Derangements

A couple of weeks ago I was at the Millbrae BART station and a young man asked me if I knew how to get to Slim’s in San Francisco. I didn’t, but I had my iPhone on me so I used Google Maps and showed him how to get there. After we got on the train we chatted some more, and he mentioned that he maybe shouldn’t be going to this event at Slim’s, because he had homework to do in probability and statistics. I told him I knew something about that stuff, and he showed me his homework.

One of the problems he hadn’t been able to solve concerned 25 letters and the 25 differently addressed envelopes that they were supposed to go into. The letters are shuffled and randomly stuffed into the envelopes. What are the odds that no letters at all wind up in their proper envelopes?

I told him I thought this was an awfully hard problem to be giving to an introductory class, but we weren’t going anywhere anyway, so we got out pen and paper and we tackled it. We (mostly me) came up with a plausible looking formula for the solution, but when I calculated it, it all reduced to (24/25)25, and I knew that that couldn’t be the correct answer. (That would be the answer if each pairing of a letter to an envelope was a completely independent event from the others; but they aren’t, because each pairing takes a letter and an envelope out of the game, and that I knew that that just had to affect the odds in some way, even though I couldn’t figure out how to figure out exactly how it did. I give myself partial credit, though, for at least recognizing that our answer could not possibly be right.)

When I got back home I did some online research and discovered that there’s a special name for a permutation (that is, a shuffling of ordered objects) that does not leave any object in its correct place in the order: a derangement. It seems inconceivable that I haven’t come across this term before at some point, but I don’t have any memory of it; maybe something I encountered in college and not since.

There’s a very tidy little formula for getting the number of possible derangements of n objects: dn = n!/e rounded to the nearest integer. And therefore the probability that a random permutation will be a derangement (that every letter ends up in the wrong envelope) is the number of derangements divided by the number of permutations, or dn/n!. This is very close (just a rounding error away) to (n!/e)/n!, which cancels out neatly to 1/e, which is about 0.368 (or 36.8%), and in fact as n increases, the probability converges toward precisely 1/e very, very rapidly.

It’s neat and counterintuitive, then, to consider that the odds don’t change significantly whether you’ve got 25 envelopes to stuff or 25 trillion.

Thing is, I got all this off a website, and the calculations needed to get that simple-looking formula for dn are pretty darned long and involved. So I have to wonder what it’s doing on the homework for an introductory class. Maybe it was meant as an exercise in Internet research?

We’re All Just Being What We Are

I just posted the following on the WELL, in a conversation about homophobia and racism and other forms of prejudice.

That’s true of a lot of hatreds. They’re complicated and unconscious and hard to pull apart and analyze. They can arise from internal conflicts and denials, or just from unconsciously picking up and imitating attitudes and behaviors from the society around you as you’re growing up, or a combination.

I myself am gay and was raised to be liberal and yet in my thirties I started to realize that I nevertheless had picked up a lot of attitudes from my childhood in Orange County that, though they weren’t homophobic in the clinical sense of projecting my inner fears and self-loathing onto other people, were nevertheless negative ideas about homosexuals I was carrying around without being conscious of it.

That was very hard to, first, admit to myself and, second, do something about. It meant getting rid of some kindly illusions about myself and about other people and about how the society around me worked. Like realizing my own thoughts and behaviors are far more influenced by unconscious habits and far less the product of rational mind than they appear to be; that this was true of other people as well; that those unconscious thoughts and behaviors could be bearers and transmitters of the very same prejudices I was consciously fiercely opposed to; that this also was true of others. It took me a while to accept that and not be furious at others or at myself for it.

So I’m always a little skeptical when someone tells me they aren’t homophobic. Maybe it’s true, but then again maybe it’s the case that they just haven’t realized it, that it’s something unconscious in them that hasn’t been raised yet to the level of self-awareness.

In the first act of the opera The Tales of Hoffmann (which is on my mind because a production in Berkeley of my adaptation of it just finished), a young man falls in love with an automaton (I guess the modern term would be android) that he believes is a living woman, and he doesn’t realize he’s only projecting onto her all his illusions and ideals about what a woman is. On some level I think that’s a metaphor for how all of us are about other people. In the opera, he only discovers his error when the automaton is pulled apart, but if things had progressed otherwise, I can imagine that he’d eventually start to realize she can only say and do the same things over and over again, and he’d come to hate her for being limited in this way, for being less than all these other women he could choose instead. But the hate would be about him and about the illusions and ideals and other baggage about women that he carries around with him; she’s just being what she is. And eventually the young man might come to realize that all the other women are automata, too, at which point maybe he’d stop hating them for not living up to his ideals and start loving them for being very good automata.

