WARNING! If you have a dense brain, are subject to seizures, epilepsy or Cerebral Palsy, you should stop reading right now. Reading beyond this point is guaranteed to twist your brain into knots!
A better question might be...where is the 4th Dimension? In my own personal imaginations along make believe scientific frontiers, I always believed it to be behind me. What the...? How in the fuck can the 4th Dimension be behind me? Al I gotta do is turn around and...shit! It's still behind me! Having trouble understanding? Imagine being born with eyes in the back of your head. Cant nobody sneak up on your ass, but your whole world of perception has now been cracked open like a dropped cantelope. A whole new dimension has just been introduced. You can see shit in all directions at once. Shit that's even better than having Spidey Sense!
Turns out I was wrong. The 4th Dimension isn't hidden behind me...it's hidden behind you!
Yeah I know this shit is melting your mind like a snowball on a 50 degree day in February, but that's the truth of it. According to calculations the 4th Dimension is the hidden side of a 3 Dimensional object. Here's a cool and simple example. You're walking down the street and you see a fine piece of homegrown coming at you. All you can see is her huge 40 double Ds. Just before you come up to her you can see that fat ass projecting back and when she passes to your left you look back to catch that round plump ass! But you never saw the long zipper she had on them tight jeans that went from her waist to her ankle on her right side. That's the 4th Dimension.
When you hold a Rubic's cube in front of your face you can only see the front side of it no matter which way you hold it. The 4th Dimension is the other side of the cube. Say the color of the cube on the front is Red and you trying to find out the color on the back. You flip it upside down and see the yellow back side. The assumption is that the back side is now the red side. But suppose you were standing close to a wall and a tiny tube came out and painted the back side. You flip it back and what the fuck? It's now white!
Yeah I know that's bullshit but this is MY mothafuken thread. I'm magic. By now I done made 2 thirds of the peeps who clicked on this link disappear!
Here's where your mind is gonna start bleedin. One more time I'll advise all you mopes with weak minds to move the fuck on cause all you gonna do is wind up reading this shit now and having kids born looking like the Elephant Man.
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There are three conventional spatial dimensions: length (or depth), width, and height, often expressed as 'x', 'y' and 'z'. 'x' and 'y' axes appear on a plane Cartesian graph. In the 3rd dimension, a 'z' is used and is found in functions such as a "z-buffer" in computer graphics, for processing "depth" in imagery. The fourth dimension is often identified with time in physics, and as such is used to explain the non-Euclidean space-time used in Einstein's theories of special relativity and general relativity.
When a reference is used to four-dimensional coordinates, it is likely that what is referred to is the three spatial dimensions plus a time-line. If 4 (or more) spatial dimensions are referred to, this should be stated at the outset, to avoid confusion with the more common notion that time is the Einsteinian fourth dimension.
If time is considered as the "fourth dimension", the additional fourth spatial dimension would be referred to as the fifth dimension. Alternatively, time can be considered as the 0th dimension, and all positive-numbered dimensions spatial.
The implications of another spatial dimension are now discussed. This would be orthogonal to the other three spatial dimensions. The cardinal directions in the three known dimensions may be referred to as up/down (altitude), north/south (latitude), and east/west (longitude). When speaking of the fourth spatial dimension, an additional pair of terms is needed. Attested terms include ana/kata (sometimes called spissitude or spassitude), vinn/vout (used by Rudy Rucker), and upsilon/delta.
Dimensional analogy
A net of a tesseractTo make the leap from three spatial dimensions into four, a device called dimensional analogy is commonly employed. Dimensional analogy is studying how (n – 1) dimensions relate to n dimensions, and then inferring how n dimensions would relate to (n + 1) dimensions.
For example, in the book Flatland, Edwin Abbott Abbott writes about a square that lives in a two-dimensional world, like the surface of a piece of paper. A three-dimensional being has seemingly god-like powers from the perspective of this square: such as being able to remove objects from a safe without breaking it open (by moving them across the third dimension), see everything that from the two-dimensional perspective is enclosed behind walls, and remaining completely invisible by standing a few inches away in the third dimension. By applying dimensional analogy, one can infer that a four-dimensional being would be capable of similar feats from our three-dimensional perspective. Rudy Rucker demonstrates this in his novel Spaceland, in which the protagonist encounters four-dimensional beings who demonstrate such powers.
