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WHenever I look online, all I find is this.
It is very cool and all, but it doesn't explain nothing to me. So I figured that I would ask the smartest fourm I know.
Please explain this to me, I feel like I need to know. I can understand the 2nd and 3rd dimensions, but the fourth is a little less understandable. Thanks!
Fourth dimension is time, the measurement between events, rather than points. WE move through the fourth dimension at... a fairly uncontrolled rate, though that rate varies slightly with our velocity. The average person doesn't have much control on their journey through time. Didn't watch the video, can't, but if there's anything more specific you want to know, you'll have to ask, since I can't do that for you.
If time is the 4th, then I am refering to the 5th. I know how time works, I have a basic grasp on how we move 'through it'. I am talking about the next dimension.
This is very helpful in attempting to understand the 4th dimension.
http://www.geocities.com/CapeCanaver.../whatis4d.html
Time does not exist except as a mesurement of space. It is not the 4th dimension.
From what I can tell from the image, I'd have to say that the fourth dimension is something that is imperceptible in a normal state of consciousness. You probably have to be on drugs to experience it from within human consciousness if it is possible at all/is even a "real" thing. Human consciousness creates a 3D perspective of reality. I suppose it's possible to visualize a four dimensional shape, but because our perspective is limited to 3 you can build anything like that.
I'd really like to see a 3D hologram of something in 4D. Now that would give you a better idea.
I've never really thought about this too much before. Every thing I've read about it seemed like complete nonsense, but that image makes some sense.
This was fun I thought
Ignore these people. The 4th spacial dimension is not time, and it is definitely not some weird plane of consciousness.
It's an unanswered question why there are 3 spacial dimensions in this universe, and not some other number. There is absolutely no reason why there shouldn't be, and anybody who tells you there is is simply an unimaginative person. All other spacial dimensions are just as mathematically - logically - consistent as these.
To think in terms of the fourth spacial dimension, it is actually extremely easy.
First, picture a dot. This is the 0th spacial dimension. There are no degrees of freedom at all.
Second, imagine this dot splitting like a cell into two dots, some distance apart, and between them, they draw a line, like a spider drawing a thread. You now have a line with two dots at each end; this is the 1st dimension, and there is 1 degree of freedom.
Now, imagine these two dots splitting into four in the same way as before. Separate the two new dots and again join them up with lines. You have a square, the 2nd dimension.
Do it again. Split these four dots into eight, separate them, and you have a cube, the 3rd spacial dimension.
And then do it again. Split the eight dots into sixteen, and separate them. You now have two superimposed cubes. Obviously this is a mere shadow of what a 4 dimensional cube (called a tesseract) actually is because it is not possible for the human neural network to comprehend such things, but nevertheless, it gives you an extremely clear idea of what one is, much like drawing a cube on paper gives you a clear idea what one is, even though the 'depth' cannot be transcribed onto the paper.
In Einstein's theory of general relativity, basically he creates a mathematical framework in which you interpret this fourth dimension as time; but that is a physical theory. It is completely separate from what you wanted to know, which is the mathematical generalisation of n-dimensional forms.
And you can continue to expand upon this; a cube in the 5th spacial dimension will have 32 verticies, a cube in the 6th spacial dimension will have 64 verticies, and so on.
Hope that helped.
If you were to travel in a straight line in our universe, you would eventually end up in the same place you started. This phenomenon is not unlike that of a two dimensional character on a mobius strip who finds that they have reached their point of origin after having traveled in a "straight line". What that two dimensional character doesn't realize is that their world actually curves through another spacial dimension one above their own (a mobius strip has to bend through three dimensional space in order for it to have only one boundless and finite side). In our universe the same things happens, but through another spacial dimension of which we are perceptually unaware of. Because of our natural inability to perceive four dimensional space, we cannot easily comprehend what exactly it "looks like".
I wish I could expound upon that further, but I think I speak for more than myself when I say that we really can't go any further with our explanation of a 4th spatial dimension without using analogies and mathematical expression.
Actually there's no evidence at all for that.
Exaclty. There's evidence to the contrary ;)Quote:
Originally Posted by Xei
If the universe is curved, the corners of a triangle wouldn't add up to 180 degrees. Very, very precise measurements have shown that this universe isn't curved, not at all. The corners of a triangle in our universe add up to exaclty 180 degrees.