And he might even come to realize that he himself is an automaton. I think we’re all something like 95% automaton (conservative estimate), only we’re focused all the time on the 5% within ourselves that is conscious, rational mind, and because of that, we fool ourselves into thinking it’s much much more than 5%. And then we get angry at others for being 95% automaton and not meeting our expectations for the imaginary rational creatures we’ve made up called human beings.

Trail Nix

On the Fourth of July, Dave and I went up to Point Reyes to go hiking. We chose a trail that was supposed to be a loop of about 4.5 miles, though it didn’t quite turn out that way. It was a great hike in any case. We saw a lot of animals, rabbits and deer and, most spectacularly, a couple of elk crossing the trail just a couple hundred feet ahead of us. In one area we walked through that was relatively sheltered from the breeze off the sea, we encountered a whole flock of intensely yellow birds — some kind of goldfinches? — that were playing and chirping and hopping from branch to branch and chasing each other around.

Unfortunately, about a mile from the end, we discovered the last leg of the trail was under construction and not passable. So we had to walk all that way back, nearly doubling the hike. By that time we were already starting to get tired, and the fog was starting in and it was getting a bit cold, but there was nothing else to be done — that was the shortest available way back. Without a compass or flashlight on us, leaving the trails and trying to find our way back more directly seemed like a good way to get lost.

Fortunately we had plenty of water on us. No extra food, but there were wild blackberries along parts of the trail. It’s early for them and there were not all that many ripe ones, but the ones we found that were ripe were pretty darned wonderful.

By the time we got back to the car it was well after eight and we were wiped and famished. We had planned to watch the fireworks with friends of ours who live right on the Bay, but by the time we got a meal in us, it was too late to get there in time.

It may have been in part our own fault. We stopped by the park headquarters and planned which trail to take, but in the car after we left the HQ we changed our minds and drove to a different trailhead that looked more interesting and only a little longer. It may well be that they had had something posted at the HQ about that trail being out, and we hadn’t seen it.

Still, you’d think they’d post something at the last crossing before the section that was being worked on. If we’d known, we could have turned to the right and taken a different loop back to our car. The “closed” sign was two miles or so past the last crossing. Oof.

Trail Nix

On the Fourth of July, Dave and I went up to Point Reyes to go hiking. We chose a trail that was supposed to be a loop of about 4.5 miles, though it didn’t quite turn out that way. It was a great hike in any case. We saw a lot of animals, rabbits and deer and, most spectacularly, a couple of elk crossing the trail just a couple hundred feet ahead of us. In one area we walked through that was relatively sheltered from the breeze off the sea, we encountered a whole flock of intensely yellow birds — some kind of goldfinches? — that were playing and chirping and hopping from branch to branch and chasing each other around.

Unfortunately, about a mile from the end, we discovered the last leg of the trail was under construction and not passable. So we had to walk all that way back, nearly doubling the hike. By that time we were already starting to get tired, and the fog was starting in and it was getting a bit cold, but there was nothing else to be done — that was the shortest available way back. Without a compass or flashlight on us, leaving the trails and trying to find our way back more directly seemed like a good way to get lost.

Fortunately we had plenty of water on us. No extra food, but there were wild blackberries along parts of the trail. It’s early for them and there were not all that many ripe ones, but the ones we found that were ripe were pretty darned wonderful.

By the time we got back to the car it was well after eight and we were wiped and famished. We had planned to watch the fireworks with friends of ours who live right on the Bay, but by the time we got a meal in us, it was too late to get there in time.

It may have been in part our own fault. We stopped by the park headquarters and planned which trail to take, but in the car after we left the HQ we changed our minds and drove to a different trailhead that looked more interesting and only a little longer. It may well be that they had had something posted at the HQ about that trail being out, and we hadn’t seen it.

Still, you’d think they’d post something at the last crossing before the section that was being worked on. If we’d known, we could have turned to the right and taken a different loop back to our car. The “closed” sign was two miles or so past the last crossing. Oof.

The Move is DONE DONE DONE!

We finished this past weekend. Moving all our stuff took about half again as much time and money as I’d first expected, and of course now there are boxes everywhere needing to be unpacked, and my back is sore, and my new bookcases still haven’t arrived, and there are still a number of two-prong outlets I need to convert to three-prong for the computer equipment, and on and on. But we are done.

