What is a Dimension?

Question

Could you please explain the meaning of the word 'dimension' and if possible to use examples.

Answer 1

The most generalized definition is called a degree of freedom. In many areas of physics, such as configuration spaces, the numbers of dimensions are near infinite. So dimensionality is simply the number of independent degrees of freedom a system has.



Even if you confine it to the the limited concept of spatial dimensions or temporal dimensions, it is still an issue of independent degrees of freedom. Space-time has four dimensions - this is the same as saying it takes 4 numbers to uniquely define a point in space-time or that an object in space-time has 4 degrees of freedom (it can move in 4 different independent ways).



It is total nonsense to say that dimensions have to be orthogonal (at right angles to each other). You can define dimensions to be at any angle with respect to each other as long as they are independent. Einstein's general relativity has non-orthogonal dimensions as a matter of course.

Answer 2

You could think of a dimension as one part of a set of coordinates.



Are you familiar with the terms of height, length, and width (or depth)? These are the 3 dimensions that you are probably already familiar with. These planes are all at right angles to each other and we have freedom of movement along these three planes. Hence we are often referred to as living in the "3rd dimension".



But there is a fourth dimension that is at right angles to the first three: time. Unlike the first three dimensions we do not have freedom of movement within this fourth dimension (time) yet it is a very real part of the world we interact in. We could never arrange to meet someone without knowing both address and time.



Some theoretical physicists theorize the presence of 7 more dimensions that we have no actual awareness of, too compact and at right angles to all the other dimensions for us to see. This notion is mainly to make the math work in M (brane) theory and string theory. No direct evidence has ever been uncovered (yet) that there are any other dimensions beyond height, length, width, and time.

Answer 3

In physics and mathematics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify any point within it. Thus a line has a dimension of one because only one coordinate is needed to specify a point on it (for example, the point at 5 on a number line). A surface such as a plane or the surface of a cylinder or sphere has a dimension of two because two coordinates are needed to specify a point on it (for example, to locate a point on the surface of a sphere you need both its latitude and its longitude). The inside of a cube, a cylinder or a sphere is three-dimensional because three coordinates are needed to locate a point within these spaces.

A temporal dimension is a dimension of time. Time is often referred to as the "fourth dimension" for this reason, but that is not to imply that it is a spatial dimension. A temporal dimension is one way to measure physical change. It is perceived differently from the three spatial dimensions in that there is only one of it, and that we cannot move freely in time but subjectively move in one direction.

In physics, three dimensions of space and one of time is the accepted norm. However, there are theories that attempt to unify the four fundamental forces by introducing more dimensions. Most notably Superstring theory requires 10 spacetime dimensions, and originates from a more fundamental 11-dimensional theory tentatively called M-theory which subsumes five previously distinct superstring theories. To date, no experimental or observational evidence is available to confirm the existence of these extra dimensions. If extra dimensions exist, they must be hidden from us by some physical mechanism. One well-studied possibility is that the extra dimensions may be "curled up" at such tiny scales as to be effectively invisible to current experiments. Limits on the size and other properties of extra dimensions are set by particle experiments, such as at the Large Hadron Collider.

Answer 4

A dimension is a measurable quantity or extent.



An example - a database of people:

Age

IQ

Friendliness

Height

Weight

These are 5 dimensions of a person. This example demonstrates that, although dimensions are generally independent of each other, they can also be dependent to a degree, like Height and Weight. Usually people think of dimensions as spatial dimensions, but in the example above, only height is a spatial dimension, the others are not spatial dimensions.



Another example - a real estate listing of houses:

Square feet living space

Price

Number of bedrooms

Number of bathrooms

Number of floors (storeys)

Age

In this example, the houses are measured in 6 dimensions.



In cosmology and astronomy, dimensions are usually spatial; either 3 spatial dimensions, or 4 spatial dimensions, or in the case of string theory, 11 spatial dimensions. Time is a non-spatial dimension.

Answer 5

A dimension is the minimum number of coordiinates required to plot a point in space.

For example, the world in which we live is three dimensional, that is, to locate a single point in the sky, you need three other of length, breadth and height.

Answer 6

A dimension is a length.

A line has one dimension.

A plane such as a flat surface has two dimensions.

A cube has three dimensions.

We live in a three dimensional space.