Friday, October 30, 2009


Ambiguity can be defined as a form of communication with two or more possible meanings. In many cases, however, one interpretation is more likely than the other. Ambiguity can be further classified into structural and lexical.

An example of ambiguity which I recall from studying linguistics is "He saw the man with binoculars". This sentence has two possible interpretations. It may mean that the subject used binoculars to see the man. In this case, the prepositional phrase "with binoculars" is a verb complement. However, another interpretation is that the subject saw a man who had binoculars. In the case, "with binoculars" is part of the noun phrase, a noun adjunct.

The likely interpretation is that the subject used binoculars to see the man. However, the other interpretation is also possible. The intended meaning is usually clear from context. If not, it is possible to disambiguate so that the intended meaning is clear. The sentences "He used his binoculars to see the man" and "He saw the man who had binoculars" are not at all ambiguous.

The sentence "He saw the man with binoculars" is an example of structural ambiguity. The position of the prepositional phrase makes two interpretations possible. However, if the prepositional phrase is shifted to the beginning of the sentence, only one interpretation is possible. This is the case with "With binoculars he saw the man". Now the phrase "with binoculars" is the verb complement of "saw".

"She drew five triangles and squares" has many possible interpretations. One interpretation is that the subject drew five triangles and five squares. In this interpretation, ellipsis leaves out "five" before the object "squares". Another interpretation is that the subject drew five triangles and an undefined number of squares. Also possible is the interpretation that the subject drew a combination of triangles and squares that totalled five. The possibilities are three triangles and two squares and two triangles and three squares. Thus the sentence "She drew five triangles and squares" has four different interpretations.

Another kind of ambiguity is lexical. For example, the sentence "They sat by the bank" is ambiguous because of the word "bank". It can refer to either a financial institution or the edge of a body of water such as a river. From context, however, the meaning is usually very clear. The more likely interpretation in this case is that "bank" refers to the edge of a river than to a financial institution.

The sentence "The lamb is too hot to eat" is ambiguous because it is not clear whether "lamb" refers to the live animal or to meat on a plate. If the lamb is alive, the animal has no appetite but may be very thirsty. If the lamb is meat to be eaten, the person who wants to eat it must wait for it to cool down. Ambiguity also occurs with the word "hot" in the interpretation in which "lamb" refers to meat. In this case, "hot" may mean at a high temperature or spicy. Despite the ambiguity of "The lamb is too hot to eat", the likely interpretation is that the meat is either at too high a temperature or too spicy to eat.

Many examples of ambiguity can be found in language. However, communication is usually clear because the meaning can be understood from the context in which it is communicated. If the meaning is not clear, it becomes necessary to disambiguate.

Sunday, October 25, 2009

Mexican Children's Song

Francisco Gabilondo Soler wrote many songs for children that are well-known in Mexico. I used to listen to them as a child. My favourite was "El Chorrito" which means "The Little Jet" referring to the little jet shooting out of a fountain. Here is the Spanish text along with my English translation.

La gota de agua que da la nube como regalo para la flor
En vapor se desvanece cuando se levanta el sol;
Y nuevamente al cielo sube hasta la nube que la soltó.
La gotita sube y baja, baja y sube al compás de esta canción.

Allá en la fuente había un chorrito, se hacía grandote se hacía chiquito; (2x)
Estaba de mal humor, pobre chorrito tenía calor. (2x)

En el paisaje siempre nevado acurrucado sobre el volcán
Hay millones de gotitas convertidas en cristal.
En el invierno la nieve crece, en el verano la funde el sol.
La gotita sube y baja, baja y sube al compás de esta canción.

Ahí va la hormiga con su paraguas y recogiéndose las enaguas, (2x)
Porque el chorrito la salpicó y sus chapitas le despintó. (2x)

The drop of water which the cloud gives as a present for the flower
Dissipates into vapour when the sun rises;
And rises again to the sky up to the cloud which released it.
The little drop rises and falls, falls and rises to the compass of this song.

Over there in the fountain there was a little jet,
It made itself big, it made itself small. (2x)
It was in a bad mood, poor little jet was hot. (2x)

On the always snowy landscape nestled over the volcano
Are millions of little drops converted into crystal.
In winter the snow grows, in summer the sun melts it.
The drop rises and falls, falls and rises to the compass of this song.

There goes the ant with its umbrella and picking up its petticoats (2x)
Because the little jet splashed it and discoloured its cheeks. (2x)

This song is much more beautiful in the original Spanish language because the rhyme and rhythm are lost in the English translation. It is a classic among Mexican songs for children.


Thursday, October 22, 2009


Konglish is an interesting variety of English used by Koreans. It bears many similarities to the English used in Japan. The word "Konglish" combines the words "Korean" and "English". In many cases, Koreans do not realize that they are using Konglish rather than standard English.

Konglish words are often very similar to English words. For example, the words "pine juice" and "hand phone" mean "pineapple juice" and "cell phone". In the first case the word "pineapple" is abbreviated and in the second the word "cell" is replaced by "hand". Another example of an abbreviation is "ballpen". This word means "ballpoint pen".

