I Used To Know That Part 3

* PERCY BYSSHE Sh.e.l.lEY (1792-1822, English) One of the great Romantic poets, married to Mary, the author of Frankenstein. Lived mostly in Europe, latterly Italy, where he drowned in a boating accident. Author of "Ode to a Skylark" (Hail to thee, blithe Spirit!), "Ozymandias" (Look on my works, ye Mighty, and despair!) and Adonais, an elegy on the death of Keats.

* EDMUND SPENSER (c.1552-99, English) Author of The Faerie Queene, an epic poem celebrating the Tudor dynasty and Elizabeth I, and known to his peers as "the prince of poets." His poem "Epithalamion" has 365 long lines, representing the sum of 52 weeks, 12 months, and 4 seasons of the annual cycle, and 24 stanzas, corresponding to the diurnal and sidereal hours.

* ALFRED LORD TENNYSON (1809-92, English) Another prolific one. His great work is "In Memoriam," written on the early death of his friend Arthur Hallam; but most people are probably more familiar with "Come into the Garden," "Maud," and "The Lady of Shalott":Out flew the web and floated wide;

The mirror crack'd from side to side;

'The curse is come upon me!' cried.

The Lady of Shalott.

* DYLAN THOMAS (1914-53, Welsh).

Famous drunkard, but you forgive him most things for having written "Under Milkwood" and enabling Richard Burton to record it for posterity.

* WILLIAM WORDSWORTH (1770-1850, English) The most important of the Lake Poets (the others were Coleridge and Robert Southey). I have to say, I think "prolix" rather than "prolific" is the mot juste for Wordsworth. He churned it out, and goodness he was dull. The often-quoted "Daffodils" (I wander'd lonely as a cloud) is one of his, as is the "Sonnet Written on Westminster Bridge" (Earth hath not anything to show more fair).

* W(ILLIAM) B(UTLER) YEATS (1865-1939, Irish) Theosophist and Rosicrucian as well as poet and playwright; dedicated his early poems to Maud Gonne. Best known are "The Song of Wandering Aengus" and "The Lake Isle of Innisfree" (I will arise and go now, and go to Innisfree).

North American Poets.

Although this is an extremely short list of extraordinary poets, the writers listed here captured the voice and history of their generations. Hopefully they will inspire you to seek out the many remarkable poets that followed in their footsteps.

* ANNE BRADSTREET (1612-72) A puritan, she immigrated with her family in 1630 to the New World. Anne, who was used to an Earl's manor, had to adjust to near-primitive living conditions. She struggled to take care of her home and raise eight children but still found time to write and became the first female writer to publish work in colonial America. Some notable poems include "The Prologue" and "To My Dear and Loving Husband."

* EMILY d.i.c.kINSON (1830-1886) d.i.c.kinson spent a large part of her 55 years writing about death and immortality. After all, her home overlooked the Amherst, Ma.s.sachusetts, burial ground, and since Emily was a bit of a recluse and spent a large part of her adult life caring for her ailing mother, she had plenty of time to contemplate life and death through her window. Fewer than a dozen of her poems were actually published during her lifetime. Some of her well-known poems include "Because I could not stop for Death," "Success is counted sweetest," and "A wounded deer"-leaps highest, which contains the line Mirth is the mail of Anguish.

* ROBERT FROST (1874-1963, American) Probably second only to Whitman as "the great American poet," Frost won the Pulitzer Prize three times. His works include "Stopping by Woods on a Snowy Evening" (And miles to go before I sleep) and "The Road Not Taken" (Two roads diverged in a wood, and I-/I took the one less traveled by).

* HENRY WADSWORTH LONGFELLOW (1807-1882) He is known for his lyric poetry-"Paul Revere's Ride," "Evangeline," and "The Song of Hiawatha" (By the sh.o.r.e of Gitche Gumee, which, incidentally, is Lake Superior). Hiawatha may be the most mocked and parodied poem of all time, receiving reconstruction from agents such as Lewis Carroll ("Hiawatha's Photographing") and the producers of Sat.u.r.day Night Live.

