Imágenes de páginas
PDF
EPUB

be 111. Twice three times (6 times) 37 will be 222; three times three times (9 times) 37 gives three threes; four times three times (12 times) 37, three fours; and so on.

The wonderfully procreative power of figures, or, rather, their accumulative growth, has been exemplified in that familiar story of the farmer who, undertaking to pay his farrier one grain of wheat for the first nail, two for the second, and so on, found that he had bargained to give the farrier more wheat than was grown in all England.

My beloved young friend who love to frequent the roulette-table, do you know that if you began with a dime, and were allowed to leave all your winnings on the table, five consecutive lucky guesses would give you a million and a half of dollars, or, to be exact, $1,450,625.52?

Yet that would be the result of winning thirty five for one five times handrunning.

Here is another example. Take the number 15, let us say. Multiply that by itself, and you get 225. Now multiply 225 by itself, and so on until fifteen products have been multiplied by themselves in turn.

You don't think that is a difficult problem? Well, you may be a clever mathematician, but it would take you about a quarter of a century to work out this simple little sum.

The final product called for contains 38,589 figures, the first of which are 1442. Allowing three figures to an inch, the answer would be over 1070 feet long. To perform the operation would require about 500,000,000 figures. If they can be made at the rate of one a minute, a person working ten hours a day for three hundred days in each year would be twenty-eight years about it. If, in multiplying, he should make a row of ciphers, as he does in other figures, the number of figures would be more than 523,939,228. This would be the precise number of figures used if the product of the left-hand figure in each multiplicand by each figure of the multiplier was always a single figure, but, as it is most frequently, though not always, two figures, the method employed to obtain the foregoing result cannot be accurately applied. Assuming that the cipher is used on an average once in ten times, 475,000,000,000 approximates the actual number.

There is a clever Persian story about a wealthy Oriental who, dying, left seventeen camels to be divided as follows: his eldest son to have half, his second son a third, and his youngest a ninth. But how divide camels into fractions? The three sons, in despair, consulted Mohammed Ali.

"Nothing easier,” said the wise man. "I'll lend you another camel to make eighteen, and now divide them yourselves.”

The consequence was, each brother got from one-eighth of a camel to onehalf more than he was entitled to, and Ali received his camel back again,— the eldest brother getting nine camels, the second six, and the third two.

There are many mathematical queries afloat whose object is to puzzle the wits of the unwary listener or to beguile him into giving an absurd reply. Some of these are very ancient, many are excellent. Who, for example, has not at some period of his existence been asked, "If a goose weighs ten pounds and half its own weight, what is the weight of the goose?" And who has not been tempted to reply on the instant, fifteen pounds? The correct answer is, of course, twenty pounds. Indeed, it is astonishing what a very simple query will sometimes catch a wise man napping. Even the following has been known to succeed:

"How many days would it take to cut up a piece of cloth fifty yards long, one yard being cut off every day?"

Or again:

"A snail climbing up a post twenty feet high ascends five feet every day,

and slips down four feet every night: how long will the snail take to reach the top of the post?"

Or again:

"A wise man having a window one yard high and one yard wide, and requiring more light, enlarged his window to twice its former size; yet the window was still only one yard high and one yard wide. How was this done?" This is a catch question in geometry, as the preceding were catch-questions in arithmetic, the window being diamond-shaped at first, and afterwards made square. As to the two former, perhaps it is scarcely necessary seriously to point out that the answer to the first is not fifty days, but forty-nine; and to the second, not twenty days, but sixteen,-since the snail, who gains one foot each day for fifteen days, climbs on the sixteenth day to the top of the pole, and there remains.

Numbers have a legendary and mystic signification. It is not only the mathematician that has been fascinated by them. The poet, the philosopher, the priest, have pondered over their changeless relations to each other, have seen in mathematical truth the one thing absolutely fixed and sure, and have come to look upon numbers and their symbols as in some sort a revelation from on high, things to be dealt with reverently and awesomely. And so almost every number has been given an esoteric meaning.

The number one, as being indivisible, and as entering into all other numbers, was always a sacred number. The Egyptians made it the symbol of life, of mind, of the creative spirit.

Three, in the Pythagorean system, was the perfect number, expressive of beginning, middle, and end. From time immemorial greater prominence has been given to it than to any other number, save perhaps seven. And as the symbol of the Trinity its influence has waxed more potent in more recent times. It appears over and over again in the Old Testament and the New. When the world was created we find land, water, and sky, sun, moon, and stars. Noah had three sons; Jonah was three days in the whale's belly; Christ three days in the tomb. There were three patriarchs,-Abraham, Isaac, and Jacob. Abraham entertained three angels. Job had three friends. Samuel was called three times. Samson deceived Delilah three times. Three times Saul essayed to kill David with a javelin. Jonathan shot three arrows on David's behalf. Daniel was thrown into a den with three lions for praying three times a day. Shadrach, Meshach, and Abednego were rescued from the fiery furnace. The Commandments were delivered on the third day. St. Paul speaks of Faith, Hope, and Charity, these three. Three wise men came to worship Christ with presents three. Christ spoke three times to Satan when tempted. He prayed three times before his betrayal. Peter denied him three times. Christ suffered three hours' agony on the cross. The superscription was in three languages, and three men were crucified. The third day Christ arose again, and appeared three times to his disciples. And so on, and so on. It were tedious to continue the enumeration.

