When my pupils have gained the quick perception and instantaneous
apprehension which always reward the studious use of In., Ex., and Con.,
they can, amongst other new achievements, always remember and never
forget figures and dates.
_Pike's Peak_, the most famous in the chain known as the Rocky Mountains
in America, is fourteen thousand one hundred and forty-seven feet high.
Instantly, one who is trained in the use of In., Ex., and Con.,
perceives that there are two fourteens [Syn., In.] in these figures, and
that the last figure is half of fourteen, or 7 In. by W. and P., making
14,147. Of course, one who is not practised in analogies, in discovering
similarities and finding differences would not have noticed any
peculiarity in these figures which would enable him to remember them.
Few people ever notice any relations among numbers. But any possible
figures or dates always possess relations to the mind trained in In.,
Ex., and Con.
_Fujiyama_, the noted volcano of Japan, is twelve thousand three hundred
and sixty-five feet high. Does any pupil who has mastered the first
lesson and who is expert in the use of In., Ex., and Con., fail to
notice that here we have the disguised statement that the height of this
mountain is expressed in the number of months and days of the year,
12,365 feet high? These figures drop into that mould and henceforth are
remembered without difficulty. These are remarkable coincidences no
doubt, but are not all sets of figures similarly impressive coincidences
to the trained eye, and the _active_, _thinking_ and _assimilative_
mind?
No reader of English history has failed to notice the three sixes in the
date of the Great Fire in London, _viz._, 1666. The "three sixes" are
generally resorted to as a signal for fire companies to turn out in full
force; yet such a coincidence of figures in a distant date makes a
slight impression compared to the vividness of events that happened in
the year of our birth, the year of graduation from school, the year of
marriage, and the year of the death of relatives, &c., &c. Keep a small
blank book for such entries, not to help remember the dates or facts,
but to have them together so as to rapidly deal with them, to classify
them and otherwise study them under the eye. You will soon be astonished
at the accumulation.
The population of New Zealand, exclusive of natives, is 672,265.
Bringing the first two figures into relation with the last two we have
67 and 65--a difference of 2 only. The two groups of 672 and 265 have
the figure 2 at the end of the first group, and another 2 at the
beginning of the second group. These two twos are in sequence (Con.),
and each of them expresses the difference between 67 and 65. _Thought_
about in this way, or in any other, the series becomes fixed in mind,
and will be hard to forget.
The population of Sydney is 386,400. Here are two groups of three
figures each. The first two figures of the first group are 38, and the
first two figures of the second group are 40--a difference of 2. Two
taken from 8 leaves 6, or the third figure of the first group, and 2
added to the first figure of the second group makes 6. The 40 ends with
a cypher, and it is a case of Syn. In. that the last figure of the
second group or the third figure of it should likewise be a cypher.
Besides, those who know anything at all about the population of Sydney
must know that it is vastly more than 38,640, and hence that there must
be another cypher after 40, making the total of 386,400.
The population of Melbourne is 490,912. Here we have 4 at the beginning
and half of 4 or 2 at the end of the six figures. The four interior
figures, viz., 9091 is a clear case of Con.--or 90 and 91. Then again 91
ending with 1, the next figure is 2--a case of sequence or Con. But
490,912 is the population of the city of Melbourne with its suburbs. The
"city" itself contains only 73,361 inhabitants, 73 reversed becomes
37--or only 1 more than 36. This 1 placed at the end of or after 36
makes the 361. Now 37 reversed is 73, and then follows 361, making the
total to be 73,361.
Let the attentive pupil observe that this method does not give any set
of rules for thinking in the same manner in regard to different sets or
example of numbers. That would be impossible. Thinking or finding
relations amongst the objects of thought must be differently worked out
in each case, since the figures themselves are differently grouped.
The foregoing cases in regard to population will suffice for those who
live in the Australian colonies, and to others they will teach the
method of handling such cases, and leave them the pleasure of working
out the process in regard to the population where they reside, or other
application of the method they may wish to make.
Great encouragement is found in the circumstance that after considerable
practice in dealing with numerous figures through In., Ex., and Con.,
new figures are self-remembered from the habit of assimilating numbers.
They henceforth make more vivid impressions than formerly.
INCLUSION embraces cases where the same kind of facts or the principles
were involved, or the same figures occur in different dates with regard
to somewhat parallel facts--End of Augustus's empire [death]
14 A.D.--End of Charlemagne's [death] 814 A.D., and end of Napoleon's
[abdication] 1814 A.D.
EXCLUSION implies facts from the opposite sides relating to the same
events, conspicuously opposite views held by the same man at different
periods, or by different men who were noticeably similar in some other
respects, or antithesis as to the character or difference in the
nationality [if the two nations are frequent foes] of different men in
whose careers, date of birth, or what not, there was something
distinctly parallel--Egbert, first King of England, died 837. William
IV., last King of England, died 1837. What a vivid exclusion here for
instance: Abraham died 1821 B.C., and Napoleon Bonaparte died 1821 A.D.
CONCURRENCES are found in events that occur on the same date or nearly
so, or follow each other somewhat closely.
Charles Darwin, who advocated evolution, now popular with scientists in
every quarter of the globe, and Sir H. Cole, who first advocated
International Exhibitions, now popular in every part of the world
[Inclusion] were born in the same year 1809 [Concurrence] and died in
the same year 1882 [Concurrence].
Garibaldi [the Italian] and Skobeleff [the Russian] [Exclusion, being of
different countries], both great and recklessly patriotic generals
[Inclusion] and both favourites in France [Inclusion], died in the same
year, 1882 [Concurrence]. Longfellow and Rossetti, both English-speaking
poets [Inclusion] who had closely studied Dante [Inclusion] died in the
same year, 1882 [Concurrence].
