Dimensional analysis

LQ · 2007-01-01 08:28:44

First I will make the statement that any dimension that has length will be equally long since a dimension has no properties besides length. If the length of D1 is a property of D2, then D2 is a property of D1 in the same way, and since there is nothing else for D1 to be property of besides Dn, they will all be equally long.

Given that length increase with time, time increase with length etc.

If you've got more of these, then post them. I will post more as I come up with more.

Ricky · 2007-01-01 17:50:13

Can you first work on a rigorous definition of what a dimension is?

MathsIsFun · 2007-01-01 18:36:45

It sounds a bit like "how do I know you really exist ... I might just be inventing this whole conversation"

You can compare lengths, though.

How about these two:

****
********

The second one is twice as long, isn't it?

(Also: "dimension" is sometimes used to mean length only, as in "what are the dimensions of the box?", or it can mean any physical measurement such as length, mass, time)

LQ · 2007-01-01 21:35:06

If a dimensions length is undependent of time, then sooner or later it will get zero length, and that could be at any time since it's time undependent. But if it is time dependent then we know for certain that the size of the dimensions are equally long since one dimension is unseperatable from the other and hence effect eachother with equal manners.

Last edited by LQ (2007-01-01 21:40:59)

LQ · 2007-01-01 21:43:24

Ricky wrote:

Can you first work on a rigorous definition of what a dimension is?

I was talking length.

Zeroface · 2007-01-02 02:46:21

The word Dimension can refer to shapes such as 2-dimensional (2d) shapes and 3-dimensional (3d) shapes. A simple example of a 2d shape is a square whilst its 3d counterpart is defined as a cube. Dimensions can be better explained using axis. On a 2d coordinates grid we have only an 'x' axis and a 'y' axis whilst on a 3d grid there is a third 'z' axis. Let's count up how many axis we have on both grids. On the 2d grid we have 2 axis, hence the definition 2-dimensional. On the 3d grid we have 3, hence the definition 3-dimensional. Humans can see only a limited number of dimensions. We mostly see 3-dimensions as some faces of opaque shapes are often hidden unless we change our viewpoint. Then again even if we change the angle at which we see something, some of the faces we could see before are then hidden. This is a simple study of dimensions and should be referred to before moving on to more complex dimensional studies.

LQ · 2007-01-03 01:33:54

Then I'll add this:
http://www.thescienceforum.com/viewtopic.php?p=51858#51858

Quote me where I'm wrong.

MathsIsFun · 2007-01-03 10:18:08

Nice explanation, Zero.

LQ: I must confess I am confused. However your ideas sound a little like my theory that "things" are only the result of "relationships". So these "dots" of yours are the end-points of relationships.

And once you build up enough "relationships" it becomes possible to have relative properties. For example, "A" is after "B", and "B" is after "C", hence "C" is also after "A".

And length, to me, is a relative property ... you define a "unit length" (by marks on a piece of metal, or wavelengths, etc), and then compare it to other lengths.

LQ · 2007-01-03 22:27:43

Yeah, zero's got it figured out and that theory is nice. As for my own, did I break any rules?
Some of the text in the link:
"So let's say that in the beginning there was nothing in form of an infinite dimensioned dot (since nothing has no boundries in any direction, since something infinitely small has no boundries). A such dot is made of smaller, (infinity - n)dimensional dots. 2^n of them, possibly. So if the overdimensional dots leaks underdimensional dots, then we sooner or later have this universe. So this universe is actualy a dot leak, and empty space is infact underdimensional dots/particles. In this theory I call the universe "the dotleak"

So the universe was an infinity dimensional dot that leaks underdimensional dots until there are only zero-dimensional dots left.

"It will take exactly one eternity for the universe to become zero-dimensional dots. (or something like that)" (

What I do understand is that it might certainly leak bakwards from time to time, and you never know if any dot can be called something else then infinity dimensional in itself (what bounds can it have if it is a dot?). In other words it is possible that every dot is a universe, and a universe can repeat sequences etc. "

So if this is true, then space will gradualy become 2dimensional, with 3dimensional photons, just like the universe today is 4(or more)dimensional matter in 3 dimensional space. When the 3dimensional space gradually becomes 2-dimensional, we will probably experience that distance becomes longer, but 2-dimensional. On the other hand, the decay of matter will cause 3d particles that makes matter seemingly gravitational, wouldn't it?

Last edited by LQ (2007-01-04 00:20:30)

MathsIsFun · 2007-01-04 09:44:59

Interesting idea, but has anyone observed something that loses a dimension?

