Dimensions

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Trekky0623

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Dimensions
« on: September 10, 2007, 08:54:17 PM »
Overview

Zero Dimension:


A point, occupying zero space.


First Dimension:


A line having only length.


Second Dimension:


A square, having and extra dimension and therefore having length and width.


Third Dimension:


A cube.  This is the dimension we most commonly associate with our surroundings.  It has three dimensions consisting of length, width, and height.  For the sake of understanding, assume your computer screen is two dimensional.  Notice how the cube does not look like a cube as it would if you were holding a block.  This is the shadow of the cube, being transfered to two dimensions.  The angles are not all 90o and all the lines are not the same length.  But it accurately shows a cube more or less.


Fourth Dimension:





Rotating:


This shape is know as a tesseract.  It has four dimensions consisting of the normal dimensions of length, width, and height and also consisting of a fourth dimension which we will call ?.  Once again this is a shadow.  You cannot point in the direction of the fourth dimension because it is something else rather than the normal up, down, left, right, forward, and back.  We can still project it though, but only as a shadow with inaccurate measurements.

Fifth Dimension:

A very complex shape known as a penteract.  It has five dimensions.  This is once again a shadow.



Notice how every time we increase a dimension, we take two of the previous shapes and connect their vertices.

Discuss.
« Last Edit: September 11, 2007, 10:02:23 PM by Trekky0623 »

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Dioptimus Drime

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Re: Dimensions
« Reply #1 on: September 10, 2007, 08:59:28 PM »
Dimensions 4 and 5 seem like more complex versions of 3. Why are they different? What different coordinate do they add, and why should I care?

~D-Draw

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Trekky0623

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Re: Dimensions
« Reply #2 on: September 10, 2007, 09:02:20 PM »
Dimensions 4 & 5 add another direction besides up, down, left, right, forward, back.  It is impossible to imagine the direction.  But we can imagine the shadow it would project on three dimensional space.

" class="bbc_link" target="_blank" rel="noopener noreferrer">MORE INFO

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BOGWarrior89

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Re: Dimensions
« Reply #3 on: September 10, 2007, 09:32:20 PM »
You forgot time.

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Trekky0623

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Re: Dimensions
« Reply #4 on: September 10, 2007, 09:42:18 PM »
That's an Einsteinium Dimension.  We're referring solely to spacial dimensions.

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Roundy the Truthinessist

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Re: Dimensions
« Reply #5 on: September 10, 2007, 10:05:06 PM »
Overview

Zero Dimension:


A point, occupying zero space.


First Dimension:


A line having only length.


Second Dimension:


A square, having and extra dimension and therefore having length and width.


Third Dimension:


A cube.  This is the dimension we most commonly associate with our surroundings.  It has three dimensions consisting of length, width, and height.  For the sake of understanding, assume your computer screen is two dimensional.  Notice how the cube does not look like a cube as it would if you were holding a block.  This is the shadow of the cube, being transfered to two dimensions.  The angles are not all 90o and all the lines are not the same length.  But it accurately shows a cube more or less.


Fourth Dimension:



Rotating:


This shape is know as a tesseract.  It has four dimensions consisting of the normal dimensions of length, width, and height and also consisting of a fourth dimension which we will call ?.  Once again this is a shadow.  You cannot point in the direction of the fourth dimension because it is something else rather than the normal up, down, left, right, forward, and back.  We can still project it though, but only as a shadow with inaccurate measurements.

Fifth Dimension:

A very complex shape known as a penteract.  It has five dimensions.  This is once again a shadow.



Notice how every time we increase a dimension, we take two of the previous shapes and connect their vertices.

Discuss.

I used to draw pictures like this when I was bored in school.  I'd get them up to 10 dimensions.   I figured out how to do it and that what I was drawing was multi-dimensional cubes on my own.  I also used to do it with pyramids.

