Three Sub-classes of Mental Phenomena. - Mathematical Prodigies. Musical Prodigies. - Measurement of Time. - Distinction between Results of Objective Education and Intuitive Perception. Zerah Colburn, the Mathematical Prodigy. - The Lightning Calculator. Blind Tom, the Musical Prodigy. - The Origin and Uses of Music. - East Indian Fakirs. - Measurement of Time. The Power possessed by Animals. Illustrative Incidents. Hypnotic Subjects. - Jouffroy's Testimony. - Bernheim's Views. - Practical Observations. - The Normal Functions of Objective Intelligence. The Limitations of Subjective Intelligence pertain to its Earthly State only. Its Kinship to God demonstrated by its Limitations. - Omniscience cannot reason inductively. - Induction is Inquiry. - Perception the Attribute of Omniscience. Conclusions regarding the Power of the Soul.

HERE are three other sub-classes of subjective mental

THERE

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 pro

duced 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, viz., 5 X 34,279, 7 × 24,485, 59 X 2,905, 83 X 2,065, 35 X 4,897, 295 X 581, and 413 X 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