W GAMES AS MATHEMATICAL PROBLEMS. E all know that Americans play

games, and prepare themselves for them, in a different spirit from our own. They are more serious, more painstaking, more precise,

and are more definitely " out to win." They may be right or wrong. Evidently a great many Englishmen think just now that Americans are right, and that the sooner we imitate them the better. The threat held over our heads is that if we do not take care we shall go under at the Olympic Games in Berlin in 1916, and that the world will never he the same again. Personally, we are inclined to advocate playing games in the spirit in which we have generally played them. We would count the game well lost if we were beaten by men for whom the game had fallen hopelessly out of perspective and had become a business instead of a recreation.

But although the difference of the American spirit from our own is obvious enough, we have never felt quite sure how far the difference was deliberately thought out and accepted by Americans. It might conceivably be an unconscious differ- ence due simply to some national ethos which lies beyond explanation or analysis. An article by Mr. Heinrich Schmidt (who played admirably in the recent amateur golf champion- ship), in the last number of Country Life, proves that in the case of at least one eminent American intense seriousness is very deliberate. First of all, he brushes away the suggestion that the American competitors lately in England played very slowly in order to tire out or baulk their English opponents. There were special reasons, such as their previous want of practice and their unfamiliarity with the course, which caused the Americans to play slower than usual. But when he has said this he frankly admits that American golfers do normally play more slowly than Englishmen.

"The Americans seem to play the game more for what the game really means to them. The game of tennis, although a mathematical game, requires a rapid analysis of short strokes and quick action to take advantage of the stroke, and con- sequently the opponent. Golf, on the other hand, is a mathe- matical game which has not the time element to consider, but instead has a greater number of mathematical problems to be solved before a stroke can be made with any certainty of the result. Slowness and care are the characteristics of the game as it is played in the States, and of course there is a tendency towards overdoing a good thing, but not intentionally, with nothing but a victory in view. When one stops to consider the various points involved in a stroke, one invariably comes to the conclusion that the game is nothing but a mathematical problem with very little exercise thrown in. And that is really what the game means to me. For instance, in every stroke the distance, kind of shot, slope of ground, and the result on the ball after it lands, effect of wind, drag or run on the ball, stance, kind of club, &c., and so on through many more time-taking problems —all must be considered before yen can really say to yourself when you are following through, have done everything I can to make that shot a success.' If enough time has been taken to solve these problems, one can never say to one's self, Well, I could have done better if I had taken time, but I played care- lessly and got what I deserved.' One such experience was enough to convince me, and since that time I have attempted to play golf, taking it as a problem and not as a game of luck in which one simply takes a chance of having the ball go just right."

Mr. Schmidt does not say that a golfer must spend a long time in his mathematical cogitations when actually addressing the ball; the golfer can solve most of his problems when walking from one stroke to the next. The choice of the club with which to play the next shot—to most of us that

represents almost the whole problem—is to Mr. Schmidt only an insignificant culmination to a comparatively long period of ambulatory thinking. Solritur ambulando is evidently his rule. Nevertheless, the mathematics of the whole question cannot be entirely disposed of while you walk. Mr. Schmidt

insists on the necessity (to himself, at all events) of a practice swing before his stroke. He says

The purpose is simply this: Before I go up to the ball I have made up my mind what the line of play is, what kind of a shot to make and how hard, or rather how far back, I must swing to obtain the desired shot and length. I therefore snake a practice swing, not simply to make a stroke to be duplicated on the real strolic, but one which will give me a check on my estimation of

the back-swing required. After making the practice stroke, I may say to myself, 'That will not be enough; I will have to give it a little more.' But I do not make the stroke over again to make doubly sure—to me it seems altogether too cautious and entirely unnecessary. The purpose of the practice stroke is to check one's mental estimate, and this is not a tiresome mental exertion, nor even a physical one."

We suppose that there can be hardly any Englishmen who have made such a mathematical study of a game as this.

When they take a practice swing at golf, for instance, they have no more profound purpose than to make sure that their shoulders are in a loose and supple condition for swinging and that their feet have settled into a comfortable stance.

It would be highly interesting to know for certain whether Mr. Schmidt's very deliberate mental attitude towards games is typical of that of most Americans. We should know exactly where we stand in relation to them, and be able to say more easily whether it would be worth while to imitate them.

For our own part, we should shrink from these mental labours among the sand dunes. Although Mr. Schmidt says they are not tiresome, we fear we should find them exhausting. Of course, many games which are truly recrea- tive, such as billiards and bridge, are a kind of mathematical problem. If one of them is chiefly a question of angles, the other is largely a tax on the memory. But these games recreate tired men because they are professedly a change of mental occupation. Change is always in a sense rest. But billiards and bridge are not played in the open air ; they are not physical recreations. True, billiards requires a certain amount of walking round the table, but probably the exercise is not mere than just enough to prolong the lives of people who would otherwise fall into the fatal habit of going to sleep after dinner. Games in the open air require a proper balance between the physical exertion and the mental application. The latter must be sufficiently firm to amount to a strong incentive—without that any game would be boring beyond words—but it does not exclude the possibility of observing the weather and the scenery, of acting on brilliant impulses, or even of chaffing one's opponent.

An American athlete or player of games is seldom " a good all-round man." He is a specialist. We should ourselves much prefer to be good enough at several different games to be a competent and useful opponent. That is enough for enjoyment. "Versatility is the secret of pleasure, for it continually happens in life that one has opportunities of playing one game in one place and another game in another place. The difference between the English idea and the American may be roughly expressed by the difference between games and athletics. The more esteemed English games, such as cricket and football, are co-operative; they succeed or fail according to the success with which a side combines. Running, jumping, and so on, are opportunities for the more self-centred aims of the specialist, and it is in these that Americans shine. The training of an eminent American athlete is a period of complete constraint. He is

dominated by his trainer, who orders every moment of his life. The question arises whether the means does not obscure the end. This, we fear, is the modern tendency, and it is perhaps inevitably encouraged by the Olympic games. We hardly see yet whither we shall be led. But

it may be necessary before long to answer these questions : Is it good enough ? Has the game become merged in the business P Have the joy and the relaxation given place to a new tax upon nervous energy? English horsemen, to take an illustration, have shown that they can school their horses to the highly technical art of jumping in the show ring, but they are quite right, we think, to care less for scoring marks at exhibitions than for the more careless and exhilarating jumping of cross-country riding. Again, every man, it is said, can become a "strong man" by assiduous training of his

muscles and make his calves stand out "like penny buns," as Stevenson says of the statue of Hercules in "The Wrong Box " ; but most of us would rather be supple and apt at popular games than be able to lift a cart-horse. Ultimately,

in a more perfect world than promises itself at present, it may be admitted that it is after all a finer and happier thing to know bow to play a game than how to win a game. Byron tells that as a boy he held that-

" Actium lost for Cleopatra's eyes Outbalanoed all the Caesar's victories."

Defeat at the Olympic Games through playing the game, —playing like its lovers rather than its slaves, like freemen rather than pieces of machinery—would be much more glorious than a mechanic victory. Drudgery is not the soil in which an olive fit to crown athletes will ever deign to grow.