Joan had gotten Vic first class tickets so that there would be room for his long legs. He also got a lot of attention from a pretty stewardess. When she bent over him in the window seat to show him how to fasten the seatbelt, it occurred to him that he had never been so close to such a glamorous woman. He then looked at her rather closely as she went up and down the aisle, doing good deeds. He was finally distracted when the big Lockheed Constellation began to start its engines. Each propeller would revolve slowly a couple of times, and then there would be a puff of smoke and a roar. At that point the blades would blur together.
When they taxied, Vic was surprised to see that the wingtips moved up and down independently. The plane wasn’t rigid, but, indeed, was rather like a huge bird. The excitement mounted as they turned and stopped on a runway. After the engines had been tested at full power, the brakes were released and they started to roll. They kept accelerating, as it seemed, forever. Would the plane ever lift? Just when Vic expected them to go right off the runway into Boston Harbor, they did lift with a slow bank over the white-capped ocean.
After his fascination with the stewardess and the aircraft had ebbed, Vic settled back with the reprint of an article Vicki had given him. She had joked, “It’s a paper about logic, which mathematicians usually don’t like. But it sounded like you.”
The paper, by an H. M. Sheffer, wasn’t meant to teach logic, but was
in the symbolism of logic. Vic soon got on to it.
could symbolize ‘Jim is taller than Mary’, and
could symbolize ‘Jim gave Adolph to Mary’. Adolph was presumably a dog or cat, but one never knew.
Where mathematicians wrote "x + 0 =x"
to mean that adding 0 to a number leaves it unchanged, logicians wrote:
(x)(x +0 = x)
meaning, "For any x, x + 0 = x." This distinguished it from the
(Ex)(x + 0 =x)
which asserted only that there is at least one number satisfying the equation.
Using the universal and existential
‘quantifiers’ to symbolize English sentences, ‘Jim gave everything to
and ‘Jim gave something to every person’ became
(x)[Px => (Ey)(Gjyx)]
Literally, ‘For any x, if x is a person, then there is some y (perhaps only one) which j gives to x.’
It was what Sheffer called ‘relational logic’, and Vic rather liked it, wondering if there was anything that couldn’t be symbolized. It would be cumbersome when applied to mathematics, thus causing frustration, but it would resolve some ambiguities.
At this point, the fortyish man on Vic’s left pointed to the paper and said, in an English accent, “I’ve messed around a bit with that. It’s much more elegant than anything we have in economics.”
The word ‘elegant’ again grabbed Vic’s attention, and the conversation began. The other man, Oliver Stanton, was a visiting professor at MIT going home for his father’s funeral, and he asked Vic about his mathematical and other interests. At one point, he said, “It might be interesting to represent the most basic concepts of economics in logic and devise some axioms.”
Vic asked what concept would be most basic, and Oliver replied, “That of a trade.”
Vic wrote on the back of the paper:
and read off, ‘x trades y to z for w at time t.”
Oliver replied, “x and z are presumably persons, y and w may, or may not, be sums of money, and we have some numerical way of stating the time.”
“Have we left anything out?”
“This would be a useful way of recording all the trades that have ever taken place. But economics isn’t just keeping records. It’s concerned with potential trades.”
Vic wrote down,
and read off, ‘x desires to degree u that he himself trades y to z for w at t.’
“Interesting. Should we say that he desires to a certain degree to trade, or that he is willing to trade, or that there is a certain probability that he will trade?”
“I guess it’s a matter of how psychological we want to be.”
“We’ve always known that economics is a branch of psychology, the study of a certain range of human behavior, but we might try to talk about probability.”
“It’s pretty clear, at any given time, that there’s a reasonable probability that any given person will trade something to someone for something.”
“Would you like to symbolize that?”
Vic responded with,
(t)[(Tt =>(x)(y)[( Px&Py&Oxzt&Oywt) => Prob(Txzywt) > K]]
“For any time, if x and y are persons owning z and w at that time, the probability of their trading is greater than k. This might be taken as an axiom.”
“What will k be?”
“Greater than 0, certainly. The closer it comes to 1, the stronger the axiom.”
“And the less probable that the probability judgment is itself true.”
“Yes. You might put in a delay factor. Almost anyone is in the market for something or other, but he might not buy it right at that moment.”
“You’re going to end up with a formula which will run off the right side of any finite blackboard.”
This was said with a laugh, at which point Oliver tilted back his seat and closed his eyes.
Vic tried to sleep, but came fully awake as they descended to refuel in Newfoundland. It was a bright night with stars above and a strange northern look. The propeller of the big inboard engine right opposite Vic’s window was beginning to make a peculiar noise, but he had stopped worrying what would happen if a blade flew off. Looking down, he saw snow everywhere. There was enough light in the sky to make it look white rather than gray, and he wondered if there were creatures able to survive in such a place.
