Putt's Watts: April 2012

THE SIGNS OF THE ZODIAC

Here's a mnemonic sentence of words whose first letters help to recall the names of the 12 signs of the western astrological zodiac in their correct order:

"A Tense Grey Cat Lay Very Low, Sneaking Slowly, Contemplating A Pounce"

(Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius, Pisces)

Here's a rhyme written by E. Cobham Brewer that tells the order of the 12 constellations by describing theirsymbols rather than names:

Our ¹vernal signs the RAM begins,
Then comes the BULL, in May the TWINS;
The CRAB in June, next LEO shines,
And VIRGO ends the northern signs.

The BALANCE brings autumnal fruits,
The SCORPION stings, the ARCHER shoots;
December's GOAT brings wintry blast,
AQUARIUS rain, the FISH comes last.

(¹vernal = of/in the season of Spring)

Here's an alternative in the form of a verse by the English hymn-writer Isaac Watts (1674-1748):

The RAM, the BULL, the heavenly TWINS,
And next the CRAB, the LION shines,
The VIRGO and the SCALES;

The SCORPION, ARCHER and SEA-GOAT,
The MAN who pours the water out
And FISH with glittering tails.

being:
dates (birth period) - sign - symbol - element
21.Mar/20.Apr - Aries - the ram - F
21.Apr/20.May - Taurus - the bull - E
21.May/20.Jun - Gemini - the twins - A
21.Jun/20.Jul - Cancer - the crab - W

23.Jul/22.Aug - Leo - the lion - F
23.Aug/22.Sep - Virgo - the virgin - E
23.Sep/22.Oct - Libra - the scales - A
23.Oct/22.Nov - Scorpio - the scorpion - W

23.Nov/22.Dec - Sagittarius - the archer - F
23.Dec/20.Jan - Capricorn - the goat - E
21.Jan/19.Feb - Aquarius - the water-bearer - A
20.Feb/20.Mar - Pisces - the fish - W

The right-hand symbols F,E,A,W above denote the four elements Fire, Earth, Air and Water. Each zodiacal sign is associated with one of these elements in turn. To help remember their strict order of rotation think how:-

To start - ready... aim... Fire

Fire has E/A/W? - Yes, E - which starts Earth
Earth has A/W/F? - Yes, A - which starts Air
Air has W/F/E? - No, but there's still Water...
And the last two end in R (the only letter found in all)!

The order can also be remembered visually as a "crossword":

			F
			I
			R
			E	A	R	T	H
				I
W	A	T	E	R

1D = Fire
2A = Earth
3D = Air
4A = Water

The western (as opposed to Chinese) system of astrology may have begun in Babylonian times but first gained popularity in ancient Greece by about 400BC. Much later Claudius Ptolemy (a Greek born in Alexandria) wrote the first comprehensive textbook on the subject, titled the Tetrabiblos, in the second century AD. It was he that first systematised astrology by dividing the constellations into groups of four elements (F,E,A,W) and three qualities which described their functions.

The only symbol shared by both the Western Zodiac and the Chinese Calender is the sheep - being Aries the ram.

DAYS IN EACH MONTH

The number of days in each month has remained unchanged for 2000 years (since 45 B.C. in fact, when Julius Caesar introduced the Julian Calendar). Here's a well-known mnemonic rhyme which has been in existence for over 400 years, to indicate the exact number of days in each different month:

30 days hath September,
  April, June and November,
All the rest have 31,
  Excepting February alone
(And that has 28 days clear,
  With 29 in each leap year).

The number of days in each month can also be found by counting across the knuckles and valleys on the back of each clenched fist (from left to right):

Each "knuckle" month has 31 days, while each "valley" month has only 30 days (excepting of course February).

February has a smaller "leftover" amount of 28 or 29 days because pre-45 B.C. it was the last month of the Roman calendar year which started every March.

Each month-name originated from the Roman calendar, and mostly from the pre-Julian (or "Nunian") calendar where September was Septilis (Latin for 'seventh month') and is still the seventh month counting from March. Similarly October, November and December mean 'eighth, ninth, and tenth month'. The fifth month wasQuinctilis until it was renamed Julius (hence July) in honour of Julius Caesar, whereupon his successor theemperor Augustus renamed Sextilis after himself too (hence August). Augustus also added a day to August (making 31) so as match that for Julius!

