I care about the Constitution for a couple of reasons beyond the narrowly patriotic:

(1) For the framers, its design posed a problem very similar to the design of Friendly AI. The newly independent British colonies were in a unique situation. On the one hand, whatever sort of nation they designed was likely to become quite powerful; it had good access to very large quantities of people, natural resources, and ideas, and the general culture of empiricism and liberty meant that the nation behaved as if it were much more intelligent than most of its competitors. On the other hand, the design they chose for the government that would steer that nation was likely to be quite permanent; it is one thing to change your system of government as you are breaking away from a distant and unpopular metropole, and another to change your government once that government is locally rooted and supported. The latter takes a lot more blood, and carries a much higher risk of simply descending into medium-term anarchy. Finally, the Founders knew that they could not see every possible obstacle that the young and unusual nation would encounter, and so they would have to create a system that could learn based on input from its environment without further input from its designers. So just as we have to figure out how to design a system that will usefully manage vast resources and intelligence in situations we cannot fully predict and with directions that, once issued, cannot be edited or recalled, so too did the Founding Fathers, and we should try to learn from their failures and successes.

(2) The Constitution has come to embody, however imperfectly, some of the core tenents of Bayesianism. I quote Chief Justice Oliver Wendell Holmes:

Persecution for the expression of opinions seems to me perfectly logical. If you have no doubt of your premises or your power and want a certain result with all your heart you naturally express your wishes in law and sweep away all opposition...But when men have realized that time has upset many fighting faiths, they may come to believe even more than they believe the very foundations of their own conduct that the ultimate good desired is better reached by free trade in ideas...that the best test of truth is the power of the thought to get itself accepted in the competition of the market, and that truth is the only ground upon which their wishes safely can be carried out. That at any rate is the theory of our Constitution.