North, east, south, and west are the four cardinal directions. The term derives from the Latin cardo, which can mean “hinge” or “pivot,” and thus figuratively a turning point or pole. It also had a derived meaning of “something on which something else depends”—because a door de-pends (i.e. hangs) on its hinges and turns about them—and thus also could mean “principal thing.” Many modern word senses of “cardinal” derive from this idea. For example, a high Catholic official was an episcopus cardinalis (i.e. “principal bishop”), and thus ultimately just a “cardinal.” The red bird was named after the red robes worn by cardinals, and the baseball and football teams are named after the bird. (Of course, they have red uniforms and logos.) The association with the compass points, however, is an ancient one that has endured. A north-south street was a cardo, and the four principal directions were quattuor cardines orbis terrarum (“the four pivots of the world”).
What should we call the four intermediate directions: northeast, southeast, southwest, and northwest? Two names with perfectly respectable Latinate justifications would be semi-cardinal (cf. “semi-annual” or “semicircle”) or intercardinal (cf. “interpolation” or “interregnum”) directions. But some sources, including Wikipedia, refer to them as the ordinal directions, a usage that is close enough to right to sound plausible if you don’t think too closely about it.
The English “ordinal” comes from the Latin ordo, which means “order,” “line,” or “regular arrangement.” Thus, a ordo could be a course of stones in a wall, a line of soldiers, a class of citizens, or anything else arranged correctly in its place. One sense that has endured in several meanings of “order” is that of a linear series, so that the adjective ordinalis described things arranged by order of succession: first in line, second in line, third in line, and so on.
And this, it appears, is how “cardinal” and “ordinal” collided. A cardinal number is a counting number: 1, 2, 3, and so on. They are so-called because they are the principal numbers; other senses in which numbers are used depend on this one. An ordinal number describes something’s place in an order: first, second, third, and so on. They are so called because they describe the order in which things are arranged. For finite numbers, cardinals and ordinals correspond exactly. You use a cardinal number to describe how many things there are in a group, but use an ordinal number if you want to pick out where one of those things falls within the group. (Mathematicians would say that the two senses diverge for infinite numbers; infinite cardinals have very different properties than infinite ordinals.) And thus, generations of students have been taught to think of “cardinal” and “ordinal” as closely related, with “cardinal” being the
At this point, you can probably guess what happened. One finds occasional pre-1970 references to “ordinal directions” in a Google Books search, but most of them appear to be by people who have mistaken “ordinal” for “cardinal” when they meant to refer to the principal directions. It’s in 1972, as noted by Redditor phalp, that we find an attested use of “ordinal” in this sense:
… classics, though as intervening routes were made the cardinal and ordinal directions were gradually used up and so arrived at South-West by West.
I think this is simply wrong, but as with all matters of language use, it will become right if enough people use it that way over time. And if Wikipedia is any guide, we are well along that road already.
Sources:
I have a new article draft, Generative Misinterpretation, with Ben Sobel and David Stein, forthcoming in the Harvard Journal on Legislation. We argue against recent proposals to use LLMs in the judicial process. We combine an empirical critique, showing that experimental results in using LLMs to perform interpretation are brittle and arbitrary, with a jurisprudential critique, explaining why commonly offered justifications for using LLMs don’t work in the context of judging. Here is the abstract:
In a series of provocative experiments, a loose group of scholars, lawyers, and judges has endorsed generative interpretation: asking large language models (LLMs) like ChatGPT and Claude to resolve interpretive issues from actual cases. With varying degrees of confidence, they argue that LLMs are (or will soon be) able to assist—–or even replace—–judges in performing interpretive tasks like determining the meaning of a term in a contract or statute. A few go even further and argue for using LLMs to decide entire cases and to generate opinions supporting those decisions.
We respectfully dissent. In this Article, we show that LLMs are not yet fit for purpose for use in judicial chambers. Generative interpretation, like all empirical methods, must bridge two gaps to be useful and legitimate. The first is a reliability gap: are its methods consistent and reproducible enough to be trusted in high-stakes, real-world settings? Unfortunately, as we show, LLM proponents’ experimental results are brittle and frequently arbitrary. The second is an epistemic gap: do these methods measure what they purport to? Here, LLM proponents have pointed to (1) LLMs’ training processes on large datasets, (2) empirical measures of LLM outputs, (3) the rhetorical persuasiveness of those outputs, and (4) the assumed predictability of algorithmic methods. We show, however, that all of these justifications rest on unstated and faulty premises about the nature of LLMs and the nature of judging.
The superficial fluency of LLM-generated text conceals fundamental gaps between what these models are currently capable of and what legal interpretation requires to be methodologically and socially legitimate. Put simply, any human or computer can put words on a page, but it takes something more to turn those words into a legitimate act of legal interpretation. LLM proponents do not yet have a plausible story of what that “something more” comprises.
Comments welcome!
I live in New Jersey, where the campaign for Governor is unusually active. There are six candidates in the Democratic primary, and most of them are in serious contention. We have been inundated with flyers, often multiple identical copies of the same one. Although many of the candidates hold similar positions on many issues, they have attempted to distinguish themselves from each other in a heated race.
On May 1, I received an email from a site called The Jersey Dispatch, linking to and including an article titled “Sherrill’s Affordability Policies Look Suspiciously Similar to Gottheimer’s”. Here are the opening paragraphs, which are representative of the whole:
As New Jersey voters count down the remaining weeks to the June 10th gubernatorial primary, Rep. Mikie Sherrill (D-NJ) is facing increasing criticism over her lack of policy plans and detail – and how closely her sparse platform mirrors plans that fellow Democrat and declared gubernatorial candidate, Rep. Josh Gottheimer (D-NJ), released months ago.
