Posts Tagged ‘Tom Lehrer’
“I am never forget the day I first meet the great Lobachevsky. / In one word he told me secret of success in mathematics: / Plagiarize!”*…
In an 1874 paper, Georg Cantor proved that there are different sizes of infinity and changed math forever. But as Joseph Howlett reports, a trove of newly unearthed letters shows that it was also an act of plagiarism…
When Demian Goos followed Karin Richter into her office on March 12 of last year, the first thing he noticed was the bust. It sat atop a tall pedestal in the corner of the room, depicting a bald, elderly gentleman with a stoic countenance. Goos saw no trace of the anxious, lonely man who had obsessed him for over a year.
Instead, this was Georg Cantor as history saw him. An intellectual giant: steadfast, strong-willed, determined to bring about a mathematical revolution over the clamorous objections of his peers.
It was here, at the University of Halle in Germany, that Cantor launched his revolution 150 years ago. Here, in 1874, he published one of the most important papers in math’s 4,000-year history. That paper crystallized a concept that had long been viewed as a mathematical malignancy to be shunned at all costs: infinity. It forced mathematicians to question some of their longest-held assumptions, rocking mathematics to its very foundations. And it gave rise to a new field of study that would eventually bring about a rewriting of the entire subject.
Now Goos, a 35-year-old mathematician and journalist, had come to Halle — a five-hour train ride from his home in Mainz — to look at some letters from Cantor’s estate. He’d seen a scan of one and was pretty sure he knew what the others would say. But he wanted to see them in person.
Richter — who, like Cantor, had spent her entire career here, first as a research mathematician and then, after retiring, as a lecturer on the history of mathematics — gestured for Goos to sit. She lifted a thin blue binder from the scattered piles of books and papers on her desk. Inside were dozens of plastic sheet protectors, each one containing an old, handwritten letter.
Goos began flipping through, contemplating the letters with the relish of an archaeologist entering a long-lost tomb. Then he reached a particular page and froze. He struggled to catch his breath.
It wasn’t the handwriting. At this point in his research on Cantor, he’d become accustomed to the strange, nearly indecipherable Gothic script known as kurrentschrift, which Germans used until around 1900.
It wasn’t the signature. He knew that the German mathematician Richard Dedekind had been a key player in Cantor’s quest to understand infinity and solidify math’s foundations, and that the two had exchanged many letters.
It was the date: November 30, 1873.
He’d never seen this letter before. No one had. It was believed to be lost, destroyed in the tumult of World War II or perhaps by Cantor himself.
This was the letter that had the power to rewrite Cantor’s legacy. The letter that proved once and for all that Cantor’s famous 1874 paper, the one that would go on to reshape all of mathematics, had been an act of plagiarism…
The extraordinary story of unearthing this extraordinary story: “The Man Who Stole Infinity,” from @quantamagazine.bsky.social.
See also: “How Can Infinity Come in Many Sizes?“
* Tom Lehrer (not just a glorious songwriter, but also a gifted mathematician), “Lobachevsky” (referring to the mathematician Nikolai Ivanovich Lobachevsky— “not intended as a slur on [Lobachevsky’s] character [but chosen]”solely for prosodic reasons”)
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As we confer credit where credit is due, we might spare a thought for Charles-Jean Étienne Gustave Nicolas, baron de la Vallée Poussin; he died on this date in 1962. A Belgian mathematician, he is best known for proving the prime number theorem (which formalized the intuitive idea that primes become less common as they become larger by precisely quantifying the rate at which this occurs). So great was the contribution that the King of Belgium ennobled him with the title of baron.
“Brains exist because the distribution of resources necessary for survival and the hazards that threaten survival vary in space and time”*…
And, it seems, they not only evolve, but in ways and with a frequency we’ve only just begun to appreciate. It’s long been noted that evolution seems to have a thing for “carcinization”– crabs have evolved separately at least five times. (Oh, and apparently also for anteaters…) Recent findings hint that evolution might have the same sort of jones for the brain. Amy Maxmen reports…
Our brains, perched atop a network of nerve cells that ascend the length of our bodies, are thought to have arisen once in an animal hundreds of millions of years ago and then evolved over time. However, new findings suggest instead that brains and nervous systems originated multiple times from scratch.
