2d

[Ethanadams]

I have come up with a great theory a GAME THEORY just kidding

so the you know how the second demes ion has no thickness? And the first no width?

My my theory may sound stupid and it probably is, but I think you no matter how hard you try you can't make a true 2d or 1d object in are universe because every thing in are universe has thinkness and width.

draw a square on a piece of paper that would be at least 1 atom thick have a projecter project something at least one photon thick

is my theory correct?

[michaelsteele3]

Dimenception

[RainDreamer]

Well, we are in 3 dimensional space, and that is all we are experiencing.

[michaelsteele3]

Can't imagine a 4D or 5D

[stupid_chris]

A singularity technically has no thickness, no width, and no depth. On paper, it's an amount of mass in a null amount of volume. Do whatever you will of that.

[Thomas988]

Yeah...2D can't possibly exist in our universe. Even lead on paper (excuse me, graphite) has a thickness, although extremely small.

[AngelLestat]

A singularity technically has no thickness, no width, and no depth. On paper, it's an amount of mass in a null amount of volume. Do whatever you will of that.

From our point of view using theories that are not quite accurate in that frame of reference.

[Ethanadams]

What would be the forth demesion (don't say time, time does not tenancy existed see my time post for that)

[RainDreamer]

Beyond our comprehension.

[lajoswinkler]

2D thing can't exist in 3D space. Remember, 2D is surface. It's not a sheet of very thin metal floating around. It's surface. a*b

1D is length, and not a very thin stick or string.

0D is not a tiny ball, but a point. Let's say it's where something is. A position.

Your hypothesis is correct, yes.

[Deutherius]

What would be the forth demesion (don't say time, time does not tenancy existed see my time post for that)

4th spatial dimension is just another dimension perpendicular to all the other ones. Mathematically it's not hard. It's just another coordinate you need to add to the system to be able to locate something. You need 2 coordinates for a 2D system (say, a map). 3 coordinates in a 3D system. And so on. Trying to imagine how it looks like in our 3D oriented minds is the hard thing, but not impossible.

Take the tesseract, a 4D cube. You know how to construct a square from a line, right? Just duplicate the line parallel to the first one (add a dimension), connect all ends with a line of the same length. Similarly you can make a cube - take the square, duplicate and connect all ends.

How do you make a 4D cube? Exactly the same way. Take a cube, duplicate, connect all ends (vertices).

The hard part for us is to imagine that all the lines made are of the same length. You just can't do that in a 3D space.

And of course, you can just keep adding the dimensions. Take the tesseract, duplicate it, connect all vertices so that every line is of the same length and you get a penteract, and so on. Fair warning, if you really try to imagine it: more dimensions = bigger headache.

EDIT:

Edited March 19, 2015 by Deutherius

[stupid_chris]

From our point of view using theories that are not quite accurate in that frame of reference.

Wow, how peculiar is it that everything is a result of our perception from the viewpoint we have, and that we can only limit ourselves to the theories we have.

A singularity, as far as we know, is dimensionless. It has mass, but no volume, and no size whatsoever. Whatever happens to the volume of the matter is not well explained, but as far as we all know that's how it is.

But appart from that physical oddity, yes, that statement is true, but only applies to matter. If you allow yourself to consider things not made out of matter (such as electromagnetic waves), you can see some object can have less than three dimensions. Light and the rest of the electomagnetic spectrum lives in one spatial dimension. It follows the same path in a straight line, and does not exists outside of that path. It's path may be curved by gravity, but that is because light evolves in a 3D environment.

Edited March 19, 2015 by stupid_chris

[lajoswinkler]

My bet is that there is still something we don't know about matter that doesn't allow singularities to form. I've always imagined a black hole to be a very stuffed ball of totally exotic matter surrounded by event horizon, photon sphere, accretion disc, etc.

[RAINCRAFTER]

Love Game Theory, and I also think that 2D is simply not possible. Drawings? Thick. Pages in a book? Thick. 2D means less than 1 atom thick, and there can be no 0 or even a decimal, since if you split an atom an explosion would happen with more intensity than most "Self-Combustion" in KSP because of the pure force, destroying the bits with it. And 0? That means nothing. Not even "half-empty" space with a gas in it, just a vacuum with-wait, I think an empty 0 atom wide vacuum would produce a paradox! Wait again, this ties in with the no 2D theory. It all ties in. There is no 2D. (Matrix reference intended)

[Bill Phil]

4th spatial dimension is just another dimension perpendicular to all the other ones. Mathematically it's not hard. It's just another coordinate you need to add to the system to be able to locate something. You need 2 coordinates for a 2D system (say, a map). 3 coordinates in a 3D system. And so on. Trying to imagine how it looks like in our 3D oriented minds is the hard thing, but not impossible.

