Full Version: Dimensions
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Can anyone explain to me what is a dimension and are they so special?
It depends on the context in which you speak of dimensions in. Generally in physics it is regarded as a property of apparent reality - spacial (length, width, height) and temporal (time). In other fields a dimension can mean any property of something ie. to stick with physics, energy can be regarded as a dimension of something although it doesn't - it's only an example.
We have interpreted the universe as a 4 dimensional spacetime and there are other theories (String Theory & derrivatives thereof) that predict (to no avail) 6, 11 and even up to 26 dimensions (includes one of time I believe). Spacial dimensions are as you would know yourself shape, size and position descriptions of space itself and objects in it. They are believed to be infinite in 2 opposing directions and all 3 perpendicular to each other. Time is what has been termed the 4th dimension and has the properties of being (as far as we can perceive) uni-directional ie. moving towards the future.
Time is the special case dimension in that it cannot be realised without some change in the apparent 3 spacial dimensions however they all become somewhat special when you consider Einstein's Special & General Relativity theories where spacetime becomes a 4D manifold (SR - flat Minkowski Spacetime manifold, GR - curved spacetime manifold). In GR spacetime becomes relative in that measurements of height, width, length & time depend on the location from where it is being measured and the speed at which the observer is moving (inertial frame) with respect to what you are measuring. Nothing is exactly what it seems! Another consequence of this is that an apparently simultaneous event (or size of something) for one observer is not necessarily the same for another observer.
And here you can read a very comprehensive article on dimensions...Dimension description at Wikipedia
Of course this is what modern science has deduced from our reality but it is not necessarily so! We thought all was well with our understanding of space and time with the Newtonian interpretations (& Euclidean space) until Einstein showed us otherwise.
As far as the multi-dimensional theories like String Theory go, it is just about dead! Billions of dollars spent over the last 20 years and no results. Scientists working in that field are now under the hammer and a recent physics book in a way proving its falsehood is selling more (50 fold) than a recent book describing it - ouch.
Cheers
Guardian
We have interpreted the universe as a 4 dimensional spacetime and there are other theories (String Theory & derrivatives thereof) that predict (to no avail) 6, 11 and even up to 26 dimensions (includes one of time I believe). Spacial dimensions are as you would know yourself shape, size and position descriptions of space itself and objects in it. They are believed to be infinite in 2 opposing directions and all 3 perpendicular to each other. Time is what has been termed the 4th dimension and has the properties of being (as far as we can perceive) uni-directional ie. moving towards the future.
Time is the special case dimension in that it cannot be realised without some change in the apparent 3 spacial dimensions however they all become somewhat special when you consider Einstein's Special & General Relativity theories where spacetime becomes a 4D manifold (SR - flat Minkowski Spacetime manifold, GR - curved spacetime manifold). In GR spacetime becomes relative in that measurements of height, width, length & time depend on the location from where it is being measured and the speed at which the observer is moving (inertial frame) with respect to what you are measuring. Nothing is exactly what it seems! Another consequence of this is that an apparently simultaneous event (or size of something) for one observer is not necessarily the same for another observer.
And here you can read a very comprehensive article on dimensions...Dimension description at Wikipedia
Of course this is what modern science has deduced from our reality but it is not necessarily so! We thought all was well with our understanding of space and time with the Newtonian interpretations (& Euclidean space) until Einstein showed us otherwise.
As far as the multi-dimensional theories like String Theory go, it is just about dead! Billions of dollars spent over the last 20 years and no results. Scientists working in that field are now under the hammer and a recent physics book in a way proving its falsehood is selling more (50 fold) than a recent book describing it - ouch.
Cheers
Guardian
Well, you start with a dot. It has no length, width, or height. But put enough dots together, you get a line. That is one-dimensional. If you lived on the line, you could only go forward or backward, and would only know the person existing on the same line immediately in front of you, and the person on the line in back of you. You couldn't get around these people, as a line is one-dimensional. Okay. Now imagine two lines intersecting each other. That is two dimensions, or a plane. If you lived on the plane, you would be very flat, but could move around in the plane itself. Imagine two planes intersecting each other. Now you have three dimensions, length, width, and height. This is our current experience.
The interesting thing is that a line is made up of dots, and when two lines intersect, that intersection defines a dot, although the lines themselves define a plane. And when two planes intersect, the intersection defines a line, although the planes together define three-dimensional space.
Time is considered to be the fourth dimension, defined, I suppose, by travel through the third dimension. As for higher dimensions, I can't help you there. Higher dimensions are supposed to be at right angles to the third dimension, but I can't wrap my brain around that one. Hope this helps some what.
The interesting thing is that a line is made up of dots, and when two lines intersect, that intersection defines a dot, although the lines themselves define a plane. And when two planes intersect, the intersection defines a line, although the planes together define three-dimensional space.