Now that I don’t have any remaining need to make the best of it, I’ve been admitting to myself how much I disliked our previous place. Too small for us and our stuff, not much storage space, a tiny yard that the landlord never did get his damn leftover metal pipes out of the back corner of, a leak in the living room roof that the landlord never did repair even after it shorted out the lighting, old appliances that would conk out and be replaced thanks to our thrifty landlord by used replacements that were smaller and older than the ones before. We were forced to move by an owner move-in shortly after my brain surgery, when we had no money and I was still somewhat disabled; friends took up a fund to pay for our move-in, and we took that house not because we liked it better than the place we were leaving but because it seemed like the best we could do with our very limited funds.

The new house is half a duplex. The rooms are about 10% bigger than the old house, and there’s more closet space, and there’s a garage. We’ve already filled the garage with utility shelving and boxes of books and records, plus whatever else we don’t want to deal with quite yet. But the records and a lot of the books will stay there. And I look around sometimes when I’m in the garage and boggle at the idea that we lived with all this stuff in the house with us, in a house that was smaller than the place we’ve moved into.

A Little Bit of My History Rolled Away This Morning

A melancholy morning: About 11 a.m. I said goodbye to my piano. The piano is nothing fancy, just a spinet for learning on and practicing on. But it’s the piano I learned on when I was six, so I’ve had it for a long time.

Actually, I didn’t have it for about seven years, from the time I left home and moved to New York City to the time I moved back to California, only this time to the Bay Area, in 1989. Then my parents thought I should have it, now that I was back within a reasonable distance, and they had it sent to me. For nearly 20 years, then, I’ve been schlepping it around every time I move, and never really using it much.

When I’m working on some lyrics for a musical or opera libretto, I use it to hear what the music sounds like. Before my surgery nine years ago, when I was singing a lot, I used it to learn my vocal lines. But really, for those things what I need is a small electronic keyboard I can plug into my computer when I need it and put away in the closet when I don’t. I don’t need a permanent, heavy piece of furniture taking up a big chunk of wall space and costing me money for piano movers every time I move to a new place.

(By the way, AA McCrea Piano Moving in Oakland is terrific and worth the extra money. It’s a show to watch these guys in action, carefully balancing the piano on this or that point like a lever on a fulcrum, so that they’re rarely dealing with its full weight as they take it down the stairs and lift it up into the truck. It’s like piano judo, working with the weight of the piano instead of against it.)

When we moved to the house on Bayview nine years ago, I considered giving the piano away to a school where a friend of mine taught music. But at the last minute Dave and I worked out a way to rearrange the furniture in the living room and squeeze it in. We shouldn’t have; I didn’t use it much and it would have been better to have had a less cramped living room all these years. But of course you hate to let go of things like this because you’re not quite sure how much you’re really going to miss them once they’re gone.

I’m already missing the piano, but it can’t be because it’s going to leave a hole in my life; I’ve used it very, very little in the last nine years. I know I’ll get myself a electronic keyboard when I need it. I know that if I ever want to take up playing the piano again, I can get a new spinet easily enough. And I know I’m very unlikely to want that anyway.

I think it’s grief for the fact that I once thought playing that piano was going to be an important part of my life, and it never turned out to be so. When I was six I started piano lessons with a teacher I really loved — I can’t remember her name now — and I think she could tell pretty quickly that I had interest in learning how music worked but wasn’t likely to ever be much of a performer — things that I didn’t even learn about myself till much later. Along with the practice, she gave me bits of information about basic music theory — the circle of fifths, stuff like that — but didn’t press me too hard about my playing.

At the age of seven I “composed” my first piece of music and proudly showed it to her. It was twelve bars long, I remember — it was all about twelves, in fact: four three-note chords in each measure, and the four chords in each measure had no tones in common, so that the twelve notes of the octave appeared exactly once in each measure. In my foolishness it didn’t occur to me that I should play it on the piano and hear what it sounded like as part of the process of “composition”; I just chose combinations of three notes in such a way that they were spaced more or less like the chords in the music I was learning and so that they used all twelve tones an equal number of times. At seven, I thought this must be how people composed.

My teacher was very amused by this. It was another 15 years or so before I learned about twelve-tone music in college and realized why she had been chuckling.

After about a year and a half, though, my teacher moved somewhere else, and I changed to a new teacher. She never told me anything about the circle of fifths or what the different kinds of chords were; mostly she just criticized my playing and drilled me on scales and etudes and even said a few bad things about how poorly my previous teacher had taught me if she had let me get away with such careless playing. Finally, after four years of weekly unhappiness, I asked my parents if I could give it up, and one of my great regrets about childhood is that I didn’t have the awareness to realize that what I really needed to ask for was a different sort of teacher, one who would teach me more music theory. That was what I had found fun; I never really cared all that much about performing. But at 10 or 12, I didn’t know enough to ask for that.

