The term dimension arises out of the difference in perception between positions that are described as external or internal to a body, where the relative positions between different points on the body and their relationship to the space external to it, remain invariant. Thus, it can only be applied to solids that have fixed spread in a given direction based on their internal arrangement independent of external factors. This way we can describe the spread of curved surfaces also in relations to points exterior or interior to them without resorting to exotic “mathematics” that does not conform to the principle of logical consistency.
For perception of the spread of the object, the electromagnetic radiation emitted by the object must interact with that of our eyes. Since electric and magnetic fields move perpendicular to each other and both are perpendicular to the direction of motion, we can perceive the spread of any object only in these three directions. Measuring the spread is essentially measuring the space occupied by any two points on it. This measurement can be done only with reference to some external frame of reference. For the above reason, we arbitrarily choose a point that we call origin and use axes that are perpendicular to each other and term these as x-y-z coordinates (length-breadth-height making it 3 dimensions or right-left, forward-backward and up-down making it 6 dimensions).
These are not absolute terms, but are related to the order of placement of the object in the coordinate system of the field in which the object is placed. Thus, they remain invariant under mutual transformation. If we rotate the object so that x-axis changes to y-axis or z-axis, there is no effect on the structure (spread) of the object, i.e. the relative positions between different points on the body and their relationship to the space external to it. Based on the positive and negative directions (spreading out from or contracting towards) the origin, these describe six unique positions (x,0,0), (-x,0,0), (0,y,0), (0,-y,0), (0,0,z), (0,0,-z), that remain invariant under mutual transformation. Besides these, there are four more unique positions, namely (x, y), (-x, y), (-x, -y) and (x, -y) where x = y for any value of x and y, which also remain invariant under mutual transformation. These are the ten dimensions and not the so-called mathematical structures. These are described in detail in our book. Since time does not fit in this description, it is not a dimension.
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