NY DP Penalty

Is it a slap in the face, salt in the wound, proportionate fees, or a bureaucratic oversight?

Likely the latter as claimed, but still it seems an amusing but niggling thing: in New York City, one pays $35 to get a marriage license, but to register a domestic partnership costs $36. Fewer rights for only a dollar more! On the other hand, DP registration has no mandatory waiting period, which might be worth the extra $1.

We're told that parity will be established soon,^* but apparently it's not known whether the marriage fee will be increased, the DP fee reduced, or some other solution will be found.
———-
^* Jennifer S. Lee, "For Marriage or Partnership, Fee Will Soon Be the Same", New York Times, 16 October 2007.

The Poverty of Conservatism vs. Gore's Nobel Prize

Congratulations to Al Gore and the UN IPCC for winning the 2007 Nobel Peace Prize. Isn't it interesting to see how quickly the American Presidency has diminished by another big step.

Liberal schadenfreude, of course, demands that I talk about conservative failures rather than Gore's successes. Conservatives today are galled (perhaps "gored"?) that yet another Democrat should win a Nobel Prize rather than someone really deserving, like man-god Reagan for single-handedly ending the cold war and the Soviet Union with one sharp lash of his tongue. Why oh why can't one of the good guys win a Nobel Prize?

For the obvious reason: conservatives don't do things; in particular, they don't do things that win Nobel Prizes. It is in the nature of conservatives not to have new ideas, since it is in their nature to conserve the status quo. While they may have occasional flashes of inspiration in repackaging old ideas that promote their most important values — "compassionate conservatism", say, or "free market" or "free trade" — these are not new ideas. Therefore, the most highly regarded conservative "ideas" do not lead to highly regarded new actions, things that actually help the world and its people live together more peaceably. Their mission, as they see it, is to slow down social and economic progress towards greater freedom and democracy.

You could make delicious vinegar from the conservative sour grapes about Gore's award, so busy are the conservatives trying to convince even those who won't listen that the Nobel prize is just a liberal popularity contest and an award that nobody values anymore. Of course, the intensity of their claims to the contrary underscore just how highly conservatives covet the Nobel Prizes.

Some people have just increased their clamoring now for Gore to enter the presidential race, but more clear-seeing liberals see the truth that the prize announcement creates: Gore can't run for president any more. He's too good for it.

I'm sure this says loads about our election process for choosing presidential candidates, but it also speaks volumes to the presidential culture of lowered expectations ushered in by Reagan and Bush I, but polished to a gleaming finish by Bush II. It now seems to be carved in stone that a president should not be smart, should not be effective, should not have good ideas, although I've never understood how it could be desirable to have an uncultured, anti-intellectual oaf as our nation's leader. Do you really want your auto-repair guy to do your brain surgery?

So, as indicated by the hyperbole of the rhetoric with which conservatives denounce the significance of the Nobel Peace Prize, we deduce that Gore is now considered by all to be too effective, too smart, and have too many good ideas ever to be president. Not to mention, of course, that with the remarkable devaluing of the office by Bush II, it is really out of the question for Gore to take what would be seen as a job demotion by running for president. As most now realize, he can be much more effective, much more smart, and make much more progress on his ideas from outside any elected office. "Statesman" does not seem to imply people of intellectual and moral stature these days.

Sure, I long for a smart, effective president who has ideas rather than an unthinking, stupid political oaf of either persuasion, but President Gore is not meant to be. His trajectory is taking him elsewhere now, and it doesn't pass through the Oval Office. This probably creates much consternation among conservative critics who would have a much easier time trying to smear his reputation if he'd just stay in politics, but so be it; perhaps it will lead them to develop smarter, more efficient tactics in character assassination.

Don't laud Gore by suggesting that being elected president (for the second time) would be assured and the highest honor he could garner. We all know better than that, even if we won't admit it yet. Instead, recognize the work he's doing and support his efforts to do it in a smarter, more effective manner of his own choosing.

National Coming Out Day 2007

Today, October 11, is celebrated annually by more and more people as "National Coming Out Day"; despite its name, people in many countries celebrate NCOD. First observed in 1988, NCOD marks the anniversary of the Second National March on Washington for Lesbian and Gay Rights in 1987. The official NCOD logo (at right) was created by Keith Haring.

I wasn't at that ground-breaking Second National March, but Isaac and I did manage to get to the Third National March in 1993, along with about a million of our most fabulous friends. Whoo, what a remarkable day that was! All of Washington DC was very gay friendly that day and we all felt, however briefly, like we were not a social minority for a change.

At the end of it all, Isaac and I traveled back to the suburbs on a Metro train. Our car was filled with smiling, carefree, non-threatening gay and lesbian people — except for one very nervous, middle-aged straight guy. We all sat and talked quietly in what we thought was a non-intimidating volume, but the poor man kept glancing around the car, clearly anxious. About what he might have been anxious I leave to the empathetic mind of my readers. At the penultimate stop the doors opened and he rushed from the car. The moment the doors close, the rest of the people in the car chuckled and bit and began talking cheerfully at normal volume. We were convinced that he rushed home to his wife with stories of being nearly attacked by an unruly mob of sexual outlaws although, truly, I don't think he was ever safer on a metro ride than he was that day.

I came out — officially, in my mind — in 1992. This was not, of course, when I knew that I was gay, but it was when I told other people and chose to stop hiding or evading the fact.^* I've never felt better, and it was a great thing to do. I recommend it to everyone who knows himself or herself but hasn't yet decided to live openly.

I came out first online, which seemed proper to me at the dawn of the internet, and not least because I am such an introvert anyway. I had found a friendly, sometimes rough-and-tumble group of compatriots in the Usenet newsgroup soc.motss.^# Regular posters numbered about a couple of hundred, so it was easy to get to know them and just start talking, easily ignoring the putative 20,000 people who read the group regularly. Anyway, it was an inviting venue and I had a great time with my friend there. I'm still trying to find a way to re-integrate it with my life, which seems so much busier these days.

Here is a brief aside to all those who think that people who find community online need to get out and get a life and meet "real" people. Two points: 1) you're all extroverts who have no idea what it's like for introverts to get out and meet "real" people; 2) an online community enhances personal interaction for introverts, it doesn't restrict it.

I've never found my coming-out stories terribly interesting, although there was one fun episode I recall. Around 1997 I was working with a group of engineers, a group not known at the time for their diversity. We had been having a meeting, the work part was over, and some started complaining, as they were prone to, about their ex-wives. Head engineer made a pronouncement about ex-wives and the state of marriage. He felt that a survey of the conference table was called for to check on marital status and the happiness of said state. He got to me and my answer — wishing to go easy on their delicate engineering sensibilities — was that I was partnered but I was not allowed by law to marry him.