Time is considered to be the fourth dimension, defined, I suppose, by travel through the third dimension. As for higher dimensions, I can't help you there. Higher dimensions are supposed to be at right angles to the third dimension, but I can't wrap my brain around that one. Hope this helps some what.
Crouton, sounds very similar to what I wrote here on a similar topic on dimensions over a year ago. To the original poster and yourself, if you're interested, read post #5 in the linked thread. Of course that view was over a year ago. I've come accross some things that have slightly changed my view but most of it still stands - but as you can tell much of it is speculation. What I wrote above in post #2 of this thread is a purely scientific oriented description of dimension.
Cheers
Guardian
Cheers
Guardian
1 dimension is 1 lifeform
QUOTE(ai_guardian @ Jun 21 2006, 09:38 PM) [snapback]1241167[/snapback]
Crouton, sounds very similar to what I wrote here on a similar topic on dimensions over a year ago. To the original poster and yourself, if you're interested, read post #5 in the linked thread. Of course that view was over a year ago. I've come accross some things that have slightly changed my view but most of it still stands - but as you can tell much of it is speculation. What I wrote above in post #2 of this thread is a purely scientific oriented description of dimension.
Cheers
Guardian
Hey Guardian, I guess great minds think alike!!!!
1st dimension is a line. It actually is a fake line since it has no width or hight.
2nd is basically a drawing to simplist forms. Hight and length like the words on the computer.
3rd is what you live in. A coordinate plane of X-length Y-Hight Z-Width. So you can go up and down left and right and forward and back.
4th doesn't exist at all. Its just a way to how time works. Think about a long table w/ foods on it and your standing outside of the table able to go in and out of each meal(time) at will. For some god.
5-10 are like 1-3 they are matter realms where matter is in existence w/o them. Basically small membranes and particles and energy flow through them. They are extremely small.
Lastly is the 11th dimension proven by the M-Theory yet not even a theory anymore that it caused the big bang. M stands for membrane. The 11th dimension is 1+20 0s wide and is infinitly long. Membranes flow freely through it and when they collide it causes a reaction that causes a big bang.
1st is the base 2nd is the hight and 3rd is the width. The others 5-11 circle around the 3 dimensions. Techcally there is only 10 realms of matter and the last is a fake one made up to explane how time works since a human cannot concieve of it any other way.
If you don't believe me check up on some quatom physics also there was an episode on the science channel in 2004 that explaned parallel universes (the result of dimensions) quite well. parallel universes is the name of the episode might be able to find it on there web site or run a quick google search.
2nd is basically a drawing to simplist forms. Hight and length like the words on the computer.
3rd is what you live in. A coordinate plane of X-length Y-Hight Z-Width. So you can go up and down left and right and forward and back.
4th doesn't exist at all. Its just a way to how time works. Think about a long table w/ foods on it and your standing outside of the table able to go in and out of each meal(time) at will. For some god.
5-10 are like 1-3 they are matter realms where matter is in existence w/o them. Basically small membranes and particles and energy flow through them. They are extremely small.
Lastly is the 11th dimension proven by the M-Theory yet not even a theory anymore that it caused the big bang. M stands for membrane. The 11th dimension is 1+20 0s wide and is infinitly long. Membranes flow freely through it and when they collide it causes a reaction that causes a big bang.
1st is the base 2nd is the hight and 3rd is the width. The others 5-11 circle around the 3 dimensions. Techcally there is only 10 realms of matter and the last is a fake one made up to explane how time works since a human cannot concieve of it any other way.
If you don't believe me check up on some quatom physics also there was an episode on the science channel in 2004 that explaned parallel universes (the result of dimensions) quite well. parallel universes is the name of the episode might be able to find it on there web site or run a quick google search.
QUOTE(Avius @ Jun 22 2006, 02:00 AM) [snapback]1241211[/snapback]
1 dimension is 1 lifeform
Thats not true. Dimensions are not life forms they are the jar that hold the water(matter).
QUOTE(Ahuizotl @ Jun 21 2006, 07:48 PM) [snapback]1240860[/snapback]
Can anyone explain to me what is a dimension and are they so special?
Put simply (perhaps oversimply), a dimension is an axis on a graph. If you have a system of 20 particles it's possible to represent the state of the system (and then chart out its evolution) as a point in a 120 dimensional phase space. What does it mean for a space to be 120 dimensional? Simply that there are 120 mutually orthogonal axes. Obviously in the physical universe it's only possible to draw three perpendicular axes at a time. Being an H. G. Wells fan, I'll defer to his explanation (written 10 years before special relativity was formulated) of how time fits in with the spatial dimensions; it's right in the spirit of what I just said about axes on graphs:
The Time Machine:
QUOTE
Filby became pensive. 'Clearly,' the Time Traveller proceeded, 'any real body must have extension in four directions: it must have Length, Breadth, Thickness, and - Duration. But through a natural infirmity of the flesh, which I will explain to you in a moment, we incline to overlook this fact. There are really four dimensions, three which we call the three planes of Space, and a fourth, Time. There is, however, a tendency to draw an unreal distinction between the former three dimensions and the latter, because it happens that our consciousness moves intermittently in one direction along the latter from the beginning to the end of our lives.'
