Page images
PDF
EPUB
[ocr errors][merged small]

principle. The stakes of success are too high; the price of defeat is too terrible. We have seen how every revolution gives opportunity to the adventurer to substitute his private ambition for the party's cause. And even when the party maintains its original purpose, the means it must utilise, the passions to which it must appeal, make it more than dubious whether the end it seeks to serve can be attained in the atmosphere it is driven by its position to create.

When conflict is so loosed, the nature of men in its context becomes what Machiavelli assumed it normally to be. That is why no man has a right to abandon the prospect of constitutional effort until he is forced by his opponents to change his ground. More, he has never the right so to act as to deprive them, as they feel, of the weapons of legitimate controversy. It must never be forgotten that what to statesmen is a struggle for power is always to the common people a struggle for bread. It is this which makes so important in a state the capacity for self-sacrifice, particularly among those who have been favoured by fortune in the struggle for existence. That capacity, at any rate, is the chief guarantee a state possesses of the continual enlargement of its freedom. Unquestionably, it means in its operation equality; and it has been the fashion even with liberal thinkers to represent equality as the enemy of liberty. It is a mistaken diagnosis. In the economic sphere, there is never liberty of contract until there is equality of bargaining power; in the political sphere liberty is always meaningless until the humble man possesses, through the medium of equality, assurance that the knowledge of his wants impresses itself with emphasis upon the holders of power. For inequality in a state is the nurse of exactly those characteristics-envy, hate, faction-which give the opportunity to what we call Machiavellianism. Without equality, the mind of the community cannot be alive either to the fascination of knowledge or to the power of beauty. Where it is absent, each class is occupied in an envious striving to dethrone its rivals; and in the heat and stress of antagonism the cement of the social structure is rapidly loosened. In a world of equals, there would still be the ambitious search for power, but it would be elevated

and ennobled by being harnessed to purposes of which the result would be widespread benefit.

In some such fashion as this, it seems possible to construct an answer to Machiavelli's theorems. It is worth while remarking how urgent it is that the effort to answer him should be made. We live in a period in which, as in the 16th and 18th centuries, the main occupation of thinkers is the dissection and discarding of the traditions we have inherited. Men are conscious of an intense malaise, and, along with it, there goes a volume of scientific discovery which makes the problem of social understanding of peculiarly high importance. We are escaping from a materialistic philosophy which closed the eyes of men to the possibilities of conscious co-operation. We know that the environment can be profoundly modified by ourselves. It can be modified along the most varied lines of which the gospel, as Machiavelli taught it, is peculiarly arresting and prominent. In a sense it is the easiest alternative to choose since it appeals to the most obvious prejudices of men and demands, less than any other, the duty of arduous reflexion. But it is a gospel of death. And it is the more disastrous because it is offered to us in a period of unstable equilibrium. It invites support from all who have an interest in disorder; it tends to persuade all who are weary of the struggle against injustice. It tempts the holders of power by suggesting to them that an onslaught upon their competitors may give them the assurance of enduring authority.

In fact, as Machiavelli himself saw, it offers no prospect save that of perpetuating all the evils it seeks to destroy. It offers a momentary advantage in exchange for the prospect of a certain renewal of war. It sharpens in men all that is most inimical to the forces that have exercised a civilising influence in history. It is the more important to reject it in an age of crisis because, as a rule, periods such as our own, when traditions, ideals, standards, are thrown into the melting pot, are the creative epochs of history. We seem, both in the sciences and the arts, to tremble on the verge of great discoveries. We need the passionate denial of maxims that make for conflict if we are to reap the advantages they seem to presage. HAROLD J. LASKI.

ges a

Art. 5.-SCHOOL MATHEMATICS: A PLEA.

DURING the past twenty and more years there have been many changes in the teaching of school mathematics. We have wandered far from the idealism of forty years ago, and have brought the subject down from the clouds to the earth, and made it more in contact with reality. There is no longer the same sting in the old question, said to have been asked of Euclid in his class-room at Alexandria, and certainly asked of many a teacher of mathematics during the past two thousand years: What is the good of all this stuff? There have been far-reaching changes in other school subjects also; it has been an age of change, no traditions have been sacred, and no foundations regarded as stable, and as a result every school time-table is horribly congested, and I, an old Public School master, am wondering, Does mathematics really deserve the generous allowance of time and of teaching capacity given to it? Does it justify, not its existence, but its greed?