In classic mythology the Graces and the Furies were three, the Muses were originally three, and Cerberus's three heads, Neptune's trident, the tripod of Delphi, are a few more instances of the sacred character of the number.

Who does not remember the three bears of nursery lore, the three feline infants who lost their mittens, the three wise men of Gotham who went to sea in a bowl, or the three finiking Frenchmen frying frogs, and recall the delight he felt in the story of the farmer's wife who vowed vengeance on the three hapless mice, or of Old King Cole with his "fiddlers three"? Then, when fairy-tales began to charm, who does not recollect learning that the elfish creatures carried bows made of the ribs of a man buried where three

lairds' lands meet? Those who followed Gulliver in his travels will call to mind that in the kingdom of Liliput the three great prizes of honor were fine silk threads, six inches long, in colors blue, red, and green; but perhaps every reader had not the opportunity of being fascinated by the German story which relates how a miller's daughter, wedded to a king, was ordered by him to spin straw into gold, and had it done for her by the dwarf Rumpelstilzchen, on condition that she gave him her first-born. She cried so bitterly that he promised to relent if she guessed his name in three days. Two days were spent in vain guesses, but the third the queen's servants heard a strange voice, singing "Little dreams my dainty dame Rumpelstilzchen is my name.” The queen saved her child, and the dwarf killed himself with rage.

France, Belgium, Holland, and Italy all fly three national colors. The Turkish vizier has his standard ornamented with three horse-tails. The Prince of Wales's crest consists of three feathers. Indeed, the annals of heraldry revel in designs of a triplicate character, the three British lions being conspicuous. The original armorial ensign of the Isle of Man was a ship in full sail; but after the battle of Ronaldsway Alexander III. substi tuted the present curious device, having probably taken it from the emblem of Sicily, the ancient Trinacria found upon Greek vases. In 1363, Charles VI., it appears, reduced the Fleurs-de-Lis to three in number, from the mystic superstition of the Church. Every one familiar with University life knows what it is to drink copus, bishop, and cardinal. Ecclesiastical history is replete with such triads, as, for example, the Bell, Book, and Candle; the Triduum, or three days' prayer; the Pope's three crowns; and "The Mystery of the Three Dons," a religious play which lasted three days.

Nay, do not life itself and nature proclaim the same truth? Have we not morning, noon, and night; fish, flesh, and fowl; water, ice, and snow; hell, earth, and heaven? The very lightning from heaven is three-forked. Life is divided into youth, manhood, and old age. The os sacrum, supposed to resist the action of water, fire, mill, or anvil, is triangular in shape. Man himself is said to be threefold,-body, soul, and spirit, or, as Laertes has it, a mortal part, a divine and ethereal part, and an aerial and vaporous part. According to the Romans, man has a threefold soul,-the anima, or spirit, the umbra, and the manes; and, as was also the opinion of the Greeks, three Parcæ, or Fates, arbitrarily controlled his birth, life, and death. Oculists affirm that our early progenitors were giants possessed of three eyes, the third eye being in the back of the head.

No wonder the witches in "Macbeth" ask, "When shall we three meet again ?"

Four, as the first square, was highly revered by the Pythagoreans. They swore by it, but ten was the more holy as the symbol of the absolute. One plus two plus three plus four make ten, and four contains the smaller numbers. Therefore, since its contents made ten, it was sacred. Besides, four represented the four elements, the four cardinal points; it stood for equilibrium and for the earth.

Five was considered the number of dominion by knowledge. The pentagram, or Solomon's seal, was its symbol, and the Gnostic schools adopted it as their crest. It was much employed in incantations, and often was used as the symbol of man, who has five senses, five members,-head and four limbs, -five fingers, etc.

Six is a perfect number; its symbol is two triangles base to base; it represents equilibrium and peace.

Seven, which is composed of four, a good number, and three, a good number, has always been regarded as sacred and mystic; indeed, it rivals in popularity the number three.

LITERARY CURIOSITIES.

Take the Bible, for example: there are seven days of creation; after seven days' respite the flood came; the years of famine and of plenty were in cycles of seven; every seventh day was a Sabbath, every seventh year the Sabbath of rest; after every seven times seven years came the jubilee; the feast of unleavened bread and the feast of tabernacles were observed seven days; the golden candlestick had seven branches; seven priests with seven trumpets encompassed Jericho once a day, and seven times on the seventh day; Jacob obtained his wives by servitudes of seven years; Samson kept his nuptials seven days, and on the seventh day he put a riddle to his wife, and he was bound with seven green withes, and seven locks of his hair were shaved off; Nebuchadnezzar was seven years a beast; Shadrach and his two companions in misfortune were cast into a furnace heated seven times more than it was wont. In the New Testament nearly everything occurs by sevens, and at the end of the sacred volume we read of seven churches, seven candlesticks, seven spirits, seven trumpets, seven seals, seven stars, seven thunders, seven vials, seven plagues, seven angels, and a seven-headed monster.