Well. That was met with some expressions along the "whew boy!" line. Head engineer decided a discussion was called for, and the project manager closed the door to the conference room. I didn't really see what needed to be discussed, but all the other guys wanted to express themselves and ask questions and talk, talk, talk. It was sort of an all-male chick-flick script. I guess they worked through what they needed to work through and it all got integrated comfortably into our working-group dynamics.

I can't really come out again today, although maybe one can do a sort of renewal-of-vows, since they seem rather popular. Again, I can use myself as an example to encourage others teetering on the edge to eat the powder-milk biscuit and do what needs to be done.

I do have one thing I've wanted to say to those in their early stages who say, of work colleagues or family, that "they all know, so I don't have to tell them". You may be correct that they all know — it's amazing how many people "knew all along" when you finally tell them — but, until you tell them, they will avoid talking about anything that comes close to your personal life, thinking that you want to be "discrete". They want to do what you want them to do, because they're your friends, but silently letting them help you maintain your closet of silence does no one any good. It is up to you to tell them about your orientation so that they have permission, from you, to talk about it, and until you give that permission it's a part of your life that you have closed off. It's unhealthy for you and uncomfortable for them.

Go ahead. Eat the biscuit.
———-
^*There was a well-recognized transition period in which one claims that the truth will be told to anyone who asks, but during which one goes to extraordinary lengths to avoid being asked the question.

^#It still exists, by the way, and maintains much the same spirit. "motss" = "members of the same sex"; there's a long and interesting story behind the name, but I won't tell it here right now. If you have a usenet newsfeed — and they're rather easier to come by today than in 1992, let me tell you! – it's easy to find them. Also, you can probably find every one of my posts archived at Google groups, if you feel motivated.

Spooky Classical Music

My big time-waster of the last couple of days was working on a Squidoo Lens^* on the subject "Spooky Classical Music for Halloween". This all came about one night when we were having dinner with our friend George, whose musical tastes range from eclectic to odd.

He was thinking about music from his collection that might be suitable for playing from darkened houses on Halloween. Isaac and I were seized by the spirit (as it were) and joined in, quickly making up a longish list of our own that included classical titles that we felt would help create a suitable ambiance.

With a nod to the greatest of all phantom-of-the-opera titles, the "Toccata & Fugue in d minor" of Bach, there are a good number of organ titles, but we also came up with works we favored in other genres, as well. There was nothing from before the Baroque, but all other time periods got coverage.

Another excellent time waster turned out to be looking through lots of YouTube videos related to the titles we chose, looking for some that were interesting for one reason or another, and I turned up some performances that I found quite interesting. But, I warn you that checking out those links will probably be a time waster for my four regular readers as well.

Now, back to work for me!
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^*If you don't know what it is, you'll find out soon enough I expect by clicking the link.

My Sputnik Childhood

I nearly let pass this notable milestone: 50 years ago today the Soviet Union^* launched the first artificial Earth-satellite, called Sputnik. It was a tiny thing — suitable I suppose to being the first baby of the birth of the space age — just 24 inches across and weighing only 184 pounds. It was made of shiny polished aluminum, so that it reflected sunlight and was easy to see from Earth. It carried two radio transmitters that emitted continuous signals that didn't say anything, not that they had to. The message was obvious.

Launching a satellite, in principle, is a simple thing. Point it in the right direction, accelerate it to a speed of something like 11 km/s (or about 7&miles/s)^# and it goes into orbit around the Earth. In practice this is not so easy. It takes a lot of rocket fuel to accelerate even 184 pounds to a speed near 7 miles/second, and that fuel takes more fuel to accelerate it, and that fuel takes more fuel to accelerate it, and so on.^& After you figure all that out, you end up with a very tall, multi-stage rocket that is very impressive when it takes off, even for the smallest payloads.^**

Then there's all that goes into getting all the stuff to the launch-pad so it can take off. There's a remarkable amount of engineering, mission planning, fabrication, transportation, and organization that goes into one of these events, and they only got bigger as the missions got more sophisticated. A modern space-shuttle launch comes at the end of years of planning and months of preparing the payloads; the launch itself involves hundreds of people at locations scattered around the world.

And it all started with that tiny little Sputnik. I was not quite two years old at the time, so I don't remember its happening. I didn't have any memorable artificial-satellite experiences until I went outside one night to see a transit of an Echo communications satellite some years later.

It surely affected my life, though. Sputnik was so alarming to the powers in Washington — perhaps to the average American, too — that we, the entire country, suddenly developed a keen, new interest in science and engineering, and in science, engineering, and mathematics education, and I was undoubtedly a product of that. When people today wring their hands about a shortage of scientists and engineers — which hasn't been true for decades — I imagine it's an echo from that time.

People looking to justify our commitment to sending a man to the moon thought of all sorts of alleged "spin-offs" from the space program, and proclaimed the marvels of Tang, Teflon, and Velcro, none of which were invented by NASA, nor invented for NASA. Computer systems and microelectronics got some boost, but the average computer user today would be shocked to see the primitive computer hardware that got Neil Armstrong to the moon.

One of the things that was touted as an accomplishment of NASA, a spin-off of the moon program, was project management. I think that may be a real contribution. My experience from doing a couple of space-shuttle missions is that the planning process is not fast nor particularly efficient, but it accomplishes its goals with deliberation and thoroughness. That care and deliberation has suffered some in recent years, perhaps a result of political and management hubris that believed we must know how to cut corners by now.

As a product of the Sputnik age, I take the growth of modern technology and America's leading role in developing it rather for granted, but it's far from established that we shall always be the leader. I believe that our remarkable achievements from the 80s and 90s in developing the personal computer, for instance, resulted from the investment our country made in science and technology education in the 60s, coupled with national interest, motivation, and pride.

Those emotions and commitments take nurturing; they musn't be taken for granted or they whither. I fear that that's been happening in recent years, and that our complacency will catch up with us if we do nothing about it. The renewal won't be fast, because it takes new generations to grow into it, although current generations can do the plowing and fertilizing.

That's part of the reason that I started Ars Hermeneutica, Limited in 2004, and that's the big motivation behind our vision of a scientifically literate America.

I didn't set out to write this as a justification or a motivational piece or an advertisement — or even as a fund-raising appeal^## — but I guess these all have one thing in common: that I care deeply about them.
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^*Which, one notes in passing, no longer exists. Things change, and even countries don't last on forever.

