Two religious works which Gauss read frequently were Braubach’s Seelenlehre (Giessen, 1843) and Süssmilch’s Göttliche Ordnung gerettet (1756); he also devoted considerable time to the New Testament in the original Greek. On November 11, 1835, Gauss wrote to Olbers that he had had a recent letter from his son Eugene, who at the time was attached to Company F of the First Regiment, U.S. Infantry, at Fort Crawford, Minnesota. During part of that time he performed the duties of librarian to the post. Captain S. Loomis, the commanding officer, wrote Gauss about the exemplary conduct of his son and went on to testify that in a religious meeting Eugene had publicly declared his decision “henceforth to serve God.” Loomis testified to Eugene’s “conscientious behavior not only as a soldier of the Government of the U.S, but also as a soldier and a follower of Our Lord and Saviour Jesus Christ.” Eugene wanted to enter a theological seminary and prepare to be a missionary. Actually he never carried out this wish, but he remained very pious the rest of his life. In the same letter to Olbers Gauss commented thus on Eugene’s attitude: “Even though much error and hypocrisy may often be mixed in such pietistic tendencies, nevertheless I recognize with all my heart the business of a missionary as a highly honorable one in so far as it leads to civilization the still semisavage part of earth’s inhabitants. May my son try it for several years.”
Although a serene man of science. Gauss attained such objectivity and calmness not without struggle. There was a streak of the mystic and Romantic in him, which sometimes penetrated the hard outer shell of logical reserve, Newton, Descartes, Pascal, Gauss, Helmholtz, and certain others were “pious,” but their faith varied in degree. In his savage attack on Gauss (1877), Eugen Dühring accused him of a narrowness in general thinking that originated in religious superstition. Today no responsible person accepts such a charge. Dühring launched out against Justus von Liebig and Clausius because they had dared to defend (with “brazen tongue”) Gauss and Riemann against his assault.
On September 3, 1805, Gauss wrote thus to Olbers: “Whomsoever the comely goddess of truth does not always shun, he who has a bride, as I have, and a friend, as you are, can overlook trivialities.”
Some writers have stated that Gauss’ life moved along like a majestic river and that he was so favored by nature as to have satisfaction from his unusual genius. But such was not the case, even though he did manifest great kindness and rectitude of character. Such a view is contradicted by the following passage in a letter to Bolyai, dated April 20, 1848:
It is true, my life is adorned with much that the world considers worthy of envy. But believe me, dear Bolyai, the austere sides of life, at least of mine, which move through it like a red thread, and which one faces more and more defenselessly in old age, are not balanced to the hundredth part by the pleasurable. I will gladly admit that the same fates which have been so hard for me to bear, and still are, would have been much easier for many another person, but the mental constitution belongs to our ego, which the creator of our existence has given us, and we can change little in it. On the other hand I find that this consciousness of the nothingness of life, which in any case the greater part of humanity must express on approaching the goal, offers me the strongest security for the following of a more beautiful metamorphosis.
On March 14, 1824, Gauss wrote Bessel that “all the measurements in the world do not balance one theorem by which the science of eternal truths is actually advanced.”
At the time of his first wife’s death in 1809 Gauss discussed his feelings on fate in a letter to Schumacher: “Of all the reasons for consolation, which I have tried, none has been stronger for me than that if fate had laid before me the alternative of choosing my present misfortune or dying myself and leaving the deceased [his first wife] disconsolate, I would have had to approve what fate has now decided.”
Again he expressed himself to Schumacher on September 24, 1831, concerning the death of his second wife:
A week ago the mortal remains, which were a main source of the indescribable pains of the poor sufferer [his second wife], were given back to the earth, and I still cannot think of these pains for one moment without the most intense shock. I could not write to you sooner. In time the promise of reason will finally replace the feeling, namely, that she, like all others, is to be congratulated on having departed from a scene where joys are fleeting and vain, where suffering, failures, and painful disappointments are the basic color. How much I would long to depart from it if so many bonds did not fetter me.
His mood was much more cheerful in a letter to Schumacher on February 9, 1823: “Dark are the paths which a higher hand allows us to traverse here . . . let us hold fast to the faith that a finer, more sublime solution of the enigmas of earthly life will be present, will become part of us.”
At the time of negotiations to get him to the University of Berlin, Gauss expressed a similar thought in a letter to Bessel on April 25, 1825: “In such apparent accidents which finally produce such a decisive influence on one’s whole life, one is inclined to recognize the tools of a higher hand. The great enigma of life never becomes clear to us here below.”
At the time Schumacher’s mother died. Gauss wrote him on November 10, 1822: “I do not attempt to console you, in such events there is no consolation except the strongest conviction that we are sitting here in ultima and hereafter are promoted in turn to a higher school.”
In another letter to Schumacher dated September 1, 1846, he expressed a similar thought: “It is the sad lot of old age gradually to see depart from us so much that was near and dear to us and to see ourselves more and more isolated, and there is no consolation in this, except the prospect of a higher world order which will some day balance everything.”
