Fatality Of Numbers





The laws governing numbers are so perplexing to the uncultivated mind,

and the results arrived at by calculation are so astonishing, that it

cannot be matter of surprise if superstition has attached itself to

numbers.



But even to those who are instructed in numeration, there is much that

is mysterious and unaccountable, much that only an advanced

mathematician can explain to his own satisfaction. The neophyte sees

the numbers obedient to certain laws; but why they obey these laws

he cannot understand; and the fact of his not being able so to do,

tends to give to numbers an atmosphere of mystery which impresses him

with awe.



For instance, the property of the number 9, discovered, I believe, by

W. Green, who died in 1794, is inexplicable to any one but a

mathematician. The property to which I allude is this, that when 9 is

multiplied by 2, by 3, by 4, by 5, by 6, &c., it will be found that

the digits composing the product, when added together, give 9. Thus:--



2 A-- 9 = 18, and 1 + 8 = 9

3 A-- 9 = 27, " 2 + 7 = 9

4 A-- 9 = 36, " 3 + 6 = 9

5 A-- 9 = 45, " 4 + 5 = 9

6 A-- 9 = 54, " 5 + 4 = 9

7 A-- 9 = 63, " 6 + 3 = 9

8 A-- 9 = 72, " 7 + 2 = 9

9 A-- 9 = 81, " 8 + 1 = 9

10 A-- 9 = 90, " 9 + 0 = 9



It will be noticed that 9 A-- 11 makes 99, the sum of the digits of

which is 18 and not 9, but the sum of the digits 1 + 8 equals 9.



9 A-- 12 = 108, and 1 + 0 + 8 = 9

9 A-- 13 = 117, " 1 + 1 + 7 = 9

9 A-- 14 = 126, " 1 + 2 + 6 = 9



And so on to any extent.



M. de Maivan discovered another singular property of the same number.

If the order of the digits expressing a number be changed, and this

number be subtracted from the former, the remainder will be 9 or a

multiple of 9, and, being a multiple, the sum of its digits will be 9.



For instance, take the number 21, reverse the digits, and you have

12; subtract 12 from 21, and the remainder is 9. Take 63, reverse the

digits, and subtract 36 from 63; you have 27, a multiple of 9, and 2 +

7 = 9. Once more, the number 13 is the reverse of 31; the difference

between these numbers is 18, or twice 9.



Again, the same property found in two numbers thus changed, is

discovered in the same numbers raised to any power.



Take 21 and 12 again. The square of 21 is 441, and the square of 12 is

144; subtract 144 from 441, and the remainder is 297, a multiple of 9;

besides, the digits expressing these powers added together give 9. The

cube of 21 is 9261, and that of 12 is 1728; their difference is 7533,

also a multiple of 9.



The number 37 has also somewhat remarkable properties; when multiplied

by 3 or a multiple of 3 up to 27, it gives in the product three digits

exactly similar. From the knowledge of this the multiplication of 37

is greatly facilitated, the method to be adopted being to multiply

merely the first cipher of the multiplicand by the first multiplier;

it is then unnecessary to proceed with the multiplication, it being

sufficient to write twice to the right hand the cipher obtained, so

that the same digit will stand in the unit, tens, and hundreds places.



