Yitzchak in the Field

At the end of this parasha, Rivka is on her way to meet Yitzchak for the first time, and the Torah describes what Yitzchak is doing at that moment and how she responds. He's going out לָשׂוּחַ בַּשָּׂדֶה‎ (laseuach basadeh) — into the שָׂדֶה‎ (sadeh) — to do something described by a Hebrew word whose meaning isn't fully clear. It's not a completely unfamiliar term, but it's rare enough that we don't immediately know what he's doing. Rivka is clearly struck by it; the Torah shows that in her reaction. But the question for us is: what was Yitzchak doing that was so meaningful, and how can we uncover it?

I'd like to take a stab at this. I have an idea forming — something that may very well be true, even though the pieces aren't all perfect yet. I'll lay out what I do have and show the picture that seems to be emerging.