^#The speeds are near the escape velocity from Earth, which is a bit more speed than is needed to establish an orbit, but it gives an idea of the speeds involved.

^&It's not an infinite sum — the sequence does converge, and it has an exponential form, for roughly the same reason that the equation for compound interest has an exponential form. If you want details, Google "rocket equation".

^**Note, however, that there are big differences in actual acceleration depending on the payload and the rocket chosen to launch it. Those of us accustomed to the Saturn V rockets launching an Apollo mission, or the rockets for shuttle launches, imagine a stately launch in which the heavy payloads seem like they're never going to move, then they finally stroll off into the wild blue yonder. With that in mind, seeing once the launch of a sounding rocket, which doesn't even attain orbit, was a surprise: it jumped off its launch-pad like a startled rabbit.

^## Although, it bears repeating that Ars Hermeneutica is a 501(c)(3) tax-exempt corporation, and contributions are tax deductible. Click to see how to Support Ars Hermeneutica.

Disentangling Religion from Public Life

Via Maud Newton, this is an excerpt of her excerpt from the introduction to the book Faith in the Halls of Power: How Evangelicals Joined the American Elite, by D. Michael Lindsay, that I found interesting:

Much of the twentieth century was spent disentangling religion from public life. Commerce and piety were once seen as complements to one another. But that connection dissolved with the rise of modern corporations, as the personal was divorced from the professional. Americans embraced pluralism in the workplace, public schools, and civic life, and these institutions worked to minimize sectarian differences among workers and citizens. In the process, religion lost some of its influence, becoming just one of many sources for individual and national identity. Gradually, religion was relegated to the private, personal sphere.

Yet even as this arrangement finally became taken for granted in many quarters of American life, opposing perspectives were emerging. In the 1970s, conservative Christians, many of whom had sequestered themselves in a distinct subculture, began returning to the cultural mainstream. Initially, they met with only limited success, and many observers ignored their entrepreneurial creativity and strong resolve to change America. Also, few connected evangelicals’ activism in politics with activism in other spheres, even though evangelicals regard these as more important.

Is Pink Dainty or Butch?

Writing about a study purporting to support the notion that girls have an inherent preference for pink — making it the girl's color — Ben Goldacre wrote the following, which I wanted to save in my "It's Always Been That Way — Hasn't It?" file.

But is colour preference cultural or genetic? Well. The “girls preferring pink” thing is not set in stone, and in fact there are good reasons to suspect it is culturally determined. I have always been led to believe by my father – the toughest man in the world – that pink is the correct colour for mens’ shirts. In fact until very recently blue was actively considered soft and girly, while boys wore pink, a tempered form of fierce, dramatic red.

There is no reason why you should take my word for this. Back in the days when ladies had a home journal (in 1918) the Ladies Home Journal wrote: “There has been a great diversity of opinion on the subject, but the generally accepted rule is pink for the boy and blue for the girl. The reason is that pink being a more decided and stronger color is more suitable for the boy, while blue, which is more delicate and dainty, is prettier for the girl.”

The Sunday Sentinel in 1914 told American mothers: “If you like the color note on the little one’s garments, use pink for the boy and blue for the girl, if you are a follower of convention.” Some sources suggest it wasn’t until the 1940s that the modern gender associations of girly pink became universally accepted. Pink is, therefore, perhaps not biologically girly. Boys who were raised in pink frilly dresses went down mines and fought in World War 2. Clothing conventions do change over time.

[from Ben Goldacre, "Bad Science: Pink, pink, pink, pink. Pink moan.", The Guardian, 25 August 2007.]

You! Rocket Scientist! Move Away…

…from the dotted hole and no one gets hurt!

Not long ago some creative googler arrived here, at this blog, by searching for these words:

how do you get the rocket scientist to move away from the dotted hole

One of the few things guaranteed to pique my interest and confuse me to atoms is seeing 1) the odd search strings that people google, and 2) discovering that said search strings bring them here. Trying for empathy, I try to imagine the reaction of the googler when faced with trying to figure out why here was an option.

I like the mental image of the rocket scientist standing close, perhaps dangerously close, to the dotted hole. What is being threatened? The rocket scientist? The dotted hole? The entire universe!

The picture I get is of an Einteinian space-time manifold with gravitational deformations — you know, one of those "rubber sheets" with masses sitting on it that is always used to demonstrate the idea from general relativity that gravity is just mass-induced deformations in space-time.

Somewhere in the picture there's the "dotted hole", sort of a monstrous black hole with a perforated event horizon, gaping open like the mouth of Hell, ready to swallow the unsuspecting rocket scientist. Where will the scientist end up? In an alternate universe? Across the galaxy? Wound up tight around an elemental string embedded in eleven dimensions? Perhaps only the mind of the CGI-special-effects designer can come up with a suitable visual concept.

Then again, it might be something more prosaic, but what fun is that? I like my image, and it makes me feel important and powerful. You know, that whole rocket-scientist super-hero thing, what with being the only one able to save the entire universe from the horrors of the dotted hole about to consume all of creation.

Or not. It turns out that there is a simple, not terribly interesting reason that the googler chose the phrase above, but I thought that finding out dispelled some of the inscrutable romance for me, so I'm not going to spoil it by telling. If you want to, google it for yourself with this link; the first entry is enough to reveal the original googler's intent.

Performance & Performing

Our "Kiss Me, Kate" rehearsal Wednesday night^# went pretty well, about where we should have been with two days to go and a few details to brush up. For me it was good because I finally remembered all my lines at all the right times, as well as lyrics and dance steps. All this was done through the expediency of some practice and keeping lots of things in my head. In addition to the lines and lyrics and dance steps, there are the mental meta-thoughts, aides-to-memory for keeping lyrics in the right order, counts and step names to keep dance steps sorted out, and personal admonitions about lines that never seem to come out right but will if one keeps thinking things like "cross right and raise the upstage arm" while speaking blank verse from Shakespeare with an ironic modern twist, and say "sister"instead of "daughter".

I think the audience doesn't realize — nor should they realize! — that while they're enjoying a seamless spectacle of acting and singing and dancing, we performers are thinking things like "step-touch-step, pas de bourée, point, point, point, point" (a passing moment in "Too Darn Hot"), with lots of mental "five, six, seven, eight", not to mention my silently practicing the word "quaff, quaff, quaff" just before I shout "Let's quaff carouses to this gentleman!" because it would never quite come off my lips as recognizably English in previous rehearsals. I'm one of the three "suitors" who sing "Tom, Dick, or Harry"^*, a novelty number we get through accurately only by mentally reciting counts and steps and hand positions while singing a quick succession of words in four-part harmony.