For instance, take the results of the following table:--



37 multiplied by 3 gives 111, and 3 times 1 = 3

37 " 6 " 222, " 3 " 2 = 6

37 " 9 " 333, " 3 " 3 = 9

37 " 12 " 444, " 3 " 4 = 12

37 " 15 " 555, " 3 " 5 = 15

37 " 18 " 666, " 3 " 6 = 18

37 " 21 " 777, " 3 " 7 = 21

37 " 24 " 888, " 3 " 8 = 24

37 " 27 " 999, " 3 " 9 = 27



The singular property of numbers the most different, when added, to

produce the same sum, originated the use of magical squares for

talismans. Although the reason may be accounted for mathematically,

yet numerous authors have written concerning them, as though there

were something "uncanny" about them. But the most remarkable and

exhaustive treatise on the subject is that by a mathematician of

Dijon, which is entitled "TraitA(C) complet des CarrA(C)s magiques, pairs et

impairs, simple et composA(C)s, A Bordures, Compartiments, Croix,

Chassis, A%querres, Bandes dA(C)tachA(C)es, &c.; suivi d'un TraitA(C) des Cubes

magiques et d'un Essai sur les Cercles magiques; par M. Violle,

GA(C)omA"tre, Chevalier de St. Louis, avec Atlas de 54 grandes Feuilles,

comprenant 400 figures." Paris, 1837. 2 vols. 8vo., the first of 593

pages, the second of 616. Price 36 fr.



I give three examples of magical squares:--



2 7 6

9 5 1

4 3 8



These nine ciphers are disposed in three horizontal lines; add the

three ciphers of each line, and the sum is 15; add the three ciphers

in each column, the sum is 15; add the three ciphers forming

diagonals, and the sum is 15.



1 2 3 4 1 7 13 19 25

2 3 2 3 18 24 5 6 12

4 1 4 1 10 11 17 23 4

3 4 1 2 22 3 9 15 16

14 20 21 2 8



The sum is 10. The sum is 65.



But the connection of certain numbers with the dogmas of religion was

sufficient, besides their marvellous properties, to make superstition

attach itself to them. Because there were thirteen at the table when

the Last Supper was celebrated, and one of the number betrayed his

Master, and then hung himself, it is looked upon through Christendom

as unlucky to sit down thirteen at table, the consequence being that

one of the number will die before the year is out. "When I see," said

Vouvenargues, "men of genius not daring to sit down thirteen at table,

there is no error, ancient or modern, which astonishes me."



Nine, having been consecrated by Buddhism, is regarded with great

veneration by the Moguls and Chinese: the latter bow nine times on

entering the presence of their Emperor.



Three is sacred among Brahminical and Christian people, because of the

Trinity of the Godhead.



Pythagoras taught that each number had its own peculiar character,

virtue, and properties.



"The unit, or the monad," he says, "is the principle and the end of

all; it is this sublime knot which binds together the chain of causes;

it is the symbol of identity, of equality, of existence, of

conservation, and of general harmony. Having no parts, the monad

represents Divinity; it announces also order, peace, and tranquillity,

which are founded on unity of sentiments; consequently ONE is a good

principle.



"The number TWO, or the dyad, the origin of contrasts, is the symbol

of diversity, or inequality, of division and of separation. TWO is

accordingly an evil principle, a number of bad augury, characterizing

disorder, confusion, and change.



"THREE, or the triad, is the first of unequals; it is the number

containing the most sublime mysteries, for everything is composed of

three substances; it represents God, the soul of the world, the spirit

of man." This number, which plays so great a part in the traditions of

Asia, and in the Platonic philosophy, is the image of the attributes

of God.



"FOUR, or the tetrad, as the first mathematical power, is also one of

the chief elements; it represents the generating virtue, whence come

all combinations; it is the most perfect of numbers; it is the root of

all things. It is holy by nature, since it constitutes the Divine

essence, by recalling His unity, His power, His goodness, and His

wisdom, the four perfections which especially characterize God.

Consequently, Pythagoricians swear by the quaternary number, which

gives the human soul its eternal nature.



"The number FIVE, or the pentad, has a peculiar force in sacred

expiations; it is everything; it stops the power of poisons, and is

redoubted by evil spirits.



"The number SIX, or the hexad, is a fortunate number, and it derives

its merit from the first sculptors having divided the face into six

portions; but, according to the Chaldeans, the reason is, because God

created the world in six days.



"SEVEN, or the heptad, is a number very powerful for good or for evil.

It belongs especially to sacred things.



"The number EIGHT, or the octad, is the first cube, that is to say,

squared in all senses, as a die, proceeding from its base two, an even

number; so is man four-square, or perfect.



"The number NINE, or the ennead, being the multiple of three, should

be regarded as sacred.



