Shabbat 96: Carrying Out of or Into the Public/Private Domain on Shabbat

Perek XI begins with a new Mishna: One who throws an object on Shabbat from the private domain to the public domain or from the public domain to the private domain is liable.  If one throws from the private to the public domain and the object passes through the public domain between the two, Rabbi Akiva deems that person liable for carrying into the public domain, but the rabbis deem him exempt. 

How is this possible?  If there are two gezuztra'ot, balconies, that are private domains opposite each other on the either side of the public domain, on who passes or throws an object from the one on tis side to the one on that side is exempt.  But if the balconies were on the same level on the same side of the thoroughfare, and the public domain separated the two, one who passes from one to the other is liable and the one who throws is exempt.  That method, passing, was the service of the Levites who carried out the beams of the Taberancle.

In the Tabernacle, tow wagons along the same level stood behind one another in the public domain, and the Levites passed beneath the beams from one wagon to the other through the public domain on the same

The Gemara brings us back to the main issue, which is throwing - a subcategory of carrying out.  The primary category is found in Exodus (36:6) where Moshe sat in the camp of the Levites in the public domain.  He said to Israel that they were not to carry out and bring object from the private domain to that of the Levites.  The Gemara argues that he was sitting and not standing during this proclamation.   There is another source disallowing carrying out from a private domain into the camps of the Levites.  It is a logical inference: Carrying out and carrying in are both forbidden, but carrying out is a primary category whereas carrying in is a subcategory.  Doing the acts of two categories requires two sin offerings.  Or is what is written in the Torah a category and what is written otherwise a subcategory? 

Needles were thrown back and forth from those who were weaving.  Are we not supposed to perform our friends' work, as well?  The Gemara notes that carrying four cubits into the public domain could be punished with stoning.