The remaining months are either named after Roman gods (Janus, Mars, Maia, Juno) or have a religious significance (Februarius meaning 'purification month' before the new year cycle, and Aprilis being connected to well-being and prosperity).

THE CHESSBOARD

Here are three useful mnemonic phrases for orientating a chessboard correctly so that the queens and other pieces can be set up properly:

(1.) " White is right! "
(2.) " Queen on her own... "
(3. )" 1-2-3, R'n'B !!

(1.) The board must always be set with a white square in each player's nearest right-hand corner before (2.) each player then places a queen on the central rear-rank square of the queen's own colour (ie. White queen on a white square and Black queen on the opposite black square), so that the queens face each other directly on White's left and Black's right side of the board.

BLACK
Queen - King

R-N-B Q-K B-N-R

WHITE
Queen - King

R-N-B Q-K B-N-R

(3.) The remaining rear-rank pieces are relatively simple (rooks in each corner, knights next to rooks, and bishops always third file in) but if you find the bishop and knight positions confusing to set up, just remember the "rhythm and blues" acronym R'n'B. In algebraic notation a knight is represented by N (rather than Kt, because K represents king), so place the pieces from the left corner as "1-2-3, R-N-B" with the reverse on the right side.

Incidentally in end-play, to force checkmate against a lone king a player requires at least (a) king and queen, or (b) king and rook, or (c) king and two bishops or (d) king, bishop and knight.

Mate cannot be forced against a lone king with just (a) king alone, or (b) king plus bishop or knight, or (c) king and two knights (although obviously poor moves may still enable mate).

Ultimately knights are weaker than bishops in end-play. To help remember this, just recall that:

"With a king, 2 days and 2 knights,
you still won't force checkmate in fights!"

SURVIVAL IN EXTREME CONDITIONS

Here's a mnemonic promoted by Ray Mears in his BBC "Extreme Survival" series in March 2000 that spells out the steps you should take to ensure you have the best chance of surviving if caught out in any extreme conditions of nature:

" S-T-O-P "

(Stop, Take Inventory, Orientate, Plan)

"Stop" is used here as an acronym (a word formed from the initial letters of other words) to indicate the four key points that will aid your chances of survival in any extreme conditions of nature (such as breaking down in the desert, being stranded in the jungle or being caught in a snowstorm):

 Stop: Don't panic - just stop and think carefully about the exact nature of your circumstances. For example, are you in any immediate danger or in a rapidly or slowly worsening situation that you may yet be able to gain control of?

 Take Inventory: Look around you for any useful items. What do you already have with you that can help you to survive? Separate what you need from what you don't need.

 Orientate Yourself: Where are North/South/East/West, and in which direction were you heading originally? From what direction would a rescue be most likely to come?

 Plan Ahead: Are you likely to be rescued? How long must you plan to endure? What is the safest way of ensuring that you can survive until rescue comes? Will anyone be searching for you? What's your best means of effecting your own escape if necessary?

The one other key element to survival is actually having the will, the determination to survive. Never think of giving up hope, because if you're determined to survive then you will definitely last longer - and thus greatly increase the probability of either escape or rescue from whatever danger you face.

ADDRESSING PEOPLE OF LETTERS

Here is a mnemonic for the order of precedence used in expressing honours and degrees after a persons' name:

" Honour before degree,
Degree before M.P."

Thus: "Mr. J.Smith, V.C., M.A." and
"Roy Jones, Esq., D.S.O., B.Sc., M.P."

COLOUR MIXTURES

Here's a useful mnemonic for the results of mixing primary and complimentary (or secondary) colours:

" Better Get Ready When
Your Mistress Comes Back "

(Primary:) Blue, Green, Red = White
(Secondary:) Yellow, Magenta, Cyan = Black.

BGR are the primary colours of light, also known as additive colours. When all three (BGR) are combined, there is total colour (ie. white light).

