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Shadow12345
12-18-2002, 01:49 PM
I am trying to think of ways to describe the 4th dimension. This explanation should describe it both spatially and why it is considered time (well, technically if you describe one then you almost have to be describing the other).

Anyway this is basically what I have come up with so far, elaborate, insult, critisize, confirm, etc:

"When you look at an object in a lower dimension you can see every single possible view of that object in an instant (meaning no time has passed) where if you were actually a part of that lower dimension it would take time to travel around and look at every possible view because you would not be able to view it all in one instant."

Just to throw more stuff in, a 4th dimensional being would be able to extract a 3dsphere from a 3dcube without passing through the walls of the cube, much in the same way a 3rd dimensional being (THAT'S US!) would be able to touch the bullseye of a dartboard without first passing through the boundaries of the outer rings (a 2 dimensional being would have to pass through the rings in order to go to the center, also keep in mind a 2d being cannot look up or down).

I am going to stop here because I want to know if people find that accurate, because I am having an argument with a friend and I think I am right :)

Davros
12-18-2002, 02:03 PM
Although a lot of people think of time as 4th dimension, and it's sometimes useful to do this, I wouldn't necessarily define it as the 4th dimension.

The problem is that time is different. In the spatial dimensions, you can move both in a negative and positive direction, but in time you can only move forward. This is often refered to as the 'arrow of time'.

>Just to throw more stuff in, a 4th dimensional being would be able to extract a 3dsphere from a 3dcube without passing through the walls of the cube...

I see what you are saying & you're kind of on the right lines. What you talking about is talking a lower dimensional slice through something. I.e. a slice through a cude is a square, and a slice through a hypercude (a 4D cube) is a cude.

Mathematically, you would describe a 4th dimension as being orthogonal to the other 3. Where orthogonal means you have a set of mutually perpendicular axes. In that you can have as many dimensions as you like, but it's just difficult to imagine more than 3.

Mind bending stuff.

Edit : What the hell is a 'cude'. I meant 'cube'. Dooh!

Shadow12345
12-18-2002, 02:10 PM
you're kind of on the right lines.

I thought I was exactly right on with everything I said (I purposely left many things out due to the fact that they may have seemed...oh what's the word, ambiguous? And that I wouldn't be able to explain what I meant)
Remember I said to criticize, so if I wasn't completely correct you need to tell me where because this is helping me learn :)




Mathematically, you would describe a 4th dimension as being orthogonal to the other 3. Where orthogonal means you have a set of mutually perpendicular axes. In that you can have as many dimensions as you like, but it's just difficult to imagine more than 3.

Mind bending stuff.


Now I want to know what the 5th dimension would be like, can you try to explain it to me davros.
EDIT:
http://dogfeathers.com/towle/star.html

EDIT1:
(from that site above)
This seems like a good excerpt to keep in mind


Briefly, plane polygons are two-dimensional polytopes, and polyhedra, three-dimensional polytopes. Where polygons are bounded by line segments, and polyhedra by polygons, a 4-polytope is bounded by polyhedra.

Davros
12-18-2002, 02:32 PM
>it always appears as 2d when you are looking at it from a higher dimension

Not sure what you mean. I suppose you could say it appears flatter when you look at it from a higher dimension. We generally think of flat as being 2D simply because we live in a 3D world.

Shadow12345
12-18-2002, 03:32 PM
Not sure what you mean. I suppose you could say it appears flatter when you look at it from a higher dimension. We generally think of flat as being 2D simply because we live in a 3D world.


I deleted what I said about that.

I cannot imagine what the axes of 4 dimensions look like. I understand how you get from 2 dimensions to 3 dimensions by adding an axis that is perpendicular to both the x and y axes, but I don't know how in the hell you would add an axis that is perpendicular to the x, y, and z axes...like you said, mind bending (obliterating is a better word).

It's going to take me forever to get comfortable with these ideas, but I want to be a higher dimensional thinking individual :) THEN MAYBE I'LL START SPEAKING IN BINARY CODE!

Davros
12-18-2002, 03:39 PM
>but I don't know how in the hell you would add an axis that is perpendicular to the x, y, and z axes

If we can have equations for solving thing in 3D, then we can have equations for 4D, 5D, 6D etc. The same principles apply when thinking about 2D v 3D, but things will be much easier if you don't try picture such things in your head.

napkin111
12-18-2002, 03:44 PM
Woah! That is very "mind <I>obliterating!</I>" My head is going numb, first from trying to think of the end of the universe, then from the 4th dimension. I think is way beyond the scope of us to comprehend the 4th dimension. Its like trying to describe color to a blind person or music to a deaf. I think a 2D being would be boggled by the 3rd dimension just as much as we are by the 4th.

//napKIN

Davros
12-18-2002, 03:50 PM
>I think a 2D being would be boggled by the 3rd dimension just as much as we are by the 4th.

Exactly.

But it's not that we can't understand it, it's just that we can't visually imagine a 4D object using a 3D mind.

Cshot
12-18-2002, 04:38 PM
Very interesting. I remember one of my math professors years ago showed us a video he made about 3D and 4D objects. I should've asked him for a copy of it because it was really trippy. He plotted 4D objects in his video and showed us how it would appear if it were to rotate. I think the whole class could not grasp what they saw including me. The only way I can describe it is while the object was rotating, it appeared as if it was swallowing itself.

EDIT - he started off the video showing us how a 3d object can be represented in 2d space. Then he moved it up a notch showing us how 4d objects can be represented in 3d space.

