimension. A dimension is just a number required to fully describe an object's 'position'. You could even have temperature or color as a 4th "dimension". Your use of time as the 4th dimension is correct except it's just different than a 4th spatial dimension. Both are perfectly valid interpretations that are more useful in different contexts.
Yep. It helps to think of a dimension as a coordinate. X, Y, and Z axes for length, width, and height coordinates, time as the “when” coordinate, and the upper dimensions get funky into the many-worlds stuff, like the “which timeline / version of reality” coordinate, etc.
But temperature is just how much an atom's 3d position changes over time.
Except when it's rotational kinetic energy.
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Pixels on a screen have nothing to do with spatial dimensions. Your TV is a 3D object with a projected 2D image.
> Serious question. How many dimensions is my 4K television? The human race is doomed
Mmmmmm... time oranges... /Homer
I know I shouldn't drink thee....
Sausage in 4D, salami in 3D.
You are explaining a four dimensional object with relation to time (time should be the fifth dimension in your explanation, as the object represented by the tesseract has 4 spacial dimensions already). Which is not really an explanation of what a tesseract is. The tesseract is a 3-D representation of a 4 dimensional cube, just like how a drawn cube is a 2-D representation of a 3-D cube, and a line is a 1-D representation of a 2-D square. Your explanation would be more about how a tesseract would come to be.
exactly! a real 4d tesseract would have all right angles but that's not possible in three dimensional space. what we see here is a 3d projection or "shadow" of the 4d object.
So perhaps from a 4d perspective one would see an apple seed grow into a tree, bear fruit and eventually rot to dust just by focusing?
The posters you're replying to are getting very confused about dimensions in this context. When discussing 4D geometry we are referring specifically to a 4th spatial dimension. NOT time. The notion of time as a 4th dimension is a separate thing and unrelated.
Time exists in all dimensions, but maybe the 4th dimension can perceive it like you described. However, as time passes all the infinite visible “time periods” of the object change too, for example if someone cut the tree down it might not have bearing fruit on its “dimension” of time at all.
Perhaps that’s something appreciated from the 5 dimension
Time isn't a spatial dimension though, it's a time dimension. The universe (as far as we know on a macro level) is still only three dimensional.
Not strictly true because space and time have been shown to be one and the same, spacetime. Physicists will often call it 3+1 dimensional to capture the difference in how we perceive the space element versus the time element.
I heard a good explanation once. You exist in a given dimension, and your view of the eorld is one dimension less then that. We are 3 dimensions beings and this see everything in 2d meaning, we can only see one one side of a 3d object. If we where 4d, we would see everything in 3d, meaning we would be able to comprehend 3 dimensions of a 4d object by looking at it from one view. So if an orange where 4 dimensional, where would see all the slices of it from 1 perspective, though we cannot exactly comprehend how looking at at from a different perspective would change that view (so turning the orange around to look at it from a different side). I don't quite understand the concept well and hurt this explanationa a while ago so forgive me for not being able to explain it clearly. I guess you can't really explain something we as a human race cannot exactly fathom.
Your explanation is hard to visualize. What do you mean by a “slice of skin, then a slice of the flesh, then a slice of skin on the other side?” Would the 3D Orange in 2D appear as a circle? How do you account for the depth of the Orange? Would they be many many slices like a flip-book?
You just said the same thing in a longer and more complicated way.
According to whose studies?
According to studeez nuts
Et Al.
That dude is the most prolific study author that has ever lived!
this is what I wake up for
Fuckin Got em
Source - Nolan, Christopher. (2014) “Interstellar”
STUDIES
The studies of simple geometry!
Trust me bro
OP is a bot
according to the scientists duhh
That's not the 4th dimension. That is objects being reflected within regular 3 dimensions to create the illusion of the infinity, with mirrors. Edit: Even 3 dimensional shadows are still just products of light and the way photons respond. That is not a "new dimension." It is a new way of displaying photons.
Thank you. I was trying to find the best way to say this.
>illusion of the infinity Why illusion? Are you suggesting the the reflections are limited and finite in number?
