Category Archives: language

Two science books in the modern expository style

Symmetry and the Monster: The Story of One of the Greatest Quests of Mathematics, By Mark Ronan. Oxford University Press, 2006.

This is an excellent way for the non-mathematician to learn about what is going on in the attempt to classify symmetries by discovering all the finite “simple groups”. The last one found was the Monster Group and the classification was completed in 1982. This book is full of fascinating information about how this came about and the tantalizing connections between physics and the Monster that have been discovered since.

The Lightness of Being, by Frank Wilczek. Basic Books, 2008

This book is an exposition for the layman of the modern theory of particle physics – the Standard Model, Supersymmetry and other possible extensions. I recommend it for anyone interested in the subject.

These two books are examples of the modern trend in science expository writing, using metaphors, anecdotes, graphs and speculation to try to communicate an understanding of how the scientists involved think about the subject and what their motivations are. Ronan and Wilczek use much the same approach that I have been using in abstractmath.org and it has made me think about what works and what doesn’t.

I will be writing about my reactions to the writing in such books in future posts.

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English pronunciation heads for catastrophe

The Yiddish word for “beautiful” sounds like shay-na (that is the feminine form). The first syllable rhymes with “say”. It was once natural, if you saw the spelling “shana”, to pronounce it “shay-na” and so people gave their daughters the name “Shana”. Younger, educated people now expect that a word that looks foreign should be pronounced (more or less) with European vowels (essentially those of Spanish), so that they would say “shah-na”. The first syllable rhymes with “pa”. So some people started naming their daughters “Shaina” to avoid this, and others named their daughters “Shana” and pronounced it “shah-na”.

In many European languages (not French) “Shaina” would be pronounce “shy-na”. So how do you spell the name so that it is pronounced “shay-na” by every native English speaker? Probably Shayna is the best choice, and there are people named Shayna. There are also people named Shawna because their parents heard the name “Shana” pronounced that way and thought it was spelled “Shawna”. (You can check these claims on Google.)

Once upon a time almost every American would say “shay-na” when seeing the spelling “Shana”. For Bernstein they would say “burn-steen” not “bairn-shtine” (the conductor said “burn-steen”). Churchill said “nazzi” for Nazi instead of “nah-tsee”. People rhymed “Lagrange” with “range” and accented “Berlin” and “Madrid” on the first syllable.

People without college education still do these things. But the educated classes have come to believe that they must pronounced foreign words as if they were speaking that language. They are inconsistent about it, they still say “Paris” to rhyme with “Harris”, but they pronounce less common foreign words in the way they think they are pronounced in the original language.

This comes out of snobbery (I am educated and you are not) but also out of genuine enjoyment at saying things in foreign languages. It is not all snobbery.

But whatever the motive, it is causing a disaster. English has always had irregular spelling, but in fact people could make a stab at saying a word they say in print and often get it right. The situation is much worse now. We have gotten to the point where we simply have to know how lots of words are pronounced. The spelling gives no clue.

This is a catastrophe for English spelling.

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Default meanings

Concerning Michael Barr’s comments on my post on terminology, I remember going to a meeting of topologists in 1965 or 1966 in which people kept spouting nonsense about free groups. The reason it was nonsense was that they were talking about free abelian groups without saying so. That may have been the first time I became aware of default meaning in different groups of mathematicians.

I became aware of default meanings in ethnic and regional groups long before that, when I joined the Air Force after never having been outside the deep south and discovered that other people thought “sweet milk” and “ink pen” were weird things to say.

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Unvoicing final consonants in English

Younger people frequently devoice final d while keeping the length of the vowel, so for example “road” ends with a t sound. The word does not become homophonic with “rote” because the latter has a shorter vowel, shorter in the time it takes to pronounce it (“long” and “short” are often used to denote vowel quality but I am not talking about that here.)

I became especially aware of this when I started singing in choirs twenty years ago. A person standing next to me would sing “Lord” ending in a distinct “t” sound, often released. I noticed younger people doing it more than older people. I have mentioned this occasionally in choir practice, and some leaders really don’t want me to end “Lord” with a voiced d, at least not a released voiced d.

Linguists have noticed this, but the articles I have found mostly discuss it happening in African American speech. But I swear I have heard it many times from white native English speakers.