Might I have become a composer? I doubt it. Since college I have studied more music theory, in an on-and-off, haphazard way, and I’ve always found it pretty slow going. I was talking with a composer friend of mine some years ago and he said he always thought he would write words for his own songs as well as the music, but writing the music always came pretty naturally to him and writing the words was painfully hard and slow. And I laughed and said it was just the opposite for me; I’ve always wished I could write my own music, but writing the words has always come pretty naturally and writing the music is difficult, and then the music isn’t even much good when I’m done with all that work. Not that there hasn’t been a lot to learn about writing words to be sung, too, but I’ve always picked it up pretty quickly and absorbed a lot just from studying lyrics on my own and taking them apart and seeing how they’re put together, and that’s always been fun for me, but doing that with music has always been hard work.

So I figure you’ve got to keep focused on what you’re best at, where your talents are. And I’ve had a pretty good career as a writer and editor that I’m sure I would never have had as a mediocre musician and composer. But there’s always been a part of me that really wishes I could have been a good composer instead of a good writer.

One very good thing about my early piano training that has been of lasting benefit is that I learned to read music at the age of six, so that it became almost as natural to me as reading words. This was a hugely useful skill when I started writing words for songs and musicals and operas later on.

Later on I joined a chorale and discovered to my surprise that I was a pretty good singer, and I learned to sightread and took part in madrigal groups and sang some small roles with Berkeley Opera and a couple of other small companies in the Bay Area. So I’ve been able to pursue music just for fun in other ways. And I’m thinking now it might be fun to learn to play guitar and have an instrument I could take places and accompany myself on.

But when I saw that hardly used piano loaded on to the moving truck this morning, I started to cry a little. Not because I’ll miss the piano. I think I was crying for that seven-year-old kid who lost something he loved a lot when he had to change piano teachers. I was crying because I want to go back with my adult knowledge and do it all over again and this time articulate what it is that I want from a new piano teacher so that my parents will know how to help me find the right one. But hanging on to that piano isn’t going undo what happened or get back the kid I was back then and turn me into somebody I’m not.

I’m giving the spinet to my friend Brent, who is excited to be getting it and who I know will get far more use out of it than I have in many years. And it’s better for a piano to be used regularly and cared for, too. So this ought to be an improvement for both of us.

Even so. (Sniff.)

Change Happens, Sure, But Enough Is Enough

I haven’t posted much for the last month, mostly because I’ve been busy and exhausted. A big project at work that I’m in charge of — the complete reorganization of one of our lines of books — has turned out to be much more complicated than expected, something like four or five times as much work as we’d originally planned (I know, I know, that’s probably true of half the big projects in the world), and yet at the same time it’s very time-sensitive — every week longer the project takes costs us money in sales, and if we’re much later finishing up than mid-March, we will miss our window of opportunity for six months’ of sales altogether and it will cost us a huge amount of money. So there’s been a lot of pressure to keep the workflow moving, which has meant some overtime, a lot of extra stress, and very little energy and time left over for blogging. Fortunately all of that is almost finished.

As if that weren’t enough, Dave and I have been crazy enough to pick February as the month to move into a new house — a duplex this time, actually. So a lot of our spare time for a month now has been spend packing and schlepping boxes of books and dishes and books and clothes and books and computer equipment and books. I think between Dave and me, our books are filling up something like 200 banker’s boxes (10″ x 12″ x 15″ boxes).

There has been a fair amount of furniture to move, too, and some of it heavy and/or very awkward. But the books are what’s taking up the most time.

Then there’s stuff at the other end to do — bolting bookcases to the wall (I have read Howards End twice, not to mention the liner notes of several albums and CDs of the music of Charles Alkan, and I have friends who had bookcases topple during Loma Prieta, though fortunately with no damage to humans — nearby furniture was another matter — so I’m a bit jumpy about the possibility of being flattened by an shower of books in an earthquake, and I bolt all my cases, and anything else that’s tall, solidly to the wall); changing some of the old two-prong outlets to properly grounded three-prong outlets, so we can plug in our computers somewhere other than the kitchen counter and the bathroom; figuring out carefully with tape measure and squared paper how the furniture is going to fit in the new space; re-figuring everything on the fly when the bookcases turn out to be an inch and a half too large to make it around the corner in the hall, no matter how many different angles and orientations we try; mixing up some plaster to patch the place where we made a dent in the wall in the hall trying to squeeze a bookcase around the corner; and of course unpacking stuff, including all those books, and finding new homes for it all.

