Over at The Volokh Conspiracy, a quick look at a funny exchange in the oral arguments of Briscoe v. Virginia:
MR. FRIEDMAN: I think that issue is entirely orthogonal to the issue here because the Commonwealth is acknowledging -
CHIEF JUSTICE ROBERTS: I’m sorry. Entirely what?
MR. FRIEDMAN: Orthogonal. Right angle. Unrelated. Irrelevant.
CHIEF JUSTICE ROBERTS: Oh.
JUSTICE SCALIA: What was that adjective? I liked that.
MR. FRIEDMAN: Orthogonal.
CHIEF JUSTICE ROBERTS: Orthogonal.
MR. FRIEDMAN: Right, right.
JUSTICE SCALIA: Orthogonal, ooh.
JUSTICE KENNEDY: I knew this case presented us a problem.
MR. FRIEDMAN: I should have — I probably should have said -
JUSTICE SCALIA: I think we should use that in the opinion.
MR. FRIEDMAN: I thought — I thought I had seen it before.
JUSTICE SCALIA: Or the dissent.
MR. FRIEDMAN: That is a bit of professorship creeping in, I suppose.
It’s a cute little locution, one which you’ll hear at lot in the halls of physics departments as well. I’ve also heard it used to mean “at cross purposes with”, but the slang translation suggested by Mr. Friedman is a better fit with the spirit of the underlying mathematics.
What precisely is orthogonal? That’s probably Sunday Function material, but condensed down to its basics it’s just a generalization of the concept of perpendicular. For instance, most of the coordinate systems we use are orthogonal. The x, y, and z directions are perpendicular no matter where in space you happen to be. Same thing with spherical coordinates: the radial, azimuthal, and altitudinal directions are also perpendicular no matter where you are, though their actual orientations with respect to rectangular coordinates changes with position. You may change your position along any one of those coordinates without necessarily changing your position with respect to the other two. They’re independent.
The coordinate example involves literal geometric perpendicularity, but this isn’t necessary. If you play a musical note on an instrument, you won’t get the pure tone of a tuning fork. Rather, you’ll get the pure note along with various other overtones at the various other natural frequencies of the instrument. Those other tones represent orthogonal modes of vibration and can actually be varied independently. Gently hold down middle C on a piano without actually playing the note and then play C the next octave up. The middle C string will resonate at that higher frequency because that higher orthogonal mode of the string has been excited.
The various states of a system in quantum mechanics can be described in any number of orthogonal basis sets too, and in fact QM is pretty much just the science characterizing these states and their development.
I don’t think the justices or lawyers worry too much about any of this, but it’s neat to see that some physics jargon/slang has found its way into the nation’s highest court.
The case itself is interesting, though I’m not a lawyer and my very amateur interest in the court hasn’t really dwelt on this kind of case. It’s a 6th amendment case hashing out some of the questions raised in Melendez-Diaz v. Massachusetts, holding more or less that crime lab reports are a form of testimony and therefore subject to the right of cross-examination. That case was also interesting in that it’s one of the numerous cases that fail to conform to the oft-stated but not often true idea that the courts decisions split between four conservatives, four liberals, and one moderate (Kennedy). The holding that the defendant’s right to confront witnesses does in fact extend to lab reports was expressed in the majority opinion by Scalia, Stevens, Souter, Thomas, and Ginsberg. Kennedy, Roberts, Breyer, and Alito dissented. I have not examined the issue in any detail myself, though my gut feeling is that the majority has the right idea here. However, Souter has since been replaced with Sotomayor – a former prosecutor – and it’s possible that the balance of the court may have shifted on this issue.