Xei, I Was really hoping you would intervine. I knew you would be able to help me out :D
It really heaps, I get it to an extent. I understand how shapes 'evolve' when they go to new dimensions. I do not understand how a teserect can be the shadow of a 4D figure, but I guess a 2D creature wouldn't be able to comprehend a 3D shadow (even if a shadow is 2D).
Thanks, I get it as much as I wanted to.
I heard that in the fourth dimension, it is possible to view a cube from all sides at once. Right?
Fun, but woefully inaccurate I'm told.Quote:
Originally Posted by dajo
I would assume so, because us 3D creatures can see a 2D square all at once. But it would be impossible for a 4D creature to see the 4D eqivilent of a 3D cube (see quote).
But it would make sense for a 4D creature to see a 3D cube all at once. Right?Quote:
Split the eight dots into sixteen, and separate them. You now have two superimposed cubes. Obviously this is a mere shadow of what a 4 dimensional cube (called a tesseract).
Exactly. We can't make sense of 4D cubes, so the ame must apply for the others.
But alternitively, we can see the shaddow. A 2D critter can see the shaddow of a cube.
http://rationalwiki.com/wiki/images/...r_cube.svg.png
That is a 2D image. Of a 3D cube. It wouldn't make sense, but it can be seen. The shaddow, anyway. So we can see the 3D shaddow (what?...) of a teserect. Right?
And would I be able to 'see' (or at least experience) a 4D shape in a LD or a AP (if you believe in AP)
Hmmm? No, that's not a cube, or a cube's shadow at all. That's a 2D drawing of what a cube looks like to us.
Double negatives make me horny. :hump:Quote:
Originally Posted by Reality_is_a_Dream
I'm on my iPod,so I'm going to have to completely ignore preceeding comments. The fourth dimension would be seeing every side of something. We see in the second dimension, only seeing a two dimension representation of an object. I'm pretty sure that seeing in he fourth dimension would be like looking at all side of something. What yu have Thier is a tesseract or hypercube. Read a wrinkle in time, it goes into it a bit
Despite what some have said here, human beings are really only capable of directly (visually) percieving 2 dimensions. What you see is not 3 dimensions, otherwise you would be able to see both the front and back (plus all other angles) of an object. What you really see is a stereoscopic 2 dimensional picture (2 eyes) and your brain approximates variable distances to create a 3 dimensional model. Now, if you can imagine the capability of truly seeing in 3 dimensions; seeing an object from every angle at once, then you might be able to imagine a situation in which you could form a sort of stereoscopic picture of the 3 dimensional world to approximate 4 dimensions. What this might be is somehow simultaneously percieving three dimensional objects in their full range of positions as they move through space. Kind of like being able to see a person live out their life from beginning to end in real three dimensions all at once.
A good way to imagine this would be to just look at the end of ruler and imagine that it is only 1 dimension, and then turn it so that you can see it head on and realize that it is really 2 dimensions (ignoring thickness).
If you want to put it in terms of the video you posted, all you have to do is realize that when the lines seem to shrink, grow and pass through each other, they aren't really changing or passing through each other, you are just seeing the object from different angles. It would be the same if you had a 2 dimensional animation of a 3 dimensional cube. The lines would appear to shrink and grow, and then pass through each other depending on which was in the foreground and which was in the background.
I found some good sources for visualization. The first is a stereoscopic image of a tesseract, found on wikipedia. You need to do the magic eye cross eye thing to see it.
The second is an article about mapping 4 dimensional objects to a 3d projection of a tesseract in order to visualize what they look like. It goes in to more depth, and also explains why this is useful.
THAT'S WHAT I FUCKING SAID!Quote:
Originally Posted by Xaqaria
Shit.
Quote:
We see in the second dimension, only seeing a two dimension representation of an object.
Calm down. Clearly you weren't part of the "some."
Haha, wow.
Visually imagining a 4 dimensional object would be extremely hard and would probably require advanced knowledge about its properties. Visualizing that is like a 2 dimensional person visualizing 3 dimensions, they just couldnt do it. The fourth dimension would be perpendicular to the 3rd dimension, so you couldnt see it or recognize it if it were there.
