What Are the Key Characteristics That Define a Dimension?

[Eusonance]

Hey everyone, I'm not a physicist, I'm a high school senior with a who stopped taking math and science after sophomore year (which I sorely regret). So, I have a question rather than a crazy hypothesis regarding the primordial cocktail antecedent to the big bang that's dubious at best.

Call me naive, but I'm curious as to the recognition of length, width, and depth as independent dimensions. Why not just "Space"? Is it that Length, Width, and Depth constitute space? or is it that each dimension is independent of the next? I understand that Depth depends on Width, and Width depends on Length, which is why they are sequential, but is Width independent of Depth, and Length of Width? Further, what defines a Dimension?

It seems to me that Length and Width are entirely intangible and abstract measurments without Depth.

Again, I'm just curious, I'm not here to challenge anything.

 

[RazorRose]

hmmmm good question.
from wiki: Spatial Dimensions: Classical physics theories describe three physical dimensions: from a particular point in space, the basic directions in which we can move are up/down, left/right, and forward/backward.
i think this is what you are referring too.
although I'm not a genius either. i think an example if possible from you would clear up my confusion.
but what i guess all of my above is trying to say is that length is one dimension. up down. width is another left right and depth is forward backward. its like have you ever watched an old fashion cartoon? they only exist in two dimensions. no depth.
might be totally off topic or not what your looking for but i hope it helps.

note: fourth dimension is Time

 

[DaveC426913]

There are 3 spatial dimensions, all orthagonal (bascially, perpendicular) to each other. Their names (length, width, height, forward, etc) are entirely arbitrary in name and entirely subjective in direction.

They simply represent three degrees of freedom. One can move in direction A while not moving in direction B or C. It requires specifiying a coordinate in all three to uniquely locate a point in space.

note: fourth dimension is Time

Only by convention, and definitely not universal convention.

The order of counting dimenions is arbitrary, purely for convenience and has no physical basis. Time is generally referred to as "the 4th dimension" only because it is one of the four that we deal with every day.

It is as meaningful as going to the zoo, pointing at a hippo and calling it the 4th zoo animal.

There may be an unlimited number of spatial dimensions. And there may be more than one time-like dimension. Count em however you like.

 

[RazorRose]

It seems to me that Length and Width are entirely intangible and abstract measurments without Depth.
QUOTE]

it seems to me that neither of us have addressed this comment.
sooooo...
when you think about length you think of a line drawn up and down? say 169 inches long hovering 169 inches off the ground, suspended by say "magnetics" or some such in mid air.

what do you think about when you picture that image? i picture a straight wooden pole. but what i have to remember next is that without width i couldn't probably even see the line. nor actually if I'm thinking correct could it even exist. because even if you draw a line on a piece of paper with a pencil that line has some amount of width. think about it one can't exist without the other. following so far? questions?

reply for dave: hmmmm your bringing up a finer point, for nothing. arbitrary lol. or it least it seems that way to me. and for us (people-humans-homo sapiens) most often time gives relavance to the other three dimensions. sorry if that comes up harsh or pointless.

 

[DaveC426913]

if you draw a line on a piece of paper with a pencil that line has some amount of width. think about it one can't exist without the other. following so far? questions?

A physical object cannot exist without all three spatial dimensions, true, but it is perfectly normal to have length without the existence of the other dimensions.

What is the length (in km) of a journey from Toronto to Huntsville? 130km. A journey does not have a width or depth.

 

[RazorRose]

Dave... it seems to me that you can present examples of how I'm not wording things right. oh and by the way if you read the entire above post of mine you would find i already mentioned that it can't exist. hmmmm so since your good at examples could you answer eusonances questions?

 

[DaveC426913]

...could you answer eusonances questions?

I did, in the top half of post 3. The spatial dimensions are not dependent on each other and are not sequential.

and for us (people-humans-homo sapiens) most often time gives relavance to the other three dimensions. sorry if that comes up harsh or pointless.

Yes, which is why it is often conventionally used that way. But it is misleading to say "the 4th dimension is time".

 

[RazorRose]

To me that doesn't seem to answer all of his questions but then again I'm as curious as a cat xD and maybe be expecting a whole long thing rotfl

 

[HallsofIvy]

The problem, then, is than neither you nor Eusonance has said what you mean by "dimension" or what your understanding of the word is. In order to specify position in space, you must use three numbers. That is true no matter what type of "coordinate system" you use. In its simplest sense, that is what "dimension" is- how many numbers you need to specify something. You could, for example, specify position in space with a single vector but it would still require three numbers- a "three dimensional" vector. Physics, rather than dealing only with position, deals with "events"- things that happen at a specific position at a specific time. That requires three number to give the position and one number to give the time- that is what is mean by "four dimensional".

