So, now that we set the pebbles, we need to do the calculation. The first number does not have any negative digits, so no pebbles in its left column. So the pebble for 10 and the one for 1 are put on the left side. Note that XLIV has two negative digits (44 = XLIV = -10 + 50 -1 + 5). You first draw the lines and put the pebbles in the corresponding squares. Why two? Because Roman numerals sometimes use negative digits. The rows represented the digit magnitude (I, V, X, etc). You drew some lines in the sand, some rows and columns. How did it go? You represented the digits of a number by a pebble. Since the word for pebble in Latin is calculus, we now call calculus calculus. People developed a very ingenious scheme to do additions and multiplications using pebbles. You often hear that it was next to impossible to calculate with Roman numerals. While the past may have pushed us, the future attracts us.
So we are more of a continuation of both the past and the future than simply a remnant of the past. So if you have only the frame/margins of an M.C Escher tesselation, the entire inside foreground (the bulk) can be recovered by gradually painting in what's missing. In fractals or the physical theories surrounding them (AdS/CFT correspondence), the boundary determines the bulk. In analysis, we use the existing conditions in a process called 'analytic continuation' to recover the whole process. In differential equations, we use the boundary conditions to solve for the dynamical behavior in the time interval between them. For any specific end to come about, our experiences must be constrained. This means that we are not simply connected to the past by cause and effect - we're also coupled to the future. The end conditions of the universe are just as symmetrical as the beginning conditions of the universe, under various cosmological models including the popular and oft subscribed to 'Heat Death.'
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