Dimension

What is the definition of Dimension? From wikipedia.org:
In mathematics and physics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify each point within it. Thus a line has a dimension of one because only one coordinate is needed to specify a point on it. 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 co-ordinates are needed to locate a point within these spaces.

Minimum number of coordinates needed to specify a point. This is also the number of perpendicular directions one can travel from a point. So how many perpendicular directions can one travel here on earth. We can move up from or down into the earths surface. We can move North or South and East and West. So we got 3. Notice in real life one direction (gravitational,up and down) is straight and the north and south, east and west directions are curved as the earth is a sphere.

Current image is of the Cartesian system flowing down a straight line of time.

from Wikipedia:

Cartesian coordinates in three dimensions

A three dimensional Cartesian coordinate system, with origin O and axis lines X, Y and Z, oriented as shown by the arrows. The tic marks on the axes are one length unit apart. The black dot shows the point with coordinates X = 2, Y = 3, and Z = 4, or (2,3,4).

Choosing a Cartesian coordinate system for a three-dimensional space means choosing an ordered triplet of lines (axes), any two of them being perpendicular; a single unit of length for all three axes; and an orientation for each axis. As in the two-dimensional case, each axis becomes a number line. The coordinates of a point p are obtained by drawing a line through p perpendicular to each coordinate axis, and reading the points where these lines meet the axes as three numbers of these number lines.
Alternatively, the coordinates of a point p can also be taken as the (signed) distances from p to the three planes defined by the three axes. If these are axes x, y, and z, then the x coordinate is the distance from the plane defined by the y and z axes. The distance is to be taken with the + or - sign, depending on which of the two half-spaces separated by that plane contains p. The y and z coordinates can be obtained in the same way from the (x,z) and (x,y) planes, respectively.

More accurate image set would be spherical. We move in and out from a gravitational foci and we orbit this focus. The orbiting of this focus could be considered perpendicular to the in toward and out from the gravitational focus. The linear 3 dimensional Cartesian construct is complete abstraction with no physical counterpart. As earlier stated of the three realistic dimensions one is straight (gravitational, up and down) and the other two (east and west, north and south) are curved. This could be considered the basic 3 physical dimensions.

Now in space, craft with out current public technology, when outside the earth''s gravitation influence, travel in and out from the sun and around the sun. Same as we do on Earth. Still 3-D one straight and 2 curved.

If Einstein's theory of relativity is true then mass causes spacetime itself to curve which would mean that the straight into and out-from dimension would in reality be a curve.

I suppose some highly advanced, very energetic technology could fly in space in all straight lines, but these paths would be against the natural gravitational pattern. I would suspect that even these craft would travel in curves of a different foci.

So all of a sudden it seems dimension is going in circles.

Dimension is Fractal

Fractal means that the same pattern appears no matter what scale one frames their point of view.

So the number of dimensions is the number of coordinates it takes to accurately describe the location of a point in a field. No matter what gravitational focus you select to define the field it takes 3 numbers. Lets say we choose the center of the Milky Way Galaxy as our focus. Our location is a certain distance from the center and theoretical longitude and latitude of the sphere with radius distance. This works but since we are most intimate with Earth to fine tune the exact location we have to make the same measurements of our location on Earth. Basically the sun is the same distance away from the center of the galaxy but the Earth varies its location as it orbits the sun. So the easiest way to be precise would be 3 coordinates to locate the sun and 3 more coordinates to pinpoint our location on the Earth. The larger scale of curved reality (galaxy) has nested within it a proportional but much smaller scaled curved reality (solar system). This doesn't mean there''s 6 dimensions but if you wanted to calculate position accurately over any length of time it would necessary to use nested sets of 3 coordinates.

This is all on the scale of large organized objects from a classical physics perspective.

Quantum Dimension

Lets look at the electron for a moment. The mathematics needed to predict the location of an electron is extremely complex and is probabilistic. You can only give probabilities of where the electron might be. Quantum mechanics says that the observer actually affects where the location will be. So how many coordinates does it take to describe the location of an electron? Somewhere between 0 and infinity. I''m not bullshitting here read about Quantum Mechanics yourself.

Energetic Dimensions

The New Age books talk about a physical dimension, a astral dimension, mental dimension, and so on. These seem to me to be more related to frequencies and wavelengths which describe the human experience as energy. Mental energy would be a higher frequency of consciousness than emotional or physical. The Earth and our bodies vibrates at 3-4 Hz. Our brain has electromagnetic waves in the same range. We see what vibrates at the same speed as us hence we see the "physical" world. If we vibrated at 20000 Hz we might think we were in another universe or "dimension" but we would just be seeing everything that vibrates at 20000 Hz. Our frequency of vibration could be considered a 4th dimension of independent travel. We can travel up and down the frequency range. It is theoretically possible that the imagination is physical reality at a higher frequency than matter. Part of our consciousness may be tuned to such a frequency and therefore we "see" it.

Summing Up

The purpose of this article is not to introduce new New Agey dimensions but to make you think about what dimension is. Think about it. We really don't know "how many" dimensions there are in this ONE universe. There may be 3 or there may be a million? How many independent directions can you travel in?