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Thursday, November 13, 2008


My nerdy and pedantic colleague Christian Turner sent around an email pointing out an error the Supreme Court made in an opinion yesterday -- in math.  Christian, it's worth noting, has a Ph.D. in math from Texas A&M so we're all prone to trusting him on this one.  With his permission (and on the condition that I introduce him as "my nerdy and pedantic colleague"), I'm sharing his email below:

It's not everyday that my prior experience in math proves useful in reading a Supreme Court opinion.  Today is still not such a day.  However, math did provide a chance to task-avoid by focusing on an inconsequential, stray remark in an opinion. Roberts just issued an opinion in Winter v. NRDC - ruling in favor of the Navy in a case involving the Navy's NEPA obligations with respect to the use of certain kinds of sonar in training exercises, where the sonar might have ill effects on marine mammals.  (Kind of an interesting case actually.)

The opinion contains the following line:  "There is an exponential relationship between radius length and surface area (Area = pi r^2)."

This is decidedly not an exponential relationship, but it could be called a power relationship, quadratic relationship, or geometric relationship.  An exponential relationship is something like y = 3^x.  The difference between the two kinds of relationship is huge, easily seen as x grows large.  (Though there's disagreement, the number of electrons in the universe is very, very likely less than 10^100.)

Correcting this could be my only shot at leaving any kind of mark on the Court.  Too bad I don't have a blog.  Maybe I could become the crank who submits nitpicky correction petitions (if such things exist) on an ongoing basis.  In fact, crank is probably my pre-destined endpoint.


Posted by Sonja West on November 13, 2008 at 01:19 PM | Permalink


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Interesting! And snappier than "putzelplustwo," I suppose.

Posted by: Orin Kerr | Nov 14, 2008 3:40:00 PM

Orin, I have always assumed the explanation is the one given by Anon: Frank is paying homage to his predecessors.

Posted by: Roy Englert | Nov 14, 2008 10:23:58 AM

I don't know whether to be more impressed by the original post or the equally benerded commentary. By the time this got to the Alexander J. Dallas, I was convinced this was the Green Blawg.

P.S. Little known fact: email sent to "dallasplus4" would not reach Howard, but rather a longish pair of knickerbockers.

Posted by: Edward Swaine | Nov 13, 2008 11:58:56 PM

FWIW, Yahoo Answers disagrees with the "involves exponents" usage.

It's interesting that elsewhere in the opinion, the Court highlights the fact that decibels are a logarithmic measurement of sound--i.e., the fact the relationship between decibels and loudness is genuinely exponential.

Posted by: Chris | Nov 13, 2008 10:13:46 PM

I bet the origin of the "dallasplus14" name is that Wagner is the 15th reporter of decisions -- that is, fourteen after the first reporter Alexander J. Dallas.

Posted by: anon | Nov 13, 2008 9:50:12 PM


So now you're raising a much more important question: How did Frank Wagner get "dallasplus14" as his official username? Did he win a bet with the late Chief Justice Rehnquist and get to commemorate the bet (Dallas Cowboys to win with a spread of 14) in a way that replaced "fwagner"?

Posted by: Orin Kerr | Nov 13, 2008 8:29:15 PM

I was just joking: It almost certainly was an unintentional error in mathiness, regardless of whether one could strain to redeem the sentence; as to it being a done deal, Jackson in fact said that the Court wasn't infallible, and you've evidenced it yet again.

Posted by: Edward Swaine | Nov 13, 2008 7:23:27 PM

It's not a done deal. The Reporter of Decisions, Frank Wagner, is very good at correcting technical errors. Send him an email at [email protected]. Also, don't assume that Chief Justice Roberts doesn't care (but certainly don't attempt to contact him directly). When I knew him in private practice, he was very open to being educated about technical subjects by people who genuinely knew more than he did.

Posted by: Roy Englert | Nov 13, 2008 5:02:15 PM

Now that my crank-ness has been exposed, I should add that of course Edward is correct, that he meant exponential in the sense that an exponent greater than one appears in the relationship. (Although I'm not sure that I agree that one can talk non-mathematically about a mathematical equation.) I just thought it was amusing, which says more about me than it does about Justice Roberts.

I also agree with Kent that this is the kind of thing one could submit to the reporter. But perhaps enough people use exponential in the sense Edward mentions, that one can't say this is really an error.

Posted by: Christian Turner | Nov 13, 2008 4:45:24 PM

The Chief Justice plainly meant "exponential" in the non-mathematical sense of having to do with an exponent: that is, the radius explains the area. He just happened to add the details of that explanation in the parenthetical, while carefully avoiding characterizing that equation in mathemetical lingo.

In any event, it's a done deal now, I'm afraid. As Justice Jackson once said: "We are not rational because we are real, but we are real only because we are either rational or irrational." Or something like that.

Posted by: Edward Swaine | Nov 13, 2008 4:21:33 PM

Please advise your nerdy and pedantic colleague that a caption at the top of the opinion proper (after the syllabus) invites corrections of "any typographical or other formal errors" to be sent to the reporter of decisions. I think the use of "exponential" instead of "quadratic" qualifies.

Posted by: Kent Scheidegger | Nov 13, 2008 3:28:27 PM

While this is certainly an example of innumeracy, I don't think it actually altered the outcome. For an example of where the Court couldn't compute a percentage correctly (!!) and it arguably altered the outcome see US Dept of Commerce v Montana 503 US 442 (1992) as detailed in Getting the Math Right: Why California Has Too Many Seats in the House of Representatives, 59 Vanderbilt L. Rev. 297 (2006).

Posted by: Paul H Edelman | Nov 13, 2008 3:05:03 PM

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