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Show THE SALT LAKE TRIBUNE, SUNDAY MORNING, APRIL Lessons on the Links Uy Stephen Leacock The Application of Mathematics to Golf. quite recently that I taken up goU. In fact, I have only played for three or four yeara, and teldom more than ten tinmen in a week, or at inoit four in a dly. " I have only had a proper golf vest for two years, I only bought a "spoon'' this year and I am not going to get Scotch toeks till next year. la short, I am atill a beginner. I have onee, it ii true, had the "of making a hole in one," ia other wordi, of hitting the ball into the pot, or ran, or receptabk, in one ihot. That ia to lay, after 1 bad hit, a ball wag found in the can ami my ball waa not found. It is what we call circumstantial evidence the same thing that people are hanged for. such Under I circumstances, should have little to teach anybody about golf. But it has occurred to ma that from a certain angle my opinions may be of value. I, at least, bring to bear on the game all the resources of a trained mind, and all the equipment of a complete education. Ia. particular, I may be able fo help the ordinary golfer, or atr' others prefer "gopher' by showing him something of the application of mathematics to gob?.'. IT CAN, INDEED, BE DONE. Many a plsyer is perhaps needlessly discouraged by not being able to calculate properly the chances, and probabilities of progress In the game. Take, for example, the simple problem of "going around in The average ordinary bogey," player, such as I am now becoming something between a beginner and an expert necessarily wonders to himself: "Shall I ever be able to go around in bogey; will the time ever come when I shall make not one hole in bogey, but all the 18 P.have I giv next a calculation of even more acute current interest. It Is in regard to "moving the sea).'' How often is an admirable stroke at golf spoiled by moving tha head! I have seen members of our golf club sit silent and flam all evening, murmuring from time to time, oiily moved To this, according to my calculations, the answer is overwhelmingly "yes." The thing is a mere matter of time and patience. Let me explain for the few people who never play golf (such as night watchmen, night clerks in hotels, night operators, astronomers, and negroes) that "bogey" is an imaginary player who does each hole at golf in the fewest strokes that a s player with ordinary luck ought to need for that hole. Now, an ordinary player finds it quite usual to do one hole out of the nine "in bogey" as we golfers, or rather, "us goofers, " call it but he wonders whether it will ever ber hig fate to do all the nine holes of the course to take a nine-holmurte tor his sake bogey. To which we answer again( with absolute assurance, he will. CONSERVATIVE CALCULATION. The thing is a simple instance of what is celled the mathematical theory of probability. If a player usually and generally makes one hole in bogey, or Comes close to it, his chance of making any one particular hole in bogey is one in nine. Let ns say, for easier calculation, that it is one in ten. When e makes it, his chance of doing the same with the next hole is also one in .ton; therefore, taken from the start, his chance of making the two holes sucof cessively in bogey is a tenth chance. In other words, it is one ia five hundred. The reader sees slreadv how en- first-clas- e one-tent- head." When Jones and I play together, I often hit the ball sideways iato the vegetable garden 'from which no ball returns (they have one o'f these oq every links; it is a Scottish inAnd whenever I ato so, vention). Jones always says, "You moved In return, when he your head. drives his ball away up into air and down again ten yards in front of aim, I always retaliate with the repartee, "Yon moved vour head, n holes!" my "I old man," la And Jones always says, "You moved your head! with a "I didn't allow for the couraging the calcination is. "en- wind." sigh, In fact, all through my is at last somthing dennite aooui that his progress. Let us carry it fur- Mass there is a general feeling over ther. His chance of making three our game is practically taken to holes in bojjey, one after the other, by the wind. We ought really will be one m a thousand; Ins etiance plsy in tho middle of the Ssahanj of four one in ten thousand, Hnd desert". It occurred to me that it might his chance of making the whole forround in bogey will be exactly one be interesting to reduce to a rethat is, one in a mula the effect exercised by the in 1,000,000,000 sistance of the wind on a moving billion games. in our game Is other words, all he has tn do golf ball. For example, is to keep right one. But for how of last Wednesday, Jones in his the ball with what he long! he asks. How long will it drive struck 'tne was his full force, hitassures number the ordinary take, playing of games in a month, to play a bil- ting it with absolute accuracy, as in the cenlion, Will it take several years! he himself admits, fair on his himself he and feeling, ter, will. it Yes, own assertion, absolutely fit, his NOT YET, NOR SOON. eye being (a