There are three other sub-classes of subjective mental phenomena which
must be grouped by themselves, inasmuch as they are governed by a
law which does not pertain to the classes mentioned in the preceding
chapter, although there are some characteristics which are common to
them all. The first of these classes of phenomena is manifested in
mathematical prodigies; the second in musical prodigies; and the third
pertains to the measurement of time.

The important distinction to be observed between the phenomena
described in the preceding chapter and those pertaining to mathematics,
music, and the measurement of time, consists in the fact that in the
former everything depends upon objective education, whilst the latter
are apparently produced by the exercise of inherent powers of the
subjective mind.

In order not to be misunderstood it must be here stated that on all
subjects of human knowledge not governed by fixed laws, the subjective
mind is dependent for its information upon objective education.
In other words, it knows only what has been imparted to it by and
through the objective senses or the operations of the objective mind.
Thus, its knowledge of the contents of books can only be acquired by
objective methods of education. Its wonderful powers of acquiring and
assimilating such knowledge are due to its perfect memory of all that
has been imparted to it by objective education, aided by its powers
of memory and of logical arrangement of the subject-matter. Leaving
clairvoyance and thought-transference out of consideration for the
present, the principle may be stated thus: The subjective mind cannot
know, by intuition, the name of a person, or a geographical location,
or a fact in human history. But it does know, by intuition, that two
and two make four.

No one without an objective education can, by the development of the
subjective faculties alone, become a great poet, or a great artist,
or a great orator, or a great statesman. But he may be a great
mathematician or a great musician, independently of objective education
or training, by the development of the subjective faculties alone.
Many facts are on record which demonstrate this proposition. Hundreds
of instances might be cited showing to what a prodigious extent the
mathematical and musical faculties can be developed in persons, not
only without objective training, but, in some instances, without a
brain capable of receiving any considerable objective education.

Mathematical prodigies of the character mentioned are numerous; one
of the most remarkable was the famous Zerah Colburn. The following
account of his early career, published when he was yet under eight
years of age, is taken from the “Annual Register” of 1812, an English
publication, and will serve to illustrate the proposition:

“The attention of the philosophical world has been lately attracted
by the most singular phenomenon in the history of human mind that
perhaps ever existed. It is the case of a child, under eight years
of age, who, without any previous knowledge of the common rules of
arithmetic, or even of the use and power of the Arabic numerals,
and without having given any attention to the subject, possesses,
as if by intuition, the singular faculty of solving a great variety
of arithmetical questions by the mere operation of the mind, and
without the usual assistance of any visible symbol or contrivance.

“The name of the child is Zerah Colburn, who was born at Cabut
(a town lying at the head of the Onion River, in Vermont, in the
United States of America), on the 1st of September, 1804. About two
years ago,–August, 1810,–although at that time not six years of
age, he first began to show these wonderful powers of calculation
which have since so much attracted the attention and excited the
astonishment of every person who has witnessed his extraordinary
abilities. The discovery was made by accident. His father, who had
not given him any other instruction than such as was to be obtained
at a small school established in that unfrequented and remote
part of the country, and which did not include either writing
or ciphering, was much surprised one day to hear him repeating
the products of several numbers. Struck with amazement at the
circumstance, he proposed a variety of arithmetical questions to
him, all of which the child solved with remarkable facility and
correctness. The news of the infant prodigy was soon circulated
through the neighborhood, and many persons came from distant parts
to witness so singular a circumstance. The father, encouraged by
the unanimous opinion of all who came to see him, was induced to
undertake with this child the tour of the United States. They were
everywhere received with the most flattering expressions, and in
several towns which they visited, various plans were suggested to
educate and bring up the child free from all expense to his family.
Yielding, however, to the pressing solicitations of his friends,
and urged by the most respectable and powerful recommendations, as
well as by a view to his son’s more complete education, the father
has brought the child to this country, where they arrived on the
12th of May last; and the inhabitants of this metropolis have for
the last three months had an opportunity of seeing and examining
this wonderful phenomenon, and verifying the reports that have
been circulated respecting him. Many persons of the first eminence
for their knowledge in mathematics, and well known for their
philosophical inquiries, have made a point of seeing and conversing
with him, and they have all been struck with astonishment at his
extraordinary powers. It is correctly true, as stated of him, that
he will not only determine with the greatest facility and despatch
the exact number of minutes or seconds in any given period of
time, but will also solve any other question of a similar kind.
He will tell the exact product arising from the multiplication of
any number consisting of two, three, or four figures by any other
number consisting of the like number of figures; or any number
consisting of six or seven places of figures being proposed, he
will determine with equal expedition and ease all the factors of
which it is composed. This singular faculty consequently extends
not only to the raising of powers, but to the extraction of the
square and cube roots of the number proposed, and likewise to the
means of determining whether it is a prime number (or a number
incapable of division by any other number); for which case there
does not exist at present any general rule amongst mathematicians.
All these and a variety of other questions connected therewith are
answered by this child with such promptness and accuracy (and in
the midst of his juvenile pursuits) as to astonish every person who
has visited him.

