I used the arbitrary exactly because it implies a judgement, on somebody's part, as to how one will divide one's representation of reality by marking it. That's really important!To me "arbitrary" also implies decisions not really based in the subject at hand. The decision to use the equator and the poles as a basis for a global grid has a different level of arbitrariness than the decision to use the pole-to-pole meridian that goes through Greenwich, England. The four cardinal directions aren't arbitrary; they're based on the direction of earth's rotations and appear to be nearly universal. On the other hand, north as up is arbitrary.
I argued in one of my last posts that the decision to use 360° of longitude was somewhere between. It's of course because of the common idea of 360° in a circle, but my assumption was that 360 was the number of choice because it is such a great factorial number (360=2 x 2 x 2 x 3 x 3 x 5; factors are 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180). Well, the consensus seems to be the circle is 360° because the Babylonians had a base-60 number system, and that this in turn is due to the proportions of a circle inscribed into a hexagon. Which seems a little more arbitrary than I had thought.
Which brings up questions of the arbitrariness of any given counting system: we use decimal (base-10) for most of our everyday activities, but binary (base-1) and hexadecimal (base-16) are pretty universal in the world of computes. While base 10 is arbitrary in the sense that it "just happens" that we generally have 10 fingers and 10 toes, so that choice wasn't totally arbitrary to those who began counting on those fingers and toes.
So again, it's a question of perspective. One person's arbitrary is another's fundamental. From our modern, detached, viewpoint, the Greenwich meridian is truly arbitrary; all Longitudes are equal. The meridian was established was established in 1851 at the Royal Observatory and because Britain's Empire was approaching its peak, it quickly became a global commonplace. It was made the international standard in 1884 at an international convention. It surprised me how late this convention was set. But in the sense that the Royal Observatory really was the center of world standards at the time, it certainly isn't totally arbitrary.
There's an interesting history and a list of other meridians on Wikipedia.
This in turn leads to an interesting article on the Washington meridian(s). This in turn leads to a discussion of where those straight lines that form so much of the west actually come from. Most, interestingly, are not based on the modern longitude (being older than the Greenwich standard), but on degrees west of Washington. But which meridian in Washington? The Capitol or the Naval Observatory?
Arbitrary? Well, in a universal sense, yes, but in the sense that American national identity is centered on that most symmetric of capital cities, it's not arbitrary at all, any more than the circular arc boundary of Delaware and Pennsylvania, nominally centered on the steeple of the old state house at New Castle.
But then there are those boundaries based on rivers or mountain crests or other actual markings on the land. These seem less "arbitrary" yet.
And then there's the whole idea of boundaries. I still often bear in mind Matthew Edney's description of the early 17th-century boundary between the France and the Holy Roman Empire, where you would go riding east from Paris, and for a while every estate owed allegiance to the King of France. Then after a while, every now and then you'd have one who was loyal to the Holy Roman Emperor. Then as you approach the Rhine, the mix would be come pretty even, and then eventually as you crossed into what is now Germany, pretty much everyone was a Holy Roman by affiliation. So when you see a historic map of that era that shows a boundary line, this is a modern artifact (AND arbitrary!); national boundaries then were often soft.
I think it would be really cool to do a world political map that also reflected relative loyalty to the central government: Somalia as a very light color, Japan as quite vivid, and the regional variation: Tibet lighter than Shanghai. Maybe just eliminate national boundaries altogether, and do a dot-scatter map of populations and loyalties.
Then again, it'd be hard to keep up to date.