Great link that explains alot : http://tetraspace.alkaline.org/ It will help you understand alot about the fourth spacial dimension
Hope i helped a bit and you find this useful :D
To better understand the difficulty of picturing 4d objects, consider the difficulty a 2d being would have conceiving of a 3D world.Quote:
Originally Posted by Reality_is_a_Dream
You should read the book Flatland, available online here:
http://www.geom.uiuc.edu/~banchoff/Flatland/
There are several movie versions of the book available as well if you can find them.
Or check out Dr Quantum
Dejo, that video has the best explaination on the internet. EVAR.
I'm too lazy to explain it as I understand it now. I'll do it tomorrow.
explain to me the 5th dimension
seriously, when did soul music go out of style?
ill always let the sun shine no matter what anyone else says
Maybe, maybe not. I am familiar with the concept. That is certainly what would happen to a triangle in a 2 dimensional world that was curved in 3 dimensional space, but we cannot say for certain that that would also be the case for a triangle (or any object) in a 3 dimensional space that curves within a 4th spatial plane. It is not the qualities of a static object in space that suggest a fourth dimension, but rather the way all objects in our universe are moving relative to one another. Or are they moving at all? Is it possible that the space itself may just be expanding?Quote:
Originally Posted by ThreeLetterSyndrom
here's a video i saw a while ago of Carl Sagan explaining the 4th demension.
http://www.youtube.com/watch?v=UnURElCzGc0
its pretty much just the same flat land story and the teserect explanation.
.......But its carl sagan so that makes it cool :D
I thought this was the best explanation of 4d yet.
http://www.youtube.com/watch?v=uDaKz...eature=related
"A 4d world implies that there are an infinite number of 3d spaces adjacent to our 3d world" ( parallel universes? )
If i had 3 transparent boxes. And there was an entity in one of the boxes, he would only know of the box he's in. Because he can only experience 3 dimensions of movement. He's constricted into that one box. Yet, I'm a 4d creature so i know that there are more boxes. He might actually think i was crazy if i told him there was more boxes than just the one he's in.
Now if i was a 4d creature, my field of vision would be in 3d. Just as we are 3d, but we can only see in 2d.
So if i had a cube, i would see it in 3d....but i probably would be able to see all sides of it at once. That's as far as i got, before i was lost in that video lol.
So basically being taken into a 4dimensional place is being taken out of a 3d reality... which you can see a multitude of of other 3d realities.
So in my 4d vision, i would see all of the 3d spaces...i'm really lost now, and only think i got part of this right. Cause it's really hard to explain this...but i feel like i know how it is.
a 4D creature would be able to see a multiple of 3d objects within a box(reality?), us 3d creatures can see a multitude of 2d objects ( paper, hands, cup, etc. ) within our rectangle( field of view).
I'm sure all this is extremely complicated in mathematics.
It needn't be to be honest. Any point in four dimensions can be written as
x
y
z
w
and a line, for example, can be easily written in vector form as
r = [x, y, z, w] + t[a, b, c, d]
There's nothing particularly special at all about three dimensions in mathematics. It's an open question why the universe should happen to have three dimensions.
Here's the 4th dimension explained by the person that come closest to a hero to me :lol:
http://www.youtube.com/watch?v=Y9KT4...rom=PL&index=3
Carl Sagan reminds me of Agent Smith.
http://www.youtube.com/watch?v=lgfYPnA_iFIQuote:
Originally Posted by grasshoppa
crumbly but good :D
The fourth dimension is like the second and third dimension, except that it has cool extradimensional alien creatures in it. Also, it rains chicken wings.
~
This is how i understand the 4th dimension.
The 4th dimension is the fabric of experience. The fabric obeys only two rules.
1st Rule: There are no rules.
2nd Rule: The rules can always change.
If you understand that the 4th dimension is infinite 3 dimensions- imagine this- imagine yourself in a room, a box, with doors on all sides in the middle of the walls. All sides and doors are the same. You walk through one door, and find yourself in the same room....forever. Its as if YOU are one box, and the box you are in is the other box. You as the observer not only perceive yourself, but the world around you. We observe the boxes.
Another way to see it is that EVERYTHING...AND I MEAN EVERYTHING, we experience or have sensed felt or whatever, has a beginning a middle and an end. Everything. That shows that we are experiencing many (one two threes), triangles if you wish. However the only way we can see different triangles is if there is room for somthing to begin again, and the 4th dimension unlike the 3rd dimension gives the opportunity.