Many English plurals only have a singular form in Konglish. For example, "sunglasses" and "slippers" are "sunglass" and "slipper" in Konglish. This is understandable because Korean, although it has a plural marker, usually does not use it.

The word "hotchkiss" may be difficult for English speakers to understand. It is the Konglish word for "stapler" and in fact is the last name of E.H. Hotchkiss, an American company that was an early manufacturer of staplers. The meaning of the compound "golden time" may also be unclear to English speakers . It is "prime time" in standard English.

The words "back mirror" and "handle" are Konglish words which mean "rear view mirror" and "steering wheel". "Vinyl" means "plastic" and is also used in "vinyl house". In this case, it means "greenhouse". The expression "eye shopping" is the Konglish term for "window shopping".

Konglish can be described as a unique variety of English that is used by Korean speakers. Though many of the words used may be identifiable to English speakers, some undoubtedly are not.

Sunday, October 18, 2009

Math Multiplication Tricks

A number of multiplication tricks can make multiplication fun and simple. In fact, these tricks make it possible to calculate equations in your head. It is simply a matter of practice.

To multiply squares of five, write down 25. All squares of five end in 25. Next, add one to the first digit and multiply. For example, 45x45=2025. We first write down 25. We then add 1 to the first digit which is 4. This gives us 5. We multiply 5x4 to get 20. We write 20 next to 25 to get the answer 2025.

Now we will do 85x85. We write down 25. We add 1 to 8 which is 9. We multiply 9 by 8 to get 72 and write it down to get 7225. 85x85=7225.

For squares of 90 to 99, we have a simple formula. Subtract the number needed to reach 100 from the square. For example, 98 is two from 100, so we subtract two to get 96. We write this number down. Next we square this number and write it down. 2x2=4, so we write down 4 but we need two digits to the right of 96, so we write 9604. 98x98 = 9604.

Now we will try 96x96. 96 is four from 100, so we write 92. Next we square four. 4x4=16, so we write 9216. 96x96=9216.

Unfortunately, not all squares are quite so simple. With 27x27, we need to use the closest multiple of ten to calculate the answer. The closest multiple of ten is thirty. It is three away, so we subtract three from 27 to get 24. Now we must multiply 24 by 30. This is 720. Now we square three to get nine and add this number. 27x27=729.

Now we can do 49x49. 49 is one from fifty, so we get 48. We multiply 48 by 50 to get 2400. Next we square one to get one. 49x49=2401.

With multiplication problems up to 20x20 we have a simple formula. We can use 16x13 as an example. Always start with the higher number because this makes the calculation easier to perform. Remove the first digit from 13 and this gives us 3. Now add 16+3. This gives us 19. Now add a 0 to 19 to get 190. Finally multiply the last digits of each number. We multiply 6x3 to get 18. We add 18 to 190 to get 208. 16x13=208.

Now we can do 19x14. We add 19+4 to get 23. Add a 0 to get 230. Now we multiply 9x4 to get 36 and add this number to 230. We get 266. 19x14=266.

With multiplication by 11, we also have a simple formula. If we want to calculate 54x11, we write down the 5 and the 4 with a space between them. We can write 5_4. Next we write the sum of 5 and 4 in this space. 5+4=9, so we write 594. 54x11= 594.

Now we can solve 72x11. We write 7_2 so that we have the 7 and 2 with a space between them. The sum of 7 and 2 is 9, so we write this in the space. 72x11=792.

If the sum if greater than ten, however, we write down the ones digit and carry over the tens digit. I can demonstrate with 67x11. We write 6_7. 6+7=13, so we write the ones digit in the space. This gives us 637 but we must add 1 to 6 to get the correct answer, 737. 67x11=737.

Multiplication tricks can make multiplication not only more enjoyable but possible to calculate with only your brain. It is simply a matter of practice. I wish that I had known these tricks when I was in school.

Thursday, October 15, 2009

Stress of Compound Nouns in English

Many compound nouns in English consist of an adjective and a noun. In constructions consisting of an adjective followed by a noun, it is the noun which carries primary stress. In a compound noun constructed of an adjective and a noun, however, it is the adjective which carries primary stress.

A house that is green is a green house with primary stress on "house". A place for growing plants and vegetables is a greenhouse with primary stress on "green". A house that is white is a white house with primary stress on "house" but the residence of the President of the United States is the White House with primary stress on "White". A suit that has gotten wet is a wet suit with primary stress on "suit" but the suit worn by a scuba diver is a wetsuit with primary stress on "wet".

Spelling is unimportant because compound nouns can be written as one word, two words or even hyphenated. For example, "softball" is a one-word compound, "high school" is a two-word compound and "two-thirds" is a hyphenated compound.

Sometimes compound nouns do not carry compound stress. In other words, certain compounds do not carry primary stress on the first syllable. Most English speakers use compound stress in "apple sauce" but not in "apple pie". Likewise, most use compound stress in "potato chips" but not in "potato soup". In the latter case, the familiarity of the item may be a factor. More people eat potato chips than potato soup. However, this does not explain "apple pie" which is a popular dessert but is not pronounced with compound stress by most speakers.

