During the first two weeks of the fall term at Social Tech High, Kelly Phillips went about from class to class largely ignorant of the can of worms she had opened.
She had made two key suggestions. The first was that the division of students between city schools could let the city’s school system as a whole mimic the compatibility model Social Tech used. That could be applicable only to a city as dense as New York, with so many schools, but it would be possible. In response to the initiative put forth by Tech Fantasies, using the Social Tech High name to attract participants, a few teachers had changed schools, making those schools more distinctive. But not much more distinctive. In response to the same initiative, some parents had used the software and found different schools for their kids to attend. But not many parents and the schools were still not distinctive enough for this to matter.
Much more would have to happen before Kelly’s idea could make a real difference, but it was full of possibilities. Kelly’s mother would keep her beloved daughter informed of progress, but warned her that it was going to be slow. “What is important is that we’ve given the schools some hope of almost catching up to Social Tech, Kelly. None of them could have done so individually, without our enormous number of international applications, but between them there is hope.”
“So they’ll first divide the kids between schools, like I suggested — when they can, that’s the hard part – but then it will be easy for any one of them to put the kids into the right classes?”
“Well, easier. Only a very few have our small classes, but still, it will make a difference. I think we’ve sold them on the idea of making their profiles as distinctive as possible. They like being distinctive. Schools always have.”
“How different are they?”
“Not much, but they are working on it. Some are doing profiles for classes, too. It looks like in the end all schools and all classes will have somewhat different profiles. Within a school, there’s lots of flexibility. They can swap kids between classes without much trouble. Getting them in the right schools is harder. Not much progress yet. I’ll let you know.”
“Maybe next year will be better.”
“I hope so. Now they want to do it. We’ve talked them into it. That’s what’s important. I am very proud of you for suggesting it.”
“Thanks Mommy. It was just an idea. You raised me to think and say what I think. You might regret that, someday.”
“I am almost beginning to regret listening to your other suggestion, about making profiles audible. Oh, Kelly, if only you knew what a can of worms that opened!”
“Sorry. I guess that came from playing and talking about music so much at school. We have two classes based on compatibility without really a subject to study. The one at the end of the day has really tight links in it, because there is no grade restriction. Homeroom class in the morning is just for us Grade Sevens. Since we have a music teacher as homeroom teacher, that is usually what we do. Music.”
“Wherever it came from, it’s quite an idea. Caused us so much trouble, though.”
Beth Green had been right that it was in principle possible to do spectral analysis of profile data, producing a spectrum which could be mapped into the audible range. Sally had been right in saying that this would only produce something which made sense if a lot of work was done on the rows of data. Neither had anticipated the amount of work that would be necessary.
Dr. Paul Grey, the new school principal was not a mathematician, but he appreciated both the basic idea and the need for a lot of mathematical work to make it happen. “OK”, he said, “suppose that I want to listen to our school. Let’s say that I should hear a sound, a single note. Do you know what to do to get me that sound?”
“Not really. We know of a lot of mathematical transformations”, Sally replied, “but we are not sure how to apply them.”
“There should be a right way and a wrong way, though. Both mathematics and music seem to be non-arbitrary languages.”
“Yes, they do. That’s the problem. We don’t want to introduce an arbitrariness by inventing some mapping between our profiles and the sounds which will represent them.”
“Have you gotten anything I could listen to, anything at all?”
“Well, yes. I guess. Let me just fetch a file from my home machine.”
Sally got a file and played it. It was not just noise, there was a definite tone colour to it, but it was not exciting. “That is from a matrix created by drawing out of the files one row of questionnaire answers per student. Then we reduced the whole matrix to a single spectrum. Actually we are listening to only the magnitudes, not the phase information, which helps us locate the source but doesn’t affect our sense of tone colour. Only the magnitudes determine what it actually sounds like.”
“You can really represent a whole table full of information by a single sound?”
“Yes, through well-known and non-arbitrary transformations. What is arbitrary is the way the matrix is composed, how the table was created.”
“Can you also create sounds for the profiles of individual people?”
“Yes. A row of the matrix would represent a person. A different kind of transformation can turn just that row into a spectrum.”
“Is the sound of the school as a whole just the sum of the sounds of the individual students?”
