Showing posts with label Mathematics. Show all posts
Showing posts with label Mathematics. Show all posts

Monday, November 10, 2008

Tautology (rhetoric)

In rhetoric, a tautology is an unnecessary (and usually unintentional) repetition of meaning, using different words that effectively say the same thing twice (often originally from different languages). It is often regarded as a fault of style and was defined by Fowler as "saying the same thing twice". It is not necessary for the entire meaning of a phrase to be repeated; if a part of the meaning is repeated in such a way that it appears as unintentional or clumsy, then it may be described as tautology. On the other hand, a repetition of meaning which improves the style of a piece of speech or writing is not usually described as tautology, although it may be a logical tautology.

A rhetorical tautology can also be defined as a series of statements that comprise an argument, whereby the statements are constructed in such a way that the truth of the proposition is guaranteed. Consequently the statement conveys no useful information regardless of its length or complexity. The statement "If you can't find something (that you lost), you are not looking in the right place" is tautological, as is "It is always in the last place you look". It is true, but conveys no useful information. As a physical example, to play a game of darts where the dart board was full of bullseyes, could be called a "tautological" game. The player wouldn't lose. Any argument containing a tautological statement is thus flawed logically and must be considered erroneous.

A tautological argument is not an argument; a tautological game is not a game. Mathematical equations, such as E = mc2, are not tautologies. The terms on both sides of the equation are defined elsewhere independently. The equal sign does not mean "is defined by" but rather equal to, thus establishing an equivalence. Acceleration and mass independently don't equal force but their product MA as derived by Newton does, hence the equation F=MA isn't a tautology, but F=F would be.

Examples
A common form of tautology is using two forms of the same word in the same construction. E.g., the British supermarket Tesco sells a brand of lemon thyme which it describes as having an "aromatic aroma".[citation needed] Synonyms may also produce a tautology; "free gift" is tautologous because a gift, by definition, is something given without charge. Other such examples of tautology include "sufficiently adequate" and "new innovation". In phrases, tautology is present in sayings such as "I can see it with my own eyes", "suddenly, without warning" and "forward planning"/"planning ahead".

Repetitions of meaning in mixed-language phrases
Repetitions of meaning sometimes occur when multiple languages are used together, such as "the La Brea Tar Pits" (the The tar Tar Pits), "monsoon season" (season season), "the hoi polloi" (the the many), "Sierra Nevada mountain range" (Snowy Mountain Range mountain range), "Sahara Desert" (Deserts Desert), "Gobi Desert" (Desert Desert), "shiba inu dog" (short-haired dog dog), "Jirisan Mountain" (Jiri mountain mountain), "shrimp scampi" (shrimp shrimp), "Mississippi River" (Great-river river) "cheese quesadilla" (cheese cheesy-thing), "Lake Tahoe" (Lake Lake), "Faroe Islands" (Sheep Island Islands), and "Angkor Wat temple" (Angkor Temple temple). The Los Angeles Angels of Anaheim (The The Angels Angels of Anaheim). Possibly the most extreme example is "Torpenhow Hill" (Hill-hill-hill Hill, in four languages).

The tautological status of these phrases is somewhat subjective and can be harder to detect than monolingual varieties, since they are only perceived as tautologous by people who understand enough of each of the involved languages, and because of the way that words change meaning as they drift from one language to another. For example, chai is Hindi for "tea", but in the United States, where the phrase "chai tea" is common, what is referred to as "chai" is more precisely "Masala chai."

Similar examples of repetitions occur when multiple languages are used in the same geographic area, even when the populations are generally well aware of the meaning of the redundant words. In bilingual (French and English) areas of Canada, for example, people may refer to the "Pont Champlain Bridge" (Bridge Champlain Bridge). Tautologies like these occur more frequently in spoken English when printed materials compress the bilingual presentation (e.g. from the expected "Pont Champlain / Champlain Bridge" to "Pont Champlain Bridge"), a technique commonly used in Canada, New Mexico and other bilingual areas to save space on road signage, grocery packaging, etc. A New Mexico example is the Spanish placename Arroyo del Oso (a ravine running through Albuquerque), known in English as Bear Canyon, but sometimes appearing as "Arroyo del Oso Canyon" (Small-canyon of-the Bear Canyon) or even "Bear Canyon Arroyo" (Bear Canyon Small-canyon). Another example of this, both in Las Cruces, New Mexico and north of Tucson, Arizona, is that of Picacho Peak (picacho being peak in Spanish).

Redundant expansion of acronyms
In some cases an acronym or abbreviation is commonly used in conjunction with a word which is actually part of the shortened form. One of the better known examples of this is "PIN number", which is often used when explaining the concept. Other examples include ATM machine, RAID array, AC/DC current, LAN network, LPG gas, RPG game, ISBN number, Hot Water Heater and "HIV virus". This phenomenon is humorously, self-referentially referred to as RAS syndrome (Redundant Acronym Syndrome - syndrome).

For more details on this topic, see RAS syndrome.