The findings, published today in Nature, highlight an ancient and gelatinous marine predator called a comb jelly [pictured at top]. Unlike pulsating jellyfish, comb jellies swim by “rowing” their many hair-like cilia, which are arranged in rows called combs. They possess rudimentary brains and sophisticated nervous systems replete with elongated cells that communicate through synapses much like our own. Some comb jellies show mirror-like bilateral symmetry, as do we. And like most animals, their muscles derive from a middle tissue layer, which does not exist in jellyfish or sponges, another ancient type of aquatic creature.
So it’s little wonder that biologists have long placed the comb jelly group close to worms, flies, and humans on the evolutionary tree of life; sponges emerge at the base, meaning that this group appeared first. In this traditional view, complex body parts like the brain and muscles arose gradually, and only once, since those parts look similar across related animals, and the chances of that same evolutionary process being repeated seems slim.
But this scenario was shaken by a report in Science last year, which suggested that the comb jelly group emerged before jellyfish and even the brainless, muscle-less sponges, more than 550 million years ago.
Some biologists doubted the rearrangement because it implied two equally uncomfortable possibilities: that the ancestor of all living animals had true muscles and a rudimentary brain, and then sponges and jellyfish lost those parts without a trace; or that the great animal ancestor was simple, and comb jellies evolved separately from all the other animals, yet ended up with rather similar nervous systems, muscles, and bilateral symmetry. When paleontologist Graham Budd heard the news last year, he said, “It is effectively saying animals evolved twice. Frankly, I’m not ready to believe it.”
Without a time machine, it’s impossible to know what our great ancestor looked like. However, today’s report adds more support to the notion that she was simple and comb jellies independently evolved their complex body parts. Leonid Moroz, a neurobiologist at the University of Florida’s Whitney Laboratory for Marine Bioscience, and his colleagues confirm comb jellies’ position below sponges at the base of the evolutionary tree with an analysis of genetic sequences from 11 comb jelly species…
… In an essay for Nautilus called “Evolution, You’re Drunk,” I described how hypotheses entrenched in the notion that evolution leads toward increasing complexity have recently begun to teeter. Now Moroz’s study adds another shove. It seconds the finding that simple sponges, long placed at the base of the evolutionary tree, actually evolved after the sophisticated comb jelly group arose. The story of how complexity evolves is more complex than scientists realized.
Furthermore, the brain—the epitome of complexity—seems to have sprouted up at least twice over evolutionary time. This clashes with the traditional notion that complex, multifaceted features come about in a very specific way, and each emerges just one time. “What everyone has said about complexity is wrong,” Moroz says. “It can happen more than once.”
Finding that comb jellies independently arrived at similar ends as other animals might also have surprised the late paleontologist Stephen Jay Gould, who famously doubted that animals would look the same today if the world were to begin again—if we could replay “the tape of life.”
Is such convergence in design a coincidence? Probably not, guesses Andreas Hejnol, an evolutionary developmental biologist at the Sars International Centre for Marine Molecular Biology in Norway. “If you need a fast communication system, it helps to have extended cells that communicate through chemicals,” he says. In other words, the structure of the nervous system reflects its function. So if intelligent life exists elsewhere in the universe, it’s not too far a stretch to think it could possess a brain comprised of trillions of neurons. Hejnol asks, “How else could it be?”…
The mysterious mechanism of evolution: “Evolution May Be Drunk, But It’s Serious About Making Brains,” from @amymaxmen.bsky.social in @nautil.us.
* John M. Allman, Evolving Brains
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As we contemplate the changing comprehension of cerebra, we might send thoughtful birthday greetings to Sir Karl Raimund Popper; he was born on this date in 1902. One of the greatest philosophers of science of the 20th century, Popper is best known for his rejection of the classical inductivist views on the scientific method, in favor of empirical falsification: a theory in the empirical sciences can never be proven, but it can be falsified, meaning that it can and should be scrutinized by decisive experiments. (Or more simply put, whereas classical inductive approaches considered hypotheses false until proven true, Popper reversed the logic: conclusions drawn from an empirical finding are true until proven false.)
