This morning, and not for the first time, I heard an NPR reporter say of a negotiation something like “both sides are still far apart.” Such a statement invites the question whether this situation is more dire than one in which only one of the two parties is far apart. Generally, “distance,” whether physical or metaphorical, is a property of two points; if a is far from b, then b is far from a. It is difficult to see how it could be otherwise. For example, if one were to suggest a violation of symmetry in the relation because one party is willing to compromise more than the other, then this “violation” is really illusory—the two measurements are not really taken the same way, and, in reality, the parties are closer together and equally close together.
In a certain logical sense “both sides are still far apart” could be considered correct, since, as I said, a far from b implies b far from a. It is wrong, however, in the sense that “both” at least suggests that the relation could be asymmetric. The reporter should merely have said that “the sides are still far apart.”