Ambiguities in Plain Language

"The die is cast - you should die" may sound like an offer one can't refuse.
I have no respect for generals who always talk in generalities.
I could not disagree with you less.
Being not yet fully grown, his trousers were too long.
When only five, Safire's grandfather took him to a baseball game.
Free gifts with every purchase.

This sentence has a twofold inconsistency: are the gifts really free if they require a purchase? Also, are not gifts free by definition? Could free gifts be any freer than plain gifts? Similarly strange is
I personally feel better.

Is it really possible to have impersonal feelings?
You really can't do that. Not really.
I smelled it from a distance - it smelled awful.
Herb O. Buckland pointed to a collection of such redundancies by Jim Stovall. Here are a few examples:
- advanced planning
- never before
- past history
- tired cliches
- sworn affidavit
- final ultimatum
In a November 17, 2004 NY Times column, W. Safire has scolded Collin Powell for describing his departure from the State Department as coming after reaching a mutual agreement with President Bush. As Safire pointed out, when two people agree, it's always mutual.
Up to 40% discount or more.
Smullyan: 'I once saw a sign in a restaurant which read: "Special prices for schools, clubs, churches, and other occasions."'
And I came across a dealer invoice that read: "Standard equipment at no extra cost."
Have you belted your kids today?
If someone called you odd, would you try to get even? (from Ken Retzer via Jerry P. Becker)
Why call it a building if it's already been built?
Isn't it a bit unnerving that doctors call what they do practice?
Do family trees form a national forest? (Rodney Dangerfield: I looked up my family tree and found three dogs using it.)
Can you round off a square deal?
One parks on a driveway and drives on a parkway. (My thanks go to Ralph for bringing this up. Dr. Mardy Grothe, Never Let a Fool Kiss You or a Kiss Fool You, p. 5, credits Richard Lederer with the idea.)
The same book quotes another of R. Lederer pronouncements: "In what other language do people play at a recital and recite at a play?"
Dr. Grothe [Oxymoronica, p. 26] credits George Carlin with a wondrous question, "How is it possible to have a civil war?"
When a package is sent by car it is called shipping, when it is sent by ship it is called cargo. (Thanks to Ralph)
A quote by E. Kasner and J. Newman (from R. L. Weber, More Random Walks In Science): Because mathematicians get along with words, many amusing ambiguities arise. For instance, the word function probably expresses the most important idea in the whole history of mathematics. Yet, most people hearing it would think of a 'function' as meaning an evening social affair, while others, less socially minded, would think of their livers.
How come a fat man is a big man but a fat chance is no greater than a small chance. (Thanks to my son David.)
It is not at all simple to define simple.
Time flies like an arrow and fruit flies like an orange. (Thanks to Michael Livshits.)
No matter how much you push the envelope, it'll still be stationery.
A dog gave birth to puppies near the road and was cited for littering.
Two silk worms had a race. They ended up in a tie.
In the classic Vanity Fair by William Makepeace Thackeray we find the following narration by Major Michael O'Dowd:

"It's General Tufto, who commands the --- cavalry division; he and I were both shot in the same leg at Talavera."

I wonder, may two people be shot in the same leg? Compare with, say, "Children wanted the same apple."
It does sound strange to refer to one, say, point, as "one point," but to zero points as "zero points"
It may console those who are confused by the fact that, say, 3+4·5 and (3+4)·5 evaluate to different values, to learn that, according to legend, one of the Russian czars had misplaced a comma in the following sentence, "To pardon may not proceed with execution". The consequences were drastic. (Compare two possibilities: "To pardon, may not proceed with execution" and "To pardon may not, proceed with execution.")
Jim McCrudden from Australia describes a similar real life incident:

I once defended a man charged with assault. He was a Turk. His statement to the police was translated and typed out in English. It read. "I hit him with the iron bar when I saw him on the ground. I felt sorry for him and picked him up." I persuaded the jury it should read. "I hit him with the iron bar. When I saw him on the ground I felt sorry for him and picked him up." In the first of course he was hitting a defenceless man for which there could be no defence. In the second there was the opportunity of raising defence. The jury agreed with me by the way.

regards,
jim
The reason Lynne Truss has titled her popular book Eats, Shoots & Leaves is concealed in this parody:

A panda walks into a café. He orders a sandwich, eats it, then draws a gun and proceeds to fire it at the other patrons.

