Matho

“ Matho had been greeted with great shouting when he had come back bearing the veil of the goddess; even those who were not of the Chanaanitish religion were made by their vague enthusiasm to feel the arrival of a genius. As to seizing the zaïmph, no one thought of it, for the mysterious manner in which he had acquired it was sufficient in the minds of the Barbarians to justify its possession; such were the thoughts of the soldiers of the African race. The others, whose hatred was not of such long standing, did not know how to make up their minds. ”

“ Matho was standing behind the balustrades. With the zaïmph which was wrapped about him, he looked like a sidereal god surrounded by the firmament. The slaves were going to fall upon him, but she stopped them:
“Touch it not! It is the mantle of the goddess!”
She had drawn back into a corner; but she took a step towards him, and stretched forth her naked arm:
“A curse upon you, you who have plundered Tanith! Hatred, vengeance, massacre, and grief! May Gurzil, god of battles, rend you! may Mastiman, god of the dead, stifle you! and may the Other—he who may not be named—burn you!” ”

“ Matho had at first refrained from fighting, the better to command the Barbarians all at once. He had been seen along the gulf with the Mercenaries, near the lagoon with the Numidians, and on the shores of the lake among the Negroes, and from the back part of the plain he urged forward masses of soldiers who came ceaselessly against the ramparts. ”

“ Matho shouted a command and all the shields sank upon the helmets; he leaped upon them in order to catch hold somewhere so as to re-enter Carthage; and, flourishing his terrible axe, ran over the shields, which resembled waves of bronze, like a marine god, with brandished trident, over his billows.
However, a man in a white robe was walking along the edge of the rampart, impassible, and indifferent to the death which surrounded him. Sometimes he would spread out his right hand above his eyes in order to find out some one. Matho happened to pass beneath him. ”

“ The Barbarians constantly expected to see Matho appear,—and from discouragement, from languor, and from the obstinacy of sick men who object to change their situation, they would not leave the mountain ”

“ He had so convinced and triumphant an air that Matho was surprised from his torpor, and felt himself carried away by it. These words, coming when his distress was at its height, drove his despair to vengeance, and pointed to food for his wrath. He bounded upon one of the camels that were among the baggage, snatched up its halter, and with the long rope, struck the stragglers with all his might, running right and left alternately, in the rear of the army, like a dog driving a flock.
At this thundering voice the lines of men closed up; even the lame hurried their steps ”

“ The trampled soil was hidden beneath splashes of red. The elephants poised their bleeding trunks between the stakes of their pens. In the open granaries might be seen sacks of spilled wheat, below the gate was a thick line of chariots which had been heaped up by the Barbarians, and the peacocks perched in the cedars were spreading their tails and beginning to utter their cry.
Matho’s immobility, however, astonished Spendius; he was even paler than he had recently been, and he was following something on the horizon with fixed eyeballs, and with both fists resting on the edge of the terrace. ”

“ Hopes of vengeance came back to him and transported him. He pressed his hand upon his mouth to check his sobs, and half-swooning with intoxication, let go the halter of his dromedary, which was proceeding with long, regular steps. Matho had relapsed into his former melancholy; his legs hung down to the ground, and the grass made a continuous rustling as it beat against his cothurni.
The journey, however, spread itself out without ever coming to an end. At the extremity of a plain they would always reach a round-shaped plateau ”

“ If it be the glory of geometry, that it is able to measure the earth and the various orbs of the creation, and to tell their distances, sizes, and forms, and if, at some new discovery of the beautiful accuracy and mathematical perfectness of proportion which pervades the universe, it exclaims "Eureka," "Eureka," "I have found it!"—then, what must be the greatness of the Divine Mathematician who made what it renders a human mathematician illustrious merely to discover? ”

“ Graufthal is not the place for you! All those whom the Being of beings has made depositaries of the treasures of science belong to humanity. What will you answer to that Great Being when the time for rendering an account of yourself shall have come? Will He not say to you, in a voice of thunder: ‘Frantz Mathéus, I had gifted you with the most magnificent intelligence, I had unveiled to you things divine and human, I had destined you from the beginning of time to spread the lights of sound philosophy ”

“ Conversing in this manner, the illustrious philosopher [78] and his disciple tranquilly went their way along the valleys of the Zorn. Mathéus, who loved nothing so well as the interior of the woods, forgot the ingratitude of the human species; the scarce perceptible sound of an insect nibbling the bark of an old tree, the flight of a bird through the rustling foliage, the vague murmur of a stream in the ravine, the whirl of the gnats dancing above the still pools—these thousand details of solitude ceaselessly furnished new texts for his anthropo-zoological meditations. ”

“ Now the illustrious philosopher had slept for three hours when Coucou Peter cried—“Maître Frantz, wake up!—Here are the pilgrims of Haslach coming down the mountain; they outnumber the grains of sand on the seashore; get up, master, and see them!”
Having raised himself, Mathéus perceived, first his disciple perched in a wild cherry-tree, gathering the fruit in the manner of the thrushes, and giving himself up heartily to the pleasure; the eyes of the good man were next directed to the neighbouring mountain. ”

“ Reflecting that the greatest philosopher of modern times, the successor of Pythagoras, of Philolaus, and all the sages of India and Egypt, the illustrious Frantz Mathéus of Graufthal, instead of being received by the population with enthusiasm, of being borne in triumph over roads strewn with palm, had run the risk of having to lie in the street and of dying of hunger, he became deeply melancholy, and while he ate, bitterly recapitulated in his mind the events of his journey ”