“At a meeting of his friends, which was held for the purpose of
concerting the best methods of promoting the views of the father,
this child undertook and completely succeeded in raising the
number 8 progressively up to the sixteenth power. And in naming
the last result, viz., 281,474,976,710,656! he was right in every
figure. He was then tried as to other numbers consisting of one
figure, all of which he raised (by actual multiplication, and
not by memory) as high as the tenth power, with so much facility
and despatch that the person appointed to take down the results
was obliged to enjoin him not to be so rapid. With respect to
numbers consisting of two figures, he would raise some of them to
the sixth, seventh, and eighth power, but not always with equal
facility; for the larger the products became, the more difficult he
found it to proceed. He was asked the square root of 106,929; and
before the number could be written down, he immediately answered,
327. He was then required to name the cube root of 268,336,125; and
with equal facility and promptness he replied, 645. Various other
questions of a similar nature, respecting the roots and powers
of very high numbers, were proposed by several of the gentlemen
present, to all of which he answered in a similar manner. One of
the party requested him to name the factors which produced the
number 247,483: this he immediately did by mentioning the numbers
941 and 263,–which, indeed, are the only two numbers that will
produce it. Another of them proposed 171,395, and he named the
following factors as the only ones, viz., 5 × 34,279, 7 × 24,485,
59 × 2,905, 83 × 2,065, 35 × 4,897, 295 × 581, and 413 × 415. He
was then asked to give the factors of 36,083; but he immediately
replied that it had none,–which in fact was the case, as 36,083
is a prime number. Other numbers were indiscriminately proposed
to him, and he always succeeded in giving the correct factors,
except in the case of prime numbers, which he discovered almost as
soon as proposed. One of the gentlemen asked him how many minutes
there were in forty-eight years; and before the question could be
written down he replied, 25,228,800; and instantly added that the
number of seconds in the same period was 1,513,728,000. Various
questions of the like kind were put to him, and to all of them he
answered with equal facility and promptitude, so as to astonish
every one present, and to excite a desire that so extraordinary a
faculty should, if possible, be rendered more extensive and useful.
It was the wish of the gentlemen present to obtain a knowledge of
the method by which the child was enabled to answer with so much
facility and correctness the questions thus put to him; but to all
their inquiries on the subject (and he was closely examined on this
point) he was unable to give them any information. He persistently
declared (and every observation that was made seemed to justify
the assertion) that he did not know how the answer came into his
mind. In the act of multiplying two numbers together, and in the
raising of powers, it was evident, not only from the motion of his
lips, but also from some singular facts which will be hereafter
mentioned, that some operations were going forward in his mind; yet
that operation could not, from the readiness with which the answers
were furnished, be at all allied to the usual mode of proceeding
with such subjects; and moreover he is entirely ignorant of the
common rules of arithmetic, and cannot perform upon paper a simple
sum in multiplication or division. But in the extraction of roots
and in mentioning the factors of high numbers, it does not appear
that any operation can take place, since he will give the answer
immediately, or in a very few seconds, where it would require,
according to the ordinary method of solution, a very difficult and
laborious calculation; and, moreover, the knowledge of a prime
number cannot be obtained by any known rule.

