A brief summary of the Dimensions

[RQ]

1 dimension, 2 dimensions, 3... how many? Nobody I know knows...

Well, let's start with the givens... Theoretically points do not exist in our dimensional totality. There is at least 1 dimension of motion... Pretty much it...

Now how do we know that we live in a 3D universe? If we get dizzy don't you see a room that is constantly spinning. That way you might actually see the fourth dimension. Of course you're only fooling yourself, but hey who knows? So how do we know that we live in a 3D universe. Simple there is gravity. Gravity gives us the perspective we need, without which we might think that we live in a 5D universe, since it pulls us down in only one direction of motion giving us the first dimension of motion. Now from there on we know that there are only two other perpendicular motions that can exist within this universe. Now we can see that the first dimension is up and down, the second forward and backward, and the third left and right.

I will leave time for some other post. Since we live in this 3D world with gravity... and stuff, we start thinking, why 3, why not 4. We couldn't possibly know why, but we probably might know where. If we have the 2D being Fred walk around in his 2D gravity driven world, he wouldn't know where the 3D dimension is because he lives in a 2D world. Now by definition, a 2D object would be infinitely smaller than a 3D one. By definition we also know that bob lives in area instead of space. Now let us think. Now Bob has a cube that is 6'6'6' and Fred has a square that is 6'6' and another one that is 3'3'. Now we know that Fred's bigger square is twice as big as his smaller one, yet both are infinitely smaller than Bob's cube, which in turn is infinitely smaller than the 4D being Emily's 3'3'3'3' hypercube. Now want to believe that we exist (I don't think Descartes was right when he said that "I think, therefore I am" because you need "to be" to be able to think, but anyway...)so all the other dimensions would have to contradict our existence...
I guess we can only exist if they don't, and they if we didn't, kinda like war of the worlds.
But this couldn't possibly be true if all of our dimensional universes were idle of each other. Now if Fred didn't exist to Bob, and vice versa, this wouldn't even become a problem because there would be no 3d dimension in Fred's world to compare his infinitely small squares to there wouldn't be this mumbo jumbo. However the problem is that there couldn't possibly be a 1st dimension, because all dimensions are independent from each other by definition (since all perpendicular motions are independent from each other) and therefore this would prove to the nonexistence of Fred's and everybody's except pointpeople's first dimension. If Fred were to say that was true he would create a paradox. This would mean that we don't exist as well. Now this couldn't possibly be true, unless we don't, but let's assume we do. How about a proof that Fred can have a 1st dimension. Well each lesser dimension would have to be infinitely smaller than its higher dimension.

[Keiji]

o_O

that is confusing...

[sup2069]

LOL, alkaline will have a good comment. I was lost with ya, no offense

[Jay]

First off, if Fred has a square of 6x6 and one of 3x3, the former is 4 times as big as the latter, not two.

Second, your entire paradox is incorrectly based on a property used when solving geometrical proofs. (If a = b, and b = c, then a = c). You said that if both squares are infinitely smaller than the cube, then they must be equal. Then you said that this could not be true b/c it was obvious that the 6x6 was bigger.

What you didn't realize is that they both are infinitely THINNER in the z-direction when compared with the cube, not infinitely smaller. This makes them have an equal measurement in the Z-DIRECTION, not the x and y directions too. The 6x6 remains four times as large as the 3x3, and the factor of width is ignored.

[RQ]

Yes that would be a good explanation for a separate 2D world, but we are talking about a 2D world within a 3D world, and whether that is even possible. (yes by the way a 6'6' square is 4 times bigger than a 3'3' one) Now if Fred were to live in Flatland, his squares would have different areas because there is no higher dimension to contradict, but if Fred were living in Bob's 3D universe, then to Bob, Fred's squares would have no difference therefore making the paradox.

[Jay]

Draw a square of 3x3 on a piece of paper. Then draw a square of 6x6. You CAN see the difference. Now turn the paper so that you are only looking at the side. NOW you can't see the difference, because you can't even see where the squares are.

[alkaline]

Well, let's start with the givens... Theoretically points do not exist in our dimensional totality. There is at least 1 dimension of motion... Pretty much it...

No, you need the second dimension for rotation. I can't remember what fundamental things you get in the third dimension.