Jesus...talking about this stuff is just ridiculous though because even the words we say, and the understanding that is brought from them, will be forgotten- (maybe remembered again) but since what we experience has a beginning a middle and an end, we can talk forever and only realize we're spiraling in and out of perceptual circles.
Otherwise...The 4th dimension is puzzling. I would say the best quote I can muster up about this is: "Its all bullshit so start eating."
hope that helps :P
You're pretty high huh.
aren't we all in some way?
Nah just the people who've had too many drugs.
depends on your own truth ;)
I resemble that remarkQuote:
Originally Posted by Xei
There are two ways of deriving another dimension. Either by adding a completely new one, or by "folding over". Imaginary numbers define a new, dependent dimension, and extend the real line to the complex plane. The number infinity adds another dimension by folding-over, because after the number infinity you are back to negative numbers - the real line becomes a circle, the complex plane becomes a sphere.
Add the number infinity to a 3d space and you define a fourth dimension already.
That's been my take on it, for the most part. I think the 4th dimension is the time line, except every "point" like entity is a static reality of space. The 5th dimension wouuld be like the next step beyond the line, but it is the next step beyond the time line-- the time plane. The 6th dimension would be an infinite number of time planes, something like a "time space". Etc. I wonder if the heirarchy has the potential of being infinite. I pissed off my metaphysics professor in college by arguing that in a paper. He told me I didn't know what I was talking about. I asked him for a counterargument, and he said, "COUNTERARGUMENT?????" and scoffed. I kept listening for an argument, but he had nothing else to say. What a dick.Quote:
Originally Posted by Xei
On the other hand... A lot of modern theoretical physicists, most famously Brian Greene, say our particular universe has 11 dimensions. They say that the human mind cannot visually comprehend dimensions beyond the 4th but that theoretical physicists can prove the existence of those dimensions with equations.
Dimensions are just dimensions. Dimensions don't have orders or meaning. They are like independent directions, though dimensions can be mutually dependent. There is no "the" 4th dimension, there can be a 4th dimension, and it can be any dimension you want it to... Time, mass, energy, eccentricity, number of breaths in a second, etc. A graph of speed X gas use X time has 3 dimensions. Basically that.
I don't think this is really true. You don't derive dimensions; you create them, as axioms. Deriving suggests there's an answer, but there isn't; if you want to talk about a 9 dimensional space you work in the framework of 9 dimensions, etcetera.Quote:
There are two ways of deriving another dimension. Either by adding a completely new one, or by "folding over". Imaginary numbers define a new, dependent dimension, and extend the real line to the complex plane. The number infinity adds another dimension by folding-over, because after the number infinity you are back to negative numbers - the real line becomes a circle, the complex plane becomes a sphere.
Add the number infinity to a 3d space and you define a fourth dimension already.
And the whole idea about the positive reals looping back to the negative reals through infinity... well, that really doesn't make much sense, because there is no 'after' infinity as you put it. And it wouldn't really make a circle, because the perimeter would be infinite...
If you were talking about something more mathematically well defined I'd like to hear it though because it's an interesting idea.
There's an important distinction actually. Some string theories suggest large numbers of hidden spacial dimensions, like 11. This is distinct from time. Time is only seen as a dimension in General Relativity, and it's probably not a good idea to call it the '4th' because that suggests it's a continuation of the 3 spacial dimensions, which it isn't. Best call it the 0th or the Zth or something.Quote:
That's been my take on it, for the most part. I think the 4th dimension is the time line, except every "point" like entity is a static reality of space. The 5th dimension wouuld be like the next step beyond the line, but it is the next step beyond the time line-- the time plane. The 6th dimension would be an infinite number of time planes, something like a "time space". Etc. I wonder if the heirarchy has the potential of being infinite. I pissed off my metaphysics professor in college by arguing that in a paper. He told me I didn't know what I was talking about. I asked him for a counterargument, and he said, "COUNTERARGUMENT?????" and scoffed. I kept listening for an argument, but he had nothing else to say. What a dick.
