Weston High School is pleased to announce a new series of talks for the whole community led by our esteemed faculty members on a broad array of topics and expertise that extend outside the classroom!

My talk was called “Making Order Out of Chaos: A Conversation about Linguistics.” We had 53 attendees, an excellent turnout for a fairly technical presentation, and I was delighted by the audience’s enthusiastic response. Everything went very well, though we ran out of time near the end and I had to skip a [...]]]> Yesterday evening I delivered the first lecture in our new Beyond the Classroom series, described as follows:

Weston High School is pleased to announce a new series of talks for the whole community led by our esteemed faculty members on a broad array of topics and expertise that extend outside the classroom!

My talk was called “Making Order Out of Chaos: A Conversation about Linguistics.” We had 53 attendees, an excellent turnout for a fairly technical presentation, and I was delighted by the audience’s enthusiastic response. Everything went very well, though we ran out of time near the end and I had to skip a detailed slide that would have added ten more minutes. I also promised the audience that I would post my list of recommended resources right here. The missing slide needs some considerable commentary — it’s definitely not a standalone piece — so let’s start with the recommended resources (four books, three websites):

• Hofstadter, Douglas. Gödel, Escher, Bach: An eternal golden braid (Basic Books, 1999)
• Jackendoff, Ray. Patterns in the mind: Language and human nature (Basic Books, 1995)
• Pinker, Steven. The language instinct: How the mind creates language (Harper, 2007)
• Yang, Charles. The infinite gift: How children learn and unlearn the languages of the world (Scribner, 2006)
• Ethnologue (www.ethnologue.com)
• Language Log (languagelog.ldc.upenn.edu/nll)
• Popular Linguistics (popularlinguisticsonline.org)

I also recommended Wikipedia as a rich source of surprisingly reliable information about linguistics (and math), even though one wouldn’t want to trust it for areas like history, politics, and biography.

The slide I had to skip was a summative list of some of the various branches of linguistics. My plan was to build it up line by line. Here is the finished result, where the black type represents notes on my intended commentary:

Here is that intended commentary:

The list goes from the smallest level of detail to the largest level to the biggest picture. For example:

• Phonetics is the study of individual speech sounds. I already talked about Turkish vowels, where we had descriptions like “high back rounded vowel.” Through phonetics you can learn about how a French accent differs from an Italian one, or how automated speech recognition is possible.
• Phonology is the study of speech sounds in context, such as which pairs of sounds can distinguish words in a particular language (or dialect). For example, the words merry, marry, and Mary are all clearly distinct to my New Jersey ears, but my wife hears them as identical. (She comes from far western New York state.)
• Morphology (yes, I know, I’ve skipped one) is the study of how the components of words are put together. Examples include things like plural suffixes, tense markers, etc.
• Morphophonology (now we can back up) is the bridge between phonology and morphology, as you might expect. For instance, although the plural in English is usually spelled with an “s,” it is sometimes pronounced like a “z.” Why? And when? Similarly, Turkish /ler/ vs. /lar/ or English past tenses in /d/ vs. /t/.
• Syntax is the study of how words are built up into phrases and phrases are built up into words. (Gee, just like math, isn’t it? Terms are built up into expressions and expressions into equations…) Examples include my discussions of basic sentence order, such as SVO, transformations of basic order, and the ways tenses are formed in languages like Chinese that don’t use morphology (suffixes, etc.).
• Semantics is the study of meaning. For example, Chomsky’s famous sentences, “Colorless green ideas sleep furiously,” is syntactically impeccable but semantically anomalous.
• Pragmatics is the study of how language is actually used in practice. For instance, when a student comes into the Math Office and asks, “Do you know where Mr. McLaughlin is?” I may decide to be an obnoxious mathematician and say “Yes.” Of course that is not truly responsive to the intended meaning, even though it is literally correct.
• Finally, there are many subfields such as historical linguistics, comparative linguistics, etc. And there are interdisciplinary fields in which linguistics is combined with other disciplines, such as psycholinguistics, sociolinguistics, computational linguistics, etc.

