Glossographia

Jim Lambek, 1922-2014

I learned the sad news today that the mathematician Joachim Lambek (Jim to all of us who knew him) passed away yesterday at the age of 91. Jim was one of my mentors and an external committee member for my Ph.D. Jim will be known to mathematicians (of whom I suppose relatively few if any will read this blog) for his many articles in formal subjects far beyond my knowledge or ability, but also as a warm and generous scholar.

I came to him in a rather roundabout way; in discussions with my advisor, Bruce Trigger, he suggested to me that if I really wanted to do this numbers thing, then I should have a mathematician on my committee just to make sure I wasn’t mucking things up too badly. As it turned out, I was very fortunate that Jim was at McGill, as he was a major pioneering figure in applying mathematical methods to linguistics (1958, 1979), had written several pieces on the analysis of kinship systems using techniques pioneered by, for instance, Floyd Lounsbury, had also published anthropological material with his son Michael (who I later met at the University of Toronto) (Lambek and Lambek 1981), and was also the co-author of a superior undergraduate text on the history of ancient mathematics, The heritage of Thales (Anglin and Lambek 1995). At our first meeting I must have seemed such the infant, but he graciously passed me an offprint of his recent paper ‘A rewrite system of the Western Pacific’ (Bhargava and Lambek 1995) and suggested that we could have some future discussions, which we did. His impact on Numerical Notation and on my work as a cognitively-oriented linguistic anthropologist is subtle but great. I am hardly the sort of person who can summarize his much broader impact on his home discipline, except to say that he will be missed.

Anglin, WS, and Joachim Lambek. 1995. The Heritage of Thales. Springer.
Bhargava, Mira, and Joachim Lambek. 1995. “A rewrite system of the Western Pacific: Lounsbury’s analysis of Trobriand kinship terminology.” Theoretical linguistics 21 (2-3): 240-253.
Lambek, Joachim. 1958. “The mathematics of sentence structure.” American mathematical monthly:154-170.
Lambek, Joachim. 1979. “A mathematician looks at Latin conjugation.” Theoretical Linguistics 6 (1-3):221-234.
Lambek, Joachim, and Michael Lambek. 1981. “The kinship terminology of Malagasy speakers in Mayotte.” Anthropological linguistics:154-182.

A new look

As you will see (at least, if you view the site on the WordPress page as opposed to on an aggregator or somewhere else), I have changed the theme and layout for the site. Hope you like it – any theme is going to have its advantages and disadvantages. Frankly I was getting annoyed at the small text size and plainness of the old theme, which had been around since the blog’s inception in 2008. This one has larger text and is more modern, and the main headings are larger and clearer (now at the left sidebar). Comments and criticisms are welcome, bearing in mind that this is a free WordPress site so my options are somewhat limited.

XLent LInguistics

As was correctly answered in the comments to the previous post, I am now 40 years old (XL) and the next time that my age in Roman numerals will be the same length as my age in Western (Hindu-Arabic) numerals will be when I am 51 (LI). 49 is not a correct answer in this case because the Romans did not habitually use subtraction in this way; irregular formations like IL (49) and XM (1900) do sometimes occur irregularly, but normally one cannot ‘skip’ a power. I can only be subtracted from V and X; X can only be subtracted from L and C; and C can only be subtracted from D and M.

As any schoolchild can tell you, one of the purported disadvantages of Roman numerals is that their numeral-phrases are long and cumbersome (e.g., 37 vs. XXXVII). And of course, for many numbers that is true. But for many other numbers (e.g., 2000 vs. MM) the Roman numeral is equal in length or shorter than its Western numeral counterpart. Note, in particular, that round numbers tend to be those that are shorter in Roman numerals; this is because, since the Roman numerals don’t have a 0, that numerals that in Western notation would have a 0 have nothing in their Roman counterpart.

Among numbers whose Roman numeral and Western numeral notations are exactly the same length, there doesn’t initially appear to be much of a pattern:

1, 5, 11, 15, 20, 40, 51, 55, 60, 90, 102, 104, 106, 109 …

but then we see a new sequence emerge –

111, 115, 120, 140, 151, 155, 160, 190 …

which are just the numbers in the sequence from 11-90 with an added C on the front, which makes sense, since you’re just adding a 1 in front of them, similarly.

You could be forgiven in thinking that these numerals come up frequently, since we’re in the midst of a giant cluster of years with this property –

… 2002, 2004, 2006, 2009, 2011, 2015, 2020 …

but then after that, it’s another 20 years before 2040.

Unsurprisingly, numerals containing 3 rarely have equal-length Roman equivalents and numerals containing 8 never do. So once you get past 3000, these numbers become extremely rare. Roman numerals don’t have a standard additive representation for 4000 and higher; you can write 4000 as MMMM, but normally one would expect a subtractive expression with M (1000) subtracted from 5000. There are Roman numerals for 5000, 10000, 50000, 100000, etc., but they are extraordinarily rare, and the Romans during the Empire instead tended to place a bar (or vinculum) above an ordinary Roman numeral to indicate multiplication by 1000; thus, IV=4000. The addition of this feature creates a real conundrum: does the vinculum count as a sign or not? If it does, then IVI=4001 has four signs; if not, then IVII=4002 does.

I’ll leave this aside and stop here to save all of our brains. Thanks for playing!

An ‘excellent’ puzzle

Yesterday was my birthday. For the first time in twenty years, the Roman numeral and the Hindu-Arabic numeral for my age are the same length. How old am I, and when will this happen again?

Edit: As noted correctly in the comments, I am now 40 (XL) and the next time will be when I am 51 (LI).

Language and Societies abstracts, vol. 6 (2014)

The abstracts below are summaries of papers by junior scholars from the 2014 edition of my course, Language and Societies, and presented at the course blog of the same name. The authors are undergraduate and graduate students in anthropology and linguistics at Wayne State University. Over the next few weeks, some students will be posting links to PDF versions of their final papers below their abstracts. Comments and questions are extremely welcome, especially at this critical juncture over the next week, when the authors are making final revisions to their papers.

Alex B. Hill: A critical discourse on Detroit’s ‘Food Desert’ metaphor

Maya Stovall: How Ballet Terminology is Disputed and Employed as the Language of Dance

Roba Hrisseh: Social Stigmas Attached to Dialectal Differences: Lebanese and Yemeni Dialects in Dearborn City, Michigan

Suzanne Walsh: The Car Becomes Me

Kyrene Collins: Color Terminology in English and French

Srinawati: Sundanese Speech Levels

Eric Boulis: Klingon as Reviewed by the Fans

Taylor Monday: Sustainability: Defining Something that Deals with Everything

Zeina Lubus: English and French code-switching – an index to Christianity and Islam in modern Lebanon

Kaitlyn Ahlers: “Bold, Brash” Brews: Sensory Description among Craft Beer Consumers

Rachel Willhite: Gender Perspectives and Prediction in Online Communication

C. Lorin Brace VI: Together Forever: Gendered Language Use in Gravestone Epitaphs