Category Archives: language

language

Goodnight, Irene

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Look at this list:

Antigone
Aphrodite
Chloe
Hermione
Irene
Kalliope
Nike
Penelope
Phoebe
Zoe

All these are originally Greek names of supernatural beings (except Antigone?). The e is a feminine ending. Most of them are used now as women’s names. When Americans pronounce these names, with one exception they usually pronounce the final e.

The exception is “Irene”. I have heard British people say “I-reenie” but never an American. Is this because of “Good Night Irene”?

At one point when I was maybe eleven years old I bought a 45 of the Weavers singing Good Night Irene. It was my favorite song. The record had Tsena Tsena on the other side. I fell in love with Tsena Tsena which I had never heard before, but I still liked GNI too. For some time after that I looked for other records by the Weavers but I never saw one. Perhaps that was about the time the McCarthyites blacklisted them?

I was also attracted by the harmonies of some pieces by Bach. Now I think that the thing TT and Bach (and others of my favorite music, like some Procol Harum) have in common is the existence of both major and minor chords in the same piece. But when I asked my music teacher what was so wonderful about Bach she said she had never understood Bach.

Oh well.

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language

Steven Brust commits a zeugma

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“…she immediately spurred her horse, yet the horse had hardly moved when Wadre moved his arm in an indication that she was not to advance beyond him, wherefore she drew rein, her sword, and the conclusion that the time was not yet quite at hand to charge.”

Steven Brust, The paths of the dead, p. 335.   New York: Tom Doherty Associates (2002), p. 335.

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category theory, exposition, language, language of math, math, representations

Composites of functions

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In my post on automatic spelling reform, I mentioned the various attempts at spelling reform that have resulted in both the old and new systems being used, which only makes things worse.  This happens in Christian denominations, too.  Someone (Martin Luther, John Wesley) tries to reform things; result: two denominations.   But a lot of the time the reform effort simply disappears.  The Chicago Tribune tried for years to get us to write “thru” and “tho” —  and failed.  Nynorsk (really a language reform rather than a spelling reform) is down to 18% of the population and the result of allowing Nynorsk forms to be used in the standard language have mostly been nil.  (See Note 1.)

In my early years as a mathematician I wrote a bunch of papers writing functions on the right (including the one mentioned in the last post).  I was inspired by some algebraists and particularly by Beck’s Thesis (available online via TAC), which I thought was exceptionally well-written.  This makes function composition read left to right and makes the pronunciation of commutative diagrams get along with notation, so when you see the diagram below you naturally write h = fg instead of h = gf. Composite

Sadly, I gave all that up before 1980 (I just looked at some of my old papers to check).  People kept complaining.  I even completely rewrote one long paper (Reference [3]) changing from right hand to left hand (just like Samoa).  I did this in Zürich when I had the gout, and I was happy to do it because it was very complicated and I had a chance to check for errors.

Well, I adapted.  I have learned to read the arrows backward (g then f in the diagram above).  Some French category theorists write the diagram backward, thus:

CompositeOp

But I was co-authoring books on category theory in those days and didn’t think people would accept it. Not to mention Mike Barr (not that he is not a people, oh, never mind).

Nevertheless, we should have gone the other way.  We should have adopted the Dvorak keyboard and Betamax, too.

Notes

[1] A lifelong Norwegian friend of ours said that when her children say “boka” instead of “boken” it sound like hillbilly talk does to Americans.  I kind of regretted this, since I grew up in north Georgia and have been a kind of hillbilly-wannabe (mostly because of the music); I don’t share that negative reaction to hillbillies.  On the other hand, you can fageddabout “ho” for “hun”.

References

[1] Charles Wells, Automorphisms of group extensions, Trans. Amer. Math. Soc, 155 (1970), 189-194.

[2] John Martino and Stewart Priddy, Group extensions and automorphism group rings. Homology, Homotopy and Applications 5 (2003), 53-70.

[3] Charles Wells, Wreath product decomposition of categories 1, Acta Sci. Math. Szeged 52 (1988), 307 – 319.

