Beweren en bewijzen/het verhaal/1. Rationaliteit/casus Graham Greene. A shocking Accident

1

Jerome was called into his housemaster's room in the break between the second and the third class on a Tuesday morning. He had no fear of trouble, for he was a warden - the name that the proprietor and headmaster of a rather expensive preparatory school had chosen to give to approved, reliable boys in the lower forms (from a warden one became a guardian and finally before leaving, it was hoped for Marlborough or Rugby, a crusader). The housemaster, Mr Wordsworth, sat behind his desk with an appearance of perplexity and apprehension. Jerome had the odd impression when he entered that he was a cause of fear.

'Sit down, Jerome,' Mr Wordsworth said. 'All going well with the trigonometry?'

'Yes, sir.'

'I've had a telephone call, Jerome. From your aunt. I'm afraid I have bad news for you.'

'Yes, sir?'

'Your father has had an accident.'

'Oh.'

Mr Wordsworth looked at him with some surprise. 'A serious accident.'

'Yes, sir?'

Jerome worshipped his father: the verb is exact. As man re-creates God, so Jerome re-created his father - from a restless widowed author into a mysterious adventurer who travelled in far places - Nice, Beirut, Majorca, even the Canaries. The time had arrived about his eighth birthday when Jerome believed that his father either 'ran guns' or was a member of the British Secret Service. Now it occurred to him that his father might have been wounded in 'a hail of machine-gun bullets'.

Mr Wordsworth played with the ruler on his desk. He seemed at a loss how to continue. He said, 'You know your father was in Naples?'

'Yes, sir.'

'Your aunt heard from the hospital today.'

'Oh.'

Mr Wordsworth said with desperation, 'It was a street accident.'

'Yes, sir?' It seemed quite likely to Jerome that they would call it a street accident. The police of course fired first; his father would not take human life except as a last resort.

'I'm afraid your father was very seriously hurt indeed.'

'Oh.'

'In fact, Jerome, he died yesterday. Quite without pain.'

'Did they shoot him through the heart?'

'I beg your pardon. What did you say, Jerome?'

'Did they shoot him through the heart?'

'Nobody shot him, Jerome. A pig fell on him.' An inexplicable convulsion took place in the nerves of Mr Wordsworth's face; it really looked for a moment as though he were going to laugh. He closed his eyes, composed his features and said rapidly as though it were necessary to expel the story as rapidly as possible. 'Your father was walking along a street in Naples when a pig fell on him. A shocking accident. Apparently in the poorer quarters of Naples they keep pigs on their balconies. This one was on the fifth floor. It had grown too fat. The balcony broke. The pig fell on your father.'

Mr Wordsworth left his desk rapidly and went to the window, turning his back on Jerome. He shook a little with emotion.

Jerome said, 'What happened to the pig?'

2

This was not callousness on the part of Jerome, as it was interpreted by Mr Wordsworth to his colleagues (he even discussed with them whether, perhaps, Jerome was yet fitted to be a warden). Jerome was only attempting to visualize the strange scene to get the details right. Nor was Jerome a boy who cried; he was a boy who brooded, and it never occurred to him at his preparatory school that the circumstances of his father's death were comic - they were still part of the mysteries of life. It was later, in his first term at his public school, when he told the story to his best friend, that he began to realize how it affected others. Naturally after that disclosure he was known, rather unreasonably, as Pig.

Unfortunately his aunt had no sense of humour. There was an enlarged snapshot of his father on the piano; a large sad man in an unsuitable dark suit posed in Capri with an umbrella (to guard him against sunstroke), the Faraglione rocks forming the background. By the age of sixteen Jerome was well aware that the portrait looked more like the author of Sunshine and Shade and Ramblers in the Balearics than an agent of the Secret Service. All the same he loved the memory of his father: he still possessed an album fitted with picture-postcards (the stamps had been soaked off long ago for his other collection), and it pained him when his aunt embarked with strangers on the story of his father's death.

'A shocking accident,' she would begin, and the stranger would compose his or her features into the correct shape for interest and commiseration. Both reactions, of course, were false, but it was terrible for Jerome to see how suddenly, midway in her rambling discourse, the interest would become genuine. 'I can't think how such things can be allowed in a civilized country,' his aunt would say. 'I suppose one has to regard Italy as civilized. One is prepared for all kinds of things abroad, of course, and my brother was a great traveller. He always carried a water-filter with him. It was far less expensive, you know, than buying all those bottles of mineral water. My brother always said that his filter paid for his dinner wine. You can see from that what a careful man he was, but who could possibly have expected when he was walking along the Via Dottore Manuele Panucci on his way to the Hydrographic Museum that a pig would fall on him?' That was the moment when the interest became genuine.