The engines would roar at times, and then fall quiet, evidently to adjust their speed as they approached the runway. Vic assumed that everything was going according to plan, even when there was a loud bumping. It turned out to be the landing gear going down.
They bounced once, and then settled down. Since Gander was a major refueling point, there had to be a town to support it somewhere around. However, outside Vic’s window there was nothing but a flat white wilderness with no trees. It was obviously very cold, and, when the plane taxied, he could feel it being buffeted by the wind. As dangerous as wintery Newfoundland looked, it might be possible to be safe, and even comfortable, with a good tent well staked down and a very good sleeping bag.
Vic slept fitfully on the next leg, but Oliver seemed to be very good at sleeping on planes. He didn’t wake until they were near London, just in time for breakfast.
The conversation soon turned to football. Vic knew that the English played soccer, but had also heard that they played Rugby football. Oliver explained, “Soccer is a gentleman’s game played by roughnecks, and rugger is a roughneck’s game played by gentlemen.”
Vic gathered that Rugby was much more intense, and the reversal did seem odd. Oliver explained, “There’s quite a bit of asceticism in the British public schools, what you call private schools. It may be that the leaders of the society have been afraid of producing an effete class, and have set the youngsters to clawing at one another in the mud.”
“It doesn’t sound as if you wanted to get down in the mud.”
“Certainly not. I had many excuses that got me out of a lot of it. I also managed to be so incompetent that they lost patience with me.”
As they left the customs area, Oliver steered Vic in the right direction, gave him his card, and went off to London with a cheery wave.
It seemed to Vic that, in getting from the airport to Oxford, he was making every possible mistake. But, all along the line, people whose speech he could hardly understand were partially correcting the mistakes. The result was a route with several changes of trains, each time going from a more travelled route to a seemingly less travelled one. Finally, sheltering from the hard rain under the roof of the station platform at Didcot, he was alarmed at the emptiness of the platform, the station, and the dark fields bordering it. Did the English play practical jokes on Americans, directing them to places from which there was no return? Just then, the train for Oxford rolled slowly in and drifted to a stop.
The sun suddenly broke through just before their arrival at Oxford. On emerging from the station, Vic encountered an intense cloud of heavy dark smoke, given off by more steam locomotives than he had ever seen in one place. He had grown up in the age of steam, and, having liked the locomotives, it was good to see them still in action in such numbers. But he had forgotten how the cinders got in one’s eyes.
After getting most of the gunk out of his eyes, Vic saw busses. But he had no idea where they might go, or what form of payment they might accept. He had already discovered that the people who ran such things spoke in indecipherable accents. The people who spoke in clear clipped accents, very likely academics, didn’t look as if they wanted to be asked questions. But he did have a map, previously supplied by Swede. He understood maps, and this one had marked on it his destination, No 12, Pusey Street. It was a way, but it was simpler to walk. Shouldering his pack, he set out.
The smoke thinned as he left the heavily industrial area, and old stone buildings began to appear. In preparation for his journey, Vic had just read a book about Oxford written by the wife of a visiting American scholar. The title of it was, ‘These Ruins are Inhabited’, and it did look as if many of the stone buildings had been around for a thousand years. It was hard to imagine how pipes and wires could have been put in, and he was glad that he wouldn’t be required to deal with them. In any case, he couldn’t tell at a glance whether the buildings, ruins or not, were inhabited.
Eventually, Vic got into a residential area very much like the ones he had seen from the trains, three storey brick houses with party walls extending the whole length of a block. From the trains he had most often seen the little back yards, each with a tiny shed and a scattering of gardening tools. Now, he saw the fronts. The houses, no more than fifteen feet wide, fronted right on the sidewalk with a single step up to the door. That, at least, would keep a moderate rain from flooding the floor.
On the next street, the houses were set back a bit, sometimes with steps leading up to the front door and other steps going down to a basement door. He guessed that these houses were more expensive, and suspected that Swede would have chosen them for his investments. He turned out to be right. The house on Pusey Street was one of the largest he had seen.
When Vic went up the front steps and knocked on the door, there was no immediate answer. Then, when he knocked again, there was a cry from down below. An older woman with a bandanna around her head was saying something to him. As Vic went down to speak to her, he was surprised to find that, despite her appearance, she spoke easily in what he took to be an elevated accent. In any case, she had already been warned of his appearance and said,
“I have a bed-sitter ready for you. Mr. Hanson said, correctly as it turns out, that I’d be able to recognize you on sight.”
There seemed to be a half joke about that, but Mrs. Bramble, as she introduced herself, didn’t explain it. Leaving off her housework, she led him upstairs to his room. A ‘bed-sitter’, short for ‘bed-sitting room’ was the English euphemism for a room in a boarding house. Mrs. Bramble said briskly,
“The lav is down the hall to the left.”