A useful application of dimensional analogy in visualizing the fourth dimension is in projection. A projection is a way for representing an n-dimensional object in n − 1 dimensions. For instance, computer screens are two-dimensional, and all the photographs of three-dimensional people, places and things are represented in two dimensions by removing information about the third dimension. In this case, depth is removed and replaced with indirect information. The retina of the eye is a two-dimensional array of receptors but it can allow the brain to perceive the nature of three-dimensional objects using indirect information (such as shading, foreshortening, binocular vision etc.). Artists use perspective to give three-dimensional depth to two-dimensional pictures.
Similarly, objects in the fourth dimension can be mathematically projected to the familiar 3 dimensions, where they can then be more conveniently examined. In this case, the 'retina' of the four-dimensional eye is a three-dimensional array of receptors. A hypothetical being with such an eye would perceive the nature of four-dimensional objects using indirect information contained in the images it receives in its retina. Perspective projection from four dimensions produces similar effects as in the three-dimensional case, such as foreshortening. This adds four-dimensional depth (depth, of course, being technically incorrect, but no proper word comes to mind) to these three-dimensional pictures.
Dimensional analogy also helps in understanding such projections. For example, two-dimensional objects are bounded by one-dimensional boundaries: a square is bounded by four edges. Three-dimensional objects are bounded by two-dimensional surfaces: a cube is bounded by 6 squares. By applying dimensional analogy, one may infer that a four-dimensional cube, known as a tesseract, is bounded by three-dimensional volumes. And indeed, this is the case mathematically: the tesseract is bounded by 8 cubes. Knowing this is key to understanding how to interpret a three-dimensional projection of the tesseract. The boundaries of the tesseract project to volumes in the image, not merely two-dimensional surfaces. This helps in understanding features of such projections that may otherwise be very puzzling.
Likewise the concept of shadows can help us better understand the theory of four dimensions. If you were to shine a light on three dimensional object, it would cast a two dimensional shadow. Therefore light on a two-dimensional object would cast a one-dimensional shadow (in a two-dimensional world), and light on a one-dimensional object in a one-dimensional world would cast a zero-dimensional shadow, that is, a point of non-light. This idea can be used in the other direction; light on a four-dimensional object would cast a three-dimensional shadow.
http://en.wikipedia.org/wiki/Fourth_dimension
A better question might be...where is the 4th Dimension? In my own personal imaginations along make believe scientific frontiers, I always believed it to be behind me. What the...? How in the fuck can the 4th Dimension be behind me? Al I gotta do is turn around and...shit! It's still behind me! Having trouble understanding? Imagine being born with eyes in the back of your head. Cant nobody sneak up on your ass, but your whole world of perception has now been cracked open like a dropped cantelope. A whole new dimension has just been introduced. You can see shit in all directions at once. Shit that's even better than having Spidey Sense!
Turns out I was wrong. The 4th Dimension isn't hidden behind me...it's hidden behind you!
Yeah I know this shit is melting your mind like a snowball on a 50 degree day in February, but that's the truth of it. According to calculations the 4th Dimension is the hidden side of a 3 Dimensional object. Here's a cool and simple example. You're walking down the street and you see a fine piece of homegrown coming at you. All you can see is her huge 40 double Ds. Just before you come up to her you can see that fat ass projecting back and when she passes to your left you look back to catch that round plump ass! But you never saw the long zipper she had on them tight jeans that went from her waist to her ankle on her right side. That's the 4th Dimension.
When you hold a Rubic's cube in front of your face you can only see the front side of it no matter which way you hold it. The 4th Dimension is the other side of the cube. Say the color of the cube on the front is Red and you trying to find out the color on the back. You flip it upside down and see the yellow back side. The assumption is that the back side is now the red side. But suppose you were standing close to a wall and a tiny tube came out and painted the back side. You flip it back and what the fuck? It's now white!
Yeah I know that's bullshit but this is MY mothafuken thread. I'm magic. By now I done made 2 thirds of the peeps who clicked on this link disappear!
Here's where your mind is gonna start bleedin. One more time I'll advise all you mopes with weak minds to move the fuck on cause all you gonna do is wind up reading this shit now and having kids born looking like the Elephant Man.