Jerome's father had not been a very distinguished writer, but the time always seems to come, after an author's death, when somebody thinks it worth his while to write a letter to the Times Literary Supplement announcing the preparation of a biography and asking to see any letters or documents or receive anecdotes from friends of the dead man. Most of the biographies, of course, never appear - one wonders whether the whole thing may not be an obscure form of blackmail and whether many a potential writer of a biography or thesis finds the means in this way to finish his education at Kansas or Nottingham. Jerome, however, as a chartered accountant, lived far from the literary world. He did not realize how small the menace really was, or that the danger period for someone of his father's obscurity had long passed. Sometimes he rehearsed the method of recounting his father's death so as to reduce the comic element to its smallest dimensions - it would be of no use to refuse information, for in that case the biographer would undoubtedly visit his aunt who was living to a great old age with no sign of flagging.

It seemed to Jerome that there were two possible methods - the first led gently up to the accident, so that by the time it was described the listener was so well prepared that the death came really as an anti-climax. The chief danger of laughter in such a story was always surprise. When he rehearsed his method Jerome began boringly enough.

'You know Naples and those high tenement buildings? Somebody once told me that the Neapolitan always feels at home in New York just as the man from Turin feels at home in London because the river runs in much the same way in both cities. Where was I? Oh, yes. Naples, of course. You'd be surprised in the poorer quarters what things they keep on the balconies of those sky-scraping tenements - not washing, you know, or bedding, but things like livestock, chickens or even pigs. Of course the pigs get no exercise whatever and fatten all the quicker.' He could imagine how his hearer's eyes would have glazed by this time. 'I've no idea, have you, how heavy a pig can be, but these old buildings are all badly in need of repair. A balcony on the fifth floor gave way under one of those pigs. It struck the third floor balcony on its way down and sort of ricochetted into the street. My father was on the way to the Hydrographic Museum when the pig hit him. Coming from that height and that angle it broke his neck.' This was really a masterly attempt to make an intrinsically interesting subject boring.

The other method Jerome rehearsed had the virtue of brevity.

'My father was killed by a pig.'

'Really? In India?'

'No, in Italy.'

'How interesting. I never realized there was pig-sticking in Italy. Was your father keen on polo?'

In course of time, neither too early nor too late, rather as though, in his capacity as a chartered accountant, Jerome had studied the statistics and taken the average, he became engaged to be married: to a pleasant fresh-faced girl of twenty-five whose father was a doctor in Pinner. Her name was Sally, her favourite author was still Hugh Walpole, and she had adored babies ever since she had been given a doll at the age of five which moved its eyes and made water. Their relationship was contented rather than exciting, as became the love-affair of a chartered accountant; it would never have done if it had interfered with the figures.

One thought worried Jerome, however. Now that within a year he might himself become a father, his love for the dead man increased; he realized what affection had gone into the picture-postcards. He felt a longing to protect his memory, and uncertain whether this quiet love of his would survive if Sally were so insensitive as to laugh when she heard the story of his father's death. Inevitably she would hear it when Jerome brought her to dinner with his aunt. Several times he tried to tell her himself, as she was naturally anxious to know all she could that concerned him.

'You were very small when your father died?'

'Just nine.'

'Poor little boy,' she said.

'I was at school. They broke the news to me.'

'Did you take it very hard?'

'I can't remember.'

'You never told me how it happened.'

'It was very sudden. A street accident.'

'You'll never drive fast, will you, Jemmy?' (She had begun to call him 'Jemmy'.) It was too late then to try the second method - the one he thought of as the pig-sticking one.

They were going to marry quietly in a registry-office and have their honeymoon at Torquay. He avoided taking her to see his aunt until a week before the wedding, but then the night came, and he could not have told himself whether his apprehension was more for his father's memory or the security of his own love.

The moment came all too soon. 'Is that Jemmy's father?' Sally asked, picking up the portrait of the man with the umbrella.

'Yes, dear. How did you guess?'