There was a sink in the room for washing and tooth brushing, and Vic suspected, too strongly to ask, that there was no shower. Even in his semi-homeless days, he had been able to take showers in gyms, but it now seemed unlikely that any gym in Oxford would welcome him. Anyhow, the bed looked adequate. Having missed most of a night’s sleep, he dropped on to it fully dressed as soon as Mrs. Bramble left. He was thankful that she was too business-like to linger with helpful advice.
Breakfast came with the price of the room, and, in the morning, Vic followed the others down to the basement breakfast room. Mrs. Bramble was presiding, but there was also a cook in the kitchen and a waitress. The food looked pretty horrible to Vic, particularly the sausages, but he settled for eggs and toast. The toast was harmless, and there was an unusual bitter marmalade which was quite good.
There were some ten people at the table, and there was conversation, both between pairs, and in the larger group. Most of the men seemed to be travelling salesmen selling to the varied industrial and commercial interests in the city. One, in introducing himself to another, used the phrase, ‘commercial traveler’, which did seem to set him apart from the sleazier American version, the ones who were the subjects of so many dirty jokes. There was also a man and wife who seemed to be tourists of the South African variety. In a very few sentences, they let it be known that they weren’t tourists of the American sort, but, rather, citizens of the British Empire paying a visit ‘home.’ Vic could see that, even in the breakfast room, there were all sorts of shades and subtleties of accent and attitude which had to be negotiated.
It was on the second morning that an attractive young woman with rich brown hair cheerfully addressed Vic, “You seem to be the only American with us this morning.”
Vic wasn’t surprised that she didn’t have to ask to know that he was American, and he replied, perhaps a little sheepishly. She caught his tone and replied, “I’m married to an American. I’m just waiting here for my visa to join him.”
It was easy for Vic to talk with a somewhat older married woman who was much more worldly than himself. Among other things, she was a fount of information about the English customs Vic would have to navigate. They ended up as the only two left at the table with their coffee. Mrs. Bramble, seemingly approving, said, “Stay as long as you like. The others are always rushing off to business.”
At that point, the young lady introduced herself as Elizabeth, remarking, “I’m originally Austrian, so it would be spelled with an ‘s’. But, since I’m about to be American, I’m using what our friends here call the ‘zed.’ Actually, I like the Italian version, ‘Elizabetta’, the best.”
“I’m plain old ‘Vic’.”
“We seem to be the only ones who don’t have to go to work.”
Vic gave a brief sketch of his position, and she replied,
“I don’t envy anyone trying to collect money. Anyhow, my husband’s best friend, an American in one of the colleges here, is coming shortly. We’re just going to wander around and drink tea, and I’m sure he’d be happy to have you come with us.”
Vic wasn’t so sure that he’d be so welcome, but Elizabeth replied,
“He’ll be delighted. I think he’s a little bored to have me on his hands at this point, and you’ll provide some variety.”
The friend, Seth Kennedy, was an astronomer already entrenched in one of the more elite Oxford colleges at a surprisingly young age. He did seem happy to meet Vic, and he suggested a tour of the tea shops.
Kennedy wasn’t the first bright young man Vic had known. In Brownsville, there were lots of smart Jewish kids who knew a lot and loved to argue. The style was rough, to the point, and sometimes enlightening. They could often embarrass their teachers, and showed the mediocre ones no mercy. But they weren’t smooth, much less sophisticated. Every discussion was a combat, and the losers were ridiculed.
There was nothing like that in Claremont, but there were lots of bright New York kids at Harvard. They had mellowed a bit, and, apart from an occasional section man, it wasn’t so easy to embarrass the teachers.
As opposed to this element, there were the brighter of the kids from New England prep schools. They said, “I’m not sure about that’, instead of, ‘bullshit’, but they argued just as tenaciously. The graduate students often fell into one of these categories, and Vic had engaged some of them in discussion. Indeed, as often as possible. It was an effective way of learning without having to pay anything.
In contrast to these people, Kennedy was a young man who had already proven himself. He didn’t have to have any sharp edges. In that respect, he was a much younger version of Ken and Yuri back in Cambridge, even to the extent of making fun of himself. In addition, he was tall, handsome, and, Vic could hardly avoid thinking it, elegant.
It was said that no American could be considered a gentleman in England. Henry James had ‘very nearly’ been one. But not quite. Ernest Hemingway, for example, had been told that, while he could never hope to be an actual gentleman, he might be taken for one in Italy.
