Sally Aston, the new principal of the barely existent Social Tech High had one student, found within a few days of the trio’s return to New York. John Calder was racially ambiguous, thinking of himself as black or white, depending on circumstances. He had three white grandparents. The fourth, now deceased, had been a light skinned Afro-American woman who was probably half-black. John might have had some Hispanic blood too, but wasn’t sure.
John’s new-found love, little Grace Ling, was not a racial mixture. She was a third generation Chinese-American. Her parents had been born in New York’s Chinatown, but her father had been raised in suburban New Jersey, while her mother had been raised on Long Island. Now living with her family in a pleasant district of Manhattan, Grace felt and acted like an ordinary member of her mostly white community.
This couple, two out of only three yet part of Social Tech High had each been invited personally by the two teachers, Sally and Ellen. John’s father had gotten his whole family to register with Technological Fantasies and undergo the registration dialogue, though he had been only seeking a new job, himself.
Grace’s parents had been seeking a better educational situation for her, unhappy with the way the other kids in her former high school had been holding back, not seeking friendship with her. She had been too conspicuously Chinese for the white students to be comfortable around her, but as a third generation Chinese-American she was just not Chinese enough to join the clique of her racial equals.
It had been somewhat disingenuous for the two teachers to approach Grace’s parents with the promise that the girl would receive personal attention from appropriate teachers while being made part of a group of truly compatible friends. What Sally and Ellen had actually planned was to grow the school to include one more student. And they had in mind one specific relationship to lead to that growth.
They would not hide this from the students. Grace had met with John and the two teachers then both of the young people had been told all about how the school was to develop.
“We think you and John might be friends, Grace. In the meanwhile you might study together. Neither Dr. Smith nor myself will teach your preferred subjects, Grace, but we will get you teachers soon. In the interim Dr. Smith and I will supervise what you do over the summer. I’m sorry we had to ask you to give up you summer holidays for this project.”
“What will we be doing?”
“Dr. Aston and I have picked out a stack of school textbooks which look suitable for a dozen different subjects. We’d like you to browse through them looking for topics which might interest both of you. That is productive work which will keep you busy for quite a while. Meanwhile, Dr. Aston will meet with John sometimes. We’ll get Grace her teacher when we can.”
In fact Sally and Ellen did not constrain the search very much at all. Instead of asking the software to find a teacher for Grace, they asked for a person, teacher or student, who would join the school as someone compatible with either of the two existing teachers or the two existing students.
The person they found was another teacher. Mrs. Alma Renwick was really a junior high school teacher, who would teach Grade Seven if possible. Since the youngest pupil would be in Grade Nine, Alma would teach that. The Tech Fantasies software described her as a true polymath, able to teach almost any subject. She had studied geography and history at college, among many other subjects, so she could help Grace with her work, but would not be the ideal teacher for a high school senior.
What tied the 30-something Mrs. Renwick to the existing school members would be her probable close friendship with Sally Aston.
Sally was more linked into the school than anyone else. Her close social connections included a probable friend, Ellen, plus one student, John Calder.
Until proper students for Alma Renwick could be found, before proper teachers for Grace Ling could be found, Alma the polymath would help John and Grace look through the stack of school textbooks for topics which might interest both of them.
The next person found was a student compatible with Grace Ling, Clarity Bond, a girl interested in psychology and sociology. It would have been nice if Clarity was compatible with Ellen Smith, since this one student could then link up two people, but unfortunately she was only slightly compatible with the teacher whose interests matched her own. Similarity of interests was not enough.
Clarity joined John and Grace in their search for mutually interesting topics amongst the pile of possible textbooks. With Mrs. Renwick’s help they found a book which contained material of interest to all three of them. It was an introduction to behavioural geography. Though not ideal for her, Alma Renwick started a senior class in behavioural geography with these three students as the only participants.
The size of the school was now seven, three teachers, Sally, Ellen and Alma; four students, John, Andy, Grace and Clarity. Considered as a network, or what computer scientists misleadingly call a graph, the school was a tree structure, fully connected but with no loops. Any person, a node of the network or vertex of the graph, could be considered the root of the tree, but Sally had more connections than anyone so far. Since she was also closely connected to the others in Tech Fantasies and was the principal of the school, it would be natural to consider Sally the root of the tree.
Over the next little while the structure grew and grew as both teachers and students were added. Meanwhile work was underway to renovate an old warehouse not yet gentrified but near the East Village. In September the small collection of teachers and students moved from the Tech Fantasies office to the partially renovated building, and felt more like a real school.
By that time, a real history teacher had been found for Grace Ling. Now John and Grace each had one teacher to study with. Their sexual relationship was a hot one, and no longer the only one in the school. But the structure of the school was still a tree, with no loops. No teacher or student was part of a cycle within the structure.
