Crunchy Frog: 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.

While that may be true, ‘orthogonal’ means something in the context while ‘perpendicular’ does not.

*needed to check that, as I haven’t used specific math terms in ~20 years.

Glorified secretaries, mostly. At least one Colorado statute describing calculations incorrectly uses “interpolate” for “extrapolate”, terms that 4th graders should know.

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.

John Spevacek: 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.

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.”

zippypinhead: 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.

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.

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.

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.

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.

John Spevacek: 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.

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.

Stas Peterson says:

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.

Roberts and Scalia were in the dissent in Mass. v. EPA, but carry on.

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.

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).

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.

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.

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.

David Schwartz: “Orthogonal, Ooh”

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.