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exposition, language, math

The revolution in technical exposition II

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In the last post I talked about the bad side of much technical exposition and the better aspects of popular science writing (exemplified by Priestley).   These two streams have continued to the present. Stuffy, formal, impersonal technical exposition has continued to be the norm for works intended for academic credit.  Math and science expositions written for the public have been much looser and some have been remarkably good.  I described two of them in a previous post.

The revolution mentioned in the title of this post is that some aspects of the style of popular science writing have begun infiltrating writing in academic journals. Consider these sentences from Jody Azzouni's essay in [1]:

It's widely observed that, unlike other cases of conformity, and where social practices really are the source of that conformity, one finds in mathematical practice nothing like the variability found cuisine, clothing, or metaphysical doctrine. (p. 202).

Add two numbers fifteen times, and you do something different each time — you do fifteen different things that (if you don't blunder) are the same in the respect needed; the sum you write down at the end of each process is the same (right) one. (p. 210).

Written material gives the reader many fewer clues as to the author's meaning in comparison with a lecture.  Azzouni increases the comprehensibility of his message by doing things that would have been unheard of in a scholarly book on the philosophy of math thirty years ago.

  • He uses italics to emphasis the thrust of his message.
  • He uses abbreviations such as "it's".
  • He says "you" instead of "one":  He does not say "If one adds two numbers fifteen times, one does something different each time…"  This phrase would probably have been nominalized to incomprehensibility thirty years ago: "A computation with fifteen repetitions of the process of numerical addition of a fixed pair of integers involves fifteen distinct actions."

In abstractmath.org I deliberately adopt a style that is similar to Azzouni's, including "you" instead of "one", "it's" instead of "it is" (and the like), and many other tricks, including bulleted prose, setting off proclamations in purple prose, and so on. (See [2].)  One difference is that I too use italics a lot (actually bold italics), but with a difference of purpose:  I use it for phrases that I think a student should mark with a highlighter.

My discussion of modus ponens from the section Conditional Assertions illustrates some of these ideas:

Method of deduction: Modus ponens

The truth table for conditional assertions may be summed up by saying: The conditional assertion “If P, then Q” is true unless P is true and Q is false.

This fits with the major use of conditional assertions in reasoning:

Method of deduction

  • If you know that a conditional assertion  is true and
  • you know that its hypothesis is true,
  • then you know its conclusion is true.

In symbols:

When “If P then Q” and P are both true,

______________________________________

then Q must be true as well.

This notation means that if the statements above the line are true, the statement below the line has to be true too.

This fact is called modus ponens and is the most used  method of deduction of all.

Remark

That modus ponens is valid is a consequence of the truth table:

  • If  P is true that means that one of the first two lines of the  truth table holds.
  • If the assertion “If P then Q” is true, then one of lines 1, 3 or 4 must hold.

The only possibility, then, is  that Q is true.

Remark

Modus ponens is not a method of proving conditional assertions. It is a method of using a conditional assertion in the proof of another assertion.  Methods for proving conditional assertions are found in the chapter on forms of proof.

This section also includes a sidebar (common in magazines) that says:  "The first statement of modus ponens does not require pattern recognition.  The second one (in purple) does require it."

Informality, bulleted lists, italics for emphasis, highlighted text, sidebars, and so on all belong in academic prose, not just in popular articles and high school textbooks.  There are plenty of other features about popular science articles that could be used in academic prose, too, and I will talk about them in later posts.

Note: Some features of popular science should not be used in academic prose, of course, such as renaming technical concepts as I discussed in the post of that name.  An example is referring to simple groups as "atoms of symmetry", since many laymen would not be able to divorce their understanding of the words "simple" and "group" from the everyday meanings:  "HOW can you say the Monster Group is SIMPLE??? You must be a GENIUS!"

References

[1] 18 Unconventional Essays on the Nature of Mathematics, by Reuben Hersh. Springer, 2005.  ISBN 978-0387257174

[2] Attitude, in abstractmath.org.

