We do not often hear those who declare that “education does not educate,”
trying to account for the failure charged against existing school
systems. Are the alleged defects to be found in the unfit nature of
the things studied, or in methods of study, or both? One of the chief
exercises—indeed _the_ chief, in common schools—depended upon for mental
development is numbers. Is the study of arithmetic worthy the place
it holds in that regard? Does it do more than to cultivate a special
faculty? Is that faculty one of the most important in the human mind?
Is it related intimately to understanding, and does its culture imply a
stimulation of the reasoning powers?
Answers to these questions would doubtless be colored by the mental
characteristics or experience of the individual answering. To some minds
mathematics is a general stimulant; to others only a useful tool; to
still others, a stumbling block and an offense. Some one has declared
that while all specialties followed exclusively, are narrowing in their
influence on the mind, the two specialties which lead straightest toward
imbecility are music and mathematics. This was probably the conclusion
of a mind which could not master the extraction of the cube root, and
did not know “Yankee Doodle” from “Old Hundred.” Oliver Goldsmith said
“Mathematics is a study to which the meanest intellect is competent.”
He remembered many floggings because of the multiplication table, and
hardly had patience to count change for a sovereign. If we appeal to
first-rate examples of achievement in music and mathematics—say to
a Mozart and a Newton—we shall find well-balanced minds; but on the
other hand we may be confounded by finding prodigies in these lines
who possess mean intellects otherwise. Blind Tom and Zerah Colburn are
illustrations. Zerah Colburn had mathematics in “the natural way.” His
parents in Vermont were poor and ignorant; the father appears to have
been both selfish and stupid, but the mother was rather a shrewd Yankee
woman. If there was any special gift in the family it was for hard work
and sharp trading—rather commonplace gifts in New England. Out of this
unpromising stock came Zerah in 1804. One day, when he was six years old,
he flashed out a mathematical meteor, a revelation. His father overheard
him reciting in his play the multiplication table, having never learned
it. Examination showed that he knew it all and more too; was, in fact,
himself a walking, frisking multiplication table. He answered instantly
the product of 13×97—1261. The gift seemed to have descended on him then
and there miraculously; the fact probably was that it had always been
there, but he had been too dull to exercise it until the whim struck the
little animal.
The event created a sensation, which, inside of a year, was felt both in
America and Europe. The popular wonder with which the child’s performance
was received very speedily turned the head of his stupidly cunning
father; he dropped his farm tools and rejecting all the offers of wealthy
gentlemen to give the boy a complete education, set out to exhibit the
prodigy through the land as a show. Thereafter, so long as both lived,
the father was the evil genius of the son.
At the outset of their wanderings, President Wheelock, of Dartmouth
College, offered to take the child and give him a thorough education,
but the father declined the offer, not including even a honorarium for
himself. In Boston a committee of wealthy gentlemen, headed by Josiah
Quincy, offered to raise $5,000, one-half to be given to the father, the
other moiety to be devoted to Zerah’s education, under their direction.
The father acceded to this, but for some reason, when the contract of
indenture was drawn, it was different in the important particular that
the father and son were to be _permitted_ to exhibit the lad publicly
until the proceeds should amount to $5,000, when the sum was to be
apportioned as before stipulated. This arrangement the father very
properly rejected, and the negotiations failed. Wrong versions of this
affair were published, imputing to the father the rejection of the
genuine benefaction first proposed. That these reports injured him and
their success thereafter wherever they went, the son always asseverated.
They now went on “a starring tour” through the country, meeting with
varied success, and in the early spring of 1811 returned to Vermont with
about $600 as the proceeds thereof. The elder Colburn gave $500 of this
to the mother, which, for the next twelve years, was all he contributed
to the family support—the family then consisting of six children under
fourteen years of age.
From the first Zerah’s performance was confounding to all spectators.
Mathematically, nothing seemed impossible to this child of six years.
Being asked, “What is the number of seconds in 2,000 years?” he readily
and accurately answered 63,072,000,000. Again, “What is the square of
1,449,” he answered, 2,099,601. More intricate calculations based on
concrete facts, were equally easy, as “Suppose I have a corn-field in
which are seven acres, having seventeen rows to each acre, sixty-four
hills to each row, eight ears on a hill, and one hundred and fifty
kernels on each ear, how many kernels in the corn-field?” The answer,
9,139,200 kernels, came readily. Asked what sum multiplied by itself will
produce 998,001, he replied in four seconds, 999; and in twenty seconds
produced the correct answer to “How many days and hours have lapsed
since the Christian era began?” viz.: 661,015 days, 15,864,360 hours.
He gave the answer to this: What is the square of 999,999×49×25; the
answer requires seventeen figures to express it. Being asked what are the
factors of 247,483 he made this reply: “941 and 263, and these are the
_only_ factors.” How could he know that?