Intentional repetition of meaning
A repetition of meaning may be intended to amplify or emphasize a certain aspect of the thing being discussed. For example, a gift is by definition free of charge, but one might talk about a "free gift" to emphasize that there are no hidden obligations, financial or otherwise, or that the gift is being given out of free will. This is related to the rhetorical device of hendiadys, where one concept is expressed through the use of two, for example "goblets and gold" meaning wealth, or "this day and age" to mean the present time. Superficially these expressions may seem tautologous, but they are stylistically sound because the repeated meaning is merely a stylized way to express a single concept.

Much Old Testament poetry features the same thing said twice, but in slightly different ways ('Deceit is their sole intention, their delight is to mislead', Psalm 62). In this example, it is not exactly the same statement in both cases (in the first, the singleness of purpose is highlighted, in the second the pleasure), but more or less the same thing is being affirmed. This can be found very many times in the Psalms, and in other areas of the Bible as well.

Further examples
Some of the notable quotes said by, or attributed to, baseball player and manager Yogi Berra are considered humorous because they are, on the surface, tautological, including "It ain't over till it's over", "We made too many wrong mistakes" and "You can observe a lot by watching."
In a 1988 campaign speech in Ohio, George H. W. Bush said, "It's no exaggeration to say the undecideds could go one way or another."[1]
The Tenth Amendment to the US Constitution: In New York v. United States, Supreme Court Justice Sandra Day O'Connor stated, "The Tenth Amendment likewise limits the power of Congress, but this limit is not derived from the text of the Tenth Amendment itself, which, as we have discussed, is essentially a tautology." O'Connor reasoned that the Tenth Amendment simply reiterated what was already built into the structure of the Constitution generally: When the States consented to the Constitution they expressly delegated certain powers to the Federal government. Implicitly, what was not given was necessarily retained by the states.
In his book Mostly Harmless, Douglas Adams used the phrase, "Anything that happens, happens. Anything that in happening causes something else to happen, causes something else to happen. Anything that in happening happens again, happens again. Though not necessarily in that order."
A story arc of the British science fiction television series Doctor Who was titled "The Deadly Assassin" — one only becomes an assassin by successfully committing murder. Originally, the title was intended to be "The Dangerous Assassin," but the title was changed by the producers as the title just "didn't sound right."
Richard B. Frank's history of the end of the Pacific War is titled Downfall: The End of the Imperial Japanese Empire. By definition, an empire is imperial.
The phrase "digital download": given that downloading is the transfer of binary or digital data from a higher level system to a lower one, all downloading is inherently digital.
Avenue Road is tautological since in most cases, an avenue is also a road.
The Hamilton Tiger-Cats are tautological, since tigers are cats, but its name is a merger of two earlier Hamilton teams.
In The Melancholy of Haruhi Suzumiya, Kyon refutes his own argument when describing Haruhi as "Haruhi is Haruhi, nothing but Haruhi", because it is tautology.
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Source: Wikipedia

Monday, June 30, 2008

Remedial

Can it be? I enjoy giving remedial more than actual teaching. The pressure of book checking is lifted and I can afford to be creative with my lessons. Proceeding with diagnostic tests for English and heuristics for Maths and maybe Science. But having fun so far and I hope I can remove the stigma of remedial in the students' minds.

Friday, June 06, 2008

Teaching Practice: 25 Feb - 9 May 08

Despite a virtual guarantee of a credit by my main CT, I only got a pass. I intend to clarify with her why this happened, but I strongly suspect my supervisor's ill-timed and ill-prepared second observation did me, Nazir and Hui Erl in. It does leave a bitter taste in the mouth, seeing we did our best and were at the mercy of general incompetence.
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9 Apr 2008, 1843hrs
I'm geting swamped here. Have been trying to keep up with my lesson plans and as a result, am falling back with my marking. The result? I bag full of worksheets and a 0.5m stack of books. Die...
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7 Mar 2008, 1343hrs
Another treat! My CTs don't require me to write daily lesson plans in painstaking detail. They just need a weekly lesson plan with details of the procedure, resources and all that. This reduces the workload by A LOT. Of course formal observations still need the detailed one lah. But thank God for His mercy and providence.
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My, my. What a surprise. Practicum's been a breeze so far with only obervations going on. Little chance of me teaching next week due to CA and my CT's wanting to finish their incumbent unit first. Looks like I'm only starting in Term 2, which means I have the term break to piah lesson plans. Term 2 Week 7-8 should be interrupted by SA1, so I'm left with 6-7 weeks to fit 10 observations in. It might not be that bad after all. I think the P2 class will be the challenge.
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21 Feb 2008, 1843hrs
This is the biggie. Ten weeks altogether. One week of observation followed by nine weeks of teaching. I'm teaching P3 & 2 English and Maths respectively. My main CT is the P3 level head. Our practicum will include CA and SA time, so that should cut down the teaching load.

Monday, January 21, 2008

My quirky alarm clock

Seems to be working. Hope it stays that way.
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19 Jan 08, 2243hrs
Reached a compromise. Scotch-taping my battery securely to my alarm clock. Let's see if it works.
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19 Jan 08, 1543hrs
No this is not a Maths problem.

When my alarm rings, it somehow shakes the battery loose and the clock stops running. So sometimes a snooze can be a really long time. I think I need a new clock. =[