λ♥[love]

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According to Stan Carey at Sentence First:

λ♥[love] is written and sung by Christine Collins, a writer and self-described time traveller [Doctor Who fan] from the U.S. She describes it as “a convenient, terminology-dropping, non-gender-specific love song for all your linguist-seducing needs”.

You can find the lyrics in Stan's blog post, along with explanatory links ("denotation", "anaphor", "allophone", etc.). He doesn't explain the title notation λ♥[love], so I'll offer a brief note below. You can go to the Wikipedia article on the lambda calculus ("a formal system for function definition, function application and recursion") for a more complete and rigorous account.

The general idea is that if t is some expression that includes a variable x, then λx.t is a function that binds its input to the occurrence(s) of x in t. Thus λx.x is the identity function, and (λx.x)s is the identity function applied to s.

In Christine Collins' song title, the relevant term is symbolized by a letter-string ("love") demarcated by square brackets, and the variable being bound (to its putative occurence(s) in that term) is ♥.

Using a similar notation, we could write a function that adds 1 to its argument as λx[x+1].

Christine begins her song with these lines

Let me have your heart and I will give you love
The denotation of my soul is the above

So just as λx[x+1] is a function that we can define as "give me a number and I'll return that number incremented by one", so λ♥[love] is a function that we can define as "give me your heart and I'll give you love".



24 Comments

  1. Jonathan Badger said,

    May 14, 2011 @ 9:44 am

    I thought it was odd that you had this here because I only knew of lambda calculus in the context of computer science, but as both the Wikipedia article and the lyrics of the song seem to imply that it has implications for linguistics as well, care to expand on this?

    [(myl) The Wikipedia article on Montague Grammar has some links for further reading, especially Barbara Partee's encyclopedia article, which observes:

    Montague’s use of a richly typed logic with lambda-abstraction made it possible for the first time to interpret noun phrases (NPs) like every man, the man, a man uniformly as semantic constituents, something impossible with the tools of first-order logic. More generally, Montague’s type theory represents an instantiation of Frege’s strategy of taking function-argument application as the basic “semantic glue” by which meanings are combined. This view, unknown in linguistics at the beginning of the 1970’s, is now widely viewed as standard.

    ]

  2. Barrie England said,

    May 14, 2011 @ 9:55 am

    Writing in the style of the OULIPO, where literature meets mathetmatics, lives.

  3. John Cowan said,

    May 14, 2011 @ 9:58 am

    Both linguistics and computer science borrowed the terminology from logic, which should be no surprise. All three deal in things like syntax, semantics, variable bindings, scope, ….

  4. Laura said,

    May 14, 2011 @ 10:28 am

    As someone who had difficulty choosing between a career path in mathematics or one in English, I love this! Thanks for sharing–I've reposted. :)

  5. Nick said,

    May 14, 2011 @ 10:29 am

    Usually things with so much linguistic name-dropping make me cringe, but this song is indeed quite lovely. Agglutination has never seemed more sexy. (Lambda calculus is always sexy.)

  6. John Cowan said,

    May 14, 2011 @ 10:32 am

    [This comment transcluded from Sentence First]

    It is a sweet song. I was jolted, though, by the singer’s pronunciation of denotation. I have always had FLEECE in the first syllable, and OED2, ODO, and m-w.com all agree; however, she makes it DRESS. Anybody else say “den-otation” rather than “dee-notation”?

  7. λ♥[love] (Linguistics Love Song) « Sentence first said,

    May 14, 2011 @ 10:53 am

    [...] Mark Liberman at Language Log has written a short explanation of the title notation, i.e., lambda [...]

  8. X said,

    May 14, 2011 @ 11:50 am

    Technically, λ♥[love] takes a variable represented by the symbol ♥ and for any value of ♥ returns the constant value "love". You really want λx[λabc[abc](♥=x)(love)(¬love)]. Constructing a representation for ♥ in lambda calculus and from that constructing the function ♥= that determines whether a particular x is equal to ♥ is left as an exercise for the reader.

  9. Brett said,

    May 14, 2011 @ 12:15 pm

    @John Cowan: I certainly pronounce "denotation" the way she does, with first syllable DEN instead of DEE. However, my pronunciation of "denote" is much more variable. If I'm speaking carefully, it probably begins with "DEE," but sometimes I use the other vowel or a schwa.

    I suspect this is influenced by the sound of the contrasting term, "connotation," which is more common than "denotation" and which I certainly encountered first. By using a shorter vowel in the first syllable of "denotation," the later later syllables are made to match those of "connotation." For the verbs, "denote" is more common than "connote," so if there's any influence on how I pronounce them, it probably goes the other way.

  10. dl said,

    May 14, 2011 @ 12:42 pm

    With all due respect to Alonzo Church and his wonderful calculus, the words "non-gender-specific love song" had me recalling that λ is also a symbol embraced by the early gay movement.

  11. Barbara Partee said,

    May 14, 2011 @ 2:31 pm

    I love Mark's explanation of λ♥[love]; if I'd been asked to do it, I'd probably have gotten stuck on the absence of any occurrence of the bound variable ♥ inside the brackets. But after reading Mark I can see how the fact that it's a constant function is just a small bit of poetic license — "input to the function is your heart, output is love" — why not — that seems like a pretty decent rendering of give me your heart, and you'll get love. (Well, I know, not really, there's no "your" or "you" anywhere there, but honestly, as a kind of pedantic type myself, I'm nevertheless much happier with this lyrical version – it's liberating and fun.)