These operations seemed the automatic action of mental power allied to
instinct rather than to reason. The child had had absolutely no education
in numbers and could neither read nor write; he would scarcely interrupt
his infantile play to make his calculations. It was not till the spring
of 1811 that he learned the names and the powers of the nine digits when
written, and this he learned from a stranger who seemed to take this
much more interest in his education than his father had ever taken.
He was at this time a bright, playful, healthy boy. He answered mere
puzzling questions with more than the ordinary shrewdness of his age, as,
“Which is the greater, six dozen dozen or half a dozen dozen?” “Which is
greater, twice twenty-five or twice five-and-twenty?” “How many black
beans make six white ones?” He answered quickly, “Six—if you skin ’em.”
During his calculations he would twist and contort like one in St. Vitus’
dance. If asked, as he often was, his method of calculation, he would cry
at the annoyance of attempting to explain.
In April, 1811, father and son went to England, the child then being six
and a half years old. The father tried (in vain, of course) to induce
his wife to put their five little ones out in care of the neighbors
and go abroad with him! Then, as at all other times, she seems to have
monopolized the wit of the family. The same one-sidedness may have been
detected in other families, for aught I know to the contrary.
In England he at first created a marked sensation. His receptions were
attended by wondering multitudes, among them being members of the
nobility and royal family and distinguished scientists and literati.
Among his achievements at this time was to multiply the number eight
by itself up to the sixteenth power, giving the inconceivable result,
281,474,976,710,656. He extracted the square and cube roots of large
numbers by a flash of his genius. It had been laid down by mathematicians
that no rule existed for finding the factors of numbers, but at the age
of nine Zerah made such a rule; it was nearly as difficult to understand
as his performance, however. Under this formula he gave the factors of
171,395, viz.: 5×34279; 7×22485; 59×2905; 83×2065; 35×4897; 295×581;
413×415. “It had been asserted,” he says, “by a French mathematician that
4294967297 is a prime number; but the celebrated Euler detected the error
by discovering that it is equal to 641×6,700,417. The same number was
proposed to this child, who found out the factors by the mere operation
of his mind.”
The father was now happy. He was in the enjoyment of means and
distinction through his child, all of which, with the usual conceit
of a father, he arrogated to himself as the due reward of merit for
having been the prodigious progenitor of so remarkable a child. Various
money-making enterprises were started in connection with the “show,” from
which others seemed to derive as much benefit as the father. Sir James
Mackintosh, Sir Humphrey Davy (inventor of the safety lamp) and Basil
Montague became a committee to superintend the publication of a book
about the child; but though several hundred subscribers were obtained,
many of whom paid in advance, the work was never published. A meeting
of distinguished gentlemen was held to devise a scheme for his special
education, which should develop his genius into a prodigy of matured
intellectual powers, such as the world had never conceived. But all these
plans were defeated by two circumstances—the boy’s general incapacity and
the father’s special rapacity.
The “show business” seemed to be the elder Colburn’s forté and he took
the boy on exhibition to Scotland and Ireland, and finally to Paris
(1814). Here, too, the extraordinary interest in his extraordinary
faculty resulted in a project for his proper education—La Place, the
author of “Méchanique Celeste,” and Guizot, the historian, being
conspicuous in his interest. It resulted in his being given a scholarship
in the Lyceum by order of Napoleon, just then back from Elba on his
little excursion to re-resubjugate the world; this intervention in behalf
of the boy being one creditable act of his brief restoration, at least.
The lad showed his gratitude to his imperial patron by ardently assisting
in the entrenchments thrown up to resist the attack of the allied armies
on Paris after the defeat at Waterloo.
The London admirers, spurred by pique at the French interest in and
control of the boy, and by the father’s importunities, set about raising
a purse to bring Zerah back and educate him in England. In furtherance
of the enterprise, the father took his boy from the Lyceum and brought
him to London in February, 1816. But this scheme fell through, owing,
it is charged, to dissatisfaction with the father’s demand of a large
endowment to himself as well as for the child; and soon both were living
in poverty, unheeded and deserted.
In a fortunate moment the Earl of Bristol interested himself in young
Colburn and made a provision of $620 a year for his education at
Westminster school, where he was regularly entered, being then a few days
over twelve years old. Here he spent two years and nine months. Though
he made creditable progress in languages he disappointed those who had
built expectations on his peculiar powers, by revolting against higher
mathematics. It was found, in fact, that his special faculty was less
susceptible of discipline than is the ordinary mathematical power of
other youth.
