The fourth dimension is generally understood to refer to a hypothetical fourth spatial dimension, added on to the standard three dimensions. It should not be confused with the view of space-time, which adds a fourth dimension of time to the universe. The space in which this dimension exists is referred to as 4-dimensional Euclidean space.
Beginning in the early part of the 19th century, people began to consider the possibilities of a fourth dimension of space. Mobius, for example, understood that, in this dimension, a three dimensional object could be taken and rotated on to its mirror image. The most common form of this, the four dimensional cube or tesseract, is generally used as a visual representation of it. Later in the century, Riemann set out the foundations for true four-dimensional geometry, which later mathematicians would build on.
In the three dimensional world, people can look at all space as existing on three planes. All things can move along three different axes: altitude, latitude, and longitude. Altitude would cover the up and down movements, latitude the north and south or forward and backward movements, and longitude the east and west or left and right movements. Each pair of directions is at a right angle to the others, and therefore is referred to as mutually orthogonal.
In the fourth dimension, these same three axes continue to exist. Added to them, however, is another axis entirely. While the three common axes are generally referred to as the x, y, and z axes, the fourth falls on the w axis. The directions that objects move along in that dimension are generally called ana and kata. These terms were coined by Charles Hinton, a British mathematician and sci-fi author, who was particularly interested in the idea. He also coined the term "tesseract" to describe the four dimensional cube.
Understanding the fourth dimension in practical terms can be rather difficult. After all, if someone is told to move five steps forward, six steps to the left, and two steps up, she would know how to move, and where she would end up in relation to where she began. If, on the other hand, a person was told to also move nine steps ana, or five steps kata, she would have no concrete way to understand that, or to visualize where it would place her.
There is a good tool to understand how to visualize this dimension, however, and that is by first looking at how the third dimension is drawn. After all, a piece of paper is a two-dimension object, roughly, and so cannot truly convey a three dimensional object, like a cube. Nonetheless, drawing a cube, and representing three-dimensional space in two dimensions, turns out to be surprisingly easy. What one does is to simply draw two sets of two-dimensional cubes, or squares, and then connect them with diagonal lines that link the vertices. To draw a tesseract, or hypercube, one can follow a similar procedure, drawing multiple cubes and connecting their vertices as well.
anon996531 Post 14 |
Not trying to be annoying here, but that's a quinterract (5d cube). If the cubes in the tesseract are extruded once more, that it goes up to 5s. |
anon994197 Post 13 |
Since gravity has been proven to be the warping of three dimensional space and time, then it seems obvious that the fourth dimension is what we, trapped within that warping of space time, perceive as "up" and "Down"! Even this simple concept is enough to make my head hurt, but there must be a way to include this idea in the math. |
anon990597 Post 11 |
I find it interesting, but it sounds a bit fictional in my opinion. |
anon322641 Post 10 |
Everyone likes to talk about Einstein and his theory of relativity, as well as metaphysics. |
anon301471 Post 9 |
As long as I can remember, learned people have talked about the fourth dimension. Now I'm over 60 years old, so to me, there must be something to it. |
anon169538 Post 6 |
parmnparsley: you are exactly right. Based on unified string theory, a fourth spatial dimension exists in a hypothetical parallel universe, not our own. -jlo |
Joellburvill Post 4 |
The third dimension is that type of thinking that believes that matter is something other than thought. Thought has no dimension, no length, height, no depth -- only mental visions of them. So then, matter is a mental illusion that objects have length, height and depth; of time and space. The fourth dimension is that dimension of thought that perceives all “things” as qualities -- and we know that qualities exist only in the mind. It’s the difference between physics and the fourth dimension of metaphysics. In a book by Lincoln Barnett called, “The Universe and Dr. Einstein,” he wrote, “Since every object is simply the sum of its qualities, and qualities exist only in the mind, then the whole objective universe of atoms and stars, matter and energy, does not exist, except as a construction of consciousness, the edifice of conventional theories, shaped by the senses of men.” That’s the fourth dimension described to a “T.” |
GlassAxe Post 2 |
You could almost think of anti-matter and the theoretical anti universe as a fourth dimension universe. The CERN Particle Accelerator has proven the existence of anti-matter, making even more plausible the prospects of a mirror universe made completely of anti-matter. Because these universes are mirrored, they would spontaneously collapse/erupt if they came into contact with each other. I am only giving a very amateur insight into the theoretical physics surrounding anti-matter and an anti universe, so if you are interested in this you should seek an expert’s point of view. Nonetheless, I find this to be a very interesting explanation of a fourth dimension. |
parmnparsley Post 1 |
Einstein’s theory of relativity relies on the dimension of time as the 4th dimension. This may not be what the article refers to, but when the fourth dimension comes up in talks about gravity or physics, the dimension of time may be what is being referred to in the conversation. |