Forgive the utter ignorance of this post.

When taught about dimensions I was told that the three axis; X, Y and Z amounted to three of them. I have always wondered however why this was not counted as six. Here is the logic. If I move in the X axis I am using one of the dimensions and if I go back I am still apparently using the same one. In my proposal the first move would be in say X1 and the move back would be in another dimension X2.

Why?

Well declaring dimensions as working in this way better fits experience. The observable world is supposed to support four dimensions in total; X, Y, Z and time. With this proposed model the observable world would consist of seven dimensions with the spacial dimensions all being doubled up alowing movement and corresponding movement back but with time being a singular dimension allowing movement forward but no movement back.

So...

On the surface this model seems to work better and explain why our experience of time time is so different to the other dimensions. Hence there must be something wrong with this model - so what is its flaw?

Because +4 along the Y axis is always distinguishable from +4 along the Z axis, but +4 along the X axis is never distinguishable from -4 along the -X axis. It's a human label without a real-world difference.

So this convention of how many real-valued coordinates you need to describe a system is the test of it's dimensionality. A numberical technique called "principle value decomposition" can be used to extract from a huge dataset with hundreds of numbers recorded at every point to the N most imporatant directions. If the data is in the shape of an ellipse, the direction of the major axis is the most important direction, for example. Such data reductions can be useful for presenting data, such as the recent false-color image of Mercury which used the R, G, and B of computer images to display the three principle components of the signals from the 11 detectors.

When considering space there are an infinite number of spatial directions. The concept of dimensions is based on independence of action. When force or action is applied, it can only be done in one direction. Only two other spatial directions are independent. Using X, Y, and Z as an example, a force applied in the X direction has no effect in moving an object in either the Y or the Z direction.

In space, motion may only take place in one direction although that motion may take place in any number of infinite directions there can only be three independent directions in reference to any action.

As an extension to this concept of dimensions, time is independent of any and all spatial directions and is therefore recognized as another dimension.