I'm new to vegetable gardening and am just beginning to plant a few seeds into raised beds. On every seed packet, and in almost every other guide or reference I've found, on- and off-line, instructions are given on the correct spacing in two perpendicular dimensions, yet none offers any explanation whatsoever of the reasoning or implementation details of this mysterious practice.
So for example I'm told that for carrots I should aim for final spacing of 4 inches on the x-axis and 12 inches on the y-axis. In keeping with tradition I hope to produce a carrot which is approximately circular about the horizontal plane, so I'm at a loss to see why its space requirements should be any greater in one dimension than the other.
The larger given distance isn't typically wide enough to offer walk-in access, so what on earth could the reasoning be? And how am I supposed to be orienting these axes with respect to their natural environment anyway? Should one or other axis be aligned to the midday sun? The magnetic pole? Ley lines? I wouldn't want to think I'd planted my whole garden at right angles to its proper orientation...