My point will be more or less obvious by this time: the audience is immersed in the performance, but the performer is immersed in performing, and the two are quite different ways of experiencing the same events.

I perform musically at the church where Isaac is music director with some regularity; sometimes I play 'cello, sometimes I sing, sometimes I'm a substitute hand-bell ringer. It all gives me lots of opportunity to sit in the chancel and watch the congregation watch me and the other performers, which includes the scripture readers, the deacon, and the minister, and think about the differences between performing and the performance.

The audience expects to see — and deserves to see — a performance that shows no seams, shows no signs of being performed. A good performance appears what it pretends to be, rather than what it actually is.

On the other hand, the performers rarely experience a performance the same way. The job of the performer is to create the seamless performance experience for the audience. Now, that may seem rather obvious, but people sometimes forget it and believe that the performers are just somehow doing what they appear to be doing without thinking much about it. It doesn't really hurt for the audience to think that — it can be part of the effect the performance creates, making it look effortless and natural, nothing really special — but woe betide the performer who falls into that trap and gives a sloppy, unprepared, untidy performance. The audience may not know exactly what went wrong, but they will feel that the show didn't really come off quite right.

Sometimes there's not a big difference between what the performer appears to be doing and what the performer actually is doing. Musicians usually have rather little in the way of stage theatrics or performance logistics to worry about and can mostly concentrate on performing their music, but there are a few fiddly bits. Not surprisingly, there's more for actors and exhibition dancers and figure skaters and opera singers to do to make their performance seem "natural". And don't forget the preacher mentioned above, who is also giving a performance.

I think this difference between performance and performing came most starkly into my mind one night, some years ago, when we were doing a staged performance of a review of Rogers & Hammerstein songs called "A Grand Night for Singing". There was a love duet going on on-stage. Part way through that number the chorus popped out to sing ethereal "oohs" and "aahs" in lovely, atmospheric harmonies. We had arranged it so that groups of three heads popped out from behind flats sort of in totem-pole fashion, one above another above another.

The audience found it surprising, slightly humorous, charming, and tenderly romantic. What I saw from my vantage point behind the flats was a group of middle-aged singers trying to get themselves positioned for this popping-out routine. It required people on hands and knees, people squatting, people leaning precariously over each other, all of us holding onto something or someone so that the whole lot of us didn't fall onto the stage.

Of course, the audience saw none of this, and that was our goal. We were temporary contortionist performers in pursuit of creating a magical performance moment for our audience.

I laughed heartily about it later, though.
———-
^#I started this rumination nearly six months ago when our theater group was just about to do its first performance of "Kiss Me, Kate!" It's taken me awhile to get back to finishing it, but let's not worry over much about just when "last Wednesday" was. Here's a backstage moment: the chorus was waiting backstage and I was making a note or two for this piece; one of the others asked me about it. I explained that I was writing about the differences between "Performance & Performing". She gave me a look that said "hmm, deep."

^*Whose lyric "dick, dick, dick, dick, a-dick a-dick, dick, dick, dick" provides another datum in our examination of subliminal gay messages in the lyrics of Cole Porter.

A Decade Without TV

I find that I get unusually irritated by admonitions that assume I'm not already doing what said admonition would like me to do. Such presumption!

There's a road sign I curse routinely that says "Slow Down!" when I'm already going the speed limit. Back in the Carter days it was "Turn Down Your Thermostat!" (in winter, of course), when mine was already set low. "Eat More Vegetables!" — more than what? Perhaps it's all part of becoming an old fart, this irritation.

Every now and then I come across someone who writes about his or her experiences with turning off their television set for a whole week, or maybe a month, sometimes even a whole year! One can almost hear the gasps of readers who suddenly are forced to imagine life without their own TV — or worse: their family's life without TV. The writers seem to find it refreshing but on the scary side. Apparently we're to be amazed with this writer's saintly fortitude, mouths agape at their stoic solidity. I read their accounts, but I never get much out of them.

For some reason I've never felt compelled — before now, at least — to bother writing about the fact that Isaac and I never watch TV. Sure, we have a television set, which we use to watch movies. Oh, and we've also watched all of "Six Feet Under" on DVD, and there was one morning during a snow storm when Isaac wanted to know whether he had to go to work. And once we had a friend visiting who had to see the end of a "Survivor" (first season) episode.

Sometimes we even see some bits of televised programs when we're at a friend's house, and at occasional holiday gatherings we're forced to be near when some watch one of the tedious sports events that seem to be ubiquitous on such days. I try to avoid the latter whenever possible, and try to shame the sports fans into not watching while there are guests (me) in the house, particularly guests who prefer root canal to televised team sports.

Not that we make a fetish of it. If we're in front of a TV that happens to be on, we look at it. This is happening more and more frequently in casual restaurants — do they hope to make patrons more comfortable by giving them less reason to create conversation?

We don't do this out of any noble principles, by the way. It just started happening some time about 10 or 12 years ago. There seemed to be less on TV that attracted our devotion, and more things that we wanted to do with that hour here or there that we would have spent watching. After awhile we'd simply stopped. We've always been more book people anyway.

Nowadays, of course, that leaves us with a blind-spot when it comes to shared pop culture, but our friends are mostly aware and it does tend to shorten those tiresome conversations that begin with "Say, did you see…?" "No," comes our instant, truncating response. One reason that we only recently got broadband internet service is that our house, now 10 years old, never has had cable TV installed — yet another expense that I didn't see the necessity for.

And, to tell the truth, I haven't noticed that our lives have suffered in any significant way for our decade without TV. I suppose I should make more of a fuss. Hey!! Look at us!! We haven't watched TV for ten years!!!

But, you'll understand, it's not really like me to do that.

The Harvest Moon

For those of us who wonder why the "harvest moon" is called that, the kind folks at Space Weather (a NOAA project: Space Weather) give this brief explanation:

HARVEST MOON: There's a full Moon tonight (Wed., Sept. 26) and it has a special name–the "Harvest Moon," the full Moon closest to the autumnal equinox. In the days before electric lights, farmers relied on moonlight to help them gather ripening autumn crops. The bright Harvest Moon allowed their work to continue late into the night. Now, post-Edison, we appreciate the Harvest Moon more for its beauty than its utility. Moonrise happens tonight at sunset; look east and enjoy the view!