'Why?' asks the confused, surviving waiter amidst the carnage, as the panda makes towards the exit. The panda produces a badly punctuated wildlife manual and tosses it over his shoulder.

'Well, I'm a panda,' he says, at the door. 'Look it up.'

The waiter turns to the relevant entry in the manual and, sure enough, finds an explanation. 'Panda. Large black-and-white bear-like mammal, native to China. Eats, shoots and leaves.'

From the same book (p. 23):

A woman, without her man, is nothing.

A woman: without her, man is nothing.

And more (p. 22):

Now I must go and get on my lover.

Now I must go and get on, my lover.
In a highly recommended book Writing with Style author John Trimble gives the following illustration - one of many - to underscore the importance of the serial comma:

The motley prisoners in that cell included an unemployed actor, a murderer, a junkie, a man obsessed with flying saucers, an ex-cop with a craving four doughnuts and assorted females - all of them coexisiting in surprising harmony.

It is hard to fathom whether the "assorted females" inhabited the ex-cop's mind or shared with him the cell.
An entry for the word "puzzle" in the Ameraican Heritage Dictionary confirms that the word has two quite opposite meanings:

puz·zle v. puz·zled, puz·zling, puz·zles. --tr. 1. To baffle or confuse mentally by presenting or being a difficult problem or matter. 2. To clarify or solve (something confusing) by reasoning or study: He puzzled out the significance of the statement. --intr. ...

Here's an excerpt from Nicholas Blake's Thou Shell of Death [The Nicholas Blake's Treasury, p. 164]:

He looked puzzled as well as nervous. Of course he looked puzzled. The fact that he did so clinched my bizzare theory. He was trying to puzzle out all the time why O'Brien had behaved in such an extraoridicanry way ...
"Oversight" is an aditional example:

o·ver·sight n. --tr. 1. An unintentional omission or mistake. 2. Watchful care or management; supervision.
"Laminate" is another example:

lam·i·nate v. lam·i·nat·ed, lam·i·nat·ing, lam·i·nates. --tr. 1. To beat or compress into a thin plate or sheet. 2. To divide into thin layers. 3. To make by uniting several layers. 4. To cover with thin sheets. --intr. 1. To split into thin layers or sheets.

"Eponym" is admittedly not a frequent word to be encountered in common discourse. Nonetheless, its entry in popular dictionaries warrants attention:

ep·o·nym, n. 'ep-o-"nim. 1. The person for whom something (as a disease) is or is believed to be named. 2. A name (as of a drug or a disease) based on or derived from the name of a person. (Merriam-Webster's Medical Dictionary, � 2002 Merriam-Webster, Inc.)

eponym n. 1. The name of a person for whom something is supposedly named; "Constantine I is the eponym for Constantinople". 2. A name derived from the name of person (real or imaginary) as the name of Alexandria is derived from the name of its founder: Alexander the Great. (WordNet � 2.0, � 2003 Princeton University)

Marcus Hill points to a similar ambiguity in the usage of the word "cleave":

cleave¹ v. cleft or cleaved or clove, cleft or cleaved or clo·ven, ... 1. To split with or as if with a sharp instrument. 2. To make or accomplish by or as if by cutting: cleave a path through the ice....
cleave² intr.v. cleaved, cleav·ing, cleaves. 1. To adhere, cling, or stick fast. 2. To be faithful: cleave to one's principles.