'He has Jemmy's eyes and brow, hasn't he?'

'Has Jerome lent you his books?'

'No.'

'I will give you a set for your wedding. He wrote so tenderly about his travels. My own favourite is Nooks and Crannies . He would have had a great future. It made that shocking accident all the worse.'

'Yes?'

Jerome longed to leave the room and not see that loved face crinkle with irresistible amusement.

'I had so many letters from his readers after the pig fell on him.' She had never been so abrupt before. And then the miracle happened. Sally did not laugh. Sally sat with open eyes of horror while his aunt told her the story, and at the end, 'How horrible,' Sally said. 'It makes you think, doesn't it? Happening like that. Out of a clear sky.'

Jerome's heart sang with joy. It was as though she had appeased his fear for ever. In the taxi going home he kissed her with more passion than he had ever shown and she returned it. There were babies in her pale blue pupils, babies that rolled their eyes and made water.

'A week today,' Jerome said, and she squeezed his hand. 'Penny for your thoughts, my darling.'

'I was wondering,' Sally said, 'what happened to the poor pig?'

'They almost certainly had it for dinner,' Jerome said happily and kissed the dear child again.

Een verificatieprobleem

Jeromes vader is dood, maar wiens schuld is dit? Advocaten en rechters zullen zich erover buigen of het de schuld is van de huiseigenaar (slecht onderhouden balkon) of van de huurder (illegaal varken in woning). Maar misschien wordt betwist of een ongeval zo als beschreven überhaupt tot de dood van de vader kan leiden. Stel, je bent als expert gevraagd om hierover een uitspraak te doen. Stel dat niet strijdig is dat het balkon op moment t afgebroken was.

We hebben te maken met een artefact uit twee onderdelen: een balkon en een varken. Kan deze constructie een mens doden, en zo ja, onder welke voorwaarden?

Je hoeft niet meer te weten dan dit:

Balkon 

Het balkon heeft de eigenschap dat alles wat zich op moment t bevindt op punt (x, y, 15), in vrije val terecht komt (bevestigd door getuigen). Daarbij zijn (x, y) coördinaten uit het kadaster. Een balkon op de 5e verdieping hangt 15m boven de grond.

Varken 

Het varken heeft een massa van 120kg (inleverbon abattoir), de elasticiteit van een zak aardappelen (dit valt uit te drukken in een bepaalde eenheid; bevestigd door landbouwuniversiteit Wageningen) en bevindt zich op moment t op punt (x, y, 15) (toegegeven door huurder).

Bij snelheden onder 500km/u is zijn luchtweerstand verwaarloosbaar.

Een kat die (in lucht van atmosferische druk) valt bereikt een topsnelheid van ca. 100 km/h; een mens bereikt een snelheid van ca. 200 km/h (Diamond, J.: Why Cats Have Nine Lives. Nature 332(1988):586–587 [1]). Bij een val over 15 m bereikt een mens een snelheid van ca. 50 km/h [2]. Een varken lijkt qua gewicht meer op een parachutist dan op een kat. (Als de luchtweerstand verwaarloosd wordt, bereikt een object bij een val over 15 m een snelheid van ca. 62 km/h.)
David Jansen → Beweren en bewijzen	Remove this comment when resolved!

Vader 

Een mens die een voorwerp met de elasticiteit van een zak aardappelen met een bepaald impuls op zijn hoofd krijgt, gaat dood (bevestigd door forensisch anatoom).

Natuurwetten 

Wetten van de mechanica (vrije val, energie, impuls), gravitatie. Natuurconstanten (gravitatie, luchtdruk, etc.)

Uit deze kennis valt te bewijzen dat de vader, mits hij zich op een bepaald moment t+ε op punt (x, y) bevindt, dood gaat.

Reflectie

Dit voorbeeld maakt de kracht van verdeel en heers en van abstractie duidelijk: de kennis over het marode balkon kan geformuleerd en geverifieerd worden zonder te refereren aan varkens en mensen. Over het varken hoeven we niet meer te weten dan zijn locatie op moment t, zijn gewicht en zijn elasticiteit. Dat het op een balkon gehouden werd, doet er niet toe.

Met deze kennis zou men ook een moordmachine kunnen bouwen. Een dierenvriendelijke zelfs, want een zak aardappelen i.p.v. een varken zou als onderdeel van de machine even geschikt zijn.