With the spherical perspective: even if you're on the right side of one hemisphere, you still have more in common with the Left side of your hemisphere then you do with the right side of the other hemisphere.
That probably explains why that even though I'm a Ron Paul supporter, I still have more in common with Ralph Nader than I do with Rush Limbaugh or Bill O'Reilly.
Concerning the definition of Left and Right: It originated from the time of the French Revolution, and various factions sat in the National Assembly. Those we would consider "conservatives" tended to sit together on the right side of the assembly, while the "liberals" and radicals sat more towards the left side. Hence how the terms were coined.