I could never figure out a good way to do it with spheres since there are no vertices.
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cmdshft

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Re: Dimensions
« Reply #6 on: September 10, 2007, 10:19:57 PM »
Physically speaking, without Einsteinium Dimensions, nor String Theory, there are only 3 dimensions: height, depth, width. Perhaps 4 if you wish to include mass.

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Trekky0623

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Re: Dimensions
« Reply #7 on: September 10, 2007, 10:25:02 PM »
4 if you include the ? direction included in the above shapes.

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divito the truthist

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Re: Dimensions
« Reply #8 on: September 10, 2007, 10:53:21 PM »
I'd type up some portions of Hyperspace, but I'm really tired.

That rotating tesseract is awesome though.
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cmdshft

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Re: Dimensions
« Reply #9 on: September 10, 2007, 11:26:05 PM »
4 if you include the ? direction included in the above shapes.

Direction cannot be a dimension. That's like saying velocity is the same thing as speed, which it is not.

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Midnight

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Re: Dimensions
« Reply #10 on: September 11, 2007, 01:33:00 AM »
I prefer 2d sprites.
My problem with his ideas is that it is a ridiculous thing.

Genius. PURE, undiluted genius.

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Chris Spaghetti

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Re: Dimensions
« Reply #11 on: September 11, 2007, 02:03:35 PM »
I got hypnotised by the tesseract for aagges. It's sooo pretty

Re: Dimensions
« Reply #12 on: September 11, 2007, 07:17:12 PM »
Rotating:


Like wow...  That thing is incredible.

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Trekky0623

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Re: Dimensions
« Reply #13 on: September 11, 2007, 08:37:49 PM »
Dimensions are referring to measurement dimensions:
length, width, height, so on...

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cmdshft

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Re: Dimensions
« Reply #14 on: September 11, 2007, 08:57:57 PM »
Dimensions are referring to measurement dimensions:
length, width, height, so on...

And thus, direction is not a dimension.

Oh, look... This is going this way, and this is going that way... NEW DIMENSIONS!

No.

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nicolin

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Re: Dimensions
« Reply #15 on: September 11, 2007, 09:22:48 PM »
Altough the graphic representation of the 4 dimensional hyper cube is interesting it however does not imply 4 dimensions.
MOVEMENT can NOT mean a 'new' dimension.
Also, the static repesentation of the said dimentional cube shows different lengths for it's constituing 'parts' (it is clear that the 'internal' cube can NOT have the same lengths as the oute cube, the 'diagonals' linkng the inner and outer cube can NOT habe the same length as the outer cube).
I'd like to see how a 4 dimentional hyper sphere looks..
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Trekky0623

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Re: Dimensions
« Reply #16 on: September 11, 2007, 10:01:34 PM »
The object shown is a 3d shadow of the 4d hypercube.

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Raist

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Re: Dimensions
« Reply #17 on: September 13, 2007, 06:08:21 AM »
Altough the graphic representation of the 4 dimensional hyper cube is interesting it however does not imply 4 dimensions.
MOVEMENT can NOT mean a 'new' dimension.
Also, the static repesentation of the said dimentional cube shows different lengths for it's constituing 'parts' (it is clear that the 'internal' cube can NOT have the same lengths as the oute cube, the 'diagonals' linkng the inner and outer cube can NOT habe the same length as the outer cube).
I'd like to see how a 4 dimentional hyper sphere looks..

Lengths in shadows change. Take your arm and move it around and look at the shadow.

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Chris Spaghetti

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Re: Dimensions
« Reply #18 on: September 13, 2007, 06:46:33 AM »
It's impossibl;e to accurately represent anything greater than 2d on a 2d surface.

oh and your hypersphere is on wiki http://en.wikipedia.org/wiki/Image:Hypersphere_coord.gif

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Roundy the Truthinessist

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Re: Dimensions
« Reply #19 on: September 13, 2007, 11:11:45 PM »
That's interesting how they derived those images, but I've always imagined that an actual image of a hypershere would just look like a circle when mapped in 2-d, just like a sphere does.

