4 dimensions

strid

Thougt of a thing, reading a topic about dimnesions...

if we think like this...

a point had 0 dimensions...
there are infinite many points in a line (which has 1 dimension)
there are infinte many lines in a square (which has 2 dimensions)
there are infinte many squares in a cube (which has 3 dimensions)

following this patterns, I see it reasonable to suggest:

that there are infinte many "cubes" (objects with 3 dimensions) in a 4 dimensional "object"...

so in an "field" (or what to call it) with 4 dimesnions we can fit EVERYTHING that we can see.. like the sun.... or maybe ven the whole univerese....

it might then be that our universe is 4 dimensional, an therfore has infinte "space" (3 dimensions).....

hope I wasnt confusing...

Kerbox

wouldnt the fourth dimension be... time? :P

danne89

Don't forget the hidden ones! You can always stuck your garbage in those...

Seriously, so you mean you can put infinity volume in a finte 4d-space? That sounds quite strange, but facsinationg.

Kerbox

I dont really think that is what he ment. I think he is confusing infinite steps with infinite size.

strid

time is not the 4th dimesion i'm talking about...
I'm talking about a 4th "spacial" dimension with the quality of fitting infinte much "3dimensional stuff"

danne89, understood my point i think......
maybe volume is the better word to use instead of space...

let me then put it like this:



in a "4 dimesnional thing" there is infinite volume
as there is infinite area in a cube...'

was this clearer

Crosson

Yeah, since the fourth dimension is time, what you say is exactly correct. Let me describe a 4-d object that contains "infinite" 3-volume: Me walking from the kitchen to my room.

If you think of this "content" (the generalization of length, area, and volume) as being made up of 3-volumes, you would need in an infinite number of them (1 three volume for each instant in time, exactly analagous to there being one square for each coordinate in the z dimension if you construct a cube from squares).

I am going to think about how a two dimensional creature could possibly use the third dimension as time.

Kerbox

If you bound the volume in all four dimensions, then the volume will be finite. I cant see how summing the area of the infinite number of cubes would make any sense.

Moo Of Doom

Actually, I do believe that's what he meant. And why couldn't you? Say you have a beach full of sand you want to clear out that is full with 1000x100x10m of sand. You could (theoretically) fit all of that sand in a 1x1x1x1m 4D box (or smaller even) by filling the first layer of 1x1x1 with sand, then adding another 1x1x1 layer on top of that, since the sand is only 3D (which we are only assuming :P), it has no hyperdepth, and so, does not take up more of the hypervolume of the box than the first one (which took up 0). You can keep going until the beach is cleared and still have infinite volume to fill. (Now getting the sand back out... that's a problem :P)

EDIT:

Actually, it is many people's belief, including mine, that the "time" dimension is indeed just a spacial one. Our brains (and eyes) just take in one "slice" at a time (much like a 2D creature would need to experience a 3D object).

strid

Crosson.. time isnt the 4th dimension, as there is a finite volume in you walking to the kitchen...

ito make an easier example.. a cube with 3*3*3cm sides is placed on the table.. over a period of time it is moved 3 cm to one side.... see it than as if you had one of this really old cameras where the photographing was really slow.. every area that is blurred is the volume... so the cube would, with the movemment include the area would be 54cm^3.... it would be as two cubes next to each other.....

But there is still a point in what you said...
if we have a point.. and move it straight.. we get a line... if we take this line and move is perpendiculat to the line we get a square... and if we move this we get a cube... so we should get some sort of 4dimensional thing if we moved a 3 dimensional thing... but the human eye can't observe it....

but we could guess of some of its qualities... whereof one is, I suggest, that it has an infinte volume...

Kerbox

Mmm... yea. So what you are saying is that a hypercube encloses infinite amount of 3d space, and a normal 3d cube encloses infinite 2d area, is that right?
Then I wonder, what possible use is it to consider the area of each of the infinite planes that makes up the 3d box?

strid

moo of doom made som good points..


about that with infinte area in a cube:

say you have a square with area 1*1cm....in a cube of 1*1*1cm, you could place infinately many such square in the cube....

Kerbox

But what physical sense would it have to sum up all the areas of the squares?
What you are doing is simply extending the 2d space to a third dimension by adding an axis perpendicular to the two others.

strid

it shows us that the same way, we could (COULD) have a 4dimensional "box" where we can just stock up infinite many 3dimensional objects...

the exmaple with sand was quite good...

Kerbox

Try stocking up infinity many planes first then, and then we can start talking about practical applications

Moo Of Doom

Well, imagine if Carl was a 2D being, and he lived in a 2D universe. He has calculated that his universe will be destroyed by a 3D object on a collision course with his plane. The only way to save his universe is to move it away. Being a brilliant scientist, he has discovered a way to create a 3D box. Now in order to save his universe, he just cuts it up into sections that will fit in the box (i. e. have the same dimensions as the base of the box). He then places each section in the box (hopefully in an ordered fashion). Since they have l*w*0 volume, he can fit as many as he needs in the box. He then moves his universe-in-a-box (don't ask me how) to a new location, and unpacks it and puts it back together. Yay, his universe is saved!

:P

strid

you might not have noted but mathematics is not neccesarily practical :)
try to show me the value of imaginary numbers then, which is a well-accepted thing... :)

I'm not saying anything about "doing" anything.. just pointing out the intresting relaionship between the dimensions that hints that a 4dimensional object has infinte volume......

Moo Of Doom

Actually, imaginary numbers have infinite (:P) application to specific types of engineering and various other fields of science. (But I forgot which, exactly >.<)