P.S. If it's not obvious that full-moon moonrise happens at sunset, you might want to ponder it for a moment. Here's a hint: solar eclipses can only happen at times of new moon, and lunar eclipses can only happen during times of full moon. Will it surprise your friends to learn that they will never see a cresent moon late at night?

Two More Bites of Pi

I can't help myself now. I've just read through another paper by some of the -algorithm people^*, and they provide two fascinating equations from the history of computing . Although they have been used in practice, my purpose here is just to look at them in amazement.

This first one is an odd and ungainly expression discovered by the Indian mathematical genius Ramanujan (1887–1920):^#

One extraordinary fact about this series is that it converges extremely rapidly: each additional term adds roughly 8 digits to the decimal expansion.

The second has been developed much more recently by David and Gregory Chudnovsky (universally called "The Chudnovsky Brothers") and used in their various calculations of . In 1994 they passed the four-billionth digit.^& This is their "favorite identity":

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^* D.H. Bailey, J.M. Borwein, and P.B. Borwein, "Ramanujan, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi", American Mathematical Monthly, vol. 96, no. 3 (March 1989), pp. 201–219; reprint available online.

^# One purpose of the paper was to show how this formula is related — deviously, it turns out, although a mathematician would say "straightforward" after seeing the answer — to things called elliptic functions.

^&Okay, it was 18 May 1994 and the number of digits they calculated was 4,044,000,000. They used a supercomputer that was "largely home-built". This record number of digits did not remain a record for long, however.

Why Pi?

As a little gloss to the previous entry on calculating π, I'm finally reading the entertaining and enlightening article "The Quest for Pi" and find this unique observation after asking why people persist in calculating π to billions of digits:

Certainly there is no need for computing π to millions or billions of digits in practical scientific or engineering work. A value of π to 40 digits would be more than enough to compute the circumference of the Milky Way galaxy to an error less than the size of a proton.

[David H. Bailey, Jonathan M. Borwein, Peter B. Borwein, and Simon Plouffe, "The Quest for Pi", Mathematical Intelligencer, vol. 19, no. 1 (Jan. 1997), pp. 50–57; reprint available online.]

A Big Piece of Pi

How innocently it all begins, sometimes. For some reason a day or two ago I decided I would take a few google-moments and look into modern computational formulæ that are use to calculate the value of . What a loaded question that turned out to be! Before I'd reached a point to pause and write — and I'm not confident that I'm there yet — I've read several mathematics papers, installed software so that I could type equations in the blog [1], thought more about number theory and complex analysis than I have for years, and even gave Isaac a short lecture on infinite series with illustrative equations written on the Taco Bell tray liner. Poor Isaac.

Suppose you want to calculate the value of . The number , you may recall, is transcendental and therefore irrational — serious categories of numbers whose details don't matter much except to remember that , written as a decimal number, has digits after the decimal point that never repeat and never end. Most famously relates the diameter of a circle, , to its radius, , in this manner:

There are also a surprising number of other mathematical equations involving that have no obvious relationship with circles. One very important and useful type of relationship involves infinite series. Infinite series are written in a very compact mathematical notation that will look very inscrutable if it's unfamiliar, but don't be alarmed, please, because the idea is relatively simple. Here's an example:

The big greek letter, capital sigma (), is the symbol that signals the series operation. The letter underneath the sigma is the index. The index is set in sequence to a series of integer values, in this case starting at one (because ), and ending with infinity, as specified by the number on top. Then, for each value of , the letter is replaced with that number in the mathematical expression following the big sigma and the successive terms are added together, the operation suggested by the sequence of fractions following the equals sign. (Feel free to look at the equation and think about it and look and think, if it's new to you. Mathematics is rarely meant to be read quickly; it takes time to absorb.)

The other important idea about the series that we have to look at is the idea of convergence, a property of the series meaning that as one adds on each new term the result (called the partial sum, for obvious reasons) gets closer and closer to some numerical value (without going over!). It is said to converge on that value, and that value is known as the limit of the successive partial sums. [2]

Provided that the series converges, the limit of the partial sums is usually treated simply as the value of the series, as thought one could indeed add up the infinite number of terms and get that value.

It turns out that the series we wrote above (the solution to the so-called "Basel problem") does indeed have a value (i.e., the partial sums converge to a limit) — a rather remarkable value, actually, given our interest in :

Really, it does. [3]

This equation also gives us a good hint of how the value of is calculated, in practical terms, and this has been true since at least the time of Newton, whether one is calculating by hand or by digital computer. One finds a convenient expression that involves an infinite series on one side of the equals sign and on the other side and starts calculating partial sums. The trick is to find a particularly clever series that converges quickly, so that each new term added to the partial sum gets you closer to the limit value as fast as possible.

It should come as no surprise that there are an infinite number of equations involving with reasonable convergence properties that could be used to calculate its value, and an astounding number that have actually been used to do that. [4]

It may also be no great surprise to hear that new equations are discovered all the time, although a new type of equation is rather more rare. Now, this part is a bit like one of those obscure jokes where we have to have some background and think about it before we get it. [5]

This is where my innocent investigation into calculating took an unexpected turn. Let me quote the fun introduction to a paper by Adamchik and Wagon [6] :

One of the charms of mathematics is that it is possible to make elementary discoveries about objects that have been studied for millenia. A most striking example occurred recently when David Bailey of NASA/Ames and Peter Borwein and Simon Plouffe of the Centre for Experimental and Computational Mathematics at Simon Fraser University (henceforth, BBP) discovered a remarkable, and remarkably simple new formula for . Here is their formula:

The original paper in which Bailey, Borwein, and Plouffe published this result appeared in 1997. [7]

Don't freak out, just breathe deeply and look at it for a bit. [8] How they came by this equation is an interesting story in itself, but not one to go into here. It's enough to know that it can be proven to be correct. (In fact, Adamchik and Wagon actually say "The formula is not too hard to prove…"; if you didn't read note #5, now would be a good time!)

Isn't it remarkable looking! I saw it and my reaction was along the lines of "how could ever be equal to that thing?" This thing, by the way, is referred to as the "BBP formula" or the "BBP algorithm". And then the talk about this equation started to get a little weird and my original train of through about how to calculate derailed.

People wrote about the BBP algorithm in very admiring terms, like "the formula of the century", which started to sound like hyperbole, but really wasn't. Then I tripped over some statements like this one [9] :

Amazingly, this formula is a digit-extraction algorithm for in base 16.

Now, there's a statement I had to pause and think for awhile to make some sense out of.

