# (Roughly) Daily

## “No part of mathematics is ever, in the long run, ‘useless’.”*…

The number 1 can be written as a sum of distinct unit fractions, such as 1/2 + 1/3 + 1/12 + 1/18 + 1/36…

Number theorists are always looking for hidden structure. And when confronted by a numerical pattern that seems unavoidable, they test its mettle, trying hard — and often failing — to devise situations in which a given pattern cannot appear.

One of the latest results to demonstrate the resilience of such patterns, by Thomas Bloom of the University of Oxford, answers a question with roots that extend all the way back to ancient Egypt.

“It might be the oldest problem ever,” said Carl Pomerance of Dartmouth College.

The question involves fractions that feature a 1 in their numerator, like 1/2, 1/7 or 1/122. These “unit fractions” were especially important to the ancient Egyptians because they were the only types of fractions their number system contained: With the exception of a single symbol for 23, they could only express more complicated fractions (like 3/4) as sums of unit fractions (1/2 + 1/4).

The modern-day interest in such sums got a boost in the 1970s, when Paul Erdős and Ronald Graham asked how hard it might be to engineer sets of whole numbers that don’t contain a subset whose reciprocals add to 1. For instance, the set {2, 3, 6, 9, 13} fails this test: It contains the subset {2, 3, 6}, whose reciprocals are the unit fractions 1/2, 1/3 and 1/6 — which sum to 1.

More exactly, Erdős and Graham conjectured that any set that samples some sufficiently large, positive proportion of the whole numbers — it could be 20% or 1% or 0.001% — must contain a subset whose reciprocals add to 1. If the initial set satisfies that simple condition of sampling enough whole numbers (known as having “positive density”), then even if its members were deliberately chosen to make it difficult to find that subset, the subset would nonetheless have to exist.

“I just thought this was an impossible question that no one in their right mind could possibly ever do,” said Andrew Granville of the University of Montreal. “I didn’t see any obvious tool that could attack it.”…

Bloom, building on work by Ernie Croot, found that tool. The ubiquity of ways to represent whole numbers as sums of fractions: “Math’s ‘Oldest Problem Ever’ Gets a New Answer,” by Jordana Cepelewicz (@jordanacep) in @QuantaMagazine.

* “No part of mathematics is ever, in the long run, ‘useless.’ Most of number theory has very few ‘practical’ applications. That does not reduce its importance, and if anything it enhances its fascination. No one can predict when what seems to be a most obscure theorem may suddenly be called upon to play some vital and hitherto unsuspected role.” – C. Stanley Ogilvy, Excursions in Number Theory

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As we recombine, we might send carefully-calculated birthday greetings to Ulugh Beg (or, officially, Mīrzā Muhammad Tāraghay bin Shāhrukh); he was born on this date in 1394. A Timurid sultan with a hearty interest in science and the arts, he is better remembered as an astronomer and mathematician.

The most important observational astronomer of the 15th century, he built the great Ulugh Beg Observatory in Samarkand between 1424 and 1429– considered by scholars to have been one of the finest observatories in the Islamic world at the time and the largest in Central Asia. In his observations he discovered a number of errors in the computations of the 2nd-century Alexandrian astronomer Ptolemy, whose figures were still being used. His star map of 994 stars was the first new one since Hipparchus. Among his contributions to mathematics were trigonometric tables of sine and tangent values correct to at least eight decimal places.

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March 22, 2022 at 1:00 am

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## “Culture is the name for what people are interested in”*…

… but “culture” (that’s to say, “high culture”) has also been a form of authority, a kind of superego for society. These days, Adam Kirsh argues, not so much…

From the 1920s to the 1950s, from jazz and blues to rock and roll, tweaking the canon was part of the appeal of pop music—and a favorite device of lyricists. Ella Fitzgerald had a signature hit with Sam Coslow’s “(If You Can’t Sing It) You’ll Have to Swing It (Mr. Paganini).” Betty Comden and Adolph Green wrote the lyrics to “It’s a Simple Little System,” from the musical Bells Are Ringing, in which a bookie uses composers’ names as code to refer to racetracks: “Beethoven is Belmont Park/ Tchaikovsky is Churchill Downs.” Chuck Berry hit the same targets in “Roll Over Beethoven”: “My heart’s beating rhythm/ And my soul keeps singing the blues/ Roll over Beethoven/ Tell Tchaikovsky the news.”

In recent decades, however, this type of indirect homage to the authority of classical music has completely disappeared from popular music. The last example may be “Rock Me, Amadeus,” a German pop hit from 1985 that was inspired less by Mozart himself than by the 1984 movie Amadeus, in which the composer is portrayed as, in the song’s words, “ein Punker” and “ein Rockidol.” Today’s pop lyricists don’t poke fun at Beethoven and Tchaikovsky because young listeners no longer recognize those names as possessing any cultural authority or prestige, if they recognize them at all. It would make as much sense to write a pop song called “Roll Over Palestrina” or “Rock Me, Hildegard von Bingen,” since all composers are equally unfamiliar to a mass audience.