Haydn, the great composer, was born in 1732, and died in 1809; this date
corresponds to that of the birth [Exclusion and Concurrence] of another
famous composer [Inclusion], Mendelssohn, who himself died in 1847, the
same year as O'Connell.
Lamarck [1744-1829], advocated a theory of development nearly
resembling the Darwinian Theory of the Origin of Species [In.]. This he
did in 1809, the year in which Charles Darwin was born [Con.]. Darwin's
writings have altered the opinions of many as to the Creation, and the
year of his birth was that of the death of Haydn, the composer of the
Oratorio "The Creation." [Con. and Ex.].
John Baptiste Robinet taught the gradual development of all forms of
existence from a single creative cause. He died in 1820, the year in
which Herbert Spencer, the English Apostle of Evolution, was born [In.,
Ex., and Con.].
Galileo, founder of Modern Astronomy, born in 1564--Shakespeare's birth
year [Con.]--died in 1642, the very year in which Sir Isaac Newton was
born. Galileo's theory was not proved but merely made probable, until
the existence of the laws of gravitation was established, and it was
Newton who discovered gravitation. This is an instance of Inclusion as
to the men, of Exclusion and Concurrence as to date of birth and death.
Two prominent _literati_ [Inclusion], one a Frenchman the other an
Englishman [Exclusion], well-known for the pomposity and sonority of
their style of writing [Inclusion], were born in the same year, 1709,
and died the same year 1784, a double Concurrence--Lefranc de
Pompignan--[pompous In. by S.], and Samuel Johnson.
General Foy, an _orator_ and artillery officer, fond of literature, was
born the same year [Concurrence] 1775, as the _orator_ [Inclusion],
Daniel O'Connell. He died in 1825, the same year [Concurrence] as
Paul-Louis Courier, who was also an artillery officer [Inclusion], fond
of literature [Inclusion], and moreover, like O'Connell, a violent
pamphleteer [Inclusion].
Two illustrious, uncompromising characters [Inclusion], both brilliant
composers [Inclusion], the one musical, the other literary, the one a
representative of the music of the future, the other of the obsolete
polemic of the past [Exclusion], Richard Wagner and Louis Veuillot, were
born in the same year, 1813, and died in the same year, 1883. The last
point is a double Concurrence.
Two foremost harbingers of modern thought [Inclusion], Voltaire and
J. J. Rousseau, died in 1778--[Concurrence]. Both gained for themselves
the reputation of having been the most reckless antagonists of
Christianity [Inclusion]. And still the one dedicated a church to the
service of God, whilst the other in his "Emile" wrote a vindication of
Christianity [Exclusion as to each of them, Inclusion as to both of
them].
A little practice makes the pupil prompt in dealing with any figures
whatever. Take the height of Mount Everest, which is 29,002 feet. We
have all heard that it is more than five miles high. Let us test this
statement. There are 5,280 feet in a mile, multiply 5,280 by 5, and we
have 26,400. Hence we see that Mount Everest being 29,002 feet high must
be more than five miles high. Half of a mile is 5,280 feet divided by 2,
or 2,640 feet. Add this to 26,400 and we have 29,040. Hence we see that
Mount Everest is 51/2 miles high lacking 38 feet, or that if we add
38 feet to its height of 29,002, it would then be exactly 51/2 miles high.
Can we then forget that it is exactly 29,002 feet high?
Shakespeare was born in 1564 and died in 1616. The First Folio Edition
of his works was printed in 1623, the Second in 1632, the Third in 1664,
and the Fourth in 1685. Can we fix these events infallibly in our
memories? We can begin with whichever date we prefer. If we add
together the figures of the year of his birth, 1564, they make 16. All
the dates hereafter considered occurred in 1600, &c. We can thus
disregard the first 16 and consider only the last two figures which
constitute the fraction of a century.
Let us begin with his death in 1616 in the _sixteens_. Is not this a
vivid collocation of figures? Can we forget it as applied to the great
dramatist? Now if we double the last 16, it gives us the date of the
second Folio in [16]32 and 32 reversed gives us the date of the first
Folio. Again, seven years after his death ["seven ages of man"] his
first Folio was published in 1623. The second Folio was published in
1632 or 23 reversed, and the third Folio in 1664, or 32 doubled, and
just 100 years after his birth in 1564. His birth might also be
remembered as occurring in the same year as that of the great astronomer
Galileo. The fourth Folio appeared in 1685 or 21 years after the third
Folio. This period measures the years that bring man's majority or full
age.
Attention to the facts of reading will be secured by increased power of
Concentration, and a familiarity with In., Ex., and Con. will enable us
to assimilate all dates and figures by numeric thinking with the
greatest promptitude, especially the longer or larger series.
Try the case of Noah's Flood, 2348 B.C. Here the figures pass by a unit
at a time from 2[3] to 4, and then by doubling the 4 we have the last
figure 8--making altogether 2348. Another method of dealing with this
date is very instructive. Read the account in Gen. ch. vii., vv. 9, 13,
and 15. Now we can proceed.
They went into the Ark by _twos_. This gives the figure 2. Now let us
find the other figures. Noah's three sons and their wives make three
pairs of persons, or _three_ families. This gives the second figure 3.
Then counting Noah and his wife, and his three sons and their wives,
there were four pairs of human beings altogether. This gives the figure
4. Finally the total number of human beings who entered the ark were
4 pairs or _eight_ persons. This gives the figure 8. Thus we have the
entire set of figures, 2348 B.C. Take the date of the creation
according to the accepted biblical chronology as 4004 B.C. We could say
the date has _four_ figures, that the expression of it begins and ends
with the figure 4, and that the two intermediates are nought, or
cyphers; or that the figures are expressed by 40 and _forty reversed_ as
40-04--or 4004.