January 11, 2010

That time Professor Friedman said "orthogonal."

David said...

Oh those droll Supremes.

JAL said...

All words and no play makes for dull decisions.

wv retlyin
redneck for red line

Supreme Court justices orthogonal to mathematicians

Angst said...

The Justices were actually Orthonormal

when Scalia said: "I think we should use that in the opinion,"

followed by

Flexo said...

Sounds like folks being too smart for their own good and, by their supposed brilliance, only spouting nonsense.

"Orthogonal," Friedman repeated, and then defined the word: "Right angle. Unrelated. Irrelevant."

However, "ortho-" -- as in orthodox -- is from the Greek meaning "straight, upright, correct." While "-gon" is from the Greek meaning "angled."

Thus, properly combining them would produce a "straight angle," which is, of course, an oxymoron.

It is true that one of the further meanings of "ortho" is "right," but "right" in the sense of "correct or straight," not "right" in the sense of direction.

"Orthogon" as a perpendicular right angle is a perversion of the word. But then again, he is a pointy-headed professor, and from U of M at that, so that is no surprise.

El Pollo Real said...

"Orthogonal" is a commonly used adjective in quantum mechanics used to distinguish to mathematical functions that have no spatial overlap, e.g., two p-orbitals on the same atom. Extending the concept to how Friedman used it is really no stretch: link.

wv: polke (original German spelling)

fizzymagic said...

"Orthogonal" is a commonly used adjective in quantum mechanics used to distinguish to mathematical functions that have no spatial overlap, e.g., two p-orbitals on the same atom.

No, "orthogonal" is a mathematical term used to describe two functions for which the inner product is zero. As it happens, some wavefunctions have that property, so that's why it is used in that context.

I don't think of "orthogonal" as an unusual word at all; and physicists (of which I am one) and math geeks use it in the same context as Friedman did all the time. It's kind of in "in" joke.

rhhardin said...

I wonder how Friedman would use parameter.

That's the test of mathematical culture.

Iapetus said...

In mathematics, orthogonal is a synonym for perpendicular, which is the same as saying that the inner product (or dot product or scalar product, all of which is the same) is equal to zero. In a law context it might be equivalent to saying that something is not "on point," i.e., not applicable or dispositive regarding the matter at hand.

Seven Machos said...

The comments to the article itself are hilarious. Best one:

pavoreal wrote:
Every high school student ought to know what 'orthogonal' means. That a Supreme Court justice did not is an embarrassment

Bob_R said...

The basic concept is taught in standard sophomore vector calculus and differential equations courses. Standard fare for every science major. More evidence that Brooks' "educated class" is really a "poorly, but expensively educated class."

EDH said...

El Pollo Real said...

"Orthogonal" is a commonly used adjective in quantum mechanics used to distinguish to mathematical functions that have no spatial overlap, e.g., two p-orbitals on the same atom. Extending the concept to how Friedman used it is really no stretch.

Except didn't he invoke geometry, which uses orthogonal to describe a specific perpendicular relationship between vectors, to explain the term to the Supreme Court?

That's where I think the muddle is -- between his use and explanation of the term.

wv-"pring" = Titus' reaction were he to see Scott Brown campaigning in Cambridge

Largo said...

David Schwartz has an excellent explanation of "orthogonal" at The Volokh Conspiracy:

"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."

AllenS said...

I once bought some ill-fitting shoes on the internets and my feet felt like they had been orthboxonal.

Paco Wové said...

I wonder how Friedman would use parameter.

"[I]t frankly does not behoove a woman of your parameters to wear them stretch pants."

Original Mike said...

Hell, I bet I say "orthogonal" five times a day.

Can I be on the Supreme Court?

Brian O'Connell said...

Meh. The whole discussion is tangential to the case before the court.

Big Mike said...

@Original Mike, are you a mathematician too? I wouldn't say I use it five times a day but several times a week is about right.

- "Big"

Paul Zrimsek said...

Good. We need more orthogonalist justices on the Court.

Original Mike said...

@Big Mike - Physicist. Five times a day may be an exagaration, but the word certainly gets a lot of use around here.

Joe M. said...

Hah. I like it.

...

Flexo: check your dictionaries before you start spouting off next time. Here's the relevant LSJ entry:

ὀρθογώνιον , τό,
rectangle, Arist.de An.413a17 ; ὀρθό-ιος, ον, rectangular, Archyt. ap. Simp. in Cat.392.8 ; τρίγωνον Ti.Locr.98a, D.L.8.12 ; κῶνος Archim.Sph. Cyl.1 Prooem.; ἐξ ὀρθογωνίου by rectangular measurement, PSI4.320.12 (i A. D.), POxy.2134.15 (ii A. D.).

Which passed into Latin as (Lewis & Short):

orthŏgōnĭus, a, um, adj., = ὀρθογώνιος,
right-angled, rectangular, orthogonal: trigonum, Vitr. 10, 11: ossicla, Aus. praef. ad Idyll. 13.

From there to Middle French, and then to English.

Gabriel Hanna said...

I don't like hearing journalists use these words, like "orthogonal", "inflection point", and "exponential"; a lot of times they get them wrong.

It filters through to my students. A lot of them will say that something "increases exponentially" without realizing that "exponential" does not mean "grows without limit"; it's a very specific claim about the RATE of growth.

I think "ortho" is best rendered "correct"; this is why we say "right angle", it's the correct one for building things. You also have orthodox (correct opinion), orthography (correct writing).

I think it's also interesting that "sinister" literally means left-handed, "dexterity" means "righthandedness". Left is evil and clumsy, right is correct and skillful.

You can learn a lot from studying words.

rhhardin said...

XVII

Are there amny little boys who think they are a
monster? But in my case I am right said Geryon to the
dog they were sitting on the bluffs The dog regarded him
joyfully

XXI Wings

Steps off a scraped March sky and sinks Up
into the blind Atlantic morning a small red
dog jumping across the beach miles below

XXII Herakles' Killing Club

Little red dog did not see it he felt it All events carry but
one

XXIII Herakles' Arrow

Arrow means kill It parted Geryon's skull like a comb Made the boy neck lean At an odd slow angle sideways As when a poppy shames itself in a sudden whip of Nude breeze

XXV Total Things Known about Geryon

He loved lightning He lived on an island His mother was a
nymph of a river that ran to the sea His father was a gold
cutting tool Old scholia say that Stesichoros says that
Geryon had six hands and six feet and wings He was red and
his strange red cattle excited envy Herakles came and
killed him for his cattle Killed the dog (named Orthos meaning Straight Up)

XXVI Geryon's End

The red world And corresponding red breezes
went on Geryon did not

- Anne Carson

Original Mike said...

@Gabriel: The incorrect usage I note most often from my students is "order of magnitude" when all they're really trying to say is "big".

mariner said...

Gabriel Hanna:
Left is evil and clumsy, right is correct and skillful.

As all right-thinking people know!

27183 said...

Vinny Gambini: It is possible that the two yutes...
Judge Chamberlain Haller: ...Ah, the two what? Uh... uh, what was that word?
Vinny Gambini: Uh... what word?
Judge Chamberlain Haller: Two what?
Vinny Gambini: What?
Judge Chamberlain Haller: Uh... did you say 'yutes'?
Vinny Gambini: Yeah, two yutes.
Judge Chamberlain Haller: What is a yute?
[beat]
Vinny Gambini: Oh, excuse me, your honor...
[exaggerated]
Vinny Gambini: Two YOUTHS.