========================================================================
There are three conventional spatial dimensions: length (or depth), width, and height, often expressed as 'x', 'y' and 'z'. 'x' and 'y' axes appear on a plane Cartesian graph. In the 3rd dimension, a 'z' is used and is found in functions such as a "z-buffer" in computer graphics, for processing "depth" in imagery. The fourth dimension is often identified with time in physics, and as such is used to explain the non-Euclidean space-time used in Einstein's theories of special relativity and general relativity.
When a reference is used to four-dimensional coordinates, it is likely that what is referred to is the three spatial dimensions plus a time-line. If 4 (or more) spatial dimensions are referred to, this should be stated at the outset, to avoid confusion with the more common notion that time is the Einsteinian fourth dimension.
If time is considered as the "fourth dimension", the additional fourth spatial dimension would be referred to as the fifth dimension. Alternatively, time can be considered as the 0th dimension, and all positive-numbered dimensions spatial.
The implications of another spatial dimension are now discussed. This would be orthogonal to the other three spatial dimensions. The cardinal directions in the three known dimensions may be referred to as up/down (altitude), north/south (latitude), and east/west (longitude). When speaking of the fourth spatial dimension, an additional pair of terms is needed. Attested terms include ana/kata (sometimes called spissitude or spassitude), vinn/vout (used by Rudy Rucker), and upsilon/delta.
Dimensional analogy
A net of a tesseractTo make the leap from three spatial dimensions into four, a device called dimensional analogy is commonly employed. Dimensional analogy is studying how (n – 1) dimensions relate to n dimensions, and then inferring how n dimensions would relate to (n + 1) dimensions.
For example, in the book Flatland, Edwin Abbott Abbott writes about a square that lives in a two-dimensional world, like the surface of a piece of paper. A three-dimensional being has seemingly god-like powers from the perspective of this square: such as being able to remove objects from a safe without breaking it open (by moving them across the third dimension), see everything that from the two-dimensional perspective is enclosed behind walls, and remaining completely invisible by standing a few inches away in the third dimension. By applying dimensional analogy, one can infer that a four-dimensional being would be capable of similar feats from our three-dimensional perspective. Rudy Rucker demonstrates this in his novel Spaceland, in which the protagonist encounters four-dimensional beings who demonstrate such powers.
A useful application of dimensional analogy in visualizing the fourth dimension is in projection. A projection is a way for representing an n-dimensional object in n − 1 dimensions. For instance, computer screens are two-dimensional, and all the photographs of three-dimensional people, places and things are represented in two dimensions by removing information about the third dimension. In this case, depth is removed and replaced with indirect information. The retina of the eye is a two-dimensional array of receptors but it can allow the brain to perceive the nature of three-dimensional objects using indirect information (such as shading, foreshortening, binocular vision etc.). Artists use perspective to give three-dimensional depth to two-dimensional pictures.
Similarly, objects in the fourth dimension can be mathematically projected to the familiar 3 dimensions, where they can then be more conveniently examined. In this case, the 'retina' of the four-dimensional eye is a three-dimensional array of receptors. A hypothetical being with such an eye would perceive the nature of four-dimensional objects using indirect information contained in the images it receives in its retina. Perspective projection from four dimensions produces similar effects as in the three-dimensional case, such as foreshortening. This adds four-dimensional depth (depth, of course, being technically incorrect, but no proper word comes to mind) to these three-dimensional pictures.
Dimensional analogy also helps in understanding such projections. For example, two-dimensional objects are bounded by one-dimensional boundaries: a square is bounded by four edges. Three-dimensional objects are bounded by two-dimensional surfaces: a cube is bounded by 6 squares. By applying dimensional analogy, one may infer that a four-dimensional cube, known as a tesseract, is bounded by three-dimensional volumes. And indeed, this is the case mathematically: the tesseract is bounded by 8 cubes. Knowing this is key to understanding how to interpret a three-dimensional projection of the tesseract. The boundaries of the tesseract project to volumes in the image, not merely two-dimensional surfaces. This helps in understanding features of such projections that may otherwise be very puzzling.
Likewise the concept of shadows can help us better understand the theory of four dimensions. If you were to shine a light on three dimensional object, it would cast a two dimensional shadow. Therefore light on a two-dimensional object would cast a one-dimensional shadow (in a two-dimensional world), and light on a one-dimensional object in a one-dimensional world would cast a zero-dimensional shadow, that is, a point of non-light. This idea can be used in the other direction; light on a four-dimensional object would cast a three-dimensional shadow.
http://en.wikipedia.org/wiki/Fourth_dimension