'That,' said a very young man, making spasmodic efforts to relight his cigar over the lamp; 'that . . . very clear indeed.'
'Now, it is very remarkable that this is so extensively overlooked,' continued the Time Traveller, with a slight accession of cheerfulness. 'Really this is what is meant by the Fourth Dimension, though some people who talk about the Fourth Dimension do not know they mean it. It is only another way of looking at Time. There is no diffirence between time and any of the three dimensions of space except that our consciousness moves along it. But some foolish people have got hold of the wrong side of that idea. You have all heard what they have to say about this Fourth Dimension?'
'I have not,' said the Provincial Mayor.
'It is simply this. That Space, as our mathematicians have it, is spoken of as having three dimensions, which one may call Length, Breadth, and Thickness, and is always definable by reference to three planes, each at right angles to the others. But some philosophical people have been asking why three dimensions particularly - why not another direction at right angles to the other three? - and have even tried to construct a Four-Dimension geometry. Professor Simon Newcomb was expounding this to the New York Mathematical Society only a month or so ago. You know how on a flat surface, which has only two dimensions, we can represent a figure of a three-dimensional solid, and similarly they think that by models of thee dimensions they could represent one of four - if they could master the perspective of the thing. See?'
'I think so,' murmured the Provincial Mayor; and, knitting his brows, he lapsed into an introspective state, his lips moving as one who repeats mystic words. 'Yes, I think I see it now,' he said after some time, brightening in a quite transitory manner.
'Well, I do not mind telling you I have been at work upon this geometry of Four Dimensions for some time. Some of my results are curious. For instance, here is a portrait of a man at eight years old, another at fifteen, another at seventeen, another at twenty-three, and so on. All these are evidently sections, as it were, Three-Dimensional representations of his Four-Dimensioned being, which is a fixed and unalterable thing.'
'Scientific people,' proceeded the Time Traveller, after the pause required for the proper assimilation of this, 'know very well that Time is only a kind of Space. Here is a popular scientific diagram, a weather record. This line I trace with my finger shows the movement of the barometer. Yesterday it was so high, yesterday night it fell, then this morning it rose again, and so gently upward to here. Surely the mercury did not trace this line in any of the dimensions of Space generally recognized? But certainly it traced such a line, and that line, therefore, we must conclude was along the Time-Dimension.'
'That,' said a very young man, making spasmodic efforts to relight his cigar over the lamp; 'that . . . very clear indeed.'
'Now, it is very remarkable that this is so extensively overlooked,' continued the Time Traveller, with a slight accession of cheerfulness. 'Really this is what is meant by the Fourth Dimension, though some people who talk about the Fourth Dimension do not know they mean it. It is only another way of looking at Time. There is no diffirence between time and any of the three dimensions of space except that our consciousness moves along it. But some foolish people have got hold of the wrong side of that idea. You have all heard what they have to say about this Fourth Dimension?'
'I have not,' said the Provincial Mayor.
'It is simply this. That Space, as our mathematicians have it, is spoken of as having three dimensions, which one may call Length, Breadth, and Thickness, and is always definable by reference to three planes, each at right angles to the others. But some philosophical people have been asking why three dimensions particularly - why not another direction at right angles to the other three? - and have even tried to construct a Four-Dimension geometry. Professor Simon Newcomb was expounding this to the New York Mathematical Society only a month or so ago. You know how on a flat surface, which has only two dimensions, we can represent a figure of a three-dimensional solid, and similarly they think that by models of thee dimensions they could represent one of four - if they could master the perspective of the thing. See?'
'I think so,' murmured the Provincial Mayor; and, knitting his brows, he lapsed into an introspective state, his lips moving as one who repeats mystic words. 'Yes, I think I see it now,' he said after some time, brightening in a quite transitory manner.
'Well, I do not mind telling you I have been at work upon this geometry of Four Dimensions for some time. Some of my results are curious. For instance, here is a portrait of a man at eight years old, another at fifteen, another at seventeen, another at twenty-three, and so on. All these are evidently sections, as it were, Three-Dimensional representations of his Four-Dimensioned being, which is a fixed and unalterable thing.'
'Scientific people,' proceeded the Time Traveller, after the pause required for the proper assimilation of this, 'know very well that Time is only a kind of Space. Here is a popular scientific diagram, a weather record. This line I trace with my finger shows the movement of the barometer. Yesterday it was so high, yesterday night it fell, then this morning it rose again, and so gently upward to here. Surely the mercury did not trace this line in any of the dimensions of Space generally recognized? But certainly it traced such a line, and that line, therefore, we must conclude was along the Time-Dimension.'
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