But, I am gratified to state, the young Yankee made a stubborn resistance
to the British form of white slavery in the school known as “fagging;”
and what with his own obstinacy and the old man’s constant harassing the
school authorities with remonstrances, the rule was suspended in the case
of Zerah—probably the first and last case of such an alarming innovation
on good old brutal British customs. Having won this emancipation the old
father submitted with equanimity to being hooted off the “campus” with
cries of “Yankee.”
But the elder Colburn next quarreled with his generous patron, and took
the boy from school. We may venture to doubt if this was after all a
great privation to the lad. The curriculum of Westminster school the
first four years consisted of Latin and fagging; the next four years
of Greek and fagging. They had made it elective in Zerah’s case to
the extent of omitting the fagging, taking away the live part of the
curriculum and leaving him only the dead. Zerah himself tells us that the
same time which was thus spent in linguistic body-snatching if spent in
the French seminary would have afforded an excellent general education.
This fatuity regarding dead languages has been since well maintained in
English high schools and colleges, and, what is more remarkable, has been
pretty faithfully imitated in higher institutions in America.
Thrown on their own resources again, they found the novelty of Zerah’s
performance had worn off, and he did not “draw.” The father now conceived
the brilliant plan of making an actor of the boy. After four months’
training by Kemble, he appeared on the stage at Margate, with a little
success; went with strolling companies through England and Ireland
during four months more, and then returned to London and ended the
histrionic career. Next Zerah was prompted by the fond father to attempt
play-writing, but as he says himself, his compositions “never had any
merit or any success”—though this is substantially his opinion of all his
own efforts through life.[B] Extreme poverty followed, almost the only
means of subsistence being genteel begging from former friends. The last
and kindest of these was at length worn out, and directed his footman to
slam the door in the poor boy’s face when he presented himself on some
alleged errand from his father.
Zerah in his autobiography, subsequently written, speaks of these dark
days with sorrow, but without one word of complaint of his father;
indeed, the memoir seems to have been written more for the purpose of
vindicating the father’s name than to do himself justice. He constantly
laments that the mysterious faculty had been given him, and attributes to
it and to his own general incapacity, all the misfortunes and sufferings
of his father and himself. He called his gift “a peculiarly painful
circumstance which destroyed all pleasing anticipations, blasted every
prospect of social happiness, and after years of absence consigned
the husband and father to a stranger’s grave.” Poor boy! He must have
suffered more than he confesses. He hints at their want, his disgust
with asking charity, the alienation of friends, and, above all his
afflictions, he chafes at his idleness; and he naively sums up the whole
experience as one of “comparative unhappiness!” How did Dickens ever miss
these unique studies from real life?
A situation as usher in a school was now obtained for young Zerah (ætat
17) and he soon after set up a school on his own account. This was
probably the first legitimate money he ever earned, and he mentions
the chance, poor as it was, with more satisfaction than he does any
of the achievements of his genius. It was far better than depending
on patronage—which seems to have galled his pride. Before anything
could come of school teaching, however, the father and son went off to
other cities on a begging expedition. The usual humiliation and misery
followed the undertaking, and they returned to London, where the young
man reopened his school. Here, in 1824, his father died of consumption
brought on by want and anxiety. One of Zerah’s biographers has said of
the father: “Unhappily he had from the first discovery of his son’s
extraordinary gifts, worked upon them with mercenary feelings, as a
source of revenue. It is true he had a father’s love for his child, and
in this respect Zerah, in the simple memoir of his own life, does his
parent more than justice; but still it was this short-sighted selfishness
which made him convert his child’s endowments into a curse to him, to his
friends, and to Zerah himself. His expectations had been lifted to such
a pitch that nothing could satisfy them. The most generous offers fell
short of what he felt to be his due; liberality was turned in his mind to
parsimony, and even his friends were regarded as little short of enemies.
Such a struggle could not always last. His mind was torn with thoughts of
his home and family, neglected for twelve years; of his life wasted, his
prospects defeated; of fond dreams ending at last in failure, shame, and
poverty.”
After the death of his father, Zerah’s course of life was not less
vacillating and unsuccessful, however, so it seems that his failures were
not altogether due to his father’s bad counsels. He remained a while in
London, making astronomical calculations and doing other mathematical
work, as chance offered it. Aided by his old benefactor, Lord Bristol, he
at last set out to seek his mother and family. She had done better alone.
“During the long absence of her husband, with a family of eight children,
and almost entirely destitute of property, she had sustained the burthen
with indomitable energy. She wrought with her own hands in house and
field; bargained away the little farm for a better one; and as her son
says, ‘by a course of persevering industry, hard fare and trials such as
few women are accustomed to, she has hitherto succeeded in supporting
herself, beside doing a good deal for her children.’” Lucky for the
family that one of them was not a genius. Mathematics, however, seems to
be a form of monomania from which her sex is generally exempt. In fact,
in the long list of eccentric Americans from which I can choose subjects
for this series of sketches, I fear there is not to be one eccentric
woman. This can be taken as complimentary to the sex or not, according as
the reader regards eccentricity.