Take the tesseract, a 4D cube. You know how to construct a square from a line, right? Just duplicate the line parallel to the first one (add a dimension), connect all ends with a line of the same length. Similarly you can make a cube - take the square, duplicate and connect all ends.

How do you make a 4D cube? Exactly the same way. Take a cube, duplicate, connect all ends (vertices).

http://upload.wikimedia.org/wikipedia/commons/thumb/4/45/Dimension_levels.svg/480px-Dimension_levels.svg.png

The hard part for us is to imagine that all the lines made are of the same length. You just can't do that in a 3D space.

And of course, you can just keep adding the dimensions. Take the tesseract, duplicate it, connect all vertices so that every line is of the same length and you get a penteract, and so on. Fair warning, if you really try to imagine it: more dimensions = bigger headache.

EDIT:

http://upload.wikimedia.org/wikipedia/commons/d/d7/8-cell.gif

How does the fourth example have new coordinates? It's just adding in lines between the points. That's still three dimensional. Unless four dimensions is the line itself...?

- - - Updated - - -

Love Game Theory, and I also think that 2D is simply not possible. Drawings? Thick. Pages in a book? Thick. 2D means less than 1 atom thick, and there can be no 0 or even a decimal, since if you split an atom an explosion would happen with more intensity than most "Self-Combustion" in KSP because of the pure force, destroying the bits with it. And 0? That means nothing. Not even "half-empty" space with a gas in it, just a vacuum with-wait, I think an empty 0 atom wide vacuum would produce a paradox! Wait again, this ties in with the no 2D theory. It all ties in. There is no 2D. (Matrix reference intended)

2D means no thickness. Even 0 thickness is still three dimensional.

[Deutherius]

How does the fourth example have new coordinates? It's just adding in lines between the points. That's still three dimensional. Unless four dimensions is the line itself...?

That's where our 3D-accustomed brains stop understanding. Take a look at the #dim part of the picture. There are dimensions X, Y and Z represented as axes in 3D space, each one of them perpendicular to all the other ones. You can define a position of a point in this space with 3 numbers (coordinates).

But, when we add the fourth dimension, W, it has to be perpendicular to all the other dimensions as well. And that cannot be truly represented in a 3D space (we ran out of 90° angles we can use), much less in a 2D space of that picture. Mathematically, you just add the fourth coordinate, and everything is fine. But visualising it is really hard.

It's the same thing as trying to truly represent a 3D cube on paper, just one dimension higher. You can't really represent a cube on paper, because you are only working in a 2D space. The picture only has width and height, but no depth (each pixel only has X and Y coordinates). Your brain can somewhat visualise how the cube looks like in 3D, but that's only because of percieved perspective and because it knows how a cube really looks like - the picture itself is still only 2D. (EDIT: So not only the fourth example, even the third example is kinda... wrong. In a sense that it is trying to represent something it can't)

Now try to imagine the 3D cube represented in 1D space. You probably can't, and neither can I. Just like the 4D tesseract in a 2D space. (The gif gives an illusion of a 3D space, and there the 4D tesseract actually looks kinda decent - just like the 3D cube on a 2D paper).

Edited March 20, 2015 by Deutherius

[Bill Phil]

Wouldn't 4d just be a change in 3d?

Adding lines connecting all the points doesn't really add a dimension. Everything is 2D in those examples. Dimensions are weird anyways...

Actually, our minds are more accustomed to 2d then 3d. That's why space is so confusing to a lot of people.

[Deutherius]

Wouldn't 4d just be a change in 3d?

Adding lines connecting all the points doesn't really add a dimension. Everything is 2D in those examples. Dimensions are weird anyways...

Actually, our minds are more accustomed to 2d then 3d. That's why space is so confusing to a lot of people.

I don't think I understand the first sentence.

The "add lines connecting all points" statement is incomplete, and I should've stated that clearer in the first post. The important thing (in case of the cube) is that duplicated objects are parallel to each other and the lines connecting them are perpendicular to said objects. This is, by definition, only possible N times in an N-dimensional space (starting from a point, just like in the first picture), after that you literally run out of places to put the higher dimensions (of the objects).

And I have to disagree - the space you percieve is 3-dimensional, and that's what your brain is most familiar with.

[maltesh]

4th spatial dimension is just another dimension perpendicular to all the other ones. Mathematically it's not hard. It's just another coordinate you need to add to the system to be able to locate something. You need 2 coordinates for a 2D system (say, a map). 3 coordinates in a 3D system. And so on. Trying to imagine how it looks like in our 3D oriented minds is the hard thing, but not impossible.

Take the tesseract, a 4D cube. You know how to construct a square from a line, right? Just duplicate the line parallel to the first one (add a dimension), connect all ends with a line of the same length. Similarly you can make a cube - take the square, duplicate and connect all ends.