Making order out of chaos: A conversation about linguistics

“Linguistics? What’s that?” This is the usual response I get from students when they hear that I majored in linguistics.

“It’s the scientific study of language,” I reply. “Linguists look for patterns, solve puzzles, develop hypotheses, and test those hypotheses.”

BSP^*: Come hear my talk on linguistics at 7:00 PM on Tuesday, February 1, at the Weston Public Library! Here’s a description:

Making order out of chaos:
A conversation about linguistics

“Linguistics? What’s that?” This is the usual response I get from students when they hear that I majored in linguistics.

“It’s the scientific study of language,” I reply. “Linguists look for patterns, solve puzzles, develop hypotheses, and test those hypotheses.”

As an example, let’s examine some data from Kurdish, a language you probably know nothing about, even though it’s spoken by over 16 million people. (Yes, you’ve heard of the Kurds in Iraq, but do you know anything at all about their language? No? I thought not. I don’t either — but I know what to look for.)

---

Here are six sentences in Kurdish, along with their English translations in the wrong order. Try to match them correctly.

1. Ez h’irç’ê dibînim. 2. Tu dir’evî. 3. Tu min dibînî. 4. H’irç’ di’eve. 5. Ez dir’evim. 6. Tu h’ireç’ê dibînî.

A. You see the bear. B. You see me. C. The bear runs. D. You run. E. I see the bear. F. I run.

---

Could you figure out the puzzle? If so, translate the sentence “H’irç’ mîn dibîne” into English. What did you learn from trying to solve this puzzle? Some of my students noticed that the word “tu” closely resembles a word in Spanish, French, and Latin. Is this just a coincidence? Why on earth should Kurdish resemble these far-away languages?

Maybe there’s a reason…

At Weston High School we care about global awareness. Linguistics reinforces that awareness. How does it happen that the Irish and the Pakistanis speak related languages, even though their countries are so far apart? Why do the Austrians and the Hungarians speak unrelated languages, even though their countries are next to each other? How do linguistic connections relate to other sorts of connections?

We can also learn a lot right at home. English too is a world language. You’re probably fluent in English, but you may be surprised to hear that it isn’t true that the vowels of English are a, e, i, o, u, and sometimes y. Why not? Doesn’t every language have the same vowels? The answer is “no.” We’ll talk about why the question itself is misleading.

Is there anything that all languages share? This time the answer is “yes.” We’ll look at some examples and their significance.

Finally, you may be wondering how and why a linguist became a math teacher. Does linguistics really have anything to do with math? Come to this talk, and you’ll learn a lot about linguistics, a little about math, and at least one Big Idea about the strange connection between the two.

*Blatant self-promotion

Since this is Weston, I would prefer to believe it’s #1…but I have to admit that it might be #2, even in Weston.

Of course we shouldn’t just throw around the claim that certain names are incorrect without producing an argument for what the correct names are. Some of my students want to look in Wikipedia or [...]]]> Why do so many of my students use incorrect names for various polygons? They claim that they are merely recalling what they have been taught; maybe this is so, maybe not.  I suppose there are two major possibilities:

1. They are remembering incorrectly.
2. They really were taught incorrectly.

Since this is Weston, I would prefer to believe it’s #1…but I have to admit that it might be #2, even in Weston.

Of course we shouldn’t just throw around the claim that certain names are incorrect without producing an argument for what the correct names are. Some of my students want to look in Wikipedia or count Google hits, but those methods lead to popularity contests, not truths. As I said in an earlier post, you can usually trust Wikipedia for mathematical information, but names occupy a middle ground between math and English, so Wikipedia is less reliable in this case than with pure math. As a better starting point,  here is Wolfram Mathworld’s reasonably authoritative list of names for polygons with n sides:

Let’s see what we can do with this list. I make the following observations:

• The very existence of a two-sided polygon sounds doubtful to most people. We’ll  discuss this one below.
• Three- and four-sided polygons, being the most common ones, commonly have Latin names (triangle and quadrilateral), even though there are also alternative Greek names, which are very rarely used.
• All other polygons have Greek names. Therefore nobody ever calls a six-sided polygons sexagon or sextagon, and nobody calls a seven-sided polygon septagon, no matter what my students claim.
• For some mysterious reason, the 11-sided polygon is listed here not only as hendecagon (the correct name, from the Greek hendeca, meaning 11), but also with an incorrect alternative Latin-Greek name, undecagon. I see no reason to do this. In fact, another Wolfram Mathworld page makes this observation:

A hendecagon is an 11-sided polygon, also variously known as the undecagon or unidecagon. The term “hendecagon” is preferable to the other two since it uses the Greek prefix and suffix instead of mixing a Roman prefix and Greek suffix.

