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About LinkBacksDoes a 2 dimensional object take up space or have a location in a 3 dimensional universe?
May 11th, 2007, 07:36 PM
Does a 2 dimensional object take up space or have a location in a 3 dimensional universe?
Space no, location yes.
But two dimensional objects CANNOT exist in 3-dimensional space. It is a mathematical impossibility. They can only be imagined.
Draw a line on a sheet of paper. Is that difficult to imagine?
Even that line is 3D though. It is a representation of a 2D object but it still has all 3 dimensions. Now whether or not it's possible for 1D or 2D objects to exist in our universe I don't know, but a line on a piece of paper isn't an example.
Perhaps this will interest some of you..... http://www.timesonline.co.uk/tol/new...cle1454663.ece
Originally Posted by The Times
I assumed the object referred to was sense 5:
ob·ject
–noun
1. anything that is visible or tangible and is relatively stable in form.
2. a thing, person, or matter to which thought or action is directed: an object of medical investigation.
3. the end toward which effort or action is directed; goal; purpose: Profit is the object of business.
4. a person or thing with reference to the impression made on the mind or the feeling or emotion elicited in an observer: an object of curiosity and pity.
5. anything that may be apprehended intellectually: objects of thought.
Euclid considered it to be two dimensional, and if Euclid thought so, then that is good enough for me.
May 16th, 2007, 10:49 AM
By definition a 2-dimensional object has only two dimensions, and thus not a 3rd, nor can it exist in any representation using 3-dimensions.
Using word trickery, the answer is yes. You can have a 2-dimensional object floating about in a 3-dimensional universe. I can take any 3-dimensional object in space, and describe one of its sides as a 2-dimensional object. In that sense of relativism, there's a lot of 2-D objects in 3-D space.
The object may only have two dimensions, but that does not prevent it existing in three dimensional space. You seem to be tricking yourself with your own words.
agreed.
I'm probably out of my league here but I can't see how a 2D object in a 3D universe actually takes up space. Without volume can an object take up space in a 3D universe? I can see the 2D side of a 3D object but is that side actually taking up space? I don't see how. It's like 2D objects are merely flat images, like shadows, a boundary or transition between dimensions.
2D objects can't take up space.
Hmm...can shadows be considered "2D objects"? The have no volume. They don't take up space...they do have location. I guess they are 2D objects.
All I know is they better be 2D objects....Just thinking about it is giving me the creeps!
The problem is that you need to define "space".
A 2D object (like a square) takes up 2D-space (area) in a 2D domain. You can imagine this 2D domain embedded in 3D space with a clearly defined position. This is by no means a controversial or unusual concept. For example, in cartesian coordinates, the xy-plane at z=0 defines a 2D-domain embedded in 3D space (xyz), with defined position and orientation. However, since it has zero thickness, any 2D-plane takes up zero 3D-space, just as any N-dimensional object has a zero (N+1)-dimensional "volume".
Another way to describe it: A 2D plane is in fact a 3-dimensional object with zero thickness and zero volume, possessing two properties: position and orientation.
Shadows are cast on 3 dimensional surfaces, but can they be cast on 2d surfaces? How can they be cast on a 2d surface when there is no such thing as a 2d surface in a 3d universe? (is there?)
They are only the absence of an amount of light relative to the surrounding area. They are more of a non-object than an object?
Is a photon considered 3 dimensional and a wave not?
You can have a 2D object in a 3D world. You just can't have a 2D object behave like a 3D object (unless you account for the 4th dimension in the 2D object).
If I stand in the way of a beam of light, my shadow will appear on the ground because I am blocking the light, and the ground's surface becomes darker. If I move a 2D plane into the area of shadow, a shadow will be cast upon it because my body is blocking the light that would shine upon it otherwise.
Well first of all, where exactly are you getting a 2-d plane from? You can't take a 2-d object as a given when the whole discussion is whether or not it can exist in the first place.
And if you don't have that 2-d plane, then the shadow is 3-d as it is reflected off of a 3-d surface - assuming a shadow qualifies as an "object" in the first place which I'm not sure it does.
I agree with benign psychosis's post
The same place he gets his 4d planes from. rofl
The shadow's reflecting off a 3D surface doesn't make it 3D.
Yup...
[quote="benign psychosis"]1st Dimension = Length (x)
2nd Dimension = Width (y)
3rd Dimension = Height (z0
4th Dimension = Time (t)
You can have a 2D object that moves through time, therefore it becomes a 3D object because it can now be described in 3 dimensions. x, y, and t.
Did I go too fast? Or did I somehow not count three dimensions in that?
BTW, before anyone gets high-n-mighty, no one actually stated that this thread defined 3D as a non-temporal 3D figure (ie - a cube of lengths).
