Meet your Maker
From the Mishnah on Shabbat 9b onward, the sugeya discusses activities that one may not pursue during Minchah time for fear that he/she may miss it. Based on the juxtaposition of this Mishnah in Masekhet Shabbat, one can read it as applying to the issue of being ready for Shabbat, aside from the issue of praying the afternoon prayer.
The Gemara discusses how and when the prohibitions of the Mishnah would apply, and the discussion leads to a similar one concerning the evening prayer. Towards the bottom of 9b, the sugeya discusses Abaye's statement that according to the opinions that the evening prayer is voluntary, one does not have to be concerned about the evening prayer if he has already removed his girdle (did women wear girdles back then?), since he should not be obligated to put it back on in order to pray. R. Sheshet asks why the person should not just pray without the girdle. The Stam responds with a verse from Amos which means "Israel, prepare to meet your God," which, in the context of the sugeya, means that we must be dressed properly before praying. At the same time, the use of the verse suggests that God's presence is something that we must prepare for, and when we pray we are supposed to envision the presence of God before us.
I think we can read this response by the Stam as also coming to add a dimension to the previous discussion about what one may do in the afternoon as well as our interpretation of the Mishnah. While the simplest explanation of the Mishnah is that it is merely talking about Minchah, the Stam offers another aspect. The application of the verse can be telling us that we should allow time to mentally prepare ourselves for encountering God in the afternoon. Even if we are able to remove ourselves from the meal, bathhouse etc. with enough time to pray, we would still not be able to achieve the sense of mental preparation and anticipation of God's presence that is truly necessary in order to pray. While we are not expected to spend an entire hour contemplating God before praying like the early pietists (Hasidim rishonim; see the beginning of the fifth chapter of Berakhot), we are still ideally supposed to mentally prepare ourselves in some minimal fashion.
The same can be said about Shabbat as well. Since the ideal Shabbat preparation involves contemplating the special sanctity of the Shabbat, such that God is more readily apparent during this Palace in Time (to quote R. Heschel), the Mishnah is also telling us that we cannot get so bogged down in our Friday afternoon activities that we are unable to prepare to greet God's added presence that will arrive Friday evening.
Some time tonight I'll post something about the continuation of the Gemara.