The "base 16" part was easy enough. Usually we see the decimal expansion of written in our everyday base 10 (this is truncated, not rounded):

In base 16 the expansion looks like this (also truncated) [10] :

In the same way that the digits after the decimal point in the base-10 expansion means this:

the hexadecimal expansion means simply this:

where the hexadecimal digits "A, B, C, D, E, and F" have the decimal values "10, 11, 12, 13, 14, and 15".

For quite awhile I didn't get the notion that it was a "decimal extraction algorithm", which I also read to mean that this algorithm could be used to compute the digit in the hexadecimal representation without calculating all the preceding digits.

Now, that's an amazing assertion that required understanding. How could that be possible. You've seen enough about series formulæ for to see that the way one calculates is to keep grinding out digits until you get to, say, the millionth one, or the billionth one, which can take a long time.

If only I had written down first thing the equation I wrote down above for how the various hexadecimal digits add together as the numerators of powers of (1/16), it would have been obvious. Look back now at the BBP equation. See that factor

that comes right after the big sigma? That's the giant clue about the "digit-extraction" property. If the expression in the parentheses happened to be a whole number between decimal values 0 and 15, then the term would be exactly the digit in the hexadecimal expansion of .

That's an amazing idea. Now, it's not exactly the digit, because that expression doesn't evaluate to a whole number between 0 and F (hexadecimal). Instead, it evaluates to some number smaller than 1, but not incredibly smaller than one. (If, e.g., k = 100 it's about 0.000002).

Philosophically, and mathematically, it's important that it's not exactly a digit-extraction algorithm, but an approximate one. You can't just calculate the millionth digit just by setting k = 1,000,000 and computing one term.

Remarkably enough, though, the BBP algorithm can be, in effect, rearranged to give a rapidly converging series for the millionth digit, if you choose to calculate that particular digit. [11]

Now, in the realm of true hyperbole, I read some headlines about the BBP algorithm that claimed the algorithm suggested that there was some pattern to the digits of and that the digits are not truly random — words evidently meant to be spoken in a hushed voice implying that the mysteries of the universe might be even more mysterious. Bugga bugga!

Now, that business about how maybe now the digits of aren't random after all — it's hogwash because the digits of never were random to begin with. It's all a confusion (or intentional obfuscation) over what "random" means. The number is and always has been irrational, transcendental, unchangeably constant, and the individual digits in the decimal (or hexadecimal) expansion are and always have been unpredictable, but not random.

They cannot be random since has a constant value that is fixed, in effect, by all the mathematical expressions that it appears in. The millionth digit has to be whatever it is in order to make satisfy the constraints of the rest of mathematics. It's the case that all of the digits are essentially fixed, and have been forever, but we don't know what their values are until we compute them.

Previously, to know the millionth digit we had to calculate digits 1 through 999,999; with the BBP algorithm that's not necessary and a shorter calculation will suffice, but that calculation still involves a (rapidly converging) infinite series. Individual digits are not specified, not really "extracted", but they are now individually calculable to arbitrary precision. And, since individual digits are whole numbers with decimal values between 0 and 15, reasonable precision on calculating the digit tells you what the actual digit is.

Still, it is an amazing formula, both practically and mathematically. And now I just tripped over a paper by the BBP authors about the history of calculating . [12] Maybe I can finally get my train of thought back on track.
———-
[1] At the core is mimeTeX, a remarkable piece of software written by John Forkosh that makes it possible for those of us familiar with TeX, the mathematical typesetting language created some two decades ago by mathematician Donald Knuth, to whip up some complicated equations with relative ease.

[2] This limit is the same concept that is central in calculus and has been examined in great care by anyone who has taken a calculus course, and even more intensively by anyone who's taken courses in analysis. But, for the present, there's no need to obsess over the refinements of the idea of limits; the casual idea that comes to mind in this context is good enough.

[3] It was proven by Leonhard Euler in 1735. If you really, really want to see a proof of this assertion, the Wikipedia article on the Basel problem will provide enough details to satisfy, I expect.

[4] The page called "Pi Formulas" at Wolfram MathWorld has a dazzling collection of such equations.

[5] There is an old joke of this type about mathematicians. We used to say "The job of a mathematician is to make things obvious." This refers to the habit among those professionals of saying "obviously" about the most obscure statements and theorems. Another version of the joke has a mathematician writing lines of equations on a chalkboard during class and reaching a point when he says "it's obvious that…", at which point he pauses and leaves the room. The class is mystified, but he returns in 20 minutes, takes up where he left off in his proof, saying "Yes, it is obvious that…."

The version of this that one finds in math and physics textbooks is the phrase, printed after some particularly obscure statement, "as the reader can easily show." That phrase appeared once in my graduate text on electrodynamic (by J.D. Jackson, of course, for those in the know), and showing it "easily" took two full periods of my course in complex analysis.

[6] Victor Adamchik and Stan Wagon, ": A 2000-Year Search Changes Direction", Mathematica in Education and Research, vol. 5, no.1, (1996), pp, 11–19.

[7] David Bailey, Peter Borwein, and Simon Plouffe, "On the Rapid Computation of Various Polylogarithmic Constants", Mathematics of Computation, vol. 66, no. 218 (April 1997), pp. 903–913; reprint available online.

[8] And remember that writing the next to the just means to multiply them together. Although I used as the index in the example above, here the index is called — the name doesn't matter, which is why it's sometimes called a dummy index.

[9] For an example: Eric W. Weisstein, "BBP Formula", MathWorld–A Wolfram Web Resource, accessed 23 September 2007 [the autumnal equinox].

[10] "Sample digits for hexa-decimal digits of pi", 18 January 2003.

[11] If you want to know the details, there's a nice paper written by one of the original authors a decade later in which he shows just how to do it: David H. Bailey, "The BBP Algorithm for Pi", 17 September 2006, (apparently unpublished).

[12] David H. Bailey, Jonathan M. Borwein, Peter B. Borwein, and Simon Plouffe, "The Quest for Pi", Mathematical Intelligencer, vol. 19, no. 1 (Jan. 1997), pp. 50–57; reprint available online.

Symphonic Dogs

I've occasionally given my opinion about music that I like, or music that I think is great, or variants on those topics, but I don't think I've ever mentioned some of the music that I detest. This came to mind because the radio station I was listening to started playing one of the pieces I name below and I had to rush to change the station. So, the topic of this post is bad symphonies, symphonies that cause me physical discomfort to listen to, symphonies that likely should never have been written in the first place. You can decide for yourself whether this is just my opinion or something that you've known all along.

Certainly these judgments are not because I don't like symphonies. I adore symphonic music, and the symphony is one pinnacle of musical invention and expression. I've always enjoyed playing symphonic music, too — that is, playing as a 'cellist in an orchestra.

