From the oral argument transcript today in Briscoe v. Virginia, a funny moment in the argument of University of Michigan law professor Richard Friedman:
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.
I think Friedman should have explained “vectors with a dot product of zero,” but I guess that would have been overly technical.
If you’re curious, the Supreme Court has never used the word “orthogonal” in a written opinion. It has usually appeared in the federal reports in patent cases, although it occasionally surfaces elsewhere. See, e.g., United States v. Harris, 491 F.3d 440 (DC Cir. 2007) (“This test is fact-intensive, and the facts at issue are often orthogonal to those explored at trial.”).
Anderson says:
Like tangential, but presumably much worse somehow.
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January 11, 2010, 6:24 pmTom in GA says:
Reading that made this math professor’s day.
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January 11, 2010, 6:28 pmMichael P says:
Anderson,
Orthogonal vectors are quite different than tangential vectors. Tangential vectors touch a curve at one point, and if they were shifted a bit would be parallel to the curve at that point (such that they never touch).
In math, you can decompose many measurement systems into series of orthogonal bases. You can represent any point in such a system as a combination of those bases, and moving along one basis would not change the measures in the other bases. For linear systems, this means you can decompose the system and look at each basis independently — and this is the usual sense of the word that is used in non-mathematical contexts, that changing one aspect does not affect a certain other aspect.
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January 11, 2010, 6:34 pmStas Peterson says:
It just goes to show that Lawyers are NOT the mental giants that they wish to appear to be. Law can be a noble profession, but it does not always require a tremendous mind.
It is disquieting to hear that the very pinnacle of legal minds though, don’t know what orthogonal means. It makes it possible to understand the rank stupidity of EPA vs Mass. I still want the Justices to discuss how they comply with a now legalized request of the EPA, to stop breathing for a certain number of hours per day.
Any intelligent, active member of C. P. Snow’s Second Culture has no problem with orthogonal or on the other hand legal concepts like ‘mens rea’. But attorneys are often wholly illiterate in understanding the other Culture out there.
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January 11, 2010, 6:37 pmDavid Schwartz says:
Programmers use this word fairly frequently. It metaphorically means “related, but separate”, and is almost always used in precisely this way. That is, if people are talking about X and someone brings up Y, Y will be said to be orthogonal to X if and only if:
1) X and Y are related in some way
2) However, X can be true and Y false, or vice versa, or they can both be true, or both false.
The point is to say that talking about Y won’t answer X. The question is both related (in the sense that it involves similar issues) yet separate (in the sense that answering one won’t answer the other).
It most commonly is used dismissively, at least in my experience. For example, two experienced programmers will be discussing some complex issue when a novice hears a word he recognizes. The novice brings up some other issue that happens to involve the same word/concept but is in fact a different issue. One of the experts will say, “that’s an orthogonal issue”, which roughly translates to “shut up, adults are talking”.
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January 11, 2010, 6:40 pmCrunchy Frog says:
I don’t know that knowledge of math geek terminology (I am one myself) translates to being part of a Capital-C Culture, but if it makes you feel better...
Had Mr. Friedman used the word ‘perpendicular’, which is the same concept in 2-dimensional space, the Justices would most likely have caught on.
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January 11, 2010, 6:44 pmaphrael says:
I find this personally amusing. When I did my moot court oral argument, one of the judges pulled the word ‘orthogonal’ out of my brief and asked me to define it, then (once I’d defined it successfully) called me on the carpet for using non-legal words that might confuse an audience without a math or engineering background.
It’s hilarious to see the same thing repeated at the Supreme Court.
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January 11, 2010, 7:00 pmEric Rasmusen says:
It’s a credit to Scalia that he realized what a useful adjective “orthogonal” is.
I wonder if it came to Prof. Friedman via economics. We use it a lot. I think we started that because of econometrics, where two variables being orthogonal means, basically, that they are uncorrelated.
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January 11, 2010, 7:00 pmRandom_Physicist says:
Absolutely fantastic...go blue!
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January 11, 2010, 7:11 pmThe Volokh Conspiracy » Blog Archive » “Orthogonal” says:
[...] post about the use of “orthogonal” in a Supreme Court argument brings back memories: I used to like using “orthogonal” in that sense, too, perhaps because of [...]