• Somewhat similarly, but worse, the 9-sided polygon is listed in both the Greek form, enneagon, and the hybrid, nonagon — but here Mathworld oddly prefers the Latin-Greek hybrid to the pure Greek. On their other page, however, they make this observation:

The nonagon, also known as an enneagon, is a 9-sided polygon. Although the term “enneagon” is perhaps preferable (since it uses the Greek prefix and suffix instead of the mixed Roman/Greek nonagon), the term “nonagon,” which is simpler to spell and pronounce, is used in this work.

Even though counting Google hits is a useless way to decide these issues, let’s check them out just for fun:

• 14,900 hits for “hendecagon”; 12,400 for “undecagon.” Hooray!
• 18,400 hits for “enneagon”; 69,500 for “nonagon.” Boo, hiss!

Oh — I also promised a discussion of two-sided polygons, didn’t I? Most people think they don’t exist, so they don’t need to be named. (Unicorns don’t exist, but they still have a name. Hmm….) Actually, however, they do exist: for example, start at the North Pole, draw a line segment along the prime meridian until it reaches the South Pole, and then draw another line segment from the North Pole along the 90° longitude line, also stopping at the South Pole. Voilà: a two-sided polygon! You may think I’ve cheated, since this polygon exists on the surface of a sphere, not on a plane, but it might be worth imagining that you lived on the surface of a sphere, not on a plane… Anyway, I’ve never heard the term digon before; I’ve seen biangle and bigon, however. Be sure to pronounce bigon with a long i, and think of the famous saying, “Let bigons be bigons.” Again we can check Google hits, useless though it may be: 14,600 hits for “digon,” 487 for “biangle,” and 7,330 for “bigon.” Even though “biangle” loses the popularity contest, I suspect that it’s the best choice, since it’s consistent with the general principle: use Latin names for polygons with four sides or fewer, Greek names for those with more than four sides, and hybrid names for none.

“Lost in Lexicon is the title of a new book by Penny Noyce, a neighbor of yours from Weston,” I replied.

“Someone in Weston wrote a book????” was her astonished response.

I assured her that there are plenty of people in Weston who have [...]]]> If you regularly see my Facebook status in your News Feed, you may have noticed that it said “I’m lost in Lexicon right now…” on October 17. This status confused some of my students. One of them asked, “How did you get lost in Lexington?” (Apparently he isn’t a very careful reader.) Another student asked me what it meant:

“Lost in Lexicon is the title of a new book by Penny Noyce, a neighbor of yours from Weston,” I replied.

“Someone in Weston wrote a book????” was her astonished response.

I assured her that there are plenty of people in Weston who have written books.

Anyway, Lost in Lexicon: An adventure in words and numbers is indeed the title of a new book by Penny Noyce. It’s a work of fiction, somewhat in the spirit of The Phantom Toolbooth, aimed at readers in middle school (in my judgment). Of course the real reason I had to get a copy was not that the author lives in Weston (and is the mother of three of my former students), but that the focus of the book is words and numbers, as the subtitle shows. What could be a better combination?

If you know children of the appropriate age (or older, for that matter), suggest this book to them. It’s both fun and informative, and should enhance or kindle interest in both math and language.

Or is the problem the lack of a hyphen? Of course the phrase is supposed to be “daylight-saving time,” i.e. a time that saves daylight, where “daylight-saving” is used as an adjective (OK, technically it’s a participial phrase in which “daylight” is the direct object of the present participle “saving,” but it’s still used adjectivally). Things [...]]]> Why is it that so many people say “daylight savings time” when the correct phrase so clearly is “daylight saving time”???? Do they think it’s like a savings account, where you put an hour of daylight in at one time and withdraw it at other?