Symphonists I like include Beethoven (like you had to ask), Brahms, Dvorák, Haydn, Hovhaness, Ives, Mahler, Prokofiev, Shostakovitch, Sibelius, Tchaikovsky (grudgingly^#), Vaughan Williams, and probably a few others whose names no doubt escape at the moment.^* I'd be hard pressed to name favorite composers of symphonies, let alone favorite symphonies, although I might say that Sibelius is the one I've been absorbing most ardently for the last few years, and I am still enthralled by the majestic mystery and compositional magic of his fifth symphony.

But enough. The point here is to point out a few tragically bad symphonies. Not necessarily bad composers, of course, just individual pieces about which I feel it would be no great loss to human culture if all printed parts and recordings were to vanish from the face of the earth.

• Bizet: Symphony in C Major
  Let's face it, not many composers can handle the key of c major well and make the result work (except, in what seems a stunning inconsistency, see below about Schubert), certainly not the young Bizet. Apparently he wrote this as a student assignment when he was 17, which he promptly put away and forgot about. Unfortunately, it was rediscovered and has become a sentimental favorite. Some find it naive and charming; I find it tedious.
• Frank: Symphony in d minor
  We once knew someone who was conducting a performance of this symphony; he thought it was utter trash, but such noisy and thrilling trash that he couldn't help himself. Noisy enough, I guess, but murky and disorganized with musical themes of no distinction and certainly not enough substance to play out into a lengthy, romantic symphony.
• Schubert: Symphony No. 5 in B-flat Major
  This symphony is praised for its effervescence, it's undiluted joie de vivre, its elegance and grace. You might guess that those are all keywords likely to make me fidget uncontrollably. To my ear this symphony has the highest density of insipid themes of any ever written. Amazingly, virtually all conductors insist on taking all the repeats, thereby enhancing the ponderous effect.
• Schubert: Symphony No. 8 in b minor, "The Unfinished"
  I have this theory that many people adore this famous unfinished piece out of some misguided romantic notion that Schubert must have died while he was writing it since it's unfinished. Well, I hasten to point out that Schubert did write a ninth symphony. (Remarkably, the Symphony No. 9 is in C Major, an unforgiving key, but Schubert could handle C major like no other^## and I adore his ninth symphony, which I'm happy to call a masterpiece.) I think this does discredit to Schubert, who was a great composer. I suspect instead that he was working on it, got to the end of the second movement, and realizing that the symphony was turning out entirely unlistenable he stopped what he was doing and hid the manuscript. We should have trusted his judgement.

Perhaps, needing a collective noun, I shall call this my gag of symphonies, for obvious reasons.
———-
^*Someone will inevitably say "But what about Mozart?" Mozart is undeniably a great composer but his music usually — not always! — leaves me cold, and that includes the symphonies for the most part. All filled with all the best classical poise, balance, and grace, which all adds up to tiresome for me.

^#I say "grudgingly" because Tchaikovsky's technique in the art of musical development and motivic deployment as commonly practiced in symphonic writing is horrible and his sense of orchestration is frequently uninspired, but his tunes nevertheless are fabulous and all of the symphonies make great listening, even the under appreciated early symphonies numbers 1 through 3.

^##His amazing string quintet is also in c major, proving that his mastery over the key was no fluke.

One Nation, One Marriage

Fascinating. Arch anti-gay conservative fundamentalist James Dobson (of so-called "Focus on Family"), in announcing that he would not, could not support a Fred Thompson presidency, had this to say:

"Isn't Thompson the candidate who is opposed to a Constitutional amendment to protect marriage, believes there should be 50 different definitions of marriage in the U.S.,…?"

[quoted in Eric Gorski, "Dobson Says He Won't Support Thompson", Associated Press, 20 September 2007]

I've gotten rather tired of listening to all the weak arguments by the fiercely anti-gay and the weak but timid kind-of-pro-gay folks who like to avoid making a commitment to marriage equality because it's a subject "best left to the states". I know I've talked before about that tired old "states' rights" gambit, which is always a cover, always a euphemism, always a diversion and has been since it was invented by segregationists as a way to avoid recognizing the human and citizen status of black people in this country.

But who ever thought we'd hear Dobson denounce an appeal to states' rights?

Who ever thought we'd hear me agree with Dobson?

There should be marriage equality in all 50 states, equally, the same. One country, one marriage. And there will be. (Dobson knows this, too, but seems to feel there's some glory to be had in putting it off for just a little while longer.)

Positive Procrastination

Yesterday morning I woke up thinking about procrastination, for some reason, perhaps from reviewing the long list of things I'd been wanting to get done recently, and I thought I'd write a few notes. This morning I woke up thinking about procrastination again, probably because I hadn't written about it yesterday.

I am a world-class procrastinator, always have been. But what does that mean, I asked myself. Certainly it can describe the fact that I frequently have lists of outstanding tasks that have been outstanding for some time before I get around to completing them.

It seems to me that the language of procrastination is oddly positive, as though "procrastination" is a sin of commission rather than a sin of omission. There are times when I look at some pending tasks and think that I'll do some later rather than now — but how does that differ from prioritizing? In intent rather than fact, it would seem. But note how everyone seems to treat "to procrastinate" as though it's a very active verb, as though one is continually making decisions to keep putting something off. You know, it just doesn't work that way, and I suspect that this approach to the verb is a vast conspiracy among tedious, extroverted, let's-do-it-now! kinds of people, those who seem to flail about a lot but not accomplish very much despite all their activity. (There are, of course, people I secretly envy who speed through tasks and accomplish a great deal, but that seems about as inscrutable to me as rocket science apparently does to normal people.)

I prefer to take up each task in the fullness of time, the ripeness of priorities. Have you ever noticed that there are frequently urgent tasks that, if they mature a bit, are shown to be not so urgent after all? Recognizing true urgency rather than manufactured urgency takes careful consideration, in my opinion.

But, still, I'd generally be recognized as a procrastinator. Sure, there are reasons — or excuses, if you prefer, it doesn't matter much to me what you call them.

In my advancing dotage I've been becoming ever more absent-minded; while I've always been a bit too much on the absent-minded-scientist side of things, it only seems to be getting worse. It's similar to the familiar refrigerator amnesia: standing in front of the open refrigerator wondering how and why one is there. Well, things I think of fly out of my head in no time at all — a few seconds can be enough. I have some idea I want to remember, I reach for my pocket notepaper to write it down, and half the time it's gone before I get the paper out of my pocket.

