Intuition, Algebra, Inspection

I was asked to look at s spreadsheet showing product sales. There seemed to be something wrong: the discount on all products was 37%, the discount on list A was 38%, and the discount on everything else, list B, was 49%. Yet the individual calculations appeared to be correct.

Intuitively this seemed wrong, but I didn't want to trust to intuition, for I know that mine isn't always reliable. I took out a piece of paper and wrote out the inequalities

a/b > (a + c)/(b + d) < c/d

Multiplying through showed that this could be true only if the inequalities

ad > bc

and

bc > ad

were both true. So intuition was correct:, there was something wrong.After a recalculation, I spotted the problem: the list B calculation was off by a cell, dividing the amount of discount by the discounted price rather than the full price. Correcting that gave a list B discount of 33% and the calculations made sense. A couple of us had looked at this for quite a while without noticing the mistake.

I don't mind math, I use it regularly in my work, but this must be the first time in years that I have fallen back on algebra. With a better eye for the cell references in the discount formula, I would not have needed to do so. Still it is comforting to remember that the tool is available.

Rod McKuen, RIP

Today's NY Times carries an obituary of Rod McKuen. I hadn't thought about the man much over the last 40 years, and not that much before that. I was interested to see, a while ago, that he was president of the American Guild of Variety Artists, a small labor union.

I remember from college the conversation of a young woman, a music major, who had been browbeaten by a graduate student, instructor of a freshman English class, after she had said that she liked McKuen's poetry. The browbeating did not, at least right away, lead to her developing a taste for such poets as the English Department approved of. It did lead to a distaste for English classes, or at least English graduate students. I believe that I heard of more than one case of such browbeating.

The Times quotes the San Francisco Chronicle to the effect that

There was a time not long ago when every enlightened suburban split-level home had its share of Rod McKuen. His mellow poetry was on the end table ...

That depends on the definition of "enlightened", I suppose. I can think of a few suburban split-level homes that had well-educated household and no McKuen. The statement reminds me of Graves and Hodges in The Reader over Your Shoulder, in "Principles of Clear Statement" glossing "You will find bee orchards almost anywhere in Devon" as "meaning perhaps in a few fields in several parishes in the Torbay district of South Devon."

Certainly McKuen sold a lot of books, and singers of his lyrics sold a lot of records. He had a difficult childhood and adventurous youth. He  lived, as poets often do, a long life, dying at 81.

Arguing About Flannery O'Connor

A few days ago, a friend emailed to remark that she had just been reading "Everything That Rises Must Converge", and thought very well of it. I replied describing it as

another of O'Connor's stories of the ineffectual, intellectual son and the embarrassingly good-natured, naive mother: "The Enduring Chill" would be another, and ["The Comforts of Home"].

The situation, I said, if not the execution, wore on me. My friend thought this "harsh".

I found and read the story that evening. It is an excellent story, and I have no trouble understanding why I like it better now than I did thirty-five or forty years ago.

Julian, like Asbury in "The Enduring Chill", like Thomas in "The Comforts of Home", is in fact intellectual and ineffectual, and well aware of his failings. He is, more than either, miserably self-conscious,  No such men are particularly comfortable for a twenty-year-old man to read of. Most of us who were not clearly on the way to glory, or wholly lacking in self-awareness, measured our aspirations against our prospects, and didn't care for the results. But few of can have survived into or past middle age still taking ourselves so seriously.

I suppose that I must have seen on first reading the odd contrast in racism between his mother and Julian, the former regarding "negroes" as persons to be feared or patronized, the latter  wishing to use them as props to demonstrate his distance from his mother. What I find interesting now is how much more trapped in the past Julian is than his mother. For her it is a source of pride, maybe a warrant of gentility. For him, who never knew the lost prosperity, it is something to long for. I don't think I picked up on that all those years ago. There is also his apparent inability to see his mother as a person until she is at the point of death.

Shaving Soap

For many years, I have used Williams Shaving Soap, about $1.25 at the local drugstore. It is about a quarter of an inch too small to fit snugly in the mug I use, but it yields a decent lather. Now the local drugstore does not carry it.

I have visited all of the local stores that are more or less on my way to work. None carry it. I had a look at a couple of places near work that cater to the highly groomed and (mostly) young. Both sold shaving soap. Unfortunately, both sold soap that costs $30 the box, and that is too big for my mug. I do not shave to look like the young and highly groomed so much as to avoid looking like a bum, so I will not pay $30 for a disk of soap that I would have to cut down. One did interest me, both in that it was from Trumpers, which is where Evelyn Waugh got his hair cut, and in that it came in a little wooden bowl. If I thought that shaving with Trumpers soap would make my prose resemble Waugh's, I might buy it. And every expended pair would offer two bowls to clap together in the manner of a Monty Python squire.

Today I found a drugstore that had not shaving soap but Deluxe Shave Soap, which I recall is what I bought last time. It had only one box, so in another few months I may have to undertake the same search.

Reading MacCulloch

Several months ago, I picked up a copy of The Reformation by Diarmaid MacCulloch. I have now read it to the end, and think it a remarkable book. Others, far more qualified to make the judgment, say the same.

A great deal of the matter is familiar to anyone who knows European history, but those of us who do not teach it or read it full time will have been vague on many of the details. Here the details are closely and lucidly mapped: Luther's movement from loyal monk to outlawed reformer; Zwingli's and Melanchthon's relations with Luther; the rise of the reformed churches and how "Calvinist" came to be a catch-all term for them; the lead in to the Council of Trent, and the council's consequences; and much more. Probably the most informative for me was MacCulloch's discussion of the Church of England, and how it moved from one dominated by those determined to align with "reform" back to one more aligned with Luther, and eventually to what it has been since. But if you picked up the book to learn the basics about the Anabaptists, the Socinians, the Arminians, the early Jesuits, or St. Francis de Sales, you would get your money's worth.

The Reformation is not a small book. However, the nearly 700 pages are broken into 17 chapters, which in turn have smaller sections, averaging about 12 pages. A reasonably attentive and rested reader can read and comprehend one or two of the smaller sections in an evening. At every other evening, one could read the book in a couple of months, a bit less than it took me.

New Years Past

There is or was a New Years race in Washington, DC, called The Hangover Classic. Back in the 1980s when I ran in it, it was at first a 10 kilometer race on the usual West Potomac Park and Hains Point course, then a 5 mile race that went past the Reflecting Pool. I haven't run in the race for almost 30 years, and I seldom think of it. But last Sunday we drove back from Reagan National over Memorial Bridge and past the Watergate (the steps down from the level of  the Lincoln Memorial to Rock Creek Parkway, that is), and that recalled those days.

It was probably 1983 when I rose more or less early on January 1, breakfasted, and got into running gear. I put regular clothes into into my backpack, and set off through Rock Creek Park toward the race. When nearly there, I ran carefully down the steps of the Watergate. About a quarter of the way down, I saw a champagne cork. I was and am sure that some reveler had discharged it from the top of the steps, hoping to put it into the Potomac. Well, people notoriously underestimate distance when looking downhill. I hope that the reveler's other ambitions for 1983 worked out better.