Last week for the umpteenth time I was in the hospital. I told the nurse I would like to walk around the halls. She asked me, “Would you like a rope?” I asked her to repeat herself and finally decided she was saying “robe”. She released the p, too. She sounded like a native English speaker from Minnesota. I couldn’t tell if she was lengthening the vowel. I suppose I could have tried to elicit a minimal pair by asking her something like, “What do you hang people with in this hospital?” but, no…

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Automatic spelling reform

The English language badly needs spelling reform. It is becoming a widely used language and the spelling is a real hindrance in learning it. But spelling reform has two big problems:

Resistance
Both the French and the Germans have tried rather minor spelling reforms in recent years that have utterly failed. The Chinese Communists made substantial changes in the characters used in Chinese and succeeded where they had dictatorial control, but failed in the diaspora. As a result, people educated in Taiwan and Hong Kong can’t read stuff printed on the mainland and vice versa. On the other hand, Greek spelling reform, mostly a matter of simplifying the accents put on vowels, seems to have succeeded.

Any English spelling reform would succeed at most partially, resulting in texts being written in two spellings, the old one and the new one. People who grew up on the old one probably could learn to read the new one, but never as easily as they read the old one. And conversely.

Dialect differences
Americans outside the south pronounce “Mary”, “merry” and “marry” the same. Southerners and Britishers distinguish between two or three of them.

Britishers pronounce “Wanda” and “wander” the same. Americans pronounce them differently.

Most Americans pronounce “bother” and “father” so they rhyme. Some Americans pronounce “cot” and “caught” the same. Canadians and Britishers distinguish these pairs.

The people who don’t distinguish between two phonemes have to learn different spellings for words that sound the same, or else people who DO distinguish them have to whether the writer meant merry or marry, for example.
 
 
Technology comes to the rescue
The text-to-speech system in Excel 2003 pronounces both of the following sentences correctly:
“We will record the song and I will make a record of it.”
“I will read the book and when I have read it I will tell you.”
It no doubt makes mistakes in some situations, too.
This system presumably operates by at least partially parsing the sentences, looking at context and perhaps using other methods as well. So it would be possible to devise a system that would convert text on the fly from a traditional spelling to a reformed spelling. This would probably work well most of the time and could allow several different spelling systems to flourish. When books involving fixed print on paper become obsolete, as they surely will, this will solve the problem.
One obvious way to do this is to add diacritics and accent marks to the existing spelling.
 
Note
On this blog I once proposed that subject and predicate phrases in English be color-coded. Writers would not want to do this by hand, but when sentence parsing gets good enough (maybe it already is) this could be done automatically in the same way as different spellings.
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Technical words in English

English is unusual among major languages in the number of technical words borrowed from other languages instead of being made up from native roots. We have some, listed under suggestive names. But how can you tell from looking at them what “parabola” or “homomorphism” mean?

The English word “carnivore” (from Latin roots) can be translated as “Fleischfresser” in German; to a German speaker, that word means literally “meat eater”. So a question such as “What does a carnivore eat” translates into something like, “What does a meat-eater eat?” (And do they do it in Grant’s tomb?) Similarly the word for “plane” (ebene) looks like “flat”.

Chinese is another language that forms words in that way: see the discussion of “diagonal” in Julia Lan Dai’s blog. (I stole the carnivore example from her blog, too.)

The result is that many technical words in English do not suggest their meaning at all to a reader not familiar with the subject. Of course, in the case of “carnivore” if you know Latin, French or Spanish you are likely to guess the meaning, but it is nevertheless true that English has a kind of elitist stratum of technical words that provide little or no clue to their meaning. German has a much smaller elitist stratum of words. I don’t know about Chinese.

This is a problem in all technical fields, not just in math.

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Set notation

Students commonly think that the notation “{Ø}” denotes the empty set. Many secondary school teachers think this, too.

Mistakes in reading math notation occur because the reader’s understanding of the notation system is different from the author’s. The most common bits of the symbolic language of math have fairly standard interpretations that most mathematicians agree on most of the time. Students develop their own non-standard interpretation for many reasons, including especially cognitive dissonance from ordinary usage and ambiguous statements by teachers.

I believe (from teaching experience) that when a student sees “{1, 2, 3, 5}” they think, “That is the set 1, 2, 3 and 5”. The (incorrect) rule they follow is that the curly braces mean that what is inside them is a set. So clearly “{Ø}” is the empty set because the symbol for the empty set is inside the braces.

However, “1, 2, 3 and 5” is not a set, it is the names of four integers. A set is not its elements. It is a single mathematical object that is different from its elements but determined exactly by what its elements are. The correct understanding of set notation is that what is inside the braces is an expression that tells you what the elements of the set are. This expression may be a list, as in “{1, 2, 3, 5}”, or it may be a statement in setbuilder format, as in “{x x > 1}”. According to this rule, “{Ø}” denotes the singleton set whose only element is the empty set.

This posting is based on the belief that that mathematical notation has a standard, (mostly) agreed-on interpretation. I made this attitude explicit in the second paragraph. Teachers rarely make it explicit; they merely assume it if they think about it at all.