"Finally, TEN, or the decad, is the measure of all, since it contains

all the numeric relations and harmonies. As the reunion of the four

first numbers, it plays an eminent part, since all the branches of

science, all nomenclatures, emanate from, and retire into it."



It is hardly necessary for me here to do more than mention the

peculiar character given to different numbers by Christianity. One is

the numeral indicating the Unity of the Godhead; Two points to the

hypostatic union; Three to the Blessed Trinity; Four to the

Evangelists; Five to the Sacred Wounds; Six is the number of sin;

Seven that of the gifts of the Spirit; Eight, that of the Beatitudes;

Ten is the number of the commandments; Eleven speaks of the Apostles

after the loss of Judas; Twelve, of the complete apostolic college.



I shall now point out certain numbers which have been regarded with

superstition, and certain events connected with numbers which are of

curious interest.



The number 14 has often been observed as having singularly influenced

the life of Henry IV. and other French princes. Let us take the

history of Henry.



On the 14th May, 1029, the first king of France named Henry was

consecrated, and on the 14th May, 1610, the last Henry was

assassinated.



Fourteen letters enter into the composition of the name of Henri de

Bourbon, who was the 14th king bearing the titles of France and

Navarre.



The 14th December, 1553, that is, 14 centuries, 14 decades, and 14

years after the birth of Christ, Henry IV. was born; the ciphers of

the date 1553, when added together, giving the number 14.



The 14th May, 1554, Henry II. ordered the enlargement of the Rue de la

Ferronnerie. The circumstance of this order not having been carried

out, occasioned the murder of Henry IV. in that street, four times 14

years after.



The 14th May, 1552, was the date of the birth of MarguA(C)rite de Valois,

first wife of Henry IV.



On the 14th May, 1588, the Parisians revolted against Henry III., at

the instigation of the Duke of Guise.



On the 14th March, 1590, Henry IV. gained the battle of Ivry.



On the 14th May, 1590, Henry was repulsed from the Fauxbourgs of

Paris.



On the 14th November, 1590, the Sixteen took oath to die rather than

serve Henry.



On the 14th November, 1592, the Parliament registered the Papal Bull

giving power to the legate to nominate a king to the exclusion of

Henry.



On the 14th December, 1599, the Duke of Savoy was reconciled to Henry

IV.



On the 14th September, 1606, the Dauphin, afterwards Louis XIII., was

baptized.



On the 14th May, 1610, the king was stopped in the Rue de la

Ferronnerie, by his carriage becoming locked with a cart, on account

of the narrowness of the street. Ravaillac took advantage of the

occasion for stabbing him.



Henry IV. lived four times 14 years, 14 weeks, and four times 14 days;

that is to say, 56 years and 5 months.



On the 14th May, 1643, died Louis XIII., son of Henry IV.; not only on

the same day of the same month as his father, but the date, 1643, when

its ciphers are added together, gives the number 14, just as the

ciphers of the date of the birth of his father gave 14.



Louis XIV. mounted the throne in 1643: 1 + 6 + 4 + 3 = 14.



He died in the year 1715: 1 + 7 + 1 + 5 = 14.



He lived 77 years, and 7 + 7 = 14.



Louis XV. mounted the throne in the same year; he died in 1774, which

also bears the stamp of 14, the extremes being 14, and the sum of the

means 7 + 7 making 14.



Louis XVI. had reigned 14 years when he convoked the States General,

which was to bring about the Revolution.



The number of years between the assassination of Henry IV. and the

dethronement of Louis XVI. is divisible by 14.



Louis XVII. died in 1794; the extreme digits of the date are 14, and

the first two give his number.



The restoration of the Bourbons took place in 1814, also marked by the

extremes being 14; also by the sum of the ciphers making 14.



The following are other curious calculations made respecting certain

French kings.



Add the ciphers composing the year of the birth or of the death of

some of the kings of the third race, and the result of each sum is

the titular number of each prince. Thus:--



Louis IX. was born in 1215; add the four ciphers of this date, and you

have IX.