Popper was also a powerful critic of historicism in political thought, and (in books like The Open Society and Its Enemies and The Poverty of Historicism) an enemy of authoritarianism and totalitarianism (in which role he was a mentor to George Soros).
“Life is like a sewer – you get out of it what you put into it”*…
Frances Beckett on the mystery of the great Tom Lehrer: in the 1950s and 60s, his songs stunned and delighted listeners with their irreverence, wit, and nihilism. Then he gave it all up to teach mathematics.
Beckett begins by recounting his own introduction to Lehrer, in 1959, at the “snobbish [British] Jesuit boarding school” to which his parents had sent him…
… Tom Lehrer’s songs burst upon my consciousness like a clown in a cathedral. Days there began with mass, and ended with an uplifting homily in the chapel from an elderly and skeletal priest, generally about death. “Your best friends will desert you leaving you nothing but a winding sheet,” was one of his more cheerful messages. Between the two there was catechism, rugby, occasional bullying and fairly frequent beatings.
But we had the “playroom”, where we could relax and listen to records, and one day an American boy called Ed Monaghan turned up clutching a Lehrer LP. It was a medicinal dose of the irreverence, nihilism and rebellion that I craved. To this day, I am word perfect in many of the songs I first heard then. There was Poisoning Pigeons in the Park, all about the joys of spring, and as darkly funny as its title suggests. There was the American football song Fight Fiercely, Harvard, which seemed to make cruel mock of those cold, dreary afternoons I was forced to spend watching my school play rugby. It was all done with such bouncing musicality that I doubt whether the Jesuits ever realised the subversive nature of what we were listening to.
Lehrer made my life bearable. I have never been able to tell him so, and it might not please him, for he has been quoted as saying: “If, after hearing my songs, just one human being is inspired to say something nasty to a friend, or perhaps to strike a loved one, it will all have been worthwhile.”
I didn’t know then that Lehrer had started out, six years earlier, by paying to have his own record cut because the record companies were shocked by his songs, and selling the LP to fellow students at Harvard. This early samizdat recording was the underground success of the decade with almost no publicity effort from Lehrer – “My songs spread slowly, like herpes, rather than Ebola,” he later recalled.
At that time, Lehrer’s principal accomplishment was that he was a mathematics prodigy who had entered Harvard aged 15, in 1943, taken a first class degree aged 18 and a master’s a year later. Born into a New York Jewish family in 1928, Lehrer had, he has said, every advantage: piano lessons, an expensive school that could get him into Harvard, and “the Broadway of Danny Kaye and Cole Porter.
In the next year or two, Ed Monaghan introduced me to other comedians who were turning the complacent world of American comedy on its head: Mort Sahl, Shelley Berman, Dick Gregory, Lenny Bruce. “What these so-called ‘sickniks’ dispense,” wrote Time magazine in July 1959, “is partly social criticism liberally laced with cyanide, partly a Charles Addams kind of jolly ghoulishness, and partly a personal and highly disturbing hostility toward all the world.”
But in 1960, the year after I discovered him, Lehrer stopped writing and performing, although he briefly re-emerged in 1965 to write new songs for the US version of the satirical British show That Was the Week That Was. The new songs were made into a live LP, and it was even more wonderful than the old one. They included The Vatican Rag – a Catholic hymn set in ragtime: “There the guy who’s got religion’ll / Tell you if your sin’s original.” Although I was by then a confirmed atheist, I probably still thought that making fun of the Catholic church would release a thunderbolt from heaven, and The Vatican Rag cured me.
The album also included three songs condemning nuclear weapons. “There’ll be no more pain and misery / When the world is our rotisserie …” They were so much better than those whiny folk songs of the era, which Lehrer rather despised. “You had to admire these folk singers,” he says on the live LP. “It takes courage to get up in a coffee house or a student auditorium and come out in favour of the things everyone else is against, like peace and justice and brotherhood, and so on.”
