ONE:In a half century past all has changed; the application of the sciences, the utilisation of natural forces, manufacturing, the transportation of material, the preparation and diffusion of printed matter, and other great matters of human interest, have come to shape our laws, control commerce, establish new relations between people and countriesin short, has revolutionised the world. So rapid has been this change that it has outrun the powers of conception, and people waken as from a dream to find themselves governed by a new master.It is best, when an apprentice thinks of entering an engineering establishment, to inquire of its character from disinterested persons who are qualified to judge of the facilities it affords. As a rule, every machine-shop proprietor imagines his own establishment to combine all the elements of an engineering businessand the fewer the facilities for learners, usually the more extravagant this estimate; so that opinions in the matter, [24] to be relied upon, should come from disinterested sources.
TWO:It was from mathematical science that the light of certainty first broke. Socrates had not encouraged the study of mathematics, either pure or applied; nor, if we may judge from some disparaging allusions to Hippias and his lectures in the Protagoras, did Plato at first regard it with any particular favour. He may have acquired some notions of arithmetic and geometry at school; but the intimate acquaintance with, and deep interest in them, manifested throughout his later works, probably dates from his visits to Italy, Sicily, Cyrn, and Egypt. In each of these places the exact sciences were cultivated with more assiduity than at Athens; in southern Italy they had been brought into close connexion with philosophy by a system of mystical interpretation. The glory of discovering their true speculative significance was reserved for Plato. Just as he had detected a profound analogy between the Socratic scepticism and the Heracleitean flux, so also, by another vivid intuition, he saw in the definitions and demonstrations of geometry a type of true reasoning, a particular application of the Socratic logic. Thus the two studies were brought into fruitful reaction, the one gaining a wider applicability, and the other an exacter method of proof. The mathematical spirit ultimately proved211 too strong for Plato, and petrified his philosophy into a lifeless formalism; but no extraneous influence helped so much to bring about the complete maturity of his constructive powers, in no direction has he more profoundly influenced the thought of later ages. Who can be calm when he is called upon to prove the existence of the gods? Who can avoid hating and abhorring the men who are and have been the cause of this argument? I speak of those who will not believe the words which they have heard as babes and sucklings from their mothers and nurses, repeated by them both in jest and earnest like charms; who have also heard and seen their parents offering up sacrifices and prayerssights and sounds delightful to childrensacrificing, I say, in the most earnest manner on behalf of them and of themselves, and with eager interest talking to the gods and beseeching them as though they were firmly convinced of their existence; who likewise see and hear the genuflexions and prostrations which are made by Hellenes and barbarians to the rising and setting sun and moon, in all the various turns of good and evil for272tune, not as if they thought that there were no gods, but as if there could be no doubt of their existence, and no suspicion of their non-existence; when men, knowing all these things, despise them on no real grounds, as would be admitted by all who have any particle of intelligence, and when they force us to say what we are now saying, how can any one in gentle terms remonstrate with the like of them, when he has to begin by proving to them the very existence of the gods?160
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