Looks like we’ll be done in one more weekend, though. Sure hope so — I’m bushed.

Holidays

Dave’s been after me to write a new entry because it’s been a month since the last one. He’s right, really — the whole point of this blog is to keep my writing chops in shape with some informal exercising. But damn, I’ve been busy and feeling pretty drained for a while. Work has been exhausting, with a big many-part project behind schedule and a lot of pressure to catch up, and us still a bit understaffed. I’m trying to concentrate on editing these difficult books on a technical subject I know little about, while every 15 or 20 minutes someone comes by with a question or, worse, something that I have to do immediately that only takes five minutes but breaks my train of thought so that when I come back to what I was working on I have trouble remembering exactly what it was I was in the middle of at the moment I broke off. I have taken to leaving a lot of sticky notes around for myself: “Ck TOC pg nos” or “perms?” to remind myself that I was about to check all the page numbers in the table of contents or do a page-by-page pass through the galleys to make sure that my list of what figures and tables are reprinted or adapted from other copyrighted sources — in others words, those things we need to be sure we have obtained permission to use before we put the galleys in final form — isn’t missing anything.

The holiday season was nice, though to some extent I spent a lot of it just crashing. I took a few vacation days so that I could be away from Christmas to New Year’s — an 11-day weekend — and it took me seven or eight of those days before I really felt rested and recharged. And then of course I get back to work and things are just as intense as I left them. I will be extremely relieved when the last of these eight books is off to the printer.

My holidays were good all the same, I just could have used a few more days of them. Christmas Eve was spent at a dinner table of in-laws, Dave’s mother and middle brother and his wife. I used to find holidays with Dave’s family harder to deal with, but with age I have realized that it is much easier to deal with someone else’s dysfunctional family than your own. It’s easier to learn how not to take things personally, not to let things cross my own boundaries. I suppose perhaps the next step ought to be to take that practice and apply it to my own family. Can one learn to be with one’s own family as lightly as if it were somebody else’s, not having any expectations, not taking any disapproval to heart, and confident that when it’s time to go home you won’t be taking any of the leftover angst home with you?

Christmas Day was pretty quiet, which is how I like it. Christmas was one of the most horrible three days of the year for me when I was growing up (the other two were Easter and Thanksgiving), and nowadays I’d be happy just spending it with Dave and maybe a couple of friends. I’d even be perfectly happy to spend it by myself, staying in bed and reading or playing computer games all day. Big holiday gatherings wear me down too easily. For Christmas this year, Dave and I were just going to do lunch and a movie with his mother (his brother and sister-in-law were going to spend Christmas Day with her family, which Dave’s mother didn’t want to do), but then the night before Dave had the idea of offering to drive his mother to Davis — an hour and a half away — to visit her mother’s grave, which she hadn’t been able to visit in nearly two years. She’s Chinese-American, born in China, and that’s an important thing in Chinese culture. Me, I can’t even remember where any of my grandparents are buried and my last visits to their graves coincided with the days on which they took occupancy.

Then dinner for just the three of us in a really good Chinese restaurant on Solano Avenue in Berkeley, Kirin. Dave’s mother seemed determined to find faults in everything about the restaurant until the food came, at which point she stopped finding nits to pick, so we must have picked a good place. And I seem to have accumulated a bushel of Good Son-in-Law points that day. Dave pointed out to me later than some of what his mother had said over dinner, she never would have said in front of me if she didn’t feel I was family. Well, that’s what he says anyway. I still don’t really know enough about Chinese culture to notice all the indicators, and Dave often has to translate for me.

Thursday after Christmas I left for a Billy Club gathering in the redwood country a few hours’ drive north of San Francisco. The Billys are a partly social, partly spiritual group that holds five or six of these gatherings each year. I got a bad headache on Thursday morning and drove up a bit queasy from all the Vicodin and coffee I’d swallowed in order to dull it (unfortunately I’m not one of those people who gets a pleasant high from Vicodin; it just upsets my stomach, though that’s still better than hurting). It was still lingering mildly by Friday morning but by Friday evening it was finally gone and I slept well.

I was in charge of creating and leading the rituals this time around, which was a lot of fun and kept me connected with others. But I also spent a lot of the time by myself, reading or writing or just napping. We’d created a lounge in one of the cabins by spreading out mattresses and a hundred or so pillows and cushions around, and draping fabric on the walls. It was cozy and warm and I spent a lot of time there, writing in my journal or napping in a corner or chatting with a friend.

Leading the rituals was a great experience for me and I learned some stuff. Mostly though this gathering for me was less about doing stuff and more about retreating and restoring myself. I got back New Year’s Day.