The Jews considered this number the embodiment of perfection and unity. Thus, they asserted that the Hebrew letters composing the name of Samuel have the value of seven,-a recognition of the greatness and perfection of his character.

Turn now to other nations than the Jews and to other religions than the Christian. The number seven still retains its mystic character.

Pythagoras pronounced the number to belong especially to sacred things. Hippocrates divided the ages of man into seven, an arrangement afterwards adopted by Shakespeare. Long before them, however, the Egyptian priests had enjoined rest on the seventh day, because it was an unlucky day; and still farther back in the mists of antiquity we find the institution of a Sabbath, or day of rest every seven days, existing in a rudimentary form among the It is singular Chaldeans. The Egyptians knew of seven planets, hence the seven days of the week, each ruled and named after its proper constellation. that the ancient Peruvians likewise had a seven-day week, though without planetary patronage or planetary names. They also had a tradition of a great deluge, wherefrom seven people saved themselves in a cave and repeopled A similar tradition existed in Mexico, but there the seven the earth. survivors were each hidden in a separate cave until the subsidence of the

waters.

Medieval legend, too, continues this mystic tribute to the number seven. Barbarossa, in his magic sleep in The delightful old slumberers carry on the idea. The great originals, the sleepers of Ephesus, are seven in number. the Kyffhäuserberg, shifts his position every seven years; Olger Danske stamps his iron mace on the floor once during the same period; Olger Redbeard, in Sweden, lifts his eyelids only once in seven years. Tanhäuser and Thomas of Ercildoune each spend seven years of magic enthralment under the earth.

The Pythagorean philosophers called eight the number of justice, because Also, as the first cube, it divided evenly, they said, into four and four, and four divides evenly into two and two, which again divides into one and one.

it represented the corner-stone and capacity, hence plenty.

Nine, representing three triangles, means the equilibrium of the three worlds, and is therefore of good omen; besides, as three is a good number, three multiplied by three is also favorable. The Chinese have a great reverence for this number. They prostrate themselves nine times before their Some African tribes have the same form of salutation for their emperor. chiefs.

Ten was considered a perfect number even before the invention of the deci 70

mal system. The fact that we have ten fingers and ten toes gave it its mathematical importance, inasmuch as it was by means of fingers and toes that our rude forefathers first learned to reckon.

St. Augustine held the number eleven to be an evil number, a transgression of ten, which is the number of the law. That thirteen is unlucky is no modern superstition.

Sixteen, the square of the just square, is lucky; eighteen is unlucky, but is used in incantations over drugs; nineteen is considered-why is hard to guess the number of the sun, hence of gold; twenty-eight implies the favor of the moon, which is an uncertain favor; fifty is a lucky number to the Kabbalists, so is sixty.

It will be seen that the most sacred and beneficent numbers are the odd ones. Hence may arise the modern superstition among gamblers that there is luck in odd numbers. But among the ancient heathens also even numbers were shunned, because each can be divided into two, a number that Pythagoras and others denounced as the symbol of death and dissolution and evil augury generally.

The antique worship of mystic numbers still shows its after-effect in various popular superstitions. For instance, the seventh son of a seventh son (called in France a marcou) is reputed to possess singular powers of healing, and even intelligent people still hold to the fallacy that young animals born blind will open their eyes on the ninth day. The truth is that the blindness-period of puppies varies from ten to sixteen days, and that of kittens from six to twelve. The frequent assertion that "colds" will run their natural course in nine days is equally erroneous. A slight catarrh, characterized by all its unmistakable symptoms, may come and depart in three times twenty-four hours, while chronic "colds" are often as persistent as their cause, and may worry a whole family from Christmas to the season of open windows. Country experts in the phenomena of rabies are apt to assure the victim of a snapping cur that the bite of a mad dog will show its effect on the seventh day, after which time (sometimes extended to the ninth day) the dread of evil consequences may be dismissed; but the truth is that the virus of hydrophobia may remain latent for more than five years.

The old idea that man changes his body entirely every seven years is part of the same general fallacy. Medieval physiologists were fond of noting that seven months is the least time in which a child may be born and live, that the teeth spring out in the seventh month and are renewed in the seventh year, that he becomes a youth at twice seven, at four times seven is in full possession of his strength, at five times seven is fitted for the business of the world, at six times seven becomes grave and wise, or never, at seven times seven is at his apogee, at eight times seven in his first climacteric, and at nine times seven in his grand climacteric.

Nutmeg State, a sobriquet for Connecticut. The Connecticut variety of Yankee has always enjoyed a singular reputation for what is known as "smartness" in business, extending even to such sharpers' tricks as substituting wooden hams (this, of course, jocosely only), and, more seriously, to the alleged manufacture of nutmegs of cedar fashioned in imitation of the real article.

[merged small][merged small][ocr errors]
« AnteriorContinuar »