1.3.1 Multidimensional objects

The problem with spacetime is that it is a four dimensional object, hence, there is great difficulty in understanding how it can be imagined using the only three dimensions available in space. Today, however, these concepts are often used in other fields like Computer science. Computer programmers use the idea of multidimensional memory cell (arrays). One array, is simply a memory cell in which they can store data. A one dimensional array, is a row of these cells which makes up a line. A two dimensional array is many rows aligned next to one another to make up a plane. A three dimensional array, is many plane aligned next to one another to make up a square solid. The pattern here is that, the last object that has been created is multiplied by the number of the next dimension, hence, if the array was 3 cell long, then the three dimensional array is 3x3x3=27 cells. Consequently, the four dimensional array is 27x3=81 cells, which is the solid formed by the three dimensional object lined up again along a row this time 3 solids long. A five dimensional array is then many of these rows aligned next to one another to form a plane of solids, and so on.
There is absolutely no difference, if instead of arrays, instants (non necessarily in time)  are considered. A one dimensional object, is simply a line (x-axis)  formed by a succession of frames (points)  at which the object has been considered (Figure 1.4a) . A two dimensional object, is the same line framed at different instants along another perpendicular line (y-axis)  to form a plane (Figure 1.4b). A three dimensional object, is that plane framed along another line (z-axis) , still perpendicular, to form a square solid (Figure 1.4c) . Therefore, a four dimensional object, is that solid framed at different instants, again placed along the first line (x-axis)  to form yet another line (Figure 1.4d), and from here the pattern repeats itself up to infinite dimensions. What all this means, is that to represent spacetime as four dimensional object, it is simply possible to imagine it as a three dimensional object, and if the fourth dimension (time)  needs to be added, then the whole object can be considered constant as a single line and framed at different instants placing the values obtained into yet another line to form a graph containing the fourth dimension alone. It is the same technique used in partial differentiation.


 

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(b)

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Figure 1.4 - Multidimentional reppresentation of an object, (a)  one, (b)  two, (c)  three, (d)  four, (e)  five dimentions.

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