It would take another two months before the first class of 8 students could be created.
During this time much communication and education flashed around within the school. Where a student had no teacher they were at least connected to another student, to learn from. A few students had the benefit of two such connections. Most of students did have a teacher, though, and learned quickly the one subject they shared.
Adding new teachers and students was easier now. Only students of good academic abilities were considered, but they could join the school if connected by mutual compatibility to any one of the growing number of people in it. The more people in the school, the faster it could grow.
Though formal education of high quality only took place when a student and teacher shared a common subject, there was a lot of informal education within a structure based on such strong social relationships. Everyone was learning, even the teachers.
The first class to be formed consisted of 8 students, including John and Grace, and was nominally a senior behavioural geography class, though it would end up discussing a wide variety of topics.
The teacher assigned to this topic had a close friendship with Alma Renwick but was not connected to any other teacher or any student in the school.
“As some of you may know”, Dr. Elliot began, “Behaviour Geography is closely related to Social Geography, the intersection of sociology and geography, but adds an additional field, that of psychology. Some linguistics is considered as well. Usually Behavioural Geography deals with geographic regions, perhaps with whole nations, sometimes even the whole world. I want to start us off with a toy model, our own school.”
“How can that be considered geography, Dr. Elliot?”, Grace Ling asked.
“We are actually dispersed geographically. This room will be for the one of 8 for this grade, and will be used for the social sciences. Nearby are some rooms to be used for mathematics. Near them are some rooms to be used for physics and chemistry. We will discuss statistics, which will also be handled by the nearby mathematics classes. Those classes will discuss algebra and basic calculus, so fundamental to physics. The geographic distribution of classrooms mirrors the way subjects are interrelated.”
“But subjects are related in many ways, aren’t they? Where are the history classes, relative to us?”
“A little further away than they should be. That’s one reason behaviour geography is hard to apply.
“I heard something about the seating arrangement within this class, Dr. Elliot”, Clarity Bond mentioned. “Is it important? Could it be considered geographical in the microscopic sense?”
“Yes, Clarity, and I am very glad you asked that question. I was going to bring it up next if nobody else did. I asked you to sit in assigned places for a very good reason.”
The room had a quarter circle of student desks, 8 of them, side by side, one curved row of students. They faced the teachers desk. Dr. Elliot was sitting on the edge of that desk, facing them. She could see all of them quite clearly, without moving her head.
“For those of you who haven’t heard, this class consists of mutually compatible people. Each of you is at least a little bit compatible with all the other members of the class. It was very difficult to put together this class, and we may swap people with other classes when more appropriate people arrive. The seating order has been chosen to make the most of what compatibility we have. We would have liked to place each of you between more compatible ones, but that has been hard to do. Can anyone tell me why it was so hard?”
“It must have been hard to estimate compatibility”, Clarity said.
Dr. Elliot turned to John Calder with a questioning look. “John?”
“I think making estimates is the easy part. The hard part is doing the combinatorial work. There are so many possible arrangements.” John had been studying math with Sally Aston, and though her speciality was not discrete mathematics, she had taught him some of it. Actually this question was an easy one to answer. Sally had just taught him one improvement over the first solution that had come to mind.
“Suppose we pick one of the 8 to sit at the extreme left. That’s 8 possibilities. Now we pick one of the remaining 7 to sit beside him or her. So we have 8 time 7 possibilities, 56 in all. Then we keep on going, picking one of 6, one of 5 and so on. The result is factorial 8, which is, uh, just a sec, 40,320”, he said, consulting a pocket calculator. But I think swapping the row end to end changes nothing, so the real number of choices is 20,160. Somehow you had to find the best arrangement out of over 20 thousand.”
“Good, John, that’s the right answer. So we first had to estimate compatibility, as Clarity said, then find the best choice from among so many. Is that all we had to do, or is the problem harder still? Anyone?”
There were no takers.
“Well, I want you to consider small group dynamics and their affect on compatibility. John and Grace are pretty compatible, if any of the school gossip is true. At the moment we have Clarity sitting next to Grace. I think they are close friends, right?”
The class, almost as one, nodded at her. It was a very small school.
“Good. So, most social situations are dependent upon context. Clarity sitting where she is provides a social context for John and Grace. A rhetorical question, just for you to consider – how would John and Grace’s feelings and behaviour differ if it was Andy sitting next to Grace? Grace would be sitting between two young men, John would see a possible rival seated beside his Grace. Let’s not go into this, which would not be fair to any of the individuals involved, just think about it.”
When the class ended, John and Grace went off together, probably to find a quiet nook for a kiss or two. But John felt a bit upset. He liked having the lovely Clarity nearby, though satisfied with Grace. He knew he would not like Andy sitting in that place. The teacher was right. Context is important.