establishment of facts and inferences, and compress our wandering conjectures into very short and meagre hypotheses, by the aid of which we seek to forecast a goal as yet unexplored, so that we are, perhaps, too much afraid of that bolder employment of scientific data which in other circumstances may be justifiable. Your letter seems to me to intimate a certain suspicion that I am a subscriber to the paltry tirades of Vogt and Moleschott. Not in the least. I must also enter an energetic protest against your treating these two gentlemen as representatives of scientific research. Neither has up to the present shown by original and specialised investigation that he has acquired that respect for facts and that prudence in reaching conclusions which men learn in the school of physical research. A prudent investigator knows very well that the fact of his having penetrated a little way into the intricate process of nature gives him no more right, not a scintilla more, than any other man to pronounce dogmatically on the nature of the soul. To my mind, too, you are not right in designating the majority of prudent scientists as enemies of Philosophy. Indifferent the greater part undoubtedly are, a state of things for which the blame rests on the extravagant speculations of Hegel and Schelling, two writers who have, I grant you, been taken to represent all philosophy. . . ." 1 ܙܙ Thus wrote Helmholtz on March 4th 1857, ten years after the publication of his essay "On the Conservation of Force". On religious questions Helmholtz never made any open declaration. His biographer describes him as “in mind and conviction a religious man, in the noblest sense of the word, although not in the orthodox sense of membership of a Church" 2, and says that the famous 1 L. Königsberger, Hermann v. Helmholtz I, Braunschweig 1902, 291 f. 2 Ib. II (1903) 75. E. Dennert (Die Religion der Naturforscher, Berlin 1901, 34) says of Von Helmholtz: "Ich erfuhr aber scientist always regarded the philosophical views of his father Ferdinand Helmholtz "not only with pious interest, but also with the highest appreciation of their scientific value, and, as appears from later utterances, with hearty agreement" 1. Ferdinand Helmholtz was a follower of the younger Fichte, and a convinced theist and spiritualist 2. Mention may be made here also of the Physicist Krönig († 1879) "who has won for himself an honoured name in the field of research by his investigations into the Theory of Gases. Clausius cites him as his predecessor in this province, and corroborates his conclusions". He published in 1874 a book on "The existence of God and the happiness of man." He denies that through "blind chance, however long a period of time we assume, the atoms could by their own forces come together and form living cells. . . . Without the guidance of a purposive intelligence, organisms could never have come into existence"3. It is interesting to note e. g. what he has to say from the standpoint of the mathematical Theory of Probability, against those who find no difficulty in the hypothesis that in the course of endless time and after endless attempts the most complex formations may have come fortuitously into existence: "If every year for a million years, a million men were born, each of whom lived to the age of ten thousand years and every minute of his life made 20 throws with 30 dice, the mathematical probability is that amongst all these throws one of thirty aces would not have even once occurred." aus bester Quelle, dass er Gottesdienst, ja sogar das Abendmahl hin und wieder besuchte." 1 Königsberger, Hermann v. Helmholtz I 333. 2 J. R(einke?) writes about an utterance of Von Helmholtz concerning the petty view that we can clear up the fundamental questions of life by scientific investigation. Deutsche Rundschau LXXXI, Berlin 1894, 131. 3 Cf. J. Reinke, Die Welt als Tat3, Berlin 1903, 12-14. We here conclude our survey of the great masters to whom we owe the largest and most fruitful scientific conception of modern times. And although certain people are good enough to appeal to their authority in proof of the 'monistic' character of the 'Law of Substance', to whom are we to appeal for the deepest interpretation of their great discoveries, to the discoverers themselves, or to those who profess to be their disciples? II. MATHEMATICS. Mathematics is not itself a branch of Physical Science, but in many instances it is by means of Mathematics that our knowledge of nature is first raised to the status of genuine science. Astronomy and Physics are scientific precisely in so far as they deal with number and measure, in so far as they enter into alliance with Mathematics, and absorb its spirit and method. In a work like this, then, which is concerned with the scientific conception of life, and with the essential spirit of Natural Science, some attention must be accorded to number and measure. We must not fail to examine the attitude of the leaders of Mathematics towards Christianity and religious belief in general, and to enquire whether the temper of Mathematics is reconcilable with that of religion. To show how little we need evade the question we appeal to the most eminent authorities on the subject, the most recent writers on the History of Mathematics. "Like most other Mathematicians", says M. Cantor1, "Euler was deeply religious without any trace of bigotry. Allg. deutsche Biographie VI 427. He was in the habit of conducting the devotions of his family, and one of his few polemical works was a "Defence of Revelation against the Objections of the Freethinkers" the publication of which in Berlin in 1747 in the immediate neighbourhood of the Court of Frederick the Great, indicates a moral courage which lifted him far above the assaults of mere scoffers." Leonhard Euler (born at Basle in 1707, died at St. Petersburg in 1783) does not come within the period with which this book is concerned. But even in the nineteenth century the praise which Cantor bestows on "most great mathematicians" is justified by many illustrious examples. At the beginning of this century the leaders of this department were Gauss in Germany, and Cauchy in France. In the latter half of the century two of the highest places were occupied by Hermite in France, and Riemann in Germany. If we are able to show that the relations to Christianity of these four were the reverse of hostile, we shall have refuted those writers who condemn religious belief as a kind of mysticism which cannot co-exist with the habit of exact thought inculcated by mathematics. In the history of Astronomy the passage from the 18th to the 19th century is marked by an event of the highest importance, at once a great discovery and a great opportunity. On New Year's Night 1801, at Palermo, Piazzi discovered the first of what we now know to be a number of small planets between Mars and Jupiter. But before the observer had ascertained the positions of the planet necessary, by the methods of computation then practised, to determine accurately its path, it approached so near the sun that it was lost from sight in the sun's radiance. Thus the planet had no sooner been discovered than it was lost again, for there was no hope of locating it unless astronomers knew in what quarter of the heavens to search for it, and this could not be known without a knowledge of its path. At this juncture there came to the aid of Astronomy a young mathematician of only four and twenty: he brought a completely new method by which, from the meagre observations of Piazzi, the path of the vanished planet could be deduced. In the spot indicated by him Ceres was re-discovered by Olbers on Jan. 1st 1802. The youthful Scientist, who thus leaped into a European reputation, was Karl Frederick Gauss, one of the foremost mathematicians of all time. It sounds incredible, but it is a well established fact that when a child of three in the workshop of his father, who was a simple artisan, he was able to detect any mistake made in the reckoning of accounts. When at nine years of age he was sent to school, the teacher of Arithmetic set as the first exercise to the class the addition of a long row of figures, each successive line of which exceeded the preceding one by a constant sum. If the first line of such a row be added to the last, the second to the second-last, and so on, the sum will always be the same; and there is consequently no need to worry oneself with a tedious addition, since the whole can be reduced to a simple exercise in multiplication. Young Gauss perceived this relation at the first glance, and while his classfellows added and added and in the end succeeded for the most part in adding wrongly, he wrote the answer on his slate and waited patiently for the termination of the affair.... This performance, and similar tokens of extraordinary ability decided his future |