* WALT WHITMAN (1819-92, American) The great American poet of the 19th century. His master-work is Leaves of Gra.s.s, a ma.s.sive collection of short poems, including "O Captain! My Captain!" and "When Lilacs Last in the Dooryard Bloom'd," both from the section "Memories of President Lincoln," inspired by the president's a.s.sa.s.sination.

International Authors.

Most of us had teachers of English or general studies who encouraged us to broaden our horizons by reading some of the foreign "greats" in translation. Keeping this to a Top 10 has meant cheating a bit on the Greek tragedians and leaving out Horace, Ovid, Rabelais, Moliere, Schiller, Balzac, Zola... and that's before I really hit the 20th century. But I think these are the ones you are most likely to have read without knowing the original language.

* DANTE ALIGHIERI (1265-1321, Italian) Known for The Divine Comedy, Dante divided his epic into three parts: Inferno (h.e.l.l), Purgatoria, and Paradiso. It narrates Dante's journey through these three worlds, the first two guided by Virgil, the final by Beatrice, a woman with whom he had been madly in love since he was nine, although it seems they met only twice. h.e.l.l is depicted as having various circles, indicating degrees of suffering, depending on how bad you had been in life: the ninth and worst contained the poets.

* MIGUEL DE CERVANTES (1547-1616, Spanish) One of the most influential works of Spanish literature is Cervantes's Don Quixote. The novel is about a man who becomes obsessed with books on chivalry and decides to go out into the world to do n.o.ble deeds. Toward this end, he imagines that a local village girl is the glamorous lady in whose name these deeds will be carried out, and he christens her Dulcinea del Toboso. His steed is actually a broken-down old horse called Rosinante, which means "previously a broken-down old horse." Along with other foolish whims, he adopts Sancho Panza as his squire and goes around attacking windmills because he thinks they are giants.

* FYODOR DOSTOEVSKY (1821-81, Russian) Often credited as a founder of 20th-century existentialism, Dostoevsky graduated as a military engineer. However, he soon resigned that career, began writing, and joined a group of utopian socialists. He was arrested and sentenced to death, but the punishment was commuted and he spent eight years in hard labor and as a soldier. His best-known works include Crime and Punishment, an account of an individual's fall and redemption, The Brothers Karamazov, a tale of four brothers involved in their father's brutal murder.

* GUSTAV FLAUBERT (1821-80, French) One of the most important novels of the 19th century, Madame Bovary was attacked for its obscenity when it was published more than 150 years ago. The novel focuses on Madame Bovary-Emma-who is married to a worthy but dull provincial doctor, Charles. She longs for glamour and pa.s.sion and has adulterous affairs, rebelling against the accepted ideas of the day. The novel served to inspire the beginnings of feminism.

* JOHANN WOLFGANG VON GOETHE (1749-1832, German) Once called "Germany's greatest man of letters," Goethe is best known for his two-part drama Faust, the tragic play about a man who sells his soul to the devil-here called Mephistopheles-in return for worldly success. Surprisingly, he is saved by angels. Christopher Marlowe's play Doctor Faustus was the inspiration for Goethe's work. Goethe's influence spread, extending across Europe, becoming a major source of inspiration in music, drama, poetry, and philosophy.

* HOMER (c. 9th century B.C., Greek) The great epics the Iliad and the Odyssey are the basis of pretty much everything we know about the Trojan War and about Odysseus (Ulysses)'s 10-year journey to get home to Ithaca. A quick rundown on the Trojan War: Paris, prince of Troy, abducted Helen, the beautiful wife of Menelaus, who was the King of Sparta (in Greece). Various Greek heroes-Odysseus, Achilles, Agamemnon-were pledged to fight to bring her back. They laid siege to Troy for 10 years before finally hitting on the idea of a wooden horse: Soldiers hid inside it, the Trojans were fooled into taking it within the city walls, the soldiers leaped out, and the Trojans were defeated. The Trojan hero was Paris's older brother, Hector. Their parents were Priam and Hecuba, and their sister Ca.s.sandra was the one who made prophecies that no one believed. Then Odysseus set off for home, encountering Circe, Calypso, and the Cyclops Polyphemus on the way. Back home his wife, Penelope, had promised her suitors that she would marry one of them when she had finished the piece of weaving she was doing, but she secretly unraveled the day's work every night.