Like the disappearance of a certain species of frog or insect, this is a small change that signals a profound transformation of the climate—in this case, the cultural climate…

And while that change has its costs, Kirsch explains, it also has its benefits : “Culture as counterculture.”

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As we contemplate canons, we might recall that on this date in 2008 the #1 song in the U.S. was “Whatever You Like” by T.I. Jared W. Dillon of Sputnikmusic called the song a “more sophisticated take” on Lil Wayne‘s “Lollipop.”

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September 6, 2021 at 1:00 am

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## “Mozart died too late rather than too soon”*…

Glenn Gould was a gloriously talented and profoundly iconoclastic pianist, unafraid to challenge the conventions of the canon.

His April 1962 performance of Brahms’ first piano concerto, with the New York Philharmonic and Leonard Bernstein conducting, gave rise to an extraordinary situation in which Mr. Bernstein disagreed with Gould’s interpretation so vehemently that he felt it necessary to warn the audience beforehand. The performance was subsequently broadcast on the radio with Bernstein’s comments included. A draft copy of those comments can be found in the Leonard Bernstein Collection at the Library of Congress and is available to read online…

But perhaps his most egregiously unpopular opinion was his conviction that Mozart– especially late Mozart– was a “bad composer.”

How Mozart Became a Bad Composer, which was originally broadcast on a weekly public television series titled Public Broadcast Laboratory in 1968. The Library of Congress National Audio-Visual Conservation Center recently digitized the episode that includes the 37-minute segment from a two-inch tape found in the Library’s collection. It is now available on the web site of the American Archive of Public Broadcasting, which is a collaborative effort by the Library of Congress and WGBH in Boston, Massachusetts.

On the reception of the program, Peter Goddard in The Great Gould (2017) wrote, “Recognizing the outrage-driven ratings possibilities here, the Public Broadcasting [sic] Laboratory series by National Educational Television, the precursor to PBS in the United States, broadcast Gould’s thirty-seven-minute-long How Mozart Became a Bad Composer on April 28, 1968. After that, the show disappeared from sight worldwide, and a version of the script was only uncovered years later by New York-based documentarian Lucille Carra.” Kevin Bazzana in Wondrous Strange: The Life and Art of Glenn Gould (2004) notes, “The program outraged viewers in both the United States and Canada, including formerly sympathetic fans and critics.” The program is now widely available to the public for the first time since its broadcast. Although, ardent Glenn Gould fans may remember his interview in Piano Quarterly, which was reprinted in The Glenn Gould Reader (1984), “Mozart and Related Matters: Glenn Gould in Conversation with Bruno Monsaingeon,” in which he expresses many of the same reservations about Mozart’s music that are heard in the television segment…

Cait Miller (of the Music Division of the Library of Congress) puts it in a personal context:

My parents are or were both musicians – my father was a composer – and so my appreciation for classical music was probably equal parts nature and nurture. So, when I entered graduate school as a musicologist and met a fellow student named Masa Yoshioka, who became one of my best friends during my doctoral study, it was more than a little shocking when, during one of our many extended conversations about music, he revealed to me that he did not think that Mozart was a particularly interesting composer. As a musicologist who had come from a previous incarnation as a classical singer, this was tantamount to heresy. However, due to my regard for Masa and his well-thought-out opinions, I did not discount it out of hand. Instead, I took it as a challenge to listen to the music of Mozart and, in fact, the music of all composers, with fresh ears every time I encountered it and to let no preconceptions that I had learned as a child allow me to speak as a child when I heard new works by a composer whom I had been conditioned to revere. It is with this spirit in mind that I hope you will view Glenn Gould’s television segment…

Your correspondent would agree. In any event, enjoy:

[image at top: source]

* Glenn Gould (who also once suggested that “Beethoven always sounds to me like the upsetting of a bag of nails, with here and there also a dropped hammer”)

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As we tickle the ivories, we might recall that it was on this date in 1976 that another group of musical iconoclasts, The Sex Pistols, released their single ‘Anarchy In The UK‘. Originally issued in a plain black sleeve, the single was the only Sex Pistols recording released by EMI, and reached the No.38 spot on the UK Singles Chart before EMI dropped the group on 6 January 1977. (The band ran through five labels; their only album, Never Mind the Bollocks, Here’s the Sex Pistols (1977; #1 on the UK charts) was released by Virgin.)