 

[sophiecentaur]

If you wanted to meet someone in a balloon, you would have to specify three parameters to describe where he could find you. You could use xyz (up/down, side to side, backwards forwards) or you could use distance, azimuth and elevation. If you only used one or two parameters, you couldn't specify the position of your meeting enough to be sure of finding each other. That's why we use three spatial dimensions.
Of course, unless you also specified the TIME, you would also fail to meet up. You may have gone home before he arrived. That's very much another dimension which needs to be considered - although it does need to be treated differently in many ways.

 

[Eusonance]

The problem, then, is than neither you nor Eusonance has said what you mean by "dimension" or what your understanding of the word is. In order to specify position in space, you must use three numbers. That is true no matter what type of "coordinate system" you use. In its simplest sense, that is what "dimension" is- how many numbers you need to specify something. You could, for example, specify position in space with a single vector but it would still require three numbers- a "three dimensional" vector.

I didn't say what a dimension is because, frankly, I don't know. If you go back you can see where I asked : )
This makes a lot of sense, a dimension being the grounds on which a thing is defined. I have some strange Idea in my head about the difference between a dimension and a measurement but I don't think it's valid nor can I articulate it fully.

A physical object cannot exist without all three spatial dimensions, true, but it is perfectly normal to have length without the existence of the other dimensions.
What is the length (in km) of a journey from Toronto to Huntsville? 130km. A journey does not have a width or depth.

I like the use of a "Journey" in this explanation, I've never realized distance as a measurement of one dimensional space, as area is a measure of two dimensional space. Regardless of their intangibility these measurements are extremely practical even in everyday conversation.

because even if you draw a line on a piece of paper with a pencil that line has some amount of width. think about it one can't exist without the other. following so far? questions?

A drawn line on a piece of paper has depth too : )
But, the line as a one dimensional distance between two points exists only as an Idea: It cannot independently as it cannot exist without operating under the preconception that there is someone there to imagine it.

Physics, rather than dealing only with position, deals with "events"- things that happen at a specific position at a specific time. That requires three number to give the position and one number to give the time- that is what is mean by "four dimensional".

There are 3 spatial dimensions, all orthagonal (bascially, perpendicular) to each other. Their names (length, width, height, forward, etc) are entirely arbitrary in name and entirely subjective in direction.

VERY informative, I'm not sure if I can see time as a dimension as our measurement of it is inconsistent with our other measurements of reality, almost purely quantitative (seconds, minutes, hours, days...), and any point-by-point measurement is generalized and inconsistent: Time didn't exist before some ******* with a finger pointed at the sky and shouted "Noooon!" Rather than existence depending on it, like the other dimensions, Time seems to govern and dictate; if time were a dimension, we could move through it, and we may move through it. But, any movement through time is entirely imperceptible as our perception is exists within it rather than on it. it seems to flow at a constant rate and, the way I'm describing it, could rewind and fast forward. But, because our perception and measurement is subjectively existent within it, we are entirely oblivious to the hypothetical fluctuations. Just a thought, an inarticulate one at that.

We have such little control over time in comparison to space. One can pick up an object and move it slightly to the left, but what in terms of time is there to move? A moment? A second? To move a second would be an equivalent to the movement of a journey: one can move a journey from Toronto to Boston, just as he can move a second from Noon to Midnight. One can also traverse a second as he can a journey, but he does not need to go anywhere. -another scattered thought.

Somebody please quote Einstein or some other Nobel prize winner and prove me wrong before I become delusional :)

Eusonance

 

[DaveC426913]

I'm not sure if I can see time as a dimension as our measurement of it is inconsistent with our other measurements of reality,

That is why we distinguish between spatial dimensions and temporal dimensions. They're not quite the same.



Note that, while we cannot freely move through time, it is still required to define a unique place in the universe.

Anyone who has agreed to meet a friend at the coffee shop and then forgotten to tell them what time to be there, becomes aware that 3 spatial coordinates and 1 time coordinate are required to result in co-incidence.

And, like the spatial dimensions, we are free to measure forward or backward along the dimension - as far as we wish or as far as it will go - without having any impact on the measurements in the other dimensions.