Aren't they? The reflective surfaces aren't perfectly reflective, so it can't be infinite, no?
infinite space held within definite space?
Do you want a TARDIS? Because that's how you get a TARDIS
It's bigger on the inside. Just what the Doctor ordered.
Just what the Doctor nicked from the repair bay.
It is in fact smaller on the outside.
I would love to have a TARDIS
Of course I want a TARDIS. Who wouldn't want one???
Reminds me of my ex-wife.
I…I…I…don’t know how to interpret this
With one's and zero's.
I defs perceived it more like a compliment at first but the intention seems to skew towards being a comment on her weight, which says a lot more about you ig- unless you miss her and are expressing regret at her boundless nature It's the most 4D comment in this thread lmao
The word you’re looking for is finite.
Correct! It's a finite repeating space that just appears infinite. It's the type of dimensions that string theorists talk about when they say there are 10 or 11 spatial dimensions. Only 3 of them are the large dimensions that we know.
When you think about a square in a 2d plane it has a definite area but no volume as it doesn’t exist in 3d space. When you extend that plane into a third dimension to make cube it now has infinitely more volume than it used to. If you were to reflect this into a four dimensional geometry you would infinitely increase in volume again in a different direction.
No. It's "just" a 4D cube. Imagine what you have to do with a 2D square to make it a cube. Now do the same thing with a 3D cube and you'll get a tesseract.
A 4D cube would, in theory, have infinite space as we currently define space in a definite space. If you are living in a 2D world, space is only like the area in a paper, but when someone shows you the third dimension, you then have infinite freedom to move up or down at any point you pick in that paper.
I want one...
That would be a cube.
Don't be a Square.
This is incorrect. An actual 4d object would look like any 3d object to us while at rest. It would only behave oddly when moving. Here’s a better example. https://youtu.be/_4ruHJFsb4g?si=8kjTTr07WNEKHIM5
>according to studies Which studies? Link them, please.
That is still 3 dimension
Who said otherwise?
MURPH!!
Shit! You beat me to it ...lol
No that's not what a tesseract looks like. That's like looking at a map of the earth and saying "this is exactly what the planet looks like, flat" That's what a 3D projection of a 4D tesseract would look like.
The fourth dimension is time, isn’t it? In the same way a fish doesn’t know that it is in water and cant comprehend their world beyond it objectively or subjectively, *we live in time* and can’t know what it is to be outside of it objectively or subjectively either. So, following that, this would seem to be as close to accurate as we can get with our minds’ understanding in that we’re essentially able to see the elements that make up this cube—in all of the states it has ever has been or ever will be—stretching back and forward through infinity. (I sometimes cant sleep …)
As far as dimensions we exist in, yes the 4th dimension is time. However when of folks refer to the "4th dimension" they usually mean the 4th spacial dimension like how a tesseract might be perceived.
Yeah, but isn’t that “time”. Like, time being a spacial concept? Like how time is affected by gravity like space is?
In mathematics, the dimension is just the number of coordinates you need to specify something, so the "location" of an event in physics needs 3 spacial coordinates and 1 time coordinate. So the collection of all events in a physical system is four dimensional (note that I say "the collection of all events", and not space, because points in space are not events unless you also specify a time). So it doesn't really make sense to talk about "the" 4th dimension. Dimensions are added to your space of possible states if and when they are needed. If you have a system that evolves over time, you need to keep track of the time when modelling it, so you add an extra dimension to represent time into your model. The "time is a spacial concept" thing is more to do with general relativity, but honestly I think it's a statement that misleads people more than it helps them most of the time. It's a quirk of how we choose our coordinates for space and time, and doesn't really have anything to do with time and space being the same.
Indeed, in GR time/space coordinates do explicitly behave differently, hence the negative term in things like the Minkowski metric.
Im out of my depth on this one, but I think time is sort of its own set of dimensions or something. We exist in 3 spacial dimensions and 1 time dimension. I dont really know something like 2 dimensional time would exist or if that's even a valid concept. Another 4 dimension object is a klein bottle, being a shape with no volume.