And ... has anyone observed something with 2 dimensions?

Ricky · 2007-01-04 10:09:14

First I will make the statement that any dimension that has length will be equally long since a dimension has no properties besides length.

How is it that a dimension has length? You say that by dimension you mean length, so are you saying that length has a length? That doesn't seem to make any sense.

And ... has anyone observed something with 2 dimensions?

I saw a plane the other day. It was pretty flat, but I'd still say that it was 3d. Flew beautifully though.

LQ · 2007-01-05 00:12:21

Yes, some things dots are still 3D, but if you look at big things, like galaxies, they are flat, aren't they? Relatively speaking...

"A dot is infinitely thin, so 2 dots in a row is also infinitely thin, why there is nothing saying that the multidimensional dot it all began with can't re order the dots internally to create a dot that has less dimensions then the first dot. Infact, even an infinitely slow movement of the dots given from the fact that the highdimensional particle has a free variable of dimensions depending on the dot's positions in them self and the other way around would still cause an imediate effect as a decay of dimensions, in the case that the dots due to this mentioned, moved. Since every dot moves, they would sooner or later form a 3 (or lower) dimensional mess that we can live in. I guess that the final decay would be 0 dimensional. I don't know what will happen then. I guess the dots will dissapear and it will start all over again. Cause the energy and momentum cannot be contained in something 0 dimensional

Right now we've got galaxies and solarsystems that are flat.

It couldn't have started in 4D, cause then there would only be 2 particles.

Last edited by LQ (2007-01-05 06:52:05)

LQ · 2007-01-05 06:50:00

Ok, I posted something new in the last post, I thought I should let you know, Incase you are interested.

Ricky · 2007-01-05 07:42:56

Yes, some things dots are still 3D, but if you look at big things, like galaxies, they are flat, aren't they?

Calling a galaxy flat is the equivalent of calling a piece of paper flat.

LQ · 2007-01-05 10:26:25

Yes, that's exactly the analogy i meant to make.

Ricky · 2007-01-05 10:35:36

But a piece of paper is not flat...

Toast · 2007-01-05 14:31:33

No?

Ricky · 2007-01-05 17:58:40

No, it has a height. A quick few searches shows this to be 0.004 inches, but I'm not certain if this is the standard.

Toast · 2007-01-05 21:01:54

Oh, lol I thought you meant the surface. Nvm

LQ · 2007-01-05 22:31:09

Yes, but if the room was about to go 2D, wouldn't it start like that?

And thanks for the neat paper width examination. You have alot of them, don't you?

Last edited by LQ (2007-01-05 22:32:57)

Ricky · 2007-01-06 11:02:47

Yes, but if the room was about to go 2D, wouldn't it start like that?

How is it that something can go 2D?

LQ · 2007-01-06 23:23:15

The same reason that something can go 3D.

Ricky · 2007-01-07 05:09:07

Heh, alright. And that would be? Sorry, I can't recall anytime I've seen something change dimensions.

LQ · 2007-01-07 07:24:57

How about a balloon?

Anyway, seriously... What I meant is that we are like a 4D line through 3D rooms, and since everything with dimensions, can change over other dimensions (dy/dx) so that it becomes less dimensional, that will happen and this means that eventually we will reach the end of the line, and then there will only be room, 3D life. That is, if it will ever end. That is, if our speed through spacetime is compareable to the length of time. The universe is a box, if you get to the end, you'll have to go sideways. But this I know very little of. Enlighten me if you can.

How about big bang?

Last edited by LQ (2007-01-07 07:29:52)

Ricky · 2007-01-07 10:17:33

What I meant is that we are like a 4D line through 3D rooms, and since everything with dimensions, can change over other dimensions (dy/dx) so that it becomes less dimensional, that will happen and this means that eventually we will reach the end of the line, and then there will only be room, 3D life.

But again, you lose me right off the bat. I don't see how you can see us as a 4d line. Space itself is four dimensional, at the very least. Also, dy/dx is not a change over other dimensions, it how y changes as a function of x.

Math Is Fun Forum

#1 2007-01-01 08:28:44

Dimensional analysis

#2 2007-01-01 17:50:13

Re: Dimensional analysis

#3 2007-01-01 18:36:45

Re: Dimensional analysis

#4 2007-01-01 21:35:06

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#5 2007-01-01 21:43:24

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#6 2007-01-02 02:46:21

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#7 2007-01-03 01:33:54

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#8 2007-01-03 10:18:08

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#9 2007-01-03 22:27:43

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