On the other hand... A lot of modern theoretical physicists, most famously Brian Greene, say our particular universe has 11 dimensions. They say that the human mind cannot visually comprehend dimensions beyond the 4th but that theoretical physicists can prove the existence of those dimensions with equations.
Think of it like a flipbook. There are 2 spacial dimensions which is the paper with pictures on, and the thickness of the book is the single temporal dimension.
I think your flipbook analogy would demonstrate that time is really another dimension of space. The 2d picture might perceive the thickness of the book as time, but we 3d creatures can see it as a spacial dimension.
What xei said.Quote:
Originally Posted by Kromoh
I think that you meant to say 'independent dimension' as that's the only type of dimension. If I have a complex variable, I can vary the real and imaginary parts independently.Quote:
Originally Posted by Kromoh
This isn't true at all. What you are talking about is the 'one point compactification' or 'Alexandroff compactification' of a space. If we do it to the reals, we get a 1-sphere which is just a circle and hence one dimensional. If we do it to the complex plane, we get the 'Reimann Sphere' which is two dimensional.Quote:
Originally Posted by Kromoh
Spoiler for actual math:
In general, heres another way of thinking about dimension that is my personal favorite. We define a point to be zero dimensions. now imagine an ant moving on a line. We ask, "how can we constrain the ant to a finite area?". We can do so by placing a 0 dimensional obstruction on either side of the ant. imagine the ant at zero. We just put an obstruction at 1 and -1 and this will stop the ant from moving out of that range. So we say that a line is 1 dimensional because we can cut out finite areas with a 0 dimensional boundary. Or the boundary of a 1 dimensional area (if the boundary exists!) is 0 dimensional. We can do the same thing on a circle so that is 1 dimensional as well. Now imagine we put the ant in a plane. Two points wont cut it anymore, we need a circle to confine it. so we say that a plane is 2 dimensional because finite bounded areas have 1-dimensional boundaries. In general, a space is n-dimensional if finite, bounded areas have (n-1)-dimensional boundaries.
One more point. people are confusing 4-space with spacetime but there is a huge difference. It has to do with how we measure length (and hence area, volume and angle). in eucliadian space, we have a^2 + b^2 = c^2. in a two dimensional spacetime (that is one space and one time dimension), we have t^2 - x^2 = d^2. we choose our units so that 1 time unit = the time that it takes light to travel one space unit or we have to divide the x^2 term by c where c is speed of light. If anyone is interested, i'll be happy to answer any questions.
Dependent dimension, as in, values in one affect the other. iČ = -1, so a number in one complex dimension actually can affect the other. The imaginary dimension is connected to the real one. You also have cases like quantum superposition, with an n number of dimensions, but the diagonal of their values must always equal 1. Yes, there are independent dimensions, but the imaginary dimension is dependent.
The Riemann Sphere is exactly what I'm talking about - difference is, I didn't know it's name, since I got there on my own, on high school.
Basically, a system with n number of dimensions means a form has n number of perpendicular projections. The dimensions can be anything you define them to be, from statistical information to hyperspatial constructions. What we usually mean by 3d, though, is that the universe has 3 spatial dimensions.
iČ = -1 has nothing to do with dimension. That equations relies on the multiplicative structure that we add to the complex numbers on top of their additive and metric structure which is just that of a two dimensional vector space with a constant, positive definite metric over the real numbers. It confuses the issue of dimension to bring the multiplicative structure into it. The fact is that one can freely choose the real and imaginary components of the complex numbers. The dimensions are independent.Quote:
Originally Posted by Kromoh
To say that a dimension is dependent on another means that you are trying to describe the space with too many dimensions. For example, if I take all the points (x, y) so that 4x + 5y = 0, then I get a line. I can describe a point with its x and y values and pretend that it's two dimensional but once I choose one, I can not freely choose the other. I can even work out the equation y = 4x/5 and then see that all points on the line will have the form (x, 4x/5). So this space has one dimension even if I want to try to describe it with two. We could say that the y dimension is dependent on the x dimension but that just means that the y dimension is an artifact of our initial description of the line. There is no such thing as a dependent dimension. If you're into math, that's very important to understand.
The 5th dimension has actually been recorded on tape. It had something to do with a soul that was stoned at a picnic.
http://www.youtube.com/watch?v=3IrJRZRZIn4
^ Serve it down brother, serve it down.
