Sukka 17 a, b

Today's daf keeps me humble.  Very humble.  I am reminded that I know just about nothing.

Amud (a) begins with a Mishna.  We learn:

1) if the roofing is more than three handbreadths from the walls, the sukka is unfit

2) if there is a breach (a hole) in a home's roof and one wants to create a sukka, there must be less than four cubits of remaining roof for the sukka to be fit.  

3) a courtyard surrounded by a portico on three sides (covering an internal courtyard) where the walls are extended to the roof and a courtyard covered with unfit roofing cannot become fit sukkot

The remainder of today's daf is the Gemara on this Mishna.  Our Sages want to understand exactly what is meant by this Mishna.  Why some details and not others? Why certain repetitions?  Why do rules apply in some circumstances and not in others?

A number of concepts are used repeatedly to better understand the Mishna. One is lavud, or joining.  If we can use the principle of lavud to join breaches, then the sukka can become fit.  In order to understand which items can be used, however, the Gemara engages in a new exploration.  A sukka cannot be fit if it is constructed with items that can contract ritual impurity.  If the roof were to become impure, the people sleeping or eating beneath it also could contract that ritual impurity.  Thus the rabbis spend a good amount of time detailing which fabrics can contract ritual impurity at which sizes.  Which fabrics should be used in the construction of a sukka?  

The principle of the curved wall continues to elude me.  I understand that in some circumstances it is understood that the wall is mentally stretched to cover the edge of the roof.  It is unclear to me how that might affect whether or not the roofing itself is unfit.

Our rabbis examine the relationship between the size of the sukka and its roofing/walls.  If there is space on the roof, a new problem is created.  What size sukka has what size roof?  And can the walls be made of animal hides, each hide able to contract ritual impurity under different circumstances and at different sizes?  The fear of ritual impurity is significant here, and I can't help but wonder if it might be related to a reaffirmation of power structures.  

We end the daf with questions asked earlier.  Why must four-cubit boards join together to be unfit?  Shouldn't they be unfit anyway, simply due to their size?

First of all, I have difficulty with the principles outlined today.  I know that I am missing the nuances that can be all-important when we attempt to understand the words of our Rabbis.  The background understanding of ritual im/purity is critical, and I am continuing to piece together my picture of how this might have worked.

I don't want to end my learning of daf yomi, but sometimes I want to throw it all up in the air and find a private tutor regarding some of the most basic Talmudic concepts.