Gauss was not a professional philosopher, and although he attempted to apply the rigid standards of mathematics to philosophy for his own satisfaction, he was very reluctant to express himself in this field. He possessed and studied carefully the works of Hume, Francis Bacon, Kant, Christian Wolff, Fries, Descartes, John Locke, and Malebranche. On one occasion he criticized some of Schelling’s work. But even among the greatest philosophers, occasionally in Kant, he found certain confusion in concepts and definitions. His special target was always Hegel, and in this connection Schumacher once wrote him: “Among Noah’s sons was one who covered the shame of his father, but the Hegelians are still tearing away the cloak which time and oblivion had sympathetically thrown over the shame of their Master.”
To this Gauss replied that he was uncertain whether the comparison with Noah was entirely suitable:
Holy Writ only tells that he was circumcised once, while he otherwise passes for a sensible man to whom we (since abusus non tollit usum) may be thankful for the fact that he saved the sprigs of the vine from the flood, even though he would have done better to turn over many other things to the flood. Hegel’s insania in the dissertation under question seems to be wisdom compared with his later ones.
In 1844 Schumacher called the attention of Gauss to a definition in one of the works of Christian Wolff which states that the center of gravity is that point through which the body is divided into two equally heavy parts.126
Immediately he got a reply from Gauss, dated November 1, 1844:
I am almost amazed that you consider a professional philosopher capable of no confusion in concepts and definitions. Such things are nowhere more at home than among philosophers who are not mathematicians, and Wolff was no mathematician, even though he made cheap compendiums. Look around among the philosophers of today, among Schelling, Hegel, Nees von Esenbeck, and their like; doesn’t your hair stand on end at their definitions? Read in the history of ancient philosophy what kinds of definitions the men of that day, Plato and others, gave (I except Aristotle). But even in Kant it is often not much better; in my opinion his distinction between analytic and synthetic theorems is such a one that either peters out in a triviality or is false.
He then proceeded to give a correct definition of the center of
gravity. In a letter to Moritz Wilhelm Drobisch dated August 14, 1834, Gauss wrote that “most so-called professional philosophers, when they venture into mathematics, sell us only aegri somnia (sick man’s dreams) for philosophy.” Most of Gauss’ references to philosophers refer to Kant’s theory of space.
On May 11, 1841, Gauss wrote to Jacob Friedrich Fries and thanked him for the copy of Geschichte der Philosophie which the author had sent him. In the letter he made this remark:
I have always had great love for philosophical speculation, and rejoice so much more to have in you a reliable leader in the study of the fate of the science from the most ancient to the most modern times, since in my own reading of the writings of many philosophers I have not always found the desired satisfaction. Namely the writings of several frequently mentioned (perhaps better, so-called) philosophers, who have appeared since Kant, reminded me sometimes of the sieve of the goat milker,127 or, instead of the ancient, to use a modern image, they reminded me of Münchhausen’s pigtail by which he pulled himself out of the water. The dilettante would not dare to give such a confession before the master if it had not occurred to him that the latter was almost of the same opinion about those merits. I have often regretted that I don’t live in the same town with you, in order to be able to gain pleasure as well as instruction from conversation with you on philosophical subjects.
Many years previously Gauss had thanked Fries for a copy of his Mathematische Naturlehre (Heidelberg, 1822). Concerning this book M. J. Schleiden, professor of botany in the University of Jena, told this story:
When I was studying in Göttingen (1830–1834), one of the more advanced students came to Gauss, saw on his desk the work mentioned, and said: “But Professor, do you devote yourself to that confused philosophical stuff?” Whereupon Gauss turned very seriously to his questioner with the words: “Young man, if in your three-year course you get to the point that you can appreciate and understand this book, then you have used your time far better than most of your fellow students.”
Schleiden told the philosopher Rudolf Eucken that Gauss read Kant’s Critique of Pure Reason five times. The fifth time he is reported to have said: “Now it’s dawning on me.” A young scholar (whose name is now unknown) had made slighting remarks to Gauss about Kant, and this led Gauss to the remark that he had devoted great effort to the Critique of Pure Reason, and he believed he was just gradually getting to understand it fully. Incidentally, Schleiden was a follower of Kant and Fries. Apparently the views of Gauss and Kant on the distinction between right and left were not so contradictory as might appear at first glance.
Gauss was interested in the manner in which Kant founded his concept of space and pioneered in the field of non-Euclidean geometry. His work led to n-dimensional space, and the whole subject has been revolutionized in our time by the work of Einstein. Gauss’ basic concept of the essence of space is contained only in separate, scattered utterances which are collected in Volume VIII of his Collected Works. It all goes back to his work in non-Euclidean geometry, as we saw in Chapter XV. In Kant the basic concept is that of absolute space, namely, that absolute space is independent of the existence of all matter and itself has its own reality as the first reason of the possibility of its composition. Reality here means empirical reality and not merely transcendental ideality ascribed to space. Kant mentions the fact that two bodies which are exactly alike, do not therefore have to be congruent, that is, through a mere movement they cannot be necessarily moved over into one another. Of such kind is a body and its reflection, or the left and right hand.
