Demensions

[Corellon]

I have ofton stopped and pondered, is there anything that is strictly one demensional? After a while I came up with the conclusion.....Time. Time is the only thing that has only one demension, length. But that also raises the problem that time has not been proven but is only a measurement.

[someguy]

time IS a dimension and it does not have any length. I was once trying to find like you things of lesser dimension like one or two or even only three. but the closest thing i could find was waves. it would seem that waves have two dimensions, three if you count time. if you consider a ripple in water caused by a stone, the ripple has length and width but no real thickness, since the water itself is not really the wave, the wave is passing through the water.

 

maybe you could say that time has only one dimension, the way you would say that width has only one, or length has only one or height has only one. but you couldn't really say that it is length because length is a spacial quantity and those can only be measurements in the first three dimensions, not time. i know we talk about a length of time, a long period of time, but that use of "length" has a different definition than length of rope, and when you speak of time the way you did you are using the word length as you would to describe a length of rope, rather than a period of time.

 

and i think you would not say that any of the spacial dimensions have only one dimension, because i think you are looking for examples that exist in our universe as we can observe, right? so you would not speak of just length because you cannot find anything with just length. if that is true then you would also find that you have that same problem when speaking of time because time cannot exist in the absence of 3 spacial dimensions, in the absence of "material" of 3 dimensions, or at least one spacial dimension. time requires that spacial dimensions exist, and more than that it requires, or enables, things in those dimensions to move. were there nothing moving at all, the universe would be just 3 dimensions. Time is motion. motion has no length.

[Corellon]

You are such an abduridical individual.

[gcol]

You are such an abduridical individual.

 

Nice word, but did you mean abjuridical?

 

My way of trying to understand it is:

 

A point is one-dimensional, a collection of points on a surface is 2-d, a boxful of points is 3-d.

 

Movement is 4-d, so any moving 1-d point imparts the 4th-d to its environment.

[insane_alien]

uh a point is 0-dimensional.

[gcol]

uh a point is 0-dimensional.

 

I first stated that was my way of looking at it. You have yours. I am sure yours (whatever it is) agrees with all standard texts.

 

I also suppose it is easier to criticise my viewpoint rather than answer the original question yourself?

 

If there was no question at all about the nature and number of dimensions, why is it still (hotly) debated?

[insane_alien]

does a point have length? no

does a point have depth? no

does a point have width? no

does a point have time? no

 

well, thats none of the 4 dimensions. thats my veiwpoint.

 

in reference to the origional question, by the same criteria, length also only has one dimension(unless they've started measuring it it m² or m³) same with width and depth.

 

these dimensions have also not been proven as well because they are only measurements by the criteria of the OP.

[Corellon]

I belive that you have a very good point in saying that gcol is wrong and also in saying that the demensions have not been proven. But that raises the question of, why are they still teaching children things that later in life they will find out are wrong?

 

By the way, if I end up giving shit about my spelling then I will let you know, until then you should focus on getting smarter and not correcting others.

[insane_alien]

uhh, no, you miss understand me, i was not saying i think dimensions have not been proven. rather i was saying that dimensions do exist unless you use dimension to mean something other than what it is defined to mean in the english language.

[pioneer]

Dimensions are used for the sake of mathematical simplicity. For example, in some crystal systems, it easier to express position with four dimensions (a,b,c,d), since this is how the planes line up. They use four dimension to express 3-D space. One can do it in 3-D or x,y,z, but the math gets too complicated. Using 4-D in distance makes it really easy. If one assumes this extra distance dimension implies the crystal exist in 5-D space, if one include time, it almost sound like a magic crystal. One needs to separate the reality of 3-D space from n-dimensional space, since n-D is just there for mathematical convenience, with little to do with reality.

 

For example, a point moving in a line, along an axis only uses 1-D in distance and one time dimension, so it is 2-D motion (x,t or velocity). If we are concerned about position in a plane, as it moves in a diagonal, it uses 3-D. If we wish to know how it moves in the diagonal of a cube, it is 4-D. If we wish to know how it moves in the 4-D crystal, it is now 5-D. If we wish to look at this in n-D space is is now n-D. Nothing has changed but the convention. It is still only a point moving in a line with only our coordinate system changing to help occur for its position in our variable laden grid. The push should be the minimal numbers of dimensions, anything beyond that minimum is for mathematical convenience. This prevents speculation like the magical 5th dimension that appears in some crystals systems, as the crystal is waved over the head, and made to move in time.

 

This just came to me. Acceleration in a line is (x,t,t). This is 3-D and uses one distance and two time dimensions. Does the acceleration of space-time add another time dimension to the 4-D to make 5-D or is this just another mathematical convention. It is an interesting question with weird implications.

[someguy]

what does abjuridical or abduridical mean?

[joshuam168]

does a point have length? no

does a point have depth? no

does a point have width? no

does a point have time? no

 

well, thats none of the 4 dimensions. thats my veiwpoint.

 

in reference to the origional question, by the same criteria, length also only has one dimension(unless they've started measuring it it m² or m³) same with width and depth.

 

these dimensions have also not been proven as well because they are only measurements by the criteria of the OP.

 

a point does have length and depth. if it did not have such things how would we measure it? it wouldnt exist according to our conception of existence. we can only measure using such dimensions therefore if it has none of those it doesnt exist. so therefore this "point" u speak of is theoretical and not factual.

[Bignose]

a point does have length and depth. if it did not have such things how would we measure it? it wouldnt exist according to our conception of existence. we can only measure using such dimensions therefore if it has none of those it doesnt exist. so therefore this "point" u speak of is theoretical and not factual.

 

No, you are confusing the mathematical concept of a point with an actual point drawn on a piece of paper. Obviously, a real point on a piece of paper will have some height and width. Even the really small ones like the words written on a grain of rice, or on the head of a pin, or electronics microimprinting, the "points" will still have height and width, even is it is only microns.

 

But, the mathematical concept of a point has no height and width. In 1-D, if I say x=5, then x is only exactly 5. If I needed x to have some "width" I'd have to write a statement like [math]x \in (4.99,5.01)[/math] so that x would have a "width" of 0.02. If there is a "height", then you'd have to invoke a second dimension, like y.

 

But, if x=5, then that doesn't include anything else, not 4.9999...1000 more 9's... 99999 nor 5.000....1000 more 0's...0001. There is no width at all. Only 5, and because there is no width or anything else, a point is zero dimensional.

 

Just because it is a physical impossibility to "create" such a point, that doesn't hamper its usefulness as a concept. Depending on the application, such as treating ideal gases, a molecule can very easily be considered a point. In real life, sure, it isn't a "point", the molecule has a width, height, and depth measured in angstroms, but working with the math treating it as a point predicts the behavior of the gas exceptionally well. Another example is gravity. If you have two objects that are spheres, and so long as the two objects don't get too close, you can predict the behavior of the interaction treating both objects as points. For example, using model of the solar system to predict how to launch a probe at Mars, the influence of Uranus and Pluto and other far away objects are important, but you don't need the level of detail of the density differences in the composition of the planets -- treating them as points is more than accurate enough. There are many examples of where something that isn't actually a "point" can be treated as a point in the mathematical sense and it is perfectly reasonably to do so.

[gcol]

Bignose: Nice one.

 

Thanks for pointing out the dimensionality of the real world versus the mathematically abstract.

 

I presume the smallest possible real-world particle known to science would have, within it, all four dimensions in order for it to exist as an entity.

 

I find it amusing to imagine a non-existent point connected to another by a non-existent line moving with non-existent velocity within a non-existent universe. Ah, the grand parlour game of the mathematics of the great nothing.