Dimension
A dimension is fundamentally a measurable aspect of physical space, described by the number of coordinates needed to define an object's position. In this framework, a point represents zero dimensions, while a one-dimensional line only has length. As we progress to two dimensions, shapes like squares add width to length, existing on a flat plane. Three-dimensional objects, such as cubes and spheres, incorporate depth, allowing movement in a volume of space. The concept of a fourth dimension is often linked to time, forming the basis of the space-time continuum, a notion popularized by physicist Albert Einstein. Some theorists propose further dimensions beyond the familiar three, suggesting that these could represent additional physical realities or alternate timelines. This idea is exemplified in Edwin Abbott's "Flatland," where two-dimensional beings struggle to comprehend the third dimension, serving as a metaphor for higher dimensions beyond human perception. The exploration of higher dimensions, including theories like superstring theory, posits the existence of at least ten dimensions, with possibilities for diverse realities shaped by different laws of space and time.
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Dimension
A dimension is a property of physical space defined by the number of coordinates needed to specify the measurement of an object. A line, for example, consists solely of length and is considered one-dimensional. A square consists of length and width and is two-dimensional. In the three-dimensional world, dimensions are measured in length, width, and depth. Scientific theories differ on the properties of the fourth dimension; some consider it to be time, while others believe that it exists in a physical space that cannot be experienced from the third dimension. More exotic theories speculate that the universe contains ten or more dimensions.
Overview
In mathematics, a point is considered to be zero-dimensional space, a measure with no length, width, or height. A one-dimensional line extends from its origin point along a measure called the x-axis. A line has length, but no width or depth. A shape such as a square adds the second dimension of width and extends along both an x-axis and a y-axis. A two-dimensional object is able to move about on a flat surface or plane. A three-dimensional object exhibits length and width and adds the dimension of depth or thickness, which is measured on the z-axis. Three-dimensional objects such as cubes or spheres can move freely in physical space.
While the observable world exists in these three dimensions, some physicists add a fourth dimension, time, to the equation. Objects can have length, width, and depth but must also have duration in time to exist. This concept is referred to as the space-time continuum and was popularized by the theories of physicist Albert Einstein in the early twentieth century.
In geometry, the fourth dimension is thought of as physical space that extends in a direction that cannot be quantified in three-dimensional thinking. An often-used example to explain this concept is found in the 1884 book Flatland by British educator Edwin Abbott. The book imagines a world consisting of two-dimensional beings that exist as simple shapes and live on a perfectly flat plane. To the inhabitants of Flatland, the other shapes would appear to be only lined segments. The only directions they would know would be "forward" and "back," and they would have no concept of "above" or "below."
If a three-dimensional being were to visit Flatland, the inhabitants would see only the lined cross-section of the visitor that intersected with the flat surface of their world. If the being were to pick up a shape into the third dimension, the Flatlander would be able to see inside his fellow beings and experience his world from a previously unknown perspective. This analogy can be used to speculate what a fourth dimension would look like to inhabitants of a three-dimensional world.
Some scientists have theorized that the universe extends beyond a fourth dimension and includes many more possible dimensions. A concept known as superstring theory—the idea that the universe is made up of subatomic, one-dimensional strings of energy—holds that at least ten dimensions, and possibly many more, may exist. The existence of these dimensions is purely theoretical, but some physicists have speculated that they may contain alternate realities with different relationships between the laws of space and time. According to the theory, some of the higher dimensions contain every possible variation of the past, present, and future.
Bibliography
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