“Well, it could be, but that’s not how we get the audible representation of the collection of individuals. If we did that, then there would be just a big blurry indistinct mass of sound.”
“Oh. Well, I won’t probe you for details, which I wouldn’t understand anyway. Can you just play me the sonic representations of a few individual students chosen at random?”
Sally did. “Hey, they do sound distinctive. Not so much like noise. Are you sure the school’s sound is not just the sum of these individual sounds?”
Sally would have to demonstrate. “Here let me just add up all the student sounds.” The result was a different kind of noise.
“More like the sound of Grand Central Station”, Paul said, “where a thousand people are all talking at once. Entirely different. I can’t explain why, but it is different.”
“Well, in the case of a lot of different sources, the actual shape of the spectrum varies from time to time in an apparently random manner. The school sound is technically the convolution of a single function, the formant of the sound, with an underlying noise.”
“Too technical, but I can hear the difference. Have you played these sounds for Kelly?”
“No. I guess I should.”
Kelly listened to the audible representation of the school. “No, that just doesn’t sound right to me. I think it should be like this:”, Kelly said, playing a big chord on her electronic keyboard with both hands. “Or this:” Another big chord. “Actually, I think it should be like this:” She played a slow chord progression, then looked expectantly up at her mother.
“Damn.”
“Mommy. Watch your language. A fine example you are setting for your sweet innocent little daughter.”
Sally didn’t really hear Kelly. She was lost in thought. “A chord progression. It is so obvious. But what does that mean? Would it be the progressive development of the overall pattern of education during the year?”
“Maybe. I guess. Not really. Actually, I’d think of a school as described by a whole piece of music. Not program music, like ‘The Moldau’, or ‘The Four Seasons’, but just some abstract piece of music. A school might sound like a piece by Beethoven, or like one by Bach. Do you see?”
“What a nuisance you are, kid!”
“Mommy! Did I mention the sweet innocent little daughter part?”
“Sweet, yes. Innocent, I hope so. Not so little anymore. But how could I have given birth to such a monster? You and your ideas! OK, you’re not a monster and I love you. Just leave the big ideas to the big people, eh?”
“OK, Mommy. I’ll try. I’ll just ignore everything you have ever taught me about thinking for myself and saying what I think.”
“No, you have to come with me and explain all this to the good people of Technological Fantasies. If this isn’t a technological fantasy, I don’t know what is.”
Getting the good people from Tech Fantasies together just meant getting Ann to walk over. She didn’t live very far away.
Sally spoke to Ann and Drake. “Now this is Kelly’s show. The young person in our midst has been thinking again, though we’ve warned her about that. Kelly?”
“Um. Well, we talked about, uh, I talked about making a sound from a profile of a school. I meant a chord, but you guys have turned this around and are looking for a, a tone colour. Like the sound of an instrument. OK, I guess so. A school which sounded like a trumpet would be different from one which sounded like a flute. Not as different as a major chord compared to one containing a tritone, but different. I can imagine really different sounds if they were like different chords played by different instruments. But they wouldn’t be as a different as two pieces of music, say one by Bach and one by Beethoven. Nor say as much. To really show the differences between things, they should be something like that, different kinds of music. Different pieces of music.”
“I told Kelly what a nuisance she was”, Sally said, pride visible on her face, “but she just looked up at me with her blue eyes wide open and an expression of utter innocence on her face, as if to say ‘Who, me?’”
“So, who you, how would a school’s profile become a piece of music?”, Ann asked.
“Uh, I don’t know. But Mr. Everett told us about Algorithmic Composition, where you just put some parameters into a program and it writes a piece of music for you. So a profile could be turned into parameters, maybe. I dunno.”
“Interesting idea, Kelly. Very hard too implement, I think”, Drake said. “I’ve heard some computer generated music, and some of it wasn’t too bad, but it didn’t appeal to me very much.”
“What about Markov Music, Drake”, his wife asked.
“You mean have a big collection of music, then generate music from it by a stochastic process. Interesting. Probably produce better music. Hey, hey, wait a minute! A school has a collection of music in it! Just download playlists from all the kids. Fetch the scores and lyrics, there’s a library of stuff to run a Markov generator on. School to piece of music, no problem.”
“Or one kid to a piece of music, Daddy”, added Kelly. “Download my playlist. Download Suzy’s. Even Katie has one, kid’s songs.”