Also interesting is that compounds with "cake" carry compound stress but compounds with "pie" usually do not. For example, the compounds "carrot cake", "plum cake", "lemon cake" and "cheesecake" carry first-syllable stress but in the English of most speakers the compounds "cherry pie", "pecan pie", "peach pie" and "lemon pie" do not.

However, the compound "chocolate cake" is a compound noun which many speakers do not pronounce with compound stress. This may be due to the syllabic structure of the compound. Speakers who stress the word "cake" in the compound "chocolate cake" use strong stress followed by weak and strong stresses to give the compound a regular rhythm. However, those who stress the first syllable use compound stress but use strong stress followed by two weak stresses to produce a rhythm which is less regular. In any case, not all compound nouns in English use compound stress.

Many of the compound nouns in English consist of an adjective and a noun. The stress of these compounds is different from the stress of constructions with an adjective and a noun. Compound nouns formed from an adjective and a noun carry primary stress on the adjective but constructions with an adjective and a noun carry primary stress on the noun. However, many compound nouns are an exception to this rule.

Saturday, October 10, 2009

Chess Match of Napoleon Bonaparte

Napoleon Bonaparte was an accomplished chess player. In this game between Napoleon Bonaparte and General Bertrand, Napoleon Bonaparte defeats his general very convincingly. Here are the moves of the game along with my commentary. Napoleon Bonaparte is white and General Bertrand is black.

1. Nf3 Nc6

A more common reply for black here is Nf6.

2. e4 e5
3. d4 Nxd4
4. Nxd4 exd4
5. Bc4 Bc5

White can take the d-pawn with his queen but prefers to develop his bishop.

6. c3 Qe7
7. 0-0 Qe5

White castles to protect his king. Black advances the queen to protect the d-pawn and prevent white's e-pawn from advancing.

8. f4 dxc3+

White aggressively attacks the black queen but black ignores the attack and puts the white king in check.

9. Kh1 cxb2

Black is one move away from queening his pawn but his queen is under attack.

10. Bxf7+ Kd8

White prepares a bishop sacrifice. Black refuses the sacrifice because if he takes Kxf7, black can play fxe5 which not only captures the queen but puts the black king in check.

11. fxe5 bxa1 (Q)

White captures black's queen but black queens on a1.

12. Bxg8 Be7

Black does not take the bishop on g8 because if he plays Rxg8, white can fork the rook and bishop with Qe5.

13. Qb3 a5

White puts the queen on a square which exerts control over the b3-g8 diagonal and protects the knight on b1 and bishop on g8 at the same time. Notice that black's king is stuck in the centre of the board and the black queen is unaided on a1.

14. Rf8+ Bxf8

White sacrifices the rook. Black's reply is forced.

15. Bg5+ Be7

Black's reply is forced. If he plays Ke8, Bf7 and Qf7 are both checkmate.

16. Bxe7+ Kxe7

Again black's reply is forced.

17. Qf7+ Kd8

This is black's only legal move.

18. Qf8#

White has less material than black but emerges the victor. Black fails to get his king to safety and launches a premature attack against the white king. Only after getting his king to safety does white prepare his attack on the black king. In this game Napoleon Bonaparte teaches his general a lesson.

Tuesday, October 6, 2009

Predicate Logic

One area of semantics is predicate logic. It analyzes the internal structure of sentences. In predicate logic symbols are used to make a number of simple statements.

The sentences "Ann is sleeping" and "Joe paints" both have a simple subject-predicate structure. The subject is a referring expression (Ann, Joe) and the predicate gives information about the subject (is sleeping, paints).

The predicate can be represented by a capital letter. In the sentence "Ann is sleeping", this is "S" and in "Joe paints" this is "P".

The subject can be represented by a lowercase letter. This is called an individual constant. In "Ann is sleeping" this is "a" and in "Joe paints" this is "j".

Predicate logic forms begin with the predicate followed by the subject. The original sentences can be represented as follows:

Ann is sleeping: S (a)
Joe paints: P (j)

If one wishes to leave the identify of the subject unspecified one can use variables such as x and y. Thus, "Someone is sleeping" can be represented as S (x) and "Someone paints" as P (y).

The examples have only one noun. However, it is possible to use symbols in the analysis of sentences with more than one. For example, we can analyze sentences such as "Mark knows William" and "Helen likes Tom". These sentences have both a subject and an object.

The sentence "Mark knows William" can be represented as K (m, w) and the sentence "Helen likes Tom" can be analyzed as L (h, t). The order of the individual constants after the predicate letter mirrors English sentence structure. The subject comes before the object.

Other relational sentences can be represented in the same way. For example, "Ellen is younger than Olivia" is Y ( e, o). Here the predicate letter represents the comparative adjective "younger". Relations with three nouns are also possible. For example, the sentence "Paul prefers Danielle to Eleanore" is P (p, d, e).

Predicate logic aims to translate a sentence from an individual language into an expression in a universal metalanguage. This can be done with symbols which identify the subject-predicate structure of each sentence. It can also be viewed as a form of shorthand notation.

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