4 dimensions

  • Thread starter strid
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  • #1
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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...
 

Answers and Replies

  • #2
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wouldnt the fourth dimension be... time? :P
 
  • #3
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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.
 
  • #4
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I dont really think that is what he ment. I think he is confusing infinite steps with infinite size.
 
  • #5
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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
 
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  • #6
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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.
 
  • #7
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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.
 
  • #8
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Kerbox said:
I dont really think that is what he ment. I think he is confusing infinite steps with infinite size.
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:

strid said:
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"
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).
 
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  • #9
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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...
 
  • #10
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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?
 
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  • #11
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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....
 
  • #12
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strid said:
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....
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.
 
  • #13
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Kerbox said:
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.
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...
 
  • #14
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strid said:
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...
Try stocking up infinity many planes first then, and then we can start talking about practical applications :rofl:
 
  • #15
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Kerbox said:
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.
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
 
  • #16
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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......
 
  • #17
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Actually, imaginary numbers have infinite (:P) application to specific types of engineering and various other fields of science. (But I forgot which, exactly >.<)
 
  • #18
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Dealing with alternating (sinousoidal) currents in electrical systems for one

And the practical aspect I brought up since in the original post, there was talk about fitting universes and suns into finite hypercubes and such...
 
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  • #19
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I didn't completly understand that time interpretation for a few posts back. Can you develop it a little.

This whole discusion reminds me of a joke: "How can you visulise 4th dimension objects" "First visulise nth dimenstion and then reduce to 4th" :) Perphaps a little too old...

If I understand popular string theory right, it exist many hidden dimenstions of 4+. If you can unhide those things, what would happen. Now I maybe quite OT, but it's a fascination discusion indeed.
 
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  • #20
Icebreaker
I don't understand the original post. Are you talking about the suggestion that the universe is a sort of higher dimensional sphere? As in, if you go straight in any direction, you'll return to the same spot?

For example, if the universe was a plane, but "in actuality" is the surface of a sphere.
 
  • #21
mathwonk
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i am ignorant. just try to educate me, i dare you.
 
  • #22
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Icebreaker said:
I don't understand the original post. Are you talking about the suggestion that the universe is a sort of higher dimensional sphere? As in, if you go straight in any direction, you'll return to the same spot?

For example, if the universe was a plane, but "in actuality" is the surface of a sphere.
No... i'm pointing on the fact that there can fit infinte many n-dimensional objects in a (n+1)-dimnesional object....

As there are infinte many points in a line...infinte many lines in a square adn etc...

so is possible (probable?) that the universe is a 4+ dimensional object that can contain infinte much 3-dimensional stuff....
 
  • #23
Icebreaker
strid said:
No... i'm pointing on the fact that there can fit infinte many n-dimensional objects in a (n+1)-dimnesional object....
Not necessarily. Depends on what you mean by "fit".

strid said:
so is possible (probable?) that the universe is a 4+ dimensional object that can contain infinte much 3-dimensional stuff....
That's more of a question for physicists. As I understand it, superstring theory says there are 10 spacial dimensions.
 
  • #24
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I've hard to imagine how physicst can caonclude that there 1re 10 spacial deminsions...how would they possibly be able to do that.. sounds fascinating and inrtesting...anyone tha can explain breifly?
 
  • #25
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strid said:
I've hard to imagine how physicst can caonclude that there 1re 10 spacial deminsions...how would they possibly be able to do that.. sounds fascinating and inrtesting...anyone tha can explain breifly?
A least one variety of string theory (and, apparently, the one most accepted) requires 11 dimensions (10 spacial and one temporal) in order to make the fundamental values come out right. The idea is that all but 3 of them are "rolled up" tight. Imagine a sheet of paper (2 dimensions) rolled up in one direction to form a cylinder of very very small radius. Looks like a one dimensional line, doesn't it?
 

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