THE LATE PROFESSOR DE MORGAN.
ON Thursday last, at Mensal Green, was buried a man of very rare intellectual power and force of character,— one of those who mould the mind and more or less profoundly strike the imagination of almost all submitted to their influence. The late Professor De Morgan was an original and very learned mathematician, but merely as a mathematician he may have had equals, and for anything the present writer knows to the contrary, even superiors, among the English mathematicians of his day. He was not the Senior Wrangler of his year, not we believe, higher than fourth wrangler ; but that speaks little as to his real rank as mathematician, for it is usually the neatest and swiftest, not the most powerful minds which carry off the highest honours in com- petitive examinations. And Professor De Morgan's mind was hardly either neat or swift. The grasp and clearness and force of his intellect were far more remarkable than either its dexterity or rapidity. The late Sir William Hamilton of Edinburgh, who had a sharp con- troversy with him on logical matters and hardly understood his opponent, once described him as " profound in mathematics, curious in logic, and wholly deficient in architectonic power,"—a description in which the only element of real truth was aimed at that somewhat awkward arrangement of his materials by which Professor De Morgan not unfrequently disguised from the world the massiveness, the precision, and the depth of his own powers. Great architectonic power he unquestionably had, though not artistic power as a mathematical architect,—for the truth is, that he buttressed the structures of his mathemati- cal arches so strongly that the effect was sometimes clumsy, though the bridge once raised was never shaken in the mind of his pupils. There was a touch of unwieldiness about his presentation of intellectual problems, especially in his books, and this unwieldiness of manner rendered them less popular than works containing less than half their learning and much less than half their thinking power. The publication of his " Arithmetic," a book which has not unnaturally been much more useful to masters than to scholars, began a new era in the history of elementary arithmetical teaching in England,—devoting, as all his books did, far more space and labour to the logi- cal processes by which the various rules are demonstrated than to the more technical parts of the subject, though of these too in their proper place Professor De Morgan was never unmindful, spending the greatest care on teaching the art of rapid and accurate computation, no less than on the true science of number. His exposition of the theory of limits from the very earliest stage in which it entered into algebraical conceptions was so masterly and exhaustive, that it haunted his pupils in the logical tangle of their later lives, and helped many a man through the puzzle of Dr. Manses conundrum-making as to " the Infinite" in his " Limits of Religious Thought." Indeed, Professor De Morgan really managed to make his pupils realize that they knew nothing at all about either zero or infinity, except as short phrases for what is respectively smaller or larger than any assignable quantity, however small or Urge; and that to treat either zero or infinity as magnitudes, even to the extent of supposing that all zeros are equal, and all infinities equal, is a delusion utterly fatal to the science of mathematical inferences. No pupil of Professor De Morgan's who ever fairly grasped the logical processes of his Double Algebra or Differential and Integral Calculus, and still less, perhaps, who had followed him through his searching and often humorous analysis of the meta- physical basis of the "Theory of Probabilities," ever yet failed to find the substance of his lectures recurring constantly and most usefully to mind in the course of the intellectual controversies of later years. Mr. De Morgan was no mere teacher of mathe- matics. His classes were training-schools in intellectual self- knowledge, logical discipline, and the theory of evidence, such as mathematical classes very rarely were before ; indeed compara- tively few even of those who have had the advantage of his books and his training have succeeded in reaching anything like the same standard of robust logical efficiency since. For giving clearness, subtlety, and strength to the reasoning faculties, no discipline like that of Professor De Morgan's classes has ever been surpassed in any University. Of Mr. De Morgan's absolute eminence as a mathematician,—of the additions he has made to mathematical knowledge,—the present writer is not competent to speak. Of course, he stood very high. We suspect, however, that his greatness would be estimated by the highest English mathe- maticians to consist more in his contributions to the philosophy of mathematics, than in the successful manipulation of its instruments of calculation. In other words, we suspect that he would be adjudged to have done more in clearing up and testing the logical methods of mathematical reasoning, than in applying its machinery to new departments of research.
But great as Professor De Morgan was as a mathematician and a logician,—his ' Formal Logic,' in spite of Sir William Hamilton's attack, holds its ground as a great addition to logical science,— the originality of his character was at least as remarkable as the originality of his intellect. He was a man almost quaintly at- tached to all his professional habits, so punctual and so uniform in his doings that his return from his college classes served as the best of time-pieces to observant stu- dents. Often, like Dr. Johnson, he might ba seen in a brown study ticking off every five or six railings with conscientious punctuality, never missing the right multiple, as he passed along the railed enclosure of University College. He was so early at his work of correcting the students' exercises before his nine o'clock class that, according to popular rumour, no man had ever yet succeeded in reaching the College at an hour when the Professor's chair was empty, and it was sometimes wildly asserted that he came overnight. The tradition, how far true we do not know, was that he disliked the vacation, and felt lost without his usual duties. Cer- tainly be never willingly gave a holiday, and we cannot remember that for many years together his health ever compelled him to give one.