Bob_R says:
Yet more evidence that David Brooks’ “educated class” should be the “poorly, but expensively educated class.” Far from being a “math geek” term, this is something from sophomore level calculus (which most students who have AP calculus available in HS take their Freshman year).
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January 11, 2010, 7:19 pmDavid Schwartz says:
Two issues are metaphorically ‘orthogonal’ if moving along one won’t change your position on the other, just as no amount of movement West or East will get you any further North.
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January 11, 2010, 7:25 pmAnon321 says:
I’m a little surprised that neither Roberts nor Scalia seems to have heard the word before. I have no background in math or computer science, but I feel like I hear it thrown around in legal circles with some regularity. It’s pretentious and usually unnecessary, but not unheard of.
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January 11, 2010, 7:45 pmAnderson says:
I assume that Michael P’s comment is vector-in-cheek.
And agreed w/ Rasmussen that Scalia probably was genuinely happy to learn a new word. He seems like that kinda guy.
... After reading this post earlier, I reviewed a brief I’d written, and wondered whether “abjured” was such a good idea.
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January 11, 2010, 7:55 pmChris says:
Professor Friedman also made a joke that the Court apparently appreciated:
JUSTICE SCALIA: Mr. Friedman, aren’t there states that have been proceeding this way even before we came down with our opinion?
MR. FRIEDMAN: Absolutely, absolutely, including -
JUSTICE SCALIA: And which States are they?
MR. FRIEDMAN: They — well, they include my own State of Michigan, they include the State of New York -
JUSTICE SCALIA: And they are not under water, are they?
MR. FRIEDMAN: The problems of the State of Michigan are not attributable to the use of this procedure, no.
(Laughter.)
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January 11, 2010, 8:00 pmBama 1L says:
The only time I’ve ever encountered orthogonal, it meant the opposite of diagonal. So in chess, a bishop moves diagonally but a rook moves orthogonally. I have the feeling this is not what the mathspeak above connotes.
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January 11, 2010, 8:37 pmGULC 3L says:
Actually, in context, that is exactly what it connotes. See David Schwartz’s comment at 7:25 and compare how a rook moves to a diagonal movement.
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January 11, 2010, 8:46 pmdevoman says:
David Schwartz, in his 7:25 PM comment, raises an interesting question: He says:
Two issues are metaphorically ‘orthogonal’ if moving along one won’t change your position on the other, just as no amount of movement West or East will get you any further North.
It is true that no movement East or West will get you further North. However, moving North ultimately will change your position East/West. I.e. from a defined position to an undefined one. Thus, I don’t think East/West movement and Northerly movement are strictly orthogonal.
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January 11, 2010, 9:39 pmPeter Shalen says:
Professor Friedman’s use of “orthogonal” is correct. It’s refreshing to see a mathematical term used correctly for a change. Recent years have brought us fashionable misuses of “lowest common denominator” and “parameters,” and just the other day Tom Friedman misused “point of inflection.”
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January 11, 2010, 10:06 pmAndrew says:
This is Orin’s best post since the one on June 3.
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January 11, 2010, 10:36 pmTGGP says:
I like using “orthogonal” in that way all the time. I am a programmer, or at least I was before last month and hope to be so again soon. I think “tangential” is a good comparison, because that also forms right angles, but “perpendicular” would seem off.
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January 11, 2010, 10:44 pmFub says:
I think this falls out of Poincaré‘s hairy ball theorem, but it’s beyond my pay grade. Mmmm. Doughnuts.
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January 11, 2010, 10:45 pmSammy Finkelman says:
Ah — so that’s where the word comes from. Not just tangential, but completely orthogonal.
You *could* say perpendicular which means the same thing, and which more people know what it means, but for some reason it does not strike the same chord.
Orthogonal is a vector, but perpendicular is a line.
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January 11, 2010, 11:05 pmJeff Walden says:
That’s...romanette.
[But seriously, “orthogonal”? Really? He wasn’t familiar with the word “orthogonal”? Sheesh, I’d never have thought of orthogonal as an overly technical word.]
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January 11, 2010, 11:07 pmLior says:
devoman: “Orthogonal” refers to directions in the plane, not on the sphere. Indeed on a flat plane moving North will not change your East-West position.
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January 11, 2010, 11:08 pmJohn Armstrong says:
@Lior but it does refer to tangent vectors to the sphere, in which case devoman is entirely correct.