“ But mathematicians, at least in Italy, have now the power of treating the principles of mathematics in an exact and masterly manner, by means of which the certainty of mathematics extends also to mathematical philosophy. Hence many of the topics which used to be placed among the great mysteries—for example, the natures of infinity, of continuity, of space, time and motion—are now no longer in any degree open to doubt or discussion. Those who wish to know the nature of these things need only read the works of such men as Peano or Georg Cantor ”

“ By dogmas that pretend to be reasons, nothing is made to generate mathematics; and by clothing mathematics with matter, we have the universe! If now we deny, as we do deny, that the highest mathematical idea is the zero;—if, on the other hand, we assert, as we do assert, that the fundamental idea underlying all mathematics, is that of equality; the whole of Oken's cosmogony disappears. ”

“ A platonistic ontology of this sort is, from the point of view of a strictly physicalistic conceptual scheme, as much a myth as that physicalistic conceptual scheme itself is for phenomenalism. This higher myth is a good and useful one, in turn, in so far as it simplifies our account of physics. Since mathematics is an integral part of this higher myth, the utility of this myth for physical science is evident enough. In speaking of it nevertheless as a myth, I echo that philosophy of mathematics to which I alluded earlier under the name of formalism. ”

“ The illustrious philosopher, however, instead of giving himself up to his habitual reflections on the affinities of races, looked on all with a dull eye. It might have been said, to see him with outstretched neck and dangling legs, that he despaired of the doctrine, and of the future of the generations to come.
“Come, Maître Frantz,” said Coucou Peter to him, “courage! Go into your friend Georges Müller’s house; he can’t fail to recognise you—then, hurrah! If we can only find a lodging for to-night, to-morrow we’ll convert the world!”
Mathéus obeyed mechanically ”

“ This worthy man was named Frantz Mathéus. He inherited from his ancestors the oldest house in the place, an orchard, some arable land on the mountain, a few acres of meadow in the valley; and if you add to this modest patrimony eggs, milk, cheese, and, from time to time, a lean fowl, sent to the Doctor by the honest peasants out of the fulness of their gratitude, you will have the whole of Maître Frantz’s income: it sufficed for his maintenance and that of his old servant Martha, as well as his horse Bruno. ”

“ The mind must originate them within itself. As an example of this kind of truth, the whole science of mathematics may be adduced. In the dialogue of Plato entitled Meno, Socrates is represented as educing from the mind of a young slave, by means of judicious questioning, some of the more elementary truths of geometry. As a very simple illustration, I may take a geometrical axiom, and I ask a person quite unskilled in mathematics, whether, if equals be added to equals, the wholes will be equal or unequal. If he understands the question, he will at once answer that the wholes will be equal. ”

“ The earth he supposed to occupy the centre of the universe. [Pg 244] It was not eternal, but was made by an intelligent God, who breathed into it a soul; so it was a living creature, self-active, and gifted with the beautiful form of the sphere.
Nor did the philosopher forget to train the reasoning powers, by the study of mathematics. The importance he attached to this science may be inferred from the sign on his school: “Let no one enter here who is a stranger to geometry.” Plato has the honor of having been the inventor of geometrical analysis. ”

“ Judged from the grades given by instructors to several thousand school and college students, the natural sciences are closer to Latin, in the kind of ability they require, than they are to mathematics. Algebra and geometry are almost as different from one another as mathematics in general are from non-mathematical subjects.
“Such facts certainly seemed to warrant the conclusions of the professor to whose guidance Portia now consigned me: ‘The mind is not a functional unit, nor even a collection of general [177] faculties which work irrespective of particular material. ”

“ Now, an empirical science is necessarily approximate, and geometry as we know it to-day is an exact science. It professes to teach us that the sum of the three angles of a Euclidean triangle is equal to 180°, and not a fraction more or a fraction less. Obviously no empirical determination could ever lay claim to such absolute certitude. Accordingly, geometry had to be subjected to a profound transformation, and this was accomplished by the Greek mathematicians Thales, Democritus, Pythagoras, and finally Euclid. ”

“ Mat was a world-philosopher of no small genius, good nature, and acumen. [1] He loved, he drank, he sang. He describes himself, in one of his lyrics, "in a little Dutch chaise on a Saturday night; on his left hand his Horace, and a friend on his right," going out of town from the Hague to pass that evening and the ensuing Sunday, boozing at a Spiel-haus with his companions, perhaps bobbing for perch in a Dutch canal, and noting down, in a strain and with a grace not unworthy of his Epicurean master, the charms of his idleness, his retreat, and his Batavian Chloe. ”

“ The problems which arise for the metaphysician from the fact that the physical order, as it is presented to our senses, consists of elements having position in space and time, are among the oldest and most perplexing of all the riddles suggested by the course of our experience. Adequate discussion of them would demand not only far more space than we are at liberty to bestow on the topic, but such a familiarity with the mathematical theory of order and series as is scarcely possible to any one but an original mathematician. ”

“ Man can know no more than he gets from observation, and yet mathematics is the great instrument of all exact inquiry. Are the results of mathematical deduction results of observation? We think it likely that Sir John Herschel would reply that Bacon, in coupling together observare re and observare mente, has done what some wags said Newton afterwards did in his study-door—cut a large hole of exit for the large cat, and a little hole for the little cat. ”

“ Euclidian geometry defined the limits of mathematics. Even mechanics was cultivated largely as a geometrical field. The metaphysical doctrine according to which physical objects had their own places and their own motions determined the limits within which astronomical speculations could be carried on. Within these limits Greek mathematical genius achieved marvelous results. The achievements of any period will be limited by two variables: the type of problem against which science formulates its methods, and the materials which analysis puts at the scientist's disposal in attacking the problems. ”