Since announcing his candidacy last year, Gottheimer has led the field of six candidates on affordability–voter’s biggest issue at the polls. He has embraced the slogan of “Lower Taxes, Lower Costs” and promised to cut property taxes by nearly 15 percent for homeowners and small businesses across New Jersey.
Early this year, Gottheimer released a comprehensive tax cut plan and lower costs plan that tackled everything from property tax relief to the cost of childcare and utility bills. Late last month, Sherrill rolled out a strikingly similar platform, drawing criticism for what some call a lack of original vision and detail.
Although the article is mostly written in the bland institutional tone of professional journalism, something about it felt off to me. My curiosity was additionally piqued by the fact that the Jersey Dispatch reached out to me. I had never heard of it until the “Sherrill’s Affordability Policies” email hit my inbox.
When I clicked through to the Jersey Dispatch site, I was struck that multiple articles there were similarly pro-Gottheimer or anti-Sherrill. Examples include “Steve Sweeney Criticizes Mikie Sherrill Over Votes Against First Responder Protections”, “Josh Gottheimer Unveils ‘Lower Costs Plan for Jersey’ to Combat Rising Expenses”, and “Gottheimer Joins International Association of Firefighters to Advocate for First Responders”. These political pieces were interspersed with more prosaic local news, like “Southern Ocean Medical Center Nurses Vote to Authorize Strike Over Staffing, Contract Demands”.
When I looked more closely, my sense that the Jersey Dispatch is not a typical local news site grew. Here are a few of the things I noticed about it:
Making matters even stranger, the Gottheimer campaign has quoted the Jersey Dispatch in its own campaign literature. One flyer that I have seen attributes the words “His plan is not only feasible but backed by a very specific strategy to get it done” to a February 3 article, “Gottheimer Leading Dems on Lower Costs and Lower Taxes”. Interestingly, while the article overall is positive on Gottheimer’s plan, it’s not as positive as the flyer makes it sound. In context, the full sentence is, “Unlike vague campaign promises, Gottheimer asserts that his plan is not only feasible but backed by a very specific strategy to get it done.” That is, the words Gottheimer attributes to the Jersey Dispatch are a summary of his own statements, not an independent endorsement.
All of these oddities lead me to wonder what the Jersey Dispatch actually is. One possibility is that it is an astroturfing operation: partisan political content presented to make it seem as though it comes from an objective and disinterested news source. Another is that it is the work of a sincere Josh Gottheimer fan who has intentionally or negligently blurred the line between personal opinion-writing and journalism. It might be something else entirely. But for the reasons above, I am skeptical that it is now a bona fide news outlet, if it ever was.
I reached out to the the Jersey Dispatch, the Gmail account, the Gottheimer campaign, and the Sherrill campaign. The Jersey Dispatch, the Gmail account, and the Gottheimer campaign did not respond to requests for comment. The Sherrill campaign acknowledged the inquiry but did not provide a statement for publication. I will update this post if I receive a response from any of them.
I have posted a new draft essay, Listeners’ Choices Online. It is a sequel to my 2017 essay Listeners’ Choices, and like that piece it was written for a symposium on listeners’ interests. This one was hosted by the Southern California Law Review in November, and the final version will come out in the SCLR later this year. Here is the abstract:
The most useful way to think about online speech intermediaries is structurally: a platform’s First Amendment treatment should depend on the patterns of speaker-listener connections that it enables. For any given type of platform, the ideal regulatory regime is the one that gives listeners the most effective control over the speech that they receive.
In particular, we should distinguish four distinct functions that intermediaries can play. Broadcast, such as radio and television, transmits speech from one speaker to a large and undifferentiated group of listeners, who receive the speech automatically. Delivery, such as telephone, email, and broadband Internet, transmits speech from a single speaker to a single listener of the speaker’s choosing. Hosting, such as YouTube and Medium, allows an individual speaker to make their speech available to any listeners who seek it out. And selection, including search engines and feed recommendation algorithms, gives listeners suggestions about speech they might want to receive. Broadcast is relevant mostly as a (poor) historical analogue, but delivery, hosting, and selection are all fundamental on the Internet.
On the one hand, delivery and hosting intermediaries can sometimes be subject to access rules designed to give speakers the ability to use their platforms to reach listeners, because doing so gives listeners more choices among speech. On the other hand, access rules are somewhere between counterproductive and nonsensical when applied to selection intermediaries, because listeners rely on them precisely to make distinctions among competing speakers. Because speakers can use delivery media to target unwilling listeners, they can be subject to filtering rules designed to allow listeners to avoid unwanted speech. Hosting media, however mostly do not face the same problem, because listeners are already able to decide which content to request. Selection media, for their part, are what enable listeners to make these filtering decisions about speech for themselves.
Comments welcome!
Let me see if I have this right.
By my reckoning, the FCC has treated broadband Internet as an information service, then a telecommunications service, then an information service again, then a telecommunications service again, and is now poised to treat it as an information service for a third time. At various times, federal appellate courts have held that the Telecommunications Act can be read to treat broadband Internet as a telecommunications service, must be read to treat broadband Internet as an telecommunications service, can be read to treat broadband Internet as an information service, and must be read to treat broadband Internet as an information service.
Is this any way to run an information superhighway?
Update, January 2: Corrected the description of the FCC’s 1998 report (I had it backwards) and added a better link.