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January 11, 2010, 11:26 pmFrater Plotter says:
Until reading this, I would have been sure that this metaphorical sense of “orthogonal” (meaning “unrelated”, “wholly separable”, or “irrelevant”) was engineers’ slang. Indeed, it’s found in the Jargon File, a glossary of technical-jargon and slang terms used by computer hackers, computer scientists, technicians, and engineers.
While many jargon words have found their way into mainstream English, this one surprises me.
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January 11, 2010, 11:27 pmChris Travers says:
It could be worse. Acute romanette could have made that mistake at argument ;-)
Is it normal for the justices to get this many vocabulary lessons?
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January 11, 2010, 11:33 pmuberVU - social comments says:
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This post was mentioned on Twitter by shoutingboy: “Orthogonal, ooh.” http://volokh.com/2010/01/11/orthogonal-ooh/...
Gramarye says:
I’m actually surprised to see that none of the justices knew this word, either. It’s a word I’m fairly sure I’ve known since high school, and it wouldn’t surprise me to see it on a high-school standardized test. Also, I know a bankruptcy judge in the geographic area in which I practice (N.D. Ohio) who generally eschews more advanced vocabulary (e.g., “eschew”), but didn’t hesitate to include “orthogonal” in a written opinion. In re Scassa, 2009 WL 1586566, *3 (Bankr. N.D. Ohio Jan. 16, 2009).
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January 12, 2010, 12:19 amyankee says:
I think “vectors with a generalized inner product of zero” would have been a far superior answer.
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January 12, 2010, 12:53 amM says:
As a student of Prof Friedman, I distinctly remember him mocking a student for his use of “zealous” — although in that case it was because he had caught on to that semester’s version of professor bingo. I liked Professor Friedman very much, but this feels like some sort of justice.
Also, for those criticizing him, he wasn’t using it in a brief, and his use obviously was natural, rather than considered. I’m sure most of us speaking extemporaneously perhaps use the closest word to what we are thinking of, even if it is not the most elegant or clear.
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January 12, 2010, 1:14 amChem_geek says:
True north or magnetic north?
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January 12, 2010, 1:38 amDavid Nieporent says:
Agreed. I use it all the time; I didn’t realize it was not in general use (among educated people).
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January 12, 2010, 2:05 amDavid Boxenhorn says:
Orthogonal is the opposite of parallel. If he had said, “I think that issue is parallel to the issue here because...” it would have had the opposite meaning.
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January 12, 2010, 2:54 amLargo says:
This is the best definition of the thread. It’s like how someone outside of the traditional left/right spectrum (I don’t mean centrist) can take a left-wing position on one issue, and a right-wing position on another. People on the wings may not understand why someone would support one position but not the other. They don’t understand how from a different political view, the issues are orthogonal to each other.
It is the perfect word. “Distinct” does not mean the same. The issues may not always be “unrelated”. And to call two issues “perpendicular” sounds mighty strange to me.
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January 12, 2010, 5:47 amAnother Kevin says:
Well, all right, p and q are orthogonal with respect to the metric tensor A if and only if <p|A|q>=0, but Dirac notation is perhaps a bit too geeky for a judge.
I hope that in context, the judge was making light-hearted fun of his own ignorance. Because otherwise, we have a playground bully on the bench. Comments of this sort, if not jovially intended, are akin to beating up the smart kid for being the teacher’s pet.
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January 12, 2010, 7:12 amAnderson says:
I hope that in context, the judge was making light-hearted fun of his own ignorance. Because otherwise, we have a playground bully on the bench.
It certainly seems light-hearted in the transcript, and while I am not a fan of Justice Scalia’s jurisprudence, he does have a lively sense of humor.
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January 12, 2010, 7:43 amStephen says:
The fact that any particular person in the thread knows what a word means naturally doesn’t prove that other people who don’t know the word are stupid, uncultured or anything else. It just means you know the meaning of a word. You know something that other people don’t, you should be happy.
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January 12, 2010, 7:51 amlgm says:
Here’s another math professor take on this.
According to a Greek student in a class I taught, the Greek word “orthogonal” means “vertical”. It is “orthogonal” to the horizontal, making a right angle with it. They seem to use “orthogonal” in this sense in chess (see Bama 1L).