There's some single-mindedness, oddly enough. Years ago I used to think that I was not very good at concentrating on a particular task, but that's not really true. I don't know whether I've changed or my self-perception has changed, but sometimes now my concentration can be consuming and immediate. Oh, I think, let's take a short break and call, say, for a doctor's appointment. Whoosh! Before I know it my mind is back to work on some absorbing task and it quickly turns into evening, tomorrow, next week, or next month. I could, of course, make notes and task lists but … (see the previous paragraph).

Yes, there's good, old-fashioned avoidance, too. There are many things that I'm quite good at avoiding these days, particularly things that need doing but cost money, since I try to minimize cash outflow while I have so little cash inflow. That sort of avoidance also depends on whether I'm feeling more or less depressed; avoidance was high on my list of coping tactics a couple of years ago, but the dark clouds are substantially reduced these days compared to those days.

So, I'm working on coming to a new, self-empowering understanding. Coupled with my absent- and single-mindedness, it's also the case that I tend to work rather slowly on my projects in progress, largely because so many of them are in progress at the same time. Over long time periods — sometimes approaching geological time-scales, it seems — I've discovered that things I'm doing do get done. I could, I suppose, try to make progress of fewer fronts simultaneously, but I have way too many things I want to get done to attempt that.

Sometimes I think that maybe my only recourse is to start a company to work on lots of these projects, and hire some employees to remember things for me.

What a lucky coincidence that that's one of the projects that I'm working on!

Conversational Time Warp

Yesterday I saw something that, until I actually saw it, I hadn't realized was such an archaic, outdated, never-seen thing of the past: I saw a young person talking on a pay phone.

To Be Rich & To Spend

I was struck by Robert Reich's concise and ringing analysis in this paragraph of what it means to be rich:

But with a recession looming, Democrats need to stop being the party of Herbert Hoover economics. And the Republican[s] need to understand tax cuts for the rich won't help because the rich don’t increase their spending when their taxes are cut. They already spend as much as they want to spend. That's what it means to be rich.

[from Robert Reich, "The Way to Prevent the Looming Recession", Robert Reich's Blog, 10 September 2007.]

Our Labor Day Daytrip

When the weather is nice and we have a Monday holiday available, we like to take an excursion, heading out in some direction to explore some unfamiliar territory. This past Labor Day happened to have beautiful weather in our part of the country, so we set out north.

Part of the excuse for the trip was a desire to take some new photographs, and we managed to do that. You can get to the new gallery, called "Lancaster County, Pennsylvania, 2007" either from the main Björnslottet Photo Gallery page, clicking on the "Lancaster County" album (and then click on one of the thumbnails to see bigger images and navigate through), or else go directly to the "Lancaster County" album's first page.

The first image in the album is a map showing our route. We started by going up through north-central Maryland (Carroll County) to Westminster, which happens to be a good jumping-off point, but which also happens to have a Roy Roger's restaurant where we could have lunch.^* Getting to Westminster is pleasant on MD Rt 32, once it turns from four-lane, divided highway into 2-lane country highway.

From Westminster we took MD Rt. 97 to Gettysburg, where we shopped a bit at the small mall of outlet stores there. As was customary, Isaac was able to buy lots of dress shirts for comfortably small amounts of money.

We headed out of Gettysburg on PA Rt 116, a road we don't often take, to head through Hanover, PA, a place we frequently pass through on our northerly excursions. Some of you on the east coast might recognize Hanover from its association with at least three food processors (Hanover Foods, Snyder's of Hanover, and Utz) and one famous shoe brand (Hanover Shoes) to its name. Given the holiday none were open, but we got to see a different side of town when we drove through the town square.

We continued on PA Rt 116 through South York, PA, and then on PA Rt 462 across the Susquehanna River nearly to Lancaster, where we turned south on US Rt. 222 until it joined with US Rt 1 and we crossed the Susquehanna again. That crossing is a dam near the Peach Bottom nuclear plant, although the dam is rather older than the power plant. Then we headed home via Rt. 1 to Baltimore, I-895 through the Harbor Tunnel (under that branch of the Chesapeake Bay) and back down I-97 to Bowie.

Although one excuse for the trip was to take pictures, I didn't really feel motivated to snap any until we were in Lancaster County already. We were driving along between towns an a two-lane road when, through a tiny gap in the trees along the road, I saw a luscious image of a small pond reflecting a row of Adirondack chairs around its opposite end, set up next to a small dock with an American flag, also reflected. Stop the car! Stop the car!

Okay, we didn't stop the car but we did turn around at the next intersection and back-track so I could try to get the picture. I did get that shot — they show up as #9 and #10 in the album — although I needed more manual intervention with the camera to get it just the way I wanted, so I didn't get quite what I wanted.

Those aren't the first images because we turned around on another side road where we saw an interesting farm scene (the Amish farmer was just behind the tractor, by the way, but didn't seem too upset by our interest), and the neat cemetery with the iron fence in front of it. I loved the look and sort of got some shots that I liked.

After that you've got various scenes along our route, of houses, rural intersections, a church where Isaac once played a recital (First English Lutheran, in Columbia, PA), picturesque farmhouses with silos, and one existential scene with a cow.

The one real destination we encountered was the Robert Fulton Birthplace. I had a lot of fun taking shots there because we had arrived just as the sun was about to go down and the light was exceptional on the house, outhouses, and gardens. So there are a number of photographs there where I was trying extra hard to capture something picturesque. The best one of the bunch I think was this Hopperesque view of a barn, where the light and the composition were just right. I find it interesting to compare with the next photograph in the album, which looks like an accurate but uninspired documentary photograph of a barn. I took the two photographs in quick succession; I didn't move except to turn the camera. There must be an aesthetic lesson in there someplace.

It was a place of remarkable serenity; since the house was closed because of the holiday, we were the only people who were visiting. It was a very pleasant way to spend the waning hours of the day.

One last note: to identify the start of the section at the Fulton Birthplace I moved the sign that names it to the first position; otherwise all the photographs are presented in the order that we took them, so you can think of it as our travelogue.
———–
^* I always used to prefer Roy's cheesburgers with fixin's bar, and I liked their french fries best, compared to the fast-food alternatives. But, maybe a decade or so ago, there was this big corporate kerfuffle where Hardee's bought all of our local Roy's restaurants, thoroughly messed them up, and then they all went out of business. So now we have to drive at least two hours to rustle us up some Roy's. The nearest Hardee's is only about 1.5 hours away, although we think we recently spotted one somewhat closer, if only we could remember where that was.

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