The typical Supreme Court oral argument lasts an hour, with the lawyer for the petitioner (whoever brought the suit) taking the first thirty minutes, and the lawyer for the respondent (the other party) taking the second. Each attorney stands at a podium when it’s his or her turn, and gives a presentation on their case to the nine justices. Or tries to.

That half hour isn’t just their time for making arguments, it’s also the justices’ time for questioning, and they can — and do — interrupt at any moment, for any reason. As an attorney arguing in front of the Supremes, you’re trying your best to get through the material you want to get through while also responding to any idea that pops into any justice’s mind. It’s a bit like batting in the World Series, but with every player on the opposite team hurling balls at your head.

It’s kind of awesome.

I’ve attended SCOTUS oral arguments only once, for a zero-profile case that a friend of a friend was arguing. (I took a road trip one other time and slept out all night trying to get in for Lawrence v. Texas, but a local college’s RA had brought her whole floor and we missed the cut.) The case I saw presented was a boring, technical, marginal one ultimately decided in a 9-0 decision, but seeing it argued in person was thrilling, strange, and — because I knew one of the attorneys — nerve-wracking even to watch.

The Supreme Court is, according to the Constitution, the final interpreter of the Constitution itself. If you don’t like what they decide, you’ve got to pass a constitutional amendment overturning them (something that’s ridiculously hard to do and hasn’t happened in four decades) or just sit tight and wait until they change their minds. And because there are only nine justices, and because they have so much discretion, changing one of their minds can change the course of history.

Supreme Court oral arguments are as close as an ordinary American can ever hope to get to watching the actual internal machinery of the federal government in operation. Whatever you think of that government, whatever you think of the institution of the Court itself, it’s impossible to observe it closely and not come away with a staggering sense of historical contingency.

Fisher v. Texas, the college admissions case SCOTUS heard argued last week, is a big deal. A win for the plaintiff, Abigail Fisher, could mean an end to affirmative action in higher education in the United States, a major transformation in the country’s colleges and universities, and an altering of the life opportunities of the next few generations of Americans. In arguing this case, the Supremes were arguing over not just higher education policy but over what kind of country we are, what principles will guide us going forward. They were arguing about the nature of race and the meaning of fairness, and because they’re the Supreme Court of the United States, they get to decide how those concepts operate in American law.

This is a big deal and a big, complicated case, and over the next week or so I’ll be making my way through the oral argument transcript, analyzing the most important (and weirdest) moments.

See you tomorrow for part one.