    So for what it's worth, I endorse Mark's explanation appreciatively. (And neither of us has paid the other for these mentions, honest!)
    I can't make heads nor tails of what X is trying to tell us. To even get started I'd need to see some "types" for the expressions, and I'd need to know whether abc is to be read as one variable or three separate ones, and how we're to interpret a sentential negation sign in front of a verb (if "love" there is a verb?). So far I doubt that there's any well-formed way to parse it or interpret it. I love lambdas and don't like to see people scaring other people away with them, which X might be doing.

  12. Ran Ari-Gur said,

    May 14, 2011 @ 7:53 pm

    @Dr. Partee: X is apparently using the (IME typical) formulation of logic described at http://en.wikipedia.org/wiki/Lambda_calculus#Logic_and_predicates, whereby if-then-else is expressed as λpab.p a b (p being a predicate, a being the value if p is true, b being the value if p is false); (s)he's using the symbols abc instead of pab, but the effect is the same. That function is then being applied with a being x=♥, b being love, and c being ¬love ("not love"? I guess it's what you're giving someone to whom you're not giving love?). So the expression as a whole is the function that maps from x to love or not-love, depending whether or not x equals ♥.

    His formulation doesn't seem to describe the song accurately, though, in that the lyrics don't explicitly say that no-heart means no-love, and in fact rather imply that the love might not actually be all that conditional on the heart!

  13. J Lee said,

    May 15, 2011 @ 3:26 am

    so the song title does not contain a weird palatal sound? o_o

  14. Rubrick said,

    May 15, 2011 @ 5:25 am

    You can lead a lambda calculus….

  15. Barbara Partee said,

    May 15, 2011 @ 7:26 am

    @Ran Ari-Gur, thanks! I see; I only knew the version of the lambda calculus that linguists use, not that combination with if-then else 'built in'. Then it makes sense, because X was objecting to the fact that the original is a constant function, and suggesting that the author really meant his formulation instead. We can agree or disagree; at least I'm glad to know it is indeed a well-formed suggestion.

  16. Ray Dillinger said,

    May 15, 2011 @ 10:58 am

    I know lambda calculus from computer science. In most CS papers, an if/then/else construction is assumed (though several take the time to define it in terms of lambda calculus, hardly anybody does without it). Also included are equality predicates and mathematical operators. These are never directly defined in lambda calculus; the interested are referred to the Church papers in the bibliography.

    It's a sweet song. I'm liking it.

    My observation is that Englishmen and West-coast Americans have been heard saying Den-otation and Midwestern Americans have been heard saying Dee-notation. I usually say the former.

  17. Mary Bull said,

    May 15, 2011 @ 4:11 pm

    This Mary, a Southern gal, says "denotation," as in "a den of notations." (Well, making the single "n" do double duty, that is.) A Dr. Who fan, myself, I love the whole idea of these lyrics and the song title, and I thank you very much for this post, Dr. Liberman,

  18. m.m. said,

    May 15, 2011 @ 4:21 pm

    I can use either for 'denotation'; 'denote' is never 'dee' though, and now I'm biased for non 'dee' denotation.

  19. EwaG's said,

    May 15, 2011 @ 11:30 pm

    I think "X" got it right. If I'm not mistaken "λ♥[love]" means "give me *anything* [syntactically represented by symbol "♥"] and I'll give you love in return." E.g. "Give me a sexually transmitted disease and I'll give you love."

    Oh well… It's the thought that counts. Anybody want to agglutinate?

  20. Jon Hanna said,

    May 16, 2011 @ 6:51 am

    Though λ has also been used as a symbol of the lesbian community, allowing for the reading "lesbians love love", which I'm sure they do, but such a reading is no longer as non-gender-specific as intended.

  21. CSC said,

    May 17, 2011 @ 6:19 pm

    Before clicking the RSS link I assumed it was the chinese character 入 (ru4, enter), rendering the title enter heart (love), and that the article would focus on the heart substitute for 心, perhaps noting the omission of 心 from the simplified version of 爱(love). This is much geekier, thanks.

  22. Hugh Buckingham said,

    May 31, 2011 @ 7:01 pm

    On the slant grammar calculus and its lambda notation, why is it that the Aristotelian physiology of the location of certain mental states is still claimed to be the cardiac muscle. Surely, Plato would have preferred you to say "I love you with all my brain." Or, even more generally, "I learned all the lines by brain." Learning, memory, and mental states of the stuff of the brain and not of the heart. I almost did not have the heart to tell you guys this.
    Hugh Buckingham

  23. Crabbadon said,

    December 12, 2011 @ 2:21 pm

    I was taking love to be a complex formula, which I believe would allow the description "The function which binds all ♥ in love"

  24. Do re mi – Linguistics Love Song | Me and my challenges said,

    July 1, 2013 @ 7:46 am

    [...] can listen to it here (and read the lyrics with some explanations) and this blog explains the [...]

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