every necessary thing An ordinary player plays about with Jones) absolutely "in," and and a in one bundled games year, he also having on his proper sweatwill, therefore, play a billion games er a further necessary condition of That in exactly 10,000,000 vpgrs. play. Under all the faball adgives us precisely the time it will vorable circumstances need for persons like the reader and vanced only fifty yards! myself to go around in bogey. It was evident at once that it was Even this calculation needs a lit- a simple matter of the wind. The tle revision. We have to allow for wind, which was of that treacherous the fact that in 100,000,000 years character that blows over the links the shrinking of the earth's crust, unnoticed, had impinged full upon the diminishing heat of the sun, and the ball, pressed it backward, and the general ilackening down, of the forced it to the earth, whole solar system, together with WHAT BALL SHOULD DO. the passing of eclipses, comets and Here, then, is a neat subject of showers of meteors, may put us off calculation. Granted that Jones our game. In fact, one begins to consider if as measured on a bitting machine we shall ever get around in bogey-afte- the week the circus was here can hit two tons, and that his whole So let us try something all. force was pressed against a golf ball else. Here is a very interesting calculation in regard to "allowing for L only one inch and a quarter in diameter. read What My happeast the wind." er will remember that the superfi WE AND THE WIND. cial area of a golf ball iTlR3 I have noticed that a great many that is, 3.141567 x ( inches) 3. golf players of my owu particular And all of this driven forward with class are always preoccupied with the power of 4000 pounds to the the question of "allowing for the inch! wind." In short, taking Jones's stateMy friend Amphibious Jones, for example, just before driv- ments at their face value, the ball ing always murmurs something, as would have traveled, had it not if in prayerj about "allowing for been for the wind, no less than six f the wind." After driving he says and miles. short, if absoluta immobility of the head could be achieved, the major problem of golf would be solved. HOW ASKANCE YOU MAY LOOK Let as put the theory mathematically. The head, poised on the neck, has a circumferential sweep or orbit of about two inches, not counting the rolling of the eves. The circumferential sweep of a golf bsll is based on a radius of 250 yards or a circumference of about 1600 yarda, which is very nearly equal to a mile. Inside this circumferenc is an area of 27,878,400 square feet, the whole of which is controlled by a tiny movement of the human neck. In other words, if a player were to wiggle his neck even of an inch, the amount of ground on which the ball might falsely alight would be half a million feet. If at the same tisse ha asafttpliai tha affect by rolling his eyes, the ball might alight anywhere. I feel certain that after reading this no sensible player will move his whole head. A further calculation remains and one perhaps of even greater practical interest taaa Mrf MM above. ' afrarybaay sro plays golf la wall aware that e aosae days he plays better than on others. Question-b- ow often does a man really play v his game BEING PUT OFT TOUR OAME. I take the case of Amphibious Jones. There are certain days when he is, ss he admit himself, "put off his game" by not having on his proper golf vest. On other days the light puts him off his game; at other times the dark; so too, the heat; so, again, the cold. He is often put off his game because he has been up too late the night before; or similarly because he has been to bed too early the night before; the barking of x dog always ehil-drputs him off his game; so do or adults; or women. Bad nefrs puts him off his game; so does good news; so does the absence of news. All of this msy be expressed by a very simple mathematically application of the theory of permutations and probability; let us ther are altogether fifty forms of disturbance any one of which puts Jones off his game. Kaeh one of these disturbances happens, say, once ia tea days. What chance is there that a day will come when not a single one of them occurs! The formula is a little complicatwill recoged, but mathematicians nize the answer at once as X over 1 plus X squared over I plus . . . (X over 1) times N. In fact, that is exactly how often Jones plays at his best X over 1 plus X squared say-th- f 29, 1928. over I . . X squared over 1, worked out la time and reckoning games to the week, and allowingjfor leap years and solar eclipses, it comes to about once in 2,030,000 M Films of Sweden To Be Screened yean,, Motion plcturea depleting aoenlc play, I Ueautles of Sweden, ths "land of the think that this is about right. midnight sun," will ha shown Tuesday In Barratt hail under ausevening (Copyright, 1928, by Metropolitan pices of the American Sons and Nw York.) Newspaper Service, Daughters of - Sweden. jT1e films were especially photographed las summer by Dr. Amandua wlohnaon noted hrstorlen. 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