When Bordas-Desmoulins, one of the first of our learned thinkers to study comparative science, said: “Without mathematics we cannot plumb the depths of philosophy; without philosophy we cannot penetrate mathematics; without the two we can reach the foundation of nothing,” did he see that this truth is so great as to be all embracing?
We see theologians walking steadily in the footsteps of those who study comparative science with conviction. Father Gratry contends that without it it is impossible to know God, man, and nature. Matter cannot be conceived without spirit, nor spirit apart from matter. Whilst a human being is in the embryonic stage, the soul, the principle of life, is occupied in forming the body, destined to cover it during its earthly existence. The moment arrives when this body is sufficiently prepared to appear in the light of day; it contains two nervous centres, the one supplying the vegetative life, the other the animal; they are distinct though not separated, and the soul still continues its work on the body, whether it sleeps or whether it wakes; but during sleep, whilst man’s will is torpid, the soul supplies by rhythmic movements of the nerves, the requisite matter for the reparation of the losses sustained during the waking periods.
This intimate union of mind and matter has been rejected by certain great philosophers. Descartes, for instance, completely separated the immaterial substance possessed of the property of thinking from the material body. Apparently we are of his way of thinking since we always speak of our soul as of one thing and our body as of another; this is to make two truths out of one and the same truth. But it is better to look upon it as one truth as Aristotle did formerly. At a later date certain doctors of the Church became of the same opinion, and at present Christian theologians, who are also thinkers, hold the same view.
A fresh science is now in process of development. It connects psychical phenomena, such as sensation, thought, and action, with that which can be weighed and measured. This science bears several more or less characteristic names; in order to keep to generalities I will call it the new psychology; it is taught in Germany, England, Paris, and Russia, and perhaps elsewhere. There is only one way of dealing rightly with so vast a science, it should be treated in its entirety; but as I am anxious only to make known some of its more recent discoveries, I will content myself by doing this briefly and with many omissions.
Kant had as his disciple the physiologist J. Müller, who applied the method of his master to the study of sensations; and Helmholtz was trained by J. Müller.
At one time, rather more than fifty years ago, the germs of life were considered to be an exception on the terrestrial globe; but Helmholtz discovered them even in rocky masses; and he proved to Liebig that putrefaction was not a simple chemical reaction, but was due to the action of a living organism. M. Pasteur was one of the first to profit by this lesson.
Each definite science has its own special sphere in which it is occupied only with itself; Helmholtz, a physician and musician, worked entirely in connection with his own science only; without reference to the conclusion that comparative science might draw from his labours, he gave himself up to the study of the rapidity of the transmission of nervous impressions, and dogmatically laid down his thesis in his book The Physiological Theory of Music, which is perhaps the most important of his works; at least it is the one of which I have made the most use.
In nature we never hear simple sounds; nothing but a fusion of noises reaches us. Helmholtz, however, succeeded in distinguishing a fundamental sound in a mass of others; but it is quickly amalgamated with two or three other sounds which are higher and feebler than itself, as distant echoes. Helmholtz became convinced that music is composed of single sounds accompanied by others of a decreasing intensity, and he demonstrated by calculation that the number of vibrations of these secondary sounds called harmonics are greater than those of the fundamental sounds; and the differences of the grouping of harmonic sounds determines the difference of timbre. In this way Helmholtz discovered the cause of musical timbre, and was able to explain the reason, hitherto unknown, of the sound of a flute differing from that of a hautbois, or of a woman’s voice from that of a man’s.