A two dimensional object could not even be existent due to the lack of mass. A
line drawn on a sheet of paper has got three dimensions, three sites A, B and C.
One, C normally, will be very little. Less than a mm, but was relevant in physical
aspects.
A two dimensional object for my terms and definitions was not even to imagine,
truly. A physical figure with a*b not yet calculated, maybe. The frame but was
yet three-dimensional.
A shadow has no mass.
A shadow is 2-dimensional, people, get it in your heads... :x
What's a shadow?
The "shadow" you observe is one part of something larger, a three-dimensional region where light is less able to reach. A piece of paper appears 2d, but it isn't. Same with a shadow, because you can stand IN the shadow of something.
A shadow is not an physical object.
True.
A shadow is more of an...absent object...I guess. It's the appearance of a surface where there is an interrupt in the light.
From a conceptual standpoint, though a shadow can be said to be a 2D entity.
I would have said a 2D illusion rather that a 2D entity. Anyway ive got to go to bed it's3 o'clock
But a paper is completely different from a shadow. It has mass; it has volume (though, granted, extremely small); it occupies space, whereas a shadow doesn't.
I don't see how the argument that a shadow is not an object is valid in this discussion.
A shadow does exist in two spatial dimensions; an 'object' must exist in three.
How could one prove that a shadow has no mass/energy over time?
When I would have may back to the wall, and behind me on that wall there would
be my shadow, that visible area on the wall being my shadow was certainly only
the visible shadow, cause the whole region behind me would be the shadow visible
on the wall actually.
The region behind me mirrors in the grayed out spot visible on the wall beginning
at my back.
Thus, the visible shadow was not two dimensional.
The best argument against a shadow being three dimensional is that it has no volume, which is something required of 3D objects. Nor does it have mass, and hence has no density.
Steve Miller,
The fact that the shadow requires a 3D surface to be seen does not make it a 3D object in and of itself--this is non-sequitur.
I didn't say something like this! I did say it's not two dimensional.
Well euclid is talking out of his backside then !!Euclid considered it to be two dimensional, and if Euclid thought so, then that is good enough for me.
The ink in the line is made from atoms, and atoms occupy 3D space !!!
Bloody hell !! I think you may be right with that one !!2D objects can't take up space.
Hmm...can shadows be considered "2D objects"? The have no volume. They don't take up space...they do have location. I guess they are 2D objects.
Actually, a shadow may be cast upon a 3D object, but the shadow itself remains 2D, it is merely "warped" by the 3D object. The shadow still has a perceivable area but absolutely no volume. When we talk of "objects" our brains naturally associate the term with anything that is 3-dimensional. So if you do away with that beleif, then yes a shadow can be called an object that has 2-dimensions. However im pretty sure that shadows are the ONLY 2D "objects" which can exist in this 3D universe. And that is only because a shadow is the absence of something (light) its NOT actually made from anything. If it were - it would have to have 3-dimensions in order for it to exist in this universe.
How about a mirage? Any mirage I've ever seen, especially those highway ones you see on a hot sunny day, appears to be 2d. Can a mirage's area actually be measured?However im pretty sure that shadows are the ONLY 2D "objects" which can exist in this 3D universe.
ID say no, because a mirage is hot air rising, so it has volume too.
Not to be anal, but a mirage is actually a visual distortion caused by thermal currents rising from the hot surface. :wink:
Technically, though, I wonder if a mirage really can be considered a volumetric object? I say that because in order to have a mirage, you must have a viewer, or a viewpoint. No matter where you look, you won't likely see the mirage any other way than the single visual distortion.
Worth exploring....FIELD TRIP!!!
Along those lines...maybe a reflection? Like, your image in a mirror? Not too sure, but...maybe it could be.
The perception of your image in the mirror is, but not the physics associated with the creation of that image.
Hopefully the original poster of this thread is starting to get an idea about the answer. There are both answers for perception and physical 2D surfaces.
I'm kind of thinking that a 2D object can only be viewed in a 3d universe. If I was 2D and living in a 2D universe how would I see a shadow, mirage or a reflection? Maybe all I could do is sense their presence and still I'm not confident about that.
Could there be such a thing as 2 dimensional light?....Ok, I just googled and found this (www.aip.org/pnu/2006/split/770-1.html), something called plasmons. Not quite understanding it however.
-->back to topic
like Steve Miller already explained on page 2 about the a b c thing, I think it wasn't completed:
x*y*z = volume (ahh, that thing...)
if z equals zero there is no volume.
so, if an object would have the size 5*2*0 the volume would be 0, that would mean it can't exist.
then if the object would have the size 5*2*1 it would have a volume.