The secondary YMC colours are the primary colours of paint (used to make most other shades), calledsubtractive because they each absorb (or subtract) one primary colour of light (reflecting the light of the other two only). When all three (YMC) combine, there is no colour (ie. light) left to see.

The mnemonic also shows the ordered relationship between BGR and YMC:

Yellow = non-Blue (ie. combined G/R only)
Magenta = non-Green (ie. combined B/R only)
Cyan = non-Red (ie. combined B/G only)
just as
Blue = non-Yellow (ie. combined M/C only)
Green = non-Magenta (ie. combined Y/C only)
Red = non-Cyan (ie. combined Y/M only)

SQUARE ROOTS

For many years mnemonics have been employed to memorise useful figures to several decimal places by constructing sentences that contain words of different lengths, each word-length representing each different digit.

Here are some sentences to recall square roots (each to 3 dec.places):

a). For the square root of 2:

" I wish I knew
( 1 . 4 1 4 ) the root of two "

b). For the square root of 3:

" O charmed was he
( 1 . 7 3 2 ) to know the root of three "

c). For the square root of 5:

" So now we strive
( 2 . 3 2 6 ) to know the root of five "

d). For the square root of 6:

" We need more logistics
( 2 . 4 4 9 ) to know the root of six "

THE LAWS OF PROBABILITY

1. Here's a new mnemonic rhyme for the formula to determine the likely outcome of two alternative events:

" For either/or, add both together
minus both at once (if ever)... "

ie. P(A or B) = P(A) + P(B) - P(A and B)

The "addition" formula governs mutually exclusive events such as "heads or tails" where P(A and B) is always zero (ie. impossible), and the occurrence of single independent outcomes such as "rich or tall".

2. For the probability of joint independent events such as "rich and tall" occurring at the same time:

" And if you need to both discover,
multiply one times the other... "

ie. P(A and B) = P(A) * P(B)

3. For conditional probability, where a likelihood of B depends upon (or is altered by) the outcome of A:

" Only when affects position,
multiply by changed condition... "

ie. P(A and B) = P(A) * P(B given A)

The "mathematical poetry" is by Peter Hobbs, but similar rhymes are likely to have been made up by far better mathematicians in the past!

CONVERTING MILES AND KILOMETRES

Here's a mnemonic device for recalling how to easily convert miles to kilometres and vice-versa, supplied by Francis Garcia of Woking, GB:

Use Fibonnacci Numbers

1, 2, 3, 5, 8, 13, 21, 34, 55, 89 etc

Fibonnacci numbers begin at 1,2 and extend in an infinite series by adding the last two numbers to get the next (ie. 1+2=3 and 2+3=5). And amazingly, any two consecutive Fibonnacci numbers give a fairly accurate "mile" and "kilometre" conversion. For example:

13 miles = 21 km!
21 miles = 34 km!

Miles are "imperial scale" measures while kilometres are "metric scale", but a "Fibonnacci" method of approximate conversion is surprisingly accurate compared with calculations using proper conversion formulas. Compare the figures in the charts below:

1 mile = 1.609 km
miles	km (Fib.)	km (exact)
1	2	1.61
2	3	3.22
3	5	4.83
5	8	8.04
8	13	12.87
13	21	20.92
21	34	33.79
34	55	54.71
55	89	88.50
89	144	143.20

1 km = 0.6214 miles
km	miles (Fib.)	miles (exact)
2	1	1.24
3	2	1.86
5	3	3.11
8	5	4.97
13	8	8.08
21	13	13.05
34	21	21.13
55	34	34.18
89	55	55.30
144	89	89.48

The Fibonnacci numbers themselves don't have to be memorised - the series can easily be recreated on paper at any time, to provide the conversion figures required. That's easier than having to memorise and multiply conversion formulas!

The Fibonnacci method can also be used to convert numbers that are not in the series. Take 40 miles or km for example - to convert it, first break down the 40 into a combination of simple Fibonnacci numbers, ie. (13*3)+1. Then any multiplication still required is relatively simple to perform, e.g.:

Fib: 40 miles = (13*3)+1 = (21*3)+2 km = 65 km
compare formula: 40 miles = 40*1.609 = 64.36 km

Fib: 40 km = (13*3)+1 = (8*3)+0 m = 25 miles
compare formula: 40 km = 40*0.6214 = 24.86 miles

Lastly, if confused about which way round the conversions go, remember that distances in miles and kilometres are like the number of letters in each word:

less in miles and more in kilometres!