Or is the problem the lack of a hyphen? Of course the phrase is supposed to be “daylight-saving time,” i.e. a time that saves daylight, where “daylight-saving” is used as an adjective (OK, technically it’s a participial phrase in which “daylight” is the direct object of the present participle “saving,” but it’s still used adjectivally). Things would be so much easier if we only spoke Latin.

My closely related rant is about the many people who think that the end of DST (now November, formerly October) is actually the beginning! The reason that this is (or may be) closely related to the phenomenon described above is that those who don’t understand the adjectival nature of  “daylight-saving” also don’t understand that it’s what the Brits call “summer time.” Of course you could argue that no daylight is actually being saved in this process; it’s just shifted from one end of the day to the other during the summer. But the theory is that you lose an hour while you’re asleep and gain an hour while you’re still awake, thus saving daylight for your waking hours.

OK, enough of that. You may now return to your regularly scheduled activities.

Teacher 1: I hear that you friend your students on Facebook.

Teacher 2: Not exactly. I accept friend requests from current and former students. But I never initiate them.

Teacher 1: Even so, it’s a really bad idea. They’ll see all sorts of personal things about you. You could get into a lot of trouble for this. Besides, you’re not their friend — you’re their teacher !

Teacher 3: Au contraire, mon frère. Teacher 2 doesn’t put personal things on Facebook. It’s a good thing to have connections with your students outside of school. And anyway, don’t you know [...]]]> Listen in on this conversation:

Teacher 1: I hear that you friend your students on Facebook.

Teacher 2: Not exactly. I accept friend requests from current and former students. But I never initiate them.

Teacher 1: Even so, it’s a really bad idea. They’ll see all sorts of personal things about you. You could get into a lot of trouble for this. Besides, you’re not their friend — you’re their teacher !

Teacher 3: Au contraire, mon frère. Teacher 2 doesn’t put personal things on Facebook. It’s a good thing to have connections with your students outside of school. And anyway, don’t you know that “friend” doesn’t really mean “friend” on Facebook?

OK, what’s going on here? This is a composite conversation, but not a fictional one. I’ve been in the roles of Teachers 2 and 3. Let’s dissect three very different points of view about this issue. The first is exemplified in a recent misguided editorial in the Boston Globe, headlined “Teachers: Friends, not ‘friends’.” Here is an excerpt:

A new policy enacted by the Norton school board that bans teachers from becoming Facebook friends with students on social media sites is a simple lesson in common sense.

…

Some argue that the policy interferes with free speech and assembly rights. Others contend that teachers and students should communicate more, not less. At the college level, that may be true. But from kindergarten to high school, teachers should not need social media to reinforce their lesson plans. If a student has questions outside the classroom, email provides sufficient connection.

What we have here is a fine example of a straw-man argument. Who said that teachers “need social media to reinforce their lesson plans”? The Globe has simply invented a point of view from an imaginary opponent in order to argue against it. The issue isn’t whether we need social media; it’s simply whether it’s acceptable to accept friend requests.

Part of the problem here is the ambiguity of the word “friend.” Facebook users certainly understand the two meanings of the word. Only a naive adult could possibly confuse the two meanings. Only a naive adult could believe that a student who friends me really thinks that I’m his friend in the usual meaning of the word. Many Facebook users have a ridiculous number of “friends”; while I have only 152, one of my former students has 3187. But no one could plausibly think that she considers 3187 people to be actual friends!

I promised three very different points of view. The first one says that accepting friend requests from students is inappropriate; the second says that it’s OK; the third says that it’s something that teachers should do. (As an aside, note that many behaviors can be viewed as this sort of trichotomy. Pick a behavior; you can prohibit it, you can stay neutral, or you can encourage it.) The third point of view came to my attention twice in the past month. The first time was an article in Education Tech News, concerning the principal of All Saints Central School in Michigan. Here is an excerpt:

Principal John Hoving…said he uses Facebook to:

• promote the school
• connect with alumni, and
• increase communication with parents.

