Mayan Calander and the Leap Year Argument

I'm not expecting this to be answered really, just trying to philosphize and get some info, you dig.
The Leap Year argument states that the date Dec 21, 2012 has already passed, and therefore the Mayan calendar ending on that date bears no significance. Somebody said that when I was talking to them maybe 6 months ago, and I never really gave this much thought until I smoked some cannabis earlier today. I suddenly thought the Gregorian calendar is based upon numbers, simple numbers and not geometry, where the Mayan calendar is based on geometry and the travel of celestial entities- a far more accurate time system. I also figured that because the Gregorian calendar shaves time from each day and then makes up for it (at least I think that's how it works, Pope whatever you confusing bastard), the argument doesn't really hold water. What do you think?

The Maya calendar developers did not use the same leap year system we use -- in fact, their system was better than European people used until the 1600s or 1700s, when the Gregorian calendar was adopted.

The Gregorian calendar is actually quite accurate, and not based on just simple numbers either.
We don't "shave time from each day" -- leap days are adjustments for the fact that an average year is not 365 days long, but instead is 365.24 -- so there is about 0.96 days extra every four years. By leaving out leap days every 100 years, we get down to a closer amount (but to get still closer, we include the leap day every 400 years. (1900 was not a leap year, but 2000 was.)

No, the Maya calendar was accurate enough to cycle after all these years on the day of the winter solstice, wasn't it. Our Gregorian calendar does the same thing. (Remember the Mayan people wore open toed shoes or sandals, so their counting was by 20s instead of 10s.)

None of the proposed "end of world" scenarios have any scientific basis.