I always thought that 4th dimensional creatures are ghosts and spirits. Things that live in the fourth dimension appearing in the third. Thats why we don't see them fully because its like taking an apple dipping it in ink and printing it in the 2nd dimension. It would look nothing like the apple we know.
But thats just me in bonkers land :boogie:
:-? I can't say I agree with that idea, but I like it.Quote:
Originally Posted by mrdeano
Even if y is an "artifact" of x, they are still different dimensions, and represent values of different nature. That is not so apparent in a line, but it is when dealing with conic curves, for example. Yet, they are dependent - as are mass and density, for example. One directly affects the other because of its very definition.
We are not in the "3rd" dimension. We are in 3 dimensions. A "fourth dimension being" would be actually one-dimensional, which means it'd be a line or a dot. Dimensions are not ordered. Objects are constituted of a number of dimensions, not an order of them.Quote:
Originally Posted by mrdeano
Our physical world is constituted of 3 dimensions, that's why we call it 3D - not because dimensions are "different worlds" or something. Matter is, all those new-ageish superstitious bitches sell the idea that a dimension is a kind of different reality.
Our physical world constitutes of many dimensions, string theory has it. We ourselves can only percieve a 3 dimensions at a time.Quote:
Originally Posted by Kromoh
I said that the need for a second coordinate is an artifact of the means with which we constructed the line.Quote:
Originally Posted by Kromoh
What I am saying is most apparent on a line but if you want to do it with conic sections, fine. take the ellipse x^2 + 2y^2 = 4. this gives y =+/- sqrt(2 - x^2/2). so now having chosen x, you have two possible values of y. y is again dependant on x and it is a one dimensional space. I might as well embed it in an n-dimensional space and say that there are n-1 'dependant dimensions'. By what you are trying to say, we are surrounded with an unbounded amount of 'dependant dimensions'. The whole point of dimension is that there are no dependancies between them. What you want to say is that the second coordinate is dependent on the first coordinate when we embed a one dimensional space in a two dimensional space. saying that one dimension depends on another or that one dimensions affects another makes no sense. You are confusing dimensions with coordinates. It's an important but (not so) subtle distinction. Mathemeticians failed to make it until the late 1800's when Peano cooked up this example of a curve that covers a 2 dimensional area so that one could label each point in a two dimensional space with one coordinate. After that, they had to redefine dimension without using the number of independent coordinates and basically arrived the explanation of dimension that I gave with ants and bounded areas to do so.Quote:
Originally Posted by Kromoh
I should also do the mathematicians walk of shame and say that I was wrong when I said that 1/t maps (-inf, inf) onto (-1, 1). It was actually the first thing that I thought when I woke up this morning so I must of dreamed about it. the function is |x|x/(x^2 + 1) . That was an ugly mistake.
You got my point. I also think space has (at least) 4 dimensions, not 3, and that'd explain things like in General Relativity when light makes a curve while not making a curve.Quote:
Originally Posted by Dreams4free
---
Philo, to quote my original post:
That is exactly it. A graph of speed X time, for example, has two dependent dimensions, because the definition of one involves the other. There can never be a change in the time value which doesn't affect the speed value (that, of course, assuming space hasn't changed too). That's why they are dependent. Deep inside, all dimensions of the universe (space, time, mass, light, whatever else) are an outcome of the fundamental concept of energy.Quote:
Dimensions are just dimensions. Dimensions don't have orders or meaning. They are like independent directions, though dimensions can be mutually dependent. There is no "the" 4th dimension, there can be a 4th dimension, and it can be any dimension you want it to... Time, mass, energy, eccentricity, number of breaths in a second, etc. A graph of speed X gas use X time has 3 dimensions. Basically that.
Quote:
Originally Posted by PhilosopherStoned
Quote:
Originally Posted by Kromoh
We're saying the same thing. You're just saying it wrong. The graph is one dimensional. I guess your set in being non-mathematical about it so i'll just let you be.
Well, maybe. What I'm really trying to convey is that dimensions derive from values, instead of values deriving from dimensions. Yes, of course we can take any number we want in any set of dimensions, but that is only hypothetical guessing. Dimensions are just a way of representing values of different nature; they are only made to show how the value in one changes in comparison to changes in another. Basically, a system of iterations.