Hoving also friends students who send him friend requests. As a result, some parents and students have accused him of using Facebook to monitor students’ online activity.

Notice the not-so-subtle use of the verb “accused” in the last sentence. The article goes on to show why it’s completely the wrong word choice. In reality, the majority have commended him for this connection. (Note that Hoving, like me, accepts friend requests from students but doesn’t initiate them.) Read the follow-up:

Hoving pointed out that students do not have to send him friend requests, but if they choose to — he accepts.

Hoving says if he happens to see students posting questionable content in public forums, he feels it is his responsibility — as a concerned adult — to help students understand the potential consequences of their digital activity.

Several parents and students spoke out in support of Hoving, saying they are fine with his efforts to “look out for” everyone at school.

…

Richard Guerry, executive director of the Institute for Responsible Online and Cell-phone Communication (IROC2)…posed an intriguing question: Would parents who have an issue with the principal’s actions really want him to ignore potential problems — especially when he has an opportunity to protect their children before something happens? Hoving should “be commended for caring and protecting his students,” according to Guerry.

The second time I heard this view in the past month came in a conference with the parent of one of my students. She said that she insisted that her teenage children had to friend her, just so she could monitor what they’re putting on Facebook. (Yes, I know, the privacy settings complicate this claim, but it’s still a good idea.) For similar reasons she was pleased that they friend their teachers. We talked about the anonymous Teacher 1 in the dialog above (who remained anonymous, of course), and both of us agreed that there’s a simple solution to the problem of not wanting students to see inappropriate personal information about teachers. The solution is for teachers to follow the same advice that I give to students: don’t post anything that you don’t want the whole world to see! It’s called the World Wide Web for a reason. Privacy is an illusion these days; when something is too personal for your teachers to see (if you’re a student) or too personal for your students to see (if you’re a teacher), then don’t post it! That’s my policy, and it should be yours.

In conclusion, I have to say that I suppose there’s actually a fourth point of view: that teachers should initiate friend requests. But I don’t hear anyone arguing for that.

Obviously I’m firmly with Hoving and Gerry on this issue. The Norton School Committee and the Boston Globe are badly off-base.

First of all, it’s absolutely essential to see it in 3-D, preferably in IMAX. The three-dimensional effects were absolutely convincing, especially in the outdoor scenes, giving the viewer the sense of being in the action rather than watching the action. The result was a thoroughly entertaining, amazing film. I was totally absorbed by it, having no trouble sitting for nearly [...]]]> What more can I add to all the chatter about James Cameron’s Avatar? Not much, except to share my opinions. You probably already know all that you need to know about this movie, and I certainly don’t want to include any spoilers.

First of all, it’s absolutely essential to see it in 3-D, preferably in IMAX. The three-dimensional effects were absolutely convincing, especially in the outdoor scenes, giving the viewer the sense of being in the action rather than watching the action. The result was a thoroughly entertaining, amazing film. I was totally absorbed by it, having no trouble sitting for nearly three hours. (The Tempur-Pedic seats definitely helped! I guess that’s one of the benefits of seeing a movie in a theater that’s located in a furniture store.)

The linguistically sophisticated artificial language of the Na’vi was of course of interest to me, though it was really a minor part of the movie. Although the three-dimensionality allowed subtitles to hover well in front of the action — thereby making them less intrusive than they would be otherwise — it was still appropriate for Cameron to use the device of having the main Na’vi characters be more-or-less capable speakers of English as a second language. Doing so allowed him to get away with minimal use of subtitles. Perhaps I’ll write a follow-up post concerning their own language .

I was surprised to see some little kids at this showing (early Sunday afternoon). Either their parents had no idea that there would be so much violence, or they didn’t care. Avatar is basically a war movie, after all, so they should have cared.