Since it would be a set of all points x distance away from a given point, x being the radius of the hypersphere, in four dimensions (a circle is the set of all points x distance away from a given point in two dimensions, and a sphere is the set of all points x distance away from a given point in three dimensions), I think an actual hypersphere would have a completely uniformly round outer edge, and so when represented in two dimensions it would look like a circle (just like a sphere does), and in three dimensions it would look like a sphere.
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me25

Re: Dimensions
« Reply #20 on: September 23, 2007, 03:41:55 PM »
I still think the 4th dimension is time, think about it, it's the only other way to measure an object that even comes close to seeming like a cube squared, plus, you can't accurately represent anything but the 3rd dimmension in this 3 dimmensional universe because even a piece of paper has to have some depth, so the dot, line and square are the shadows and the cube isn't even any different from the square.

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divito the truthist

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Re: Dimensions
« Reply #21 on: September 23, 2007, 03:52:33 PM »
I'm subscribe to the notion that time is unreal.
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Raist

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Re: Dimensions
« Reply #22 on: September 23, 2007, 03:58:50 PM »
Then how is it warped along with space? Perhaps they are the same thing or space/time.

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divito the truthist

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Re: Dimensions
« Reply #23 on: September 23, 2007, 04:00:28 PM »
In physics, it can work fine as spacetime.

But - 'In 5th century BC Greece, Antiphon the Sophist, in a fragment preserved from his chief work On Truth held that: "Time is not a reality (hupostasis), but a concept (noêma) or a measure (metron)."'
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BOGWarrior89

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Re: Dimensions
« Reply #24 on: September 23, 2007, 05:54:38 PM »
I still think the 4th dimension is time, think about it, it's the only other way to measure an object that even comes close to seeming like a cube squared, plus, you can't accurately represent anything but the 3rd dimmension in this 3 dimmensional universe because even a piece of paper has to have some depth, so the dot, line and square are the shadows and the cube isn't even any different from the square.

It's more like half of a dimension, for we don't know if we can travel in the other direction.

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Pope Zera

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Re: Dimensions
« Reply #25 on: September 23, 2007, 09:13:16 PM »


I could stare at this for hours.

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Chris Spaghetti

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Re: Dimensions
« Reply #26 on: September 24, 2007, 06:13:30 AM »


I could stare at this for hours.

It's quite hypnotic-notic-notic-notic

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Re: Dimensions
« Reply #27 on: September 27, 2007, 10:12:49 AM »
anyone have this in layman's terms?
http://en.wikipedia.org/wiki/Hypersphere

i can't make much sense of it....

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ﮎingulaЯiτy

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Re: Dimensions
« Reply #28 on: November 20, 2007, 04:42:43 PM »
Holy shit. My brother made this picture.  :o
I didn't expect to find it on this site...




anyone have this in layman's terms?
http://en.wikipedia.org/wiki/Hypersphere

i can't make much sense of it....
It's a sphere that is curved in 4-D space. like a circle is related to a sphere and sphere extends to a hypersphere. We cannot look in the 4-D space anymore than a hypothetical 2-D being could look into 3-D space. We are 4th dimensionally flat so to speak.

Now imagine that a sphere intersects the 2-D plane so 2-D beings could see a cross section. It would conceive a single circle. As it passes through the plane the circle would grow and then shrink.

Extend this to 3-D beings. A hypersphere passing through 3-D space would show us cross sections which would appear like a sphere which grows and then shrinks. If this doesn't help you understand it, perhaps you could specify your current understanding or what I should elaborate on?
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ﮎingulaЯiτy

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Re: Dimensions
« Reply #29 on: November 20, 2007, 04:47:52 PM »
Dimensions 4 & 5 add another direction besides up, down, left, right, forward, back.  It is impossible to imagine the direction.  But we can imagine the shadow it would project on three dimensional space.

The other directions are called "ana" and "kata" I believe.

On an unrelated note, these were other 4-D objects he rendered:  :D
http://en.wikipedia.org/wiki/User:JasonHise
« Last Edit: November 20, 2007, 05:02:56 PM by L0gic »
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