Thread: Explain to me the 4th dimension.

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

Originally Posted by ThreeLetterSyndrom

If the universe is curved, the corners of a triangle wouldn't add up to 180 degrees.

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?

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

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

http://www.youtube.com/watch?v=Y9KT4...rom=PL&index=3

Carl Sagan reminds me of Agent Smith.

Originally Posted by grasshoppa

Carl Sagan reminds me of Agent Smith.

http://www.youtube.com/watch?v=lgfYPnA_iFI

crumbly but good

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

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

Originally Posted by Xei

Nah just the people who've had too many drugs.

I resemble that remark

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.

Originally Posted by Xei

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.

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.

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.

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.

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.

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.

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.

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.

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.

Originally Posted by Kromoh

There are two ways of deriving another dimension. Either by adding a completely new one, or by "folding over".

What xei said.

Originally Posted by Kromoh

Imaginary numbers define a new, dependent dimension, and extend the real line to the complex plane.

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.

Originally Posted by Kromoh

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.

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.

Spoiler for actual math:

Originally Posted by Xei

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.

one can do this by mapping the plane onto (-1, 1) by the map t -> t^-1. Theres a singularity at t=0 that you need some topology to get rid of but that's the basic idea.

Then you map (-1, 1) onto the sphere with the map t -> [cos( pi*t), sin (pi*t)]

There is a geometric construction as well. imagine a circle sitting with its lowest point on the real line and such that the real line is tangent to it at 0. then draw a line between the point on the circle opposite to zero and touching the point p on the real line. this line intersects the circle in two spots; the point opposite and zero and a point that we'll call p2. As p moves, so does p2 and we just identify p and p2. We can do this because for a given p, p2 is uniquely determined.

We can do the same thing with the 2-sphere and the plane.

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. i² = -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.

Originally Posted by Kromoh

Dependent dimension, as in, values in one affect the other. i² = -1, so a number in one complex dimension actually can affect the other.

i² = -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.

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.