The student’s interpretation is a natural one. (Proof: So many of them make that interpretation!) Did the teacher tell the student that math notation has a standard interpretation and that this is not always what an otherwise literate person would expect? Did the teacher explain the specific and rather subtle rule about set notation that I described two paragraphs above? If not, the student does not deserve to be ridiculed for making this mistake.

Many people who get advanced degrees in math understood the correct rule for set notation when they first learned it, without having to be told. Being good at abstract math requires that kind of talent, which is linguistic as well as mathematical. Most students in abstract math classes are not going to get an advanced degree in math and don’t have that talent. They need to be taught things explicitly that the hotshots knew without being told. If all math teachers had this attitude there would be fewer people who hate math.

PS: My claim about how students think that leads them to believe that “{Ø}” denotes the empty set is a testable claim. There are many reports in the math ed literature from investigators who have been able to get students to talk about what they understand, for example, while working a word problem, but I don’t know of any reports about my assertion about “{Ø}” .

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Most annoying bug in English?

I said in a recent posting, “Perhaps the most annoying bug in English is the fact that “two”, “to” and “too” are pronounced identically.” That may be the most annoying bug in spoken English but the lack of a gender neutral third person pronoun is annoying in both spoken and written English.

This bug may be on its way to being eliminated by using “they” for “he or she”. This has got me to thinking about the future of the language. The plural “you” has already replaced the singular “thou/thee” in English. Perhaps someday “they” will oust “he” and “she” completely and become the only third person pronoun, or perhaps more likely the animate third person pronoun, contrasting with “it”.

English has a compulsory plural for nouns, like other European languages (except Turkish) and unlike most East Asian languages. But if the second and third person pronouns stop marking the plural, will nouns be far behind? A few dialects already eliminate it — notably in the West Indies. This development will only be encouraged as English becomes more and more everyone’s second language. I hope someone reads this in 2107 and puts me down in history as a linguistic Notradamus.

There is lots of interesting stuff about singular “they” on the web: See the comments on World Wide Words and by Geoff Pullum . (Was the previous sentence a zeugma?)

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Who owns the language?

Back in Ancient Times (even before Elvis) computer people had to deal with the problem that printers did not distinguish between the digit zero and the letter “O”. So they designed printers that printed “Ø” (a circle with a slash through it) for zero. For many years after that students in technical fields wrote their zeros “Ø”. This became a mark of their subculture – they were conscious of doing it as a statement of their geekhood. (See note 1).

Some countries have tried to reform their languages. In 1951 the Norwegian powers that be tried to get people to say the equivalent of “forty two” instead of “two and forty”. This was desirable because it causes confusion when telephone numbers are pronounced. For example, “2317 3251” would be said as if it were “three and twenty seventeen two and thirty one and fifty”. As this article shows, fifty years later a sizeable minority of Norwegians were still saying it that way.

Both France and Germany tried some modest spelling reforms in the 1990’s. Both met with stiff opposition and have had only spotty success.

Perhaps the most annoying bug in English is the fact that “two”, “to” and “too” are pronounced identically. (See note 2) This could be repaired easily by having everyone use the Scottish form “twa” (the confusion in practice comes mostly between “two” and one of the others). But if a joint Anglo-American commission tried to introduce this all hell would break loose. A minority would probably start using it, but I predict many local American school systems would try to ban it.

Technical people have a different feeling about changing their language. Some technical fields have organizations that occasionally promulgate changes in terminology. This can be good. What is really really bad is the practice of some mathematicians to redefine commonly used terms at the beginning of a book rather than introducing new terms. This makes it difficult to dip into the middle of a book (what Steenrod called being a “grasshopper”) or to have conversations with people in different fields. I ran into this when I was a brand new professor in a department with topologists who talked about “free groups”, by which they meant free Abelian groups. That raised this abuse to my consciousness and I have noticed many examples since then. One of the most egregious was that Bourbaki tried to redefine “positive” to mean “nonnegative”. A few people still follow that usage, including, I am told, some French public schools.

Note 1 Someone please give me a good internet reference to marks of subculture – the wikipedia site is too narrow. See my comments on grits in the covert curriculum.

Note 2 Actually, “to” may be pronounced with a schwa when it is unemphasized. But it is emphasized when you read a highway sign that says “to 95”, which sounds like “295”.

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Heschl's Gyrus

This report from Science Daily describes the discovery of a correlation between the size of “Heschl’s Gyrus” in the brain and the ability to learn foreign languages. It also mentions an intriguing study that found that musical training started at an early age contributed to more successful spoken foreign language learning.

I have been pushing the idea that learning abstract math requires (among other things) learning a foreign language. So, I wonder, does the size of Heschl’s Gyrus correlated with ability at higher math? Also, the study about musical training suggests a reason for the commonly noted tendency for mathematicians to be musical, but I suppose that idea is pretty longshottish.

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