“It must be evident, from what has here been stated, that the
singular faculty which this child possesses is not altogether
dependent on his memory. In the multiplication of numbers and in
the raising of powers, he is doubtless considerably assisted by
that remarkable quality of the mind; and in this respect he might
be considered as bearing some resemblance (if the difference
of age did not prevent the justness of the comparison) to the
celebrated Jedidiah Buxton, and other persons of similar note. But
in the extraction of the roots of numbers and in determining their
factors (if any), it is clear to all those who have witnessed the
astonishing quickness and accuracy of this child that the memory
has nothing to do with the process. And in this particular point
consists the remarkable difference between the present and all
former instances of an apparently similar kind.”

The latter remark above quoted would not apply to the present day, for
many parallel cases have been reported within the present decade.

It was hoped that the powers of this child would develop by education;
and for this purpose he was placed in school and trained in objective
methods of mathematical calculation. It was believed that when his
mind became mature he would be able to impart to others the process
by which his calculations were made. But his friends were doomed to
disappointment. His powers did not improve by objective training. On
the contrary, they deteriorated just in proportion to his efforts
in that direction, and his pupils derived no benefit from the
extraordinary faculties with which he was endowed. This has been the
invariable rule in such cases.

A few years ago a gentleman travelled through this country teaching
arithmetic. He was known as the “lightning calculator.” His powers were
indeed marvellous. He could add a column of as many numbers as could
be written on a sheet of legal cap, by casting an instantaneous glance
upon the page; but he succeeded no better as a teacher than thousands
of others who could not add a column of numbers without reading every
figure by the usual laborious, objective process. He could give no
explanation of his powers other than that he possessed extraordinary
quickness of vision. But any one who is sufficiently acquainted with
the elements of optical laws to be aware that in the light of a flash
of lightning a drop of falling rain appears to be suspended motionless
in the air, knows that objective vision is not capable of such rapid
transition as to enable one to see at a glance each particular figure
in a column of a hundred numbers. When to this is added the labor
of calculating the relation and aggregate values of the numbers,
the conclusion is inevitable that such powers are not given to our
objective senses, but must be inherent in the human soul, and beyond
the range of objective explanation or comprehension.

Musical prodigies furnish further illustrations of the principle
involved. Of these the most remarkable is the negro idiot, known
as Blind Tom. This person was not only blind from birth, but was
little above the brute creation in point of objective intelligence or
capacity to receive objective instruction. Yet his musical capacity
was prodigious. Almost in his infancy it was discovered that he could
reproduce on the piano any piece of music that he had ever heard. A
piece of music, however long or difficult, once heard, seemed to be
fixed indelibly in his memory, and usually could be reproduced with
a surprising degree of accuracy. His capacity for improvisation was
equally great, and a discordant note rarely, if ever, marred the
harmony of his measures.

These well known facts of Blind Tom’s history furnish complete
illustrations,–first of the perfection of subjective memory; and
second, of the inherent power of the subjective mind to grasp the
laws of harmony of sounds; and that, too, independently of objective

Music belongs to the realm of the subjective; it is a passion of the
human soul, and it may be safely affirmed that all really good music
is the direct product of the subjective mind. It is true that there is
much so-called music to be heard which is the product of the objective
intelligence. But no one can fail to recognize its origin, from its
hard, mechanical, soulless character and quality. It bears the same
relation to the product of the subjective mind that mere rhyme does
to the poetry of a Milton. Music is at once the legitimate offspring
of the subjective mind and one of the most potent means of inducing
the subjective condition. It is a well-known practice of so-called
“spiritual mediums” to have music at their séances, for the ostensible
purpose of securing the “harmonious conditions” necessary to insure a
successful performance. Their theory is that the music harmonizes the
audience, and that by a reflex action the medium is favorably affected.
It is probable that such would be the effect to a limited extent, but
the greatest effect is direct and positive upon the medium.