So how do we know that we live in a 3D universe. Simple there is gravity. Gravity gives us the perspective we need, without which we might think that we live in a 5D universe, since it pulls us down in only one direction of motion giving us the first dimension of motion.

You can have gravity in any dimension 1 or higher (assuming classical physics of basic attraction of matter to other matter) - all you need is a large mass, and it will attract smaller masses to it. No matter what the dimension, gravity will only act linearly. Thus, the presence of gravity tells you nothing of what dimension you are in.

Now want to believe that we exist (I don't think Descartes was right when he said that "I think, therefore I am" because you need "to be" to be able to think, but anyway...)so all the other dimensions would have to contradict our existence...
I guess we can only exist if they don't, and they if we didn't, kinda like war of the worlds.

I don't think this is true. This is a purely philisophical belief, and it can't be proved - likewise i can't prove that it possible for two universes of different dimensions to both exist at the same time.

But this couldn't possibly be true if all of our dimensional universes were idle of each other. Now if Fred didn't exist to Bob, and vice versa, this wouldn't even become a problem because there would be no 3d dimension in Fred's world to compare his infinitely small squares to there wouldn't be this mumbo jumbo. However the problem is that there couldn't possibly be a 1st dimension, because all dimensions are independent from each other by definition (since all perpendicular motions are independent from each other) and therefore this would prove to the nonexistence of Fred's and everybody's except pointpeople's first dimension.

The fact that all dimensions are linearly independent/perpendicular to each other says nothing about a 1st dimension not existing. It is independent in itself, and thus classifies as a dimensional universe.

If Fred were to say that was true he would create a paradox. This would mean that we don't exist as well. Now this couldn't possibly be true, unless we don't, but let's assume we do. How about a proof that Fred can have a 1st dimension. Well each lesser dimension would have to be infinitely smaller than its higher dimension.

What is your conclusion? I am missing something. Also, what do you mean by "Fred can have a 1st dimension"? Do you mean "Fred's planespace can have a 1st dimension embedded in it"? I personally think it would be fine to happen.

I think it would be fine to have a three dimensional universe and a four dimensional universe both embedded in the fifth dimension, so you'd have to travel to the fifth dimension in order to get to the four-dimensional universe. Then you wouldn't have the problem of the third dimension splitting the fourth dimension in half.

[RQ]

1. I mean one dimension of motion as in there is at least a one dimensional universe with motion in it as linear.
2. Gravity can exist in all dimensional universes, but it is what gives us a perspective... Perhaps maybe this isn't a very good or meaningful point.
3. Brainstorming
4. I'm trying to say that if Fred were in Bob's universe then his 2D world would have to not exist, since to a 3D world, his world would have to have no z dimension and therefore no existence since x times x times 0 makes 0 volume. If Fred were to exist since 2 dimensions do exist for 3 to be able to make space, then that would make us non-existent. Maybe the dimensions being independent has nothing to do with it.
5. Yes, I did mean to say that for us to be able to exist, we would have to solve the paradox with the fact that if 2 dimensions alone cannot exist then how could they be incorporated?

[RQ]

Aale de Winkle mentioned somewhere that Infinity times 0 = -1 since on a graph, two perpendicular slopes when multiplied make -1, just twist the graph so that it falls right on x/0 times 0. And if x/0 times 0 =-1 then 0/0=-1. Now this would mean that 0/0= all numbers since we just divide each side by any number and get 0/0.

[alkaline]

2. Gravity can exist in all dimensional universes, but it is what gives us a perspective... Perhaps maybe this isn't a very good or meaningful point.

You don't need gravity for perspective - you just need some kind of reference surface in order to figure out your directions. Gravity just tends to create bodies with (locally) flat surfaces so that we can perform this.

4. I'm trying to say that if Fred were in Bob's universe then his 2D world would have to not exist, since to a 3D world, his world would have to have no z dimension and therefore no existence since x times x times 0 makes 0 volume. If Fred were to exist since 2 dimensions do exist for 3 to be able to make space, then that would make us non-existent. Maybe the dimensions being independent has nothing to do with it.

