# The Higher Math of Briscoe v. Virginia?

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.

(Laughter.)

JUSTICE KENNEDY: I knew this case presented us a problem.

(Laughter.)

MR. FRIEDMAN: I should have — I probably should have said –

JUSTICE SCALIA: I think we should use that in the opinion.

(Laughter.)

MR. FRIEDMAN: I thought — I thought I had seen it before.

JUSTICE SCALIA: Or the dissent.

(Laughter.)

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.

1. #1 6EQUJ5
January 12, 2010

I don’t like it. When people adopt words from disciplines they don’t understand, they cannot be trusted to use the words sensibly.

A roomful of engineers were addressed by a non-technical person who talked about a ‘continuum’, when what she really had was a dichotomy with third part which was a subset of one of the other parts. It turned out she didn’t understand ‘dichotomy’ or ‘subset’ either. She was calling the three a continuum because they ‘went together’.

I once had a boss who asked for a ‘snapshot’ of activity over the past month. As I tried finding out his meaning, he realized he had no idea: he was just copying the behavior of another boss.

2. #2 rob
January 12, 2010

i don’t like it either.

quantum, energy, force, momentum, etc etc etc are all misused.

heck, quantum is often used in a way that is *opposite* it’s acutal meaning.

3. #3 Uncle Al
January 12, 2010

Orthogonality is vital to organic synthesis! Legendre polynomials are orthogonal (dot products are zero). Organikers thus ignore the entire theoretical shopping bag and get on with synthesizing improved anus bleach for cougars and panthers.

4. #4 Matt Springer
January 12, 2010

That’s a good point, but I’m not worried about it in this particular case for two reasons.

First, whatever we may think of their various opinions, these are Supreme Court justices. They are all learned and erudite scholars whose entire mission is to precisely and carefully interpret the shades of meaning of words. They should be at very little risk of misusing this particular word, especially after its remarkably concise and accurate definition by Mr. Friedman.

Second, something as concrete as “right angle” is not really the kind of thing that gets blown into woo-land very much. The nutty “The Secret” types love to use physics words that are inherently much more malleable by virtue of non-trivial scientific meanings combined with widely-ranging colloquial definitions. But everyone knows what a right angle is, people will be much less prone to misunderstand it.

5. #5 Scott
January 12, 2010

I find it rather appalling that Scalia and Roberts, people as supposedly bright as a Supreme Court justice is supposed to be, have never heard of the term “orthogonal”. Did they never have to take a math course beyond basic algebra? Introductory high school geometry introduces “orthogonal”.

To make it worse, Scalia then appears to make fun of the new scary “big” word, or perhaps of the Counsel for using it. Why should the Counsel have to back pedal on a perfectly good, completely appropriate word? It sounds like Counsel has to dumb down his language to make it acceptable to the members of the Court. Is that the kind of intellectual rigor we want on our highest court? Is that the kind of example to set? Sheeze!

6. #6 CDRealist
January 12, 2010

Give it up. Language changes, and when people take words from one discipline to use in another, or from one language to another, the meaning often changes. You might as well object to gravity. See Paradigm.

7. #7 Matt Springer
January 12, 2010

Nah, if you read their opinions or hear them speak it’s clear that Scalia and Roberts are both men of truly exceptional intelligence. Scalia in particular is legendary even among his harshest critics for his astonishing command of the language. That they weren’t familiar with a technical term from geometry after decades removed from college is no large mark against them – Volokh notes that the word has never been used in an opinion in the whole history of the court. As such it’s very clear that the exchange is humorous banter among intellectuals, not frat boys boggling at that big-word-using nerd.

8. #8 Nathan Myers
January 12, 2010

Scalia is not legendary for his command of the language. He is legendary for the deviousness of his reasoning. Having chosen a position based on his prejudices, he constructs an edifice of support cherry-picked from an astonishing range of cases. It’s impossible to argue against without reference to a similarly wide range of cases, and without intimate familiarity with the cases cited, however specious the reasoning itself. Lawyers are self-selected from among those who admire this sort of thing, but it’s far from admirable.

Unfamiliarity with “orthogonal” is a disgrace in a Supreme Court judge, completely orthogonally to one’s expectations about their memories of grade-school geometry. Needling counsel about the word is also disgraceful.

9. #9 Matt Springer
January 12, 2010

Nathan, I suggest an experiment. Pick at random a group of college-educated professionals who are very successful in their (non-science) fields. Make sure they’ve all been out of college for 20+ years. Ask them what “orthogonal” means. Dollars to dougnhuts none of them will. I am certain neither of my college-educated professional parents would, for instance. (No offense, mom and dad.) I’d bet good money that not one Supreme Court justice could have done so before it presented itself in oral arguments.

I’m pretty sure your dislike of Scalia’s jurispridence is badly miscoloring your impressions here. It could well be that my general agreement with his jurisprudence is similarly coloring mine. Still, if you try the experiment I suggest I think you might be surprised.

10. #10 Tom
January 12, 2010

It doesn’t bother me that much that the justices don’t know what orthogonal means. But it DOES bother me that, if I interpret the “laughter” correctly, Mr. Friedman was held up to ridicule for knowing a word with more than 2 syllables. That has happened to me in meetings, but should not happen in the Supreme Court. Sigh. I guess we should all have paid more attention to sports, and not have bothered improving our vocabularies. We would fit in better.

11. #11 Matt Springer
January 12, 2010

It’s pretty clear the justices were laughing at themselves for not knowing that word yet. As people who write for a living, they’re certainly not afraid of obscure and/or polysyllabic words. Cf. a representative paragraph of Scalia’s opinion in the previous major case on the subject:

Respondent and the dissent advance a potpourri of analytic arguments in an effort to avoid this rather straightforward application of our holding in Crawford. Before addressing them, however, we must assure the reader of the falsity of the dissent’s opening alarum that we are “sweep[ing] away an accepted rule governing the admission of scientific evidence” that has been “established for at least 90 years” and “extends across at least 35 States and six Federal Courts of Appeals.”

12. #12 kumasama
January 13, 2010

No problems with this exchange; it’s just that some words common in some disciplines are absent in others. In science/engineering especially, we have our own lexicon, often appropriating technical terms for use in ordinary conversation. I’ve run into the same problem using the word ‘cruft’ to a group of English teachers. It was very hard to get them to accept that I hadn’t just made it up.

As for the complaints about words losing their precise meaning when they are coopted: that’s just language changing. Deal with it. It happens to all words, not just technical ones.

13. #13 Nathan Myers
January 13, 2010

The problem is that it demonstrates not just forgetfulness of grammar-school geometry, but an utterly profound ignorance of every useful form of mathematics and physics, from statistics to statics. That’s maybe OK for Joe the Plumber, but a Supreme Court justice should be better equipped.

As for Scalia’s jurisprudence, it’s easy to understand admiration of extremely well-constructed dishonesty. However, such understanding need not lead to a favorable opinion of the admirer. One so led would be as great a scoundrel as the other two.