Gauss disagreed with Kant, as shown in the following passage of a letter to Schumacher on February 8, 1846:
The distinction between right and left cannot be defined, but only shown, so that it is thereby a case similar to sweet and bitter. Omne simile claudicat, but the latter is valid only for beings which have organs of taste, while the former is valid for minds to whom the material world is perceptible, two such minds, however, cannot make themselves directly understood concerning right and left unless one and the same individual thing forms a bridge between them.
In a letter to Gerling on June 23, 1846, Gauss repeats the same thought:
One cannot reduce to concepts the distinction between two systems of three straight lines each (directed lines, of which the one system points forward, upward to the right, the other forward, upward to the left), but one can only demonstrate by holding to actually present spatial things. Two minds cannot reach agreement about it unless their views connect up with one and the same system present in the real world.
Gauss and Kant thus differed in the manner of founding a theory of space, but there is scarcely any difference in their views about space. Gauss did not deny the a priori character of space. Kant once predicted the geometry of n-dimensions and was thus in agreement with Gauss on this point also. Gauss denied that space is merely the form of our external perception, but he did not want to maintain the existence of a real space independent of our perception. Since Kant one can regard space neither as a thing nor as a property of things, but as a kind of presentation of actually present things. Gauss was undoubtedly right when he said that the distinction between right and left can be transmitted only from one person to another. Physicians say that it is frequently impossible to teach this distinction to the feebleminded.
When people read the lives of men like Goethe, Schiller, Humboldt, and even Kant, those of ordinary intelligence may form some idea of what existence meant for those great men, and what lessons their lives convey to humanity. What has been presented in this chapter gives an answer to the inquiry embodied in the following quotation from Gauss’ Göttingen colleague, the philosopher Lotze, in his Microcosmus:
If the object of all human investigation were but to produce in cognition a reflection of the world as it exists, of what value would be all its labor and pains, which could result only in vain repetition, in an imitation within the soul of that which exists without it? What significance could there be in this barren rehearsal—what should oblige thinking minds to be mere mirrors of that which does not think, unless the discovery of truth were in all cases likewise the production of some good, valuable enough to justify the pains expended in attaining it? The individual, ensnared by that division of intellectual labor that inevitably results from the widening compass of knowledge, may at times forget the connection of his narrow sphere of work with the great ends of human life; it may at times seem to him as though the furtherance of knowledge for the sake of knowledge were an intelligible and worthy aim of human effort. But all his endeavors have in the last resort but this meaning, that they, in connection with those of countless others, should combine to trace an image of the world from which we may learn what we have to reverence as the true significance of existence, that we have to do and what to hope.
XXIII
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Sunset and Eventide: Renunciation
Almost the only physical recreation which Gauss permitted himself in his last years was a daily walk to the literary museum, several blocks away from the observatory, where he spent most of the time between eleven and one o’clock. During the last twenty years of his life he took little part in social activity and during the last ten scarcely any. At the literary museum he scanned rapidly the various scientific, literary, and political periodicals, noting on paper or storing in his remarkable memory little interesting titbits of new information. He seemed to need more rest, and his friends noted that at home he relaxed more than formerly by engaging in light reading. His correspondence with friends and colleagues in all parts of the world claimed a considerable portion of his time. Up until the last he corresponded regularly with Alexander von Humboldt. Death interrupted his correspondence with Olbers in 1840, with Bessel in 1846, and with Schumacher in 1850. With Schumacher he corresponded weekly.
In the winters of 1852 and 1853 Gauss complained repeatedly about his health. Throughout most of his life he had been very healthy and had enjoyed a st
rong constitution. He suffered from congestion due to phlegm and mucus, which he considered his principal complaint. As a consequence of this condition he had become accustomed to get up at 3 a.m. and to drink Seltzer water and warm milk. It was a simple remedy but seemed to relieve him. Forty years earlier Olbers had given him two prescriptions, but all use of medicine had been otherwise foreign to him. Gauss had little confidence in medical science and for a long time could not make up his mind to call in a doctor.
Finally after the repeated persuasion of his family and closest friends he decided to seek the aid of his university colleague and friend Dr. Wilhelm Baum (1799–1883), professor of surgery and director of the surgical clinic from 1849 until his death. Baum made his first professional call on January 21, 1854, and after a thorough examination continued through several days he gave enlargement of the heart as his diagnosis. From the very beginning he held out little hope of recovery or survival for very long. The condition, which became more pronounced in advanced age, seemed to be an old one, for Olbers had recognized or supposed it years before and had advised Gauss on certain precautionary measures. The application of practical remedies and the coming of spring had a favorable effect on Gauss’ condition, so that in the course of the spring and summer of 1854 he was able to put in his regular appearance at the literary museum, as well as to take little walks in the neighborhood.
Carl Friedrich Gauss, Titan of Science_A Study of His Life and Work Page 36