Shadow12345
12-18-2002, 05:11 PM
The best way I can think of to describe 4d is to say that a 4d being has access to every part that makes up a 3d being all in the same instant, that a 4d being does not have to travel through space (and time) to touch something, but rather the 4d being has already accessed it and is already touching everything in the same instant. I think that makes sense. It is much like the 2d vs 3d concept: if you have a 2d circle with a 2d cube inside it, a 2d being absolutely must go through the circle in order to touch the cube, however a 3d being (THAT'S US!) can simply lift the cube without ever touching the circle.

Now don't take 'being' to mean something living, my remote control is a 3d being.

It is not exactly correct to say the 4th dimension is 'time' because that makes it sound like you can go forward and backwards in time (what Davros was saying makes sense now). Rather a 4th dimensional being can 'save time' by making jumps into the 'future'. Lets say there is an object in the middle of the room you are currently in, let's just say it is a ball (shape doesn't matter). Davros you can play the 3d being! In order for davros to touch the ball, he would have to enter the doorway, travel through space (thus taking time because you cannot move across any distance in an instant because an instant means no time has passed) to touch the ball. Now lets imagine you take that very same room with the ball in it and slice it into infinitely small pieces so that instead of being a single three dimensional room it is made up of many 2d slices. A 4d being would 'save time' by simply touching one of the slices that contain the ball instead of having to travel anywhere to touch it.

the pictures i'm attaching show first our 3d room, you cannot have lines overlap in paint so just imagine there is a ball in the center of the room. The second one shows 4 of these so called slices of the room in the fourth dimension (again, no overlapping lines so i can't do it exactly as i wanted), one of these slices already has part of the ball so you don't have to do any traveling to touch it, you already have it because you ahve all of the slices of the room.

god dammit i make no sense im a slut

Shadow12345
12-18-2002, 05:12 PM
these are some of our slices that make up the room:

EDIT: I think I am somewhat wrong about this whole thing, although the underlying ideas seem fundamentally correct. i.e the cube shouldn't actually be split up into 2d slices, rather the same cube exists at different times but it is still 3d (i looked at some 4d pictures on the internet)

does anyone know how to actually draw 4d objects?? Does the placement and order matter when drawing them, or does it just have to be the original overlapping itself or what?

sean
12-18-2002, 06:59 PM
Corect me if I'm wrong, but there is no "THE 4th dimesnion". Dimensions are what you set them to be right? It's just that the 3 most common are L, W, and H, but if the trend would continue, the 4th would be time because that the most common. No one's making you do otherwise.

salvelinus
12-18-2002, 08:00 PM
Originally posted by Shadow12345

Now I want to know what the 5th dimension would be like
Try here (http://members.aol.com/laruemccoo/)

Aran
12-18-2002, 08:32 PM
ah, so that's the meaning of life!

you can't "picture" 4-d. much like you can't picture an electron, but you know it must exist.

I think it is very near physically impossible for a 3-d person to see any other dimension, because vision is 3 dimensional, therefore no matter what dimension we are claiming to be picturing, we are still seeing a 3-d representation of it, therefore it is simply 3-d.

napkin111
12-18-2002, 09:28 PM
[i]
god dammit i make no sense im a slut [/B]

^--Thats the only part I could understand and agree with ;) jk

I don't think you can even represent 4D (assuming there even is a 4th Dimension) objects in 2D (on your monitor)...just as you cannot represent 3D objects in 1D space...but you can in 2D, you just need to have 3 pictures...maybe you can only represent objects in 1 less Dimension or higher than the origional object. (erm...that makes no sense...Example: 3D objects can only be represented in 2D space or higher; 4D objects can only be represented in 3D space or higher, etc, etc) Or perhaps I just have no clue what I'm talking about........yeah....

//napKIN

Shadow12345
12-19-2002, 07:14 AM
actually napkin (and aran) I believe you are both exactly right on the money. Let me say this:we would need a truly three dimensional monitor (well a three dimensional viewport) in order to view objects that exist in the four dimensions. Do we agree on that?



^--Thats the only part I could understand and agree with jk

:) lol

EDIT:
Is it possible the 4th dimension is forward in time, and the 5th dimension is backwards in time?

EDIT1:


you can't "picture" 4-d. much like you can't picture an electron, but you know it must exist.

I agree, although electrons can easily be pictured because when you come right down to it they are still 3d beings (the quantum number 'm' used in electron configurations represents the 3d orientation of the orbital of the electron) , and there is nothing that says the fourth dimension must exist because even if it does exist it would never effect us and we could never be a part of it, where as electrons have a very big impact on our lives.

Scourfish
12-19-2002, 09:47 PM
http://www.timecube.com

napkin111
12-19-2002, 10:48 PM
Dang, I've only read a few so far, but that is messed up...**continues reading**...and I was planning on going to bed now too....

//napKIN

P.S. Does that have anything to do with the topic?

Cobras2
12-20-2002, 12:15 PM
have you ever read:
http://promo.net/cgi-promo/pg/t9.cgi?entry=201&full=yes&ftpsite=http://www.ibiblio.org/gutenberg/

it's a very interesting book (plus it only takes an hour or two to read)

on a totally absolutely unrelated side note.. while I was searching for the book.. I found a document on gutenburg called "the square rot of 4 to the precision of 1 million digits".
This peaked my curiosity, and I got about 1/4th of the way down the document before I caught on.. umm lol.. that is funny.
goto
http://promo.net/cgi-promo/pg/t9.cgi?entry=3651&full=yes&ftpsite=http://www.ibiblio.org/gutenberg/
if you haven't caught on yet...

Shadow12345
12-20-2002, 02:47 PM
What about the square root of 11.11111111111111111111111111111111111111111111111 11111111111111111111111111111111111111111111111111 11111111111111111 to eighty trillion places?