All school instruction is suffering from the ceaseless flow of new material which is coming into it, the steady and constant increase in the number of claims successfully made upon the hours of work, music, singing, art, handicraft, gymnasium, to say nothing of the insistent demands of new-new to school work-branches of Science, biology, zoology, and of languages. Perhaps, as Euchen, in his 'Life's Basis and Life's Ideals,' suggests, in itself each single demand may be justifiable and admirable, but whether it is better than the other can only be decided from the idea which governs the whole; and if no such idea exists a gain in one department may be a loss to the whole. In face of that which has been handed down from the past and that which arises in the present, it is very difficult to come to a balanced judgment. The immediate impression tends to give the balance in favour of the present, and from this point of view all occupation with the past may appear to be a flight from the living to the dead. Perhaps this, in an age of vast material progress, has unconsciously influenced all educational ideals; in the din of the revolving wheels of our gigantic machines and their

increasing needs, we have hurried too far from an ideal which transcends time to the immediate requirements of our own period.

It is not easy for those actively engaged in teaching to be the best judges of their aims; they are so prescribed in their limits, so busy in their routine, so intent upon their actual task, and withal so narrowed by that impending examination-the very antithesis of all real education-that they cannot see the forest for the trees. For many years it was my function to try to guide the mathematics at Harrow, and I realise how difficult it was to grasp what (beyond getting boys up to such a standard of superficiality as would enable them to get marks in certain examinations) was the educational value of the work we were doing with much patience and expenditure of energy; wider opportunities have since made me wonder whether school mathematics to the extent to which it is now being carried as a general subject is not just as tyrannical as was the Classical domination of old. Has not the subject really suffered from a swing of the pendulum which has gone too far? A reaction which swept away the one-sided curriculum of the mid and later Victorian age has assumed that where Classics failed, Science and Mathematics must succeed: and the assumption is not proven.

Schools formerly had a much easier time-table than they have to-day. Latin and Greek were the main subjects of intellectual supply: from a very tender age we learnt the Latin Grammar, with its syntax from Kennedy or the Public School Primer; we knew and could repeat with unconscious effort:

'Many nouns in is we find

To the mascula assigned,'

and could apply these rhythmical rules more or less accurately; we stumbled through Farrar's unintelligible Greek Syntax with difficulty. We hitched Latin verses into shape with the aid of a Gradus as an intellectual jigsaw puzzle not devoid of pleasure when the words went together. We read Latin and Greek authors; those who reached the VIth Form-for all boys were treated alike, there were no specialists-were familiar with Cicero and Tacitus, Thucydides and Plato; Ovid,

and Virgil, and Horace, Euripides, Eschylus, and Sophocles-and that, too, in the little Oxford Press editions without notes, without divisions into Acts and a Scenes, and with the enigmatic and dubious utterances of the Chorus to unravel or not as best we could. The work was not made as easy as it is to-day with the annotated editions, the expunged choruses, the marginal explanations, and the many subdivisions, all bypaths to the royal road to learning. Then there was French, still in the hands of the old-fashioned French pedagogue, for no school was properly staffed without a Frenchman whatever might be the measure of his inefficiency; German, if taught at all, was in a more parlous state; Science was an extra and so was Drawing; and then there was Mathematics, which came a long way behind Classics in pride of place, but it was the only other study seriously regarded. It was Classics first, Mathematics a very poor second, only indeed placed at all because it was in a better position than the other work, which was nowhere.

And for the greater part of the school-indeed, for all but for those who could be counted on the fingers of one hand-the only mathematical subjects were arithmetic, algebra, and Euclid; of these arithmetic was the staple work. We worked at sums, applied certain rules and got answers-the main thing was to get a right answer, method, style, continuity were little seen. 'I will read out the answers to the sums; 5 marks each for those right, 0 for those wrong,' was a common dictum heard in many a room from a master who faced his class with an air of boredom. Times must then have been easy for the masters, for we were left alone to do long exercises to a pattern type; it was all drill, little thinking. Much the same prevailed in algebra, an explanation followed by long, wearisome exercises; and then Euclid, how familiar was that little brown-backed Todhunter, how thumbed, how dreaded! there was a tradition of impossibility associated with the pons asinorum, that was the real test; the first four propositions, except, perhaps, the fourth, were fairly easy, though the first with its formality, its apparent unnecessary verbiage, its seeming attempt to obscure the obvious, gave one a strange feeling of dabbling with the unreal. Many years

« EelmineJätka »