Yet in spite of this deep instinct of habit, in Professor De Morgan, as in Dr. Johnson, originality of character was as notable as his attachment to definite grooves of action. He was incapable of being anything but himself, and be had not a self which society could modify. His intellectual life was lonely, though his affec- tions were deep and his regard for old friends extremely tenacious. To those who were not of his own standing in life, to his pupils, he was always benignant, but on extra- mathematical subjects a little constrained. There was something sudden about his humour, which,—like everything about him, his learning, his sagacity, his common-sense, — was huge, but sometimes puzzling to those who did not know his ways. His " Budget of Paradoxes," published in 1863-5, and again in 1866 in the Athenaeum, was curiously characteristic of his wonderful antiquarian learning, his great sagacity, his shrewdness of reflec- tion on human ways, and that turn for the broadly ludicrous which gave him so strong an appreciation of the humour of Dickens. The humorous turns of his thought,—the great gambols of his massive mind,—were often so abrupt as to betray that Mr. De Morgan's humour was the product of lonely mental operations, for it had none of that easy, gradual shading off into common conversation which marks the humour of social life. The following, which occurs in one of his notes on the paradox of the celebrated " sympathetic " powder, falsely, he thinks, attributed to Sir Kenelm Digby,—the powder supposed to cure by being put on the sword which inflicted the wound, instead of on the wound,— is a fair specimen of the humour of this " Budget " :—" The sympathetic powder was that which cared by anointing the weapon with its salve instead of the wound. I have long been convinced that it was efficacious. The directions were to keep the
wound clean and cool, and to take care of diet, rubbing the salve on the knife or sword. If we remember the dreadful notions upon drugs which prevailed, both as to quantity and quality, we shall readily see that any way of not dressing the wound would have been useful. If the physicians had taken the hint, had been care- ful of diet, &c., and had poured the little barrels of medicine down the throat of a practicable doll, they would have had their magical cures as well as the surgeons. Matters are much improved now ; the quantity of medicine given, even by orthodox physicians, would have been called infinitesimal by their professional ances- tors. Accordingly, the College of Physicians has a right to abandon its motto, which is ' Ars Tonga, vita brevis,' mean- ing ' Practice is long, so life is short." Or take this, as indicating the kind of sagacity for which his life-long study of mathematical measure had made Mr. De Morgan remark- able,—the reconstruction of common maxims so as to come mach nearer to the true drift at which their popular form only vaguely pointed. He was commenting on the common assertion that "a little knowledge is a dangerous thing," which he denied, but substituted for it, " A person with small knowledge is in danger of trying to make his little do the work of more ; but a person without any is in danger of making his no knowledge do the work of sonte," of which he produced many most amusing instances from his personal knowledge of paradoxmongers. Yet even to these quacks,—for quacks many, perhaps most, of them were,—Mr. De Morgan was scrupulously fair. His moral weights and measures were as accurate as his intellectual. He bore witness, evi- dently with pleasure, in describing the intellectual crazes with which men were afflicted who had no knowledge or little know- ledge on the subjects on which they professed to be discoverers, that they were not mercenary ; " they are very earnest people, and their purpose is bond fide in the dissemination of their paradoxes. A great many, the mass, indeed, are illiterate,_ and a great many waste their means and are in, or approaching,. penury. But I -must say that never in any one instance has the quadrature of the circle, or the like, been made a pretext for begging,—even to be asked to purchase a book is of rare occur- rence." Few who knew Professor De Morgan would have called him exactly an imaginative man ; and perhaps his imaginative gifts were principally of that kind which are useful to realize vigorously—to score deep on the mind—the precise intellectual conditions of any case under consideration ; but this sort of ima- gination he had in a high degree, and that, too, not unfrequently in matters half intellectual, half moral. In his note on that grim religious paradox of Pascal's, addressed to sceptics, as to the wisdom of being a believer lest, if God exist, you should be punished for not believing, while if the sceptics are right and Christians wrong, there will be no punishment for having believed falsely,—or as Pascal expressed it, " not to wager that God exists, is in fact to wager that he does not exist,"—Mr. De Morgan translated the notion at the bottom of this argument that you are bound to hedge carefully as to your spiritual prospects, into language of quite Dantesque force of imagination as well as mathematical precision :—" Leaving Pascal's argument," he says, " to make its way with a person who, being a sceptic, is yet positive that the issue is salvation or perdition, if a God there be,—for the case as put by Pascal requires this,—I shall merely observe that a person who elects to believe in God, as the best chance of gain, is not one who, according to Pascal's creed, or any other worth naming, will really secure that gain. I wonder whether Pascal's curious ima- gination ever presented to him in sleep his convert, in the future state, shaken out of a red-hot dice-box upon a red-hot hazard- table, as perhaps he might have been, if Dante had been the later of the two." A judicious selection from Professor De Morgan's " Budget of Paradoxes " would be a very characteristic memorial of him, as well as a book full of curious learning, of quaint sagacity, and of a grotesque humour.