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November 26, 2020 at 1:01 am

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## “Hollywood is a place where a man can get stabbed in the back while climbing a ladder”*…

Cartoon of the brothers Warner drawn by Faulkner for his daughter Jill. Early 1940s. Center for Faulkner Studies, Southeast Missouri State University

William Faulkner disparaged his two decades of work in film, even though he spent the equivalent of four years in Hollywood and worked at MGM, Universal, Twentieth Century-Fox, RKO, and Warner Bros. Biographies of Faulkner treat his film work as more or less ancillary to his life and fiction, but in fact his screenwriting transformed his conception of himself and his writing. An understanding of the man and his work changes when his contributions to cinema are integrated into a capacious conception of his career…   – “The Cinematic Faulkner: Framing Hollywood

Jill Faulkner Summers found the screenplay for the vampire film Dreadful Hollow among her father’s papers in 1999.  An adaption of Irina Karlova’s lesbian vampire tale of the same title, it remains unpublished (except for excerpts) and unproduced… but not unstudied:

Faulkner wrote Dreadful Hollow immediately following To Have and Have Not and The Big Sleep, and so it should be read along with those two films as indicative of the kind of work he produced for Hawks at the time. The screenplay reveals Faulkner’s approach to adaptation was to add elements that could deepen an audience’s appreciation of a form. In doing so, he resists the Hollywood Studio system’s tendency to whitewash corners and soften the shadows of source materials, something that would have been appreciated by his friend and sometimes employer, Hawks. Because the film has not been produced, the multiple script revisions that usually accompanied any script Faulkner wrote for a studio have not happened and the script is completely Faulkner’s own. The screenplay reveals him to be a serious and focused screenwriter with a wide knowledge of early film narratives and techniques who by 1945 had become quite good at his trade. Faulkner stamped the screenplay with his signature multiple times and so it contains large traces of his more canonical work. These echoes serve to further blur the lines between his “literary work” and his “commercial work” and suggest, instead, that for Faulkner, the distinction was perhaps not as clear as scholars have made it out to be. It therefore, should be considered a supplement to his more literary work. I wholeheartedly agree with Kawin’s 1977 assessment of the script: It’s Faulkner’s best screenplay and it deserves a place among his better-known and published work…

Grateful TotH to friend CE…

For a review of Faulkner’s entire career as a screenwriter, visit the essay cited at the top: “The Cinematic Faulkner: Framing Hollywood.”

* William Faulkner

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As we reframe fame, we might spare a thought for Martin E. Segal; he died on this date in 2012.  A Russian emigre to the U.S., Segal built a successful international human resources and employee benefit consulting firm.  But he is much better remembered for his passionate support for the arts– perhaps most particularly, as a champion of Lincoln Center and as the co-founder (in 1969, with William F. May and Schuyler G. Chapin) of the Film Society of Lincoln Center, and as its first President.  Now know as Film at Lincoln Center, it hosts The New York Film Festival and (with the Museum of Modern Art) the New Directors/NewFilms Festival.

As The New York Times noted in its obituary, while Marty “was generous with his money, he was perhaps most admired for the donations he managed to extract from others. He used to say he had no trouble giving people the ‘opportunity’ to contribute to the causes he cared most about, whether it be Lincoln Center’s redevelopment project, which updated the campus; Public Radio International [now PRX], of which he was a founding member; or the Library of America, a nonprofit publisher dedicated to publishing, and keeping in print, editions of America’s most significant writing.”

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August 5, 2020 at 1:01 am

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## “Life without industry is guilt; industry without art is brutality”*…

It is often said that art feeds the soul. But culture and the arts also fuel the economy directly: The arts contribute more than \$800 billion a year to U.S. economic output, amounting to more than 4 percent of GDP.

That figure is based on detailed data from the U.S. Bureau of Economic Analysis (part of the Department of Commerce) and the National Endowment for the Arts, summarized in a report released earlier this month.The report tracks the aggregate performance of 35 key arts-and-culture fields, including broadcasting, movies, streaming, publishing, the performing arts, arts-related retail, and more…

The contribution of culture and art to the U.S. economy is bigger than the economic output of Sweden or Switzerland; learn more at “The Economic Power of American Arts and Culture.”

* John Ruskin

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As we see to our souls, we might spare a pining thought for Petrarch (Francesco Petrarca); it was on this date in 1327, after he’d given up his vocation as a priest, that he first set eyes on “Laura” in the church of Sainte-Claire d’Avignon– an encounter that awoke in him a passion that spawned the 366 poems in Il Canzoniere (“Song Book”).

Considered by many to have been “the Father of Humanism,” and reputed to have coined the term “Renaissance,” Petrarch was most famous in his time for his paeans to his idealized lover (who was, many scholars believe, Laura de Noves, the wife of Hugues de Sade).  But Petrarch’s more fundamental and lasting contribution to culture came via Pietro Bembo who created the model for the modern Italian language in the 16th century largely based on the works of Petrarch (and to a lesser degree, those of Dante and Boccaccio).

Laura de Noves died on this date in 1348.

Lura de Noves

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Petrarch

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Written by (Roughly) Daily

April 6, 2019 at 1:01 am