So the actual question is:
do you count an 2d object as the first or second alternative.
assuming the universe has more than 3 dimensions (Not counting time),
we as 3 dimensional beeings would have a problem.
lets say I have the size 3*7*3 (x;y;z)
if I would add a dimension (a) it would look like this:
3*7*3*0
what would lead up that I do not have any volume.
so, if our universe is indeed 10 dimensional (or so) a 2d object would be calculated x*y*1 which would mean that it has 1 times z (it may be infinitly small but it exists)
so, a 2 dimensional can have both a position and a pretty small mass (if you find a way to calculate a number 0. period 00000000..... 1)
regards,
miomaz
I disagree. A 2 dimensional object cannot have mass. Something of zero volume (a 2-dimensional object) cannot have mass, or perhaps the concept of 'zero volume' is what confuses you. It would be better to state: 'non-existent' volume.
So the statement
can be revised as 'if z equals zero, or doesn't exist...'
If z equals zero, then it's a non-existent 3D object.
If z is non-existent, then it's a 2D object (composed of the dimensions x and y).
scientstphilosophertheist, we are(all of us) discussing if 2d objects are x,y,1 or x,y,0 , If it is 1 it does exist and with 0 it cannot have volume (does not exist).
then this would proove that higher dimensions are not possible.
Apparently you didn't read the latter part of my post. I'm saying it's neither x,y,1 nor x,y,0, but rather x,y: that's what defines a 2 dimensional object. If you were to add 0 or 1, that would be adding a third dimension (though 0 would make the object non-existent, it would be a non-existent three dimensional object, not a 2 dimensional object).
Here's what I'm saying:
x*y*z = 3 dimensional (volume)
x*y = 2 dimensional (area)
x*y*0 = 3 dimensional = volume = 0 => non-existent 3D object
x*y*1 = xy*1 = 3 dimensional = volume = xy =>3D object of volume xy
x*y = 2 dimensional = area = xy => 2D object of area xy
Where you're getting mixed up is in saying xy = xy*1, meaning that a 2D object can be x*y*1, but that's incorrect. If we added units, it would be:
xcm * ycm * 1cm = xy cm^3
versus
xcm * ycm = xy cm^2
The 1 is the dimension that makes the object 3D. You must view 1 as the "z" dimension here, not a number: whether the object has a "z" or not is what determines whether 3D or 2D; thus, xy1 is a 3D, not a 2D object.
Zero volume in a 3D object means the object doesn't exist, but the same cannot be said for zero volume in a 2D object, because a 2D object doesn't have volume to begin with. "A 2D object of zero volume" is a paradoxical statement (volume, 2D), as is "A 2D object of volume 1", as both zero and one can be classified as the 'z' dimension (see above).
While I don't necessarily believe that higher dimensions exist, your x*y*z*0 example doesn't prove they don't exist. x*y*z*0 would simply be a non-existent 4D object with those dimensions.
P.S. nobody was really discussing xy1 vs xy0, just whether a 2D object can exist in a 3D world or not.
Saying a shadow has no mass is like saying that a hole in the ground (on the moon, so no air in it) has negative mass.
Then we'd be saying that it's possible for an object to have a mass less than zero.
Yet......... a hole has sides, and those sides weigh something. A shadow has edges, and those edges are made of light - or actually of mass that is emitting/reflecting light.
Ill ignor the last post, it humiliates science.
Everything what you said was right, but you still have missed something.
this was the question.Does a 2 dimensional object take up space or have a location in a 3 dimensional universe?
3 spatial dimensions is what I suspect he means.
And you know the formula for 3d? that would be: x*y*z and not x*y, which would be 2d. which would leave us ot the question 1 or 0?
isnt the universe 4D? cuz the 4th dimension is time.
Dear starwars fan,
allot of people think that the 4th dimension is "time" it can be also the first the second or the 32.
I damn the person that didn't seperate the two in the firstplace.
and besides we are talking of spatial dimensions which means that they are spatial (....).
No honest attempt to explain things humiliates science. I believe Kojax made an honest attempt. The fact that it failed is secondary.
Ok guys, I have another one for ya. I was out in the boat fishing the other day and got caught in a quick rain shower. Once the clouds had parted and the Sun emerged I was staring at a double rainbow. My mind went directly to this thread and I began to wonder if a rainbow should be considered a 2D object.
Personally I think it is but I'm not sure if anyone ever tried to measure one dimensionally.
true, in a very wierd way but still it is true.No honest attempt to explain things humiliates science. I believe Kojax made an honest attempt. The fact that it failed is secondary.
(I would see his thoght philosopical)
the rainbow is light being bent or reflected in a certain way so that the wavelengh is increased/decreased, our eye picks it up as colors.
i think, that is.
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