Dimensions

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I don't really know where this would go so I've put it in uncategorised..

Most scientific people seem to think, when thinking about dimensions, that the fourth dimension is time. I personally disagree.

I think there are dimensions in both time and space. We are in the third spatial dimension, and the first time dimension.

Spatial Dimensions:
0: a point
1: a line (connecting those points)
2: a flat plane (connecting those lines)
3: a solid object with depth (connecting those planes)
4: something we cannot comprehend (yet.. as far as i know..)

Time Dimensions:
0: a single moment
1: a linear time-line, connecting those moments
2: something we cannot comprehend

In Space, we have 3D bodies, in a 3D world.
In Time, we seem to have a 0D existence, in a 1D world (we live in the moment, moving along the time-line).

Any thoughts?

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@Welshie,

The reason time became treated as a dimension on a par with space is because its relationship with spatial dimensions is similar, if not identical, to the relationships between the spatial dimensions. For instance, orthogonality (e.g. the energy of a body depends on m*c^2 in the same way it depends on momentum function p*c), rotations (frame transformations are rotations of both space and time such that the time axis becomes partially space-like and spatial axes become partically time-like), invariance of momentum (all objects move through 4-D spacetime with the same speed c) and of course, latterly, spacetime curvature. Who is to say what the underlying truth is, but your statement is certainly inconsistent with relativity.

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@Welshie,

1 dimension is simply an infinitely thin line - which is impossible, so the logic of the first dimension is flawed without course to include the traditional 1st and 2nd dimensions as one in the same dimension.

In this case the 2nd dimension (depth) is fairly straightforward, incorporating the 'in-the-round' objective nature of objects.

3rd dimensions are multiple (as with the 1st) and incorporate the motion of an object in accordance with a time-frame.

That time is a 'framing' of events should not lead to the confusion of the definitions of 'dimensions' - ie 'picture-frame' compared with 'time-frame' (two totally different concepts of frame and dimension).

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@Doobah47,

We cannot logically comprehend the 4th dimension, so why would we be able to comprehend the 2nd? Or the 1st? No depth, infinitely small line.

Dimensions are a matter of complexity. The fourth dimension is the self realizing fractal of the third dimension which is the self realizing fractal of the second dimension. Why not?

In actuality there'd be no dimension, because dimension is organization of complexity/potential which must happen to be the same in reality. In actuality dimension is undefined.

But in reality you have this long extension equation to bring about self-realizing complexities in an infinite span; such is the syntax of infinity as it is only valid in reality.

Yes, no, maybe....

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@Welshie,

I don't know why you guys are saying we cannot comprehend the 4th spatial dimension - we most definitely can. Here's a good illustration: YouTube - Fourth Spatial Dimension 101

If we were able to see in 4d, we could see all 3d points of an object at once. That means if you looked at your friend, you would not see your friend from a visualization we're accustomed. Instead, you'd be able to see every point around and inside him. Just like if you drew a 2d picture of your friend, you could see all points of him at once from a 3d perspective.

The interesting thing to think about is that we only visualize in 3d, because, of course, we are predisposed to this 3d realm, and this affects every facet of our thought processing. If we saw in 4d, every facet of our objective reasoning could be altered. 1 wouldn't necessarily be reasoned as 1, because we could see all points of that object, inside and out - where would we draw the line? A human wouldn't even appear human, and our understanding of physics, biology, every attempt at objectification would have to be seen in a new light.

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@Zetherin,

Zetherin;47538 wrote:

If we were able to see in 4d, we could see all 3d points of an object at once. That means if you looked at your friend, you would not see your friend from a visualization we're accustomed. Instead, you'd be able to see every point around and inside him. Just like if you drew a 2d picture of your friend, you could see all points of him at once from a 3d perspective.

More acurately, (if the forth dimension is something similar to linear time), you would see all 3d snapshots of your friend during his lifetime? similar to al the 2d slivers of his 3d self at one moment in time.

in other words, if you could see in 4d, you would not only see all points in 3d but also at all times?

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@Welshie,

I cannot see Welshie, how you get a point to equal zero dimention, when it is two dimentional, especialy when viewing through space. For a line that joins these two points is now three. Zero is not a dimention, it is simply nothing at all. If one considers a single dimention, then they are concerned with the abstract. Take an idea in your mind for example. It has neither form nor body, yet it exists. Drawing the idea outside the mind gives it a second dimention, while building it forms the third dimentional aspect.

I wonder whether we should consider the effect the object has on zero as the fourth dimentional plane.

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@urangutan,

urangutan;81048 wrote:

I cannot see Welshie, how you get a point to equal zero dimention, when it is two dimentional, especialy when viewing through space. For a line that joins these two points is now three. Zero is not a dimention, it is simply nothing at all. If one considers a single dimention, then they are concerned with the abstract.

A point can be considered the 0th dimension in this way: We are familiar with 3 dimensions (let's call them lenth, width, depth). when you remove one (let's say depth) you only have 2 dimensions left, lenth and width; a 2d surface. Now remove the width dimension and you only have a 1d line. so, what happens when you remove the length from a line you say? It turns into something without dimension, a point.

A line joining two points is not 3 dimensional.

---------- Post added 08-03-2009 at 10:51 AM ----------

Doobah47;47486 wrote:

1 dimension is simply an infinitely thin line - which is impossible, so the logic of the first dimension is flawed without course to include the traditional 1st and 2nd dimensions as one in the same dimension.

In what way is an infinitely thin line impossible and why is that important when deciding that a line IS 1 demensional?