In this far more political new record, he satirised the Americans teaming up with West Germany against the USSR (“Once all the Germans were warlike and mean / But that couldn’t happen again / We taught them a lesson in 1918 / And they’ve hardly bothered us since then”), and was horrified that Hitler’s chief rocket scientist was now working for Washington, singing: “‘When the rockets go up who cares where they come down? / That’s not my department,’ says Wernher von Braun.”
And then he gave it up again, and he has spent the rest of his life as an obscure mathematics lecturer. He lives in the house he has occupied for decades, in Cambridge, Massachusetts, and he was 96 last month…
The quest to understand: “‘My songs spread like herpes’: why did satirical genius Tom Lehrer swap worldwide fame for obscurity?” from @francisbeckett in @guardian.
A reminder: in 2020, Lehrer his lyrics, and free streaming and downloadable versions of all of his albums– a satirical gold mine: “Songs and Lyrics by Tom Lehrer.”
* Tom Lehrer
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As we appreciate art, we might recall that it was on this date in 1972, amid Queen Elizabeth II’s Silver Jubilee celebrations, that the Sex Pistols threw a party aboard a boat called The Queen Elizabeth, inviting friends, journalists, and a film crew to sail along London’s River Thames– a promotion for the band’s new single, “God Save the Queen.” As the sun went down and the boat floated near the Houses of Parliament, the band lit up their amps and performed “Anarchy in the UK,” followed by “God Save the Queen,” “No Feelings,” and “Pretty Vacant.” Upon docking, the band and their fellow partygoers were met by police.
“I know that there are people who do not love their fellow man, and I hate people like that!”*…
After this post, your correspondent begins his annual Holiday Hiatus, so let me pass along a gift. Regular service will resume on January 2; meantime, thanks to you all for reading– and Happy Holidays!
Ladies and Gentlemen, the remarkable Tom Lehrer…
Between the… Weird Al biopic and and Kelly Bachman and Dylan Adler’s new comedy album, Rape Victims Are Horny Too, parody songsters have rarely been such a central part of the cultural zeitgeist. Yet comedy musicians have been trailblazing for much longer than we may realize, and before the popularity of Weird Al, or even Bo Burnham, Adam Sandler, and Steve Martin, there was Tom Lehrer.
Lehrer is perhaps best known for “The Elements,” an impossibly fast and impossibly tongue-twisty song that consists of all the periodic elements put to the tune of a “Major-General’s Song” from Pirates of Penzance. This is a classic Tom Lehrer song, so classic in fact that Daniel Radcliffe’s rendition of it on The Graham Norton Show helped score him the role of Weird Al, who has noted Lehrer as a major comedic influence. This full circle loop only emphasizes how important Lehrer was and continues to be in the musical comedy scene, and diving into his diverse oeuvre solidifies just how innovative he was…
“Tom Lehrer Deserves Your Attention” (source of the photo above)
And it’s now easier than ever for you to pay him that attention: the remarkable Mr. Lehrer is also remarkably generous. Last month, a new web site appeared, the home page of which explains…
I, Tom Lehrer, and the Tom Lehrer Trust 2007, hereby grant the following permissions:
All copyrights to lyrics or music written or composed by me have been relinquished, and therefore such songs are now in the public domain. All of my songs that have never been copyrighted, having been available for free for so long, are now also in the public domain.
The latter includes all lyrics which I have written to music by others, although the music to such parodies, if copyrighted by their composers, are of course not included without permission of their copyright owners. The translated songs on this website may be found on YouTube in their original languages.
Performing and recording rights to all of my songs are included in this permission. Translation rights are also included….
The site contains all of his lyrics, and free streaming and downloadable versions of all of his albums– a satirical gold mine: “Songs and Lyrics by Tom Lehrer.”
* Tom Lehrer
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As we soak ourselves in satire, we might recall that it was on this date in 1986 that Fran Oz’s film Little Shop of Horrors premiered. Based on the Off-Broadway musical adaptation of the 1960 original Roger Corman movie, it was a huge success with critics and a modest success with audiences on release, but has since become cult film.
As Oz’s friend and Muppet colleague Jim Henson said, “the lip sync on the plant in that film is just absolutely amazing.”
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