I agree that the distance metaphor may be what Friedman was after. Suppose there are 100 miles between A and B and you are at A. If you move one mile in the direction of B, then you are one mile closer to B. If you move one mile in an orthogonal direction, your distance to B hardly changes (For calculus buffs, the change is second order, not first order). In this sense, a legal argument is orthogonal to an issue if the argument doesn’t get you closer or further from a decision on the issue. David Schwartz was making this point, but you don’t have to be on a sphere for it to be true, at least in the small.
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January 12, 2010, 8:09 amBama 1L says:
Wow, a math professor said I was not completely wrong. I peaked early today.
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January 12, 2010, 9:07 amAnderson says:
... Though, an orthogonal line resembles a tangent in that both intersect the argument/issue at only one point. The difference would seem, well, academic.
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January 12, 2010, 9:12 amSCOTUSblog » Tuesday round-up says:
[...] Tony Mauro at the BLT and the Volokh Conspiracy both post on the expansive vocabulary sometimes overheard at Supreme Court arguments [...]
arch1 says:
While typical use of “orthogonal” in the metaphorical sense has always seemed to me true to its mathematical origins, I now realize that
1) My subconscious has been telling me all along that the same is not true of “tangential.”
2) This is I think because I’ve been interpreting “tangential” used metaphorically as meaning roughly “related, but not central to the issue at hand.”
3) Maybe I should instead have been interpreting “tangential” to mean an observation or consideration which is valid locally but which misses out on important aspects of the bigger picture (as a line tangent to a curve at a given point faithfully conveys that curve’s direction at and near the point of tangency, but, constrained as it is to constant slope, can’t in general reflect the curve’s global behavior).
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January 12, 2010, 10:00 amJeb Jones says:
I love the way the use of the word orthogonal led to a tangential discussion.
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January 12, 2010, 11:04 amJohn Spevacek says:
The visual difference between “tangential” and “orthogonal” is that that tangentail line slowly separates from the point of intersection, whereas an orthogonal line moves as quickly as possible from the point of intersection.
So to say somethings are tangentially related means that they are close to start with, but further apart as time goes on. Orthogonally related means that they aren’t related at all.
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January 12, 2010, 12:05 pmThe Higher Math of Briscoe v. Virginia? [Built on Facts] « Random Information says:
[...] at The Volokh Conspiracy, a quick look at a funny exchange in the oral arguments of Briscoe v. Virginia: MR. FRIEDMAN: I [...]
dll111 says:
Roberts and Scalia were in the dissent in Mass. v. EPA, but carry on.
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January 12, 2010, 12:36 pmBruce Hayden says:
So, would you say that an line orthogonal to a circle is orthogonal to a tangent to the circle? Or, is this a situation where you can have a perpendicular that is orthogonal to the tangent, but not to the circle?
I hate to admit my ignorance here, but while I have a math degree, it has been almost 40 years since I worked with this stuff.
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January 12, 2010, 1:40 pmAnderson says:
Arch1, “going off on a tangent” is the expression to keep in mind, I think.
My mental image is of an ice-skater twirling while holding her kid brother by the hands, so that he moves in a circle. Then she lets go, and he travels in a tangent, into the bushes beside the pond.
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January 12, 2010, 2:46 pmOrthogonal « Blog Test says:
[...] Volokh and Orin Kerr have interesting blog posts on the word [...]
zippypinhead says:
I suspect this is an example of the legal version of a “micro-regional-dialect.” With the micro-region being Hutchins Hall at the University of Michigan Law School. I encountered this word being used by at least a couple of professors when I was a law student there shortly before Friedman’s arrival on campus. It was a commonly-enough used term in those days that it eventually entered my own active vocabulary — at least until I got out into the “real world” and the term was mockingly stricken from a first draft of one of the earliest briefs I tried to write. Professor Friedman, being a 20+ year inhabitant of Hutchins Hall, likely never realized until Justice Roberts whacked him between the eyes, just how seldom the world at large uses “orthogonal” in a legal context.
Incidentally, in the classroom at U.Mich Law, “orthogonal” was a polite adjective used when the professor needed to tell a student his analysis had just gone off on an irrelevant tangent and totally missed the point.
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January 12, 2010, 3:52 pmuh_clem says:
I am also surprised that a putatively educated person wouldn’t be familiar with the word orthogonal. But maybe that’s a result of 25 years of living in Ann Arbor. (c:
At least he used “orthogonal” rather than the synonym “normal”.