* VICTOR HUGO (1802-85, French) One of the most notable French Romantic writers, Hugo created his own version of the historical novel by combining historical fact with vivid, imaginative details. His great achievements were Notre-Dame de Paris, known to us as The Hunchback of Notre-Dame, and Les Miserables. The hunchback Quasimodo is the bell ringer at Notre-Dame, and the plot concerns his love for the Gypsy girl Esmeralda. Les Miserables, known to many because of its successful stage adaptations, is set in Paris in 1815, at the time of the Battle of Waterloo. The central character, Jean Valjean, is a reformed thief who is persecuted by the police agent Javert.

* SOPHOCLES (c. 496-406 B.C., Greek); EURIPIDES (c. 480-406 B.C.); ARISTOPHANES (c. 448-380 B.C.) Oedipus Rex, also known as Oedipus the King, is the play about the man who accidentally married his mother. It is the first in Sophicles's Oedipus Trilogy, followed by Oedipus at Colonus and then Antigone. Medea, the play about the woman who murdered her children to avenge herself on their father is by Euripides, who lived around the same time. And while we're at it, there was the comic playwright Aristophanes, who wrote Lysistrata, about the women who put a stop to the Peloponnesian War by refusing to have s.e.x with their husbands.

* LEO TOLSTOY (1828-1910, Russian) Born into Russian n.o.bility and widely regarded by fellow writers as one of the world's greatest novelists, Tolstoy is best known for his epic, War and Peace. A rich tale of early 19th century czarist Russia under Alexander I, it discusses the absurdity and shallowness of war and aristocratic society. Tolstoy's Anna Karenina is the book he considered to be his first novel. Considered a true example of realist fiction, it centers on adultery and self-discovery while social changes storm through Russia.

* VIRGIL (70-19 B.C., Roman) His most famous work is The Aeneid, the story of the Trojan prince Aeneas, the ancestor of the Roman people (also an ancestor of Romulus and Remus, who actually founded the city). Some of The Aeneid was inspired by Homer and relates to the story of the fall of Troy. Escaping from Troy, Aeneas eventually reached Italy but stopped off en route in Carthage, where he had an affair with the queen, Dido, who burned herself alive when he left her. The first words of the Aeneid are "Arma virumque cano"-"I sing of arms and the man"-which is where the t.i.tle of George Bernard Shaw's play comes from.

MATH.

Remember when you used to harangue your parents about why you needed to know "this stuff"? It was only later that you found out why as you wrestled with the challenges of chemistry, engineering, physics, architecture or more ordinary kinds of problems such as figuring your income tax and balancing your checkbook. That math you found so useless as a child is not so useless after all, is it? But perhaps over the years you have found yourself floundering for some of those rules and answers you might have known if you hadn't been doodling on your notebook during cla.s.s. Well, flounder no more....

Arithmetic.

Arithmetic is all about sums-adding, subtracting, multiplying, and dividing-each with its own vocabulary:* If you add two or more numbers together, their total is a sum. So 7 is the sum of 4 + 3.

* With subtraction you find the difference between two numbers. The difference between 9 and 7 is the smaller number subtracted from the larger: 9 - 7, and the difference is 2.

* If you multiply two or more numbers together, the answer is a product. So 30 is the product of 6 x 5.

* With division you divide a divisor into a dividend and the answer is a quotient. If there is anything left over, it is called a remainder. So 15 divided by 2 gives a quotient of 7 with a remainder of 1.

* LONG MULTIPLICATION If you are old enough to have taken math exams without the aid of a calculator, you will have learned the times tables. The easiest one is the 11 times table because it goes 11, 22, 33, 44, and so on-but it all goes a bit wrong after 99. Many people learn by rote up to 12 x 12 = 144; beyond that a person really needs to understand what they are doing. For example: After the number 9, you have to use two digits. The right-hand digit in any whole number represents the units; to the left are the tens and then the hundreds and so on. So 63 is made up of 6 tens, or 60, plus 3 units. And in this problem, you need to multiply 147 by each of those elements separately.

Start from the right: 3 x 7 = 21, so you write down the 1 and "carry" the 2 to the next column; 3 x 4 = 12, plus the 2 you have carried = 14. Write down the 4 and carry the 1; 3 x 1 = 3, plus the 1 you carried = 4.