" Please Excuse My Dear Aunt Sally! "

(Parentheses, Exponents, Multiplications, Divisions, Additions, Subtractions)

THE PARTS OF SPEECH

Each word in a sentence belongs to one or another class of grammar. These classes are collectively called "the parts of speech". Here's an old mnemonic children's teaching rhyme (possibly Edwardian), describing theeight parts of speech in English grammar:

"Every name is called a NOUN,
  As field and fountain, street and town;
In place of noun the PRONOUN stands,
  As he and she can clap their hands;
The ADJECTIVE describes a thing,
  As magic wand and bridal ring;
The VERB means action, something done -
  To read and write, to jump and run;
How things are done, the ADVERBS tell,
  As quickly, slowly, badly, well;
The PREPOSITION shows relation,
  As in the street, or at the station;
CONJUNCTIONS join, in many ways,
  Sentences, words, or phrase and phrase;
The INTERJECTION cries out, 'Hark!
  I need an exclamation mark!'
Through Poetry, we learn how each
  of these make up the PARTS OF SPEECH."

Modern language tuition has since substituted the DETERMINER (an indefinite/definite article such as a, anor the) for the INTERJECTION as the eighth part of speech. Peter Hobbs therefore suggests this humourous addition to the poem:

"But oh! The modern now prefer
The relative DETERMINER...'

CONJUNCTIONS

Here is a first-letter mnemonic for remembering the coordinating conjunctions in English grammar, based on an e-mail suggestion by "Carden":

BOY SAT with BEN

( But, Or, Yet, So, And, Then,
Both...and, Either...or, Neither...nor ).

Conjunctions are one of the eight parts of speech in English grammar, and are used to combine simple phrases into compound patterns. There are two forms of conjunction. Coordinating conjunctions are so called because they join units of equal status. Subordinating conjunctions join subordinate or dependent clauses to the main clause of a sentence, and include a number of "wh-words".

The coordinating conjunctions are:

... and ... both ... and

... but ... either ... or

... or ... neither ... nor

... so ...

... then ...

... yet ...

The units being conjoined can be simple words or whole clauses, but must carry equal status (e.g. Fish and chips. Sunny at first, then rainy. He called, yet said nothing about tomorrow. It was neither fish nor fowl).

The subordinating conjunctions are:

after if when

(al)though in case whenever

as in order to where

as ... as more than whereas

as if rather than wherever

because since whether

before so that while

even if that

except till/until

Subordinate conjunctions join main and dependent clauses, but can occur at the beginning of a sentence or in mid-sentence (e.g. I must run in case I miss the bus. John scored after Fred crossed the ball. Whether or not he will play is uncertain. As you know, today has been difficult.After the game finished, I went straight home).

THE SEVEN WONDERS OF THE WORLD

Here's a useful mnemonic sentence to recall the names and locations of all seven wonders of the ancient world:

"PEGGI'S GARB, PAL? COLOR TEMP, DEF..", STATES JO (OZ) TO MAHAL

1. Pyramids of Egypt (Giza)
2. Hanging Gardens of Babylon (Baghdad)
3. Pharos of Alexandria
4. Colossus of Rhodes
5. Temple of Diana (Ephesus)
6. Statue of Jupiter (or Zeus) in Olympia
7. Tomb of Mausolus (Halicarnassus)

(Phonetic key to sentence:)
P-Eg-Giz, Gar-B, P-Al, Colo-R, Temp-D-Eph, Stat-J-O(Z), To-Ma-Hal

"Jo (Oz)" is also a reminder that Jupiter was the Roman name for the Greek God Zeus.

The last part ("..To-Ma-Hal") is a double reminder:
a) of the most difficult name/place, and
b) that the Taj Mahal is not included!
One can also memorise "..to Mahal, a minor" (as Halicarnassus is in Asia Minor).