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exposition, language

The revolution in technical exposition

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Most of the posts on G&G are in the streams math or language.   Many articles are also in various subcategories. The articles in each stream can be found by looking to the column to the left of this post and scrolling down to "categories".   (That word has too many meanings…)  I have added a new stream, exposition, and have put four earlier articles in the stream.  They concern expository prose in the sciences.

Old fashioned mathematical and scientific exposition appears to be designed to put as many barriers as possible in the way of the reader.  Some of its properties:

  • Highly formal
  • Full of pronouncements worded in an impersonal way (noun phrases, everything objectified)
  • All traces obliterated of how the results came to be discovered
  • No intuitive explanations

References [2] and [3] go into detail about some of these characteristics.

Steven Johnson, in the Invention of Air [1] describes the classical expository style of Isaac Newton as having these properties. (But see Isaac buys him a prism).  He also says that Priestley's book [4] on electricity is in some sense the first popular science book.  It is narrative, not didactic; it uses "I" a lot; it goes into great detail about how the experiments were conducted (read his account of Benjamin Franklin's experiments starting on page 222), including what were in his opinion the many mistakes of other researchers, and occasionally attempts intuitive descriptions of electricity.

I see that I accidentally published this post, so I will stop here and continue in another post.

References

[1] Steven Johnson, The Invention of Air.  Riverhead Books, 2008.  ISBN 9781594488528.  Reviewed in my post on Priestley.

[2] O’Halloran, K. L. (2005), Mathematical Discourse: Language, Symbolism And Visual Images. Continuum International Publishing Group.  ISBN 978-0826468574.

[3] Halliday, M. A. K. and J. R. Martin (1993), Writing Science: Literacy and Discursive Power. University
of Pittsburgh Press.  ISBN 978-0822961031

[4] Joseph Priestley, The History and Present State of Electricity, with Original Experiments (1775).

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language

Must, have to, gotta

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A volunteer helping in an intermediate-level ESL class reports that one day the teacher introduced “must” and  “have to”, in contexts such as

  • You must renew your visa = You have to renew your visa.
  • You must have a ticket to get into the show  = You have to have a ticket to get into the show.

In the volunteer’s discussion group this provoked two phenomena:

1.  A heated discussion about “have to have”.  Many students thought that was crazy and couldn’t figure out what it meant.  They didn’t think “have to renew” was crazy, but the usage was unfamiliar to many of them.

2. Partway through the discussion in the subgroup moderated by the volunteer, a student suddenly Saw The Light:  “They’re talking about GOTTA!”  (You gotta renew your visa.  You gotta have a ticket to get into the show.)

“Must” “have to” and “gotta” occur in three different registers of English.  In America, in my experience, “must” is uncommon in speech and occurs mostly in formal writing.  “Have to” (or “hafta”)  is informal and widely used in both speech and writing.  In street-conversation, “gotta” is the usual usage.  It is uncommon in writing.  “You gotta” would be spelled “You’ve got to”.  (You do hear “you’ve gotta” as well as “you gotta”.)

New immigrants are exposed to English in the work place and on the street, not in the home and not usually in formal circumstances.  The teacher should have given “gotta” as a third alternative way of saying “must” right from the start, since clearly that is the term most familiar to most of them.  She should probably have also pointed out the pronunciation “hafta”, which is not obvious from the “have to” spelling unless you are a Sophisticated Amateur Linguist like me.

PS

I should add that negating these expressions introduces complications.  “Must not” does not mean the same thing as “don’t have to”.  “Don’t got” is considered wrong, and plenty of people who say “gotta” in conversation, including me, don’t say “don’t gotta”; I would say “don’t have to” or “don’t need to” instead.

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exposition, language, language of math, math, representations

Commonword names for technical concepts

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In a previous post I talked about the use of commonword names for technical concepts, for example, “simple group” for a group with no proper normal subgroups.  This makes the monster group a simple group!  Lay readers on the subject might very well feel terminally put-down by such usage.  (If he calls that “simple” he must be a genius.  How could I ever understand that?  See note 1.)  Mark Ronan used of “atom of symmetry” instead of “simple group” in his book Symmetry and the Monster, probably for some such reason.

