Of course what I call Mathematics is only what the Civil Service Commissioners expected you to know to pass a very rudimentary examination. I suppose that to those who enjoy this peculiar gift, Senior Wranglers and the like, the waters in which I swam must seem only a duck-puddle compared to the Atlantic Ocean. Nevertheless, when I plunged in, I was soon out of my depth. When I look back upon those care-laden months, their prominent features rise from the abyss of memory. Of course I had progressed far beyond Vulgar Fractions and the Decimal System. We were arrived in an 'Alice-in-Wonderland' world, at the portals of which stood 'A Quadratic Equation.' This with a strange grimace pointed the way to the Theory of Indices, which again handed on the intruder to the full rigours of the Binomial Theorem. Further dim chambers lighted by sullen, sulphurous fires were reputed to contain a dragon called the 'Differential Calculus.' But this monster was beyond the bounds appointed by the Civil Service Commissioners who regulated this stage of Pilgrim's heavy journey. We turned aside, not indeed to the uplands of the Delectable Mountains, but into a strange corridor of things like anagrams and acrostics called Sines, Cosines and Tangents. Apparently they were very important, especially when multiplied by each other, or by themselves! They had also this merit—you could learn many of their evolutions off by heart. There was a question in my third and last Examination about these Cosines and Tangents in a highly square-rooted condition which must have been decisive upon the whole of my after life. It was a problem. But luckily I had seen its ugly face only a few days before and recognised it at first sight.
I have never met any of these creatures since. With my third and successful examination they passed away like the phantasmagoria of a fevered dream. I am assured that they are most helpful in engineering, astronomy and things like that. It is very important to build bridges and canals and to comprehend all the stresses and potentialities of matter, to say nothing of counting all the stars and even universes and measuring how far off they are, and foretelling eclipses, the arrival of comets and such like. I am very glad there are quite a number of people born with a gift and a liking for all of this; like great chess-players who play sixteen games at once blindfold and die quite soon of epilepsy. Serve them right! I hope the Mathematicians, however, are well rewarded. I promise never to blackleg their profession nor take the bread out of their mouths.
I had a feeling once about Mathematics, that I saw it all—Depth beyond depth was revealed to me—the Byss and the Abyss. I saw, as one might see the transit of Venus—or even the Lord Mayor's Show, a quantity passing through infinity and changing its sign from plus to minus. I saw exactly how it happened and why the tergiversation was inevitable: and how the one step involved all the others. It was like politics. But it was after dinner and I let it go!
The practical point is that if this aged, weary-souled Civil Service Commissioner had not asked this particular question about these Cosines or Tangents in their squared or even cubed condition, which I happened to have learned scarcely a week before, not one of the subsequent chapters of this book would ever have been written. I might have gone into the Church and preached orthodox sermons in a spirit of audacious contradiction to the age. I might have gone into the City and made a fortune. I might have resorted to the Colonies, or 'Dominions' as they are now called, in the hopes of pleasing, or at least placating them; and thus had, à la Lindsay Gordon or Cecil Rhodes, a lurid career. I might even have gravitated to the Bar, and persons might have been hanged through my defence who now nurse their guilty secrets with complacency. Anyhow the whole of my life would have been altered, and that I suppose would have altered a great many other lives, which in their turn, and so on....
But here we seem to be getting back to mathematics, which I quitted for ever in the year 1894. Let it suffice that this Civil Service Commissioner putting this particular question in routine or caprice deflected, so far as I was concerned, the entire sequence of events. I have seen Civil Service Commissioners since. I have seen them in the flesh. I have even appointed their Chief. I admire them. I honour them. We all do. But no one, least of all themselves, would suppose they could play so decisive and cardinal a part in human affairs. Which brings me to my conclusion upon Free Will and Predestination; namely—let the reader mark it—that they are identical.
I have always loved butterflies. In Uganda I saw glorious butterflies the colour of whose wings changed from the deepest russet brown to the most brilliant blue, according to the angle from which you saw them. In Brazil as everyone knows there are butterflies of this kind even larger and more vivid. The contrast is extreme. You could not conceive colour effects more violently opposed; but it is the same butterfly. The butterfly is the Fact—gleaming, fluttering, settling for an instant with wings fully spread to the sun, then vanishing in the shades of the forest. Whether you believe in Free Will or Predestination, all depends on the slanting glimpse you had of the colour of his wings—which are in fact at least two colours at the same time. But I have not quitted and renounced the Mathematick to fall into the Metaphysick. Let us return to the pathway of narrative.
When I failed for the second time to pass into Sandhurst, I bade farewell to Harrow and was relegated as a forlorn hope to a 'crammer.' Captain James and his highly competent partners kept an establishment in the Cromwell Road. It was said that no one who was not a congenital idiot could avoid passing thence into the Army. The Firm had made a scientific study of the mentality of the Civil Service Commissioners. They knew with almost Papal infallibility the sort of questions which that sort of person would be bound on the average to ask on any of the selected subjects. They specialised on these questions and on the answering of them. They fired a large number of efficient shot-guns into the brown of the covey, and they claimed a high and steady average of birds. Captain James—if he had known it—was really the ingenious forerunner of the inventors of the artillery barrages of the Great War. He fired from carefully selected positions upon the areas which he knew must be tenanted by large bodies of enemy troops. He had only to fire a given number of shells per acre per hour to get his bag. He did not need to see the enemy soldiers. Drill was all he had to teach his gunners. Thus year by year for at least two decades he held the Blue Ribbon among the Crammers. He was like one of those people who have a sure system for breaking the Bank at Monte Carlo, with the important difference that in a great majority of cases his system produced success. Even the very hardest cases could be handled. No absolute guarantee was given, but there would always be far more than a sporting chance.
However, just as I was about to enjoy the advantage of this renowned system of intensive poultry-farming, I met with a very serious accident.
My aunt, Lady Wimborne, had lent us her comfortable estate at Bournemouth for the winter. Forty or fifty acres of pine forest descended by sandy undulations terminating in cliffs to the smooth beach of the English Channel. It was a small, wild place and through the middle there fell to the sea level a deep cleft called a 'chine.' Across this 'chine' a rustic bridge nearly 50 yards long had been thrown. I was just 18 and on my holidays. My younger brother aged 12, and a cousin aged 14, proposed to chase me. After I had been hunted for twenty minutes and was rather short of breath, I decided to cross the bridge. Arrived at its centre I saw to my consternation that the pursuers had divided their forces. One stood at each end of the bridge; capture seemed certain. But in a flash there came across me a great project. The chine which the bridge spanned was full of young fir trees. Their slender tops reached to the level of the footway. 'Would it not' I asked myself 'be possible to leap on to one of them and slip down the pole-like stem, breaking off each tier of branches as one descended, until the fall was broken?' I looked at it. I computed it. I meditated. Meanwhile I climbed over the balustrade. My young pursuers stood wonder-struck at either end of the bridge. To plunge or not to plunge, that was the question! In a second I had plunged, throwing out my arms to embrace the summit of the fir tree. The argument was correct; the data were absolutely wrong. It was three days before I regained consciousness and more than three months before I crawled from my bed. The measured fall was 29 feet on