As a war movie, it included every cliché in the book, and therein lies its major flaw. The flaw isn’t the lack of originality; I discount critics who observe that this movie has been made before. Yes, the theme and story line are taken from other efforts, but so what? It’s commonplace for plays and films to do this; even Shakespeare took story lines from elsewhere. No, the flaw is the piling on of cliché after cliché. Fortunately the action and the visual effects are so stunning that it’s almost possible to ignore this problem, but “almost” isn’t good enough. As an unsubtle metaphor for the Europeans’ destruction of American Indians and their lands, it was bound to be somewhat predictable — but it didn’t have to go to such extremes. The result was a collection of one- and two-dimensional characters who fell into situations that anyone in the audience would have expected.

Despite that flaw, and despite its transparent political correctness, Avatar is still a successful film. Aside from the special effects, the spectacular scenery and the attention to detail redeem the story. Go see it — warts and all!

It also got me [...]]]> “I make order out of chaos.” This is how an old friend whom I hadn’t seen in years explains her transition from linguistics to statistics, when people think it’s a complete change of field. It’s how she explains it to non-linguists, of course — as I already knew the connection. But the phrasing really resonates with me. I’ve described elsewhere how the search for patterns and abstract generalizations is what unites linguistics and math teaching in my mind, but I rather like the step up the ladder of abstraction implied by “I make order out of chaos.”

It also got me thinking about why I like the mystery and science fiction genres in popular fiction. My liking for science fiction is no mystery, so to speak: anyone with a mathematical bent is likely to enjoy the conventions of that genre. But what about mysteries? I’d been thinking about that lately, and it occurred to me that mystery writers also make order out of chaos: the unsolved crime is cognitively chaotic, and the solution creates order out of it. Furthermore, the puzzle that’s often involved bears definite kinship to the kinds of puzzles we solve in both math and linguistics. Just a thought…

“pet; petted; petting” <http://www.merriam-webster.com/dictionary/pet>

“The past participle of ‘to pet’ is ‘petted’.” <http://www.usingenglish.com/forum/ask-teacher/19711-pet-petted.html>

But Barbara and I have recently noticed that several people we know have switched to pet as its own past participle. For example:

“My dog likes to be pet all the time.” <overheard> “That cat really likes to be pet.” <overheard> “Do snakes like to be petted?” <http://answers.yahoo.com/question/index?qid=20090310231953AAm1xeY>

Most interestingly, a post from the UK contains the sentence, “But, [...]]]> Maybe I am inadvertently committing the Recency Fallacy, but it seems to me that up until last year or so the past participle of pet was petted:

“Where do your cats like to be petted?” <http://www.mihav.com/en/forum/share-amp-chat/where-do-your-cats-like-to-162014>

“pet; petted; petting” <http://www.merriam-webster.com/dictionary/pet>

“The past participle of ‘to pet’ is ‘petted’.” <http://www.usingenglish.com/forum/ask-teacher/19711-pet-petted.html>

But Barbara and I have recently noticed that several people we know have switched to pet as its own past participle. For example:

“My dog likes to be pet all the time.” <overheard>
“That cat really likes to be pet.” <overheard>
“Do snakes like to be petted?” <http://answers.yahoo.com/question/index?qid=20090310231953AAm1xeY>

Most interestingly, a post from the UK contains the sentence, “But, when my rabbit is laying down, he definitely likes to be pet around his whole body,” even though the headline (presumably written by someone else) reads, “How do i know my bunny likes being petted?” <http://uk.answers.yahoo.com/question/index?qid=20091011130535AAHEC77>

It may or may not be relevant, but all the attested forms overheard by Barbara and me come from highly educated women — even our veterinarian — so it’s not an illiteracy. Somehow a weak verb has turned into a strong verb, which is the reverse of the natural course of events. (For example, work → wrought changed to work → worked.) We could gather some evidence of what’s going on by checking other verbs that rhyme with pet, some of which provide possibly explanatory paradigms:

set → set (possibly the model for pet → pet)
bet → bet (likewise)
let → let (likewise)
get → gotten (a different strong-verb paradigm)
jet → jetted (a regular, i.e. weak verb)
net → netted (regular)
wet → wetted (regular)
abet → abetted (regular)
whet → whetted (regular)
fret → fretted (regular)
vet → vetted (regular)

