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.

"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 pi 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.