Wandering around Oxford, Vic had seen some people who, by their dress and manner, were obviously of the elite. They were the sorts of people who were taken for gentlemen, not only in Italy, but in England. One, driving his sports car, had forced another motorist into a roadside bush. However, with a cheery wave and smile, he had pardoned himself and driven happily off while the other, a woman, dejectedly untangled her car from the shrubbery. There were others who were rude to waiters and serving people, not with any ill intent, but simply because these were ‘persons whom one could not know.’ It did seem odd. Vic wondered if these folks realized that Kennedy was, in fact, what they only thought they were.
As they walked around and sat with tea, there was a series of encounters with people who hailed Kennedy and wanted to talk. In each case, he carefully introduced Elizabeth and Vic, telling each enough about the others to generate a conversation. It amused Vic to see that, while these people fairly obviously wanted to talk to Kennedy, and not his companions, they were prevented from doing so. However, there was one young man, a statistician named Howley, who wanted to talk with Vic. Indeed, he finished by giving Vic his card and asking him to call.
After they had parted, Kennedy remarked calmly,
“I think it would be better not to call him. He’s presently being had up for stabbing his boy friend. It seems to have been a matter of conflicting loyalties.”
It turned out that the boy friend hadn’t been seriously injured, but this sort of homosexuality was new to Vic. There had been some in Brownsville, but among quite low level people, not anyone remotely like Howley. Elizabeth, seeing that he was puzzled, asked why. When Vic explained, she replied, "Homosexuality is probably more accepted here, and it very seldom leads to violence. When it does, it’s hard to know what sort of face to put on when meeting the participants.”
“I’m learning something new every ten minutes these days.”
“You seem to be on your own at a very young age.”
“I’ve certainly left my family far behind.”
“My family mostly disappeared in the war, and I also lost a fiancé.”
Elizabeth looked sad at that point, and Kennedy put in, “Here in Europe, a great many people were killed in the war. Those left behind have had to pretty much start over.”
“It didn’t help to be born into a country that went on to lose a war. The boys in my generation all belonged to the Hitler Youth, which was really just the German version of the Boy Scouts. But it sounds horrible.”
She said it with a smile, and Kennedy asked, “You were in something like the American WACs, weren’t you, Elizabeth?”
“When I was eighteen I was in the Helferinnen von Dienst , the ‘Little Helpers of the Services.’ It was the Luftwaffe branch, but we did mostly clerical work. Again, the name is more than suggestive.”
It was, indeed. Vic wondered if a ‘little helper of the Luftwaffe’ did more than keep records of airplanes needing maintenance. Elizabeth elaborated, “It was there, of course, that I met Gerd, the pilot of a transport plane. He didn’t exactly have the glamour of a Red Baron, but, at the time, almost any pilot was a minor celebrity.”
“It must always have been dangerous.”
“Oh yes. Gerd was killed in an odd way. The Red Baron of the second war, Werner Molders, wanted Gerd to fly him from Russia to Berlin to attend the funeral of Ernst Udet. Gerd refused to take off because the weather was so bad. But Molders, a colonel, ordered him to. Gerd did, and they were all killed. Molders’ death was a huge event, but Gerd was put down as, at best, an incompetent. As the bereaved fiancé, it was almost as if I shared the blame.”
Kennedy shook his head, “Vic, Elizabeth has been put in some very strange positions. But see how cheerful she is!”
“Yes. I left an odd situation back in America, but I’m pretty cheerful myself.”
Vic was determined not to spell any beans about the Mafia, or indeed, the likelihood that his father had been tortured to death by his inability to produce hidden money. He therefore concentrated on the awfulness of his mother. It was a funny thing because he’d never thought that she was really evil, and he did have some sympathy for her present state.
Elizabeth said, “I wasn’t thrilled with my mother either, but I do have some guilt over not feeling worse about her loss. Do you have the feeling that you could have managed things better with your family?”
“Well, yes. If I’d been like them, it would’ve been okay. A lot of it may be that they just aren’t intelligent. Which, as they say, they can’t help.”
“It’s a wonder that you’re so smart yourself. You must be some sort of genetic throwback.”
When Vic went out the next morning to look up one of the mathematicians, he was wondering if he really was smart enough to be at Oxford. He caught Frank Collins as he was leaving a lecture hall and nervously introduced himself. He needn’t have worried.
Collins was an Australian who spoke with some sort of mixed accent, but had Brownsville gestures. Of medium height and wiry, he looked as if he played soccer, but not rugby. He even recognized the assumed name, ‘Ross’, that Vic had been using ever since leaving Claremont. Collins added,
“I’ve had letters about you, young man, and I saw that little piece you had in the journal.”
“It’s only two paragraphs long.”
“The better for reading. Ken Martz said you have lots of these little proofs. By the law of averages you can eventually put some of them together to get a big proof.”
This was a joke, and Vic was now relaxed enough to be amused. Collins eventually suggested, “If you can stand the warm English beer, we could drink a pint some night next week.”
Vic was sure that he could deal with the warm beer.