E. Cobham Brewer wrote a poem on the subject which, despite its eloquence, can create some confusion:

The PYRAMIDS first, which in Egypt were laid;
Then BABYLON'S GARDENS, for Am'ytis made;
Third, MAUSOLUS' TOMB, of affection and guilt;
Fourth, the TEMPLE OF DIAN, in Ephesus built;
Fifth, COLOSSUS OF RHODES, cast in bronze, to the sun;
Sixth, JUPITER'S STATUE, by Philidas done;
The PHAROS OF EGYPT, last wonder of old,
Or the PALACE OF CYRUS, cemented with gold.

ROMAN NUMERALS

Roman numerals are numbers expressed by using letters of the Roman alphabet. Here's a mnemonic rhyme written by Peter Hobbs that explains the 7 basic roman numerals (I, V, X, L, C, D and M):

M's "mille" (or 1000 said)
D's half (500 - quickly read!)
C's just a 100 (century!)
and L is half again - 50!
So all that's left is X and V
(or 10 and 5) - and I - easy!

Thus M D C I I I = 1603
(or 1000 + 500 + 100 + 1 + 1 + 1)
and
D C C L X X V = 775
(or 500 + 100 + 100 + 50 + 10 + 10 +5)

Many people are familiar with reading I, V and X from clockfaces and just have trouble with the "higher" numerals. Here's an established acronym for just the four high ones (in ascending order):

"Lucy Can't Drink Milk"
(L,C,D,M - 50, 100, 500 and 1000)

The numeral "I" began as a finger-digit, while "V" represented the simplified outline of a hand (like a thumb and five closed fingers), this being clearer to write than five "IIIII" digits. In the same way the "X" represented two hands (ie. two V's mirrored), or ten. Later the Romans also used combinations of "one less than the next-highest numeral" for figures such as 9 (ie. "IX" rather than "VIIII"). An old established rhyme summarises how to read such combinations:

When "left" is small and "right" is bigger,
Subtract the "left" from "right-hand" figure.

Thus M C M L I X = 1959
(M+CM+L+IX = 1000 +[1000-100] +50 +[10-1])

Lastly, here's a popular and interesting pub quiz question. What number do you get if you add up all of the Roman numerals?

M D C L X V I = 1666
(or 1000 + 500 + 100 + 50 + 10 + 5 +1)
which just happens to be the year of the Great Fire of London!

THE TROPICS OF CANCER AND CAPRICORN

Here's a mnemonic device to help distinguish between the two global geographical regions:

" Ca-N-cer lies North of the Equator
and Capric-O-rn lies Opposite (South). "

The Tropic of Cancer is a line of latitude (running parallel with the equator) indicating the extreme northern positions (around the globe) at which the sun appears directly overhead at noon. The sun only reaches this position once a year, at the Summer Solstice of the Northern Hemisphere.

The Tropic of Capricorn is the parallel latitude indicating the extreme southern global positions at which the sun appears directly overhead at noon. again, the sun only reaches this position once a year, at the Summer Solstice of the Southern Hemisphere (ie. the Northern Winter Solstice).

For their degrees of latitude:

" Ca-n-cer = letters 2 +(n halfway=½°N) +3 letters = 23½°N
while Capric-o-rn (being opposite) is 23½°S. "

The Tropic of Cancer passes (W-E) through the Sahara, the Bahamas, Mexico, southern China, India, Saudi Arabia and Egypt. The Tropic of Capricorn passes through Namibia, Brazil, Chile, Australia, Madagascar and Mozambique.

Both latitudes take their names from the Zodiac of stellar constellations set along the ecliptic (the path followed by the sun and planets through the celestial sphere in course of a year). Cancer and Capricorn lie opposite each other on the ecliptic 6 months apart in the cycle (mid-June/July and mid-Dec./Jan.), and when the Sun was at its highest point in the N. Hemisphere it was (historically) in the region of Cancer (although nowadays at such times the Sun is actually in the next constellation, and leaving Gemini for Taurus).

