Robbert –
With today’s daf we are squarely (no pun intended) back in hard-core eruvin territory – although we are, strictly speaking, not dealing with eruvin, but with the cities of the levi’im. I don’t know how the gemara gets here, but that happens more often – Talmudic discourse is, not to put too fine a point on it, often somewhat less than linear. I guess that since we are talking about the surface area of a techum we can talk about any surface area. The surface area that is discussed is the migrash – a strip that surrounds a city. The gemara is trying to figure out through somewhat iffy math how a migrash of one thousand ama (which seems to be the standard size) constitutes one quarter of the area of such a city. The discussion goes on for more than a daf. I am not at all sure that I understand why the gemara goes at such extreme lengths to figure this out and to be completely honest I am afraid that I don’t think that I can reproduce any of it.
What struck me, though, was the question how to deal with the fact that the gemara seems to say things on this daf that are just plainly wrong. You don’t, for instance, need to have a deep understanding of mathematics to know that that pi does not equal three, as the gemara quite clearly suggests by saying that a square is one fourth bigger that a circle with the same radius. I mean: the gemara is the institutional repository of the Jewish tradition. Discovering that that wisdom contains parts that are just plainly wrong is somewhat disconcerting. It raises the question how this affects the other (non-scientific) parts of the gemara: how are we to trust the wisdom of the rabbis regarding those parts?
I guess that there are really two, very different, ways to deal with this. I will ignore the simplistic/dogmatic approach that in the event of a conflict between the rabbis and science, it is of course the rabbis that must be right – every first grader can tell you that pi is not three, and I would invite anybody who does not believe that to find out for himself with a compass and a piece of paper.
The first way to deal with this is to realize that the gemara is very much a product of its time, so that, as far as scientific knowledge goes, the rabbis had no other choice but to rely on what was known in their era. But this is only true for scientific knowledge – knowledge of the physical world. As far as halacha goes, their insights are eternal. Although we may be better at surveying land and calculating its surface, modern man has no deeper understanding than chazal had of the ancient concept of a techum. So when it comes to the calculation of a techum, we may use modern techniques, but we do that by reference to the age-old principles that our tradition commands.
The second way to deal with this is to assume that scientific reality is irrelevant for halacha. It may well be true that the rabbis wrongly assume that pi equals three and if this were an exercise in math, they would surely fail. But this is no exercise in math – it is a theologically driven, normative, discourse. Halacha is its own domain, with its own rules and precepts, so that we have to take the statements of the rabbis within that domain at face value. The rabbis are not opining about the value of pi – they are dealing with techumin and with what it means to stay in one place on shabbat. Comparing their statements to science is only a distraction.
I am not at all sure which of these approaches I like more (or if I even like either of them). What I do know is that I don’t think I am much bothered by scientific mistakes – it seems to me quite clear that modern science and halacha are talking about very different things. Does it bother you?
Hope you are doing well in these idiotic times. I love to keep on hearing your thoughts on the daf and keep our conversation going. I take a lot of comfort from the fact that whatever idiocy is thrown our way, the daf remains (or should I say: abides). Politics and pandemics may come and go, but in 7.5 years we will find ourselves exactly here – at Eruvin 57.
Joel