Recently I had what used to be called a CAT scan and (perhaps) what used to be called a PET scan on the same day.   The medically community now refers to CT scan or nuclear imaging.   This may be because too many clients were thinking of doing sadistic testing on cats or other pets.   But I have not been able to confirm that.

The nurse called the CT scan an x-ray.  Well, of course, it is an x-ray, but it is an x-ray with tomography.  She explicitly said that calling CT scans x-rays was common usage in their lab.  In the past, other medical people have said to me, “It used to be called CAT scan but now it is CT scan.”   But no one said why.

The situation about PET scan is more complicated.  I didn’t raise the question with the nurse, and Wikipedia has separate articles about PET scans and nuclear imaging, even though they both use positrons and tomography.   The chemicals mentioned for PET are isotopes of low-atomic-number elements, whereas the nuclear medicine article mentions technetium99 as the most commonly used isotope.  Nowhere does it explain the difference.  I wrote a querulous note in the comments section of the NM article requesting clarification.

Note 1.  “If he calls that ‘simple’ he must be a genius.  How could I ever understand that?”   Do not dismiss this as the reaction of a stupid person.  This kind of ready-to-be-intimidated attitude is very common among intelligent, educated, but non-technically-oriented people.   If mathematicians dismiss people like that we will  continue to find mathematics anathema among educated people.  We need people to feel that they understand something about what mathematicians do (I use that wording advisedly).  Even if you are an elitist who doesn’t give a damn about ordinary people, remember who funds the NSF. See co-intimidator.

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abstractmath.org, language, language of math, math

Distributive plurals

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A statement in English such as “all squared nonzero real numbers are positive” is called a distributive plural.  This means that the statement “the square of x is positive” is true for every nonzero real number.  It can be translated directly into symbolic notation:  \forall x\,(\text{if }x\ne 0\text{ then }{{x}^{2}}>0)

Not all statements involving plurals in English are distributive plurals.  The statement “The agents are surrounding the building” does not imply that Agent James is surrounding the building.  This type of statement is called a collective plural. Such a statement cannot be translated directly into a statement involving a universal quantifier.  More about this here.  This discussion on Wordwizard suggests that there may be a difference between British and American usage.

The word “distributive” as used here is analogous to the distributive law of arithmetic.  If the set of things referred to is finite, for example the set {-2, -1, 1, 3} then one can say  that “\forall x\,({{x}^{2}}>0)” is equivalent to “{{(-2)}^{2}}>0\text{ and }{{(-1)}^{2}}>0\text{ and }{{\text{1}}^{2}}>0\text{ and }{{\text{3}}^{2}}>0”.

I once found a report on the internet that a Quaker Oats box contained this exhortation: “Eating a good-sized bowl of Quaker Oatmeal for 30 days will actually help remove cholesterol from your body.”  This undoubtedly exhibits a confusion between distributive plurals and the other kind of plural, but I don’t understand the connection well enough to explain it.

I can no longer find the report on the internet.  This may mean the Quaker Oats box with that label never existed.

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abstractmath.org, Handbook, language, language of math, math

Handbook now online

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I have placed an interactive version of the Handbook of Mathematical Discourse on line here. Its formatting is still a little rough, and it omits the quotations and illustrations from the printed book. It also needs the backlinks from the citations and bibliography reactivated. I will do that when I Get Around To It.

Now I can refer to the Handbook via a direct link from a blog post or from abstractmath, and you can click on a lexicographical citation and go directly to the text of the citation.

Comments and error reports are welcome.

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language

Pronouncing the Indefinite Article

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In his speeches, President Obama commonly pronounces the indefinite article “a” like the “a” in “may”.  You can hear it in this speech.  Most people, most of the time, pronounce it with the schwa.   In that speech, I have also caught him pronounce “to” like “too” before a vowel, but with a schwa before a consonant.

Hilary Clinton pronounces “a” that way in speeches, too.  Example.

They may not use this pronunciation mode in ordinary conversation.   Is this a generational change or do they have the same speech teacher?

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