Rabbi Chaim Wilschansky asked the following question: Rebbi Yoshiya says in the name of Rav that the Machlokes between Rebbi Yehudah and the Chachamim applies only when the walls do not reach the Sechach. Does this mean that they must reach to within three Tefachim of the Sechach, since then Lavud applies? Or, since this is a technical matter of drawing one's eyes to the Sechach, must the walls reach all the way to the Sechach with no space whatsoever?
Moshie Cohen, Yerushalayim
Since we are speaking about a physical phenomenon - that the eye is drawn upward to the ceiling of a room as long as there is no gap between the walls and the ceiling - I would say that the walls need to reach all the way to the Sechach, and that we cannot rely on the concept of Lavud.
It is clear that Lavud does not create a physical reality. One could construct a Kosher Mechitzah out of a few pieces of string using the concept of Lavud (Shulchan Aruch, OC 362:5), but this Mechitzah would be useless for an Ezras Nashim or other instances where a Mechitzah is needed for privacy.
Nonetheless, it could be that Rebbi Yoshiya does not require the Sechach to come right up to the Sechach and that there is some acceptable gap that would not interfere with our ocular phenomenon. If so, then three Tefachim might, in fact, be a reasonable Shiur for that gap. Not because of the Halachic effect of Lavud but because three Tefachim is considered a small gap. We find this, in fact, by Sechach Pasul (Shulchan Aruch OC 632:1). If the Sukah is only 7x7 Tefachim, then having more than three Tefachim of Sechach Pasul invalidates the Sukah. The TAZ explains that less than three Tefachim is insignificant. The Shaar haTzion there says that the Taz is not using the concept of Lavud because Lavud only applies to empty spaces.
I would suggest two possible alternatives to three Tefachim. We find that a Ner Chanuka must be Tefach Samuch lePesach (Shabbos 22a, Shulchan Aruch, OC 671:7). Rashi explains that if it is within one Tefach then it is recognizable that the Baal ha'Bayis placed it there. One possible explanation of this Din is that two objects that are within one Tefach of each other are seen by the eye to be related to each other. Therefore the Baal ha'Bayis is careful to put it that close to his property so everyone will know it is his. Perhaps we could apply that to our Sukah and say that the eye will automatically connect the wall with the Sechach if they are within a Tefach of each other.
An even better possibility is four Tefachim. Four Tefachim is considered to be a Makom Chashuv (Rashi, Sukah 10a). Four Tefachim of Sechach Pasul invalidate a large Sukah (Shulchan Aruch, OC 632:1). The Mishnah Berurah explains that we are speaking about a four Tefachim strip of Sechach Pasul down the middle of the Sukah. Because four Tefachim is a Makom Chashuv, it has the effect of making the Sukah appear to be split in half and therefore invalid because each half is lacking a sufficient number of walls. This would suggest that a four Tefachim gap is that gap which psychologically splits one object from another.