How do you make a 4D cube? Exactly the same way. Take a cube, duplicate, connect all ends (vertices).

http://upload.wikimedia.org/wikipedia/commons/thumb/4/45/Dimension_levels.svg/480px-Dimension_levels.svg.png

The hard part for us is to imagine that all the lines made are of the same length. You just can't do that in a 3D space.

And of course, you can just keep adding the dimensions. Take the tesseract, duplicate it, connect all vertices so that every line is of the same length and you get a penteract, and so on. Fair warning, if you really try to imagine it: more dimensions = bigger headache.

EDIT:

http://upload.wikimedia.org/wikipedia/commons/d/d7/8-cell.gif

A couple years ago, I spent some time throwing together 3-dimensional wireframe shadows of the four-dimensional polytopes in Sketchup. Got as far as the 24-Cell.

In an actual 24-cell, the 24 octahedrons are of course, regular and all the same size. I can just about get my head around working out how the 120 regular dodecahedrons fit together in the 120-cell. Haven't really had a good go at fathoming the 600-cell, though.

[Deutherius]

A couple years ago, I spent some time throwing together 3-dimensional wireframe shadows of the four-dimensional polytopes in Sketchup. Got as far as the 24-Cell.

https://dl.dropboxusercontent.com/u/4057920/Shadow-of-the-Icositetrachoron.PNG

In an actual 24-cell, the 24 octahedrons are of course, regular and all the same size. I can just about get my head around working out how the 120 regular dodecahedrons fit together in the 120-cell. Haven't really had a good go at fathoming the 600-cell, though.

I haven't really played around with other 4D objects before (kinda always got stuck trying to figure out higher dimensional hypercubes), that looks cool as hell. The 600-cell just makes my head hurt But I really like the 120-cell, the hyperspherical description seems pretty easy to understand and not so hard to imagine (read as "my brain doesn't immediately shutdown while looking at it"). Thank you

[pincushionman]

Just because something can't exist as an object doesn't mean it can't exist. a picture on a piece of paper in reality has thickness, but it's a representation of the 2D shape we imagine it to be. Likewise, a point is represented by a dot, or a sphere…or a crosshairs or an "x" or any number of things, but really is a zero-dimensional entity at the arbitrary center of that representation, simply because we all agree that's what it is and that's where it is.

[AngelLestat]

Wow, how peculiar is it that everything is a result of our perception from the viewpoint we have, and that we can only limit ourselves to the theories we have.

A singularity, as far as we know, is dimensionless. It has mass, but no volume, and no size whatsoever. Whatever happens to the volume of the matter is not well explained, but as far as we all know that's how it is.

But appart from that physical oddity, yes, that statement is true, but only applies to matter. If you allow yourself to consider things not made out of matter (such as electromagnetic waves), you can see some object can have less than three dimensions. Light and the rest of the electomagnetic spectrum lives in one spatial dimension. It follows the same path in a straight line, and does not exists outside of that path. It's path may be curved by gravity, but that is because light evolves in a 3D environment.

Yeah I know what you mean about photons.

But even if is dimensionless, singularities had ring shape, which is weird from our point.

[stupid_chris]

Yeah I know what you mean about photons.

But even if is dimensionless, singularities had ring shape, which is weird from our point.

Rotating singularities are disc shaped. But it's a disc.... of no lenght, width, or height. With a volume of zero. Physics are fun no? A non rotating singularity would be shaped as a classical perfect sphere of no dimensions either. We don't know much about singularities, but we know that they can exist, and we know getting past the event horizon and very close to it breaks every law of classical physics we know. Quantum mechanics still kind of work, but quantum mechanics are already odd by themselves.

[cicatrix]

A singularity technically has no thickness, no width, and no depth. On paper, it's an amount of mass in a null amount of volume. Do whatever you will of that.

A singularity is not yet proven to be a real object. Just a mathematical concept that comes out of certain equations. These equations are commonly acknowledged to be the best thing we have so far in explaining the Universe. There might be such a thing as a singularity or it might be that our equations simply go out of scope at some point due to some unknown parameter we missed.

[stupid_chris]

A singularity is not yet proven to be a real object. Just a mathematical concept that comes out of certain equations. These equations are commonly acknowledged to be the best thing we have so far in explaining the Universe. There might be such a thing as a singularity or it might be that our equations simply go out of scope at some point due to some unknown parameter we missed.

Yes, and they're such a concept that proving they exist/don't exist is going to be a hard task since we can't observe them directly due to the formation of event horizons. Really, using the "they exist in theory" argument is running in circles. Most of what we know about outer space is emergent behaviour from the mathematical models we made, but we still don't go by thinking they're inherently wrong. We work with what we have until we're able to prove it wrong. We know more about singularities than we do about dark matter, and it's yet the most widely accepted answer to "why does everything appear much more massive than it is". But until we're able to find a flaw in one of the law of physics, we discover dark matter, or somewhat prove it does not exist, we're gonna roll with it.