Here's one more from from The American Heritage Dictionary I came by by accident:
rock² v. rocked, rock·ing, rocks
1. To move back and forth or from side to side, especially gently or rhythmically.
2. To sway violently, as from a blow or shock. See Synonyms at swing.
Thanks to Devon McCormick for an additional example, "ravel":

rav·el v. rav·eled also rav·elled, rav·el·ing rav·el·ling, rav·els rav·els. --tr. 1. To separate the fibers or threads of (cloth, for example); unravel. 2. To clarify by separating the aspects of. 3. To tangle or complicate. --intr. 1. To become separated into its component threads; unravel or fray. 2. To become tangled or confused. --rav·el n. 1. A raveling. 2. A broken or discarded thread. 3. A tangle.
Also from The American Heritage Dictionary

ir·re·gard·less adv. Non-Standard. Regardless. [Perhaps from ir(respective) + regardless.]
Among its various meanings, the word fixed has quite opposite two (From the NCTM 21st Yearbook (originally 1953, reprint 1995), p. 170):

A car may be "fixed," for example, to better win the race; but a horse may be "fixed" to lose a race ...
One half is a term with broad usage in the everyday life. In Fear No More, the authors, P. Hilton and J. Pedersen, give this example (p 54):

Offered a piece of cake, we may reply "Please, just give me a half." Our hostess or host may then cut the piece of cake into two equal pieces and give us one of those pieces - we have received a half of the original piece of cake. On the other hand, a realtor, showing us two possible lots for purchase may say "Lot A is more attractively situated but there is only half as much land as on lot B." There is no suggestion that lot A has been created by cutting up lot B.
Here is a quote from How The Mind Works by Steven Pinker (p 70):

Another problem with using English as the medium of knowledge is that English sentences can be ambiguous. When the serial killer Ted Bundy wins a stay of execution and the headlines read "Bundy Beats Date with Chair," we do a double take because our mind assigns two meanings to the string of words. /p>
The following comes from Mathematics and the Imagination by Edward Kasner and James Newman. The book was first published in 1940. The quote comes from the 16th printing (1958)

Alice was criticizing Humpty Dumpty for the liberties he took with words: "When I use a word," Humpty replied, in a scornful tone, "it means just what I choose it to mean-neither more nor less." "The question is," said Alice, "whether you can make a word mean so many different things." "The question is," said Humpty, "which is to be master, that's all."

Those who are troubled (and there are many) by the word "imaginary" as it is used in mathematics, should hearken unto the words of H. Dumpty. At most, of course, it is a small matter. In mathematics familiar words are repeatedly given technical meanings. But as Whitehead has so aptly said, this is confusing only to minor intellects. When a word is precisely defined, and signifies only one thing, there is no more reason to criticize its use than to criticize the use of a proper name. Our Christian names may not suit us, may not suit our friends, but they occasion little misunderstanding. Confusion arises only when the same word packs several meanings and is what Humpty D. calls a "portmanteau."

Semantics, a rather fashionable science nowadays, is devoted to the study of the proper use of words. Yet there is much more need for semantics in other branches of knowledge than in mathematics. Indeed, the larger part of the world's troubles today arise from the fact that some of its more voluble magnificoes are definitely antisemantic.
H. P. Ginsburg (Children's Arithmetic, pro-ed, 1989) notes (pp 103-104) that children must learn that mathematics is a special language, different from ordinary speech. He tells of seven-year old Sally who was asked in school, "What is the difference between 11 and 6?" She answered first that, "Eleven has two numbers [referring to the two 1's in 11], whereas 6 has only one." After a while she added, "6 is curly, whereas 11 is straight."

Neither answer of course was expected by her teacher. Ginsburg concludes that "Sally needed to learn that in school questions about numbers usually refer to calculations or to mathematical ideas: they do not refer to such superficial characteristics as shape." I think they may. But more importantly not every sentence that somehow refers to numbers is necessarily arithmetic. I do not believe that the question posed to Sally belongs to that special language we call mathematics. "Compute 11 - 6" is quite unequivocal. The example actually shows how ambiguous is the common language. Learning about teacher's expectations is in the realm of metaknowledge that has nothing to do with mathematics.

Curiously, a Math Magazine publication seems to suggest that young Sally might have been more of a mathematician than her teacher or Prof. Ginsburg.

