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I don’t want to abandon you!
Send to KindleAbouot twenty years ago I went to Reed College in Portland, Oregon to give a talk at a computer science meeting. As I walked onto campus, a gardener looked up and said “Howdy”. I thought that was a stereotype, but I guess they really do say that in the west. (Australians really say G’dye Myte, too.)
Then I saw a sign pasted on a wall:
VISUALIZE INDUSTRIAL COLLAPSE
Message to Reed College: All right, you’ve done that, now visualize World Peace, please.
Send to KindleMany middle class Americans over seventy grew up hearing and singing to a pipe organ on Sundays. Far, far more young people have heard electronic keyboards than have heard pipe organs. I have an acquaintance who trained as a pipe organist who now plays for two churches on Sunday. In at least one of them he plays a keyboard (I don’t know about the other). He hates it when people tell him how wonderful his keyboard playing is. This is not the real thing, and you have never heard a real organ and you have no conception of how tacky a keyboard sounds compared to the real thing! (He also would not like it that I wrote “pipe organ”. “Organ” ought to mean what it always meant!) (See Note). He is witnessing a change in the world and he doesn’t like it.
I once attended a discussion in an Episcopal church that featured a progressive churchman and a traditional churchman in a discussion. Being one of the usual Anglican it’s-all-wonderful but-not necessarily-literally-true people, I was really wanting to hear what the traditionalist would say. Well, his argument was just like my friend the pipe (sorry) organist. For one thing, he made a vehement defense of King James English. In particular that the distinction between “thou” and “you” was important: “Thou” was the form you used with family and close friends and — God! That meant something and modern translations lose the distinction.
Well, I was disappointed. All his arguments were railing against the world changing, which means they weren’t arguments at all but merely venting at the world going to hell.
I’ll conjecture that not one American in 500 knows about the familiar-formal distinction between thou and you in 16th century English, and those who are familiar with “thou” in religious usage think it is something highly formal because after all it is used for God! (See note 2.) This completely reverses the point of the traditionalist who was saying that the use of “thou” means we are addressing God like someone close, like a friend or a member of the family. Must have been as irritating as hearing someone praise your playing an electronic keyboard when they have never heard an organ.
Now, I love language and I love King James English, not least because I grew up with it. But it is dead. I love singing in Latin, too. And anyway, if you want something like King James English that is a living language, try German. It has lots of those old distinctions and more that King James never heard of. KJ me no KJ, try Luther’s translation if you want old style language!
Note 1: Years ago my father got upset when I referred to a car with a bench seat. When he found out what I meant he was annoyed. That’s what you call a seat. The rise of bucket seats had left him behind. I knew someone else who dislikes “acoustic guitar” for similar reasons. And wait till the greenies get told that sea salt is inorganic.
Note 2. There are churches here and there with names like “Thee Greater Blessing Church of God.” (An example.) That’s taking confusion to a new level.
Send to KindleMy favorite current mystery novels are the Brodie Farrell mysteries by Jo Bannister. One character is a high school math teacher (as Americans would call him) named Daniel Hood. Here are some things he says about math in Breaking Faith:
“Numbers are different. Numbers I can do. There are no nuances, no room for debate. They always and only mean one thing: you can’t twist them to mean something else… (page 63).
“Look, I’m a mathematician. I’ve never had an original thought in my life. I can’t imagine how you create something entirely new…” (page 116).
Daniel is expressing a widely-held attitude, but he is wrong. Mathematical research does have a place for applying a known method to a problem that obviously can be solved in that way. But math usually requires more creativity than that.
Most research papers fit (1) or (2). They both involve what I would call minor-league creativity and can get your paper published. (3), (4) and (5) can get you wide recognition in your field. In exceptional cases you may receive one of the several prizes awarded to mathematicians (Fields medal, Wolf prize). Then many mathematicians outside your field will have heard of you.
When you do serious math research you always find yourself thinking of the objects involved in many ways. (For example, if you “twist” the meaning of complex numbers to be vectors in 2-space then you get the Argand representation, which makes some baffling things about complex numbers obvious.) You cannot do serious math without having several metaphors for each object in your head at once.
Jo Bannister may have been putting her understanding of math in Daniel’s mouth. Or she might think that many high-school math teachers think that way even though she knows better. For all I know, many high-school math teachers do think that way.
Send to KindleI have been recovering from a hospital stay. I probably won’t contribute anything to this blog until some time in January.
Charles Wells
Send to KindleMass nouns seem to be rare in math writing. I have done a little poking around the math journals in JStor and have several observations to make. All are tentative observations based on a small amount of evidence (and thinking).
“Space” as a mass noun
“Space” as a mass noun was common before WWII but is rare now. A search for “in space” (in quotes to make it the phrase that is searched for) gives mostly references to outer space and to very old papers, mostly before 1930. Conjecture: The disappearance of mass nouns in math writing is a consequence of the rise of structural thinking in math.
One recent paper where “space” occurs seemingly as a mass noun, in the title no less, is: F. W. Lawvere, Categories of Space and Quantity, in J. Echeverria et al. eds. The Space of Mathematics: Philosophical, Epistemological and Historical Explorations, DeGruyter, Berlin (1992), 14-30. However, the word “space” appears as a mass noun only once in the body of the paper (according to my hasty scan) and many times as a count noun. Anyway I am not sure it is being used as a count noun in the title. It is paired with “quantity”, which is surely an abstract noun, not a count noun.
Areas of math as mass nouns
Areas of math are commonly used as mass nouns, for example, “Using calculus, we see that the function has one maximum”, or “the result follows by straightforward algebra”. The language of math contains several sublanguages with different uses (symbolic language, rigorous language, “rich” language) and one of them is the metalanguage used for talking about doing math, as those examples surely are.
Mass nouns and plurals
In the paper La Palme Reyes M., Macnamara J. and G. E. Reyes (1999). Count nouns, mass nouns and their transformations: a unified category-theoretic semantics, in Language, logic and concepts: Bradford Book, MIT Press, Cambridge, Ma, 1999, pp 427-452, the authors say that plural nouns are mass nouns, in fact they are the free mass nouns corresponding to count nouns under the adjunction developed in that paper. (The Wikipedia article on mass nouns doesn’t seem to regard plurals of count nouns as mass nouns.) Now plurals are mass nouns with atoms (like “furniture” rather than like “water”). Of course, plurals occur all over the place in math writing. Conjecture: In rigorous math prose the only mass nouns that occur are plurals, or at least are mass nouns with atoms.
I am suspicious of the way Reyes, Macnamara and Reyes smush together mass nouns with atoms (furniture) and mass nouns without atoms (water). (“Atom” means in the lattice of parts. “Some of my furniture” can include a bed and two tables, but not the leg of a table. “Water” is treated in language as if it were infinitely divisible. Of course it really does have atoms in the physical sense.)
These two kinds of mass nouns behave differently in many ways. The most important is that plural nouns can refer to either distributive plurals or collective plurals. (“All groups have identities” is distributive, “the voters were in favor of the proposition” is collective.) I doubt that these different kinds of mass nouns constitute a natural grammatical class.
Send to KindleIn gyre&gimble I will comment on ideas that occur to me, centering around math and language but not limited to that. This is a revival of a blog I ran a few years ago and I expect to repost here a few of the postings from the former incarnation.
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