Charles VII. was born in 1402; the sum of 1 + 4 + 2 gives VII.



Louis XII. was born in 1461; and 1 + 4 + 6 + 1 = XII.



Henry IV. died in 1610; and 1 + 6 + 1 = twice IV.



Louis XIV. was crowned in 1643; and these four ciphers give XIV. The

same king died in 1715; and this date gives also XIV. He was aged 77

years, and again 7 + 7 = 14.



Louis XVIII. was born in 1755; add the digits, and you have XVIII.



What is remarkable is, that this number 18 is double the number of the

king to whom the law first applies, and is triple the number of the

kings to whom it has applied.



Here is another curious calculation:--



Robespierre fell in 1794;



Napoleon in 1815, and Charles X. in 1830.



Now, the remarkable fact in connection with these dates is, that the

sum of the digits composing them, added to the dates, gives the date

of the fall of the successor. Robespierre fell in 1794; 1 + 7 + 9 + 4

= 21, 1794 + 21 = 1815, the date of the fall of Napoleon; 1 + 8 + 1 +

5 = 15, and 1815 + 15 = 1830, the date of the fall of Charles X.



There is a singular rule which has been supposed to determine the

length of the reigning Pope's life, in the earlier half of a century.

Add his number to that of his predecessor, to that add ten, and the

result gives the year of his death.



Pius VII. succeeded Pius VI.; 6 + 7 = 13; add 10, and the sum is 23.

Pius VII. died in 1823.



Leo XII. succeeded Pius VII.; 12 + 7 + 10 = 29; and Leo XII. died in

1829.



Pius VIII. succeeded Leo XII.; 8 + 12 + 10 = 30; and Pius VIII. died

in 1830.



However, this calculation does not always apply.



Gregory XVI. ought to have died in 1834, but he did not actually

vacate his see till 1846.



It is also well known that an ancient tradition forbids the hope of

any of St. Peter's successors, pervenire ad annos Petri; i. e., to

reign 25 years.



Those who sat longest are



Years. Months. Days.

Pius VI., who reigned 24 6 14

Hadrian I. " 23 10 17

Pius VII. " 23 5 6

Alexander III. " 21 11 23

St. Silvester I. " 21 0 4



There is one numerical curiosity of a very remarkable character, which

I must not omit.



The ancient Chamber of Deputies, such as it existed in 1830, was

composed of 402 members, and was divided into two parties. The one,

numbering 221 members, declared itself strongly for the revolution of

July; the other party, numbering 181, did not favor a change. The

result was the constitutional monarchy, which re-established order

after the three memorable days of July. The parties were known by the

following nicknames. The larger was commonly called La queue de

Robespierre, and the smaller, Les honnAªtes gens. Now, the

remarkable fact is, that if we give to the letters of the alphabet

their numerical values as they stand in their order, as 1 for A, 2 for

B, 3 for C, and so on to Z, which is valued at 25, and then write

vertically on the left hand the words, La queue de Robespierre,

with the number equivalent to each letter opposite to it, and on the

right hand, in like manner, Les honnAªtes gens, if each column of

numbers be summed up, the result is the number of members who formed

each party.



1 2 3 4 5 6 7 8 9 10 11 12 13

A B C D E F G H I J K L M



14 15 16 17 18 19 20 21 22 23 24 25

N O P Q R S T U V X Y Z



L--12 L--12

A-- 1 E-- 5

S--19

Q--17

U--21 H-- 8

E-- 5 O--15

U-- 5 N--14

E-- 5 N--14

E-- 5

D-- 4 T--20

E-- 5 E-- 5

S--19

R--18

O--15 G-- 7

B-- 2 E-- 5

E-- 5 N--14

S--19 S--19

P--16 -----

I-- 9 181

E-- 5

R--18

R--18

E-- 5

-----

221



Majority 221

Minority 181

----

Total 402



Some coincidences of dates are very remarkable.



On the 25th August, 1569, the Calvinists massacred the Catholic nobles

and priests at BA(C)arn and Navarre.