The Tropics usually refers to the whole pan-equatorial region lying between the Tropic of Cancer and the Tropic of Capricorn. For obvious climactic reasons (the sun always being high in the sky and directky overhead twice a year) it is sometimes called the Torrid Zone!

THE WORLD'S LONGEST RIVERS

Here's a useful new mnemonic phrase for remembering the world's eight longest rivers:

" NAM-MI YACH-Y! "

Nile (Africa) - 4,145 miles
Amazon (S.America) - 4,050 miles
Mississippi-Missouri (USA) - 3,760 miles
Irtysh (Russia) - 3,200 miles
Yangtse (China) - 3,100 miles
Amur (Asia) - 2,900 miles
Congo (Africa) - 2,718 miles
Huang-Ho (or Yellow) (China) - 2,700 miles

After the above 8 came another 4 rivers in "L-M-N" order:

Lena (Russia) - 2,645 miles
Mackenzie (Canada) - 2,635 miles
Mekong (Asia) - 2,600 miles
Niger (Africa) - 2,600 miles

By comparison, Europe's longest river (the Danube) comes only 26th at 1770 miles.

Fact Source: Readers Digest Great World Atlas (5th r, 1975)

Note: The "top ten" can vary between publications according to the chosen determination of river plus tributaries comprising the longest watercourse. For example the "Larousse Pocket Factfinder (1995)" lists the longest 14 rivers as (in miles):

4,160: Nile - Kagera - Ruvuvu - Ruvusu - Luvironza
4,080: Amazon - Ucayali - Tambo - Ene - Apurimac
3,740: Mississippi - Missouri - Jefferson - Beaverhead - Red Rock
then:
3,720: Chang Jiang (Yangtze)
3,650: Yenisey - Angara - Selenga - Ider
3,590: Amur - Argun - Kerulen
3,360: Ob-Irtysh
3,030: Plata - Parana - Grande
3,010: Huang Ho (Yellow)
2,880: Congo (Zaire) - Lualaba
then:
2,730: Lena
2,630: Mckenzie - Slave - Peace - Finlay
2,600: Mekong
2,550: Niger

LATITUDE and LONGITUDE

Here's a mnemonic means of remembering the difference between the two geographical means of measurement:

Long-itude is the distance ALONG the Equator from Greenwich (in degrees)
and
Lat-itude is the lateral (or sideways) distance North/South from the Equator (in degrees)

Greenwich (London) is at 0° long. and 51½°N. lat.
Accra (in Ghana) is at 0° long. and 5°N. lat.
Quito (in Ecuador) is at 78½° long. and ½°S. lat.

It also helps to recall that one often hears of Northern Latitudes or Southern Latitudes (describing climatic regions) but one never hears of plural Longitudes. The Tropics are good example of specific latitudes.

THE CONTINENTS

Here is a mnemonic sentence that gives the names of the seven continents of the earth via the first two letters of (almost) every word:

"Eat An Aspirin After A Naff Sandwich"

(Europe, Antarctica, Asia, Africa, Australia, N.America, S.America)

A continent is a large, unbroken land mass, of which geographers recognise seven in total. Notably, Europe and Asia are counted as two separate continents (divided by the Ural mountains) because historically the Old World has always been "divided" between East and West at the Bosphorus in Istanbul (Turkey). Also Australia (often called Oceania) is recognised as a continent (albeit the smallest at 3.5 million square miles or 6% of the earth's land mass) rather than an island, leaving Greenland as the largest island on earth (its 850,000 square miles being only 1.5% of the land mass).

Asia is the largest continent, being 17 million square miles (or 24%), but in colloquial English speech "the continent" refers to the land mass of mainland Europe excluding the British Isles.

INSECT STINGS

Here's a useful mnemonic for remembering their treatment:

"Use Ammonia for a Bee sting,
and Vinegar for a Wasp sting"

(A is followed by B, and V by W).

Coincidentally "A-B, V-W" also provides a mnemonic for their Latin family classifications because:

Apoidae are Bees - and - Vespidae are Wasps.

Another useful thing to remember is that throughout the order of Hymenoptera (ie. Bees, Ants and Wasps), only the females sting, so the probability of being stung at all may be less than you think!