Oct 8, 2002
I finally passed Maths I in 1949 at the fourth attempt. I don’t know why I kept on at it for I was never very fond of maths. I suppose that after each failed attempt I felt I had more to lose by abandoning it. Be that as it may, in 1949 we got a new maths lecturer called W W. Sawyer, a little Englishman who had formerly taught at some polytech in the Midlands. Alone among the mathematicians I have met he recognised that maths is a foreign language, and needs to be translated into English to be understood by ordinary folk. Not only is it a foreign language, but is a foreign language rendered into shorthand for the precise expression of certain logical processes and sequences, some of which are quite obscure, while others are so commonplace in our ordinary experience that one wonders why the analysis of them is not also part of our everyday experience.
That the knight’s move in chess approximates as near as dammit to part of the circumference of a circle may not be a concept that confronts us all at frequent intervals, but that the powers of numbers, (squares, cubes, etc.) express precisely the amount of purchase one can obtain by winding a rope once, twice, three times, etc. around a bollard is a matter of such common experience to anyone who has tried to stop a vehicle running down a hill, or a boat drifting downstream, that one wonders why the analysis of it had to be left to the mathematicians. If, say, for the sake of argument, a man can just restrain a single goat, by a rope tied around its neck, then by taking a turn of the rope around a suitable bollard, he could restrain 10 goats, they being all of one mind, and by taking two turns he could restrain 100 goats, three turns a thousand, and so on. Thus 10 to the power of 0 = 1, 10 to the power of 1 = 10, 10 to the power of 2, (10 squared) = 100, 10 to the power of 3 = 1000, -- and each further turn of the rope around the bollard increases the power of the goatherd by a further 10 fold. Not only that, but any number in between can be expressed as so many turns of the rope and a further partial turn. And this is the basis for logarithms and slide rules, and a whole raft of clever magic that engineers and others can work with numbers. Sawyer says that if you ask an engineer what’s 3 times 4, he won’t answer immediately, but will take a sort of ruler thing out of his hip pocket, fiddle with it for a minute or two, and then say, “It’s about twelve.”
Now bollards and ropes and such were things I could comprehend. My father me about a day in the 1920’s when he and a certain Mr White were loitering on the wharf at Westport where a big American freighter had been taking on coal. At Westport the wharves are on the bank of the Buller River, and ships are moored with their bows pointing upstream. When a ship is ready to put to sea the engines are used to take the strain off the mooring lines, the bow lines are cast off, and the current of the river carries the bow away from the wharf and while the stern remains attached, the ship swings around until it is pointing downstream. At the critical moment the stern line is released and the ship speeds down river to the open sea.
On this particular day, a specially robust wharfie, (he must have weighed 150 kilos) was in control of the stern line, and he had taken several turns around a bollard to give him purchase. When the ship’s engines had taken the strain, the American officer of the watch ordered the bow lines cast off, and the Buller, which was in flood, began to take over. As the bow swung out into the current, the extra pressure caused the ship to lurch, and the big wharfie was obliged to take an involuntary step forward. This brought a peremptory “Hold that stern line!” from the officer on the deck, but the words had scarcely left his lips when an even greater buffet caused the wharfie to take two more steps forward. The officer’s voice went up a register and he launched into a further more urgent instruction which included reference to a flat footed son of a bitch whose intention seemed to be to bring about the ship’s destruction. By now the ship was beginning to point downstream, but a final lurch wrenched the wharfie three or four more steps forward, and sent the officer into a high pitched stream of invective rarely heard and mercifully poorly comprehended in this part of the world.
In response, the big wharfie let the rope go slack, walked casually forward and unwound it from the bollard and dropped it contemptuously into the river. Then, cupping his hands around his mouth, he bellowed at the rapidly receding officer, “Kiss my bloody arse!”
I imagine the old wharfie had, in his time, guided a hundred ships through this manoeuvre, and didn’t feel he needed advice on the subject from any upstart hysterical deck officer.
Mr White, who was of a philosophical turn of mind, mused that these might be the last words the officer ever heard from the New Zealand mainland, and that they could well leave him with an impression of hostility which our brave and purposeful little nation ill deserved.
And thus through the inspiration of W.W.Sawyer, did I finally come to grips with stage I maths.