So 3 x 147 = 441.

To multiply 147 by 60, put a 0 in the right-hand column and multiply by 6 (because any number multiplied by 10 or a multiple of 10 ends in 0); 6 x 7 = 42, so write down the 2 and carry 4; 6 x 4 = 24, plus the 4 you have carried = 28. Write down the 8 and carry 2; 6 x 1 = 6, plus the 2 you have carried = 8.

So 60 x 147 = 8,820; 63 x 147 is therefore the sum of 60 x 147 (8,820) and 3 x 147 (441), which equals 9,261.

Or Songwriter and mathematician Tom Lehrer plays a tune about New Math, in which he does his problem in base 8. If you do a search on Youtube.com for Lehrer's New Math, you'll see why this section avoids that technique.

* LONG DIVISION Division is multiplication in reverse, so start with 9,261 and divide it by 63.

If you have a divisor of 12 or less, the times tables does or did the work for you: You know or knew that 72 divided by 8 was 9, without having to work it out. But with a number larger than 12, you need to be more scientific: With division you work through the number from left to right.

You can't divide 63 into 9, for the simple reason that 63 is larger than 9. So look at the next column. You can divide 63 into 92-once-so you write a 1 at the top of the sum. But it doesn't go into 92 once exactly-there is a remainder, which is the difference between 92 and 63; in other words, 92 minus 63, which is 29.

Carry 29 forward into the next column and put it in front of the 6 to give you 296. Does 63 go into 296? Yes, it must, because 296 is bigger than 63, but how many times? Well, look at the left-hand figures of the two numbers and you'll see something that you can solve using the times table: 6 into 29. That's easy: Four 6s are 24, so 6 goes into 29 four times, with a bit left over. So it's likely that 63 will go into 296 four times with a bit left over. Indeed 4 x 63 = 252, and the bit left over is 296 minus 252, which equals 44.

Write 4 at the top of the sum, next to the 1, and carry 44 forward into the next column to make 441. How many times does 63 go into 441? Well, 6 goes into 44 seven times (6 x 7 = 42), so let's try that. And, conveniently, 63 x 7 = 441. Which means that 63 goes into 441 exactly seven times, with nothing left over, and that answers the problem: 147.

Fractions, Decimals, and Percentages.

* PROPER FRACTIONS A fraction is technically any form of number that is not a whole number; what most people think of as fractions-numbers such as , , , and so on-are properly called vulgar, simple, or common fractions (as opposed to decimal fractions; see page 60).

The top number in these fractions is called the numerator, the bottom one the denominator (remember, denominator down).

In fact, the examples given above are all proper fractions, with the numerator smaller than the denominator (the fraction represents less than 1). In an improper fraction the reverse is true, as in (an approximation for pi, see page 73), which can also be written as , because 7 goes into 22 three times, with a remainder of 1.

If you want to solve problems that involve fractions, it is important to know that if you divide or multiply both the numerator and denominator by the same number, you produce a fraction that is the same value as the original fraction. Take . Multiply both numerator and denominator by 2 and you get Which is still a half, because 2 is half of 4. Or multiply by 3 and you get . Which again is still a half, because 3 is half of 6.

The same principle applies to division: If you start with and divide top and bottom by 3, you reduce your fraction down to again. This process is called canceling. When you can't cancel anymore, the fraction is in its lowest terms.

With addition and subtraction, however, you can only add and subtract fractions that have the same denominator. You can add + and get , which equals 1, because two halves make a whole. But what you have done is add the two numerators together. The denominator stays the same, because you are adding like to like. (It's no different from adding 1 apple to 1 apple to get 2 apples.) Now say you want to add + . It's easy to do, but first you must convert them so they have the same denominator. The lowest common denominator of 2 and 3 (the smallest number into which both will divide) is 6. To turn into sixths, you need to multiply both parts of the fraction by 3: So is the same thing as .

To convert into sixths, you need to multiply both parts by 2: So is the same thing as .

Now you have something that you can add, on the same principle of adding the numerators together: The same applies to subtraction:

But both 4 and 10 can be divided by 2, to give the simpler fraction ..

