The little party at my bed-sitter had a number of consequences. Arnold Buckmaster became very nearly besotted with Brenda. Flowers and messages arrived in great profusion. She asked me to come over one afternoon to discuss ways of getting rid of him.

We were alone, for once, in her large comfortable drawing room. I wished that we were discussing something else, but recognized my obligation to a friend. I had heard it all before, of course. Here was another man who, while hardly my type, seemed to me to have nothing much wrong with him. But Brenda spoke as if there were not much right with him. She had formerly had affairs first, and then spoken of the man in this way afterwards. This time, she seemed to be skipping the sexual part. I didn't know whether that was an improvement, but pointed it out to her. Brenda has always liked to be told home truths about herself. I then asked her to describe her ideal man. She started to laugh me off, but I replied,

"Physically, I don't see how you could improve on Buckmaster. He also ...."

She cut me off.

"Oh Thomas, you don't understand. He looks all wrong. It doesn't matter how many muscles a man has, it's a certain coolness ..."

"He's a naval officer. I bet he'd stand on the bridge of a ship with perfect aplomb while other ships fired fifteen inch shells at him."

"Women don't care about that. I'd rather have a dashing scoundrel who'd hide in the chain locker when the guns started firing. Anything is better than heavy honorability."

I smiled and Brenda blushed. She had let something out, and we both knew it. She changed the subject, saying,

"Incidentally, I didn't think too much of that little bint you and Ralph take turns with."

"Muggs? What's wrong with her?"

"She's all right, I guess. I'd just expected something madly glamourous."

That was puzzling. I had never said anything of the sort, and it was unlikely that Ralph had. I answered,

"She may not be beautiful, but she's far nicer and more intelligent than one would have any right to expect."

"I suppose so. Perhaps I should take up the same profession. I could use a little extra income."

Brenda had always talked that way, and I took no particular notice. She then asked,

"How much do you pay her?"

I had told her before, and, considering her fascination with the subject, was surprised that she had forgotten. In any case, I said,

"Three guineas a time."

The price, which I had insisted on, was more than the going rate. It was also a joke between Muggs and myself, and, for that matter, between Ralph, Muggs, and myself. The guinea, now disappeared, was twenty one shillings to the twenty shillings of the pound. The English have always liked absurd monetary units, but this one was used only by such people as antique dealers and fashionable doctors. I was enjoying the thought of being a person who got such bills when Brenda answered,

"I'd do it for that."

I was getting tired of her pretensions. There was no one good enough to marry her, but she'd hit the streets for three guineas a crack. I was composing a suitably sharp retort when she stood and pulled her dress over her head. I must have looked aghast. She stood there with her characteristic little smile.

"What's the matter, Thomas? Have I departed from the standards of approved behavior? You pay Muggs, so you must want it. Aren't you willing to try an alternative vendor?"

With that, she continued to undress. She was bigger and curvier than Muggs, but still slim-waisted. I wanted her very much, and must have showed it. She said,

"This doesn't mean the world is turning upside down, Thomas. It's just sex, that's all. I'll kill you if you send me roses afterwards. Now, please, unhook me in back. You can give me the three guineas before you leave."

I followed Brenda's instructions thereafter. It was nice, in fact very nice, but actually not very different than with Muggs. It was, as Brenda said, just sex. Afterwards, she went through my pockets and counted out the money. She also decided to give herself a tip of one shilling sixpence.

I was still lying on the rug, where the activity had taken place, but Brenda was up getting dressed. Obviously delighted, she said,

"I've always wanted to be a prostitute. Now I am one. I'll have to buy something that costs exactly three guineas, one and six to commemorate the occasion."

"Are you going to do business with Ralph on the same terms?"

"No. He's my relative. Besides, Jane wouldn't like it. She doesn't even like his going to Muggs."

I began to pick myself up, and replied,

"I might understand if she intended to marry and have sex later, but I understand she's sworn off it permanently. In that case ...."

"She's still got normal female jealousy. Not in an extreme degree, but she does love Ralph. No one wants a loved one to be with someone else."

After I left Brenda's house, I was, for a while, a very confused middle-aged man. In order to clear my head, I walked down to Camden Town, and then over to Kings Cross station. My confusion remained, so I walked another mile or two, down the Euston Road, finally ending up in a little cafe in the Marylebone High Street. One thing was, by then, clear. Brenda hadn't done it for the money. No matter what she said, it couldn't be enough to make any difference. I had the impression that she meant to repeat the exercise once a month or so, and thirty six guineas a year, even in 1936, was a small sum by her standards.