Perhaps even in consequence of his powerful grasp of the prin- ciples of exact measure and of the difficulties in applying those principles, Mr. De Morgan was never one of those in- credulous mathematicians who depreciate the force of evi- dence which they cannot accurately weigh. He was fond of asking how any one who really believes that every little particle in the earth is tugging away at every little particle in fixed stars so distant from the earth that their light takes thousands of years to travel here, and vice versa, can suppose anything whatever not in contradiction with the world's best-sifted knowledge to be really incredible. And he was sometimes charged, not very justly we believe, with being even credulous, because he gave a certain amount of extremely reserved and very carefully limited credence to certain abnormal phenomena, which, whether true or false, he believed he had tested carefully and with the professional acuteness of a mind always on the alert against both fraud and illusion. He may, no doubt, have missed some necessary intellec- tual safeguard in testing these phenomena, and have given the cautiously limited credence he did give, erroneously. But no one can read his own account of the guarantees against deception which he either really took or fully believed that he had taken, without being struck by the curious subtlety and sagacity with which he had endeavoured to provide against deception.
On all matters of faith, Professor De Morgan was quaintly reti- cent, acting on what seems to us the rather too elaborate and somewhat old-world conception that as professions of faith con- duce unfairly to worldly success, he would rather be accounted a sceptic falsely and lose by it, than be known as a Christian and gain by it. Everyone knows how strong a line he took when he believed, as we believed, that University College had deviated from its professed principle of not taking into account religious creed and position at all, in refusing to elect to the Professorship of Mental and Moral Philosophy one of the greatest, if not, as we hold, the greatest, of English metaphysicians, who happened to be also known as an eminent preacher among the Unitarians,—a connection deemed undesirable by some of the members of the Council. It was on this occasion that Professor De Morgan resigned the professorship he had held with so much distinction for solong a period, though without, as we believe, breaking with or alienating a single one of his old friends. His dread lest religious belief should be allowed either to benefit his own worldly prospects or to injure any other man's, was intense with the intensity of a different genera- tion from ours; and a quaint and touching passage in his will shows that he resolutely concealed his own faith from what seems to us the almost morbid fear of its conducing to his advancement. "I commit," he says, " my future destiny with hope derived from experience to Almighty God, who has been and will be my guide and my support ; to God the Father of our Lord Jesus Christ, of whom I believe in my heart that God has raised him from the dead, and whom I have not confessed with my mouth in the sense usually attached to these words, because such confession has been in my time the only way up in the world." What a singular and yet genuine burst of piety is here. And real though very reticent piety was deep in his character. One who has a right to speak, says of him, " His trust in God in the smallest details, as well as in the most important matters of his life, was living and unvarying. Three days before he was taken, I said to him, ' I hope you will not go yet.' He answered very quietly and cheer- fully, ' Leave it all in God's hands.'" It was not true that he had ever had a paralytic stroke. His mind retained its full power to the last moment.
And so passed away, in the simplicity of perfect faith, one of the greatest mathematicians of the day,—probably, in relation to the investigation of the reasoning processes of mathematics and the thorough analysis of their intellectual weight, the very greatest of them all,—into a world where it is not very easy for us to con- ceive how all this great apparatus for attaining accurate know- ledge, this wonderful array of the balustrades by which we hold in climbing up towards truth, is to be turned to full account. This master of the great intellectual processes, this reasoner who knew how to cheat the weaknesses of human reason wherever they can be cheated, and reap all the benefit of an intellectual machinery stronger in many senses than the intellects which use it, is gone where we often rashly suppose that Method is swallowed up in Knowledge. But if it be true, as Plato held, that God is the great geometer,—and every century seems to make it less possible to deny it,—it may be that the knowledge of method will prove to be itself knowledge, and that the mind which held the key to so many theorems, and to which all the Calculuses—of Generating Functions, of Finite Differences, of Variations, — were almost as familiar as the multiplication-table, will find that it holds also the key to many of the generating functions, differences, and variations of creation,—to the architecture of the universe and the economy of thought,—in a very much larger sense than any of which we have as yet any clear apprehensions.
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