What is the true definition of a dimension ?

Question

and how many are there ?

Answer 1

Short answer: there are many mathematical definitions and not one of them is "true". However, only one of them corresponds to the dimension that you see around you in the "real world".

The basic definition of dimension is the dimension of a finite vector space, or an "inner product space" (this is a space where you can measure angles). You would need to study the subject called "Linear Algebra" in order to fully understand what this type of dimension is. In an inner product space, dimensions is basically the number of different directions which are perpendicular to each other. (Try it yourself--a paper has only 2 perpendicular directions--but space has 3.) In a vector space (not an inner product space) dimension depends on the idea of linear dependence--how many vectors can you make before it's possible to write one as a "linear combination" of others (by adding and multiplying). These notions of dimension generalize into notions for infinite dimensional spaces (you may see stuff about Hilbert Space dimension--that's what this is).

The other definitions of dimension are very abstract but I will do my best to communicate them. Most of them require some knowledge of Topology, a branch of mathematics studying very deep properties of spaces, and many require some knowledge of Measure Theory, an area of math which generalizes notions of length and distance. One basic kind of dimension using topology is the "Dimension of a Manifold", which basically means that if you "zoom in" on a surface, the surface will look like basic n-dimensional space. For example, a sphere's surface is 2-dimensional, because when you zoom in it looks like a basic 2-dimensional flat space.

Topological Dimension, or Lebesgue Covering Dimension is a kind of dimension that involves covering a space with open sets. It coincides with the notion of vector space dimension for vector spaces but it can be used to study things that aren't vector spaces too.

A lot of times, dimensions are useful when studying fractals--and sometimes fractals will have dimensions that are fractional. Types of dimension used to study fractals include "Fractal Dimension" and "Hausdorff Dimension", among many others.

"Krull Dimension" is a type of dimension based on Algebra. It's used in Algebraic geometry and is very hard to describe without advanced knowledge of abstract algebra.

These are only a few--there are many more definitions out there. Mathematicians have been discovering new ways to define dimension for quite some time. As they discover new types of dimension, often they find that other types of dimension are related to each other. There are a lot of open questions and unsolved problems about dimension--for example, there are certain cases where people do not even know whether or not different definitions of dimension agree with each other for certain spaces.

I hope this can be helpful. The resources below should be a good place to go for further information. The books are rather advanced but have more complete information than the online sources.

Answer 2

Here is Wikepedia's:
http://en.wikipedia.org/wiki/Dimension

There are three commonly-known physical dimensions, plus time, which is also considered a dimension. To some, that is probably all there are. If you read a good book on string theory called "The elegant universe", you learn that there are 11 or so "curled up" dimensions.

Answer 3

littleblueeyes has the right definition, but the wrong answer. There are three dimensions as is clearly stated in the first definition. Time is not a dimension, it is a manifold. A manifold is like a dimension but it is theoretical. Time is not a measurement in physics, only in relativity. A dimension is not a measurement of anything, it is a measurement of the physical parameters of an object. Anyone who thinks time is the fourth dimension is reading too much 19th century sci-fi.

Answer 4

Four
Definition:
1 a (1) : measure in one direction; specifically : one of three coordinates determining a position in space or four coordinates determining a position in space and time (2) : one of a group of properties whose number is necessary and sufficient to determine uniquely each element of a system of usually mathematical entities (as an aggregate of points in real or abstract space) ; also : a parameter or coordinate variable assigned to such a property (3) : the number of elements in a basis of a vector space

Answer 5

I would say yes. But you believe in a religion. Like a previous poster stated, different dimensions and devas don't have anything to do with Atheism.

Answer 6

Measure in one direction..right?

Answer 7

THE SIZE (MEASUREMENT) OF ANYTHING. THERE ARE 4 DIMENSION