And perhaps the most apt definition for orthogonal would be “linearly independent” — it’s not only mathematically correct, but immediately gives the unfamiliar listener a clue what the speaker meant.
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January 12, 2010, 5:51 pmJustin Longo says:
This insight explains a lot: Roberts and Scalia knew exactly what Friedman meant by orthogonal — they were just having fun with him (“you’re not in Ann Arbor anymore, Toto”). Justice Kennedy too: “I knew this case presented us a problem.” It seemed too unlikely that Roberts and Scalia would have been genuinely stumped by the word.
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January 12, 2010, 5:54 pmChris Travers says:
Metaphorically, tangential and orthogonal are almost opposite in many ways.
I see tangential as meaning “related but deceptively outside the scope of inquiry” while orthogonal as meaning “deceptively unrelated but inside the scope of inquiry.”
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January 12, 2010, 6:05 pmDaniel Schuman says:
In another use case:
Richard Nixon was the founder of the “orthogonian society” at Whittier college. In popular culture, Rick Perlstein’s book Nixonland described what he considered Nixon’s followers as orthogonians.
If only Bill Safire were still around and able to shed some light on this.
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January 12, 2010, 10:24 pmA. Criminal says:
It just goes to show that Lawyers are NOT the mental giants that they wish to appear to be.
Glorified secretaries, mostly. At least one Colorado statute describing calculations incorrectly uses “interpolate” for “extrapolate”, terms that 4th graders should know.
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January 12, 2010, 11:41 pmScalia Bullish on “Orthogonal” « The Progressive Internal Critique says:
[...] ♣ Volokh Conspiracy: Orthogonal [...]
Ennuyer.net » Blog Archive » The U.S. Supreme Court has a Sarah Palin moment. says:
[...] The Volokh Conspiracy » Blog Archive » “Orthogonal, Ooh”. [...]
zaleriana says:
I realize the discussion has moved on, but wanted to note that *metaphorically* an argument (“A”) moves along a Euclidean vector* (i.e., it has length *and* direction). Thus, *metaphorically* a tangential argument (“T”) touches A and then continues on along T in a direction that may (or may not) be similar to A and might re-intersect A somewhere/time else. And *metaphorically* a orthogonal argument (“O”) *seems* to touch A (but may not) at a single point and continues in a direction that will *never* re-intersect A at any time or place.
*needed to check that, as I haven’t used specific math terms in ~20 years.
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January 13, 2010, 12:11 pmBL1Y says:
If I had known this was what lawyers considered funny, I never would have gone to law school.
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January 13, 2010, 11:31 pmPrometheeFeu says:
While that may be true, ‘orthogonal’ means something in the context while ‘perpendicular’ does not.
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January 14, 2010, 10:33 amReason Not to Go to Law School #13 « BL1Y says:
[...] exchange like this in the Supreme Court is what passes as high comedy in the legal world: MR. FRIEDMAN: I think that [...]
links for 2010-01-14 « omniprasan says:
[...] “Orthogonal, Ooh” That is a bit of professorship creeping in, I suppose [...]
Round Up – January 12, 2010 « Restrained Radical says:
[...] A funny exchange at the Supreme Court. “Orthogonal, Ooh” [...]
Blawg Review #247 | a public defender says:
[...] Court has been in the news a lot this week, here in these United States. Starting on Monday with a thrillingly academic sidetrack on the meaning of the word “orthogonal” during oral argument in a case revisiting [...]
Orthoganal « Sigmud says:
[...] in an argument made by the Supreme Court, an advocate used the word “orthogonal” to describe an issue that was independent of or irrelevant to the issue being decided before the [...]
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[...] oral arguments at the SCOTUS, a lawyer used the word “orthogonal.” Roberts and Scalia were fascinated by the word and seemed to want to make it the secret word of the [...]
Jeremy Pierce says:
In philosophy, saying two views are orthogonal is pretty much the standard way to say that two views are orthogonal. See, I can’t even think of a better way to say it.
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January 24, 2010, 5:07 pmWe can believe, but we can’t know « Celebrating Time says:
[...] at least I’m in good company! Here’s a bit of transcript from a recent oral argument before the Supreme [...]