This is based on the assumption that something has to have volume for it to "exist". Maybe it's reasonable to say that in a realmspace, if an object doesn't have 3 dimensions to it, then it doesn't exist, but i'm not so sure that that is a necessity.

5. Yes, I did mean to say that for us to be able to exist, we would have to solve the paradox with the fact that if 2 dimensions alone cannot exist then how could they be incorporated?

I would say the way to solve all this is to say that any number of dimensions is actually possible, but every being is limited to his brane, and an n-dimensional brane can have (n-1) or lower dimensional branes within it.

[Aale de Winkel]

Aale de Winkle mentioned somewhere that Infinity times 0 = -1 since on a graph, two perpendicular slopes when multiplied make -1, just twist the graph so that it falls right on x/0 times 0. And if x/0 times 0 =-1 then 0/0=-1. Now this would mean that 0/0= all numbers since we just divide each side by any number and get 0/0.

go easy with divisions by 0, since indeed it can mean anything. as an example any number devided by itself give 1. (ie x/x = 1) let x = 0 and you have 0/0 = 1; combining this would give -1 = 1 and henche the collapse of the whole of mathematics.

Cogito Ergo Sum, is Descartes entry point of reasoning, equaly valid to yet another: I think therefore you exist (or something to that effect, I currently don't remember which phylosopher postulated this). Holding this viewpoint though it is foggy to me why I thought up my currently running nose, or even being involved in these kind of discussion. Probably without it I would float in empty space, and have but mmy length as a reference line to figure out that there is also a front, a back, a left and a right. Darn with my own bodies up and down my space would be 3d (no gravity or whatever force in this reasoning, but merely the fact that my (current) brain is 3d oriented)

The lower dimension I think need some small extrusion in to the higher dimension to exist. Flatland might exist on some sheet of paper, bionians simply are not aware of this fact. So we trionians might have some thrength, to enable Emily to hang our realm on her wall (our trionian brain simply doesn't see that). To say otherwise I agree in order to exist there might be need for some infinitisimal volume for the lower dimensions to exist, letting this volume be 0 the lower dimensions are not physically present, but do exist merely phylosophically!

[alkaline]

well, if any particular dimension needs thickness to exist, then that necessitates an infinite number of dimensions. Or, you could just say that dimension K can have zero thickness but every dimension below it must have thickness, and set K to some theoretical value.

[RQ]

0/0 doesn't just equal 1... it equals all numbers!

[Aale de Winkel]

0/0 doesn't just equal 1... it equals all numbers!

That's what I'm saying, just what approach you take 0/0 can mean anything. I can't refute my funny geometric proof of 0/0 = -1 as well as my analitic argument of 0/0 = 1. Together they would collapse mathematics (since -1 = 1). Just be carefull with infinity

[RQ]

well 0/0 does equal to all numbers, just like x^2=49, makes 7 and -7 equal in that respect, although they are just the possible values for the equation...

[Geosphere]

0/0 does not equal all numbers. There are many conflicting systems of math on this question, and saying that is just wrong.

[alkaline]

why does 0/0 really even matter? in our math system, it is undefined. It doesn't equal anything. Because it is undefined, then we have the ability to manipulate equations however we want to make it equal what we want. It is unscientific to do so. It seems like people who don't know much mathematical theory fixate on division by zero and infinity, and i can't figure out why they do - there are more interesting things to study.

[Aale de Winkel]

well 0/0 does equal to all numbers, just like x^2=49, makes 7 and -7 equal in that respect, although they are just the possible values for the equation...

This is a wrong conclusion y=x[sup]2[/sup] is a many-to-one function,see
http://mathworld.wolfram.com/Function.html

concluding that 7 would be -7 is the same as pe the following reasoning:
1. a human being is a primate
2. a chimpasee is a primate
ergo a human being is a chimpansee.

no dear RQ this ain't a Q.E.D., I gather you'll get this once you study functiontheory.

[RQ]

It's undefined because we havent defined it.
Geosphere, are there websites where I can see this sort of thing because that's the only way I could explain the fact that we have 2 dimensions incorporated in our 3D world.

[RQ]

0/0 is a lot more interesting than it seems. By the way, Geosphere, I read a book that said that stated similar things. It was called Playing with Mathematics or something. I think it was playing with infinity