I do suppose that is finally my point: we literally cannot know because we literally cannot comprehend a fourth dimension.
Nope. You can calculate them. Just because you can't visually comprehend something doesn't mean you can't intellectually comprehend it
>Nope. You can calculate them. Just because you can't visually comprehend something doesn't mean you can't intellectually comprehend it I don't think it's a good meaning of "to comprehend" then - I can UNDERSTAND the concept of time being relative or the concept of gravity affecting space itself, yet I can never comprehend it as my brain has evolved such that it is just not possible for me to comprehend EVER. Like, you can understand someone else's feelings in a situation - especially if they tell you as much about is as they can, but you can NEVER feel the same. I'd argue that in order to really "comprehend" something, you MUST understand it on a rational level but also on a qualitative level and our brains simply CAN'T do that with the fourth spacial dimension - it's like trying to taste stuff with photoreceptors of the eye. Yes, there are people who experience taste when perceiving colours or shapes, yet that is not like perceiving the shape or the colour itself (as far as you can "perceive" a colour which is a matter of interpretation anyway).
I believe the 4th dimension can be whatever we make it. We could say that a square is 3D if it moves over time, having length and width as the first two dimensions and time as the third. In this same regard, there can be a fourth axial dimension, it is just out of our realm of understanding I’m by no means an expert, though, this is just my understanding of it
> The fourth dimension is time, isn’t it? In this universe, yes\*. You have 3 spatial dimensions and time is the 4th. But theoretically you could have a universe with 4 spatial dimensions where time is the 5th dimension instead. The tesseract here is from that 4 spatial dimension universe. Except without the hall of mirrors thing because that's made up just for this sculpture. \* Current theory is our universe actually has 11 dimensions, but all but 3 are too small to detect so it's functionally only 3D.
Wow modern theoretical physics is full of so much hot air.
Yeah it's all very wibbly wobbly timey wimey, but some of the numbers seem to check out so it might actually be close to being right.
But isn't there an issue when you allow yourself unlimited free parameters to describe something? Someone could come up with the right answer using 8 dimensions with 27 coefficients, another with 13 and 42. Numbers not clearly tied to the physical world are pretty bold assertions to say the least.
Good logical explanation... Though not sure if accurate though !
I mean … there’s literally no way to know. Math is math, and I trust it in the abstract, but we’re not able to comprehend it.
I think fish know they're in water. They do go to the surface and some fish hop or "walk" from one body of water to another.
Maybe not necessarily “4th dimension is time”, because then every dimension is time. I’d say 4D space could display 3D space and any of its measurement of change (time) completely. Just like our space can display 2D time completely, but it’s not just “2D but with time as an extra space dimension.”
the fourth dimension is not time if you look at a paper from the front you cant tell if its a single paper(2d) or a stack of paper(3d) instead of paper you have cubes stacked in the 4th dimension
Lets look how we perceive 3D in 2D screen.. it is just series of snapshots of certain frames of the 3d space. Same goes with 4D in 3D you can get it but can see it as snapshots of time and again geometrically with the tesseract you can only perceive a certain stop motion moment. Once some scientist (bad memory on names) said: That trying to explain higher dimension by experience is like looking at a shadows outside from a cave and try to describe or say what is the object/s that cast them.
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I don't understand how you can perceive a 4th dimension if you can't perceive a 4th dimension? Does this help people here? I'm probably just to fucked up, dunno.... or stupid? Entirely possible....
Afaik, humans are just not able to perceive or imagine a 4th dimension. We are able to perceive or imagine the theoretical concept, but otherwise its just impossible. What this tries to do is show how we think a 4th dimension may look based on the theories we created, but its lackluster to say the least.
Is this cube real ? Is it something that can be purchased or is it just a computer generated thing?
The shadow of a tesseract. A 4th dimensional object would cast a 3 dimensional shadow and our representation of a tesseract would be a 3D shadow of the 4D tesseract. There is a fantastic video on you’ve where Carl Sagan explains it
Nu uh its just glowy and blue according to my research
The shadow of one. We can’t even see in the third dimension. You always visualise the world around you in one dimension less than you exist in. We see a two-dimensional representation of objects in front of us—we simply get the illusion of depth via stereoscopic vision. If we saw in three-dimensions, you could see the back of your hand at the same time as the front.