(There is another difference between 11 and 6: if written with a scalpel, 6 will cut the paper into two pieces, 11 will not.)
A complementary example comes from viva la repartee by Dr. Mardy Grothe:

During his major league baseball career, Alex Johnson developed a reputation as a talented ball player with an attitude problem. Regarded by managers and coaches as surly and uncooperative, he ended up playing for eight separate teams in his thirteen-year career. An aggressive contact hitter who rarely struck out, he was never much of a home run threat. In 1969, while playing with Cincinnati Reds, he hit a career-high seven home runs, fifteen more than the previous year. A few months into the season, reporters began to take notice of the newfound punch in his bat. One day, an interviewer said, "Alex, you hit only two homers all of last year and this season you already have seven. What's the difference?" Proving he could be just as challenging with reporters as with managers, the ballplayer with a chip on his shoulder said, "Five."
Jennifer Kramer gave this example

Subject: Two Twins

Date: Thu, 19 Aug 2000 18:23:46 -0400

From: Jennifer Kramer

Hi!

I can't believe I only just found your site, it's really boss. You mention in Math As Language: "I welcome any examples of language misuse or inherent ambiguity you may want to send me."

I did a sitewide phrase search on "two twins" that came up blank. Wm. Safire once wrote in his regular NY Times Magazine column (I can't cite exactly, it was years ago) that this phrase is redundant.

When I got married, my dad (an old white guy whose fraternal twin makes a Mutt & Jeff match) was of course in the wedding party. His twin attended but wasn't in the wedding party. My matron of honor was a big young black girl whose identical twin wasn't invited to the wedding for lack of space. When you see my dad and matron of honor together in pictures, according to Safire's advice you can only refer to them as "twins" - but that would imply that they are twins to each other! Should I say I had two twins, a pair of twins, two temporarily twinless twins or just plain twins in my wedding party?

Jennifer Kramer
Edited by E.Berlekamp and T.Roger, collection The Mathemagician and Pied Puzzler of short articles presented in honor of Martin Gardner is an unusual, often humorous, combination of mathematics and magic. In the chapter A Powerful Procedure for Proving Practical Propositions by Solomon W. Golomb we find several inspiring syllogisms à la Lewis Carroll

All human beings are different.
All apathetic people are indifferent.
Therefore, no apathetic people are human beings.

Every incomplete investigation is a partial investigation
Every unbiased investigation is impartial investigation.
Therefore, no incomplete investigation is unbiased.

In addition, there is a proven political statement: All governments are unjust.

To prove the assertion for all governments, it is sufficient to prove it for an arbitrary government. If a government is arbitrary, it is obviously unjust. And since this is true for an arbitrary government, it is true for all governments.
A similar semantic fallacy was quoted at Wikipedia

Nothing is better than eternal happiness.
Eating a hamburger is better than nothing.
Therefore, eating a hamburger is better than eternal happiness.
Robin Wilson (Lewis Carroll in Numberland, p. 194) quotes a paradox by Lewis Carroll:

Men over 5 feet high are numerous.
Men over 10 feet high are not numerous.
Therefore, men over 10 feet high are not over 5 feet high.
Here is a short passage from I. Stewart's Game, Set and Math that may well serve as an entertaining party prank:

"What," I said, "do you think you're doing with my lunch?"

The newspaper was lowered and a thin face with spectacles and long fair hair appeared. The man wore a black cloak and had what looked like a wooden chain round his neck; he carried a strange stick carved into spirals with a cleft at the top like a devil's horns. Apart from the spectacles he looked like an Old Testament prophet. "I was pushing your banana through this hole," he said. I bet you $5 you can't push your orange through it too."

"Of course I can't! The hole's too small!"

He smiled. "So if I push your orange through the hole, you owe me $5?

"Provided you don't tear the paper, or cut up the orange, certainly!" I snapped.

He picked up the orange and held it close to the hole in one hand. With the other he stuck a finger through the hole and gave the fruit a push. "There!" he said. "As promised, I have just pushed your orange through the hole!"