The other thing that was certain was that she didn't want me to become sentimental or romantic. That was no problem. She had always been for me the epitome of all that was exciting, glamorous, and desirable. But I had never loved her. I still didn't. Therefore, I reasoned, matters stood very well. In addition to Muggs, I could have, not only Brenda's continued friendship, but a sexual partner who would be worth, on the open market, far more than three guineas a time.

Happening to be in the neighborhood, I drifted toward the Walker and Holtzapfel establishment to see if Ralph was working that day. By contrast with Brenda's clearly delineated goal, that of rebuilding the Sanderson fortune, Ralph's activities appeared to be much more diffuse and less purposeful. He had acquired a home of a sort, a paid mistress of a much better sort, and, in Jane, an object of love so bizarre as to hardly belong to any sort at all. In addition, he had taken a part-time job of which I could only approve.

All this was very well in its way. The primary object in taking Ralph to England had been to get his finances under control. That had been well and truly accomplished. However, none of this seemed to lead anywhere. What, one wondered, was he trying to accomplish in life?

When I first met Ralph, he was a boy of sixteen or so. Wilhelmina Sanderson liked to have him around, and encouraged him in many activities of a harmlessly foolish sort. He collected postage stamps, which she bought him in profusion. She would have bought him anything else, but he had never seemed to want much.

He did engage in a practice that could only be described as playing with numbers. He was fascinated by progressions. He would give me a string of numbers and want me to guess the next. It seemed silly to me, but Wilhelmina encouraged him, so I would have to guess. I was always wrong, and I never even understood why. Oddly enough, she could often guess the correct number. After a time, I was no longer subjected to this humiliation. Either Ralph or Wilhelmina, or both, must have taken pity on me.

I had recently found out that Ralph was still playing games with numbers. Evidently he had never stopped. It wouldn't have mattered, except that, in conjunction with the matter of Muggs, it created something of a rift between Ralph and Jane.

It was Brenda who told me that Jane had said something insulting about numbers to Ralph. I replied,

"Here's a young man who can't be insulted whatever one says to him. But he storms out of the room if one speaks disrespectfully of, say, the number three."

Brenda had that look of hers that she produced only when she thought someone had said something outrageously unfair or unreasonable. She retorted,

"It's not the number three, of course. Ralph is concerned with infinite numbers."

"When he was younger he played with small numbers. Now that he's growing up, he plays with larger ones. What difference does it make?"

"I bet you're one who believes that you get an infinite number by adding one to the largest finite number."

I knew that she was making fun of me, and stopped to think. After a moment, I realized that there was no largest finite number. One could always add to it and get a larger one yet. I said, somewhat sharply,

"Then there are no infinite numbers. How could one possibly count up to one?"

"Think of all the finite numbers that there are. Taken together, they form a group or set. Since there is no largest finite number, that set has an infinite membership. If you like, there are an infinite number of finite numbers."

When I saw Muggs a few days later, I asked her if Ralph talked with her about numbers. She assented as if it would have been remarkable if he hadn't. Since it didn't seem to involve a breach of confidence, I probed a little further. Muggs also mentioned infinite numbers. It now turned out that there was more than one such number, and that some were larger than others. Beyond that, Muggs was rather vague. I had the impression that Brenda had had some knowledge of the subject independent of Ralph, but that Muggs had learned everything she knew from him. I did say to her,

"Ralph didn't talk with me about railways because he didn't think I was the type. Evidently he talks with everyone but me about numbers. He must think I'm not the type for them either."

Muggs was consoling.

"You talk very nicely about history. Not everyone has to talk about everything."

"Jane doesn't talk about numbers either. She evidently insulted Ralph by making light of them."

"Oh, I wondered what had happened. He's been upset lately."

"Muggs, how could anyone, particularly anyone as easygoing as Ralph, be so upset by such a thing?"

"Well, I have the impression that most of Ralph's time and energy goes into mathematics. I do know that he's trying to solve some unsolved problem. From the little I've seen of Jane, she might have been rather tactless."

"She might indeed. I suppose that she said or implied that he was wasting his time."