* DECIMAL FRACTIONS The word decimal refers to anything with the number 10, and the English system is based on multiples of 10. As previously mentioned in the multiplication section, a single-digit number-say, 6-means that you have six units of whatever it is. When you have more than nine, you have to use two digits, with one digit representing the tens on the left and one digit representing the units on the right.

Decimal fractions work on the same principle, except that they go from right to left. The fraction is separated from the whole number by a dot called a decimal point. The figure immediately to the right of it represents tenths, to the right of that is hundredths, and so on. So 1.1 (p.r.o.nounced one point one) = 1 plus one tenth of 1; 1.2 = 1 + 2/10 (or ); 1.25 (p.r.o.nounced one point two five) , or .

An interesting example is 1.25, because it is the same as 1. How do we know that? Well, return to the idea of dividing numerators and denominators by the same thing. For example, can be divided by 5 to give . But 5 and 20 are both also divisible by 5, giving . (Once you've got your numerator down to 1, you know that you have simplified the fraction as far as it will go.) So 1.25 is exactly the same as 1.

Decimal fractions that are less than 1 can be written either 0.25 or just .25-it's the same thing.

* RECURRING DECIMALS Not everything divides neatly into tens, so sometimes a decimal fraction can be no more than an approximation. For example, is 0.333 recurring-no matter how many threes you add, you will never get a decimal that is exactly equal to one third.

If a decimal recurs, you can be certain that it's the same as some common fraction. For example, 0.222 recurring is ; 0.142857142857142857 recurring is . A recurring decimal is sometimes indicated with a dot above the last digit, which is sort of the equivalent of ellipses (...) or "etc., etc., etc."

Pi is different (see page 73). Its decimal expansion goes on forever but without recurring, because it isn't the same as any common fraction. Pi is called a transcendental number, and it's probably the only one you'll ever meet.

* PERCENTAGES Percent means by a hundred, so anything expressed as a percentage is a fraction (or part, if you prefer) of 100. So 25 percent is twenty-five parts of 100, or or 0.25. If you've been paying attention, you'll know that this is the same as .

Similarly, 50 percent is , which can be canceled down to , which is , which is .

Mean, Median, and Mode.

In arithmetical terms, mean is simply a fancy word for average. You calculate a mean by adding a group of numbers together and dividing by the number of numbers. (Strictly speaking, this is the arithmetic mean-there are other sorts of mean, too, but of interest only to mathematicians.) So the mean of 4, 8, 12, and 16 is the total of the four numbers, divided by 4:4 + 8 + 12 + 16 = 40 divided by 4 = 10.

And it works for any number of numbers. For example, if a cla.s.s of 11 children gets the following marks on an exam-55, 57, 57, 65, 66, 69, 70, 72, 75, 79, and 83-the total of the marks is 748. Divide that by 11, and you get a mean of 68.

The median of a set of values is literally the middle one. In the set of grades above, it is 69. There are five marks lower than 69 and five marks higher than 69-never mind their actual values. The median of an even number of values is the average of the middle two. For example, the median of 1, 4, 9, 16, 25, and 36 is 12.5-halfway between 9 and 16.

The mode of a set of values is the most common value. The mode of our set of marks is 57, because it is the only one that occurs more than once.

Measurements.

Metric units and imperial (or what we will refer to as American) units are two different ways to measure the same things. Just as Fahrenheit and Celsius both measure temperature but in different ways (see page 94), so the metric system and system of American units quantify length, weight, and all sorts of other things, using different units. Metric units are also sometimes called SI units, which stands for Systeme Internationale.

The metric system calculates in tens or multiples of tens. The system of American units doesn't, and to the uninitiated it can seem pretty random. (American units used to mean something sensible, such as the foot was the length of a man's foot and the yard was the distance from his nose to the tip of his outstretched arm.) * LENGTH In American units length is measured in inches, feet, yards, and miles, and occasionally also in chains and furlongs. There are 12 inches in a foot, 3 feet (36 inches) in a yard, 22 yards in a chain, 10 chains in a furlong, and 8 furlongs (1,760 yards, 5,280 feet) in a mile. Other units are still in use for some special purposes, such as the fathom (6 feet) for measuring the depth of the sea, and the hand (4 inches) for measuring the height of a horse.