On the same day of the same month, in 1572, the Calvinists were

massacred in Paris and elsewhere.



On the 25th October, 1615, Louis XIII. married Anne of Austria,

infanta of Spain, whereupon we may remark the following

coincidences:--



The name Loys[36] de Bourbon contains 13 letters; so does the name

Anne d'Austriche.



Louis was 13 years old when this marriage was decided on; Anne was the

same age.



He was the thirteenth king of France bearing the name of Louis, and

she was the thirteenth infanta of the name of Anne of Austria.



On the 23d April, 1616, died Shakspeare: on the same day of the same

month, in the same year, died the great poet Cervantes.



On the 29th May, 1630, King Charles II. was born.



On the 29th May, 1660, he was restored.



On the 29th May, 1672, the fleet was beaten by the Dutch.



On the 29th May, 1679, the rebellion of the Covenanters broke out in

Scotland.



The Emperor Charles V. was born on February 24, 1500; on that day he

won the battle of Pavia, in 1525, and on the same day was crowned in

1530.



On the 29th January, 1697, M. de Broquemar, president of the

Parliament of Paris, died suddenly in that city; next day his brother,

an officer, died suddenly at Bergue, where he was governor. The lives

of these brothers present remarkable coincidences. One day the

officer, being engaged in battle, was wounded in his leg by a

sword-blow. On the same day, at the same moment, the president was

afflicted with acute pain, which attacked him suddenly in the same leg

as that of his brother which had been injured.



John Aubrey mentions the case of a friend of his who was born on the

15th November; his eldest son was born on the 15th November; and his

second son's first son on the same day of the same month.



At the hour of prime, April 6, 1327, Petrarch first saw his mistress

Laura, in the Church of St. Clara in Avignon. In the same city, same

month, same hour, 1348, she died.



The deputation charged with offering the crown of Greece to Prince

Otho, arrived in Munich on the 13th October, 1832; and it was on the

13th October, 1862, that King Otho left Athens, to return to it no

more.



On the 21st April, 1770, Louis XVI. was married at Vienna, by the

sending of the ring.



On the 21st June, in the same year, took place the fatal festivities

of his marriage.



On the 21st January, 1781, was the fAªte at the HA'tel de Ville, for

the birth of the Dauphin.



On the 21st June, 1791, took place the flight to Varennes.



On the 21st January, 1793, he died on the scaffold.



There is said to be a tradition of Norman-monkish origin, that the

number 3 is stamped on the Royal line of England, so that there shall

not be more than three princes in succession without a revolution.



William I., William II., Henry I.; then followed the revolution of

Stephen.



Henry II., Richard I., John; invasion of Louis, Dauphin of France, who

claimed the throne.



Henry III., Edward I., Edward II., who was dethroned and put to death.



Edward III., Richard II., who was dethroned.



Henry IV., Henry V., Henry VI.; the crown passed to the house of York.



Edward IV., Edward V., Richard III.; the crown claimed and won by

Henry Tudor.



Henry VII., Henry VIII., Edward VI.; usurpation of Lady Jane Grey.



Mary I., Elizabeth; the crown passed to the house of Stuart.



James I., Charles I.; Revolution.



Charles II., James II.; invasion of William of Orange.



William of Orange and Mary II., Anne; arrival of the house of

Brunswick.



George I., George II., George III., George IV., William IV., Victoria.

The law has proved faulty in the last case; but certainly there was a

crisis in the reign of George IV.



As I am on the subject of the English princes, I will add another

singular coincidence, though it has nothing to do with the fatality of

numbers.



It is that Saturday has been a day of ill omen to the later kings.



William of Orange died Saturday, 18th March, 1702.



Anne died Saturday, 1st August, 1704.



George I. died Saturday, 10th June, 1727.



George II. died Saturday, 25th October, 1760.



George III. died Saturday, 30th January, 1820.



George IV. died Saturday, 26th June, 1830.



FOOTNOTE:



[36] Up to Louis XIII. all the kings of this name spelled Louis as

Loys.





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