The fact that we cannot "make" a line with any sort of material is of no consequence...the logic of conceptualizing the first dimension is not flawed. We use it in everyday geometry!

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@Lentini,

Lentini;81108 wrote:

In what way is an infinitely thin line impossible and why is that important when deciding that a line IS 1 demensional?

The fact that we cannot "make" a line with any sort of material is of no consequence...the logic of conceptualizing the first dimension is not flawed. We use it in everyday geometry!

There is no line to make. Why did we first choose spatiality to involve lines, and does this represent what dimensions really are?

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@Holiday20310401,

Holiday20310401;81117 wrote:

Why did we first choose spatiality to involve lines, and does this represent what dimensions really are?

um, because of matrix algebra and the properties of vector subspaces... they give rise to the "hard definition" of the word dimension. yes, spaces involve lines.

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@Welshie,

Anything that exists Lentini and is referenced or pointed out, and especially when refering to a place, whether you consider it a point or not, it occupies that region of whatever. Hence it has two dimentions. It occupies the point of inferance and all else is elsewhere. You cannot place a point nowhere and expect any other to assume it is somehow there. Your point has reference, so therfore it is 2 dimentional.

Understanding that if you wish to draw a line between two randomly obscure points of reference, then you have added a third facet to your points. You cannot claim that a line drawn from Ontario to Lima is not three dimentional. If you place an imaginary line between them then yes the result is still two dimentional. However if you join two points together, that do not exist on the same two dimentional frame, like a piece of parchment, then you have a three dimentional construct.

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@urangutan,

Thanks Uragutan, let me try to clear up a few things.

urangutan;81162 wrote:

Anything that exists Lentini and is referenced or pointed out, and especially when refering to a place, whether you consider it a point or not, it occupies that region of whatever. Hence it has two dimentions. It occupies the point of inferance and all else is elsewhere. You cannot place a point nowhere and expect any other to assume it is somehow there. Your point has reference, so therfore it is 2 dimentional.

A point in space has coordinates to explain it's position in reference to something else (usually the origin). But the point itself is still only one dimensional (because it has no hieght, width, depth, etc).

urangutan;81162 wrote:

Understanding that if you wish to draw a line between two randomly obscure points of reference, then you have added a third facet to your points. You cannot claim that a line drawn from Ontario to Lima is not three dimentional. If you place an imaginary line between them then yes the result is still two dimentional. However if you join two points together, that do not exist on the same two dimentional frame, like a piece of parchment, then you have a three dimentional construct.

Consider this: a line is drawn from one point to another on a 3d graph. example: from point (0,0,0) to (1,1,1) [ontario and lima Very Happy

].

It only takes one vector <1,1,1> and it's scalar multiples to span the space that this line takes up. This is the definition of dimension.

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@Welshie,

Incorrect, this is a definition of drawing. You cannot pick a point in the real world or universe and then say it has no depth or existence at all. Once you leave the field of drawing on paper or on the screen or on whatever and classify an existing point in the real visible universe you have forgone the fundamental aspect of drawing to represent your concept and entered the world of accessable.

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@urangutan,

I'm glad someone brought up coordinates. This is the way I see it for now, but I expect to be corrected as I study further...

1st dimension: linear, coordinate signified by (x) along single axis x

2nd dimension: planar, coordinates signified by (x,y) on plane containing 2 intersecting lines x and y

3rd dimension: spatial, coordinates signified by (x,y,z) on 3-d grid made possible by addition of line z perpendicular to the x,y plane

4th dimension: time, coordinates signified by (x,y,z,t) also known as an event...even a stationary object at location (x,y,z) is given different coordinates as t changes

5th dimension: ?????

The pattern seen here is that when a point on a given dimension is kept fixed at its coordinate(s), the addition of the next dimension allows it to remain fixed while "escaping" the grid of the prior dimension. (I know I explained this terribly...)

For example, take any point on the planar grid (x,y). Fix their values. Add the z-axis. Given the fixed coordinates of (x,y), a z value now allows us to locate a point outside of the x,y plane. The t value allows the same for spatial coordinates (x,y,z) thus differentiating an event from a simple spatial location.

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@urangutan,

urangutan;84499 wrote:

Incorrect, this is a definition of drawing. You cannot pick a point in the real world or universe and then say it has no depth or existence at all. Once you leave the field of drawing on paper or on the screen or on whatever and classify an existing point in the real visible universe you have forgone the fundamental aspect of drawing to represent your concept and entered the world of accessable.

I appologize, I'm not following you.
I don't mean to sound rude but... have you taken geometry before? the first 3-4 dimensions seem very simple.

please elaborate if I'm mistaken, thanks.

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@Welshie,

Sorry, but by the 3/4, you mean 3 or 4, not three quarter.
No I have not taken geometry.

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@Lentini,

Lentini;81040 wrote:

More acurately, (if the forth dimension is something similar to linear time), you would see all 3d snapshots of your friend during his lifetime? similar to al the 2d slivers of his 3d self at one moment in time.

in other words, if you could see in 4d, you would not only see all points in 3d but also at all times?

Walk into your bathroom and hold an empty plastic water bottle in front of a mirror.Now slightly tilt it towards you and focus your vision through the bottle into the mirror while allowing you peripheral to adjust.

All points at all time,crude indeed but not nearly as complicated as explaining how to capture a snapshot of that continuous flow of "unseen"space between the image in the mirror,and the time it takes for your brain to interrupt the signal itself.For all we know,that could very well be the hiding place for our architect's blueprints.5d

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