Our arithmetical prodigy, now twenty years old, went to teaching a
country school for a living, and at last fetched up in that other safe
retreat of preaching the gospel. He followed this vocation with more
persistence and credit than he had brought to any other of his numerous
professions, though on his own modest representation he was not much of a
preacher. His last venture was to become professor of—not mathematics—but
languages in the “Vermont University” at Norwich. In this situation
his life terminated, March 2, 1840. He plaintively, but in a somewhat
pedantic style, sums up his career as follows:
“Perhaps it has fallen to the lot of very few, if any individuals, while
attracting curiosity and notice, to receive at the same time so many
flattering marks of kindness, and it is not unfrequently a sorrowful
reflection to him that after all the sympathy and benevolence shown
by the liberal and scientific, certain unforeseen and unfortunate
causes have prevented and still prevent his reaching and sustaining
that distinguished place in the mathematical literature of the age to
which, on account of the singular gift bestowed on him, he seemed to be
destined. Now, after possessing that talent twenty-two years, he feels
unable to account for its donation, and is unaware of its object.”
Some facts regarding this singular gift may furnish suggestions to those
who think upon educational matters.
1. His peculiar faculty was _arithmetical_, not generally mathematical.
He had little or no taste for higher mathematics: those which, like
geometry and surveying, appeal to the perceptions, those which,
like algebra, appeal to the imagination, and those which, like pure
mathematics, appeal to the analytical reasoning powers, he disliked.
His gift was natural, rudimentary and unreasoning, and as he reached
adult life it passed from him, either because he outgrew it or lost it
by over-use or disuse. Constant and long continued practice in mental
calculation brought the possessor of this special mathematical gift,
as he says, neither intellectual growth nor better capacity for mental
application. In fact, the more he used it the stupider he grew.
May we infer from this that arithmetic is a primitive, rudimentary
and low branch of mathematics, having little or no relation to the
perceptions of childhood, the imagination of youth and the reasoning
powers of the matured mind, and hence of little or no value for the
purpose of mental exercise and stimulation?
2. His whole process was that of _multiplication_, and its inversion
(division). He seems not to have practiced addition, which is in reality
the rudiments of multiplication, or its converse, subtraction, which
is only the long process of division. In the multiplication of large
numbers, which so astounded people, he performed mentally several
operations to get the result.
May we infer from this analysis—arithmetic being assumed to be the most
unintellectual form of mathematics—that multiplication is the least
valuable part of arithmetic?
If psychologists should grant these inferences to be sound, it remains
the duty of teachers to address themselves to improving the teaching
of the multiplication table, as the weak spot in all our primary
education in numbers. Something can be done, perhaps, to idealize the
multiplication table, and to make instruction in it concrete, objective,
rational. Can not a child be shown why or how six times seven make
forty-two? If arithmetic is so abstract, arbitrary and barren of ideas
that this can not be done, were it not better to cease compelling the
miniature mind to repeat year after year such stale and silly truisms
as, “twice two are four,” etc., under the absurd expectation that some
prodigious mental outburst must result from it in some mysterious manner?
Why not substitute for this endless repetition “Eiry eiry, ickery Ann,
fillisy follisy, Nicholas John,” to accomplish the same result?
Some good teachers, here and there, are working on the problem of how to
make arithmetic educational as well as useful. A person who has lively
recollections of days and weeks and months wasted on the dead-lift of
memorizing the multiplication table, as an achievement by the side of
which all subsequent labors of life were easy, will find comfort in the
perfect uselessness of Colburn’s wonderful genius for multiplication
without effort.
But it _was_ a wonderful faculty. What if a man were born with _all_ his
faculties expanded to the same degree! Shall education and inherited
progress yet produce minds as nearly infinite in every power as Zerah
Colburn’s was in one? Is there, _is_ there an educational method which
can take the shackles off all the faculties?
If not, may there be somewhere a life in which the mind, let out of
the strait earthly house of its tabernacle and freed from the sore
limitations of physical nature may reach that acme in all its functions?
Some of the operations of mind in a condition of suspended physical
existence seem to suggest this as a probability for even common-place
natures, as occasionally do such splendid exhibitions of a single faculty
in so weak a nature as Zerah Colburn’s.
[B] Another expedient adopted to keep the wolf from the door was to ask
subscriptions to the yet unpublished and unwritten memoir of the lad. As
he had by this time been able to formulate the method by which he made
his mental computations, the father advertised to impart the secret of
Zerah’s mysterious power to any one who would subscribe for ten copies of
the memoir at eight dollars the copy.