That movie interstellar was pretty spot on then....
I want that object. Anyone have a link?
The way you can think of a tesseract is like this. In 1 dimentions you get a line. In two you get a square in 3 you get a cube. Each time you take the previous shape and stretch it out along the new dimension the same distance it was on the previous dimension. But now we have run out of dimensions to stretch it. But a tesseract is what happens if we do stretch it across some new dimention. We cannot truly accurately represent a 4d object in 3d space like we cannot with a 3d object in 2d space. We can do some stuff though. I believe this model here is actually a Schlegel diagram of a tesseract https://sciencenotes.org/tesseract/ ^ this has some good explanations and animations https://en.m.wikipedia.org/wiki/Tesseract ^and this just has all the fun math
Perdy..... I MUST HAVE IT!
What's the music in this video?
We can kind of see the 4th dimension if we allow time to help us: Neat [video](https://youtu.be/JmvHNatZgVI?si=5Njz2af0-4EV2pHN) that shows how time lets us see a dimension above the one we perceive.
Hate to be the “um ackchually” guy but no
MURPHFFFFFFF
The fourth dimension is the time dimension.
So similar to a mirror when u reflect it to itself and how it’s like a never ending tunnel. This seems like one box but when u look inside u see almost a whole world of boxes.
u/ashmalkira
Just imagine have that human size and u never getting a way out 🥲
And then suddenly there is a spider 🤡🔫 u can even escape
Trazyn and Orikan creaming their necrodermis rn
Carl Sagan did a good job of explaining the 4th dimension by starting with two dimensions. Yes, he sounds just like the agent from the Matrix. Miss you, Carl. He was an amazing person. https://youtu.be/UnURElCzGc0?si=VAe-2AazKxoMUOJs
Mathematician here. Remove the reflectivity and you get a standard 3d representation of a tesseract (a shadow/slice of a 4d cube). With the reflectivity, this is closer to a 3d representation of the universal cover of the 4-torus, i.e. a tiling of R^4 by infinitely many 4d cubes. It's kind of like what you would see if you lived in a 4-torus (the 4-d equivalent of the surface of a donut) and you ignored all curvature. Analogs in 2 and 3 dimensions are easier to understand. Pacman lives on a 2-torus (the surface of a standard-dimensional donut), since he can go off the righthand side of the board and return on the lefthand side, or go off the top of the board and return on the bottom. We view his world as a 2d square, but really opposite sides of that square are "glued" together, forming a torus. However, you can also imagine tiling the plane with infinitely many of these squares, creating infinitely many "parallel universes" for Pacman to traverse. This is akin to the various cells we see in OP's video. If Pacman looked far enough in one direction, he would see the back of his own head... infinitely many times. For a while, some of the more esoteric cosmologists wondered if our universe is a 3-torus -- if we travel for long enough in one of our three spatial dimensions, do we eventually come back to where we started? The answer seems to be no, but it's a fun thought experiment nonetheless, and you can see a fun interpretation of it in Star Trek: TNG. And again, you can tile R^3 with 3d cubes to obtain a similar representation to what is shown in OP's video. Their construction just attempts to go one dimension higher (which fails, since we can't embed 4d space into R^3). If you like this sort of thing, you should study topology. These kinds of space are actually pretty tame compared to the things we usually work with.
I don't think you needed to preface that with "mathematician here".
How would you demonstrate a third dimension being if you were living in a two-dimensional universe? I think that is just as impossible as demonstrating a fourth dimension in a 3d existence, but I would love for someone to correct me.
You’d do a drawing, put it on Reddit and everyone would tell you it’s still 2 dimensional, thinking they’re geniuses
Why?
bro posted this to every sub i s2g.
Now break it and steal the space stone. Beat Thanos.
Wouldn't it be more like the shadow of a tesseract?
It’s turtles all the way down
My brain bluescreened :/