The East Indian fakirs invariably invoke the aid of music to enable
them to enter the subjective state when they are about to give an
exhibition of occult power. In fact, the power of music over the
subjective mind is practically unlimited. It speaks the universal
language of the soul, and is comprehended alike by prince and by
peasant. It is the most powerful auxiliary of love, of religion, and of
war. It nerves the soldier to deeds of heroism, and soothes his dying
moments. It inspires alike the devotee of pleasure and the worshipper
of God. But whilst it interprets every human emotion and embodies the
inward feelings of which all other arts can but exhibit the outward
effect, its laws are as fixed and immutable as the laws of mathematics.

The next subdivision or branch of the subject pertains to the faculty
of measuring the lapse of time. This power is inherent in the
subjective mind, and in that alone; the objective mind, _per se_,
does not possess it. The only means by which the objective mind can
measure time is by the exercise of the physical senses, either in the
observation of the motions of the heavenly bodies, or of some other
physical object or phenomenon which objective experience has shown to
be a safe criterion upon which to base an estimate.

The subjective mind, on the other hand, possesses an inherent power
in that direction, independent of objective aids or the exercise
of reason. It is possessed by man in common with many of the brute
creation. It is strikingly exhibited in dogs, horses, and other
domestic animals accustomed to regular hours of employment.

A friend of the writer once owned a large plantation in one of the
Southwestern States, upon which he worked a large number of mules.
They were regularly employed on week-days, but on Sundays they were
turned into a corral and allowed to rest. On regular work-days they
were tractable and easily handled; but if one was wanted for a Sunday
excursion it was with the greatest difficulty that he could be caught
or made to perform any labor whatever.

An English gentleman, well known to the writer, relates a curious
anecdote of a dog which was raised in his family. After the dog had
come to maturity, one of the sons married and set up an establishment
about three miles from the parental mansion. It was the habit of the
family to see that the dog was fed regularly, immediately after each
meal, with the scraps from the table. At the home mansion the Sunday
dinner-hour was the same as on week-days, but was just two hours
earlier than that adopted at the son’s establishment. This fact the
dog by some means became acquainted with, and he never failed to take
advantage of the information. Every Sunday he would wait patiently for
the home dinner; and having finished it, he would promptly take his
departure, and never failed to put in an appearance at the son’s house
on time for dinner, where he was sure to be welcomed and entertained as
an honored guest. On week-days the dinner-hour at the two houses was
the same, and consequently he never made a pilgrimage in search of an
extra meal on any day but Sunday.

A favorite mastiff in the family of the writer has taken upon himself
the regulation of the household affairs. He awakens the family in the
morning at a certain hour, and insists upon promptitude in rising. At
precisely twelve o’clock he notifies the family that it is time to feed
the horse, and will give no one any peace until his friend’s wants are
supplied. His own meal seems to be a secondary consideration. At three
o’clock he notifies his mistress that it is time to visit the kitchen
and give directions for preparing dinner. It is not because he expects
to be fed at that time, for he is never fed until the family have
dined, two hours later. At nine o’clock he rises from his rug on the
library floor, and insists upon a visit to the kitchen for a lunch. It
is rare that he varies five minutes from the regular hours above noted,
but is generally within a minute.

This power is exhibited in its perfection in hypnotic subjects and in
ordinary sleep. It is that faculty which enables one to awake at an
appointed hour in the night, when, before going to sleep, he has made
a firm resolution to do so. M. Jouffroy, one of the most celebrated
philosophers of France, in speaking of this subject says:–

“I have this power in perfection, but I notice that I lose it if
I depend on any one calling me. In this latter case my mind does
not take the trouble of reasoning the time or of listening to the
clock. But in the former it is necessary that it do so, otherwise
the phenomenon is inexplicable. Every one has made or can make this

M. Jouffroy is doubtless mistaken in supposing that the mind is
necessarily employed in watching the clock; for the experiment is just
as successful in the absence of any timepiece. Besides, the fact that
animals possess the faculty shows that it is an inherent attribute of
the subjective mind. It is the lapse of time that is noted by men as
well as by animals, and is wholly independent of artificial methods
or instruments for marking the divisions of time. Every one possesses
this faculty in a greater or less degree, and the subject need not,
therefore, be enlarged upon.

