It may be just an accident that Jefferson’s Monticello and Madison’s Montpelier, for all their similarities, such as Doric columns, bricks, and fine views, have a fundamental difference in orientation: Jefferson’s creation faces east, toward the flatter part of Virginia, while Madison’s inherited house looks westward, toward the mountains and, beyond them, the future of the nation. After all, buildings can convey messages their designers may not have intended.