With this conversation in mind, I hastened down Paddington Street past the pretty little park and the squalid gents' restroom where cab drivers gather to relieve themselves, smoke, and devise new ways of cheating their customers. I was determined to get to the bottom of this business about numbers. Unfortunately, Ralph wasn't in the shop. I loitered for a while, and ended up buying a new goods wagon.

I happened to see both Jane and Brenda a few days later when I stopped by for a drink. Jane joked about her little contretemps with Ralph, but I could see that Brenda was somewhat concerned. In any case, as I had another sherry and began to swim a little, I made common cause with Jane against the incursion of mathematics into decent society. Brenda, taking the opposed position, said,

"God knows, I'm far from a mathematician, but I did learn a few things in college, and I'm glad I did. There are a few basic ideas that are really rather beautiful. One might expect a poet to appreciate them."

I strongly suspected that Brenda had read the poem by what's her name which contains the claim that Euclid alone has looked at beauty bare. I responded to that twaddle in a spirited fashion, causing Brenda to reply rather soberly,

"A little knowledge of some sort is important to women, Thomas. It's so easy for us to get sunk so deeply in our relations with men that hardly anything else seems to matter. I had lunch alone the other day, and I heard everything the two women at the next table said. One of them was mourning her desertion by a man, and talked of little else for an hour. I've been in states like that myself, so I could sympathize. On the other hand, I realized that this poor woman had no objectivity left at all. Everything was different now that she was on her own. The whole world was reeling, so to speak. If she had had just a little real knowledge of anything impersonal, it wouldn't have been so bad."

Jane responded,

"I don't have anything at all that you could call knowledge. I'm only interested in buying nice clothes and spending money generally."

Brenda caught her up.

"Someone of whom that's true would be much less intelligent and interesting than you are."

"Ralph says things like that to me, too. He was also upset because he took me to a concert at the Albert Hall, and I didn't go into transports of delight over the pianist. Evidently he was the best in the world at something or other. I was just bored, really."

It was hard to know how to reply. I was happy to join Jane in tossing mathematics into the dustbin, but it looked as if music and art might soon follow. Anyway, at that moment, there was a rumpus at the door and Arnold Buckmaster arrived. It transpired that Brenda had finally agreed to go to a matinee with him, and he sat down for a quick cup of tea.

One wouldn't have guessed from Brenda's behavior that she had been resisting Buckmaster so strenuously. Still, though she might do many surprising things, Brenda had the kind of consistency and rationality which dictated that, if she did go out with a man, she 'd be nice to him. It was Jane, I thought, who might turn such an outing into a disaster if she were in a bad mood.

I could easily have left when Brenda and Buckmaster did, but, when I made a motion to, Jane offered me another cup of tea. I remained, I think, out of curiosity. I had been intrigued by her from the beginning, but didn't even know where she came from or who her father was. Looking back on it, it seems to me that I only wanted the sort of elementary information which would allow me to place her more precisely in English society, and perhaps to understand the kinds of forces it had taken to produce her. In the event, I found out something rather different.

We started by talking as if Brenda had still been there, but it wasn't long before Jane changed the subject abruptly.

"You go to that same woman Ralph does, don't you? The one called Muggs I met at your flat."

It seemed that Jane also had an agenda for our little discussion. I could see that, like Brenda a few days previously, Jane wanted to talk about prostitution, albeit with a different object. As I drew a deep breath, I was glad that she didn't know that I also "went" to Brenda.

Jane soon made it clear that she thought it revolting that any man would go to a prostitute. It was also a major, but perhaps undeclared, source of friction between herself and Ralph. I replied,

"For me it's quite simple. I do like sexual intimacy, but I've never found anyone I wanted to marry who also wanted to marry me. I suppose I might get some sex by pretending to love someone, and then abandoning her, but this seems a good deal more honest. I was lucky enough to come upon Muggs. It'll be a sad day for me if she marries and I have to pretend to be only her literary employer at her wedding."

"Do you think she wants to marry Ralph?"

This, of course, was the crux of the matter. Jane might refuse sex with Ralph, but she wanted to have him exclusively just the same. She feared competition from others, particularly those who took "unfair" advantage of him with respect to his carnal appetites. I managed, I think, to somewhat reassure her. I also discovered that, apart from sex, she was willing to do whatever she had to in order to keep Ralph. Already knowing how attracted to her he was, I concluded that she would succeed. I didn't share that conclusion with Jane on the assumption that she might be nicer to Ralph if she felt some uncertainty concerning his affections for her.