As before intimated, hypnotic subjects possess in a very remarkable
degree the faculty of noting the lapse of time. On this subject
Professor Bernheim[10] says:–

“If a somnambulist is made to promise during his sleep that he will
come back on such and such a day, at such and such an hour, he
will almost surely return on the day and at the hour, although he
has no remembrance of his promise when he wakes up. I made A say
that he would come back to me in thirteen days, at ten o’clock in
the morning. He remembered nothing when he waked. On the thirteenth
day, at ten o’clock in the morning, he appeared, having come three
kilometres from his house to the hospital. He had been working in
the foundries all night, went to bed at six in the morning, and
woke up at nine with the idea that he had to come to the hospital
to see me. He told me that he had had no such idea on the preceding
days, and did not know that he had to come to see me. It came into
his head just at the time when he ought to carry it out.”

It is also well known to all hypnotists that subjects in a hypnotic
sleep will awaken at any hour prescribed to them by the operator,
seldom varying more than five minutes from the time set, even when the
sleep is prolonged for hours. If the subject is commanded to sleep,
say, ten or fifteen minutes, he will generally awaken exactly on
time. This fact also is universally recognized by those familiar with
hypnotic phenomena, and the subject need not be further illustrated.

In concluding this chapter, it is impossible to refrain from indulging
in a few general observations regarding the conclusions derivable from
the peculiar characteristics of the subjective intelligence thus far
noted. We have seen that certain phenomena depend for their perfect
development upon objective education, and that certain other phenomena
are exhibited in perfection independent of objective education.
In other words, certain powers are inherent in the subjective
intelligence. These powers appear to pertain to the comprehension of
the laws of Nature. We have seen that, under certain conditions, the
subjective mind comprehends by intuition the laws of mathematics. It
comprehends the laws of harmony of sounds, independently of objective
education. By true artists the laws of the harmony of colors are also
perceived intuitively.[11] These facts have been again and again
demonstrated. It would seem, therefore, to be a just conclusion that
the subjective mind, untrammelled by its objective environment, will be
enabled to comprehend all the laws of Nature, to perceive, to know all
truth, independent of the slow, laborious process of induction.

We are so accustomed to boast of the “god-like reason” with which man
is endowed, that the proposition that the subjective mind–the soul–of
man is incapable of exercising that function, in what we regard as the
highest form of reasoning, seems, at first glance, to be a limitation
of the intellectual power of the soul, and inconsistent with what we
have been accustomed to regard as the highest attributes of human
intelligence. But a moment’s reflection will develop the fact that this
apparent limitation of intellectual power is, in reality, a god-like
attribute of mind. God himself cannot reason inductively. Inductive
reasoning presupposes an inquiry, a search after knowledge, an effort
to arrive at correct conclusions regarding something of which we are
ignorant. To suppose God to be an inquirer, a seeker after knowledge,
by finite processes of reasoning, is a conception of the Deity which
negatives his omniscience, and measures Infinite Intelligence by purely
finite standards. For our boasted “god-like reason” is of the earth,
earthy. It is the noblest attribute of the finite mind, it is true,
but it is essentially finite. It is the outgrowth of our objective
existence. It is our safest guide in the walks of earthly life. It
is our faithful monitor and guardian in our daily struggle with our
physical environment. It is our most reliable auxiliary in our efforts
to penetrate the secrets of Nature, and wrest from her the means of
subsistence. But its functions cease with the necessities which called
it into existence; for it will be no longer useful when the physical
form has perished, and the veil is lifted which hides from mortal eyes
that world where all truth is revealed. Then it is that the soul–the
subjective mind–will perform its normal functions, untrammelled by
the physical form which imprisons it and binds it to earth, and in its
native realm of truth, unimpeded by the laborious processes of finite
reasoning, it will imbibe all truth from its Eternal Source.