I should have known better than to accept a sucker bet.
Steve Cushing wondered on twitter.com
If electricity comes from electrons, does morality come from morons?
The following is taken from Sarah Flannery's In Code, where, on the occasion of introducing modular arithmetic, she quotes Richard Guy:

Here's a charming story from Richard Guy, quoted in Lure of the Integers (p. 204) by Joe Roberts, which has some connection with our discussion. In Guy's words:

There used to be an admission examination, the "11-plus," to British secondary schools. A question that was asked on one occasion was "Take 7 from 93 as many times as you can." One child answered, "I get 86 every time." I hope she got her place.

Did the examiners expect the students to know that, in our "mod" notations, 93 mod 7 = 2, or did they want them to say that you can take 7 from 93 thirteen times?
Here's one from Paul Slattery who noticed a sign frequently posted next to escalators:

Dogs Must Be Carried on Escalator

A business opportunity perhaps ?

Going Up/Down, Lease-a-Hound $1.50 one-way, $2.00 Round Trip

Paul's letter brought to mind a few common signs. For example, Right Lane Must Turn Right. Does it ever? On the other hand, Use Left Lane to Pass is clearly addressed to carriers of driving licenses who may or may not obey the conveyed regulation.

Subject:	Two Twins
Date:	Thu, 19 Aug 2000 18:23:46 -0400
From:	Jennifer Kramer

In the 777 Mathematical Conversation Starters (pp. 52-53) we find the following:

The following was found in a jewelry shop window. Its two meanings are opposite of each other:

Nothing makes you feel as good as gold.

Meaning 1.	If you are looking for something to make you feel really good (as good as gold, say), then forget it -- nothing will do the job.
Meaning 2.	If you are looking for something to make you feel good, then gold will do the job -- and nothing does it better. (Presumably, this is the jeweler's intended meaning.)

John Faben perceived a third meaning:

Meaning 3.	If you are looking for something that will make you feel as good as gold will make you feel, don't try too hard, as nothing at all will suffice.

The classic sentence -- Time flies like an arrow -- that was mentioned earlier in a different context has, according to 777 Mathematical Conversation Starters (p. 52), two different meanings:

Meaning 1. Time (a verb) flies (a noun) in flight just as you time arrows in flight.

Meaning 2. Time (the noun) passes as quickly as an arrow flies.

The following lateral puzzle [Challenging Lateral Thinking Puzzles, P. Sloane & D. MacHale, #1.4] depends on the inherent language ambiguity:

A man walked all the way from Dublin to Cork along main roads without passing a single pub. How did he manage that? (Pubs or "public houses", that is, bars, are very common in Ireland.)

(Answer: the man did not pass a single bar because he went into every one!)
Here's a tweet from Evelyn Lamb (Jan 21, 2015):

Hilarious topology joke that my students did not appreciate this morning: if a space isn't simply connected, maybe it's simply connected.
I have forgotten the source of this exchange:

Q: Did you live in the US all your life?
A: Not yet.
In a column in The Gardian, Oliver Burkeman wrote thus:

It�s a cliché that certain things we do can change us enormously: having children, above all, followed perhaps by getting married, or moving to a foreign country.

The author had in mind the order of importance of some events as affecting our life. If you remove "or moving to a foreign country" or replace it with ellipses, the sentence acquires an unintended meaning, introducing as a possibility a temporal order among the events.
In March, 2015, the Jerusalem Post had an article with a caption, "75% of Israeli Jews want civil divorce." Even if you know that for Israeli Jews the only way to marry is by following a religious traditional wedding and to divorce also only in the traditional way, the announcement wouls still sound ambiguos. The intention is that 75% of the Israeli Jews would support a ligislation allowing civil mariages and civil divorces. The unintended reading is that 75% would divorce in a civil ceremony, if only allowed.

Meaning 1.	Time (a verb) flies (a noun) in flight just as you time arrows in flight.
Meaning 2.	Time (the noun) passes as quickly as an arrow flies.

References

The American Heritage Dictionary
J. dePillis, 777 Mathematical Conversation Starters, MAA, 2002
W. Safire, On Language, Times Books, 1981
W. Safire, Take My Word For It, Times Books, 1986
R. Smullyan, This Book Needs No Title, Touchstone, 1980

Language of Mathematics, Language of Science and Plain Language

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