“Drake, Kelly, that’s brilliant!”, Sally said, so proud of her husband and daughter. “Sure, there are problems with Markov generators, but nothing that can’t be solved. Lower the weights on the most recently used sequences, for example, to solve the banana problem.”
“I agree. You’re right Drake”, Ann said, truly impressed, “and you too, Kelly. You might want to edit your playlist a bit before letting us use it as your profile, but there it is, an audible presentation of a person, with no fancy mathematics. Markov stuff is simple. As Sally said, we can tart it up a bit, keep it from being too repetitive. Easy.”
They tried it with everybody they knew, first, getting the source music in machine readable form as Midi files. Kelly had eclectic taste, pop music, classical music, showtunes, country, jazz, just about everything. That didn’t make her stochastic music a boring blur of different styles at all, instead it made it richer, with a wider range, reflecting the complex girl underneath the pretty one. Suzy liked mostly classical music, as it quickly became clear. As predicted, little Kate Phillips translated into an unending sequence of children’s tunes. But not all children’s tunes, just those of a certain style.
As this was done more and more, everyone involved was impressed with how clearly the generated music portrayed the individual person. “Now. The school.”
These days it was fairly easy to get the scores and lyrics for music, though a fee had to be paid to the copyright holder. It took a significant amount of money to get access to all the music a whole school played, but no, Sarah Rivers said it was insignificant and paid the bill herself, fascinated.
With a big library of music to draw from the new Tech Fantasies Markov Music Profiler went to work and produced an endless stream of music. With no opposition from the students after they had heard the whole story, some of this music was played over the school’s loudspeaker system during lunch hour. Popular music did predominate the output but not overwhelm it. Instead of the large number of student inputs tending to produce a blur, they added instead a richness. There seemed to be at least one student who liked every single known kind of music, so occasionally the output would draw something from each of the more esoteric styles.
Endlessly fascinating, this was just what one school produced. Another local school was persuaded to do the same thing once all the funds and work to accomplish it were provided by others. Here the result was different. Lacking the large international population, this school produced a much narrower range of music, with popular music even more dominant. The experiment had to be repeated. Sarah Rivers again provided the funds. By now there was a large student following, so many volunteers were eager to do the actual work. Different schools did produce different kinds of music. They reflected the ethnic composition of neighbourhoods, the academic standings and ambitions of the students, the kinds of music programs the school offered, and several other factors.
For all that this was fascinating, it did not quite solve the original problem. It would have been so nice to get a single note, a detailed spectrum for a school, to which a student could be compared, as in Kelly’s original idea. It was Alice Ames who provided the answer. Now a student at MIT, she had followed these developments, trying to make sense of them. She wished she could get music generated from students at MIT and Harvard, for example. Alice supposed it was only a matter of time until the big universities caught on the idea and tried it. Still having a close connection with Ann Kelly, usually based on long-distance communication through video walls, Alice passed on an idea she’d had.
“Change the time scale, Ann. Consider the waveform of a single note. The Fourier transform produces its spectrum, which is how we hear it. Now consider a whole piece of music, the actual waveform of a piece lasting at least several minutes. Do its Fourier transform.”
“That would be interesting. It would have too many data points to be heard as a single tone, but I guess they could be compressed. Run through a smoothing filter, then subsampled, I suppose. It would be a non-arbitrary way of turning a piece of music into a single sound, like we were trying to get before.”
“I think so”, Alice said. “You’re almost getting the arbitrariness out of the whole process. Students like what they like, which depends on deep-seated aspects of their being. They collect music, you do Markov generation based on their collections, which is a non-arbitrary process. If you then do what I said, there is no real arbitrariness in producing a single tone which would represent either an entire school or a single individual from their piece of music.”
“Then we could do exactly what Kelly said when we first discussed this. Compare the sound representing the new student to the sound of a school. Pick the best school by how well the sounds mesh.”
“I do hope they give that girl an A-plus in music, Ann.”
“Well, Kelly says she doesn’t play the keyboards all that well, but she sure should get an A-plus in something.”
Indeed she should. Before long every school in New York City had a piece of stochastic music generated from its students playlists. All were enjoyable, all fascinating, but because of its extraordinary emphasis on compatibility and predominance of international students, Social Tech High sounded better than any.