So these data don’t really explain why petted would become pet. And it’s interesting that all the surprising examples that I could find on the Web or in overheard speech have occurred in the phrase “likes to be pet”; maybe this has become new idiom that I’ve been unaware of, in which case the past participle remains petted elsewhere? Just a conjecture…

“That’s not a very high bar,” she replied. She’s right, of course. This article was probably 99% accurate, which is as much as [...]]]> Junior Lauren Avery, one of the editors of Weston High School’s student newspaper, Wildcat Tracks, asked if she could interview me. Of course I said yes, and the result was a half-page article that focused on my transition from linguistics to teaching math. I was pleased with the depth and breadth of the writing, as well as by its unusually high degree of accuracy. “It’s much more accurate than Fox News,” I said to one of my colleagues.

“That’s not a very high bar,” she replied. She’s right, of course. This article was probably 99% accurate, which is as much as anyone could ask for — and I was just kidding about Fox News.

Here are a few excerpts from Lauren’s article:

Davidson’s smooth switch between two seemingly incompatible fields often surprises his students. Despite this, Davidson sees a great deal of similarities between linguistics and mathematics, and to this day he continues to pursue both subjects.

…

A linguist is a person who studies the origins and usage of ancient and modern languages…. By studying multiple languages instead of focusing on a single language, Davidson was able to begin to identify trends and patterns between languages, a concept that played a major role in his interest in mathematics later on.

…

To his current and former students, Davidson’s ability to switch between two fields has given them a new perspective about choosing a career in the future. “It lets me think that it’s not really too late to change what you are passionate about,” said junior Mir Bokhari.

…

Davidson’s switch between two fields has affected him both as a teacher and as a person, and it reflects some valuable lessons concerning education. “You never know if sometimes something you’re interested in can come back. My jobs make use of all the linguistics I had done 20 years earlier in new contexts. My linguistics training helped in math,” Davidson said. “There are surprising connections. Nothing you learn is ever wasted.”

This usage has long seemed completely wrong to me. To my mind, I have some students who struggle and do well. I also have some students who are unsuccessful — precisely [...]]]> At this week’s Math Department meeting, we spent the first 15 minutes or so discussing what we do to help “struggling students” succeed in our courses — particularly what resources we provide. Something was bothering me about the whole discussion, so I waited a few minutes before I said anything. Then I realized what was bothering me: the participle “struggling” was apparently being used as a synonym for “unsuccessful.”

This usage has long seemed completely wrong to me. To my mind, I have some students who struggle and do well. I also have some students who are unsuccessful — precisely because they don’t struggle.

It all comes down, of course, to the meaning of the verb “struggle.” Let’s see what a couple of reputable dictionaries say about the matter. In each case I’ve selected the appropriate sense of the word:

1. to make strenuous…efforts in the face of difficulties… <struggling with the problem>
2. to proceed with difficulty or with great effort <struggled through the high grass> <struggling to make a living>

—Merriam-Webster

1. to be strenuously engaged with a problem, a task, or an undertaking
2. to progress with difficulty <struggled with calculus>

—American Heritage Dictionary

Linguists, of course, always insist on being descriptive rather than prescriptive, and yet they usually rely on introspection or on the use of a small number of informants. I suppose a more accurate technique in this context would be to survey a large number of people and find out how they use the word “struggle”; I have no idea what we would find, but at least the dictionary definitions make it absolutely clear to me that we should stop using this verb as a synonym for “be unsucessful.”

On another front, we spent the next 25 minutes of the department meeting discussing how to solve the equation x² = 2^x. I told my Algebra II class about this, since we’re currently transitioning from quadratic functions to exponential functions, and one of their homework problems called for a comparison between y = x² and y = 2^x. They found it an unlikely topic for a meeting — and they were especially surprised that we were so geeky that the meeting ran ten minutes over before anybody looked at the clock and noticed that we had gone past the announced end of the meeting.

By the way, there are three solutions to this equation. One solution, 2, is immediately obvious; a second solution, 4, is not at all obvious until you give it some considerable thought, at which point it “becomes obvious.” The third solution can be estimated by looking at a graph. Finding this solution is left as an exercise for the reader.